PRE Calculator Directions
What Is It
The PRE calculator is used when you have estimated both a compact and an augmented model using regression procedures. Now you question whether the augmented model (the one with more predictors) is practically and significantly better than the compact model (the one with fewer predictors). All of the information needed for the PRE calculator comes from the output from the two previously conducted regressions.
What Do I Need
In the PRE calculator, you must provide five pieces of information. They are defined below.
- PC = the number of parameters in the compact model. This is the number of predictor variables in this model plus 1 for the constant.
- PA = the number of parameters in the augmented modes. This is the number of predictor variables in this model plus 1 for the constant.
- ERROR C = the error in the compact model. From most regression programs this will be the sum of squares due to residuals. It will be a larger number than that for ERROR A.
- ERROR A = the error in the augmented model. Again, you will find this value from the regression output for the augmented model. It will be a smaller number than that for ERROR C.
- N = the number of subjects involved. Note the same subjects must be involved in both regression analyses or you are comparing apples with oranges.
Just Fooling Around
If you are just trying this program for fun, I suggest trying the following as inputs:
- PC = 3
- PA = 4
- ERROR C = 2000
- ERROR A = 1000
- N = 100
You should calculate a PRE = .5, and an F statistic with 1 and 96 degrees of freedom = 96.
What Does It Mean
The PRE that is calculated tells you the Proportional Reduction in Error, and is a direct measure of the practicality of the difference in the two models. Multiplying this value by 100 provides a percent reduction in error.
The F statistic can be compared to a critical F value to determine if the difference between the models is statistically significant.
Using the suggested input above, you would say that the augmented model, compared to the compact model reduces the error by 50 percent. The F value of 96 with 1 and 96 degrees of freedom is statistically significant.