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Question

A household appliance manufacturer wants to analyze the relationship between total sales and the company's three primary means of advertising (television, magazines, and radio). All values were in millions of dollars. They found the regression equation

Sales^\widehat{\text{Sales}} = 250 + 6.75 TV + 3.5 Radio + 2.3 Magazines.

One of the interpretations below is correct. Which is it? Explain what's wrong with the others.

Every million dollars spent on radio makes sales increase $3.5 million, all other things being equal.

Solution

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Answered 8 months ago
Answered 8 months ago
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Given:

Sales^=250+6.75TV+3.5Radio+2.3Magazines\begin{align*} \widehat{Sales}&=250+6.75TV+3.5Radio+2.3Magazines \end{align*}

A coefficient of variable represents the average increase/decrease in the dependent variable (Price) per unit of the independent variable (when the other independent variables remain constant).

The coefficient of determination describes the proportion of the observed variation in the dependent variable that is explained by the least squares regression line.

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