Instruction 13-6
One of the Most Common Questions of Prospective

question 111

Multiple Choice

Instruction 13-6
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 Celsius (X₁) ,the amount of insulation in cm (X₂) ,the number of windows in the house (X₃) ,and the age of the furnace in years (X₄) .Given below are the Microsoft Excel outputs of two regression models.
$\begin{array}{lr}{\text { Model 1 }} \\\hline {\text { Regression Statistics }} \\\hline \text { R Square } & 0.8080 \\\text { Adjusted R Square } & 0.7568 \\\text { Observations } & 20 \\\hline\end{array}$
ANOVA
$\begin{array}{lrrrrrr}\hline & d f & & S S & M S & F & \text { Significance } F \\\hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 2.96869 \mathrm{E}-05 \\\text { Residual } & 15 & 40262.3259 & 2684.155 & & \\\text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrrr}\hline & \text { Coefficients } & \text { Standard Error } & {t \text { Stat }} & {\text { P-value }} & \text { Lower 90.0\% } & \text { Upper 90.0\% } \\\hline \text { Intercept } & 421.4277 & 77.8614 & 5.4125 & 7.2 \mathrm{E}-05 & 284.9327 & 557.9227 \\\mathrm{X}_{1} \text { (Temperature) } & -4.5098 & 0.8129 & -5.5476 & 5.58 \mathrm{E}-05 & -5.9349 & -3.0847 \\\mathrm{X}_{2} \text { (Insulation) } & -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\\mathrm{X}_{3} \text { (Windows) } & 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\\mathrm{X}_{4} \text { (Furnace Age) } & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702\end{array}$ $\begin{array}{l}\text { Model } 2\\\begin{array}{lr}\hline {\text { Regression Statistics }} \\\hline \text { R Square } & 0.7768 \\\text { Adjusted R } & \\\text { Square } & 0.7506 \\\text { Observations } & 20 \\\hline\end{array}\end{array}$
ANOVA
$\begin{array}{lrrrrrr} & d f & &{\text { SS }} & M S & F & \text { Significance } F \\\hline \text { Regression } & & 2 & 162958.2277 & 81479.11 & 29.5923 & 2.9036 \mathrm{E}-06 \\\text { Residual } & 17 & 46807.5222 & 2753.384 & & \\\text { Total } & 19 & 209765.75 & & & \\\hline\end{array}$

$\begin{array}{lrrrrrrr} & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 489.3227 & 43.9826 & 11.1253 & 3.17 \mathrm{E}-09 & 396.5273 & 582.1180 \\\mathrm{X}_{1} \text { (Temperature) } & -5.1103 & 0.6951 & -7.3515 & 1.13 \mathrm{E}-06 & -6.5769 & -3.6437 \\\mathrm{X}_{2} \text { (Insulation) } & -14.7195 & 4.8864 & -3.0123 & 0.0078 & -25.0290 & -4.4099\end{array}$
-Referring to Instruction 13-6 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 vs.H₁: At least one ?_j ? 0,j = 1,2,... ,4 using Model 1?

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

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Definitions:

Price Elasticity of Demand

An indicator of the responsiveness of demand for a product to variations in its price, demonstrating how sensitive the quantity of the product demanded is to price fluctuations.

Advertising Elasticity of Demand

A measure of how advertising expenditures influence the quantity demanded of a product or service.

Price Elasticity of Demand

Measures how much the quantity demanded of a good responds to a change in its price, with higher elasticity indicating greater sensitivity to price changes.

Marginal Cost of Production

The increase in total production cost that arises from producing one additional unit of a good or service.