V. A real estate builder wishes to determine how house size (House) is influenced by family income

Question:

V. A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Family Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below:

Exhibit 1

SUMMARY OUTPUT of House Size (in 100s of square feet) Regression Statistics Multiple R R Square Adjusted R Square Standa

1. Referring to exhibit 1, what fraction of the variability in house size is explained by income, size of family, and education?
27.0%
33.4%
74.8%
86.5%
2. Referring to exhibit 1, which of the independent variables in the model are significant at the 2% level?
Income, Size, School
Income, Size
Size, School
Income, School
3. Referring to exhibit 1, when the builder used a simple linear regression model with house size (House) as the dependent variable and education (School) as the independent variables, he obtained an r2 value of 23.0%. What additional percentage of the total variation in house size has been explained by including family size and income in the multiple regression?
2.8%
51.8%
72.6%
74.8%
4. Referring to exhibit 1, which of the following values for the level of significance is the smallest for which all explanatory variables are significant individually?
0.01
0.025
0.05
0.15
5. Referring to exhibit 1, which of the following values for the level of significance is the smallest for which the regression model as a whole is significant?
0.00005
0.005
0.01
0.05
6. Referring to exhibit 1, what is the predicted house size (in hundreds of square feet) for an individual earning an annual income of $40,000, having a family size of 4, and going to school a total of 13 years?
11.43
15.15
24.88
53.87
7. Referring to exhibit 1, 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?
5.286
5.195
3.945
- 1.509
8. Referring to exhibit 1, at the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of Income in the regression model?
Income is significant in explaining house size and should be included in the model because its p value is less than 0.01.
Income is significant in explaining house size and should be included in the model because its p value is more than 0.01.
Income is not significant in explaining house size and should not be included in the model because its p value is less than 0.01.
Income is not significant in explaining house size and should not be included in the model because its p value is more than 0.01.
9. Referring to exhibit 1, what is the value of the calculated F test statistic that is missing from the output for testing whether the whole regression model is significant?
0.0001
0.0299
0.726
33.408
10. Referring to exhibit 1, at the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of School in the regression model?
School is significant in explaining house size and should be included in the model because its p value is less than 0.01.
School is significant in explaining house size and should be included in the model because its p value is more than 0.01.
School is not significant in explaining house size and should not be included in the model because its p value is less than 0.01.
School is not significant in explaining house size and should not be included in the model because its p value is more than 0.01.
11. Referring to exhibit 1, what are the regression degrees of freedom that are missing from the output?
3
46
48
4
12. Referring to exhibit 1, what are the residual degrees of freedom that are missing from the output?
4
46
49
50