Pomona Collegepages.pomona.edu/.../math158/ClickerQ_158_s16_post.docx · Web viewAn application of the multiple regression model generated the following results involving the F test

Math 158 – Linear ModelsSpring 2016Jo HardiniClicker Questions

Review

1. The p-value is defined as:

(a) The probability that H0 is true.(b) The probability that H0 is true given the observed data.(c) The probability of observing the data.(d) The probability of observing the data given H0 is true.(e) I’ve never encountered the definition of the p-value.

Review

2. In order to draw a causative conclusion, we typically need:

(a) a randomization experimental design(b) a random sample(c) a very large sample(d) a good theory for why the causation should exist(e) I have no idea

Review

3. Power is:

(a) The probability that H0 is true.(b) The probability that H0 is false.(c) The probability of observing our data.(d) The probability of rejecting H0.(e) I know power is good, but I can’t remember why.

SLR

4. True or False:The equation y = 5x + 2 represents the equation of a line with slope 2.

(a) True.(b) False.

SLR

5. True or False:

The lines y = 3x + 6 andy = -1/3x + 2

are perpendicular.

(a) True(b) False

SLR

6. Does the equation 12x - 8y + 4 = 0 determine a linear function of x?

(a) It does determine a linear function.(b) It does not determine a linear function.

SLR7. If the null hypothesis (that β1=0) is true, our SSE reduces to:(a) ∑ (Y i - Y) 2

(b) ∑ (Yi – Y i) 2

(c) ∑ (Yi - Y) 2

SLR

8. The regression technical conditions include:

(a) The Y variable is normally distributed(b) The X variable is normally distributed(c) The residuals are normally distributed(d) The slope coefficient is normally distributed(e) The intercept coefficient is normally distributed

SLR

9. What happens if the technical assumptions are violated?

(a) The inference goes askew.(b) The line doesn’t fit.(c) The sample isn’t representative.(d) It isn’t appropriate to draw a causation conclusion.

SLR

10. What other approach could we use to evaluate the relationship betweenbelonging to a Greek organization and GPA?Consider: 110 students: GPA & 46 in a Greek organization & 64 not.

(a) chi-squared test of independence(b) t-test for comparing means of independent groups(c) t-test for comparing means of dependent groups(d) z-test for comparing means of independent groups(e) chi-squared test of goodness-of-fit

SLR

11. Assuming that the 2009 season is representative of all MLB seasons, we would like to test if these data provide convincing evidence that the slope of the regression line for predicting runs from on-base plus slugging is different than 0. What are the appropriate hypotheses?(a) H0: b0 = 0

Ha: b0 ≠ 0(b) H0: b1 = 0

Ha: b1 ≠ 0(c) H0: β0 = 0

Ha: β0 ≠ 0(d) H0: β1 = 0

Ha: β1 ≠ 0

SLR12. Which of the below is the correct set of hypotheses and the p-value for testing the slope of the relationship between absences and GPACoefficients: Estimate Std. Err t-val Pr(>|t|)(Inter) 3.47 0.42 8.35 7.8e-09Absences -0.016 0.01 -1.9 0.068

(a) H0:b1=0 Ha:b1≠0 p-value=0.068

(b) H0:β1=0 Ha:β1 < 0p-value = 0.068/2 = 0.034

(c) H0:β1=0 Ha:β1 ≠ 0p-value = 0.068/2 = 0.034

(d) H0:b1=0 Ha:b1 < 0 p-value = 0.068/2 = 0.034

(e) H0:β1=0 Ha:β1 ≠ 0 p-value=7.8x10-9

SLR13. We created a 95% confidence interval for the mean GPA given 10 absences to be (3.20, 3.42). What is the correct interpretation?(a) There is a 95% chance that the mean GPA of students with 10 absences is between 3.20 and 3.42.(b) 95% of GPA averages (for students with 10 absences) are between 3.20 and 3.42.(c) 95% of GPAs (for students with 10 absences) are between 3.20 and 3.42.(d) We are 95% confident that the true mean GPA (for students with 10 absences) is between 3.20 and 3.42.(e) 95% of our intervals will have a mean GPA between 3.20 and 3.42.SLR

