Question

# Assume you ran a multiple regression to gain a better understanding of the relationship between lumber...

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

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

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