## Related questions with answers

Commercial contractors and home improvement merchants like Lowe's and Home Depot can purchase roofing and siding supplies from Great Plains Distributors Inc. The business owner is curious to know how different factors affect how much fiber-cement siding is sold. In the United States, the corporation operates 26 marketing districts. It gathered data on the following factors in each district: sales volume (in thousands of dollars), advertising spending (in thousands of dollars), the number of active accounts, the number of rival brands, and an assessment of market potential.

$\begin{array}{|ccccc|} \begin{array}{c} \text { Sales } \\ \text { (000s) } \end{array} & \begin{array}{c} \text { Advertising } \\ \text { Dollars } \\ \text { (000s) } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Accounts } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Competitors } \end{array} & \begin{array}{c} \text { Market } \\ \text { Potential } \end{array} \\ \hline 79.3 & 5.5 & 31 & 10 & 8 \\ 200.1 & 2.5 & 55 & 8 & 6 \\ 163.2 & 8.0 & 67 & 12 & 9 \\ 200.1 & 3.0 & 50 & 7 & 16 \\ 146.0 & 3.0 & 38 & 8 & 15 \\ 177.7 & 2.9 & 71 & 12 & 17 \\ \vdots & \vdots & \vdots & & \\ 93.5 & 4.2 & 26 & 8 & 3 \\ 259.0 & 4.5 & 75 & 4 & 9 \\ 331.2 & 5.6 & 71 & & \\ \hline \end{array}$

Find the most accurate sales predictors by performing a multivariate regression analysis. Using this, develop a histogram of the residuals and a normal probability plot. Are there any problems?

Solution

VerifiedNote that the formula for the residuals is:

$y-\hat y$

where $y$ is the real value and $\hat y$ is the estimated or fitted value.

The real values $y$ can be obtained from the given data of sales while the estimated or fitted values $\hat y$ can be calculated from the multiple linear regression equation.

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