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COLD CEREAL PRICES AND INGREDIENT CONTENT
Cold Breakfast Cereal Unit Cost and
Corresponding Ingredient Content
Introduction
Currently the United States is experiencing a less than perfect financial situation, where
economic hardships are encouraging consumers to give extra attention on spending habits.
Financial difficulties can be felt with almost every facet of daily living. The effects of a
lackluster national economy and the resulting consequences felt among families across the nation
have yielded in a heightened awareness of monetary value- many times the discussion of
economic deprivations arise first thing in the morning during breakfast. Morning conversations
regarding the distressed finances often stem from what is presented on the dining table.
Consumer food choices and its relationship with breakfast food spending can be expressed with a
myriad of selections and one the primary breakfast items found in virtually every house in the
nation is cold, ready-to-eat (RTE) cereal.
Available finances frequently dictate the decisions consumers make regarding cereal
selection. Pursuing personal flavor preferences while simultaneously adhering to a grocery
budget is not always an available consumer option for many households. By determining
whether a relationship exists between cold, RTE ingredients and unit price provides for a better
assessment as to which types of cereal are purchasable within the financial means of the
consumer.
Many cereal consumers have to forgo personal brand preferences in lieu for more
economical varieties of cereals with an implicit belief that a reduction in cereal unit cost has an
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COLD CEREAL PRICES AND INGREDIENT CONTENTinherent negative consequence in flavor and nutritional health benefits. Whether or not this is
true can be determined by assessing the nutritional value of the cereals; sugar content, for
example, where a greater amount of sugar found in a particular cereal corresponds to greater unit
cost of cold, RTE cereals. For consumers that are restricted to a limited income and are
constrained to a short list of cereal options, being aware of how cereal ingredients are related to
unit cost will aid determining if personal nutritional preferences are within personal economic
means.
By expressing how cereal ingredients are related to the unit price the consumer will be
better informed as to how to best maintain personal cereal flavor preferences within limited
monetary dispositions. Furthermore, additional insights can also be determined, such as: whether
or not traditional and healthier cereal varieties are cheaper or more expensive than cereals that
are comparatively laden with substantially greater amount of sugar. Ultimately, not only does
this research seek to determine the corresponding relationship between cold breakfast cereal unit
cost and ingredient content, but also facilitates in providing greater knowledge of which types of
cereals are available within specific monetary ranges. Providing cereal flavor preference while
simultaneously saving money and supplementing for additional expendable income not only
makes for a more satisfying breakfast experience (especially for households with many
dwellers), but also stimulates discretionary spending among consumers.
Literature Review
Breakfast choices, regarding RTE cereals, are responsible for a substantial part of both
personal and/or household monetary spending. RTE cereal is by far the most popular breakfast
food choice in the United States- beyond other breakfast foodstuffs, such as: bagels, quick
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COLD CEREAL PRICES AND INGREDIENT CONTENTbreads, or eggs and toast (Gejdenson and Schumer 1999). The RTE cereal industry is a
metaphorical Goliath when compared to other breakfast food preparations. An average, RTE
cereal represents about two-thirds of all breakfast foods and consumers purchase more than a
billion units of RTE cereals annually (Gejdenson and Schumer 1999 and Gillespie 1995). When
combined, the total average of RTE cereal consumption per person equates to about 12 pounds
per year (Gejdenson and Schumer 1999).
RTE cereal consumers in the United States are responsible for creating a gargantuan
industry that yields sizable revenues within the breakfast foods market. It has been determined
that in 1987 the combined sales within the RTE cereal market were approximately $4 billion
(Levy 1987) and $9 billion in 2005 (Lee 2005 and Gejdenson and Schumer 1999). This rise in
gross sales is disproportionately large when compared to national inflation rates: 5.5% for 1980-
1989 and 3.0% for 1990-1999 (Metzen, S.R and Morgan, K.J. 1979). As the price of cold RTE
cereals increase in price over time the choices in product purchase will become more limited.
The importance in finding the best RTE cereal item selection within a monetary budget while
maintaining desired flavor, while simultaneously achieving superior nutritional benefits is
becoming a grocery shopping topic that is being discussed with greater frequency.
When identifying and categorizing the numerous kinds of cereals in the local supermarket
into subsets of levels of nutritional value in regards to price the Food and Drug Administration,
FDA, recommends cereals that are energy-dense and are made of whole-wheat or whole-wheat
bran provide are a primary component in satisfying daily nutritional values (Drewnowski and
Fulgoni 2008).
“To meet the FDA definition of “healthy” foods, the food had to
contain at least 10% of the RDI or the daily reference value (DRV)
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COLD CEREAL PRICES AND INGREDIENT CONTENTper reference amount of one or more of six nutrients: protein, fiber,
vitamins A and C, calcium, and iron; it also had to be low in fat
(<3 g), saturated fat (<1 g), cholesterol (<60 mg), and sodium
(<480 mg). Foods were disqualified from health claims if a
serving of food contained >13 g of fat, >4 g of saturated fat, >60
mg of cholesterol, or >480 mg of sodium.” (FDA 2002).
Cereal continues to be the dominant breakfast food and in regards to nutritional health is
also a major contributor. However, “In the years 2000 to 2004, Americans consumed 22.2
teaspoons of added sugar each day; this amount of sugar is equivalent to an excess 355 calories
daily” (Hetzler 2010). This excessive intake of sugar means that unneeded calories are
consumed, yielding in adverse health complications that may include: weight gain, diabetes
mellitus, and heart disease. Although consumers demand to have healthier cereal selections,
customers continue to purchase cereals that are greatly considered as sugary kids’ cereals- it can
be said that RTE cereal is experiencing a popularity comparable to that of fast food, such as
hamburgers and pizzas: RTE cereal is the new junk food.
According to Canstar Blue (2011), an Australian consumer review agency, 25% of cereal
consumers surveyed do not review nutritional information labelling prior to choosing a breakfast
cereal. In addition, 34% of participants didn’t rate low sugar content as a key consideration
when choosing a cereal. The percentage of RTE cereal purchasers are experiencing a nutrition-
taste tradeoff, where the growth of, “food processing sectors adept at producing foods [are]
aimed at the consumer’s palate” (Blaylock et al. 1999). RTE foods are becoming more
commonly found with the addition of fats, sweeteners and salt, all of which create for an
enhanced taste, but yield in negative health effects.
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COLD CEREAL PRICES AND INGREDIENT CONTENTOver the past few years, Public Health Authorities have become increasingly
concerned about the evolution of the nutritional quality of processed food products
(Combris, et al. 2010). Processed foods, such as RTE cereals, are a significant source of
dietary nutrition and highlight the necessity and feasibility of reformulation of many
foods that are more favorable in creating a healthier consumer. Furthermore, the cereal
consumer can be deceived by less-than honest promotions of beneficial nutrition from
manufacturers. Although a particular cereal may contain some or many of the ingredients
necessary to qualify as a healthy food, it could be not as nutritious as perceived. The
addition of refined sugars, fats, and other additives could potentially make what would be
popularly considered as healthy as the opposite. Cereal consumers must exercise
heightened visual awareness of possible misleading nutritional claims.
By the 1970’s research has shown that there was a relationship between the
consumption of insoluble dietary fiber and the incidence of colon cancer; continued
research provided evidence that fiber prevents cancer (Ippolito and Mathios 1990). This
scientific proof has provide cereal manufacturers to create RTE cereals that claim to have
nutritious levels of fiber and other healthy ingredients and could conceivably increase
sales as result of information about the health benefits claimed (Levy, A.S. and Stokes,
R.C. 1987).
“Many manufacturers try to entice you by promising their cereal
is "Made with Whole Grain." In fact, it might appear that those
rainbow-colored, sugar-coated rings are the nutritional equal of a
bran flake or shredded wheat, but it's not the case.” (Mclndoo
2010).
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COLD CEREAL PRICES AND INGREDIENT CONTENT Although there are numerous references that assess which ingredients are healthier than
others, the existence of a universal cereal nutrition categorization, in which RTE cereals that are
most nutritious and provide the most benefit for optimal health are compared to inferior products
that do not have such healthy components, does not exist. Despite research, there is no definite
government guidelines for sugar serving recommendations other than ‘use sparingly’, according
to the FDA, and a reasonable amount can be assigned by acknowledging previous studies
involving the measurement of sugar in RTE cereals.
Cereal consumers viewed RTE cereals that are high in fiber, protein, and minerals to be
healthy, in that a healthy cereal should contain low sugar, low levels of sodium or fat, whole
grain and/or 100% recommended daily allowance of vitamins. However, a general consensus
was made that healthy cereals are not was flavorful and do not provide a comparative tasty
experience when compared to much less healthy sugary cereals. Whether considered healthy or
not, the taste of the RTE cereal must be good enough to be willingly consumed (Lee and Lee
2006).
The importance of reading the nutrition label of the RTE cereal box and comparing which
ingredients are most beneficial may aid in detouring from front-of-the-box health benefits that
could be used to merely entice an uneducated consumer into making an impulse purchase at not
only the consequence of the customers’ health, but also the bottom dollar.
The most common concerns for RTE cereal customers are as follows
(Canstar Blue 2011):
Too expensive
Cereal goes soggy quickly
High sugar content
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COLD CEREAL PRICES AND INGREDIENT CONTENT Lack of nutritional value
Value for money
Determining how RTE cereal ingredients correspond to superior nutritional levels and
price depends on which ingredients are responsible for categorizing cereal healthiness factor.
Although there is a proven relationship between the use of healthier food ingredients, such as
fiber, and the reduction of less healthy ingredients, such as sugar, salts, and fat, with the
prevention of diet related disorders, there are no definitive guidelines, provided by federal health
authorities, that dictate which cereals qualify as beneficial for dietary health. Therefore, the
application of previous studies related to the classification of RTE cereals according to
nutritional value must be observed.
Previous research (namely Consumer Report’s Consumer Union, Cereal Food
Advertising to Children and Teens Score, and the United Kingdom Food Standards Agency
Nutrient Profiling Model), although fundamentally different in ultimate objective share
similarities in the analysis of cereal nutritional comparison. The similarities found between these
studies measure the following variables: sugar, sodium, and dietary fiber content. These
variables will be used in this report’s analysis of cereals and its respective healthiness in regards
to price. Furthermore, an additional common trait found throughout these studies was the
predominance of sugary cereals and the association with higher cereal prices; this trend however,
was not thoroughly assessed with other divisions or categories of cereals according to nutritional
content, but rather other elements, such as advertising and marketing.
Variables including cereal item price and nutritional content will be compared, where a
relationship will be determined that will suggest that when greater quantities of refined sugar is
founded per serving of a particular cereals divided into nutritional health categories the price will
increase.
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COLD CEREAL PRICES AND INGREDIENT CONTENTNull Hypothesis: H0: There is no relationship between the price of ready-to-eat cereal and its
ingredients.
Alternate Hypothesis: H1: As the quantity of unhealthy ingredients increases per serving of
ready-to-eat cereal, the cost price of the cereal item will also increase.
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COLD CEREAL PRICES AND INGREDIENT CONTENTData and Method
The data acquired for this research was primarily compiled from the Wal-Mart website,
where recent prices and nutrition information was gathered from the grocery shopping portal.
The usefulness of this data was helpful in that the listed prices were uniform across the nation,
with the differed option to shop locally via the online portal. From this website the necessary
variables were identified to determine whether or not there is a correlation between the RTE
cereal ingredients and its price.
Dependent Variable: Cost of cereal
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COLD CEREAL PRICES AND INGREDIENT CONTENTIndependent Variables: Calories per serving, Amounts of sugar, dietary fiber, and sodium.
Although the Wal-Mart website is very informative in providing detailed nutrition
information, as well as the item price, the website fails to provide for a uniform standard that
creates for a consistent serving size for all RTE cereals. Furthermore, the identifying
classifications of which cereals fall into particular health categories was a responsibility for the
researcher, as Wal-Mart did not provide such information.
Searching for a nutritional categorical cereal standard for both dependent and
independent variable required additional research among academic journals and consumer
review agencies. In regards to the dependent variable, the division of cereal prices per package
was determined on two primary factors. The first being that all cereals researched on the Wal-
Mart web page were not on sale or temporary shoppers’ special. Furthermore, only common
package sizes were selected; value-size or economical bargains were forgone as the product
promotion could adversely affect the results of the research.
Searching for a method to divide RTE cereal product prices was aided by the research
methods employed by Lee and Lee’s 2006 work, Consumer Insights on Healthy Breakfast
Cereal. In this report the authors segmented the prices of RTE cereals into three ranges: low,
medium, and high. The respective prices were: $2-2.99 for low, $3-3.99 for medium, and $4+
for high priced RTE cereals. As Wal-Mart did not have such a wide plethora of varied priced
cereals, a slight adjustment was made so as to better address the prices provided in the Wal-Mart
website. The divisions of price ranges are as follows: $0-1.99 for low, $2-2.99 for medium, and
$3+ for high. However, although a new range in price schematics was established, its relevance
to nutrition was irrelevant unless the package prices of each cereal was converted to make a
standard measure of value by dividing the package price of the cereal
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COLD CEREAL PRICES AND INGREDIENT CONTENTIn regards to independent variables, a similar strategy was employed, as with the
dependent variable where additional research reports that addressed similar topics and methods
as this report were used. For designating sugar, fiber, and sodium levels the official website for
Consumer Reports, Union Reports, was accessed. Within this website it was determined that
dividing sugar, fiber, and sodium ingredients were each divided into low and high ranges, where
the break point for each of the mention independent variables are 5, 5, and 0.140 grams
respectively.
Yet, like the dilemma with the dependent variable, where the assessment of nutrition and
its placement in its respective ranges are not practiced with a universal set range while adhering
to the serving size. It could be very well possible that a particular cereal could out-perform
another brand due to having a different serving size. Therefore, in order to make for a leveled
ground for all cereals, sugar, fiber, and sodium content was calculated by its serving size in
grams, then divided by the how many grams constitute the serving size of each cereal.
The division of each independent variable foodstuff was made into 2 categories of high
and low content after assessing its nutritional food stuff-serving size ratio. Superior content for
fiber was awarded with a number 1 for containing more than 5 grams of dietary fiber, but the
inverse was given for the sugar and sodium, as elevated intake of these ingredients are inherently
detrimental to dietary health. A score of 1 for sugar yields less than 5 grams per serving and a
score of 1 for sodium yields less than 0.140 grams per serving. The same method was employed
for determining the caloric ratio of each RTE cereal by dividing the number of calories per
serving by the serving size in grams.
In order to make for a more simplistic perspective of which cereals are healthy and those
that are not, it was agreed that by collapsing the identifiers of determining nutritional quality in
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COLD CEREAL PRICES AND INGREDIENT CONTENTregards to the independent variables. Creating a nutritional index by combining the three
foodstuffs (sugar, fiber, and sodium) ratios into a binomial representation aids in reducing
potential misinterpretation of what constitutes a healthy or less healthy cereal item purchase.
Should any cereal fulfill in obtaining a nutritional index of 3 means that it has score of
superior healthiness by minimizing the levels of sugar and sodium in each cereal serving, while
elevating the presence of fiber. A score of 2 could be a superior result of two out of three
foodstuffs, a score of 1 would result in only one superior foodstuff result meeting the nutritional
criteria, and a score of 0 would yield the least healthy of cereal selections, where it does not meet
any of the minimum requirements to be considered healthy. The path to collapsing the
independent variable data continues by further condensing the identity of what is a healthy cereal
choice by combining nutrition factor scores 3 or 2 were translated into scores of 1 and nutritional
scores of 1 or 0 were translated in scores of 0; thus, making the nutritional index a nominal
index.
The methods chosen to assess the data are as follows:
1. Hypothesis testing with Samples: This testing method was selected as a primary
model due to its popular use among social scientists. Not only is the data to be assessed in
respects to formulated hypotheses, but is to be a determining factor in identifying the strength of
relationships between the dependent and independent variables through statistical inference. A
clear assumption can be made as whether the provided information is strong enough to
definitively reject or not reject the null hypothesis, where no relationships can be determined.
2. Contingency table with Chi-Square Test: Assuming that there is no relationship
between the dependent and independent variables determines whether any apparent relationship
obtained in a sample cross-tabulation is attributable to chance. As the Chi-square statistic is
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COLD CEREAL PRICES AND INGREDIENT CONTENTacquired, it can be assessed that as the deviation between observed and expected frequencies
increases as does the inference that a relationship does exist between studied variables.
Furthermore, the calculation of the Chi-square statistic also determines a precise degree of
confidence acknowledging the degree of the relationship between variables.
3. Regression Analysis: As the data provided are interval-level data, the decision to
chose regression analysis for determining the relationship between dependent and independent
variables is obvious, as the statistical relationship focuses on the value of the independent
variable so as to estimate the value of the dependent variable.
A linear regression model will be employed so as to reveal both the direction and
strength of association between cereal ingredients and product price. In addition, an ANOVA
data output will also evaluate any potential the amount of error present in the model and to detail
the proportion of variance between variables, with the application of an F-statistic. Beta weights,
which include R-squared values, will aid in assessing any change in price due to foodstuff
modification. The Durbin-Watson measure will monitor the possibility of multicolliniarity found
among independent variables and finally, the hypothesis will be again acknowledged by studying
p-value measures.
Analysis and Results
1. Hypothesis Testing with Samples:
Step 1: Estimate the population mean. The population mean would be the average of the
price of cereal for every cereal name.
MeanPop: $0.28
Step 2: Estimate the population standard deviation. S = $0.10
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COLD CEREAL PRICES AND INGREDIENT CONTENTStep 3: Calculate the standard error of the mean. Divide the population standard
deviation by the square root of the total number found within the sample population.
s.e. = s / (square root 93) = 0.10 / 9.64 = 0.01
Step 4:Test the hypothesis. Find the difference between the sample mean and the
population mean divided by the population standard deviation.
t-score = (Population mean- Sample mean) / standard error of the mean = (0.27 – 0.28) / 0.01 = 1
df = n-1 = 74 – 1 = 73
A t-score of 1 assessed with a level of significance of 0.05, with 73 degrees of freedom,
yields a distribution value of 1.645; thus, tcalc= 1 and t= 1.645. Looking up a t-score of 1 in the
t-table (df=73), the probability of a sample of 74 with a mean of $0.27 is less than 0.1
Step 5: Accept or Reject null hypothesis.
As the t-alpha value is greater than the t-calculated score, it can be determined that the
null hypothesis cannot be rejected, or in other words, the research hypothesis cannot be accepted.
As more than 90% of increased cereal prices in relation to added sugar are due to chance.
