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 = β_{0} +β_{1}Housing Starts + β_{2} 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: R^{2} = 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.
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