Question

A real estate builder wishes to determine how house sze is influenced by family income, family size, and education of the head of household. House size is measured in hundreds of square feet, inome 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
What is the predicted house size (in hundreds of squae feet) for an individual earning an annual income of 60 (which is measured in thousands of dollars), having a family size of 3, and having 13 years of education?
Select one:
a. 2.42
b. 7.16
c. 48.17
d. 31.22
e. 29.59
At 3% 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
Based on the above model, how does increasing family size by 1 member influence the house size, assuming that all other variables remain unchanged?
Select one:
a. House size will increase on average by 426.15 sq. feet
b. House size will increase on average by 5.286 sq. feet
c. House size will change on average by 4.26 sq. feet
d. House size will change on average by 0.865 sq. feet

Answer 1

1.) 29.59

2.) Education

3.) a. House size will increase on average by 426.15 sq. feet

Explanation:

From the computer output given, we can create a multiple regression equation in the form ;

y = b1x1 + b2x2 + b3x3 +.. + c

y = house size

x1 = family income ; x2 = Family size ; x3 = Education

Multiple Regression equation :

y = 0.4485x1 + 4.2615x2 - 0.6517x3 - 1.6335

To predict y ;

Where x1 = 60 ; x2 = 3 ; x3 = 13

y = 0.4485(60) + 4.2615(3) - 0.6517(13) - 1.6335

y = 29.5889

2.)

The Pvalue of the variables from the computer output are as follows :

Family income = 0.0003

Family size = 0.0001

Education = 0.1383

Comparing the Pvalue and α

When Pvalue > α ; then we fail to reject the null and conclude that no correlation exists between the dependent and independent variable.

Hence at α = 3% ; α = 0.03

Only the Pvalue of education is > α ; hence, we conclude that at 3% confidence level, Education can be removed without significantly hurting the model.

3.)

Increasing family size by 1 will lead to a corresponding change in house size by the slope Coefficient of family size, the slope Coefficient of family size is 4.2615