Table 1. Calculations for Two Different Sample Sizes
Experimental Sample Control Sample Total Population
Less Healthy Healthy Both
N 74 19 93
Means $0.27 $0.34 $0.28
S 0.09 0.13 0.10
s.e. 0.01 0.03 0.01
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COLD CEREAL PRICES AND INGREDIENT CONTENTT-test Assuming Proportions
Step 1: Experimental: p1= 74/93 = 0.796
S1= sqrt(p(1-p))= sqrt(0.796(1-0.796))= 0.403Control: p2= 19/93 = 0.204
S2= sqrt(p(1-p))= sqrt(0.204(1-0.204))= 0.403
Step 2: Calculate s.e for both groups
Experimental: s1/sqrt(n1)= 0.403/sqrt(74)= 0.0468Control: s2/sqt(n2)= 0.403/sqrt(19)= 0.0924
Step 3: Calculate overall s.e.d= sqrt(0.0468^2 + 0.0924^2)= 0.1035
Step 4: Convert the difference between groups in a t-score with df= infinity as thenumber of cases exceeds 30.
(p1-p2) /s.e.d= (0.403-0.403) / 0.1035= 0
A conclusion can be made that the t-calculated statistic found in step 4 (t= 0) does not
exceed 1.282, the t-score associated with the 0.10 level of significance.
Step 5: A probability greater than 0.10 is not good enough to reject the null hypothesis;
the result suggests that there is a greater than 0.10 probability that the null
hypothesis is correct- 90% chance that ingredients have
relationship with cereal price. It can
be concluded that the
experimental
group, less healthy
cereals that
many contain
elevated levels of
sugar and sodium,
with diminished levels of dietary
Table 3. Percent Distribution for Data:
Relationship Between Nutrition Level
and Price
Nutrition, %
Price, % Low High
Low 13.51 5.26
Medium 40.54 21.05
High 45.95 73.68
Total 100.00 100.00
Table 4. Hypothetical No-Relationship
Cross-Tabulation for Chi-Square
Nutrition, %
Price, % Low High
Low 11.83 11.83
Medium 36.56 36.56
High 51.61 51.61
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COLD CEREAL PRICES AND INGREDIENT CONTENTfiber, did not yield an increase in cereal cost. Therefore, the null
hypothesis cannot be rejected: There is no relationship between the price of ready-
to-eat cereal and its ingredients.
2. Contingency Tables with Chi-Square Test
Step1: Determine the dependent and independent variables, as noted in the research
hypothesis- As the quantity of sugar and other unhealthy ingredients
increases per serving of ready-to-eat cereal, the cost price of the cereal item will also
increase. The dependent variable would be the price and the independent
variables will be the nutritional value of the cereals as calculated by creating
a collapsed frequency of four possible nutritional categories to 2.
Step 2, 3: Calculate percentages within the variables and ccompute expected frequencies.
Table 5. Calculations for Expected Frequencies and Chi-Square
Price Nutrition Lev. Obs Freq. Exp Freq. (Obs-Exp)^2/ExpLow Low 10 =.1183*74 8.75 0.18 Low High 1 =.3656*74 27.05 25.09
Medium Low 30 =.5161*74 38.19 1.76
Medium High 4 =.1183*19 2.25 1.37
High Low 34 =.3656*19 6.95 105.36
High High 14 =.5161*19 9.81 1.79
Total 93 93.00 135.55 =Chi-Square
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COLD CEREAL PRICES AND INGREDIENT CONTENT
Step 4: Compare the value of Chi-Square computed for the actual cross-tabulation with the appropriate value of Chi-square tabulated in the table of theoretical
values. Degrees of freedom equal (3-1) x (2-1) = 2
Chi-square computed= 135.55
Chi-Square tabulated= p<0.005 = 10.60
There is a probability of 1% that in the long run, an inference will be made that a
relationship will be made that exists in the population when in fact it does not. According to the
decision rule, where if the calculated Chi-square value is greater than the tabulated value for Chi-
square, while considering degrees of freedom, then the null hypothesis must be rejected, or the
null hypothesis cannot be accepted. Therefore, the null hypothesis that claims that there is no
relationship between the cost of cereal and its ingredients must be rejected or the experimental
hypothesis that claims that a relationship does exist must be accepted.
Nominal Measure of Association Based on Chi-Square: Cramer’s V:
V= sqrt(chi-square/(mN)) where m= # of columns – 1= 2N= size of sample= 93
=sqrt(135.55/(2*93) =sqrt(135.55/186) =0.854
Like all measures of association for nominal-level variable, Cramer’s V is always a
positive number. The measure ranges from 0, indicating no relationship between variables, to
1.0+, indicating a perfect relationship.
3. Regression Analysis
Table 6. Variables and Descriptive Statistics
Variable Mean Std. Deviation N= ObsPricePS 0.2803 0.10504 93NutritionIndex 0.2043 0.40538 93
Sugar 0.2648 0.11905 93
Fiber 0.0759 0.0762 93
Sodium 0.0047 0.00239 93
Calories 3.6948 0.37218 93
Table 7. Regression Coefficients
Model B, Coefficients: y- t Sig.PricePS 0.67 3.985 0NutritionIndex -0.061 -1.643 0.104
Sugar -0.24 -2.442 0.017
Fiber -0.1 -0.509 0.612
Sodium -23.497 -4.019 0
Calories -0.053 -1.373 0.173
* Dependent Variable: PricePS
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COLD CEREAL PRICES AND INGREDIENT CONTENT
Table 8. Model Summary
R2 Adjusted R2 Std. Error of the Durbin-Watson Std. Error of the ANOVA F-score0.233 0.217 0.189 1.286 0.09457 5.301
Predictors: (Constant), Calories, Sodium, Sugar, Fiber, Nutrition Index
*Dependent Variable: PricePS
Step 1-7: Calculate slope and intercepts, note appendix for table calculations.
Step 8: Y-hat = a + b1X1 + b2X2 + b3X3 + b4X4 + b5X5 + e
=0.67 + 1.06 X1 – 0.12X2 – 0.02X3 + 0.00X4 + 0.16X5 + e
Table 9. Regression intercepts and slopes
Intercepts a Slopes b a * b
a1 -0.0919 b1 1.0566 -0.0971
a2 0.3 b2 -0.12081 -0.0362
a3 0.07764 b3 -0.01831 -0.0014
a4 0.00461 b4 0.00025 0.0000
a5 3.65461 b5 0.15604 0.5703
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COLD CEREAL PRICES AND INGREDIENT CONTENTStep 9: Calculate: standard error of the estimate, coefficient of determination, and
standard error of the slope- assess measures of goodness. Note
appendix for calculations.
Table 10. Measures of Goodness
Std. Er. Est. Coef. Det. Std.Err,b
Sy|x r^2 sb
Y1 0.395 0.0725 0.3983
Y2 0.12 0.2074 0.0901
Y3 0.077 0.0031 0.054
Y4 0.002 0 0.0016
Y5 0.375 0 0.2391
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COLD CEREAL PRICES AND INGREDIENT CONTENTDiscussion and Further Analysis
The results found with the provided data made for less than perfect results, where
conflicts in the relationships between the dependent and independent variables were evident.
Initial hypothesis tests have found that inferior t-test scores for both the initial calculations and
later another t-test with assuming proportions with a control variable comprised of foodstuffs
other than sugar, i.e. fiber and sodium. Thus, it can be determined that there is a low likelihood
of these foodstuffs influencing the individual prices of RTE cereals.
The great majority of the relationship between the dependent and independent variables
are left to chance, as the correlation strength between these variables determined by t-test has
shown to be weak, with scores falling below the 0.10 probability on the t-distribution table with
infinite degrees of freedom. Therefore, provided the processed data and the dismal result
compared with the t-scores yield in the rejection of the alternate hypothesis and the refusal the
reject the null hypothesis.
Null Hypothesis: H0: There is no relationship between the price of ready-to-eat cereal
and its ingredients.
Alternate Hypothesis: H1: As the quantity of unhealthy ingredients increases per serving
of ready-to-eat cereal, the cost price of the cereal item will also increase.
More interestingly, the second method, contingency table with applied chi-square test,
used to assess the possible relationship between cereal ingredients and the respective price
yielded a result that provided for a strong possibility for a relationship between the dependent
and independent variables. According to the contingency data, it can be noted that the
percentage relationship between nutrition level and price per serving demonstrates a strong
relationship with high nutrition and high prices, however, chi-squared analysis proves that the
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COLD CEREAL PRICES AND INGREDIENT CONTENTrelationship between cereal cost and nutrition have alternate results. Chi-square testing has
demonstrated a relationship between moderately price RTE cereals and low nutritional health.
The compared value of the calculated chi-square value to that of the tabulated score
favors the calculated score, about 136 v. 11. As the calculated value of chi-square is much
greater than its tabulated counter-part, there is a probability of 1% that in the long run, an
inference will be made that a relationship will be made that exists in the population when in fact
it does not. This means that despite having a very sizable calculated chi-square statistic, it could
misrepresent the data in misidentifying particular independent variables’ potential weight to
influence the cereal price.
Indeed, this is true as with Cramer’s V, the calculated chi-square statistic is again proven
that a relationship between dependent and independent variables exists, however pinpointing the
origin of relationship when compared to contingency tables is not as specific. However, the
resulting score for Cramer’s V was 0.854; as this number more closely approaches 1, the
stronger the possibility of inter-variable action, where the independent variables, such as sugar,
fiber, or sodium content determines the strength of its relationship with cereal price. The null
hypothesis, as stated in the beginning of this document, is rejected- a relationship between
independent variable or variables do exist.
In regards to linear regression, the results were not favorable and will provide much
opportunity for improvement. The relationship between cereal price and constituting ingredients
are very small, despite numerous evaluations and measures. In researching for a commonality
between ingredients and cost this report has yielded confronting analyses that prove that this
report has many flaws that need to be addressed.
Measures of goodness of fit are primary tools in evaluating data and explaining
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COLD CEREAL PRICES AND INGREDIENT CONTENTcorrelation and variance. The first measure of goodness of fit is the standard error of the
estimate; this measures the amount of error when predicting Y, when given X. A well-designed
statistical analysis can accurately estimate Y hat variation with a predicted value of Y. However,
prevalence in the amount of errors undermines the center hypothetical topic, that the ingredients
of a cereal dictate the cost of the item. Similarly, when comparing the coefficients of
determination also stresses that the ratio of experimental variance to total variance in Y. Due to
the provided data the coefficient of determination fails to acknowledge the reduction of error be
using the regression line to the total error guessing the mean. Furthermore, a seemingly small r-
square value prevents a relationship from being observed; the r-square rating totaled only about
0.3- as smaller ranks are deemed more likely to fail in gaining strong, reciprocal dependent-
independent relationship.
The coefficient of determination’s r-square rating prevents this project from identifying
price-ingredient relationships. Perhaps, an adjusted r-square measurement would provide for a
more accurate picture of the explanatory power of this model by adjusting for the presence of
partial slopes with insignificant values. After running the data through SPSS, the adjusted r-
square was 0.217- lower than the original r-square value. When the adjusted r-square value is
greater than the r-square the statistical significance it can be determined that the data model does
not much statistical significance and has possibly has significant partial slopes. It can be
assumed that by either acknowledging the common r-square or the adjusted modification, the
data presented does not matter the experimental hypothesis. In fact, this project’s r-square values
can assume that the relationship between cereal cost and its ingredients only comprise about 30%
of correlation; therefore, it can be determined that about 70% of cereal prices are governed by
chance and the ingredients have little responsibility in the overall cost for a box of RTE cereal.
23
COLD CEREAL PRICES AND INGREDIENT CONTENTThe third measurement of goodness of fit, standard error of the slope, explains variance
as a percentage and much like the previous tools of statistical measurement has demonstrated
that with its low numbers of coefficiency the data provided and the method it was studied yielded
in scores close to zero, indicating that the likelihood of a relationship between dependent and
independent variables to be very small. In addition, standard of error scores that hover around
the zero mark exhibit insignificant slopes and often are found to have reduced r-square values,
thus inclining the message that the choice in independent variables were in poor in an attempt to
convey a relationship with unit cost of RTE cereals. The measurements of goodness of fit have
all reached the same conclusion that small numerical coefficients are not conducive in creating
strong relations between the variable provided.
In an effort to continue to assess the dearth of potentially valuable and useful data and
affiliated relations between dependent and independent variables more statistical diagnoses were
undertaken. Testing for multicollinearity identifies an important assumption when creating
linear relationships, where variables can be identified and determined if it shares a linear path
with another variable. The presence of inflated and inconsistent standard error of the estimate
statistics is a trademark of multicollinearity. Also, multicollinearity can also be pinpointed by
linear equations that yield in high adjusted r-squares with insignificant slope coefficients- the
closer the r-square value is to one, the more likely that multicollinearity is a problem. Although
the coefficient statistics have provided for less than streamlined and perfect relationships that
ideally correspond to each other, the prevalence of multicollinearity is present, but not
devastating.
Yet another test to demonstrate the relationship between the provided variables is the F-
statistic. This measurement assesses whether partial slope coefficients for all the independent
24
COLD CEREAL PRICES AND INGREDIENT CONTENTvariables should be identified and taken as a group and are equaled to zero. Should most or all of
the slope coefficients in a multiple regression lack explanatory power, the F-statistic will be low.
Conversely, a larger F-statistic is more likely to identify one or more of independent variables as
statistically significant. The F-statistic produced by SPSS has yielded in a small number, 5.301.
Just like how small slope values correspond to diminished variable relationships, a small F-score
is also an indicator of increased multicollinearity. Compared to larger F-scores, such as 50,
which indicates that there is almost, if not any, chance that all the partial slopes are equal to zero.
The F-statistic provided in this report indicates that the possibility of the independent variables
being too closely related is strong and the prevalence of multicollinearity to be unavoidable.
25
COLD CEREAL PRICES AND INGREDIENT CONTENTAnother concern that needs to be brought to attention is the possibility of autocorrelation,
or the assumption that errors are not correlated. Although correlated errors are predominantly an
issue that is usually found in time series analyses, the problem with autocorrelation is that the
standard errors of the slopes are not given enough attention. Statistical mistakes could
potentially result in slopes that may appear to be significant, when in fact, they are not. To test
for the possibility of autocorrelation the Durbin-Watson statistic will be used. By counting the
number of independent variables and the number of observations or cases within a study an
assessment can be made as to how error positively or negatively affects the null and
experimental hypotheses.
SPSS has provided this study with a Durbin-Watson score of 1.286. Upon reception of
this score a Durbin-Watson table aids in guiding that score within an upper and lower range.
Should the lower limit be less than 4, the perfect positive autocorrelation, and less than the
Durbin-Watson value one must reject the proposed null hypothesis with negative autocorrelation.
On the other hand, a lower limit score that outperforms both the Durbin-Watson score and is
greater than zero forces the researcher to reject the null hypothesis with positive autocorrelation.
The provided Durbin-Watson score of 1.286 is smaller than, the upper and lower limits, 1.776
and 1.542, provided in the statistical table. Therefore, it can be determined, that the null
hypothesis must be rejected and that the research has a propensity for greater positive
autocorrelation.
26
COLD CEREAL PRICES AND INGREDIENT CONTENTConclusion
The experimental hypothesis that a relationship, or relationships, exists between the
contents of RTE cereals and its respective price cannot be completely determined. Although chi-
square testing has revealed a relationship between moderately price RTE cereals and low
nutritional health from its ingredients, alternative assumptions can be made. Furthermore, a
graphic analysis visually demonstrates that a relationship between a couple independent
variables and the dependent variable does exist. It can be observed that sugary cereals have
achieved the title as most expensive RTE cereal and that as less sugar is found within the
ingredients, the product price of the cereal goes up as well. This negatively reciprocal
relationship is noted, however, the weight that should be placed on the reliability of this
observation is not definitive. Likewise, a slight positive relationship can be noted with the
presence of fiber, where increased prevalence of this product in RTE cereals yields in a positive
correlation- the price increased with more dietary fiber found in the cereal. Yet, like with the
sugar example just mentioned, these trends are not to be trusted as they are highly variable and
more closely resembles a heteroskedastic representation that is heavily loaded with outliers,
potential errors in data acquisition, and disagreeable independent variables.
In order to improve upon this research model it is advisable that additional considerations
be addressed, so as to aid in the elimination of collinear trends and prevent autocorrelation, while
seeking more advantageous independent variables that also contribute in identifying additional
routes to positively influence the dependent variable. Additional variables that could be
responsible for varying the price of a box of cereal may include a multitude of variables.
When purchasing RTE cereal the time of the year could dictate eating frequency and
choice of product. It can be assumed that more cold cereal is consumed during warm seasons,
27
COLD CEREAL PRICES AND INGREDIENT CONTENThowever, that is to be assessed. Additionally, a factor that is probably more important than the
ingredients of the cereal itself is the advertising and marketing that promotes that particular
product. Initial research for this project revealed that the cereal industry is governed by public
awareness and the ability to coax shoppers into purchasing particular cereal items is paramount.
The amount of revenue that is invested in the marketing and promotion of RTE cereals are more
than any other industry, as noted on a blog from the Consumer Reports website. Frequently, the
influence of advertising on purchase power transcends personal necessity. Those that are more
susceptible to being influenced by such campaigns could have a strong influence on the overall
pricing schematics of RTE cereals. Additionally, those that could be identified, as potential
marketing targets are also additional independent variables, as age and gender probably also
dictate how cereals are manufactured and sold. In searching for the relationship between cereal
ingredients and cost, comparing product prices across multiple grocers would also aid the
production of better results and more distinctive variable relations. Although the cereal industry
may seem benign in its operations, however, manufacturers may attempt to sell unhealthy
selections under the guise of something more nutritiously beneficial. Ultimately, it is up to the
consumer to make the best decisions when purchasing their favorite cereals, be it because of any
reason from health preference to financial fastidiousness.
