Question

A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (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:

SUMMARY OUTPUT

            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                      3605.7736         1201.9245                                 0.0000

Residual                          1214.2264             26.3962

Total                  49         4820.0000

                        Coeff             StdError               t Stat             p-value

Intercept         -1.6335             5.8078              -0.281              0.7798

Income             0.4485             0.1137             3.9545              0.0003

Size                  4.2615             0.8062               5.286              0.0001

School            -0.6517             0.4319              -1.509              0.1383

Referring to Table 14-4, which of the independent variables in the model are significant at the 5% level?

		Income, School
		Income, Size
		Size, School
		Income, Size, School

Answer 1

Given Information:

A real estate builder wants to know how house size (House) is influenced by family income (Income), family size (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 model in excel whose output is given.

To determine which independent variables in the model are significant at 5% level of significance by using p-value, we use the decision rule that if the p-value is less than 0.05 then the independent variable in the model is significant.

Independent variables	p-value
Income	0.0003
Size	0.0001
School	0.1383

The independent variable having p-value less than 0.05 are Income and size.

Hence, the second option is the correct answer.