The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature (x1), the number of days in the month (x2), the average product purity (x3), and the tons of product produced (x4). The past year's historical data are available and are presented in the following table:
|
y
|
x1
|
x2
|
x3
|
x4
|
|
240
|
25
|
24
|
91
|
100
|
|
236
|
31
|
21
|
90
|
95
|
|
270
|
45
|
24
|
88
|
110
|
|
274
|
60
|
25
|
87
|
88
|
|
301
|
65
|
25
|
91
|
94
|
|
316
|
72
|
26
|
94
|
99
|
|
300
|
80
|
25
|
87
|
97
|
|
296
|
84
|
25
|
86
|
96
|
|
267
|
75
|
24
|
88
|
110
|
|
276
|
60
|
25
|
91
|
105
|
|
288
|
50
|
25
|
90
|
100
|
|
261
|
38
|
23
|
89
|
98
|
Fit a multiple linear regression model to this data. Determine whether or not the model you have assumed can be simplified by dropping any of the terms. Calculate the ANOVA table for the model, which you have determined. What is the estimate of the variance in the electric power measurement? Plot residual plots to determine if the assumptions underlying your analysis are met. Is this normal assumption a good one here? Calculate parameter covariance and parameter correlation matrix for your model. Do you have any concerns on the basis of this matrix?