The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in F) for that month. The past year's usage and temp are shown in the following table:
Month Temp Usage/1000
Jan. 24 185.79
Feb 28 214.47
Mar 36 288.03
Apr 42 424.84
May 56 454.58
June 54 539.03
July 68 621.55
Aug 72 675.06
Sept 62 562.03
Oct 65 452.93
Nov 46 369.95
Dec 39 273.98
a) Assuming that a simple linear regression model is appropriate, fit the regression model relating steam usage (y) to the average temperature (x). What is the estimate of ?2? Graph the regression line.
b) What is the estimate of expected steam usage when the average temperature is 55 degrees F.
c) What change in mean steam usage is expected when the monthly average temp changes by 1 degree F?
d) Compute the fitted values.
e) Compute the residuals. Which point has the residual with the largest magnitude?
f) Compute the correlation between temp. and usage.