A real estate builder wishes to determine how house size (House) is influenced b
ID: 3319206 • Letter: A
Question
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:
Also SSR (X1 X2) = 36400.6326 and SSR (X2 X1) = 3297.7917
Referring to Table 14-4, what fraction of the variability in house size is explained by income and size of family?
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:
Referring to Table 14-4, when the builder used a simple linear regression model with house size (House) as the dependent variable and family size (Size) as the independent variable, he obtained an r2 value of 1.25%. What additional percentage of the total variation in house size has been explained by including income in the multiple regression? A. 70.64% B. 71.50% C. 73.62% D. 15.00%
Also SSR (X1 X2) = 36400.6326 and SSR (X2 X1) = 3297.7917
Referring to Table 14-4, 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
Referring to Table 14-4, 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 R Square Adjusted R Square Standard Error Observations 0.8479 0.7189 0.7069 17.5571 50 ANOVA Significance F 0.0000 df MS Regression Residual Total 37043.3236 18521.6618 14487.7627 51531.0863 308.2503 49 Coefficients Standard Error 7.2273 0.0392 1.6949 t Stat P-value Intercept Income Size 5.5146 0.4262 5.5437 0.4493 0.0000 0.0020 -0.7630 10.8668 0 3.2708
Explanation / Answer
DFR= K-1= 3-1=2
DFE= N-K =50-3= 47
F= MSR/MSE =60.08644
A) fraction of the variability in house size is explained by income and size of family?
R-squared or SSR/SST = 0.7189 or 71.89%
B) a simple linear regression model with house size (House) as the dependent variable and family size (Size) as the independent variable, he obtained an r2 value of 1.25%. What has additional percentage of the total variation in house size been explained by including income in the multiple regression?
R-squared- r2 value= 0.7189- 0.0125 =0.7064= 70.64%
C) The coefficient on Income test statistic: t -value of coefficient= 10.8668 p-value:0
D) at the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of Size in the regression model?
Answer: A. Size is significant in explaining house size and should be included in the model because its p-value is less than 0.01. Because p-value is 0.0020
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