5. (25pts) Can gender, educational level, and age predict the odds that someone votes for a particular candidate in the election? Over 1500 voters were selected, and data were col- lected on the highest year of school completed, their age, and their gender. We wish to fit a logistic regression model: log(?) = Bo + B. Age + B, Education +BGender, where p is the binomial probability that a person voted for candidate Johnson, and gender is coded as the indicator for female. The Routput is given below. parameter d estimate s.e 2 p.value (Intercept) 1 -1119 3481 321 5708 Age 1 .0020 20032 .613 .54 Education 1 -0100 .0184 -547 585 Gender 1 .4282 1040 4.117 000 Null deviance: 255/95 on 1499 degrees of freedom Renidual deviance: 220.80 on 1496 degrees of freedom (a) Write down the fitted logistic regression and give a short summary about the data analysis. (5pts) (b) Calculate the probability of voting for Johnson for a 35-year-old male with 16 years of school? (5pts) (c) Find the odds ratio of voting for Johnson between female and male while controlling age and education and interpret the odds ratio (5pts) (c) Find the odds ratio of voting for Johnson between female and male while controlling age and education and interpret the odds ratio.(5pts) (d) Find the 95% confidence interval for the odds ratio of voting for Johnson between female and male (5pts). (e) The researcher fitted another model with Gender as the only predictor and get the result below. Test whether the two nonsignificant terms (Age and Education can be both removed from the model in (a), write down the HO, Ha, test statistic, p-value and conclusion (5pts): parameter p-value Intercept) 091 870 Gender 6723 1258 5.344 Null devince: 2660 on 1190 degrees of freedom Residual deviance: 227.39 on 1898 degrees of freedom d 1 1 estimate 1320 ON