A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below: Allso SSR (X1 ∣ X2) = 36400.6326 and SSR (X2 ∣ X1) = 3297.7917
1. What fraction of the variability in house size is explained by income and size of family?
A. 84.79%
B. 71.89%
C. 17.56%
D. 70.69%
2. A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:
A. 70.64%
B. 71.50%
C. 73.62%
D. 15.00%
Also SSR (X1 ∣ X2) = 36400.6326 and SSR (X2 ∣ X1) = 3297.7917
3. Suppose the builder wants to test whether the coefficient on Income is significantly different from 0. What is the value of the relevant t-statistic?
A. 10.8668
B. 3.2708
C. 60.0864
D. -0.7630
Also SSR (X1 ∣ X2) = 36400.6326 and SSR (X2 ∣ X1) = 3297.7917
4. At the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of Size in the regression model?
A. Size is significant in explaining house size and should be included in the model because its p-value is less than 0.01.
B. Size is significant in explaining house size and should be included in the model because its p-value is more than 0.01.
C. Size is not significant in explaining house size and should not be included in the model because its p-value is more than 0.01.
D. Size is not significant in explaining house size and should not be included in the model because its p-value is less than 0.01.
Regression Statistics
Multiple R 0.8479
R Square 0.7189
Adjusted R Square 0.7069
Standard Error 17.5571
Observations 50
ANOVA
df SS MS F Significance F
Regression 37043.3236 18521.6618 o.
Residual 14487.7627 308.2503
Total 49 51531.0863
Coefficients Standard Error t Stat P-value
Intercept -5.5146 7.2273 -0.7630 0.4493
Income 0.4262 0.0392 10.8668 0.0000
Size 5.5437 1.6949 3.2708 0.0000