For Table 2.6 on x = mother’s alcohol consumption and Y = whether a baby has sex organ malformation, ML fitting of the linear probability model with x scores 0, 0.5, 1.5, 4.0, 7.0 has output:

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Parameter Estimate Std Error Intercept 0.00255 0.0003 alcohol 0.00109 0.0007

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a. State the prediction equation and interpret the intercept and slope.

b. Use the model fit to estimate the (i) probabilities of malformation for alcohol levels 0 and 7.0, (ii) relative risk comparing those levels.

c. Is the result sensitive to the choice of scores? Re-fit the linear probability model using scores 0, 1, 2, 3, 4, and re-evaluate fitted probabilities at alcohol levels 0 and 7 and the relative risk.

d. 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. Are results sensitive to this single malformation? Fit the logistic regression or linear probability model with and without that observation, and evaluate fitted probabilities at alcohol levels 0 and 7 and the relative risk.