28
COLD CEREAL PRICES AND INGREDIENT CONTENT
References
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Lee, C.M. and Lee, S.Y. (2007). Consumer Insights on Healthy Breakfast Cereal- A Focus
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Levy, A.S. and Stokes, R.C. (1987). Effects of a Health Promotion Advertising Campaign on
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30
COLD CEREAL PRICES AND INGREDIENT CONTENT
31
COLD CEREAL PRICES AND INGREDIENT CONTENT
32
COLD CEREAL PRICES AND INGREDIENT CONTENTAppendix
Appendix: Master Data Sheet 1Table A-1. Master Data Sheet 1
Cereal Price per Serving Refined Sugar, g Dietary Fiber, g Sodium, g Collapsed N. Index1 $0.00 0 2 0.00 12 $0.27 9 1 0.16 0
3 $0.33 4 2 0.01 1
4 $0.33 6 2 0.00 0
5 $0.41 16 2 0.20 0
6 $0.41 14 2 0.11 0
7 $0.41 14 3 0.10 0
8 $0.25 12 1 0.12 0
9 $0.29 1 1 0.19 0
10 $0.25 9 1 0.17 0
11 $0.25 9 2 0.14 0
12 $0.25 9 2 0.19 0
13 $0.21 9 2 0.18 0
14 $0.30 8 0 0.19 0
15 $0.23 3 1 0.29 0
16 $0.27 9 1 0.23 0
17 $0.25 2 0 0.24 0
18 $0.41 5 1 0.34 0
19 $0.22 10 1 0.22 0
20 $0.19 12 1 0.15 0
21 $0.24 11 1 0.15 0
22 $0.46 16 4 0.13 0
23 $0.40 10 9 0.26 0
24 $0.46 6 13 0.28 0
25 $0.40 13 11 0.26 0
26 $0.24 0 14 0.11 1
27 $0.29 6 3 0.23 0
28 $0.26 11 1 0.27 0
29 $0.21 20 4 0.20 0
30 $0.33 10 1 0.22 0
31 $0.12 12 0 0.17 0
32 $0.16 5 5 0.21 0
33 $0.13 10 1 0.21 0
34 $0.21 11 5 0.00 1
35 $0.17 13 1 0.16 0
36 $0.15 12 0 0.15 0
37 $0.17 15 0 0.05 0
38 $0.15 11 1 0.16 0
39 $0.20 18 7 0.35 0
33
COLD CEREAL PRICES AND INGREDIENT CONTENT40 $0.13 13 1 0.20 0
41 $0.15 1 3 0.19 0
42 $0.44 7 6 0.00 1
43 $0.44 9 5 0.00 1
44 $0.39 12 8 0.13 1
45 $0.39 12 8 0.14 0
46 $0.39 13 8 0.10 1
47 $0.28 5 5 0.09 1
48 $0.45 13 4 0.13 0
49 $0.44 9 6 0.01 1
50 $0.44 9 1 0.20 0
51 $0.66 10 7 0.13 1
52 $0.28 12 1 0.12 0
53 $0.18 8 13 0.20 0
54 $0.31 15 6 0.15 0
55 $0.25 16 0 0.11 0
56 $0.27 12 0 0.13 0
57 $0.28 12 6 0.01 1
58 $0.39 12 5 0.00 1
59 $0.27 19 7 0.35 0
60 $0.35 14 3 0.26 0
61 $0.16 12 1 0.14 0
62 $0.26 7 1 0.18 0
63 $0.15 2 1 0.20 0
64 $0.15 12 0 0.11 0
65 $0.25 3 1 0.21 0
67 $0.23 10 0 0.13 0
68 $0.14 11 1 0.14 0
69 $0.29 12 5 0.00 1
70 $0.32 12 6 0.20 0
71 $0.28 4 1 0.22 0
72 $0.25 19 7 0.35 0
73 $0.22 20 4 0.21 0
74 $0.20 3 0 0.32 0
75 $0.28 7 1 0.17 0
76 $0.22 11 1 0.14 0
77 $0.45 10 5 0.11 1
78 $0.28 10 1 0.22 0
79 $0.24 9 1 0.16 0
80 $0.26 3 3 0.21 0
81 $0.21 11 1 0.19 0
82 $0.36 11 6 0.10 1
83 $0.37 6 3 0.20 0
84 $0.18 12 1 0.17 0
34
COLD CEREAL PRICES AND INGREDIENT CONTENT85 $0.17 4 3 0.13 1
86 $0.36 14 5 0.23 0
87 $0.24 12 1 0.18 0
88 $0.40 17 5 0.23 0
89 $0.24 5 3 0.19 0
90 $0.25 13 0 0.18 0
91 $0.24 4 0 0.19 0
92 $0.44 14 5 0.15 0
93 $0.33 9 5 0.13 1
94 $0.19 6 2 0.16 1
Appendix: Master Data Sheet 2
Table. A2- Master data sheet: Price and Nutrition
Cereal Price
per Hi (2), Med (1),
Refined Sugar,
High (0),
Dietary Fiber,
High (1),
Sodium, g
High (0),
N. Ratingagg.:
N. Collapsed Alf's Puffed Red Wheat $0.09 0 0 1 2 0 0.00 1 2 1
Banana Nut Cheerios $0.27 2 9 0 1 0 0.16 0 0 0Bear Naked Fit Vanilla Almond $0.33 2 4 1 2 0 0.01 1 2 1Bear Naked Fruit And Nut $0.33 2 6 0 2 0 0.00 1 1 0Cascadian Farm Cinnamon Raisin $0.41 2 16 0 2 0 0.20 0 0 0Cascadian Farm Oats & Honey $0.41 2 14 0 2 0 0.11 1 1 0Cascadian Farm Fruit And Nut $0.41 2 14 0 3 0 0.10 1 1 0Cheerios Apple Cinnamon Cereal $0.25 1 12 0 1 0 0.12 1 1 0Cheerios Cereal $0.29 2 1 1 1 0 0.19 0 1 0Cheerios Chocolate $0.25 1 9 0 1 0 0.17 0 0 0Cheerios Fruity Cereal $0.25 1 9 0 2 0 0.14 0 0 0Cheerios Honey Nut $0.25 1 9 0 2 0 0.19 0 0 0Cheerios Yogurt Burst $0.21 1 9 0 2 0 0.18 0 0 0Chex Cinnamon $0.30 2 8 0 0 0 0.19 0 0 0Chex Corn Cereal $0.23 1 3 1 1 0 0.29 0 1 0Chex Honey Nut $0.27 2 9 0 1 0 0.23 0 0 0Chex Rice $0.25 1 2 1 0 0 0.24 0 1 0Chex Wheat $0.41 2 5 0 1 0 0.34 0 0 0Cinnamon Toast Crunch $0.22 1 10 0 1 0 0.22 0 0 0Cocoa Puffs $0.19 1 12 0 1 0 0.15 0 0 0Cookie Crisp $0.24 1 11 0 1 0 0.15 0 0 0Crunchy Almond Oatmeal Crisp $0.46 2 16 0 4 0 0.13 1 1 0Fiber One Caramel Delight $0.40 2 10 0 9 1 0.26 0 1 0Fiber One Honey Clusters $0.46 2 6 0 13 1 0.28 0 1 0Fiber One Sweetened Wheat & Bran $0.40 2 13 0 11 1 0.26 0 1 0Fiber One Original $0.24 1 0 1 14 1 0.11 1 3 1Honey Kix $0.29 2 6 0 3 0 0.23 0 0 0Golden Grahams $0.26 2 11 0 1 0 0.27 0 0 0
35
COLD CEREAL PRICES AND INGREDIENT CONTENTGreat Value Crunchy Raisin Bran $0.21 1 20 0 4 0 0.20 0 0 0Great Value Strawberry Awake $0.33 2 10 0 1 0 0.22 0 0 0Great Value Berry Crunch $0.12 0 12 0 0 0 0.17 0 0 0Great Value Bran Flakes $0.16 0 5 0 5 1 0.21 0 1 0Great Value Cinnamon Crunch $0.13 0 10 0 1 0 0.21 0 0 0Great Value Frosted Shredded Wheat $0.21 1 11 0 5 1 0.00 1 2 1Great Value Fruity Puffs $0.17 1 13 0 1 0 0.16 0 0 0Great Value Fruity Sparkles $0.15 0 12 0 0 0 0.15 0 0 0Great Value Honey Crunch $0.17 1 15 0 0 0 0.05 1 1 0Great Value Honey Nut Spins $0.15 0 11 0 1 0 0.16 0 0 0Great Value Raisin Bran $0.20 1 18 0 7 1 0.35 0 1 0Great Value Sugar Frosted Flakes $0.13 0 13 0 1 0 0.20 0 0 0Great Value Toasted Whole Grain $0.15 0 1 1 3 0 0.19 0 1 0Kashi Autumn Wheat $0.44 2 7 0 6 1 0.00 1 2 1Kashi Cinnamon Harvest $0.44 2 9 0 5 1 0.00 1 2 1Kashi Golean Crisp! $0.39 2 12 0 8 1 0.13 1 2 1Kashi Golean Crunch Honey Almond $0.39 2 12 0 8 1 0.14 0 1 0Kashi Golean Crunch! Protein $0.39 2 13 0 8 1 0.10 1 2 1Kashi Heart To Heart Honey Oat $0.28 2 5 0 5 1 0.09 1 2 1Kashi Heart To Heart Blueberry $0.45 2 13 0 4 0 0.13 1 1 0Kashi Organic Promise $0.44 2 9 0 6 1 0.01 1 2 1Kashi Strawberry Fields $0.44 2 9 0 1 0 0.20 0 0 0Kashi U Black Currants $0.66 2 10 0 7 1 0.13 1 2 1Kellogg's Cinnabon Crunchy $0.28 2 12 0 1 0 0.12 1 1 0All-Bran Branbuds $0.18 1 8 0 13 1 0.20 0 1 0Cracklin' Oat Bran $0.31 2 15 0 6 1 0.15 0 1 0Froot Loops Marshmallow $0.25 2 16 0 0 0 0.11 1 1 0Frosted Krispies $0.27 2 12 0 0 0 0.13 1 1 0Frosted Mini-Wheats $0.28 2 12 0 6 1 0.01 1 2 1Frosted Mini-Wheats Blueberry $0.39 2 12 0 5 1 0.00 1 2 1Raisin Bran Sweet Raisins $0.27 2 19 0 7 1 0.35 0 1 0Smart Start $0.35 2 14 0 3 0 0.26 0 0 0Apple Jacks $0.16 0 12 0 1 0 0.14 0 0 0Cinnamon Pecan $0.26 2 7 0 1 0 0.18 0 0 0Kellogg's Corn Flakes $0.15 0 2 1 1 0 0.20 0 1 0Corn Pops $0.15 0 12 0 0 0 0.11 1 1 0Crispix $0.25 1 3 1 1 0 0.21 0 1 0Crunchy Nut Golden Honey $0.23 1 10 0 0 0 0.13 1 1 0Kellogg's Frosted Flakes $0.14 0 11 0 1 0 0.14 0 0 0Frosted Mini-Wheats Strawberry $0.29 2 12 0 5 1 0.00 1 2 1Frosted Mini-Wheats Chocolate $0.32 2 12 0 6 1 0.20 0 1 0Special K $0.28 2 4 1 1 0 0.22 0 1 0Kellogg's Raisin Bran $0.25 1 19 0 7 1 0.35 0 1 0Kellogg's Raisin Bran Crunch $0.22 1 20 0 4 0 0.21 0 0 0
36
COLD CEREAL PRICES AND INGREDIENT CONTENTKellogg's Rice Krispies $0.20 1 3 1 0 0 0.32 0 1 0Special K Blueberry $0.28 2 7 0 1 0 0.17 0 0 0Special K Fruit & Yogurt $0.22 1 11 0 1 0 0.14 0 0 0Special K Low Fat Touch Of Honey $0.45 2 10 0 5 1 0.11 1 2 1Special K Red Berries $0.28 2 10 0 1 0 0.22 0 0 0Special K Vanilla Almond $0.24 1 9 0 1 0 0.16 0 0 0Kix Crispy Corn Puffs $0.26 2 3 1 3 0 0.21 0 1 0Lucky Charms $0.21 1 11 0 1 0 0.19 0 0 0Malt-O-Meal Blueberry Mini Spooners $0.36 2 11 0 6 1 0.10 1 2 1Multigrain Cheerios $0.37 2 6 0 3 0 0.20 0 0 0Honey Graham $0.18 1 12 0 1 0 0.17 0 0 0Grape-Nuts Flakes $0.17 1 4 1 3 0 0.13 1 2 1Raisin Nut Bran Almond Raisin $0.36 2 14 0 5 1 0.23 0 1 0Reese's Puffs $0.24 1 12 0 1 0 0.18 0 0 0Total Raisin Bran $0.40 2 17 0 5 1 0.23 0 1 0Total Whole Grain $0.24 1 5 0 3 0 0.19 0 0 0Trix Cereal $0.25 1 13 0 0 0 0.18 0 0 0Wheaties Cereal $0.24 1 4 1 0 0 0.19 0 1 0Wheaties Fuel Cereal $0.44 2 14 0 5 1 0.15 0 1 0Cinnamon Burst Cheerios $0.33 2 9 0 5 1 0.13 1 2 1Life Original Cereal $0.19 1 6 0 2 0 0.16 0 0 1
Appendix: Master Data Sheet 3Table A3: Master Data Sheet- Ratio of Serving
Cereal Serving,
gSugar,g Sugar, g
Sugar rat
Fiber, g
Fiber,rat. NaCl,g NaCl, rat Cal,g Cal. Rat.Alf's Puffed Red Wheat 14 0 0 2 0.14 0.00 0.000 60 4.29Banana Nut Cheerios 28 9 0.32 1 0.04 0.16 0.006 100 3.57Bear Naked Fit Vanilla Almond 30 4 0.13 2 0.07 0.01 0.000 120 4.00Bear Naked Fruit And Nut 30 6 0.20 2 0.07 0.00 0.000 140 4.67Cascadian Farm Cinnamon Raisin
55 16 0.29 2 0.04 0.20 0.004 210 3.82Cascadian Farm Oats & Honey 55 14 0.25 2 0.04 0.11 0.002 230 4.18Cascadian Farm Fruit And Nut 52 14 0.27 3 0.06 0.10 0.002 210 4.04Cheerios Apple Cinnamon Cereal
30 12 0.40 1 0.03 0.12 0.004 120 4.00Cheerios Cereal 28 1 0.04 1 0.04 0.19 0.007 100 3.57Cheerios Chocolate 27 9 0.33 1 0.04 0.17 0.006 100 3.70Cheerios Fruity Cereal 27 9 0.33 2 0.07 0.14 0.005 100 3.70Cheerios Honey Nut 28 9 0.32 2 0.07 0.19 0.007 110 3.93Cheerios Yogurt Burst 30 9 0.30 2 0.07 0.18 0.006 120 4.00Chex Cinnamon 30 8 0.27 0 0.00 0.19 0.006 120 4.00Chex Corn Cereal 31 3 0.10 1 0.03 0.29 0.009 120 3.87Chex Honey Nut 32 9 0.28 1 0.03 0.23 0.007 120 3.75Chex Rice 27 2 0.07 0 0.00 0.24 0.009 100 3.70Chex Wheat 47 5 0.11 1 0.02 0.34 0.007 160 3.40Cinnamon Toast Crunch 31 10 0.32 1 0.03 0.22 0.007 130 4.19
37
COLD CEREAL PRICES AND INGREDIENT CONTENTCocoa Puffs 27 12 0.44 1 0.04 0.15 0.006 110 4.07Cookie Crisp 26 11 0.42 1 0.04 0.15 0.006 100 3.85Crunchy Almond Oatmeal Crisp 60 16 0.27 4 0.07 0.13 0.002 240 4.00Fiber One Caramel Delight 50 10 0.20 9 0.18 0.26 0.005 180 3.60Fiber One Honey Clusters 52 6 0.12 13 0.25 0.28 0.005 160 3.08Fiber One Sweetened Wheat & Bran
55 13 0.24 11 0.20 0.26 0.005 170 3.09Fiber One Original 30 0 0.00 14 0.47 0.11 0.004 60 2.00Honey Kix 33 6 0.18 3 0.09 0.23 0.007 120 3.64Golden Grahams 31 11 0.35 1 0.03 0.27 0.009 120 3.87Great Value Crunchy Raisin Bran
53 20 0.38 4 0.08 0.20 0.004 190 3.58Great Value Strawberry Awake 31 10 0.32 1 0.03 0.22 0.007 110 3.55Great Value Berry Crunch 26 12 0.46 0 0.00 0.17 0.007 100 3.85Great Value Bran Flakes 29 5 0.17 5 0.17 0.21 0.007 90 3.10Great Value Cinnamon Crunch 30 10 0.33 1 0.03 0.21 0.007 130 4.33Great Value Frosted Shredded Wheat
52 11 0.21 5 0.10 0.00 0.000 180 3.46Great Value Fruity Puffs 30 13 0.43 1 0.03 0.16 0.005 120 4.00Great Value Fruity Sparkles 28 12 0.43 0 0.00 0.15 0.005 110 3.93Great Value Honey Crunch 27 15 0.56 0 0.00 0.05 0.002 100 3.70Great Value Honey Nut Spins 30 11 0.37 1 0.03 0.16 0.005 120 4.00Great Value Raisin Bran 56 18 0.32 7 0.13 0.35 0.006 210 3.75Great Value Sugar Frosted Flakes
31 13 0.42 1 0.03 0.20 0.006 120 3.87Great Value Toasted Whole Grain
28 1 0.04 3 0.11 0.19 0.007 100 3.57Kashi Autumn Wheat 54 7 0.13 6 0.11 0.00 0.000 190 3.52Kashi Cinnamon Harvest 54 9 0.17 5 0.09 0.00 0.000 190 3.52Kashi Golean Crisp! 51 12 0.24 8 0.16 0.13 0.003 190 3.73Kashi Golean Crunch Honey Almond
53 12 0.23 8 0.15 0.14 0.003 200 3.77Kashi Golean Crunch! Protein 53 13 0.25 8 0.15 0.10 0.002 190 3.58Kashi Heart To Heart Honey Oat
33 5 0.15 5 0.15 0.09 0.003 110 3.33Kashi Heart To Heart Blueberry 55 13 0.24 4 0.07 0.13 0.002 200 3.64Kashi Organic Promise 55 9 0.16 6 0.11 0.01 0.000 160 2.91Kashi Strawberry Fields 32 9 0.28 1 0.03 0.20 0.006 120 3.75Kashi U Black Currants 55 10 0.18 7 0.13 0.13 0.002 200 3.64Kellogg's Cinnabon Crunchy 30 12 0.40 1 0.03 0.12 0.004 120 4.00All-Bran Branbuds 30 8 0.27 13 0.43 0.20 0.007 70 2.33Cracklin' Oat Bran 49 15 0.31 6 0.12 0.15 0.003 200 4.08Froot Loops Marshmallow 30 16 0.53 0 0.00 0.11 0.004 120 4.00Frosted Krispies 30 12 0.40 0 0.00 0.13 0.004 110 3.67Frosted Mini-Wheats 59 12 0.20 6 0.10 0.01 0.000 200 3.39Frosted Mini-Wheats Blueberry 52 12 0.23 5 0.10 0.00 0.000 180 3.46Raisin Bran Sweet Raisins 59 19 0.32 7 0.12 0.35 0.006 190 3.22Smart Start 50 14 0.28 3 0.06 0.26 0.005 190 3.80Apple Jacks 28 12 0.43 1 0.04 0.14 0.005 110 3.93Cinnamon Pecan 30 7 0.23 1 0.03 0.18 0.006 120 4.00Kellogg's Corn Flakes 28 2 0.07 1 0.04 0.20 0.007 100 3.57
