TABLE 14-4
a Real Estate Builder Wishes to Determine

Multiple Choice

TABLE 14-4
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:
$\begin{array}{ll} & \text { Regression Stuistics } \\\hline \text { Multiple R } & 0.865 \\\text { R Square } & 0.748 \\\text { Adjusted R Square } & 0.726 \\\text { Standard Error } & 5.195 \\\text { Observations } &50 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrrr}\hline & \text { d f }& \text {S S } & \text {M S } & \text {F } & \text {Significance F } \\\hline \text {Regression} & & 3605.7736 & 1201.9245 & &0.0000 \\\text {Residual} & & 1214.2264 & 26.3962 & \\Total & 49 & 4820.0000 & & & \\\hline\end{array}$

$\begin{array}{lcccc}\hline & \text { Coefficients} & \text {Standard Error} & \text {t Stat }& \text {p -value} \\\hline \text {Intercept }& -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text {Income} & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text {Size} & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text {School }& -0.6517 & 0.4319 & -1.509 & 0.1383 \\\hline\end{array}$

-Referring to Table 14-4, when the builder used a simple linear regression model with house size (House) as the dependent variable and education (School) as the independent variable, he obtained an r² 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?

A) 51.8%
B) 72.6%
C) 2.8%
D) 74.8%