14. We created a 95% prediction interval for an individual GPA given 10 absences to be (3, 3.62). What is the correct interpretation?(a) There is a 95% chance that the mean GPA of students with 10 absences is between 3 and 3.62.(b) 95% of GPA averages (for students with 10 absences) are between 3 and 3.62.(c) 95% of GPAs (for students with 10 absences) are between 3 and 3.62.(d) We are 95% confident that the true mean GPA (for students with 10 absences) is between 3 and 3.62.(e) 95% of our intervals will have a mean GPA between 3 and 3.62.SLR

15. A confidence interval for a mean response at X:(a) has a constant (width) for any value of X.(b) increases in width as X increases.(c) decreases in width as X increases.(d) increases in width as X gets farther from X.(e) decreases in width as X gets farther from X.

SLR16. A prediction interval for an individual observation at X:(a) has a constant (width) for any value of X.(b) increases in width as X increases.(c) decreases in width as X increases.(d) increases in width as X gets farther from X.(e) decreases in width as X gets farther from X.

SLR17. R2 for the regression line for predicting runs from on-base plus slugging is 91.31%. Which of the below is the correct interpretation of this value?91.31% of(a) runs can be accurately predicted by on-base plus slugging.(b) variability in predictions of runs is explained by on-base plus slugging.(c) variability in predictions of on-base plus slugging is explained byruns.(d) variability in runs is explained by on-base plus slugging.(e) variability in on-base plus slugging is explained by runs.

SLR

18. Which SLR assumption is violated?

(a) linearity (b) constant variance of errors(c) independent errors(d) normal errors(e) outliers

SLR19. Which SLR assumption is violated?

(a) linearity(b) constant errors(c) independent errors(d) normal errors(e) outliers

SLR20. Which residuals are “best” ?

SLR21. Why do we plot the residuals versus fitted instead of explanatory?(a) because the residuals are correlated with the fitted variable. (b) because the residuals are correlated with the explanatory variable (c) because we want to be able to extend the model to incorporate more variables(d) because the explanatory variable is a linear combination of the fitted values

SLR22. Why do we plot the residuals versus fitted instead of observed?(a) because the residuals are correlated with the fitted variable. (b) because the residuals are correlated with the observed variable(c) because we want to be able to extend the model to incorporate more variables(d) because the observed variable is a linear combination of the fitted values

SLR23. Consider the following regression model:

E [Y ]=β0+β1∗X

If we go from X=20 to X = 40 in the model, we can interpret β1 as(a) E[Y] is larger by an amount of 20β1

(b) median[Y] is larger by a factor of e20 β1

.(c) E[Y] is larger by an amount of β1 ln2.(d) median[Y] is larger by a factor of2β1.


E [ ln (Y ) ]=β0+ β1 X





E [ ln (Y ) ]=β0+ β1 ln (X )





E [Y ]=β0+β1∗ln (X )




SLR27. The intercept in the multiple regression model

a. should be excluded if one explanatory variable has negative values. b. determines the height of the regression line. c. should be excluded because the population regression function does not go through the origin. d.is statistically significant if it is larger than 1.96.

SLR28. The local utility company surveys 101 randomly selected customers. For each survey participant, the company collects the following: annual electric bill ($) and home size (sq ft).

Regression equation:Annual bill = 0.55 * Home size + 15Predictor Coef SE Coef T PConstant 15 3 5.0 0.00Home size 0.55 0.24 2.29 0.024

What is the 99% confidence interval for the slope of the regression line?(A) 0.25 to 0.85 (B) 0.02 to 1.08 (C) -0.08 to 1.18 (D) 0.20 to 1.30 (E) 0.30 to 1.40

SLR29. The confidence interval for a single coefficient in a multiple regression a. makes little sense because the population parameter is unknown. b. should not be computed because there are other coefficients present in the model. c. contains information from other hypothesis tests (here only β0). d. should only be calculated if the regression R2 is large.

