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In: Statistics and Probability

The following Regression function has been developed to check the relationship between Y- ‘Sales’ and the...

The following Regression function has been developed to check the relationship between Y- ‘Sales’ and the following independent variables;

X1- Time (Length of time employed in months)

X2 –Poten (Market potential)

X3 – AdvExp (Advertising expenditure in the sales territory)

X4 – Accounts (Number of accounts assigned to sales rep)

3 Consider the following Minitab output and answer the questions. Regression Analysis: Sales versus Time, Poten, AdvExp,

Accounts Regression Equation Sales = -391 - 0.58 Time + 0.02227 Poten + 0.2178 AdvExp + 16.31

Accounts Coefficients Term Coef SE Coef T-Value P-Value VIF Constant -391 470 -0.83 0.415 Time -0.58 2.20 -0.26 0.794 2.46

Poten 0.02227 0.00895 2.49 0.022 1.34

AdvExp 0.2178 0.0468 4.65 0.000 1.07

Accounts 16.31 4.20 3.88 0.001 2.48

Model Summary S R-sq R-sq(adj) R-sq(pred) 595.985 82.83% 79.40% 72.74%

Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 4 34275579 8568895 24.12 0.000

Time 1 24781 24781 0.07 0.794

Poten 1 2198350 2198350 6.19 0.022

AdvExp 1 7683578 7683578 21.63 0.000

Accounts 1 5346156 5346156 15.05 0.001

Error 20 7103970 355198 Total 24 41379549

e. 4 pts. What can you say about “goodness of fit” for the above regression model fit based on the appropriate value from the output?

f. 4 pts. Is normality assumption about the error ? satisfied based on the above Minitab output? Explain.

g. 4 pts. Is constant variance assumption about the error ? satisfied based on the above Minitab output? Explain.

h. 6pts. Why do we use R-sq(adj) in multiple linear regression rather than R_sq? Make sure to explain in detail.

Solutions

Expert Solution

orchestra answered 1 year ago
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