1. Using SPSS Note: The use of another statistical package such as Minitab is similar to using SPSS

2. After starting the SSPS program the following dialogue box appears:

3. If you select Opening an existing file and press OK the following dialogue box appears

4. The following dialogue box appears:

5. If the variable names are in the file ask it to read the names. If you do not specify the Range the program will identify the Range: Once you “click OK”, two windows will appear

6. One that will contain the output:

7. The other containing the data:

8. To perform any statistical Analysis select the Analyze menu:

9. Then select Regression and Linear.

10. The following Regression dialogue box appears

11. Select the Dependent variable Y.

12. Select the Independent variables X 1, X 2, etc.

13. If you select the Method - Enter.

14. All variables will be put into the equation. There are also several other methods that can be used : 1.Forward selection 2.Backward Elimination 3.Stepwise Regression

16. Forward selection 1.This method starts with no variables in the equation 2.Carries out statistical tests on variables not in the equation to see which have a significant effect on the dependent variable. 3.Adds the most significant. 4.Continues until all variables not in the equation have no significant effect on the dependent variable.

17. Backward Elimination 1.This method starts with all variables in the equation 2.Carries out statistical tests on variables in the equation to see which have no significant effect on the dependent variable. 3.Deletes the least significant. 4.Continues until all variables in the equation have a significant effect on the dependent variable.

18. Stepwise Regression (uses both forward and backward techniques) 1.This method starts with no variables in the equation 2.Carries out statistical tests on variables not in the equation to see which have a significant effect on the dependent variable. 3.It then adds the most significant. 4.After a variable is added it checks to see if any variables added earlier can now be deleted. 5.Continues until all variables not in the equation have no significant effect on the dependent variable.

19. All of these methods are procedures for attempting to find the best equation The best equation is the equation that is the simplest (not containing variables that are not important) yet adequate (containing variables that are important)

20. Once the dependent variable, the independent variables and the Method have been selected if you press OK, the Analysis will be performed.

21. The output will contain the following table R 2 and R 2 adjusted measures the proportion of variance in Y that is explained by X 1, X 2, X 3, etc (67.6% and 67.3%) R is the Multiple correlation coefficient (the maximum correlation between Y and a linear combination of X 1, X 2, X 3, etc)

22. The next table is the Analysis of Variance Table The F test is testing if the regression coefficients of the predictor variables are all zero. Namely none of the independent variables X 1, X 2, X 3, etc have any effect on Y

23. The final table in the output Gives the estimates of the regression coefficients, there standard error and the t test for testing if they are zero Note: Engine size has no significant effect on Mileage

24. The estimated equation from the table below: Is:

25. Note the equation is: Mileage decreases with: 1.With increases in Engine Size (not significant, p = 0.432) With increases in Horsepower (significant, p = 0.000) With increases in Weight (significant, p = 0.000)