The Manufacturer of a Light Fixture Believes That the Dollars

question 137

Essay

The manufacturer of a light fixture believes that the dollars spent on advertising,the price of the fixture,and the number of retail stores selling the fixture in a particular month influence the light fixture sales.The manufacturer randomly selects 10 months and collects the following data: $$\begin{array} { l l l l } \text { Sales } & \text { Advertising } & \text { Price } & \text { \# of stores } \\41 & 20 & 40 & 1 \\42 & 40 & 60 & 3 \\59 & 40 & 20 & 4 \\60 & 50 & 80 & 5 \\81 & 50 & 10 & 6 \\80 & 60 & 40 & 6 \\100 & 70 & 20 & 7 \\82 & 70 & 60 & 8 \\101 & 80 & 30 & 9 \\110 & 90 & 40 & 10\end{array}$$ The sales are in thousands of units per month,the advertising is given in hundreds of dollars per month,the price is the unit retail price for the particular month.Using this data,the following computer output is obtained.
The regression equation is
Sales = 31.0 + 0.820 Advertising - 0.325 Price + 1.84 Stores $$\begin{array} { l l l l l } \text { Predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P } \\\text { Constant } & 30.992 & 7.728 & 4.01 & 0.007 \\\text { Advertising } & 0.8202 & 0.5023 & 1.63 & 0.154 \\\text { Price } & - 0.32502 & 0.08935 & - 3.64 & 0.011 \\\text { Stores } & 1.841 & 3.855 & 0.48 & 0.650\end{array}$$ S = 5.465R-Sq = 96.7%R-Sq(adj)= 95.0%
Analysis of Variance $$\begin{array} { l l l l l l } \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\\text { Regression } & 3 & 5179.2 & 1726.4 & 57.81 & 0.000 \\\text { Residual Error } & 6 & 179.2 & 29.9 & & \\\text { Total } & 9 & 5358.4 & & &\end{array}$$
-Calculate the 95% prediction interval for this point estimate.

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Definitions:

Deferred Gain

A profit from the sale of property or an investment that has been realized but not recognized for tax purposes in the current period.

IRC Section 121

A provision in the Internal Revenue Code that allows homeowners to exclude up to $250,000 ($500,000 if married filing jointly) of capital gains on the sale of their primary residence, subject to certain conditions.

Receipt of Boot

Tax term referring to non-like-kind property or cash received in an exchange, which may trigger taxable gain.

Like-kind Exchange

A tax-deferred exchange of similar properties under section 1031 of the U.S. Tax Code.