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The Manufacturer of a Light Fixture Believes That the Dollars

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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:  Sales  Advertising  Price  # of stores 41204014240603594020460508058150106806040610070207827060810180309110904010\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  Predictor  Coef  StDev TP Constant 30.9927.7284.010.007 Advertising 0.82020.50231.630.154 Price 0.325020.089353.640.011 Stores 1.8413.8550.480.650\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  Source  DF  SS  MS  F  P  Regression 35179.21726.457.810.000 Residual Error 6179.229.9\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.  Obs.  Advert  Sales  Fit  StDev Fit  Residual  St Resid. 240.042.0049.823.537.821.87\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.

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Definitions:

Labour Need

The requirement for a specific number and type of employees to perform tasks within an organization.

Forecast Demand

The process of estimating the future demand for goods and services within a market, often used for strategic planning and resource allocation.

Human Resource Planning Process

A strategic approach to managing an organization's most valuable assets - its human capital - by aligning workforce requirements with business objectives.

Workforce Planning Activities

The process of assessing, predicting, and managing the needs of the workforce to achieve organizational goals.

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