Linear Algebra30. Calculate [ 2 0

−3 1] [0 −12 2 ]

(a) [ 3 −1−2 2 ]

(b) [0 −22 5 ]

(c) [ 0 0−6 2]

(d) None of the above(e) This matrix multiplication is impossible

Linear Algebra31. If A and B are both 2x3 matrices, which of the following is not defined?(a) A+B(b) AtB(c) BA(d) ABt

(e) More than one of the above

Linear Algebra32. If A = [ 2 3 1

0 −1 3−2 0 4 ] and

B = [3 0 21 2 −13 1 0 ], what is the (3,2)-entry of AB?

(a) 0(b) 1(c) 3(d) 4(e) 8

Multiple Linear Regression33. Which of the below correctly describes the roles of variables in this regression model?

Est SE t value Pr(>|t|)(Intercept) 197.96 59.20 3.34 0.0058volume 0.71 0.06 11.67 0.0000coverpb -184.05 40.49 -4.55 0.0007

(a) response: weight explanatory: volume, paperback cover(b) response: weight explanatory: volume, hardcover cover(c) response: volume explanatory: weight, cover type(d) response: weight explanatory: volume, cover type

MLR34. An econometrician is interested in evaluating the relation of demand for building materials to mortgage rates in LA and SF.

Y = 10 + 5X1 + 8X2whereX1 = mortgage rate in %X2 = 1 if SF, 0 if LAY = demand in $100 per capita

holding constant the effect of city, each additional increase of 1% in the mortgage rate would lead to an estimated average ________ in the mean demand.(a) predicted $500 more per capita(b) predicted $500 less per capita(c) predicted $5 more per capita(d) predicted $5 less per capita

MLR35. Referring to


the effect of living in LA rather than SF is a ________ demand by an estimated ________ holding the effect of mortgage rate constant.(a) larger; $800 per capita(b) smaller; $800 per capita(c) larger, $8 per capita(d) smaller, $8 per capita

MLR36. Referring to


the fitted model for predicting demand in LA is ________.(a) 10 + 5X1(b) 10 + 13X1(c) 15 + 8X2(d) 18 + 5X1

MLR37. Referring to


the fitted model for predicting demand in SF is ________.(a) 10 + 5X1(b) 10 + 13X1(c) 15 + 8X2(d) 18 + 5X1

MLR38. A dummy variable (0,1) is used as an explanatory variable in a regression model when: (a) the variable involved is numerical.(b) the variable involved is categorical.(c) a quadratic relationship is suspected.(d) when two explanatory variables interact.

MLR39. If a categorical explanatory variable contains three categories, then _________ dummy variable(s) will be needed to uniquely represent these categories. (a) 1(b) 2(c) 3(d) 4

MLR40. An interaction term in a multiple regression model may be used when: (a) the coefficient of determination is small.(b) there is a quadratic relationship between the response and explanatory variables.(c) neither one of two explanatory variables contribute significantly to the regression model.(d) the relationship between X1 and Y changes for differing values of X2.

MLR41. Referring to


to test whether there is a location effect on demand, one would use:(a) an F test on the significance of the whole regression model.(b) a t test on the significance of β1.(c) a t test on the significance of β2.(d) None of the above.

MLR42. The F statistic for testing the entire regression model can be expressed as:

(a) SSR/SSE.(b) MSE/MSR.(c) MSR/MSE.(d) MSR/SST.

MLR43. The adjusted R2 is "adjusted for" the:

(a) number of predictors only.(b) sample size only.(c) number of predictors and the sample size.(d) None of the above.

