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

question 143

Multiple Choice

SCENARIO 13-6
One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y) .To provide its customers with information on that matter, a large real estate firm used the following 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X1 ) and the amount of insulation in inches ( X 2 ) .Given below is EXCEL output of the regression model. $$\begin{array}{l}\begin{array} { l r } \hline { \text { Regression Statistics } } \\\hline \text { Multiple R } & 0.5270 \\\text { R Square } & 0.2778 \\\text { Adjusted R Square } & 0.1928 \\\text { Standard Error } & 40.9107 \\\text { Observations } & 20 \\\hline\end{array}\\\end{array}$$
$\begin{array}{lrrrrr}\text { ANOVA }\\\hline&\text { df } & \text { SS } & \text { MS } & F & \text { Significance F }\\\hline\text { Regression } & 2 & 10943.0190 & 5471.5095 & 3.2691 & 0.0629 \\\text { Residual } & 17 & 28452.6027 & 1673.6825 & & \\\text { Total } & 19 & 39395.6218 & & &\end{array}$ 13-22 Multiple Regression $$\begin{array}{l}\begin{array} { l r r r r r r } \hline & \text { Coefficients } &{ \text { Standard Error } } & { \text { t Stat } } & \text { P-volue } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 448.2925 & 90.7853 & 4.9379 & 0.0001 & 256.7522 & 639.8328 \\\text { Temperature } & - 2.7621 & 1.2371 & - 2.2327 & 0.0393 & - 5.3721 & - 0.1520 \\\text { Insulation } & - 15.9408 & 10.0638 & - 1.5840 & 0.1316 & - 37.1736 & 5.2919 \\\hline\end{array}\\\text { Also } \operatorname { SSR } \left( X _ { 1 } \mid X _ { 2 } \right) = 8343.3572 \text { and } \operatorname { SSR } \left( X _ { 2 } \mid X _ { 1 } \right) = 4199.2672\end{array}$$
-Referring to SCENARIO 13-6, what is your decision and conclusion for the testH0 : $\beta$ 2 = 0 vs.H1 : $\beta$ 2 $\neq$ 0 at the $\alpha$ = 0.01 level of significance?

• A)Do not reject H0 and conclude that the amount of insulation has a linear effect on heating costs.
• B)Reject H0 and conclude that the amount of insulation does not have a linear effect on heating costs.
• C)Reject H0 and conclude that the amount of insulation has a linear effect on heating costs.
• D)Do not reject H0 and conclude that the amount of insulation does not have a linear effect on heating costs.

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Definitions:

Total Assets

The sum of all resources owned by a company, valued in monetary terms, including current and long-term assets.

Dependent Means

Statistical measures that represent the average outcomes within an experiment that are expected to change in response to the independent variable.

Independent Samples

Two or more groups of data that are collected from separate, non-related populations or entities.

Dependent Samples

Pairs of samples where the members of one sample are related or matched to the members of the other sample, often used in before-and-after studies.