8.1 For Table 8.14, let Y = belief in existence of heaven, x1 = gender (1 = females, 0 = males), and x2 = race (1 = blacks, 0 = whites). Table 8.15 shows the fit of the model log(n, 3) = a; + By x1 + Bj x2. j = 1, 2. with SE values in parentheses. a. Find the prediction equation for log(1 /72). b. Using the yes and no response categories, interpret the conditional gender effect using a 95% confidence interval for an odds ratio. Table 8.14 Data on Belief in Existence of Heaven for Exercise 8.1 Belief in Heaven Race Gender Yes Unsure No Black Female 88 16 2 Male 54 7 5 White Female 397 141 24 Male 235 189 39 Source: 2008 General Social Survey. Table 8.15 Fit of Model for Belief in Heaven for Exercise 8.1 Belief Categories for Logit Parameter Yes/No Unsure/No Intercept 1.785 (0.168) 1.554 (0.172) Gender 1.044 (0.259) 0.254 (0.269) Race 0.703 (0.41 1) -0.106 (0.438) 330 MODELS FOR MULTINOMIAL RESPONSES c. Find it1 = P(Y = yes) for white females. d. Without calculating estimated probabilities, explain why the intercept estimates indicate that for white males, it , > it2 > #3. Use the intercept and gender esti- mates to show that the same ordering applies for black females. e. Without calculating estimated probabilities, explain why the estimates in the gender row indicate that it is higher for females than for males, for each race. f. For this fit, G2 = 0.69. Explain why residual df = 2. Deleting the gender effect, G2 = 47.64. Conduct a likelihood-ratio test of whether opinion is independent of gender, given race. Interpret