Quantitative Research

11.3 Comparing Two Regression Models

We have seen how PHStat can be used to fit regression models with just quantitative variables and regression models with just qualitative variables. For more complicated models, PHStat allows the user to input both quantitative and qualitative variables into a single multiple regression model. The variables must be located in adjacent columns of data within the PHStat worksheet. By specifying the appropriate columns in the Regression data analysis menu, any number of quantitative and qualitative variables can be combined.

The final step in the model building topic is to develop a method that allows the user to compare two regression models to determine which is the better predictor of the dependent variable. Section 11.11 in the text details the partial-F test for testing a portion of the regression model. By fitting two separate models within PHStat, it is possible to calculate the partial-F test statistic that the book details. We demonstrate with the following example.

Exercise 11.4: We use Example 11.12 found in the Statistics for Business and Economics text.

Many companies manufacture products (e.g., steel, paint, and gasoline) that are at least partially chemically produced. In many instances, the quality of the finished product is a function of the temperature and pressure at which the chemical reactions take place. Suppose you want to model the quality y of a product as a function of the temperature x1 and the pressure x2 at which it is produced. Four inspectors independently assign a quality score between 0 and 100 to each product, and then the quality y is calculated by averaging the four scores. An experiment is conducted by varying temperature between 80oF and 100oF and pressure between 50 and 60 pounds per square inch (psi).