A real estate builder wishes to determine how house size (House) is influenced b
ID: 3200577 • Letter: A
Question
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Family 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:
Exhibit 1
SUMMARY OUTPUT of House Size (in 100s of square feet)
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 901.4434 0.0001
Residual 1214.2264 26.9828
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
Family_Size 4.2615 0.8062 5.286 0.0001
School – 0.6517 0.4319 – 1.509 0.1383
Referring to exhibit 1, what fraction of the variability in house size is explained by income, size of family, and education?
27.0%
33.4%
74.8%
86.5%
Explanation / Answer
as fraction of the variability in output is explained by input is given by R square in any regression analysis
therefore
fraction of the variability in house size is explained by income, size of family, and education =74.8%
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