The electric power consumed each month by a chemical plant isthought to be related to the average ambient temperature (x1), thenumber of days in the month (x2), the average product purity (x3),and the tons of product produced (x4). The past year’s historicaldata 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. Determinewhether or not the model you have assumed can be simplified bydropping any of the terms. Calculate the ANOVA table for the model,which you have determined. What is the estimate of the variance inthe electric power measurement? Plot residual plots to determine ifthe assumptions underlying your analysis are met. Is this normalassumption a good one here? Calculate parameter covariance andparameter correlation matrix for your model. Do you have anyconcerns on the basis of this matrix?
