5 The variable smokes is a binary variable equal to one if a person smokes, and zero otherwise. Using the data in SMOKE, we estimate a linear probability model for smokes: smokes = .656 - .069 log(cigpric) + .012 log(income) - .029 educ (.855) (.204) (.026) (.006) [.856] [.207] [.026] [.006] + .020 age - .00026 age2 - .101 restaura - .026 white the (.006) (.00006) (.039) (.052) [.005 ] [.00006 ] [.038] [.050] n = 807, R2 = .062. The variable white equals one if the respondent is white, and zero otherwise; the other independent variables are defined in Example 8.7. Both the usual and heteroskedasticity-robust standard errors are reported. (i) Are there any important differences between the two sets of standard errors? (ii) Holding other factors fixed, if education increases by four years, what happens to the estimated probability of smoking? (iii) At what point does another year of age reduce the probability of smoking? (iv) Interpret the coefficient on the binary variable restaura dummy variable equal to one if the person lives in a state with restaurant smoking restrictions). (v ) Person number 206 in the data set has the following characteristics: cigpric = 67.44, income = 6,500, educ = 16, age = 77, restaurate = 0, and smokes = 0. Compute the predicted probability of smoking for this person and comment on the result