Using SPSS

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

After starting the SSPS program the following dialogue box appears:

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

The following dialogue box appears:

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

One that will contain the output:

The other containing the data:

To perform any statistical Analysis select the Analyze menu:

Then select Regression and Linear.

The following Regression dialogue box appears

Select the Dependent variable Y.

Select the Independent variables X1, X2, etc.

If you select the Method - Enter.

All variables will be put into the equation.

There are also several other methods that can be used :

1. Forward selection2. Backward Elimination3. Stepwise Regression

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.

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.

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.

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)

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

The output will contain the following table

Model Summary

.822a .676 .673 4.46Model1

R R SquareAdjustedR Square

Std. Errorof the

Estimate

Predictors: (Constant), WEIGHT, HORSE, ENGINEa.

R2 and R2 adjusted measures the proportion of variance in Y that is explained by X1, X2, X3, etc (67.6% and 67.3%)

R is the Multiple correlation coefficient (the maximum correlation between Y and a linear combination of X1, X2, X3, etc)

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 X1, X2, X3, etc have any effect on Y

ANOVAb

16098.158 3 5366.053 269.664 .000a

7720.836 388 19.89923818.993 391

RegressionResidualTotal

Model1

Sum ofSquares df

MeanSquare F Sig.

Predictors: (Constant), WEIGHT, HORSE, ENGINEa.

Dependent Variable: MPGb.

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 zeroNote: Engine size has no significant effect on Mileage

Coefficientsa

44.015 1.272 34.597 .000-5.53E-03 .007 -.074 -.786 .432-5.56E-02 .013 -.273 -4.153 .000-4.62E-03 .001 -.504 -6.186 .000

(Constant)ENGINEHORSEWEIGHT

Model1

B Std. Error

UnstandardizedCoefficients

Beta

Standardized

Coefficients

t Sig.

Dependent Variable: MPGa.

The estimated equation from the table below:

Is:

Coefficientsa

44.015 1.272 34.597 .000-5.53E-03 .007 -.074 -.786 .432-5.56E-02 .013 -.273 -4.153 .000-4.62E-03 .001 -.504 -6.186 .000

(Constant)ENGINEHORSEWEIGHT

Model1

B Std. Error

UnstandardizedCoefficients

Beta

Standardized

Coefficients

t Sig.

Dependent Variable: MPGa.

5.53 5.56 4.6244.01000 100 1000

Mileage Engine Horse Weight Error

Note the equation is:

Mileage decreases with:

5.53 5.56 4.6244.01000 100 1000

Mileage Engine Horse Weight Error

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)