A power company located in southern Alabama wants to predict the peak power load (i.e., Y, the maximum amount of power that must be generated each day to meet demand) as a function of the daily high temperature (X). A random sample of 25 summer days is chosen, and the peak power load and the high temperature are recorded on each day. The file P10_40.xlsx contain these observations.
a. Use the given data to estimate a simple linear regression equation. How well does the regression equation fit the given data?
b. Examine the residuals of the estimated regression equation. Do you see evidence of any violations of the assumptions regarding the errors of the regression model?
c. Calculate the Durbin–Watson statistic on the model’s residuals. What does it indicate?
d. Given your result in part d, do you recommend modifying the original regression model in this case? If so, how would you revise it?
e. Use the final version of your regression equation to predict the peak power load on a summer day with a high temperature of 90 degrees.
f. Find a 95% prediction interval for the peak power load on a summer day with a high temperature of 90 degrees.
h. Find a 95% confidence interval for the average peak power load on all summer days with a high temperature of 90 degrees.