Question: The president of a company that manufactures drywall wants to analyze the variables that affect demand for his product. Drywall is used to construct walls in houses and offices. Consequently, the president decides to develop a regression model in which the dependent variable is monthly sales of drywall (in hundreds of 4x8 sheets and the independent variables are
Number of building permits issued in the county
Five year mortgage rates (in percentage points)
Vacancy rate in apartments (in percentage points)
To estimate a multiple regression model, he took monthly observations from the past 2 years.
a) Analyze the data using multiple regression
b) What is the standard error of estimate? Can you use this statistic to assess the model's fit? If so, how?
c) What is the coefficient of determination, and what does it tell you about the regression model?
d) Test the overall validity of the model
e) Interpret each of the coefficients
f) Test to determine whether each of the independent variables is linearly related to drywall demand in this model
g) Predict next month's drywall sales with 95% confidence if the number of building permits is 50,the 5-year mortgage rate is 9.0% and the vacancy rates are 3.6% in apartments and 14.3% in office buildings.
|
Drywall
|
Permits
|
Mortgage
|
A Vacancy
|
O Vacancy
|
|
|
328
|
49
|
8.35
|
2.98
|
13.43
|
|
|
376
|
79
|
8.08
|
5.6
|
14.51
|
|
|
373
|
79
|
7.9
|
2.25
|
14.24
|
|
|
144
|
50
|
7.69
|
4.26
|
14.3
|
|
|
194
|
37
|
7
|
2.6
|
11.64
|
|
|
220
|
53
|
7.32
|
2.97
|
10.61
|
|
|
126
|
22
|
8.4
|
5.35
|
18.45
|
|
|
301
|
69
|
8.28
|
3.13
|
18.52
|
|
|
54
|
21
|
8
|
5.6
|
10.29
|
|
|
252
|
46
|
8.95
|
4.81
|
11.91
|
|
|
381
|
79
|
8.21
|
5.88
|
17.75
|
|
|
173
|
30
|
7.24
|
2.98
|
18.16
|
|
|
152
|
38
|
7.35
|
5.69
|
17.14
|
|
|
351
|
73
|
7.27
|
4.86
|
16.11
|
|
|
233
|
55
|
7.08
|
5.68
|
18.54
|
|
|
35
|
12
|
7.76
|
4.46
|
19.46
|
|
|
290
|
62
|
8.21
|
2.23
|
19.26
|
|
|
5
|
12
|
7.76
|
5
|
17.28
|
|
|
335
|
60
|
7.2
|
2.42
|
15.15
|
|
|
280
|
49
|
7.57
|
3.25
|
19.94
|
|
|
101
|
14
|
8.44
|
3.61
|
15.47
|
|
|
297
|
66
|
8.43
|
2.13
|
12.75
|
|
|
309
|
62
|
8.14
|
4.35
|
12.24
|
|
|
233
|
40
|
8.81
|
2.31
|
18.65
|
|