4.4. A survey of adolescents indicated that 17% had used marijuana in the last year. In addition to standard demographic predictors of drug use, a researcher expects that school performance also affects the likelihood of marijuana use. The researcher's table of results follows: STANDARD VARIABLE MEAN DEVIATION b SE Age (years) 14.6 3.1 0.07 0.03 Sex (1 male, 0female) 0.55 0.50 0.36 0.15 Race (1 white, 0 = nonwhite) 0.75 0.43 -0.42 0.30 Grade point average 2.76 1.98 -0.89 0.24 Think of self as a good student 0.59 0.49 -0.65 0.33 (1=yes, 0 = no) Constant -0.87 (a) Calculate the predicted probability of marijuana use for each of the following persons: -A 14-year-old white male who does not think of himself as a good student and has a GPA of 3.07. -A 17-year-old nonwhite female who thinks of herself as a good student and has a GPA of 3.22. -A 15-year-old white female who thinks of herself as a good student and has a GPA of 2.53.

(b) Calculate the standardized logistic regression coefficient for each of the independent variables in the model. Which variable appears to have the largest effect on marijuana use? (c) Calculate the derivative at mean for each of the independent vari- ables in the model. Which variable appears to have the largest effect on marijuana use? (d) Compare your answers for parts (b) and (c). How do you explain this pattern?