MLR44. In a multiple regression model, which of the following is correct regarding the value of the adjusted R2?

(a) It can be negative.(b) It has to be positive.(c) It has to be larger than the coefficient of multiple determination (R2).(d) It can be larger than 1.

MLR 45. Which of the following is NOT an assumption for the multiple regression model?(a) Positive autocorrelation of error terms.(b) Normality of error terms.(c) Independence of error terms.(d) Constant variation of error terms.(e) At any combination of values of the independent variables, the error terms have a mean of 0.

MLR46. It is often a good idea to compute R2

adj, the adjusted R2, rather than just R2. This is done in order to(a) avoid overestimating the importance of the independent variables.(b) correct any problems that may arise from any of the model assumptions being violated.(c) avoid having a multiple regression model that contains too many variables.(d) avoid conducting t tests for each independent variable.

MLR47. An application of the multiple regression model generated the following results involving the F test of the overall regression model: p-value = 0.0012, R2 = 0.67, s = 0.076. The null hypothesis, which states that none of the explanatory variables are significantly related to the response variable, should be rejected, at the 0.05 level of significance.

A) TrueB) False

MLR48.

E [Y ]=β0+ β1 X1+β2X 2+β3 X12+β4 X2

2

Which test should be used to test the significance of the higher ordered terms (X1

2and X22)?

H0: β3=β4=0

Ha: At least one of β3 and β4 does not equal 0.

A) the overall nested F test.B) the R2

C) the partial nested F test.D) the t test.

MLR49. In a nested F test, the reduced model corresponds to the null hypothesis being true.(a) True(b) False

MLR50. In a nested F test, the full model corresponds to the alternative hypothesis being true.(a) True(b) False

MLR51. Each of the following linear hypothesis can be tested using the nested F-test with the exception of (a) β2 = 1 and β3 = β4 / β5

(b) β2 = 0(c) β1 + β2 = 1 and β3 = -2β4

(d) β0 = β1 and β1 = 0

MLR52. A multiple regression analysis was conducted for a dependent variable Y on 100 independent variables X1, X2, …, X100. Among other things, R2 was computed to be 0.87. What is the most appropriate way to interpret this?(a) 87 of the independent variables in the model are capable of accurately predicting Y.(b) We will accurately predict Y 87% of the time.(c) 87 of the independent variables are statistically significant, while the remaining 13 variables should be removed from the model.(d) 87% of the variation in the observed values y can be explained by the independent variables.

MLR53. Based on data from 9 days, a multiple regression was fit to the Dow Jones Index on the following 7 explanatory variables:i. high tempii. low tempiii. 1 if sunny iv. 1 if Yankees won v. # runs Yankees scoredvi. 1 if Mets wonvii. # runs Mets scored

What do you think of R2?(a) It will be low because none of the variables are likely to predict the Dow.(b) It will be high because that combo of variables is likely to predict the Dow.(c) It will be low for other (mathematical) reasons.(d) It will be high for other (mathematical) reasons.MLR54. In case of multiple regression the _______________ is the proportion of variation in the response variable that is explained by the combination of explanatory variables. (a) coefficient of correlation

(b) coefficient of partial determination(c) coefficient of regression(d) coefficient of multiple determination

MLR55. The _______________measures the proportion of variation in the response variable that is explained by each explanatory variable holding all other explanatory variables constant. (a) coefficient of correlation(b) coefficient of partial determination(c) coefficient of regression(d) coefficient of multiple determination

MLR56. For a multiple regression model, the computer output shows that the simple correlation coefficient between the response variable and one of the explanatory variables is 0.99. This result indicates that most likely the problem of multicollinearity exists in this model.

