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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Definitions:

Labour and Overhead

Combined costs associated with the workforce (labour) and indirect expenses (overhead) necessary for production but not directly tied to specific units of product.

Process Costing System

An accounting method used where production is continuous, assigning costs to units of product based on the processes they undergo.

Weighted-Average Method

An inventory costing method that calculates the cost of ending inventory and cost of goods sold based on the average cost of all similar items in the inventory.

Process Costing System

An accounting method used where goods are produced in a continuous process, costs are averaged over the units produced to determine per unit cost.