Question

Assume you ran a multiple regression to gain a better understanding of the relationship between lumber sales, housing starts, and commercial construction. The regression uses lumber sales (in $100,000s) as the response variable with housing starts (in 1,000s) and commercial construction (in 1,000s) as the explanatory variables. The estimated model is Lumber Sales = β₀ +β₁Housing Starts + β₂ Commercial Constructions + ε. The following ANOVA table summarizes a portion of the regression results.

	df	SS	MS	F
Regression	2	180,770	90,385	103.3
Residual	45	39,375	875
Total	47	220,145
	Coefficients	Standard Error	t-stat	p-value
Intercept	5.37	1.71	3.14	0.0030
Housing Starts	0.76	0.09	8.44	0.0000
Commercial Construction	1.25	0.33	3.78	0.0005

The sample regression equation explains approximately ________% of the variation in the response LumberSales.

Multiple Choice

18

22

78

82

Answer 1

Solution:

We are given following Regression analysis output table:

	df	SS	MS	F
Regression	2	1,80,770	90,385	103.3
Residual	45	39,375	875
Total	47	2,20,145
	Coefficients	Standard Error	t-stat	p-value
Intercept	5.37	1.71	3.14	0.003
Housing Starts	0.76	0.09	8.44	0
Commercial Construction	1.25	0.33	3.78	0.0005

The sample regression equation explains approximately ________% of the variation in the response LumberSales.

That is we have to find: R² = coefficient of determination and it is given by:

From given table, SSR = 1,80,770 and SST = 2,20,145

Thus

Thus answer is D) 82

The sample regression equation explains approximately 82 % of the variation in the response LumberSales.