(a) TRUE(b) FALSE

MLR57. Suppose that in a multiple regression the F is significant, but none of the t-ratios are significant. This means that:(a) multicollinearity may be present(b) residuals are not independent(c) the regression is good(d) a nonlinear model would be a better fit(e) none of the above

MLR58. All of the following are possible effects of multicollinearity EXCEPT:a) the variances of regression

coefficients estimators may be larger than expected

b) the signs of the regression coefficients may be opposite of what is expected

c) a significant F ratio may result even though the t ratios are not significant

d) removal of one data point may cause large changes in the coefficient estimates

e) the VIF is zero

MLR59. For a quiz on 100 topics(you know nothing):Kelly knows 85 topics. Jamie knows 75 topics. Parker knows 55 topics. Riley knows 45 topics. Who should you choose to help you answer the questions?(a) Kelly(b) Jamie(c) Parker(d) Riley(e) can’t tell

MLR60. Who do you want to choose next?Kelly knows 85 topics. Jamie knows 75 topics. Parker knows 55 topics. Riley knows 45 topics. (a) Jamie(b) Parker(c) Riley(d) depends on overlap with Kelly(e) depends on overlap with Jamie, Parker, and Riley

MLR61. If you can pick two people, who do you pick?Kelly knows 85 topics. Jamie knows 75 topics. Parker knows 55 topics. Riley knows 45 topics. (a) Kelly plus person who overlaps least(b) Kelly plus person who overlaps the most(c) The two with the least overlap(d) The two with the most overlap(e) The two who have the largest union.

p-values

RA Fisher (1929)

“… An observation is judged significant, if it would rarely have been produced, in the absence of a real cause of the kind we are seeking. It is a common practice to judge a result significant, if it is of such a magnitude that it would have been produced by chance not more frequently than once in twenty trials. This is an arbitrary, but convenient, level of significance for the practical investigator, but it does not mean that he allows himself to be deceived once in every twenty experiments. The test of significance only tells him what to ignore, namely all experiments in which significant results are not obtained. He should only claim that a phenomenon is experimentally demonstrable when he knows how to design an experiment so that it will rarely fail to give a significant result. Consequently, isolated significant results which he does not know how to reproduce are left in suspense pending further investigation.”

George Cobb (2014)

Q: Why do so many colleges and grad schools teach p = .05?

A: Because that's still what the scientific community and journal editors use.

Q: Why do so many people still use p = 0.05?

A: Because that's what they were taught in college or grad school.

Basic and Applied Social Psychology (2015)With the banning of the NHSTP (null hypothesis significance testing procedures) from BASP, what are the implications for authors? Question 3. Are any inferential statistical procedures required? Answer to Question 3. No, because the state of the art remains uncertain. However, BASP will require strong descriptive statistics, including effect sizes. We also encourage the presentation of frequency or distributional data when this is feasible. Finally, we encourage the use of larger sample sizes than is typical in much psychology research, because as the sample size increases, descriptive statistics become increasingly stable and sampling error is less of a problem. However, we will stop short of requiring particular sample sizes, because it is possible to imagine circumstances where more typical sample sizes might be justifiable.

American Statistical Association’s Statement on p-values (2016)

1. P-values can indicate how incompatible the data are with a specified statistical model.

(a) TRUE(b) FALSE

2. P-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone.(a) TRUE(b) FALSE

3. Scientific conclusions and business or policy decisions should not be based only on whether a p- value passes a specific threshold.

(a) TRUE(b) FALSE

4. Proper inference requires full reporting and transparency.

(a) TRUE(b) FALSE

5. A p-value, or statistical significance, does not measure the size of an effect or the importance of a result.

(a) TRUE(b) FALSE

6. By itself, a p-value does not provide a good measure of evidence regarding a model or hypothesis.

(a) TRUE(b) FALSE

Dance of the p-values:

https://www.youtube.com/watch?v=5OL1RqHrZQ8

Your own p-value:

https://www.openintro.org/stat/why05.php?stat_book=os





MLR

62. Which of following is true?

(a) Influential points always reduce R2.

(b) High leverage points always reduce R2.

