A real estate builder wishes to determine how house size is influenced by family income, family size, and education of the head
of household. House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is measured in years. A computer output is shown below.
Regression Statistics
Multiple R
0.865
R Square
0.748
Adjusted R Square
0.726
Standard Error
5.195
Observations
50
ANOVA
df
SS
MS
F
Signif F
Regression
3
3605.7736
901.4434
33.4081
0.0001
Residual
46
1214.2264
26.9828
49
4820.0000
Coeff.
St.Error
t Stat
P-value
Intercept
-1.6335
5.8078
-0.281
0.7798
Family Income
0.4485
0.1137
3.9545
0.0003
Family Size
4.2615
0.8062
5.286
0.0001
Education
-0.6517
0.4319
-1.509
0.1383
1) What is the predicted house size (in hundreds of square feet) for an individual earning an annual income of 40 (which is measured in thousands of dollars), having a family size of 4, and having 13 years of education?
Select one:
a. 2.42
b. 162.15
c. 19.20
d. 24.88
e. 7.16
2) Conduct a test to see if the multiple linear regression model seems reasonable overall at the 1% level of significance. The test would reveal that …
Select one:
a. Model is reasonable
b. Model is not reasonable
c. Not enough information to draw any conclusion
3) At 1% level of significance, which of the following variables can be removed without significantly hurting the model?
Select one:
a. Family income
b. Family size
c. Education
d. Both family income and family size
e. None
Regression Statistics
Multiple R
0.865
R Square
0.748
Adjusted R Square
0.726
Standard Error
5.195
Observations
50
ANOVA
df
SS
MS
F
Signif F
Regression
3
3605.7736
901.4434
33.4081
0.0001
Residual
46
1214.2264
26.9828
49
4820.0000
Coeff.
St.Error
t Stat
P-value
Intercept
-1.6335
5.8078
-0.281
0.7798
Family Income
0.4485
0.1137
3.9545
0.0003
Family Size
4.2615
0.8062
5.286
0.0001
Education
-0.6517
0.4319
-1.509
0.1383
1) What is the predicted house size (in hundreds of square feet) for an individual earning an annual income of 40 (which is measured in thousands of dollars), having a family size of 4, and having 13 years of education?
Select one:
a. 2.42
b. 162.15
c. 19.20
d. 24.88
e. 7.16
2) Conduct a test to see if the multiple linear regression model seems reasonable overall at the 1% level of significance. The test would reveal that …
Select one:
a. Model is reasonable
b. Model is not reasonable
c. Not enough information to draw any conclusion
3) At 1% level of significance, which of the following variables can be removed without significantly hurting the model?
Select one:
a. Family income
b. Family size
c. Education
d. Both family income and family size
e. None
1 answer:
Answer:
see explaination
Step-by-step explanation:
1) Lets form the regression equation from the data results
Size = -1.633+ 0.4485*FamilyIncome + 4.2615*FamilySize - 0.6517*Education
-1.633+ 0.4485*40+ 4.2615*4 - 0.6517*13 =24.88
2) For the model to be reasonable, we must check the significant F stat from the anova table( see attachment)
From the table at attachment we can deduce; as the significant F is less 0.01 , we can safely conclude that the model is signifcant
3) all variables that have a p value less than 0.01 can be safely removed from the model as they do not contribute sigificantly from the model
so education can be removed from the model
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