1. ENM 310 Design of Experiments and Regression Analysis
Simple Linear Regression
An Example with Minitab Outputs

2. Example
a) The weekly advertising expenditure (x) and weekly sales (y) are presented in the following table. An analyst wants to find the relationship between advertising expenditure and weekly sales. Find the regression line.

5. Minitab Output

7. b) Management is interested in testing whether or not there is a linear association between advertising expenditure and weekly sales, using regression model. Use  =0.05 and show 2 approaches for the test procedure.

8. The first approach:

9. The second approach:
Conclusion: Since t =4.5 > then we reject H0. There is a linear association between advertising expenditure and weekly sales.

12. c) Now, the management wishes an estimate of 1 with a 95% confidence coefficient.
For a 95 percent confidence coefficient, we require t (0.025; 8). From the t table, we find t(0.025; 8) =
The 95% confidence interval is:

14. d) Residual plots

15. e) Present a test for the goodness of fit of the regression model.

16. f) What percentage of total variability is explained by the model
f) What percentage of total variability is explained by the model? (Find the coefficient of determination-R squared value. ) g) Find the correlation coefficient between x and y. Comment on it.