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# Multiple Regression Explanation

Write the regression equation.
Discuss the significance of the regression coefficients.
Examine and discuss the residual plots.

#### Solution Preview

Solution (1) :
Following is the Regression Output generated using Excel Data Analysis

SUMMARY OUTPUT

Regression Statistics
Multiple R 0.5938
R Square 0.3526
Standard Error 332.0687
Observations 20.0000

ANOVA
df SS MS F Significance F
Regression 2 1021166 510583.2 4.630316 0.024815436
Residual 17 1874584 110269.6
Total 19 2895750

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 993.92 788.0986 1.261168 0.224281 -668.8204742 2656.67
Intelligence 8.22 7.01256 1.17217 0.257294 -6.575316911 23.01514
Extroversion 49.71 19.63374 2.531796 0.0215 8.285001189 91.13227

1(a)
From the lower portion of ANOVA output the regression equation with values rounded to two decimal places is

Sales per week = 993.92 + 8.22 *(Intelligence) + 49.71*(Extroversion)

If Y = Sales per week , X1 = Intelligence , X2 = ...

#### Solution Summary

The solution writes a regression equation, discusses the adjusted r square value, and its significance. This leads to a discussion of the residual plots of the data.

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