Lab03 Solution

8/6/2019 Lab03 Solution

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Lab03-Solution STAT02-Spring2011


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(2) Climate change is a hot topic these days. One of the factors that may explain increases in global

temperatures is the amount of carbon dioxide in the atmosphere. Annual atmospheric carbon dioxide

(CO2) concentrations measured as parts per million by volume (ppmv) are derived from air samples

collected at Mauna Loa Observatory in Hawaii. Additionally the annual average global temperatures(degrees Celsius) are recorded. The data plotted below are for years from 1958 through 2003.


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(3) problem 2 looked at the relationship between global temperatures and the amount of carbon

dioxide in the atmosphere. Annual atmospheric carbon dioxide (CO2) concentrations measured as

parts per million by volume (ppmv) are derived from air samples collected at Mauna Loa

Observatory in Hawaii. Additionally the annual average global temperatures (degrees Celsius) are

recorded. Below are a plot and summaries of the data.


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4. In most jurisdictions, driving an automobile with a blood alcohol level(BAC) in excess of .08 is a

felony. Because of a number of factors, it is difficult to provide guidelines on when it is safe for

someone who has consumed alcohol to drive a car. In an experiment to examine the relationship

between blood alcohol level and the weight of a drinker, 50 men of varying weights were each given

three beers to drink and 1 hour later their blood alcohol level was measured. The data are stored in

bloodalcohol.JMP on the blackboard. we will assume that the simple linear regression model holds .

The graph suggests that the regression function looks approximately like a straight line and that a

simple linear regression model might be appropriate. The equation for the least squares regression line

is xy 0.000225+0.0331795 = . The residual plot shows that the simple linear regression model

appears to be reasonable. There does not seem to be any clear pattern in the residuals and the variance

of the residuals appears to be approximately stable.


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(a). A 95% confidence interval for the slope of the regression line is:

)0003671.0,000083.0()00007.0(011.2000225.0)(121 == bSEtb n .

.


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Note that t is the 5%(2tail) value from the t-table with n - 2= 48 degrees of freedom. The 95%

confidence interval can also be obtained directly from the JMP output by right clicking in parameter

estimates and clicking Columns and then Upper 95% and Lower 95%.

(b). A 90% confidence interval for the slope of the regression line is:

)00034239.0,00001076.0()00007.0(677.1000225.0)( 121 == bSEtb n .

Note that t is the 10 %( 2tail) value from the t-table with n - 2= 48 degrees of freedom.

(c). Assume that the simple linear regression model holds and xxyE10

)|( += . If drinking more

beers is associated with an increase in average blood alcohol content in the population of all students,

then 01 > . If we want to test whether drinking more beers is associated with an increase in average

blood alcohol content, then we should do a one sided test of 0: 10 =H vs. 0: 1 >aH . It is also

acceptable to do a two-sided test 0: 10 =H vs. From the JMP output, we see that the p-value for the

two sided test is =0.0025. The estimated slope1 is 0.002250>0 and the p-value is


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0: 10 =H vs. 0: 1 aH

Test statistics from JMP ANOVA table F= 10.1462. ( Note here which is (3.19)^2= square of the t-value.

This is true for simple linear regression.)

df denominator =48 (df2)

df numerator=1 (df1)

p-value=0.0025 ( Notice this is the same as the p-value for t-test-this is true for simple linear regression)

So we reject Ho and conclude that there is linear dependency or model is useful.

(f) For the above test the test statistics F-ratio= 10.17.

The critical value from the F-table, we need df1=1, df2=48, alpha=0.05.

We dont have the 48, we will use the closer one which is 50.

The value is 4.03.And hence the test statistics is in the rejection region.

We will reject Ho and conclude that the model is useful.

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Lab03 Solution