38
COLD CEREAL PRICES AND INGREDIENT CONTENTCorn Pops 29 12 0.41 0 0.00 0.11 0.004 110 3.79Crispix 29 3 0.10 1 0.03 0.21 0.007 110 3.79Crunchy Nut Golden Honey 31 10 0.32 0 0.00 0.13 0.004 120 3.87Kellogg's Frosted Flakes 30 11 0.37 1 0.03 0.14 0.005 110 3.67Frosted Mini-Wheats Strawberry
52 12 0.23 5 0.10 0.00 0.000 180 3.46Frosted Mini-Wheats Chocolate 55 12 0.22 6 0.11 0.20 0.004 200 3.64Special K 31 4 0.13 1 0.03 0.22 0.007 120 3.87Kellogg's Raisin Bran 59 19 0.32 7 0.12 0.35 0.006 190 3.22Kellogg's Raisin Bran Crunch 53 20 0.38 4 0.08 0.21 0.004 190 3.58Kellogg's Rice Krispies 33 3 0.09 0 0.00 0.32 0.010 120 3.64Special K Blueberry 27 7 0.26 1 0.04 0.17 0.006 100 3.70Special K Fruit & Yogurt 32 11 0.34 1 0.03 0.14 0.004 120 3.75Special K Low Fat Touch Of Honey
52 10 0.19 5 0.10 0.11 0.002 190 3.65Special K Red Berries 31 10 0.32 1 0.03 0.22 0.007 110 3.55Special K Vanilla Almond 30 9 0.30 1 0.03 0.16 0.005 110 3.67Kix Crispy Corn Puffs 30 3 0.10 3 0.10 0.21 0.007 110 3.67Lucky Charms 27 11 0.41 1 0.04 0.19 0.007 110 4.07Malt-O-Meal Blueberry Mini Spooners
55 11 0.20 6 0.11 0.10 0.002 190 3.45Multigrain Cheerios 29 6 0.21 3 0.10 0.20 0.007 110 3.79Honey Graham 27 12 0.44 1 0.04 0.17 0.006 110 4.07Grape-Nuts Flakes 29 4 0.14 3 0.10 0.13 0.004 110 3.79Raisin Nut Bran Almond Raisin 49 14 0.29 5 0.10 0.23 0.005 180 3.67Reese's Puffs 29 12 0.41 1 0.03 0.18 0.006 120 4.14Total Raisin Bran 53 17 0.32 5 0.09 0.23 0.004 160 3.02Total Whole Grain 30 5 0.17 3 0.10 0.19 0.006 100 3.33Trix Cereal 32 13 0.41 0 0.00 0.18 0.006 120 3.75Wheaties Cereal 27 4 0.15 0 0.00 0.19 0.007 100 3.70Wheaties Fuel Cereal 55 14 0.25 5 0.09 0.15 0.003 210 3.82Cinnamon Burst Cheerios 33 9 0.27 5 0.15 0.13 0.004 120 3.64Life Original Cereal 32 6 0.19 2 0.06 0.16 0.005 120 3.75
Table A-4: Linear Regression: Y1- NutritionIndex
(X -X bar) *
Cereal X X bar X - X bar Y1 Y1 bar Y1 - Y1 bar (Y1 - Y1 bar) (X - X bar)^2
1 0.0909 0.2803 -0.1894 1 0.2043 0.7957 -0.1507 0.0359
2 0.2709 0.2803 -0.0094 0 0.2043 -0.2043 0.0019 0.0001
3 0.3255 0.2803 0.0452 1 0.2043 0.7957 0.0359 0.0020
4 0.3255 0.2803 0.0452 0 0.2043 -0.2043 -0.0092 0.0020
39
COLD CEREAL PRICES AND INGREDIENT CONTENT5 0.4100 0.2803 0.1297 0 0.2043 -0.2043 -0.0265 0.0168
6 0.4100 0.2803 0.1297 0 0.2043 -0.2043 -0.0265 0.0168
7 0.4100 0.2803 0.1297 0 0.2043 -0.2043 -0.0265 0.0168
8 0.2483 0.2803 -0.0320 0 0.2043 -0.2043 0.0065 0.0010
9 0.2867 0.2803 0.0064 0 0.2043 -0.2043 -0.0013 0.0000
10 0.2483 0.2803 -0.0320 0 0.2043 -0.2043 0.0065 0.0010
11 0.2483 0.2803 -0.0320 0 0.2043 -0.2043 0.0065 0.0010
12 0.2483 0.2803 -0.0320 0 0.2043 -0.2043 0.0065 0.0010
13 0.2129 0.2803 -0.0674 0 0.2043 -0.2043 0.0138 0.0045
14 0.2982 0.2803 0.0179 0 0.2043 -0.2043 -0.0037 0.0003
15 0.2308 0.2803 -0.0495 0 0.2043 -0.2043 0.0101 0.0025
16 0.2733 0.2803 -0.0070 0 0.2043 -0.2043 0.0014 0.0000
17 0.2523 0.2803 -0.0280 0 0.2043 -0.2043 0.0057 0.0008
18 0.4100 0.2803 0.1297 0 0.2043 -0.2043 -0.0265 0.0168
19 0.2187 0.2803 -0.0616 0 0.2043 -0.2043 0.0126 0.0038
20 0.1929 0.2803 -0.0874 0 0.2043 -0.2043 0.0178 0.0076
21 0.2400 0.2803 -0.0403 0 0.2043 -0.2043 0.0082 0.0016
22 0.4550 0.2803 0.1747 0 0.2043 -0.2043 -0.0357 0.0305
23 0.4044 0.2803 0.1241 0 0.2043 -0.2043 -0.0254 0.0154
24 0.4550 0.2803 0.1747 0 0.2043 -0.2043 -0.0357 0.0305
25 0.4044 0.2803 0.1241 0 0.2043 -0.2043 -0.0254 0.0154
26 0.2427 0.2803 -0.0376 1 0.2043 0.7957 -0.0299 0.0014
27 0.2880 0.2803 0.0077 0 0.2043 -0.2043 -0.0016 0.0001
28 0.2618 0.2803 -0.0185 0 0.2043 -0.2043 0.0038 0.0003
29 0.2114 0.2803 -0.0689 0 0.2043 -0.2043 0.0141 0.0047
30 0.3255 0.2803 0.0452 0 0.2043 -0.2043 -0.0092 0.0020
31 0.1165 0.2803 -0.1638 0 0.2043 -0.2043 0.0335 0.0268
40
COLD CEREAL PRICES AND INGREDIENT CONTENT
32 0.1576 0.2803 -0.1227 0 0.2043 -0.2043 0.0251 0.0150
33 0.1338 0.2803 -0.1466 0 0.2043 -0.2043 0.0299 0.0215
34 0.2062 0.2803 -0.0741 1 0.2043 0.7957 -0.0590 0.0055
35 0.1657 0.2803 -0.1146 0 0.2043 -0.2043 0.0234 0.0131
36 0.1538 0.2803 -0.1265 0 0.2043 -0.2043 0.0258 0.0160
37 0.1675 0.2803 -0.1128 0 0.2043 -0.2043 0.0230 0.0127
38 0.1450 0.2803 -0.1353 0 0.2043 -0.2043 0.0276 0.0183
39 0.2000 0.2803 -0.0803 0 0.2043 -0.2043 0.0164 0.0064
40 0.1276 0.2803 -0.1527 0 0.2043 -0.2043 0.0312 0.0233
41 0.1489 0.2803 -0.1314 0 0.2043 -0.2043 0.0268 0.0173
42 0.4422 0.2803 0.1619 1 0.2043 0.7957 0.1288 0.0262
43 0.4422 0.2803 0.1619 1 0.2043 0.7957 0.1288 0.0262
44 0.3900 0.2803 0.1097 1 0.2043 0.7957 0.0873 0.0120
45 0.3900 0.2803 0.1097 0 0.2043 -0.2043 -0.0224 0.0120
46 0.3900 0.2803 0.1097 1 0.2043 0.7957 0.0873 0.0120
47 0.2836 0.2803 0.0033 1 0.2043 0.7957 0.0027 0.0000
48 0.4457 0.2803 0.1654 0 0.2043 -0.2043 -0.0338 0.0274
49 0.4422 0.2803 0.1619 1 0.2043 0.7957 0.1288 0.0262
50 0.4422 0.2803 0.1619 0 0.2043 -0.2043 -0.0331 0.0262
51 0.6633 0.2803 0.3830 1 0.2043 0.7957 0.3048 0.1467
52 0.2778 0.2803 -0.0025 0 0.2043 -0.2043 0.0005 0.0000
53 0.1835 0.2803 -0.0968 0 0.2043 -0.2043 0.0198 0.0094
54 0.3120 0.2803 0.0317 0 0.2043 -0.2043 -0.0065 0.0010
55 0.2483 0.2803 -0.0320 0 0.2043 -0.2043 0.0065 0.0010
56 0.2709 0.2803 -0.0094 0 0.2043 -0.2043 0.0019 0.0001
57 0.2836 0.2803 0.0033 1 0.2043 0.7957 0.0027 0.0000
41
COLD CEREAL PRICES AND INGREDIENT CONTENT
58 0.3900 0.2803 0.1097 1 0.2043 0.7957 0.0873 0.0120
59 0.2680 0.2803 -0.0123 0 0.2043 -0.2043 0.0025 0.0002
60 0.3500 0.2803 0.0697 0 0.2043 -0.2043 -0.0142 0.0049
61 0.1576 0.2803 -0.1227 0 0.2043 -0.2043 0.0251 0.0150
62 0.2600 0.2803 -0.0203 0 0.2043 -0.2043 0.0041 0.0004
63 0.1489 0.2803 -0.1314 0 0.2043 -0.2043 0.0268 0.0173
64 0.1488 0.2803 -0.1316 0 0.2043 -0.2043 0.0269 0.0173
65 0.2483 0.2803 -0.0320 0 0.2043 -0.2043 0.0065 0.0010
67 0.2292 0.2803 -0.0511 0 0.2043 -0.2043 0.0104 0.0026
68 0.1355 0.2803 -0.1448 0 0.2043 -0.2043 0.0296 0.0210
69 0.2867 0.2803 0.0064 1 0.2043 0.7957 0.0051 0.0000
70 0.3225 0.2803 0.0422 0 0.2043 -0.2043 -0.0086 0.0018
71 0.2836 0.2803 0.0033 0 0.2043 -0.2043 -0.0007 0.0000
72 0.2483 0.2803 -0.0320 0 0.2043 -0.2043 0.0065 0.0010
73 0.2229 0.2803 -0.0574 0 0.2043 -0.2043 0.0117 0.0033
74 0.1987 0.2803 -0.0816 0 0.2043 -0.2043 0.0167 0.0067
75 0.2836 0.2803 0.0033 0 0.2043 -0.2043 -0.0007 0.0000
76 0.2150 0.2803 -0.0653 0 0.2043 -0.2043 0.0133 0.0043
77 0.4457 0.2803 0.1654 1 0.2043 0.7957 0.1316 0.0274
78 0.2836 0.2803 0.0033 0 0.2043 -0.2043 -0.0007 0.0000
79 0.2400 0.2803 -0.0403 0 0.2043 -0.2043 0.0082 0.0016
80 0.2618 0.2803 -0.0185 0 0.2043 -0.2043 0.0038 0.0003
81 0.2050 0.2803 -0.0753 0 0.2043 -0.2043 0.0154 0.0057
82 0.3644 0.2803 0.0841 1 0.2043 0.7957 0.0670 0.0071
83 0.3725 0.2803 0.0922 0 0.2043 -0.2043 -0.0188 0.0085
84 0.1800 0.2803 -0.1003 0 0.2043 -0.2043 0.0205 0.0101
42
COLD CEREAL PRICES AND INGREDIENT CONTENT
85 0.1733 0.2803 -0.1070 1 0.2043 0.7957 -0.0851 0.0114
86 0.3640 0.2803 0.0837 0 0.2043 -0.2043 -0.0171 0.0070
87 0.2400 0.2803 -0.0403 0 0.2043 -0.2043 0.0082 0.0016
88 0.4044 0.2803 0.1241 0 0.2043 -0.2043 -0.0254 0.0154
89 0.2427 0.2803 -0.0376 0 0.2043 -0.2043 0.0077 0.0014
90 0.2523 0.2803 -0.0280 0 0.2043 -0.2043 0.0057 0.0008
91 0.2363 0.2803 -0.0441 0 0.2043 -0.2043 0.0090 0.0019
92 0.4422 0.2803 0.1619 0 0.2043 -0.2043 -0.0331 0.0262
93 0.3311 0.2803 0.0508 1 0.2043 0.7957 0.0404 0.0026
94 0.1875 0.2803 -0.0928 1 0.2043 0.7957 -0.0738 0.0086
Intercept, a1= -0.0919 =Y1 bar - b1*X bar 1.0377 0.9822
Slope, b1= 1.0566 =1.0377/0.9822 numerator, b denominator, b
Table A-5: Linear Regression: Y2- Sugar
(X -X bar) *
Cereal X X bar X - X bar Y2 Y2 bar Y2 - Y2 bar (Y2 - Y2 bar) (X - X bar)^2
1 0.3255 0.2803 0.0452 0.000 0.2648 -0.2648 -0.0120 0.0020
2 0.4100 0.2803 0.1297 0.321 0.2648 0.0566 0.0073 0.0168
3 0.4100 0.2803 0.1297 0.133 0.2648 -0.1315 -0.0171 0.0168
4 0.4100 0.2803 0.1297 0.200 0.2648 -0.0648 -0.0084 0.0168
5 0.2483 0.2803 -0.0320 0.291 0.2648 0.0261 -0.0008 0.0010
6 0.2867 0.2803 0.0064 0.255 0.2648 -0.0103 -0.0001 0.0000
7 0.2483 0.2803 -0.0320 0.269 0.2648 0.0044 -0.0001 0.0010
8 0.2483 0.2803 -0.0320 0.400 0.2648 0.1352 -0.0043 0.0010
9 0.2483 0.2803 -0.0320 0.036 0.2648 -0.2291 0.0073 0.0010
43
COLD CEREAL PRICES AND INGREDIENT CONTENT
10 0.2129 0.2803 -0.0674 0.333 0.2648 0.0685 -0.0046 0.0045
11 0.2982 0.2803 0.0179 0.333 0.2648 0.0685 0.0012 0.0003
12 0.2308 0.2803 -0.0495 0.321 0.2648 0.0566 -0.0028 0.0025
13 0.2733 0.2803 -0.0070 0.300 0.2648 0.0352 -0.0002 0.0000
14 0.2523 0.2803 -0.0280 0.267 0.2648 0.0019 -0.0001 0.0008
15 0.4100 0.2803 0.1297 0.097 0.2648 -0.1680 -0.0218 0.0168
16 0.2187 0.2803 -0.0616 0.281 0.2648 0.0165 -0.0010 0.0038
17 0.1929 0.2803 -0.0874 0.074 0.2648 -0.1907 0.0167 0.0076
18 0.2400 0.2803 -0.0403 0.106 0.2648 -0.1584 0.0064 0.0016
19 0.4550 0.2803 0.1747 0.323 0.2648 0.0578 0.0101 0.0305
20 0.4044 0.2803 0.1241 0.444 0.2648 0.1796 0.0223 0.0154
21 0.4550 0.2803 0.1747 0.423 0.2648 0.1583 0.0277 0.0305
22 0.4044 0.2803 0.1241 0.267 0.2648 0.0019 0.0002 0.0154
23 0.2427 0.2803 -0.0376 0.200 0.2648 -0.0648 0.0024 0.0014
24 0.2880 0.2803 0.0077 0.115 0.2648 -0.1494 -0.0012 0.0001
25 0.2618 0.2803 -0.0185 0.236 0.2648 -0.0284 0.0005 0.0003
26 0.2114 0.2803 -0.0689 0.000 0.2648 -0.2648 0.0182 0.0047
27 0.3255 0.2803 0.0452 0.182 0.2648 -0.0830 -0.0037 0.0020
28 0.1165 0.2803 -0.1638 0.355 0.2648 0.0900 -0.0147 0.0268
29 0.1576 0.2803 -0.1227 0.377 0.2648 0.1126 -0.0138 0.0150
30 0.1338 0.2803 -0.1466 0.323 0.2648 0.0578 -0.0085 0.0215
31 0.2062 0.2803 -0.0741 0.462 0.2648 0.1967 -0.0146 0.0055
32 0.1657 0.2803 -0.1146 0.172 0.2648 -0.0924 0.0106 0.0131
33 0.1538 0.2803 -0.1265 0.333 0.2648 0.0685 -0.0087 0.0160
34 0.1675 0.2803 -0.1128 0.212 0.2648 -0.0533 0.0060 0.0127
35 0.1450 0.2803 -0.1353 0.433 0.2648 0.1685 -0.0228 0.0183
44
COLD CEREAL PRICES AND INGREDIENT CONTENT
36 0.2000 0.2803 -0.0803 0.429 0.2648 0.1638 -0.0132 0.0064
37 0.1276 0.2803 -0.1527 0.556 0.2648 0.2908 -0.0444 0.0233
38 0.1489 0.2803 -0.1314 0.367 0.2648 0.1019 -0.0134 0.0173
39 0.4422 0.2803 0.1619 0.321 0.2648 0.0566 0.0092 0.0262
40 0.4422 0.2803 0.1619 0.419 0.2648 0.1546 0.0250 0.0262
41 0.3900 0.2803 0.1097 0.036 0.2648 -0.2291 -0.0251 0.0120
42 0.3900 0.2803 0.1097 0.130 0.2648 -0.1352 -0.0148 0.0120
43 0.3900 0.2803 0.1097 0.167 0.2648 -0.0981 -0.0108 0.0120
44 0.2836 0.2803 0.0033 0.235 0.2648 -0.0295 -0.0001 0.0000
45 0.4457 0.2803 0.1654 0.226 0.2648 -0.0384 -0.0063 0.0274
46 0.4422 0.2803 0.1619 0.245 0.2648 -0.0195 -0.0032 0.0262
47 0.4422 0.2803 0.1619 0.152 0.2648 -0.1133 -0.0183 0.0262
48 0.6633 0.2803 0.3830 0.236 0.2648 -0.0284 -0.0109 0.1467
49 0.2778 0.2803 -0.0025 0.164 0.2648 -0.1012 0.0003 0.0000
50 0.1835 0.2803 -0.0968 0.281 0.2648 0.0165 -0.0016 0.0094
51 0.3120 0.2803 0.0317 0.182 0.2648 -0.0830 -0.0026 0.0010
52 0.2483 0.2803 -0.0320 0.400 0.2648 0.1352 -0.0043 0.0010
53 0.2709 0.2803 -0.0094 0.267 0.2648 0.0019 0.0000 0.0001
54 0.2836 0.2803 0.0033 0.306 0.2648 0.0413 0.0001 0.0000
55 0.3900 0.2803 0.1097 0.533 0.2648 0.2685 0.0295 0.0120
56 0.2680 0.2803 -0.0123 0.400 0.2648 0.1352 -0.0017 0.0002
57 0.3500 0.2803 0.0697 0.203 0.2648 -0.0614 -0.0043 0.0049
58 0.1576 0.2803 -0.1227 0.231 0.2648 -0.0340 0.0042 0.0150
59 0.2600 0.2803 -0.0203 0.322 0.2648 0.0572 -0.0012 0.0004
60 0.1489 0.2803 -0.1314 0.280 0.2648 0.0152 -0.0020 0.0173
61 0.1488 0.2803 -0.1316 0.429 0.2648 0.1638 -0.0215 0.0173
45
