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hC - Stat 5102(Geyer Spring 2012 Homework Assignment 12 Due...

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Stat 5102 (Geyer) Spring 2012 Homework Assignment 12 Due Wednesday, May 2, 2012 Solve each problem. Explain your reasoning. No credit for answers with no explanation. If the problem is a proof, then you need words as well as formulas. Explain why your formulas follow one from another. 12-1. The data set in the URL http://www.stat.umn.edu/geyer/5102/data/prob12-1.txt has two variables x (the predictor variable) and y (the response variable). The response is zero-or-one-valued, so these data are suitable for logistic regression. (a) Fit a GLM with logit link having natural parameter (linear predictor) that is quadratic in x , that is θ i = β 1 + β 2 x i + β 3 x 2 i Report the regression coefficients table for this fit. (b) Give a 95% confidence interval for the natural parameter value for an individual with x i = 30. (c) Give a 95% confidence interval for the mean parameter value for an indi- vidual with x i = 30 that is of the form point estimate ± critical value × standard error.
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