The Energy Conservation Committee at National Electronics Company is trying to understand energy use at their plant. As a first step, the committee wants to build a model that will predict monthly energy use as a function of production volumes (Production), daily outside tempera-ture (Temperature), and number of workdays (Days). The following table summarizes the data they have been able to collect for the previous year.
|
Month
|
Energy
use
|
Temperature
|
Days
|
Production
|
|
1
|
450
|
42
|
24
|
121
|
|
2
|
442
|
56
|
21
|
116
|
|
3
|
499
|
62
|
24
|
132
|
|
4
|
484
|
68
|
25
|
109
|
|
5
|
479
|
78
|
25
|
115
|
|
6
|
507
|
85
|
26
|
119
|
|
7
|
515
|
89
|
25
|
118
|
|
8
|
501
|
81
|
24
|
116
|
|
9
|
513
|
73
|
24
|
132
|
|
10
|
480
|
67
|
25
|
127
|
|
11
|
492
|
58
|
24
|
122
|
|
12
|
466
|
50
|
23
|
117
|
a. Build a linear model to predict energy use based on all three potential explanatory variables.
b. What level of energy use would the model in (a) predict for a month in which there was an average temperature of 44, monthly production of 120, and 25 days of work at the plant?
c. What percentage of the variability in energy use is accounted for by the model in (a)?
d. According to the model in (a), what are the marginal impacts on energy use of a one-unit increase in temperature and a one-unit increase in production?
e. Evaluate each of the four regression parameters in (a) to determine whether any are likely to be zero. Eliminate those parameters with a high probability of being zero from the model and estimate a new model. Compare the advantages and disadvantages of this model to the one in (a).