The Manufacturer of a Light Fixture Believes That the Dollars

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.With this data,the following computer output is obtained.
The regression equation is
Sales = 31.0 + 0.820 Advertising - 0.325 Price + 1.84 Stores $$\begin{array} { l l l l l } \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm { T } & \mathrm { P } \\\text { Constant } & 30.992 & 7.728 & 4.01 & 0.007 \\\text { Advertising } & 0.8202 & 0.5023 & 1.63 & 0.154 \\\text { Price } & - 0.32502 & 0.08935 & - 3.64 & 0.011 \\\text { Stores } & 1.841 & 3.855 & 0.48 & 0.650\end{array}$$ S = 5.465 R-Sq = 96.7% R-Sq(adj)= 95.0%
Analysis of Variance $$\begin{array} { l l l l l l } \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\\text { Regression } & 3 & 5179.2 & 1726.4 & 57.81 & 0.000 \\\text { Residual Error } & 6 & 179.2 & 29.9 & &\end{array}$$ Based on the multiple regression model given above,the point estimate of the monthly light fixture sales corresponding to second sample data is 49.82 or 49,820 units.This point estimate is calculated based on the assumption that the company spends $4000 on advertising,the price of the fixture is $60,and the fixture is being sold at 3 retail stores.Additional information related to this point estimate is given below. $$\begin{array} { l l l l l l l } \text { Obs. } & \text { Advert } & \text { Sales } & \text { Fit } & \text { StDev Fit } & \text { Residual } & \text { St Resid. } \\2 & 40.0 & 42.00 & 49.82 & 3.53 & - 7.82 & - 1.87\end{array}$$
-Determine the 95% confidence interval for this point estimate and interpret its meaning.