COLD CEREAL PRICES AND INGREDIENT CONTENT
62 0.2483 0.2803 -0.0320 0.233 0.2648 -0.0315 0.0010 0.0010
63 0.2292 0.2803 -0.0511 0.071 0.2648 -0.1934 0.0099 0.0026
64 0.1355 0.2803 -0.1448 0.414 0.2648 0.1490 -0.0216 0.0210
65 0.2867 0.2803 0.0064 0.103 0.2648 -0.1614 -0.0010 0.0000
67 0.3225 0.2803 0.0422 0.323 0.2648 0.0578 0.0024 0.0018
68 0.2836 0.2803 0.0033 0.367 0.2648 0.1019 0.0003 0.0000
69 0.2483 0.2803 -0.0320 0.231 0.2648 -0.0340 0.0011 0.0010
70 0.2229 0.2803 -0.0574 0.218 0.2648 -0.0466 0.0027 0.0033
71 0.1987 0.2803 -0.0816 0.129 0.2648 -0.1358 0.0111 0.0067
72 0.2836 0.2803 0.0033 0.322 0.2648 0.0572 0.0002 0.0000
73 0.2150 0.2803 -0.0653 0.377 0.2648 0.1126 -0.0074 0.0043
74 0.4457 0.2803 0.1654 0.091 0.2648 -0.1739 -0.0288 0.0274
75 0.2836 0.2803 0.0033 0.259 0.2648 -0.0055 0.0000 0.0000
76 0.2400 0.2803 -0.0403 0.344 0.2648 0.0790 -0.0032 0.0016
77 0.2618 0.2803 -0.0185 0.192 0.2648 -0.0725 0.0013 0.0003
78 0.2050 0.2803 -0.0753 0.323 0.2648 0.0578 -0.0044 0.0057
79 0.3644 0.2803 0.0841 0.300 0.2648 0.0352 0.0030 0.0071
80 0.3725 0.2803 0.0922 0.100 0.2648 -0.1648 -0.0152 0.0085
81 0.1800 0.2803 -0.1003 0.407 0.2648 0.1426 -0.0143 0.0101
82 0.1733 0.2803 -0.1070 0.200 0.2648 -0.0648 0.0069 0.0114
83 0.3640 0.2803 0.0837 0.207 0.2648 -0.0579 -0.0048 0.0070
84 0.2400 0.2803 -0.0403 0.444 0.2648 0.1796 -0.0072 0.0016
85 0.4044 0.2803 0.1241 0.138 0.2648 -0.1269 -0.0158 0.0154
86 0.2427 0.2803 -0.0376 0.286 0.2648 0.0209 -0.0008 0.0014
87 0.2523 0.2803 -0.0280 0.414 0.2648 0.1490 -0.0042 0.0008
88 0.2363 0.2803 -0.0441 0.321 0.2648 0.0560 -0.0025 0.0019
46
COLD CEREAL PRICES AND INGREDIENT CONTENT
89 0.4422 0.2803 0.1619 0.167 0.2648 -0.0981 -0.0159 0.0262
90 0.3311 0.2803 0.0508 0.406 0.2648 0.1415 0.0072 0.0026
91 0.1875 0.2803 -0.0928 0.148 0.2648 -0.1167 0.0108 0.0086
92 -0.0919 0.2803 -0.3722 0.255 0.2648 -0.0103 0.0038 0.1385
93 1.0566 0.2803 0.7763 0.273 0.2648 0.0079 0.0062 0.6026
94 0.0000 0.2803 -0.2803 0.188 0.2648 -0.0773 0.0217 0.0786
Intercept, a2= 0.3000057 =Y2 bar - b2* X bar -0.2131 1.7638
Slope, b2= -0.1208104 =-0.2140/1.7039 numerator, b denominator, b
Table A-6: Linear Regression: Y3- Fiber
(X -X bar) *
Cereal X X bar X - X bar Y3 Y3 bar Y3 - Y3 bar (Y3 - Y3 bar) (X - X bar)^2
1 0.2483 0.2803 -0.0320 0.143 0.0759 0.0670 -0.0021 0.0010
2 0.2867 0.2803 0.0064 0.036 0.0759 -0.0402 -0.0003 0.0000
3 0.2483 0.2803 -0.0320 0.067 0.0759 -0.0092 0.0003 0.0010
4 0.2483 0.2803 -0.0320 0.067 0.0759 -0.0092 0.0003 0.0010
5 0.2483 0.2803 -0.0320 0.036 0.0759 -0.0395 0.0013 0.0010
6 0.2129 0.2803 -0.0674 0.036 0.0759 -0.0395 0.0027 0.0045
7 0.2982 0.2803 0.0179 0.058 0.0759 -0.0182 -0.0003 0.0003
8 0.2308 0.2803 -0.0495 0.033 0.0759 -0.0426 0.0021 0.0025
9 0.2733 0.2803 -0.0070 0.036 0.0759 -0.0402 0.0003 0.0000
10 0.2523 0.2803 -0.0280 0.037 0.0759 -0.0389 0.0011 0.0008
11 0.4100 0.2803 0.1297 0.074 0.0759 -0.0018 -0.0002 0.0168
12 0.2187 0.2803 -0.0616 0.071 0.0759 -0.0045 0.0003 0.0038
47
COLD CEREAL PRICES AND INGREDIENT CONTENT
13 0.1929 0.2803 -0.0874 0.067 0.0759 -0.0092 0.0008 0.0076
14 0.2400 0.2803 -0.0403 0.000 0.0759 -0.0759 0.0031 0.0016
15 0.4550 0.2803 0.1747 0.032 0.0759 -0.0436 -0.0076 0.0305
16 0.4044 0.2803 0.1241 0.031 0.0759 -0.0447 -0.0055 0.0154
17 0.4550 0.2803 0.1747 0.000 0.0759 -0.0759 -0.0133 0.0305
18 0.4044 0.2803 0.1241 0.021 0.0759 -0.0546 -0.0068 0.0154
19 0.2427 0.2803 -0.0376 0.032 0.0759 -0.0436 0.0016 0.0014
20 0.2880 0.2803 0.0077 0.037 0.0759 -0.0389 -0.0003 0.0001
21 0.2618 0.2803 -0.0185 0.038 0.0759 -0.0374 0.0007 0.0003
22 0.2114 0.2803 -0.0689 0.067 0.0759 -0.0092 0.0006 0.0047
23 0.3255 0.2803 0.0452 0.180 0.0759 0.1041 0.0047 0.0020
24 0.1165 0.2803 -0.1638 0.250 0.0759 0.1741 -0.0285 0.0268
25 0.1576 0.2803 -0.1227 0.200 0.0759 0.1241 -0.0152 0.0150
26 0.1338 0.2803 -0.1466 0.467 0.0759 0.3908 -0.0573 0.0215
27 0.2062 0.2803 -0.0741 0.091 0.0759 0.0150 -0.0011 0.0055
28 0.1657 0.2803 -0.1146 0.032 0.0759 -0.0436 0.0050 0.0131
29 0.1538 0.2803 -0.1265 0.075 0.0759 -0.0004 0.0001 0.0160
30 0.1675 0.2803 -0.1128 0.032 0.0759 -0.0436 0.0049 0.0127
31 0.1450 0.2803 -0.1353 0.000 0.0759 -0.0759 0.0103 0.0183
32 0.2000 0.2803 -0.0803 0.172 0.0759 0.0965 -0.0078 0.0064
33 0.1276 0.2803 -0.1527 0.033 0.0759 -0.0426 0.0065 0.0233
34 0.1489 0.2803 -0.1314 0.096 0.0759 0.0203 -0.0027 0.0173
35 0.4422 0.2803 0.1619 0.033 0.0759 -0.0426 -0.0069 0.0262
36 0.4422 0.2803 0.1619 0.000 0.0759 -0.0759 -0.0123 0.0262
37 0.3900 0.2803 0.1097 0.000 0.0759 -0.0759 -0.0083 0.0120
38 0.3900 0.2803 0.1097 0.033 0.0759 -0.0426 -0.0047 0.0120
48
COLD CEREAL PRICES AND INGREDIENT CONTENT
39 0.3900 0.2803 0.1097 0.125 0.0759 0.0491 0.0054 0.0120
40 0.2836 0.2803 0.0033 0.032 0.0759 -0.0436 -0.0001 0.0000
41 0.4457 0.2803 0.1654 0.107 0.0759 0.0312 0.0052 0.0274
42 0.4422 0.2803 0.1619 0.111 0.0759 0.0352 0.0057 0.0262
43 0.4422 0.2803 0.1619 0.093 0.0759 0.0167 0.0027 0.0262
44 0.6633 0.2803 0.3830 0.157 0.0759 0.0810 0.0310 0.1467
45 0.2778 0.2803 -0.0025 0.151 0.0759 0.0750 -0.0002 0.0000
46 0.1835 0.2803 -0.0968 0.151 0.0759 0.0750 -0.0073 0.0094
47 0.3120 0.2803 0.0317 0.152 0.0759 0.0756 0.0024 0.0010
48 0.2483 0.2803 -0.0320 0.073 0.0759 -0.0032 0.0001 0.0010
49 0.2709 0.2803 -0.0094 0.109 0.0759 0.0332 -0.0003 0.0001
50 0.2836 0.2803 0.0033 0.031 0.0759 -0.0447 -0.0001 0.0000
51 0.3900 0.2803 0.1097 0.127 0.0759 0.0514 0.0056 0.0120
52 0.2680 0.2803 -0.0123 0.033 0.0759 -0.0426 0.0005 0.0002
53 0.3500 0.2803 0.0697 0.433 0.0759 0.3574 0.0249 0.0049
54 0.1576 0.2803 -0.1227 0.122 0.0759 0.0465 -0.0057 0.0150
55 0.2600 0.2803 -0.0203 0.000 0.0759 -0.0759 0.0015 0.0004
56 0.1489 0.2803 -0.1314 0.000 0.0759 -0.0759 0.0100 0.0173
57 0.1488 0.2803 -0.1316 0.102 0.0759 0.0258 -0.0034 0.0173
58 0.2483 0.2803 -0.0320 0.096 0.0759 0.0203 -0.0006 0.0010
59 0.2292 0.2803 -0.0511 0.119 0.0759 0.0427 -0.0022 0.0026
60 0.1355 0.2803 -0.1448 0.060 0.0759 -0.0159 0.0023 0.0210
61 0.2867 0.2803 0.0064 0.036 0.0759 -0.0402 -0.0003 0.0000
62 0.3225 0.2803 0.0422 0.033 0.0759 -0.0426 -0.0018 0.0018
63 0.2836 0.2803 0.0033 0.036 0.0759 -0.0402 -0.0001 0.0000
64 0.2483 0.2803 -0.0320 0.000 0.0759 -0.0759 0.0024 0.0010
49
COLD CEREAL PRICES AND INGREDIENT CONTENT
65 0.2229 0.2803 -0.0574 0.034 0.0759 -0.0414 0.0024 0.0033
67 0.1987 0.2803 -0.0816 0.000 0.0759 -0.0759 0.0062 0.0067
68 0.2836 0.2803 0.0033 0.033 0.0759 -0.0426 -0.0001 0.0000
69 0.2150 0.2803 -0.0653 0.096 0.0759 0.0203 -0.0013 0.0043
70 0.4457 0.2803 0.1654 0.109 0.0759 0.0332 0.0055 0.0274
71 0.2836 0.2803 0.0033 0.032 0.0759 -0.0436 -0.0001 0.0000
72 0.2400 0.2803 -0.0403 0.119 0.0759 0.0427 -0.0017 0.0016
73 0.2618 0.2803 -0.0185 0.075 0.0759 -0.0004 0.0000 0.0003
74 0.2050 0.2803 -0.0753 0.000 0.0759 -0.0759 0.0057 0.0057
75 0.3644 0.2803 0.0841 0.037 0.0759 -0.0389 -0.0033 0.0071
76 0.3725 0.2803 0.0922 0.031 0.0759 -0.0447 -0.0041 0.0085
77 0.1800 0.2803 -0.1003 0.096 0.0759 0.0203 -0.0020 0.0101
78 0.1733 0.2803 -0.1070 0.032 0.0759 -0.0436 0.0047 0.0114
79 0.3640 0.2803 0.0837 0.033 0.0759 -0.0426 -0.0036 0.0070
80 0.2400 0.2803 -0.0403 0.100 0.0759 0.0241 -0.0010 0.0016
81 0.4044 0.2803 0.1241 0.037 0.0759 -0.0389 -0.0048 0.0154
82 0.2427 0.2803 -0.0376 0.109 0.0759 0.0332 -0.0012 0.0014
83 0.2523 0.2803 -0.0280 0.103 0.0759 0.0275 -0.0008 0.0008
84 0.2363 0.2803 -0.0441 0.037 0.0759 -0.0389 0.0017 0.0019
85 0.4422 0.2803 0.1619 0.103 0.0759 0.0275 0.0045 0.0262
86 0.3311 0.2803 0.0508 0.102 0.0759 0.0261 0.0013 0.0026
87 0.1875 0.2803 -0.0928 0.034 0.0759 -0.0414 0.0038 0.0086
88 -0.0919 0.2803 -0.3722 0.094 0.0759 0.0184 -0.0069 0.1385
89 1.0566 0.2803 0.7763 0.100 0.0759 0.0241 0.0187 0.6026
90 0.0000 0.2803 -0.2803 0.000 0.0759 -0.0759 0.0213 0.0786
91 0.3000 0.2803 0.0197 0.000 0.0759 -0.0759 -0.0015 0.0004
50
COLD CEREAL PRICES AND INGREDIENT CONTENT
92 -0.1208 0.2803 -0.4011 0.091 0.0759 0.0150 -0.0060 0.1609
93 0.0000 0.2803 -0.2803 0.152 0.0759 0.0756 -0.0212 0.0786
94 0.0000 0.2803 -0.2803 0.063 0.0759 -0.0134 0.0038 0.0786
Intercept, a3= 0.0776379 =Y3 bar - b3* X bar -0.0372 2.0298
Slope, b3= -0.0183131 =-0.0187/2.0144 numerator, b denominator, b
Table A-7: Linear Regression: Y4- Sodium
(X -X bar) *
Cereal X X bar X - X bar Y4 Y4 bar Y4 - Y4 bar (Y4 - Y4 bar) (X - X bar)^2
1 0.2483 0.2803 -0.0320 0.000 0.0047 -0.0047 0.0002 0.0010
2 0.2483 0.2803 -0.0320 0.006 0.0047 0.0010 0.0000 0.0010
3 0.2129 0.2803 -0.0674 0.000 0.0047 -0.0044 0.0003 0.0045
4 0.2982 0.2803 0.0179 0.000 0.0047 -0.0047 -0.0001 0.0003
5 0.2308 0.2803 -0.0495 0.004 0.0047 -0.0011 0.0001 0.0025
6 0.2733 0.2803 -0.0070 0.002 0.0047 -0.0027 0.0000 0.0000
7 0.2523 0.2803 -0.0280 0.002 0.0047 -0.0029 0.0001 0.0008
8 0.4100 0.2803 0.1297 0.004 0.0047 -0.0007 -0.0001 0.0168
9 0.2187 0.2803 -0.0616 0.007 0.0047 0.0021 -0.0001 0.0038
10 0.1929 0.2803 -0.0874 0.006 0.0047 0.0016 -0.0001 0.0076
11 0.2400 0.2803 -0.0403 0.005 0.0047 0.0003 0.0000 0.0016
12 0.4550 0.2803 0.1747 0.007 0.0047 0.0021 0.0004 0.0305
13 0.4044 0.2803 0.1241 0.006 0.0047 0.0013 0.0002 0.0154
14 0.4550 0.2803 0.1747 0.006 0.0047 0.0016 0.0003 0.0305
15 0.4044 0.2803 0.1241 0.009 0.0047 0.0047 0.0006 0.0154
16 0.2427 0.2803 -0.0376 0.007 0.0047 0.0025 -0.0001 0.0014
51
COLD CEREAL PRICES AND INGREDIENT CONTENT
17 0.2880 0.2803 0.0077 0.009 0.0047 0.0042 0.0000 0.0001
18 0.2618 0.2803 -0.0185 0.007 0.0047 0.0025 0.0000 0.0003
19 0.2114 0.2803 -0.0689 0.007 0.0047 0.0024 -0.0002 0.0047
20 0.3255 0.2803 0.0452 0.006 0.0047 0.0009 0.0000 0.0020
21 0.1165 0.2803 -0.1638 0.006 0.0047 0.0011 -0.0002 0.0268
22 0.1576 0.2803 -0.1227 0.002 0.0047 -0.0025 0.0003 0.0150
23 0.1338 0.2803 -0.1466 0.005 0.0047 0.0005 -0.0001 0.0215
24 0.2062 0.2803 -0.0741 0.005 0.0047 0.0007 -0.0001 0.0055
25 0.1657 0.2803 -0.1146 0.005 0.0047 0.0000 0.0000 0.0131
26 0.1538 0.2803 -0.1265 0.004 0.0047 -0.0012 0.0002 0.0160
27 0.1675 0.2803 -0.1128 0.007 0.0047 0.0023 -0.0003 0.0127
28 0.1450 0.2803 -0.1353 0.009 0.0047 0.0040 -0.0005 0.0183
29 0.2000 0.2803 -0.0803 0.004 0.0047 -0.0009 0.0001 0.0064
30 0.1276 0.2803 -0.1527 0.007 0.0047 0.0024 -0.0004 0.0233
31 0.1489 0.2803 -0.1314 0.007 0.0047 0.0018 -0.0002 0.0173
32 0.4422 0.2803 0.1619 0.007 0.0047 0.0025 0.0004 0.0262
33 0.4422 0.2803 0.1619 0.007 0.0047 0.0023 0.0004 0.0262
34 0.3900 0.2803 0.1097 0.000 0.0047 -0.0047 -0.0005 0.0120
35 0.3900 0.2803 0.1097 0.005 0.0047 0.0006 0.0001 0.0120
36 0.3900 0.2803 0.1097 0.005 0.0047 0.0007 0.0001 0.0120
37 0.2836 0.2803 0.0033 0.002 0.0047 -0.0028 0.0000 0.0000
38 0.4457 0.2803 0.1654 0.005 0.0047 0.0006 0.0001 0.0274
39 0.4422 0.2803 0.1619 0.006 0.0047 0.0016 0.0003 0.0262
40 0.4422 0.2803 0.1619 0.006 0.0047 0.0018 0.0003 0.0262
41 0.6633 0.2803 0.3830 0.007 0.0047 0.0021 0.0008 0.1467
42 0.2778 0.2803 -0.0025 0.000 0.0047 -0.0047 0.0000 0.0000
52
COLD CEREAL PRICES AND INGREDIENT CONTENT
43 0.1835 0.2803 -0.0968 0.000 0.0047 -0.0047 0.0005 0.0094
44 0.3120 0.2803 0.0317 0.003 0.0047 -0.0022 -0.0001 0.0010
45 0.2483 0.2803 -0.0320 0.003 0.0047 -0.0021 0.0001 0.0010
46 0.2709 0.2803 -0.0094 0.002 0.0047 -0.0028 0.0000 0.0001
47 0.2836 0.2803 0.0033 0.003 0.0047 -0.0020 0.0000 0.0000
48 0.3900 0.2803 0.1097 0.002 0.0047 -0.0023 -0.0003 0.0120
49 0.2680 0.2803 -0.0123 0.000 0.0047 -0.0046 0.0001 0.0002
50 0.3500 0.2803 0.0697 0.006 0.0047 0.0016 0.0001 0.0049
51 0.1576 0.2803 -0.1227 0.002 0.0047 -0.0024 0.0003 0.0150
52 0.2600 0.2803 -0.0203 0.004 0.0047 -0.0009 0.0000 0.0004
