Linear regression model
Montgomery, Peck, and Vining [2006] present data on the number of pounds of steam used per month at a plant. Steam usage is thought to be related to the average monthly ambient temperature. The past year"s usages and temperatures are shown in Table E3.2.
a. Fit a simple linear regression model to the data.
b. Test for significance of regression.
c. Analyze the residuals from this model.
d. Plant management believes that an increase in average ambient temperature of one degree will increase average monthly steam consumption by 10,000 lb. Do the data support this statement?
e. Construct a 99% prediction interval on steam usage in a month with average ambient temperature of 58°F.
TABLE E3.2 Monthly Steam Usage and Average Ambient Temperature
|
Month
|
Temperature (°F)
|
Usage/1000
|
Month
|
Temperature (°F)
|
Usage/1000
|
|
January
|
21
|
185.79
|
July
|
68
|
621.55
|
|
February
|
24
|
214.47
|
August
|
74
|
675.06
|
|
March
|
32
|
288.03
|
September
|
62
|
562.03
|
|
April
|
47
|
424.84
|
October
|
50
|
452.93
|
|
May
|
50
|
454.68
|
November
|
41
|
369.95
|
|
June
|
59
|
539.03
|
December
|
30
|
273.98
|