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

question 371

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

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Agricultural Economies

Economic systems primarily based on the production, distribution, and consumption of agricultural goods and services, often characterized by a reliance on farming and livestock.

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The act of searching and obtaining food resources in the wild, practiced by humans and animals alike.

Climate Changes

refers to significant and lasting changes in the statistical distribution of weather patterns over periods that range from decades to millions of years.

Herd Animals

Animals that naturally live, travel, and graze in groups, displaying collective behavior for protection and efficiency.