53 0.1489 0.2803 -0.1314 0.007 0.0047 0.0020 -0.0003 0.0173
54 0.1488 0.2803 -0.1316 0.003 0.0047 -0.0016 0.0002 0.0173
55 0.2483 0.2803 -0.0320 0.004 0.0047 -0.0010 0.0000 0.0010
56 0.2292 0.2803 -0.0511 0.004 0.0047 -0.0004 0.0000 0.0026
57 0.1355 0.2803 -0.1448 0.000 0.0047 -0.0046 0.0007 0.0210
58 0.2867 0.2803 0.0064 0.000 0.0047 -0.0047 0.0000 0.0000
59 0.3225 0.2803 0.0422 0.006 0.0047 0.0012 0.0001 0.0018
60 0.2836 0.2803 0.0033 0.005 0.0047 0.0005 0.0000 0.0000
61 0.2483 0.2803 -0.0320 0.005 0.0047 0.0001 0.0000 0.0010
62 0.2229 0.2803 -0.0574 0.006 0.0047 0.0013 -0.0001 0.0033
63 0.1987 0.2803 -0.0816 0.007 0.0047 0.0024 -0.0002 0.0067
64 0.2836 0.2803 0.0033 0.004 0.0047 -0.0009 0.0000 0.0000
65 0.2150 0.2803 -0.0653 0.007 0.0047 0.0025 -0.0002 0.0043
67 0.4457 0.2803 0.1654 0.004 0.0047 -0.0005 -0.0001 0.0274
68 0.2836 0.2803 0.0033 0.005 0.0047 0.0000 0.0000 0.0000
69 0.2400 0.2803 -0.0403 0.000 0.0047 -0.0047 0.0002 0.0016
53
COLD CEREAL PRICES AND INGREDIENT CONTENT
70 0.2618 0.2803 -0.0185 0.004 0.0047 -0.0011 0.0000 0.0003
71 0.2050 0.2803 -0.0753 0.007 0.0047 0.0024 -0.0002 0.0057
72 0.3644 0.2803 0.0841 0.006 0.0047 0.0012 0.0001 0.0071
73 0.3725 0.2803 0.0922 0.004 0.0047 -0.0007 -0.0001 0.0085
74 0.1800 0.2803 -0.1003 0.010 0.0047 0.0050 -0.0005 0.0101
75 0.1733 0.2803 -0.1070 0.006 0.0047 0.0016 -0.0002 0.0114
76 0.3640 0.2803 0.0837 0.004 0.0047 -0.0005 0.0000 0.0070
77 0.2400 0.2803 -0.0403 0.002 0.0047 -0.0027 0.0001 0.0016
78 0.4044 0.2803 0.1241 0.007 0.0047 0.0024 0.0003 0.0154
79 0.2427 0.2803 -0.0376 0.005 0.0047 0.0006 0.0000 0.0014
80 0.2523 0.2803 -0.0280 0.007 0.0047 0.0023 -0.0001 0.0008
81 0.2363 0.2803 -0.0441 0.007 0.0047 0.0023 -0.0001 0.0019
82 0.4422 0.2803 0.1619 0.002 0.0047 -0.0029 -0.0005 0.0262
83 0.3311 0.2803 0.0508 0.007 0.0047 0.0022 0.0001 0.0026
84 0.1875 0.2803 -0.0928 0.006 0.0047 0.0016 -0.0001 0.0086
85 -0.0919 0.2803 -0.3722 0.004 0.0047 -0.0004 0.0001 0.1385
86 1.0566 0.2803 0.7763 0.005 0.0047 0.0000 0.0000 0.6026
87 0.0000 0.2803 -0.2803 0.006 0.0047 0.0015 -0.0004 0.0786
88 0.3000 0.2803 0.0197 0.004 0.0047 -0.0004 0.0000 0.0004
89 -0.1208 0.2803 -0.4011 0.006 0.0047 0.0016 -0.0007 0.1609
90 0.0000 0.2803 -0.2803 0.006 0.0047 0.0009 -0.0003 0.0786
91 0.0000 0.2803 -0.2803 0.007 0.0047 0.0023 -0.0007 0.0786
92 0.0776 0.2803 -0.2027 0.003 0.0047 -0.0020 0.0004 0.0411
93 -0.0183 0.2803 -0.2986 0.004 0.0047 -0.0008 0.0002 0.0892
94 0.0000 0.2803 -0.2803 0.005 0.0047 0.0003 -0.0001 0.0786
Intercept, a4= 0.0046075 =Y4 bar - b4* X bar 0.0006 2.2365
54
COLD CEREAL PRICES AND INGREDIENT CONTENT
Slope, b4= 0.0002488 =0.0008/2.2890 numerator, b denominator, b
Table A-8: Linear Regression: Y5- Calories
(X -X bar) *
Cereal X X bar X - X bar Y5 Y5 bar Y5 - Y5 bar (Y5 - Y5 bar) (X - X bar)^2
1 0.2982 0.2803 0.0179 4.286 3.6948 0.5909 0.0106 0.0003
2 0.2308 0.2803 -0.0495 3.571 3.6948 -0.1234 0.0061 0.0025
3 0.2733 0.2803 -0.0070 4.000 3.6948 0.3052 -0.0021 0.0000
4 0.2523 0.2803 -0.0280 4.667 3.6948 0.9719 -0.0272 0.0008
5 0.4100 0.2803 0.1297 3.818 3.6948 0.1234 0.0160 0.0168
6 0.2187 0.2803 -0.0616 4.182 3.6948 0.4870 -0.0300 0.0038
7 0.1929 0.2803 -0.0874 4.038 3.6948 0.3437 -0.0300 0.0076
8 0.2400 0.2803 -0.0403 4.000 3.6948 0.3052 -0.0123 0.0016
9 0.4550 0.2803 0.1747 3.571 3.6948 -0.1234 -0.0216 0.0305
10 0.4044 0.2803 0.1241 3.704 3.6948 0.0089 0.0011 0.0154
11 0.4550 0.2803 0.1747 3.704 3.6948 0.0089 0.0016 0.0305
12 0.4044 0.2803 0.1241 3.929 3.6948 0.2338 0.0290 0.0154
13 0.2427 0.2803 -0.0376 4.000 3.6948 0.3052 -0.0115 0.0014
14 0.2880 0.2803 0.0077 4.000 3.6948 0.3052 0.0024 0.0001
15 0.2618 0.2803 -0.0185 3.871 3.6948 0.1762 -0.0033 0.0003
16 0.2114 0.2803 -0.0689 3.750 3.6948 0.0552 -0.0038 0.0047
17 0.3255 0.2803 0.0452 3.704 3.6948 0.0089 0.0004 0.0020
18 0.1165 0.2803 -0.1638 3.404 3.6948 -0.2905 0.0476 0.0268
19 0.1576 0.2803 -0.1227 4.194 3.6948 0.4987 -0.0612 0.0150
55
COLD CEREAL PRICES AND INGREDIENT CONTENT20 0.1338 0.2803 -0.1466 4.074 3.6948 0.3793 -0.0556 0.0215
21 0.2062 0.2803 -0.0741 3.846 3.6948 0.1514 -0.0112 0.0055
22 0.1657 0.2803 -0.1146 4.000 3.6948 0.3052 -0.0350 0.0131
23 0.1538 0.2803 -0.1265 3.600 3.6948 -0.0948 0.0120 0.0160
24 0.1675 0.2803 -0.1128 3.077 3.6948 -0.6179 0.0697 0.0127
25 0.1450 0.2803 -0.1353 3.091 3.6948 -0.6039 0.0817 0.0183
26 0.2000 0.2803 -0.0803 2.000 3.6948 -1.6948 0.1361 0.0064
27 0.1276 0.2803 -0.1527 3.636 3.6948 -0.0584 0.0089 0.0233
28 0.1489 0.2803 -0.1314 3.871 3.6948 0.1762 -0.0232 0.0173
29 0.4422 0.2803 0.1619 3.585 3.6948 -0.1099 -0.0178 0.0262
30 0.4422 0.2803 0.1619 3.548 3.6948 -0.1464 -0.0237 0.0262
31 0.3900 0.2803 0.1097 3.846 3.6948 0.1514 0.0166 0.0120
32 0.3900 0.2803 0.1097 3.103 3.6948 -0.5914 -0.0649 0.0120
33 0.3900 0.2803 0.1097 4.333 3.6948 0.6385 0.0700 0.0120
34 0.2836 0.2803 0.0033 3.462 3.6948 -0.2333 -0.0008 0.0000
35 0.4457 0.2803 0.1654 4.000 3.6948 0.3052 0.0505 0.0274
36 0.4422 0.2803 0.1619 3.929 3.6948 0.2338 0.0379 0.0262
37 0.4422 0.2803 0.1619 3.704 3.6948 0.0089 0.0014 0.0262
38 0.6633 0.2803 0.3830 4.000 3.6948 0.3052 0.1169 0.1467
39 0.2778 0.2803 -0.0025 3.750 3.6948 0.0552 -0.0001 0.0000
40 0.1835 0.2803 -0.0968 3.871 3.6948 0.1762 -0.0170 0.0094
41 0.3120 0.2803 0.0317 3.571 3.6948 -0.1234 -0.0039 0.0010
42 0.2483 0.2803 -0.0320 3.519 3.6948 -0.1763 0.0056 0.0010
43 0.2709 0.2803 -0.0094 3.519 3.6948 -0.1763 0.0017 0.0001
44 0.2836 0.2803 0.0033 3.725 3.6948 0.0307 0.0001 0.0000
45 0.3900 0.2803 0.1097 3.774 3.6948 0.0788 0.0086 0.0120
56
COLD CEREAL PRICES AND INGREDIENT CONTENT46 0.2680 0.2803 -0.0123 3.585 3.6948 -0.1099 0.0014 0.0002
47 0.3500 0.2803 0.0697 3.333 3.6948 -0.3615 -0.0252 0.0049
48 0.1576 0.2803 -0.1227 3.636 3.6948 -0.0584 0.0072 0.0150
49 0.2600 0.2803 -0.0203 2.909 3.6948 -0.7857 0.0159 0.0004
50 0.1489 0.2803 -0.1314 3.750 3.6948 0.0552 -0.0073 0.0173
51 0.1488 0.2803 -0.1316 3.636 3.6948 -0.0584 0.0077 0.0173
52 0.2483 0.2803 -0.0320 4.000 3.6948 0.3052 -0.0098 0.0010
53 0.2292 0.2803 -0.0511 2.333 3.6948 -1.3615 0.0695 0.0026
54 0.1355 0.2803 -0.1448 4.082 3.6948 0.3868 -0.0560 0.0210
55 0.2867 0.2803 0.0064 4.000 3.6948 0.3052 0.0019 0.0000
56 0.3225 0.2803 0.0422 3.667 3.6948 -0.0281 -0.0012 0.0018
57 0.2836 0.2803 0.0033 3.390 3.6948 -0.3050 -0.0010 0.0000
58 0.2483 0.2803 -0.0320 3.462 3.6948 -0.2333 0.0075 0.0010
59 0.2229 0.2803 -0.0574 3.220 3.6948 -0.4745 0.0273 0.0033
60 0.1987 0.2803 -0.0816 3.800 3.6948 0.1052 -0.0086 0.0067
61 0.2836 0.2803 0.0033 3.929 3.6948 0.2338 0.0008 0.0000
62 0.2150 0.2803 -0.0653 4.000 3.6948 0.3052 -0.0199 0.0043
63 0.4457 0.2803 0.1654 3.571 3.6948 -0.1234 -0.0204 0.0274
64 0.2836 0.2803 0.0033 3.793 3.6948 0.0983 0.0003 0.0000
65 0.2400 0.2803 -0.0403 3.793 3.6948 0.0983 -0.0040 0.0016
67 0.2618 0.2803 -0.0185 3.871 3.6948 0.1762 -0.0033 0.0003
68 0.2050 0.2803 -0.0753 3.667 3.6948 -0.0281 0.0021 0.0057
69 0.3644 0.2803 0.0841 3.462 3.6948 -0.2333 -0.0196 0.0071
70 0.3725 0.2803 0.0922 3.636 3.6948 -0.0584 -0.0054 0.0085
71 0.1800 0.2803 -0.1003 3.871 3.6948 0.1762 -0.0177 0.0101
72 0.1733 0.2803 -0.1070 3.220 3.6948 -0.4745 0.0508 0.0114
57
COLD CEREAL PRICES AND INGREDIENT CONTENT73 0.3640 0.2803 0.0837 3.585 3.6948 -0.1099 -0.0092 0.0070
74 0.2400 0.2803 -0.0403 3.636 3.6948 -0.0584 0.0024 0.0016
75 0.4044 0.2803 0.1241 3.704 3.6948 0.0089 0.0011 0.0154
76 0.2427 0.2803 -0.0376 3.750 3.6948 0.0552 -0.0021 0.0014
77 0.2523 0.2803 -0.0280 3.654 3.6948 -0.0410 0.0011 0.0008
78 0.2363 0.2803 -0.0441 3.548 3.6948 -0.1464 0.0064 0.0019
79 0.4422 0.2803 0.1619 3.667 3.6948 -0.0281 -0.0046 0.0262
80 0.3311 0.2803 0.0508 3.667 3.6948 -0.0281 -0.0014 0.0026
81 0.1875 0.2803 -0.0928 4.074 3.6948 0.3793 -0.0352 0.0086
82 -0.0919 0.2803 -0.3722 3.455 3.6948 -0.2403 0.0894 0.1385
83 1.0566 0.2803 0.7763 3.793 3.6948 0.0983 0.0763 0.6026
84 0.0000 0.2803 -0.2803 4.074 3.6948 0.3793 -0.1063 0.0786
85 0.3000 0.2803 0.0197 3.793 3.6948 0.0983 0.0019 0.0004
86 -0.1208 0.2803 -0.4011 3.673 3.6948 -0.0213 0.0086 0.1609
87 0.0000 0.2803 -0.2803 4.138 3.6948 0.4431 -0.1242 0.0786
88 0.0000 0.2803 -0.2803 3.019 3.6948 -0.6759 0.1895 0.0786
89 0.0776 0.2803 -0.2027 3.333 3.6948 -0.3615 0.0733 0.0411
90 -0.0183 0.2803 -0.2986 3.750 3.6948 0.0552 -0.0165 0.0892
91 0.0000 0.2803 -0.2803 3.704 3.6948 0.0089 -0.0025 0.0786
92 0.0046 0.2803 -0.2757 3.818 3.6948 0.1234 -0.0340 0.0760
93 0.0002 0.2803 -0.2801 3.636 3.6948 -0.0584 0.0164 0.0784
94 0.0000 0.2803 -0.2803 3.750 3.6948 0.0552 -0.0155 0.0786
Intercept, a5= 3.6546106 =Y5 bar - b5* X bar 0.3843 2.4629
Slope, b5= 0.1560445 =0.3610/2.5180 numerator, b denominator, b
Table A-9. Standard Error of Estimate: Y1- Nutrition Index
58
COLD CEREAL PRICES AND INGREDIENT CONTENT Yhat =
X * b1 ( X * b1) + a1 Y1 - Yhat (Y1-Yhat)^2
0.10 0.004 0.996 0.992
0.29 0.194 -0.194 0.038
0.34 0.252 0.748 0.560
0.34 0.252 -0.252 0.064
0.43 0.341 -0.341 0.117
0.43 0.341 -0.341 0.117
0.43 0.341 -0.341 0.117
0.26 0.171 -0.171 0.029
0.30 0.211 -0.211 0.045
0.26 0.171 -0.171 0.029
0.26 0.171 -0.171 0.029
0.26 0.171 -0.171 0.029
0.22 0.133 -0.133 0.018
0.32 0.223 -0.223 0.050
0.24 0.152 -0.152 0.023
0.29 0.197 -0.197 0.039
0.27 0.175 -0.175 0.031
0.43 0.341 -0.341 0.117
0.23 0.139 -0.139 0.019
0.20 0.112 -0.112 0.013
0.25 0.162 -0.162 0.026
0.48 0.389 -0.389 0.151
0.43 0.335 -0.335 0.113
0.48 0.389 -0.389 0.151
0.43 0.335 -0.335 0.113
59
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.26 0.165 0.835 0.698
0.30 0.212 -0.212 0.045
0.28 0.185 -0.185 0.034
0.22 0.132 -0.132 0.017
0.34 0.252 -0.252 0.064
0.12 0.031 -0.031 0.001
0.17 0.075 -0.075 0.006
0.14 0.049 -0.049 0.002
0.22 0.126 0.874 0.764
0.18 0.083 -0.083 0.007
0.16 0.071 -0.071 0.005
0.18 0.085 -0.085 0.007
0.15 0.061 -0.061 0.004
0.21 0.119 -0.119 0.014
0.13 0.043 -0.043 0.002
0.16 0.065 -0.065 0.004
0.47 0.375 0.625 0.390
0.47 0.375 0.625 0.390
0.41 0.320 0.680 0.462
0.41 0.320 -0.320 0.103
0.41 0.320 0.680 0.462
0.30 0.208 0.792 0.628
0.47 0.379 -0.379 0.144
0.47 0.375 0.625 0.390
0.47 0.375 -0.375 0.141
0.70 0.609 0.391 0.153
60
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.29 0.202 -0.202 0.041
0.19 0.102 -0.102 0.010
0.33 0.238 -0.238 0.057
0.26 0.171 -0.171 0.029
0.29 0.194 -0.194 0.038
0.30 0.208 0.792 0.628
0.41 0.320 0.680 0.462
0.28 0.191 -0.191 0.037
0.37 0.278 -0.278 0.077
0.17 0.075 -0.075 0.006
0.27 0.183 -0.183 0.033
0.16 0.065 -0.065 0.004
0.16 0.065 -0.065 0.004
0.26 0.171 -0.171 0.029
0.24 0.150 -0.150 0.023
0.14 0.051 -0.051 0.003
0.30 0.211 0.789 0.622
0.34 0.249 -0.249 0.062
0.30 0.208 -0.208 0.043
0.26 0.171 -0.171 0.029
0.24 0.144 -0.144 0.021
0.21 0.118 -0.118 0.014
0.30 0.208 -0.208 0.043
0.23 0.135 -0.135 0.018
0.47 0.379 0.621 0.386
0.30 0.208 -0.208 0.043
61
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.25 0.162 -0.162 0.026
0.28 0.185 -0.185 0.034
0.22 0.125 -0.125 0.016
0.39 0.293 0.707 0.500
0.39 0.302 -0.302 0.091
0.19 0.098 -0.098 0.010
0.18 0.091 0.909 0.826
0.38 0.293 -0.293 0.086
0.25 0.162 -0.162 0.026
0.43 0.335 -0.335 0.113
0.26 0.165 -0.165 0.027
0.27 0.175 -0.175 0.031
0.25 0.158 -0.158 0.025
0.47 0.375 -0.375 0.141
0.35 0.258 0.742 0.551
0.20 0.106 0.894 0.799
sum of sq err. 14.022
Std. Err. Est. 0.395
Table A-10. Standard Error of Estimate: Y2-Sugar
Yhat =
X * b2 ( X * b2) + a2 Y2 - Yhat (Y2-Yhat)^2
-0.04 0.26 -0.261 0.068
-0.050 0.25 0.071 0.005
-0.050 0.25 -0.117 0.014
62
COLD CEREAL PRICES AND INGREDIENT CONTENT
-0.050 0.25 -0.050 0.003