(c) All outliers are influential points.

(d) When the data set includes an influential point, the relationship between x and y is nonlinear.

(e) None of the above.

MLR63. Which of the below best describes the outlier?

(a) influential(b) low leverage(c) high leverage(d) none of the above

MLR64. Which of the below best describes the outlier?

(a) influential(b) low leverage(c) high leverage(d) none of the above

MLR65. 1 obs in top left, 25 each in bottom right. r (correlation) is:

(a) 0.9-0.99(b) 0.7-0.89(c) 0.4-0.69(d) 0 – 0.39(e) < 0

MLR65. Why does a case with large leverage have only the potential to be influential?(a) If the sample size is large, all outliers will be mitigated.(b) If the response at that point is consistent with the model given by the other points, the model won’t change.(c) It may influence the coefficients but not the residuals.(d) It doesn’t, high leverage points will always be influential.

MLR66. To check whether the ϵ i have homogeneous variance:(a) leverage plot(b) Cook’s Distance plot(c) DFBETAS plot(d) Residual plot(e) VIF plot

MLR67. To check whether the regression is being unduly influenced by the 11th observation.(a) leverage plot(b) Cook’s Distance plot(c) DFBETAS plot(d) Residual plot(e) VIF plot

MLR68. To check whether the regression on X3 is really linear (as the model states).(a) leverage plot(b) Cook’s Distance plot(c) DFBETAS plot(d) Residual plot(e) VIF plot

MLR69. Is there an observation that does not seem to fit the model?(a) leverage plot(b) Cook’s Distance plot(c) DFBETAS plot(d) Residual plot(e) VIF plot

Shrinkage Methods70. Recall that n is the size of the data set and p is the dimension of the coefficient vector.

What is the size of the matrix that gets inverted in ridge regression?

(a) p x p(b) n x n(c) np x np(d) n2 x n2

Shrinkage Methods

71. As λ 0 (in ridge regression or lasso)

(a) RR coefficients ∞(b) RR coefficients 0(c) RR coefficients OLS coefficients

Shrinkage Methods

72. As λ ∞ (in ridge regression or lasso)

(a) RR coefficients ∞(b) RR coefficients 0(c) RR coefficients OLS coefficients

Shrinkage Methods73. The main motivation of ridge regression is that it:

(a) minimizes bias(b) minimizes variance(c) minimizes bias and variance(d) maximizes bias(e) maximizes variance

Shrinkage Methods74. The best procedure to test for multicollinearity is(a) to examine the correlation matrix. (b) to examine the pairs plot(c) to use the variance inflation factor. (d) to use ridge regression.

Shrinkage Methods75. The lasso outperforms ridge regression at the cost of an increase in complexity.(a) Always(b) Sometimes(c) Never

Shrinkage Methods76. Which of the following is associated with the procedure to get regression parameter estimates with smaller standard errors (a) piece-wise regression (b) polynomial regression (c) ridge regression (d) stepwise regression(e) lasso regression

Smoothing77. With step basis function, C0 through CK, (a) all K+1 functions can be used as explanatory variables.(b) any K functions can be used as explanatory variables(c) C1 through CK should be used as explanatory variables(d) any K-1 functions can be used as explanatory variables(e) C2 through CK should be used as explanatory variables

Smoothing78. In the step function model, how is β j interpreted? (On the basis function I(cj <= X < cj+1) .)

(a) the value of Y over cj <= X < cj+1

(b) the average value of Y over cj <= X < cj+1

(c) the increase in Y from X < c1 to cj <= X < cj+1

(d) the increase in average Y from X < c1 to cj <= X < cj+1

Smoothing

79. In a polynomial model, what is the jth basis function?

(a) X(b) X2

(c) Xj-1

(d) Xj

(e) Xj+1

Smoothing80. What mathematics gives the needed information in order to perform inference for any basis function model?

