(please show your work for each question (including equations used and how to use them and the answers) Thank you

2. 17.3 Xr17-03 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 4 8 sheets) and the independent variables are as follows:

Number of building permits issued in the county

Five-year mortgage rates (in percentage points) Vacancy rate in apartments (in percentage points) Vacancy rate in office buildings (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.

Drywall

328

376

373

144

194

220

126

301

54

252

381

173

152

351

233

35

290

5

335

280

101

297

309

233

------------------------

Permits

49

79

79

50

37

53

22

69

21

46

79

30

38

73

55

12

62

12

60

49

14

66

62

40

---------------------------------

Mortgage

8.35

8.08

7.9

7.69

7

7.32

8.4

8.28

8

8.95

8.21

7.24

7.35

7.27

7.08

7.76

8.21

7.76

7.2

7.57

8.44

8.43

8.14

8.81

-------------------------

A Vacancy

2.98

5.6

2.25

4.26

2.6

2.97

5.35

3.13

5.6

4.81

5.88

2.98

5.69

4.86

5.68

4.46

2.23

5

2.42

3.25

3.61

2.13

4.35

2.31

-------------------------

O Vacancy

13.43

14.51

14.24

14.3

11.64

10.61

18.45

18.52

10.29

11.91

17.75

18.16

17.14

16.11

18.54

19.46

19.26

17.28

15.15

19.94

15.47

12.75

12.24

18.65