TABLE 14-6
One of the Most Common Questions of Prospective

TABLE 14-6
One of the most common questions of prospective house buyers pertains to the average cost of heating in dollars (Y) . To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X₁) , the amount of insulation in inches (X₂) , the number of windows in the house (X₃) , and the age of the furnace in years (X₄) . Given below are the EXCEL outputs of two regression models.
$\begin{array}{ll}\text { Model } 1 \\\text { Regression Statistics } \\\hline \text { R Square }& 0.8080 \\\text { AdjustedR S quare }& 0.7568 \\\text { Observations } &20 \end{array}$

ANOVA
$\begin{array}{lrrccc} & \text { df } &{S S} & M S & F & \text { Signuficance F } \\\hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 2.96869 E-05 \\\text { Residual } & 15 & 40262.3259 & 2684.155 & & \\\text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrrr} && \text { Standard } & & \text {Lower} & \text {Upper }\\& \text {Coefficients} & \text {Error} & \text { t Stat } & \text {p -value} & 90.0 \% & 90.0 \% \\ \hline \text { Intercept }& 421.4277 & 77.8614 & 5.4125 & 7.2 \mathrm{E}-05& 284.9327 & 557.9227 \\ \text { X{1} (Temperature) } & -4.5098 & 0.8129 & -5.5476 &5.58 \mathrm{E}-05 & -5.9349 & -3.0847 \\ \text {X{2} (Insulation) }& -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\ \text { X{3} (Windows) }& 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\ \text { X{4} (Furnace Age) } & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702 \\\hline\end{array}$

$\begin{array}{ll} \text { Model 2} \\\hline \text {Regression Statistics} \\\hline \text {R Square }& 0.7768\\ \text {Adjusted R Square }&0.7506 \\ \text {Observations }& 20 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrcc}\hline & \text { d f} & \text { SS } & \text { MS } & \text {SS } & \text {Significance F } \\\hline \text {Regression} & 2 & 162958.2277 & 81479.11 & 29.5923 & 2.9036 \mathrm{E}-06 \\ \text {Residual }& 17 & 46807.5222 & 2753.384 & & \\ \text {Total }& 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lcccccc} && \text { Standard } & &\text { Lower} &\text { Upper} \\& \text {Coefficients }&\text { Error }&\text { t Stat }& \text { p -value} &95 \%& 95 \% \\\hline \text {Intercept }& 489.3227 & 43.982611 .1253 &3.17 \mathrm{E}-09& 396.5273 & 582.1180 \\\text { X{1} (Temperature) }& -5.1103 & 0.6951-7.3515 & 1.13 \mathrm{E}-06 & -6.5769 & -3.6437 \\\text { X{2} (Insulation) }& -14.7195 & 4.8864-3.0123 & 0.0078 & -25.0290 & -4.4099 \\\hline\end{array}$

-Referring to Table 14-6 and allowing for a 1% probability of committing a type I error, what is the decision and conclusion for the test H₀ :?₁ = ?₂ = ?₃ = ?₄ = 0 versus H₁ : At least one ?j ? 0, j = 1, 2,...,4 using Model 1?

A) Reject H₀ and conclude that the 4 independent variables taken as a group have significant linear effects on average heating costs.
B) Do not reject H₀ and conclude that the 4 independent variables taken as a group do not have significant linear effects on average heating costs.
C) Reject H₀ and conclude that the 4 independent variables taken as a group do not have significant linear effects on average heating costs.
D) Do not reject H₀ and conclude that the 4 independent variables have significant individual linear effects on average heating costs.