This problem uses the teengamb data set in the faraway package. Fit a model with gamble as the response and the other variables as predictors. (a) Predict the amount that men with average (given the data) status, income and verbal score would gamble along with an appropriate 95% confidence interval for the mean amount. (b) Repeat the prediction for men with maximal values (for this data) of status, income and verbal score. Which confidence interval is wider and why is the result expected? (c) Fit a model with sqrt(gamble) as the response but with the same predictors. Now predict the response and give a 95% prediction interval for an individual in (a). Take care to give your answer in the original units of the response.