SCENARIO 13-4
a Real Estate Builder Wishes to Determine How

SCENARIO 13-4
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size) .House size is measured in hundreds of square feet and income is measured in thousands of dollars.The builder randomly selected 50 families and ran the multiple regression.Partial Microsoft Excel output is provided below: $\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.8479 \\\text { R Square } & 0.7189 \\\text { Adjusted R Square } & 0.7069 \\\text { Standard Error } & 17.5571 \\\text { Observations } & 50\\\hline \end{array}$

$\text { ANOVA }$
$\begin{array}{lrrrrr} & d f & \text { SS } & {M S} & F & \text { Significance } F \\\hline \text { Regression } & & & 37043.3236 & 18521.6618 & 0.0000 \\\text { Residual } & & 14487.7627 & 308.2503 & \\\text { Total } & & 49 & 51531.0863 & &\end{array}$

$\begin{array}{lrrrr}\hline & \text { Coefficients } & \text { Standard Error } &{t \text { Stat }} & \text { P-value } \\\hline \text { Intercept } & -5.5146 & 7.2273 & -0.7630 & 0.4493 \\\text { Income } & 0.4262 & 0.0392 & 10.8668 & 0.0000 \\\text { Size } & 5.5437 & 1.6949 & 3.2708 & 0.0020\\\hline \end{array}$

$\text { Also } \operatorname{SSR}\left(X_{1} \mid X_{2}\right) =36400.6326 \text { and } \operatorname{SSR}\left(X_{2} \mid X_{1}\right) =3297.7917$


-Referring to SCENARIO 13-4 and allowing for a 1% probability of committing a type I error,what is the decision and conclusion for the test H: $\beta$ 1 - $\beta$ 2=0 vs.H : At least one $\beta$ j $\neq$ 0, j - 1, 20 1 2 1 j?

A) Do not reject H0 and conclude that the 2 independent variables taken as a group have significant linear effects on house size.
B) Do not reject H0 and conclude that the 2 independent variables taken as a group do not have significant linear effects on house size.
C) Reject H0 and conclude that the 2 independent variables taken as a group have significant linear effects on house size.
D) Reject H0 and conclude that the 2 independent variables taken as a group do not have significant linear effects on house size.