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

question 130

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, the estimated value of the regression parameter $\beta$ 1 in means that

• A)holding the effect of the amount of insulation constant, an estimated expected $1 increase in heating costs is associated with a decrease in the daily minimum outside temperature
• By 2.76 degrees.
• B)holding the effect of the amount of insulation constant, a 1 degree increase in the daily minimum outside temperature results in a decrease in heating costs by $2.76.
• C)holding the effect of the amount of insulation constant, a 1 degree increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by $2.76.
• D)holding the effect of the amount of insulation constant, a 1% increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by 2.76%.

---

Definitions:

Frequency Distribution

A representation of data that shows how often each value or range of values occurs.

Sample

A portion of the overall population picked for conducting studies or inquiries in order to collect demographic data.

Frequency Polygon

A graphical representation of the distribution of a dataset that shows how often each value occurs, connecting each data point by straight lines.

Frequency Distribution

A summarization of data by reporting the number of observations that fall within each range or bin of values for a specific variable.