1. Refer to Agresti Table 2.7 on x = mother's alcohol consumption and Y = whether a baby has sex organ malformation . With scores (0, 0.5, 1.5, 4.0, 7.0) for alcohol consumption , fit a linear model to the data . Table 2.7. Infant Malformation and Mother's Alcohol Consumption Malformation Alcohol Percentage Standardized Consumption Absent Present Total Present Residual 0 17.066 48 17.114 0.28 -0.18 14.464 38 14.502 0.26 -0.71 1-2 788 5 793 0.63 1.84 126 127 0.79 1.06 37 38 2.63 2.71 Source: B. I. Grasbard and E. L. Korn, Biometrics, 43: 471-476, 1987. Reprinted with permission from the Biometric Society. a. State the prediction equation , and interpret the intercept and slope . b. Use the model fit equation to estimate the (i) probabilities of malformation for alcohol levels 0 and 7.0, (ii) relative risk comparing alcohol level 7.0 with 0. C. The sample proportion of malformations is much higher in the highest alcohol category than the others because , although it has only one malformation , its sample size is only 38. The result might be sensitive to this single malformation observation . Re -fit the model without it (using 0 malformations in 37 observations at that level ), and re- evaluate estimated probabilities of malformation at alcohol levels 0 and 7 and the relative risk . d. Is the result sensitive to the choice of scores ? Re -fit the model using scores (0, 1, 2, 3, 4), and re-evaluate estimated probabilities of malformation at the lowest and highest alcohol levels and the relative risk . e. Fit a logistic regression model . Report the prediction equation . Use the predicted equation to estimate probabilities of malformation at the lowest and highest alcohol levels and the relative risk. f. Fit a probit regression model . Report the prediction equation . Use the predicted equation to estimate probabilities of malformation at the lowest and highest alcohol levels and the relative risk. g. (Extra Credit ) Plot on the same graph the predicted probabilities of malformation from the linear , logistic , and probit regression models , as well as the observed probabilities