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 Question 7: For this problem, use the “plastic hardness” data described in the text with problem #1

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 Question 7: For this problem, use the “plastic hardness” data described in the text with problem #1 .22.
(CHO1PR22.TXT) Make sure you understand which column is X and which is }° and
tead in the data accordingly.

a. Plot the data using PROC GPLOT. Include a smoothed function on the plot. Is the
relationship approximately linear?

b. Plot the 85% bounds (confidence band) for the mean (use i = riclm on the symbol1
statement).

c. Plot the 85% bounds for individual observations (use i = ricli on the symbol1
statement).

d. Give an estimate of the mean hardness that you would expect after 36 and 43 hours;
and a 95% confidence interval for each estimate. Which confidence interval is wider
and why is it wider?

e. Give a prediction for the hardness that you would expect for an individual piece of
plastic after 43 hours; give a 99% prediction interval for this quantity.

f. Calculate power for rejecting the null hypothesis that the regression slope is zero,
using a = 0.05 when 3; = 0.5.

g. Calculate power for the slope 3,: Assume n = 16, o? = MSE, and SS, = 1280.
(Note: this last value could be obtained with SAS using:

3
a
proc univariate data = (dataset name);

var time;

and looking at the output titled “Corrected SS” in the Moment s section.) Find the power for

rejecting the null hypotheses 3, = 0 using a = 0.08 significance test when 3; = 0.9. Then plot

the power as a function of 3, for values of 3, between -2.4 and 2.4 in increments of 0.3.

Question: 8. Given that R? = SSM/SST , show that R?/(1— R?) = SSM/SSE. If you have n = 25
cases and R? = 0.35, what is the F-statistic for the test that the slope is equal to zero?