(a) calculus(b) Lagrange multipliers(c) linear algebra

Smoothing

81. Fitting separate polynomial models locally can be problematic because

(a) the variability at the extremes is high(b) the higher order derivatives may not be continuous(c) the step function may not be continuous(d) the model can be numerically unstable because the explanatory variables are highly correlated

Smoothing

82. T o fit a piecewise linear function with 3 knots, continuous at the nodes, one needs(A) 3 bases functions(B) 4 bases functions(C) 5 bases functions(D) 6 bases functions

Smoothing

83. How many degrees of freedom do we have left when fitting a cubic regression spline with K knots?

(a) K(b) K + 3(c) K + 4(d) n – K (e) n – K – 4

Smoothing84. Why is it difficult to extend local regression (loess) to higher dimension?

(a) in high dimensions all points are far from one another(b) inverting matrices with p > 2 is computationally difficult(c) distance is difficult to compute in high dimensions

Smoothing85. Tricubic weight functions:

(a) give decreasing (non-zero) weights for all Xi values(b) cannot be computed for s > 1 “proportion” of the data(c) can only be computed using Euclidean distance(d) can sometimes be negative(e) none of the above

ANOVA86. Which of the following is a necessary assumption to conduct a one-way ANOVA comparing r population means?(a) The r populations have equal variances.(b) The r populations all have normal distributions.(c) The samples are randomly selected, independent samples.(d) All of the above.

ANOVA87. In a one-way ANOVA F test, the "between group" variation is attributable to:(a) experimental error.(b) unexplained variation.(c) treatment effects.(d) residual variation

ANOVA88. Which of the following components in an ANOVA table are not additive? (a) Sum of squares.(b) Degrees of freedom.(c) Mean squares.(d) It is not possible to tell.

ANOVA89. The ______ sum of squares measures the variability of the observed values of the response variable around their respective treatment means.(a) treatment(b) error(c) interaction(d) total

ANOVA90. The ________ sum of squares measures the variability of the sample treatment means around the overall mean.(a) treatment(b) error(c) interaction(d) total

ANOVA91. What are the correct hypotheses for testing for a difference between the mean concentrations among the three levels?(a) H0: µ1=µ2=µ3

Ha: µ1≠µ2≠µ3

(b) H0: µ1≠µ2≠µ3

Ha: µ1=µ2=µ3

(c) H0: µ1=µ2=µ3

Ha: at least one pair of means are different

(d) H0: µ1=µ2=µ3=0Ha: at least one pair of means are

different(e) H0: µ1=µ2=µ3

Ha: µ1>µ2>µ3

ANOVA92. When conducting a one-way ANOVA, the ______ the between-treatment variability is when compared to the within-treatment variability, the ________ the value of F will be tend to be.

(a)smaller, larger(b)larger, smaller(c) larger, larger(d)smaller, more random(e)larger, more random

ANOVA93. What is the conclusion of the hypothesis test? (p=0.0064, F test)The data provide convincing evidence that the average concentration(a) is different for all groups.(b) at level 1 is lower than the other levels.(c) is different for at least two of the groups.(d) is the same for all groups

ANOVA94. The degrees of freedom for the F test in a one-way ANOVA are: (a)(nT - r) and (r - 1)(b)(r - 1) and (nT - r)(c) (r – nT) and (nT - 1)(d)(nT - 1) and (r – nT)

ANOVA95. After rejecting the null hypothesis of equal treatments, a researcher decided to compute a 95% confidence interval for the difference between the mean of treatment 1 and mean of treatment 2 based on Tukey's procedure. At α = 0.05, if the confidence interval includes the value of zero, then we can reject the hypothesis that the two population means are equal.(a)True(b)False

ANOVA96. The Tukey procedure is used: (a)to test for normality.(b) to test for homogeneity of variance.(c) to test independence of errors.(d)to test for differences in pair-wise means

