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(1) 3. The data file titanic.dat (accessible from MOODLE) contains information about 1046 passengers on RMS Titanic in 1912 and whether or not they survived the sinking of the ship (survived = 1 or died = 0). In R, fit a Bernoulli regression model to the survival of passengers with the linear predictor: logit (14) = 20 + Q age; (a) What is the fitted probability of surviving, ii, for a 20 year old passenger? (b) Evaluate a 95% confidence interval for the age co-efficient. Is age a good explanatory variable for predicting the survival of passengers? You may assume the regression coefficient estimator has a normal distribution with mean given by the true value of the regression coefficient and standard deviation approximated by the standard error from the R output. [2] Consider instead the following Bernoulli regression model where the linear predictor is based on the sex of the passengers: logit() = 3, female, + Bymale; where female; is an indicator variable that is 1 if passenger i is female or 0 otherwise, and likewise for the indicator variable males. Fit this regression model in R. Note that there is no intercept term. (c) What is the fitted probability of surviving for a male passenger? (d) Is this model adequate in describing the variability in the data at the 5% significance level? (1) 3. The data file titanic.dat (accessible from MOODLE) contains information about 1046 passengers on RMS Titanic in 1912 and whether or not they survived the sinking of the ship (survived = 1 or died = 0). In R, fit a Bernoulli regression model to the survival of passengers with the linear predictor: logit (14) = 20 + Q age; (a) What is the fitted probability of surviving, ii, for a 20 year old passenger? (b) Evaluate a 95% confidence interval for the age co-efficient. Is age a good explanatory variable for predicting the survival of passengers? You may assume the regression coefficient estimator has a normal distribution with mean given by the true value of the regression coefficient and standard deviation approximated by the standard error from the R output. [2] Consider instead the following Bernoulli regression model where the linear predictor is based on the sex of the passengers: logit() = 3, female, + Bymale; where female; is an indicator variable that is 1 if passenger i is female or 0 otherwise, and likewise for the indicator variable males. Fit this regression model in R. Note that there is no intercept term. (c) What is the fitted probability of surviving for a male passenger? (d) Is this model adequate in describing the variability in the data at the 5% significance level