10-4 Multiple Regression 559 Logistic Regression In Example 3, we could use the same methods of Part 1 in this section because the dummy variable of sex is a predictor variable. However, if the dummy variable is the response 1y2 variable, we cannot use the methods in Part 1 of this section, and we should use a different method known as logistic regression. This section does not include detailed procedures for using logistic regression, but many books are devoted to this topic. Example 4 briefly illustrates the method of logistic regression. Logistic Regression EXAMPLE 4 Let a sample data set consist of the heights (cm) and arm circumferences (cm) of women and men as listed in Data Set 1 “Body Data” in Appendix B. Let the response y variable represent gender (0 = female, 1 = male). Using the gender values of y and the combined list of corresponding heights and arm circumferences, logistic regression could be used to obtain this model: ln a p 1 - pb = -40.6 + 0.2421HT2 + 0.0001291ArmCirc2 In the expression above, p is the probability of a male, so p = 1 indicates that the subject is definitely a male, and p = 0 indicates that the subject is definitely not a male (so the subject is a female). [To solve for p, substitute values for height and arm circumference to get a value v, then p = ev>11 + ev2.] See the following two sets of results. ■ If we use the model above and substitute a height of 183 cm (or 72.0 in.) and an arm circumference of 33 cm (or 13.0 in.), we can solve for p to get p = 0.976, indicating that such a person has a 97.6% chance of being a male. ■ In contrast, a smaller person with a height of 150 cm (or 59.1 in.) and an arm circumference of 20 cm (or 7.9 in.) results in a probability of p = 0.0134, indicating that such a small person is very unlikely to be a male. Multiple Regression Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER Statdisk 1. Click Analysis in the top menu. 2. Select Multiple Regression from the dropdown menu. 3. Select the columns to be included in the regression analysis. For Dependent variable column, select the column to be used for the dependent y variable. 4. Click Evaluate. StatCrunch 1. Click Stat in the top menu. 2. Select Regression from the dropdown menu, then select Multiple Linear from the submenu. 3. Select the column to be used for the y variable and columns to be used for the x variable. 4. Click Compute! Minitab 1. Click Stat in the top menu. 2. Select Regression from the dropdown menu and select Regression—Fit Regression Model from the submenu. 3. Under Responses select the column that contains the dependent y values. Under Continuous predictors select the columns that contain the variables you want included as predictor x variables. 4. Click OK. The regression equation is included in the results. continued
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