ANOVA97. Suppose a variable has 3 levels: high, middle, and low. If

α= 0.05 (FWER), what should be the modified significance level (using Bonferroni) for two sample t- tests for determining which pairs of groups have significantly different means?(a) * α = 0.05(b) * α = 0.05/2 = 0.025(c) * α = 0.05/3 = 0.0167(d) * α = 0.05/6 = 0.083

ANOVA98. Based on the p-values given below, which pairs of means are significantly different? (Use the Bonferroni criterion)t-test between low & high: p=0.0052t-test between low & mid: p=0.1236t-test between mid & high: p=0.0544(a) low & high(b) mid & high(c) low & mid; mid & high(d) low & mid; low & high; mid & high(e) none of the above

ANOVA99. Which procedure cannot be used for data snooping? (a)Bonferroni(b)Tukey(c) Scheffé(d)they can all be used

ANOVA100. If the F-test for treatments is not significant but the t-test for one of the contrasts is significant, is it proper to report the contrast?(a) Yes(b) Only if the contrast was planned in advance.(c) If you adjust for multiple comparisons and it is still significant.(d) Maybe(e) No

ANOVA101. In a balanced two-way ANOVA the degrees of freedom for the error term are (n is group size): (a)(a - 1)(b - 1)(b)ab(n - 1)(c) (a - 1)(d)abn + 1

ANOVA102. In a balanced two-way ANOVA the degrees of freedom for the interaction term are: (a)(a - 1)(b - 1)(b)ab(n - 1)(c) (a - 1)(d)abn + 1

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103. If you are comparing the average sales between two different brands you are dealing with a two-way ANOVA design.

(a)True(b) False

ANOVA104. In a two-way ANOVA, the interpretations of the main effects (on their own) make sense only when the interaction component is not significant.

(a) True(b) False

ANOVA105. In a two-way ANOVA setting, when there are more than two levels of a factor and there is no significant interaction effect, Tukey's multiple comparison procedure can be used to perform pair-wise mean comparisons.(a)True (b) False

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106. If a plot of the means of Factor B verses the Factor A treatments produces parallel plots, then one could conclude that there was an interaction effect between A and B.

(a)True(b)False

ANOVA107. In two-way ANOVA, what should you always test first?(a) The significance of factor A.(b) The significance of factor B.(c) The interaction between factors A and B.(d) None of the above.

ANOVA108. Based on the results of a two-way ANOVA (without interaction), the SSE was computed to be 139.42. If we ignore one of the factors and perform a one-way ANOVA using the same data, will the SSE be smaller than 139.42?(a) Yes. Using the same data, the SSE based on a one-way ANOVA is always smaller than the SSE based on a two-way ANOVA.(b) No. Using the same data, the SSE based on a one-way ANOVA is never smaller than the SSE based on a two-way ANOVA.(c) Possibly. The SSE based on a one-way ANOVA could be smaller or larger than the SSE based on a two-way ANOVA.

ANOVA109. The R2 from the interactive model is 0.928 and the R2 from the additive model is 0.893. All else being equal (i.e. response is the same!), we should take the model with interaction because the R2 is higher.

(a) TRUE(b) FALSE

ANOVA110. Why is balance important?(a) easier calculations(b) easier interpretations(c) increased power(d) some of the above(e) all of the above

The simple row and column means in a balanced table produce simple estimate of model parameters.To see that the treatment effects (A) are not influenced by block differences (B), try adding a certain fixed amount to all responses in one block. It will not change any of the treatment differences in a balanced table. But it will in an unbalanced table.

ANOVA111. If the interaction is significant but the main effects aren’t:(a) report on the significance of the main effects(b) remove the main effects from the SSTR(c) avoid talking about main effects(d) test whether the main effects are significant without interaction in the model

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Pomona Collegepages.pomona.edu/.../math158/ClickerQ_158_s16_post.docx · Web viewAn application of the multiple regression model generated the following results involving the F test