-0.030 0.27 0.021 0.000
-0.035 0.27 -0.011 0.000
-0.030 0.27 -0.001 0.000
-0.030 0.27 0.130 0.017
-0.030 0.27 -0.234 0.055
-0.026 0.27 0.059 0.003
-0.036 0.26 0.069 0.005
-0.028 0.27 0.049 0.002
-0.033 0.27 0.033 0.001
-0.030 0.27 -0.003 0.000
-0.050 0.25 -0.154 0.024
-0.026 0.27 0.008 0.000
-0.023 0.28 -0.203 0.041
-0.029 0.27 -0.165 0.027
-0.055 0.25 0.078 0.006
-0.049 0.25 0.193 0.037
-0.055 0.25 0.178 0.032
-0.049 0.25 0.016 0.000
-0.029 0.27 -0.071 0.005
-0.035 0.27 -0.150 0.022
-0.032 0.27 -0.032 0.001
-0.026 0.27 -0.274 0.075
-0.039 0.26 -0.079 0.006
-0.014 0.29 0.069 0.005
-0.019 0.28 0.096 0.009
63
COLD CEREAL PRICES AND INGREDIENT CONTENT
-0.016 0.28 0.039 0.002
-0.025 0.28 0.186 0.035
-0.020 0.28 -0.108 0.012
-0.019 0.28 0.052 0.003
-0.020 0.28 -0.068 0.005
-0.018 0.28 0.151 0.023
-0.024 0.28 0.153 0.023
-0.015 0.28 0.271 0.073
-0.018 0.28 0.085 0.007
-0.053 0.25 0.075 0.006
-0.053 0.25 0.173 0.030
-0.047 0.25 -0.217 0.047
-0.047 0.25 -0.123 0.015
-0.047 0.25 -0.086 0.007
-0.034 0.27 -0.030 0.001
-0.054 0.25 -0.020 0.000
-0.053 0.25 -0.001 0.000
-0.053 0.25 -0.095 0.009
-0.080 0.22 0.016 0.000
-0.034 0.27 -0.103 0.011
-0.022 0.28 0.003 0.000
-0.038 0.26 -0.080 0.006
-0.030 0.27 0.130 0.017
-0.033 0.27 -0.001 0.000
-0.034 0.27 0.040 0.002
-0.047 0.25 0.280 0.079
64
COLD CEREAL PRICES AND INGREDIENT CONTENT
-0.032 0.27 0.132 0.018
-0.042 0.26 -0.054 0.003
-0.019 0.28 -0.050 0.003
-0.031 0.27 0.053 0.003
-0.018 0.28 -0.002 0.000
-0.018 0.28 0.147 0.021
-0.030 0.27 -0.037 0.001
-0.028 0.27 -0.201 0.040
-0.016 0.28 0.130 0.017
-0.035 0.27 -0.162 0.026
-0.039 0.26 0.062 0.004
-0.034 0.27 0.101 0.010
-0.030 0.27 -0.039 0.002
-0.027 0.27 -0.055 0.003
-0.024 0.28 -0.147 0.022
-0.034 0.27 0.056 0.003
-0.026 0.27 0.103 0.011
-0.054 0.25 -0.155 0.024
-0.034 0.27 -0.006 0.000
-0.029 0.27 0.073 0.005
-0.032 0.27 -0.076 0.006
-0.025 0.28 0.047 0.002
-0.044 0.26 0.044 0.002
-0.045 0.26 -0.155 0.024
-0.022 0.28 0.129 0.017
-0.021 0.28 -0.079 0.006
65
COLD CEREAL PRICES AND INGREDIENT CONTENT
-0.044 0.26 -0.049 0.002
-0.029 0.27 0.173 0.030
-0.049 0.25 -0.113 0.013
-0.029 0.27 0.015 0.000
-0.030 0.27 0.144 0.021
-0.029 0.27 0.049 0.002
-0.053 0.25 -0.080 0.006
-0.040 0.26 0.146 0.021
-0.023 0.28 -0.129 0.017
0.011 0.31 -0.057 0.003
-0.128 0.17 0.100 0.010
0.000 0.30 -0.113 0.013
sum of sq err 1.288
Std. Er. Est. 0.120
Table A-11. Standard Error of Estimate: Y3- Fiber
Yhat =
X * b3 ( X * b3) + a3 Y3 - Yhat (Y3-Yhat)^2
-0.005 0.073 0.070 0.005
-0.005 0.072 -0.037 0.001
-0.005 0.073 -0.006 0.000
-0.005 0.073 -0.006 0.000
-0.005 0.073 -0.037 0.001
-0.004 0.074 -0.037 0.001
66
COLD CEREAL PRICES AND INGREDIENT CONTENT
-0.005 0.072 -0.014 0.000
-0.004 0.073 -0.040 0.002
-0.005 0.073 -0.037 0.001
-0.005 0.073 -0.036 0.001
-0.008 0.070 0.004 0.000
-0.004 0.074 -0.002 0.000
-0.004 0.074 -0.007 0.000
-0.004 0.073 -0.073 0.005
-0.008 0.069 -0.037 0.001
-0.007 0.070 -0.039 0.002
-0.008 0.069 -0.069 0.005
-0.007 0.070 -0.049 0.002
-0.004 0.073 -0.041 0.002
-0.005 0.072 -0.035 0.001
-0.005 0.073 -0.034 0.001
-0.004 0.074 -0.007 0.000
-0.006 0.072 0.108 0.012
-0.002 0.076 0.174 0.030
-0.003 0.075 0.125 0.016
-0.002 0.075 0.391 0.153
-0.004 0.074 0.017 0.000
-0.003 0.075 -0.042 0.002
-0.003 0.075 0.001 0.000
-0.003 0.075 -0.042 0.002
-0.003 0.075 -0.075 0.006
-0.004 0.074 0.098 0.010
67
COLD CEREAL PRICES AND INGREDIENT CONTENT
-0.002 0.075 -0.042 0.002
-0.003 0.075 0.021 0.000
-0.008 0.070 -0.036 0.001
-0.008 0.070 -0.070 0.005
-0.007 0.070 -0.070 0.005
-0.007 0.070 -0.037 0.001
-0.007 0.070 0.055 0.003
-0.005 0.072 -0.040 0.002
-0.008 0.069 0.038 0.001
-0.008 0.070 0.042 0.002
-0.008 0.070 0.023 0.001
-0.012 0.065 0.091 0.008
-0.005 0.073 0.078 0.006
-0.003 0.074 0.077 0.006
-0.006 0.072 0.080 0.006
-0.005 0.073 0.000 0.000
-0.005 0.073 0.036 0.001
-0.005 0.072 -0.041 0.002
-0.007 0.070 0.057 0.003
-0.005 0.073 -0.039 0.002
-0.006 0.071 0.362 0.131
-0.003 0.075 0.048 0.002
-0.005 0.073 -0.073 0.005
-0.003 0.075 -0.075 0.006
-0.003 0.075 0.027 0.001
-0.005 0.073 0.023 0.001
68
COLD CEREAL PRICES AND INGREDIENT CONTENT
-0.004 0.073 0.045 0.002
-0.002 0.075 -0.015 0.000
-0.005 0.072 -0.037 0.001
-0.006 0.072 -0.038 0.001
-0.005 0.072 -0.037 0.001
-0.005 0.073 -0.073 0.005
-0.004 0.074 -0.039 0.002
-0.004 0.074 -0.074 0.005
-0.005 0.072 -0.039 0.002
-0.004 0.074 0.022 0.001
-0.008 0.069 0.040 0.002
-0.005 0.072 -0.040 0.002
-0.004 0.073 0.045 0.002
-0.005 0.073 0.003 0.000
-0.004 0.074 -0.074 0.005
-0.007 0.071 -0.034 0.001
-0.007 0.071 -0.040 0.002
-0.003 0.074 0.022 0.000
-0.003 0.074 -0.042 0.002
-0.007 0.071 -0.038 0.001
-0.004 0.073 0.027 0.001
-0.007 0.070 -0.033 0.001
-0.004 0.073 0.036 0.001
-0.005 0.073 0.030 0.001
-0.004 0.073 -0.036 0.001
-0.008 0.070 0.034 0.001
69
COLD CEREAL PRICES AND INGREDIENT CONTENT
-0.006 0.072 0.030 0.001
-0.003 0.074 -0.040 0.002
0.002 0.079 0.015 0.000
-0.019 0.058 0.042 0.002
0.000 0.078 -0.078 0.006
-0.005 0.072 -0.072 0.005
0.002 0.080 0.011 0.000
0.000 0.078 0.074 0.005
0.000 0.078 -0.015 0.000
sum of sq err 0.532
Std. Er. Est. 0.077
Table A-12. Standard Error of Estimate: Y4- Sodium
Yhat =
X * b4 ( X * b4) + a4 Y4 - Yhat (Y4-Yhat)^2
0.000 0.005 -0.005 0.000
0.000 0.005 0.001 0.000
0.000 0.005 -0.004 0.000
0.000 0.005 -0.005 0.000
0.000 0.005 -0.001 0.000
0.000 0.005 -0.003 0.000
0.000 0.005 -0.003 0.000
0.000 0.005 -0.001 0.000
0.000 0.005 0.002 0.000
0.000 0.005 0.002 0.000
70
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.000 0.005 0.000 0.000
0.000 0.005 0.002 0.000
0.000 0.005 0.001 0.000
0.000 0.005 0.002 0.000
0.000 0.005 0.005 0.000
0.000 0.005 0.003 0.000
0.000 0.005 0.004 0.000
0.000 0.005 0.003 0.000
0.000 0.005 0.002 0.000
0.000 0.005 0.001 0.000
0.000 0.005 0.001 0.000
0.000 0.005 -0.002 0.000
0.000 0.005 0.001 0.000
0.000 0.005 0.001 0.000
0.000 0.005 0.000 0.000
0.000 0.005 -0.001 0.000
0.000 0.005 0.002 0.000
0.000 0.005 0.004 0.000
0.000 0.005 -0.001 0.000
0.000 0.005 0.002 0.000
0.000 0.005 0.002 0.000
0.000 0.005 0.003 0.000
0.000 0.005 0.002 0.000
0.000 0.005 -0.005 0.000
0.000 0.005 0.001 0.000
0.000 0.005 0.001 0.000
71
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.000 0.005 -0.003 0.000
0.000 0.005 0.001 0.000
0.000 0.005 0.002 0.000
0.000 0.005 0.002 0.000
0.000 0.005 0.002 0.000
0.000 0.005 -0.005 0.000
0.000 0.005 -0.005 0.000
0.000 0.005 -0.002 0.000
0.000 0.005 -0.002 0.000
0.000 0.005 -0.003 0.000
0.000 0.005 -0.002 0.000
0.000 0.005 -0.002 0.000
0.000 0.005 -0.005 0.000
0.000 0.005 0.002 0.000
0.000 0.005 -0.002 0.000
0.000 0.005 -0.001 0.000
0.000 0.005 0.002 0.000
0.000 0.005 -0.002 0.000
0.000 0.005 -0.001 0.000
0.000 0.005 0.000 0.000
0.000 0.005 -0.005 0.000
0.000 0.005 -0.005 0.000
0.000 0.005 0.001 0.000
0.000 0.005 0.001 0.000
0.000 0.005 0.000 0.000
0.000 0.005 0.001 0.000
72
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.000 0.005 0.002 0.000
0.000 0.005 -0.001 0.000
0.000 0.005 0.003 0.000
0.000 0.005 -0.001 0.000
0.000 0.005 0.000 0.000
0.000 0.005 -0.005 0.000
0.000 0.005 -0.001 0.000
0.000 0.005 0.002 0.000
0.000 0.005 0.001 0.000
0.000 0.005 -0.001 0.000
0.000 0.005 0.005 0.000
0.000 0.005 0.002 0.000
0.000 0.005 0.000 0.000
0.000 0.005 -0.003 0.000
0.000 0.005 0.002 0.000
0.000 0.005 0.001 0.000
0.000 0.005 0.002 0.000
0.000 0.005 0.002 0.000
0.000 0.005 -0.003 0.000
0.000 0.005 0.002 0.000
0.000 0.005 0.002 0.000
0.000 0.005 0.000 0.000
0.000 0.005 0.000 0.000
0.000 0.005 0.002 0.000
0.000 0.005 0.000 0.000
0.000 0.005 0.002 0.000
73
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.000 0.005 0.001 0.000
0.000 0.005 0.002 0.000
0.000 0.005 -0.002 0.000
0.000 0.005 -0.001 0.000
0.000 0.005 0.000 0.000
sum of sq err 0.001
Std. Er. Est. 0.002
Table A-13. Standard Error of Estimate: Y5- Calories
Yhat =
X * b5 ( X * b5) + a5 Y5 - Yhat (Y5-Yhat)^2
0.047 3.701 0.585 0.342
0.036 3.691 -0.119 0.014
0.043 3.697 0.303 0.092
0.039 3.694 0.973 0.946
0.064 3.719 0.100 0.010
0.034 3.689 0.493 0.243
0.030 3.685 0.354 0.125
0.037 3.692 0.308 0.095
0.071 3.726 -0.154 0.024
0.063 3.718 -0.014 0.000
0.071 3.726 -0.022 0.000
0.063 3.718 0.211 0.044
0.038 3.692 0.308 0.095
74
COLD CEREAL PRICES AND INGREDIENT CONTENT0.045 3.700 0.300 0.090
0.041 3.695 0.176 0.031
0.033 3.688 0.062 0.004
0.051 3.705 -0.002 0.000
0.018 3.673 -0.269 0.072
0.025 3.679 0.514 0.265
0.021 3.675 0.399 0.159
0.032 3.687 0.159 0.025
0.026 3.680 0.320 0.102
0.024 3.679 -0.079 0.006
0.026 3.681 -0.604 0.365
0.023 3.677 -0.586 0.344
0.031 3.686 -1.686 2.842
0.020 3.675 -0.038 0.001
0.023 3.678 0.193 0.037
0.069 3.724 -0.139 0.019
0.069 3.724 -0.175 0.031
0.061 3.715 0.131 0.017
0.061 3.715 -0.612 0.375
0.061 3.715 0.618 0.382
0.044 3.699 -0.237 0.056
0.070 3.724 0.276 0.076
0.069 3.724 0.205 0.042
0.069 3.724 -0.020 0.000
0.104 3.758 0.242 0.059
0.043 3.698 0.052 0.003
75
COLD CEREAL PRICES AND INGREDIENT CONTENT0.029 3.683 0.188 0.035
0.049 3.703 -0.132 0.017
0.039 3.693 -0.175 0.031
0.042 3.697 -0.178 0.032
0.044 3.699 0.027 0.001
0.061 3.715 0.058 0.003
0.042 3.696 -0.112 0.012
0.055 3.709 -0.376 0.141
0.025 3.679 -0.043 0.002
0.041 3.695 -0.786 0.618
0.023 3.678 0.072 0.005
0.023 3.678 -0.041 0.002
0.039 3.693 0.307 0.094
0.036 3.690 -1.357 1.842
0.021 3.676 0.406 0.165
0.045 3.699 0.301 0.090
0.050 3.705 -0.038 0.001
0.044 3.699 -0.309 0.096
0.039 3.693 -0.232 0.054
0.035 3.689 -0.469 0.220
0.031 3.686 0.114 0.013
0.044 3.699 0.230 0.053
0.034 3.688 0.312 0.097
0.070 3.724 -0.153 0.023
0.044 3.699 0.094 0.009
0.037 3.692 0.101 0.010
76
COLD CEREAL PRICES AND INGREDIENT CONTENT0.041 3.695 0.176 0.031
0.032 3.687 -0.020 0.000
0.057 3.711 -0.250 0.062
0.058 3.713 -0.076 0.006
0.028 3.683 0.188 0.035
0.027 3.682 -0.461 0.213
0.057 3.711 -0.127 0.016
0.037 3.692 -0.056 0.003
0.063 3.718 -0.014 0.000
0.038 3.692 0.058 0.003
0.039 3.694 -0.040 0.002
0.037 3.691 -0.143 0.020
0.069 3.724 -0.057 0.003
0.052 3.706 -0.040 0.002
0.029 3.684 0.390 0.152
-0.014 3.640 -0.186 0.034
0.165 3.819 -0.026 0.001
0.000 3.655 0.419 0.176
0.047 3.701 0.092 0.008
-0.019 3.636 0.038 0.001
0.000 3.655 0.483 0.234
0.000 3.655 -0.636 0.404
0.012 3.667 -0.333 0.111
-0.003 3.652 0.098 0.010
0.000 3.655 0.049 0.002
0.001 3.655 0.163 0.027
77
COLD CEREAL PRICES AND INGREDIENT CONTENT0.000 3.655 -0.018 0.000
0.000 3.655 0.095 0.009
sum of sq err 12.667
Std. Er. Est. 0.375
Table A-14. Coef.of Det.:: Y1- Nutrition Index
Yhat-Y1 bar (Yhat - Y bar)^2 (Y1-Y bar)^2
-0.200 0.040 0.633
-0.010 0.000 0.042
0.048 0.002 0.633
0.048 0.002 0.042
0.137 0.019 0.042
0.137 0.019 0.042
0.137 0.019 0.042
-0.034 0.001 0.042
0.007 0.000 0.042
-0.034 0.001 0.042
-0.034 0.001 0.042
-0.034 0.001 0.042
-0.071 0.005 0.042
0.019 0.000 0.042
-0.052 0.003 0.042
-0.007 0.000 0.042
-0.030 0.001 0.042
0.137 0.019 0.042
78
COLD CEREAL PRICES AND INGREDIENT CONTENT-0.065 0.004 0.042
-0.092 0.009 0.042
-0.043 0.002 0.042
0.185 0.034 0.042
0.131 0.017 0.042
0.185 0.034 0.042
0.131 0.017 0.042
-0.040 0.002 0.633
0.008 0.000 0.042
-0.020 0.000 0.042
-0.073 0.005 0.042
0.048 0.002 0.042
-0.173 0.030 0.042
-0.130 0.017 0.042
-0.155 0.024 0.042
-0.078 0.006 0.633
-0.121 0.015 0.042
-0.134 0.018 0.042
-0.119 0.014 0.042
-0.143 0.020 0.042
-0.085 0.007 0.042
-0.161 0.026 0.042
-0.139 0.019 0.042
0.171 0.029 0.633
0.171 0.029 0.633
0.116 0.013 0.633
0.116 0.013 0.042
79
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.116 0.013 0.633
0.004 0.000 0.633
0.175 0.031 0.042
0.171 0.029 0.633
0.171 0.029 0.042
