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

question 222

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,what are the degrees of freedom of the partial F test for H₀: ?₃ = ?₄ = 0 vs.H₁: At least one ?_j ? 0,j = 3,4?

• A)17 numerator degrees of freedom and 2 denominator degrees of freedom.
• B)2 numerator degrees of freedom and 15 denominator degrees of freedom.
• C)2 numerator degrees of freedom and 17 denominator degrees of freedom.
• D)15 numerator degrees of freedom and 2 denominator degrees of freedom.

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Definitions:

Cost of Goods Manufactured

The total cost of all materials, labor, and manufacturing overhead used in producing finished goods over a specific period.

Flexible Budgeting

A budgeting process that adjusts for changes in the volume of activity, rather than remaining static.

Direct Labor

The wages and related benefits of employees who are directly involved in the production of goods or the delivery of services.

Direct Materials

Raw materials that are directly incorporated into a finished product and are easily traceable to specific goods or services.