# THE FRESH DETERGENT CASE

See the attached file for the table.

2 THE FRESH DETERGENT CASE

Model: y = b0 + b1 x1 + b2 x2 + b3 x3 + e Sample size: n = 30

Regression Statistics

Multiple R 0.9453

R Square 0.8936

Adjusted R Square 0.8813

Standard Error 0.2347

Observations 30

ANOVA df SS MS F Significance F

Regression 3 12.0268 4.0089 72.7973 0.0000

Residual 26 1.4318 0.0551

Total 29 13.4586

METHODS AND APPLICATIONS

In the Exercise we give outputs of regression analyses of the data sets above each output we give the regression model and the number of observations, n, used to perform the regression analysis under consideration. Using the appropriate model, sample size n, and output:

1 Report SSE, s2, and s as shown on the output. Calculate s2 from SSE and other numbers.

2 Report the total variation, unexplained variation, and explained variation as shown on the output.

3 Report R2 and R-bar2 as shown on the output. Interpret R2 and R-bar2. Show how R-bar2 has been calculated from R2 and other numbers.

4 Calculate the F (model) statistic by using the explained variation, the unexplained variation, and other relevant quantities. Find F (model) on the output to check your answer (within rounding).

5 Use the F (model) statistic and the appropriate critical value to test the significance of the linear regression model under consideration by setting ? equal to .05.

6 Use the F (model) statistic and the appropriate critical value to test the significance of the linear regression model under consideration by setting ? equal to .01.

7 Find the p-value related to F (model) on the output. Using the p-value, test the significance of the linear regression model by setting ? = .10, .05, .01, and .001. What do you conclude?

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#### Solution Summary

The solution provides step by step method for the calculation of regression analysis. Formula for the calculation and Interpretations of the results are also included.