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 measured in years. The builder randomly selected 50 families and ran a multiple regression. The regression statistics are below:

Regression Statistics

R Square		0.748
Adjusted R Square		0.726
Standard Error		5.195
Observations		50

ANOVA Table
	df	SS			MS			F			Sig. F
Regression			3605.7736			901.4434						0.0001
Error			1214.2264			29.9892
Total	49		4820.0000

	Coefficient				Std. Error			T-test				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

Dependent variable is House.

Referring to the Real Estate Builder regression results, when the builder used a simple linear regression model with house size (House) as the dependent variable and education (School) as the independent variable, she obtained an Adjusted R Squared 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?

rev: 09_28_2018_QC_CS-140829

Multiple Choice

• 72.6%

• 2.8%

• 74.8%

• 49.6%

Answer 1

using given information. =o.748 R² gives idea about total variation explain by the independent variable tout dependent of variable :, Ans! 14.8%.