Question

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

Answer 1

see explaination

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