0.405 0.164 0.633
-0.003 0.000 0.042
-0.102 0.010 0.042
0.033 0.001 0.042
-0.034 0.001 0.042
-0.010 0.000 0.042
0.004 0.000 0.633
0.116 0.013 0.633
-0.013 0.000 0.042
0.074 0.005 0.042
-0.130 0.017 0.042
-0.021 0.000 0.042
-0.139 0.019 0.042
-0.139 0.019 0.042
-0.034 0.001 0.042
-0.054 0.003 0.042
-0.153 0.023 0.042
0.007 0.000 0.633
0.045 0.002 0.042
0.004 0.000 0.042
-0.034 0.001 0.042
80
COLD CEREAL PRICES AND INGREDIENT CONTENT
-0.061 0.004 0.042
-0.086 0.007 0.042
0.004 0.000 0.042
-0.069 0.005 0.042
0.175 0.031 0.633
0.004 0.000 0.042
-0.043 0.002 0.042
-0.020 0.000 0.042
-0.080 0.006 0.042
0.089 0.008 0.633
0.097 0.009 0.042
-0.106 0.011 0.042
-0.113 0.013 0.633
0.088 0.008 0.042
-0.043 0.002 0.042
0.131 0.017 0.042
-0.040 0.002 0.042
-0.030 0.001 0.042
-0.047 0.002 0.042
0.171 0.029 0.042
0.054 0.003 0.633
-0.098 0.010 0.633
0.0725 1.096 15.118
Coef. Of Det. Coef.Det. Num. Coef.Det.Den
81
COLD CEREAL PRICES AND INGREDIENT CONTENT
Table A-15. Coef.of Det.:: Y2- Sugar
Yhat-Y2 bar (Yhat - Y bar)^2 (Y2-Y bar)^2
0.00002 0.07012
0.00021 0.00321
0.00021 0.01728
0.00021 0.00420
0.00003 0.00068
0.00000 0.00011
0.00003 0.00002
0.00003 0.01828
0.00003 0.05248
0.00009 0.00470
0.00000 0.00470
0.00005 0.00321
0.00000 0.00124
0.00002 0.00000
0.00021 0.02823
0.00008 0.00027
0.00014 0.03638
0.00004 0.02510
0.00039 0.00334
0.00019 0.03227
0.00039 0.02505
0.00019 0.00000
0.00003 0.00420
82
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.00000 0.02232
0.00001 0.00081
0.00009 0.07012
0.00002 0.00689
0.00045 0.00811
0.00026 0.01267
0.00036 0.00334
0.00011 0.03871
0.00023 0.00854
0.00028 0.00470
0.00022 0.00284
0.00031 0.02840
0.00012 0.02682
0.00039 0.08454
0.00030 0.01038
0.00033 0.00321
0.00033 0.02389
0.00014 0.05248
0.00014 0.01827
0.00014 0.00963
0.00000 0.00087
0.00035 0.00147
0.00033 0.00038
0.00033 0.01283
0.00202 0.00081
0.00000 0.01023
83
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.00017 0.00027
0.00001 0.00689
0.00003 0.01828
0.00001 0.00000
0.00000 0.00171
0.00014 0.07211
0.00001 0.01828
0.00005 0.00377
0.00026 0.00116
0.00001 0.00328
0.00030 0.00023
0.00030 0.02682
0.00003 0.00099
0.00006 0.03739
0.00035 0.02220
0.00000 0.02603
0.00001 0.00334
0.00000 0.01038
0.00003 0.00116
0.00007 0.00217
0.00013 0.01843
0.00000 0.00328
0.00009 0.01267
0.00035 0.03024
0.00000 0.00003
0.00004 0.00623
84
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.00001 0.00526
0.00011 0.00334
0.00008 0.00124
0.00010 0.02716
0.00018 0.02034
0.00020 0.00420
0.00008 0.00335
0.00004 0.03227
0.00019 0.01610
0.00003 0.00044
0.00002 0.02220
0.00004 0.00313
0.00033 0.00963
0.00002 0.02001
0.00016 0.01361
0.00214 0.00011
0.00855 0.00006
0.00124 0.00598
0.2074 0.02579 1.31404
Coef. Of Det. Coef.Det. Num. Coef.Det.Den
Table A-16. Coef.of Det.: Y3- Fiber
Yhat-Y3 bar (Yhat - Y bar)^2 (Y3-Y bar)^2
85
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.00001 0.00448
0.00001 0.00161
0.00001 0.00009
0.00001 0.00009
0.00001 0.00156
0.00000 0.00156
0.00001 0.00033
0.00001 0.00181
0.00001 0.00161
0.00001 0.00151
0.00003 0.00000
0.00001 0.00002
0.00000 0.00009
0.00001 0.00576
0.00004 0.00190
0.00003 0.00199
0.00004 0.00576
0.00003 0.00298
0.00001 0.00190
0.00001 0.00151
0.00001 0.00140
0.00000 0.00009
0.00002 0.01084
0.00000 0.03031
0.00000 0.01540
0.00000 0.15270
86
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.00000 0.00023
0.00000 0.00190
0.00000 0.00000
0.00000 0.00190
0.00000 0.00576
0.00000 0.00931
0.00000 0.00181
0.00000 0.00041
0.00004 0.00181
0.00004 0.00576
0.00003 0.00576
0.00003 0.00181
0.00003 0.00241
0.00001 0.00190
0.00004 0.00098
0.00004 0.00124
0.00004 0.00028
0.00011 0.00655
0.00001 0.00563
0.00000 0.00563
0.00002 0.00572
0.00001 0.00001
0.00001 0.00110
0.00001 0.00199
0.00003 0.00264
0.00001 0.00181
87
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.00002 0.12776
0.00000 0.00217
0.00001 0.00576
0.00000 0.00576
0.00000 0.00067
0.00001 0.00041
0.00001 0.00183
0.00000 0.00025
0.00001 0.00161
0.00002 0.00181
0.00001 0.00161
0.00001 0.00576
0.00001 0.00172
0.00000 0.00576
0.00001 0.00181
0.00000 0.00041
0.00004 0.00110
0.00001 0.00190
0.00001 0.00183
0.00001 0.00000
0.00000 0.00576
0.00002 0.00151
0.00003 0.00199
0.00000 0.00041
0.00000 0.00190
0.00002 0.00181
88
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.00001 0.00058
0.00003 0.00151
0.00001 0.00110
0.00001 0.00076
0.00001 0.00151
0.00004 0.00076
0.00002 0.00068
0.00000 0.00172
0.00001 0.00034
0.00031 0.00058
0.00000 0.00576
0.00001 0.00576
0.00002 0.00023
0.00000 0.00572
0.00000 0.00018
0.0031 0.00163 0.53222
Coef. Of Det. Coef.Det. Num. Coef.Det.Den
Table A-17. Coef.of Det.: Y4- Sodium
Yhat-Y4 bar (Yhat - Y bar)^2 (Y4-Y bar)^2
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
89
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
90
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
91
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
92
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000
0.0000 0.0000 0.0000
Coef. Of Det. Coef.Det. Num. Coef.Det.Den
Table A-18. Coef.of Det.: Y5- Calories
Yhat-Y4 bar (Yhat - Y bar)^2 (Y4-Y bar)^2
0.0000 0.3492
0.0000 0.0152
0.0000 0.0931
0.0000 0.9445
0.0006 0.0152
0.0000 0.2372
0.0001 0.1181
0.0000 0.0931
93
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0009 0.0152
0.0005 0.0001
0.0009 0.0001
0.0005 0.0546
0.0000 0.0931
0.0000 0.0931
0.0000 0.0310
0.0001 0.0030
0.0001 0.0001
0.0005 0.0844
0.0002 0.2487
0.0004 0.1438
0.0001 0.0229
0.0002 0.0931
0.0003 0.0090
0.0002 0.3818
0.0003 0.3647
0.0001 2.8723
0.0004 0.0034
0.0003 0.0310
0.0008 0.0121
0.0008 0.0214
0.0004 0.0229
0.0004 0.3497
0.0004 0.4077
94
COLD CEREAL PRICES AND INGREDIENT CONTENT 0.0000 0.0544
0.0009 0.0931
0.0008 0.0546
0.0008 0.0001
0.0040 0.0931
0.0000 0.0030
0.0001 0.0310
0.0001 0.0152
0.0000 0.0311
0.0000 0.0311
0.0000 0.0009
0.0004 0.0062
0.0000 0.0121
0.0002 0.1307
0.0002 0.0034
0.0000 0.6173
0.0003 0.0030
0.0003 0.0034
0.0000 0.0931
0.0000 1.8536
0.0004 0.1496
0.0000 0.0931
0.0001 0.0008
0.0000 0.0930
0.0000 0.0544
0.0000 0.2251
95
COLD CEREAL PRICES AND INGREDIENT CONTENT 0.0001 0.0111
0.0000 0.0546
0.0000 0.0931
0.0009 0.0152
0.0000 0.0097
0.0000 0.0097
0.0000 0.0310
0.0001 0.0008
0.0003 0.0544
0.0003 0.0034
0.0001 0.0310
0.0002 0.2251
0.0003 0.0121
0.0000 0.0034
0.0005 0.0001
0.0000 0.0030
0.0000 0.0017
0.0000 0.0214
0.0008 0.0008
0.0001 0.0008
0.0001 0.1438
0.0030 0.0577
0.0155 0.0097
0.0016 0.1438
0.0000 0.0097
0.0035 0.0005
96
COLD CEREAL PRICES AND INGREDIENT CONTENT 0.0016 0.1964
0.0016 0.4569
0.0008 0.1307
0.0019 0.0030
0.0016 0.0001
0.0016 0.0152
0.0016 0.0034
0.0016 0.0030
0.0000 0.0584 5511.6974
Coef. Of Det. Coef.Det. Num. Coef.Det.Den
97
COLD CEREAL PRICES AND INGREDIENT CONTENT
Table A-19. Std. Error of b:
Y1- Nutrition Index
(X - X bar)^2
0.0359
0.0001
0.0020
0.0020
0.0168
0.0168
0.0168
0.0010
0.0000
0.0010
0.0010
0.0010
0.0045
0.0003
0.0025
0.0000
0.0008
0.0168
0.0038
0.0076
0.0016
0.0305
0.0154
98
COLD CEREAL PRICES AND INGREDIENT CONTENT0.0305
0.0154
0.0014
0.0001
0.0003
0.0047
0.0020
0.0268
0.0150
0.0215
0.0055
0.0131
0.0160
0.0127
0.0183
0.0064
0.0233
0.0173
0.0262
0.0262
0.0120
0.0120
0.0120
0.0000
0.0274
0.0262
0.0262
99
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.1467
0.0000
0.0094
0.0010
0.0010
0.0001
0.0000
0.0120
0.0002
0.0049
0.0150
0.0004
0.0173
0.0173
0.0010
0.0026
0.0210
0.0000
0.0018
0.0000
0.0010
0.0033
0.0067
0.0000
0.0043
0.0274
100
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0000
0.0016
0.0003
0.0057
0.0071
0.0085
0.0101
0.0114
0.0070
0.0016
0.0154
0.0014
0.0008
0.0019
0.0262
0.0026
0.0086
0.9822
0.3983 Std. Err. B
Table 20. Std. Error of b:
Y2- Sugar
(X - X bar)^2
0.0020
0.0168
101
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0168
0.0168
0.0010
0.0000
0.0010
0.0010
0.0010
0.0045
0.0003
0.0025
0.0000
0.0008
0.0168
0.0038
0.0076
0.0016
0.0305
0.0154
0.0305
0.0154
0.0014
0.0001
0.0003
0.0047
0.0020
0.0268
102
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0150
0.0215
0.0055
0.0131
0.0160
0.0127
0.0183
0.0064
0.0233
0.0173
0.0262
0.0262
0.0120
0.0120
0.0120
0.0000
0.0274
0.0262
0.0262
0.1467
0.0000
0.0094
0.0010
0.0010
0.0001
0.0000
103
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0120
0.0002
0.0049
0.0150
0.0004
0.0173
0.0173
0.0010
0.0026
0.0210
0.0000
0.0018
0.0000
0.0010
0.0033
0.0067
0.0000
0.0043
0.0274
0.0000
0.0016
0.0003
0.0057
0.0071
0.0085
0.0101
104
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0114
0.0070
0.0016
0.0154
0.0014
0.0008
0.0019
0.0262
0.0026
0.0086
0.1385
0.6026
0.0786
1.7638
0.0901 Std. Err. B
Table A-21. Std. Error of b:
Y3- Fiber
(X - X bar)^2
0.0010
0.0000
0.0010
0.0010
0.0010
105
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0045
0.0003
0.0025
0.0000
0.0008
0.0168
0.0038
0.0076
0.0016
0.0305
0.0154
0.0305
0.0154
0.0014
0.0001
0.0003
0.0047
0.0020
0.0268
0.0150
0.0215
0.0055
0.0131
0.0160
0.0127
0.0183
106
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0064
0.0233
0.0173
0.0262
0.0262
0.0120
0.0120
0.0120
0.0000
0.0274
0.0262
0.0262
0.1467
0.0000
0.0094
0.0010
0.0010
0.0001
0.0000
0.0120
0.0002
0.0049
0.0150
0.0004
0.0173
0.0173
107
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0010
0.0026
0.0210
0.0000
0.0018
0.0000
0.0010
0.0033
0.0067
0.0000
0.0043
0.0274
0.0000
0.0016
0.0003
0.0057
0.0071
0.0085
0.0101
0.0114
0.0070
0.0016
0.0154
0.0014
0.0008
0.0019
108
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0262
0.0026
0.0086
0.1385
0.6026
0.0786
0.0004
0.1609
0.0786
0.0786
2.0298
0.0540 Std. Err. B
Table A-22. Std. Error of b:
Y4- Sodium
(X - X bar)^2
0.0010
0.0010
0.0045
0.0003
0.0025
0.0000
0.0008
0.0168
0.0038
0.0076
109
COLD CEREAL PRICES AND INGREDIENT CONTENT0.0016
0.0305
0.0154
0.0305
0.0154
0.0014
0.0001
0.0003
0.0047
0.0020
0.0268
0.0150
0.0215
0.0055
0.0131
0.0160
0.0127
0.0183
0.0064
0.0233
0.0173
0.0262
0.0262
0.0120
0.0120
0.0120
0.0000
110
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0274
0.0262
0.0262
0.1467
0.0000
0.0094
0.0010
0.0010
0.0001
0.0000
0.0120
0.0002
0.0049
0.0150
0.0004
0.0173
0.0173
0.0010
0.0026
0.0210
0.0000
0.0018
0.0000
0.0010
0.0033
0.0067
111
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0000
0.0043
0.0274
0.0000
0.0016
0.0003
0.0057
0.0071
0.0085
0.0101
0.0114
0.0070
0.0016
0.0154
0.0014
0.0008
0.0019
0.0262
0.0026
0.0086
0.1385
0.6026
0.0786
0.0004
0.1609
0.0786
112
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0786
0.0411
0.0892
0.0786
2.2365
0.0016 Std. Err. B
Table A-23. Std. Error of b:
Y5- Calories
(X - X bar)^2
0.0003
0.0025
0.0000
0.0008
0.0168
0.0038
0.0076
0.0016
0.0305
0.0154
0.0305
0.0154
0.0014
0.0001
0.0003
113
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0047
0.0020
0.0268
0.0150
0.0215
0.0055
0.0131
0.0160
0.0127
0.0183
0.0064
0.0233
0.0173
0.0262
0.0262
0.0120
0.0120
0.0120
0.0000
0.0274
0.0262
0.0262
0.1467
0.0000
0.0094
0.0010
114
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0010
0.0001
0.0000
0.0120
0.0002
0.0049
0.0150
0.0004
0.0173
0.0173
0.0010
0.0026
0.0210
0.0000
0.0018
0.0000
0.0010
0.0033
0.0067
0.0000
0.0043
0.0274
0.0000
0.0016
0.0003
0.0057
115
COLD CEREAL PRICES AND INGREDIENT CONTENT
0.0071
0.0085
0.0101
0.0114
0.0070
0.0016
0.0154
0.0014
0.0008
0.0019
0.0262
0.0026
0.0086
0.1385
0.6026
0.0786
0.0004
0.1609
0.0786
0.0786
0.0411
0.0892
0.0786
0.0760
0.0784
0.0786
116
COLD CEREAL PRICES AND INGREDIENT CONTENT
2.4629
0.2391 Std. Err. B