Categorical variables with only two categories (such as male/female or yes/no) can be used in a multiple regression model if we code the answers with numbers. In Chapter 9, we looked at a simple linear model to predict Weight based on Height. What role does gender play? If a male and a female are the same height (say 5€™7€), do we predict the same weight for both of them? Is gender a significant factor in predicting weight? We can answer these questions by using a multiple regression model to predict weight based on height and gender. Using 1 for females and 0 for males in a new variable called GenderCode in the dataset StudentSurvey, we obtain the following output:

(a) What weight does the model predict for a male who is 5€™7€ (67 inches)? For a female who is 5€™7€?
(b) Which predictors are significant at a 5% level?
(c) Interpret the coefficient of Height in context.
(d) Interpret the coefficient of GenderCode in context. (Pay attention to how the variable is coded.)
(e) What is R² for this model? Interpret it in context.

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The regression equation is Weight = - 23.9 + 2.86 Height-25.5 GenderCode Predictor Coef SE Coef -23.92 2.8589 Constant 27.36 -0.87 0.383 Height 0.3855 7.42 0.000 GenderCode -25.470 3.138 -8.12 0.000 S= 22.8603 R-Sq = 48.2% R-Sq(adj) = 47.9%