Linear regression

We get a lot of questions about regression analysis. We have dug into this and decided to write a post about it, so we can help everyone with this.

You do a regression when you assume that a variable is influencing another one, like in the following example: We assume that cars that run on Diesel have higher costs.

To test this assumption, we run a Linear Regression in SPSS. Take the following steps:

- Define your dependent and independent variable. In our example Fuel is the indepent variable and Costs is the dependent one.
- Click Analyze
- Go to Regression and click Linear
- Click “Fuel” into the Independent variable field, and “Costs” into the Dependent variable field.

The output exists of:

1 Model Summary, in which you can find the relation between the variables.

R stands for the correlation and gives us the relation between the dependent and the independent variables. The correlation between Fuel and Costs is ,839.

R Square is the proportion of variance in the dependent variable (Costs) which can be predicted from the independent variable (Fuel). This value indicates that 70% of the variance in costs can be predicted from the variable fuel. The Adjusted R-square tries to give an even better calculation for the whole population.

2 ANOVA, which holds data about the significance of the regressionmodel.

The value under Sig. holds the significance value of the regression. In most cases this should be under 0.05. In our example this is 0.00, better it cannot get!

3 Coefficients, gives information about the first line of regression.

Conclusion would be that this regression analysis is significant and that 70% of the variance in costs can be predicted from the variable fuel.

Please find below the SPSS file we used to create this example. Just one note, the information in the SPSS file is not based on anything. Even more, it’s just random data. Please don’t sue us.

Linear Regression Example Cars

5 comments August 21st, 2006 andris