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 4×8 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)

           Vacancy rate in office buildings (in percentage points)

            To estimate a multiple regression model, he took monthly observations from the past 2 years.

1. Determine the regression line.
2. What is the standard error of estimate? Can you use this statistic to assess the model’s fit? If so, how?
3. What is the coefficient of determination, and what does it tell you about the regression model?
4. Test the overall validity of the model.
5. Test to determine whether each of the independent variables is linearly related to drywall demand in this model.
6. 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.

         g. Does it appear that the error variable is not normally distributed? Explain

         h. Is the variance of the error variable constant? Explain

         i. Is multicollinearity a problem in this model? Why?

         j. Use D-W test to determine if there are evidence of positive first-order autocorrelation?

Drywall	Permits	Mortgage	A Vacancy	O Vacancy
328	49	8.35	2.98	13.43
376	79	8.08	5.6	14.51
365	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
298	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
282	49	7.57	3.25	19.94
101	14	8.44	3.61	15.47

Answer 1

Summary output of this regression:

Regression Statistics
Multiple R	0.945307312
R Square	0.893605915
Adjusted R Square	0.867007394
Standard Error	42.63602162
Observations	21
ANOVA
	df	SS	MS	F	Significance F
Regression	4	244287.8574	61071.96436	33.59607496	1.33794E-07
Residual	16	29085.28543	1817.83034
Total	20	273373.1429
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-122.7502005	152.9559982	-0.802519692	0.434011698	-447.0024316	201.5020306	-447.0024316	201.5020306
Permits	4.775133752	0.429532573	11.11704688	6.1747E-09	3.864565373	5.68570213	3.864565373	5.68570213
Mortgage	20.02897754	18.05789756	1.109153348	0.283757601	-18.25205519	58.31001027	-18.25205519	58.31001027
A Vacancy	-12.511585	7.487834745	-1.670921625	0.11417856	-28.38508555	3.361915558	-28.38508555	3.361915558
O Vacancy	1.009482378	3.192951133	0.31615967	0.755968394	-5.75927165	7.778236405	-5.75927165	7.778236405

A.

Regression Line:

Drywall = -122.75 + 4.775*Permits + 20.0289*Mortgage -12.5115*(A vacany) + 1.0095*(O Vacancy)

B.

Std. error of the estimate = 42.636

We use Std. error to calculate the F-statistics which tells us about the model validity.

F-value = MS_Regression/(Std. error)²

C.

R², coefficient of determination = 0.8936

The coefficient of determination is interpreted as the proportion of the variance in the dependent variable that is predictable from the independent variables.

D.

Since the p-value for the F-statistics = 1.3379*10^-7 < 0.05

Thus model is significant.