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

question 323

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 partial F test for $H _ { 0 }$ : Variable $X _ { 1 }$ does not significantly improve the model after variable $X _ { 2 }$ has been included $H _ { l }$ : Variable $X _ { l }$ significantly improves the model after variable $X _ { 2 }$ has been included has $\underline{\quad\quad}$ and $\underline{\quad\quad}$ degrees of freedom.

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Definitions:

Vehicles

Means of transportation that are used to move people or goods from one place to another, including cars, trucks, bicycles, and airplanes.

Standard Deviation

A statistical metric that quantifies the spread or dispersion of a dataset relative to its mean, showcasing variability.

Annual Snowfall

The total amount of snow that falls within a specific geographic area over the course of a year.

Mean

The average of a data set, found by adding all the numbers together and dividing by the quantity of numbers.