14-22 Introduction to Multiple Regression One of the Most Common $( Y )$

question 1

Multiple Choice

14-22 Introduction to Multiple Regression 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 $\left( X _ { 1 } \right)$ and the amount of insulation in inches $\left( X _ { 2 } \right)$ . Given below is EXCEL output of the regression model.
$\begin{array}{lr}\hline {\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.5270 \\\text { R Square } & 0.2778 \\\text { Adjusted R Square } & 0.1928 \\\text { Standard Error } & 40.9107 \\\text { Observations } & 20 \\\hline\end{array}$

ANOVA


$\begin{array}{lrrrrrr} & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 448.2925 & 90.7853 & 4.9379 & 0.0001 & 256.7522 & 639.8328 \\\text { Temperature } & -2.7621 & 1.2371 & -2.2327 & 0.0393 & -5.3721 & -0.1520 \\\text { Insulation } & -15.9408 & 10.0638 & -1.5840 & 0.1316 & -37.1736\end{array}$

Also $\operatorname { SSR } \left( X _ { 1 } \mid X _ { 2 } \right) = 8343.3572$ and $\operatorname { SSR } \left( X _ { 2 } \mid X _ { 1 } \right) = 4199.2672$
-Referring to Scenario 14-6, what is the 95% confidence interval for the expected change in heating costs as a result of a 1 degree Fahrenheit change in the daily minimum outside
Temperature?

• A) [256.7522, 639.8328]
• B) [204.7854, 497.1733]
• C) [?5.3721, ?0.1520]
• D) [?37.1736, 5.2919]

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Definitions:

Intuitive Method

A cost-based approach to finding an initial solution to a transportation problem.

Improvement Index

An indicator or metric used to quantify the level of improvement in a process, product, or service over time.

Stepping-Stone Method

An iterative technique for moving from an initial feasible solution to an optimal solution in the transportation method.

Fixed Costs

Expenses that do not change with the level of production or sales over a certain period, such as rent, salaries, and insurance.