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

question 165

Short Answer

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, the value of the partial F test statistic is ____ for $H _ { 0 }$ : Variable $X _ { 1 }$ does not significantly improve the model after variable $X _ { 2 }$ has been included
$H _ { 1 }$ : Variable $X _ { 1 }$ significantly improves the model after variable $X _ { 2 }$ has been included

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Definitions:

Income Statement

A financial report detailing a firm's income and expenditures within a certain timeframe, resulting in the total earnings or deficit experienced during that interval.

Net Operating Income

The income generated from normal business operations after deducting operating expenses but before interest and taxes.

Contribution Format

A type of income statement that separates variable costs from fixed costs to show the contribution margin.

Income Statement

A financial statement that shows a company's revenues, expenses, and net income or loss over a specific period of time.