A survey of high school students on Y = whether the subject has driven a motor vehicle after consuming a substantial amount of alcohol (1 = yes), s = gender (1 = female), r = race (1 = black: 0 = white), and g = grade (g₁ = 1, grade 9; g₂ = 1, grade 10; g₃ = 1, grade 11; g₁ = g₂ = g₃ = 0, grade 12) has prediction equation logit[ P̂(Y = 1) = –0.88 – 0.40s – 0.72r – 2.22g₁ – 1.43g₂ – 0.58g₃ + 0.74rg₁ + 0.38rg₂ + 0.01rg₃.]

a. Carefully interpret effects. Explain the interaction by describing the race effect at each grade and the grade effect for each race.

b. Replace r above by r₁ (1 = black, 0 = other). The study also measured r₂ (1 = Hispanic, 0 = other), with r₁ = r₂ = 0 for white. Suppose that the prediction equation is as above but with additional terms –0.29 r₂ + 0.53 r₂g₁ + 0.25 r₂g₂ – 0.06 r₃g₃. Interpret the effects.