The data can be retrieved by:

install.packages("faraway")

library(faraway)

data(wbca)

in r studio.

Problem 3,4,5 are under the same conditions.

3. Problems 3, 4 and 5 will use the wbca dataset of the faraway package. a. Fit a logistic regression model of Class on all the other variables as predic tors. Which coefficients are significantly different from 0 at the 0.05 significance level? b. Now do variable selection doing backward elimination, eliminating the predictor with the highest p-value for the Wald test for its coefficient until all p-values are lessthan 0.05. Show a summary of your final model. How do the standard errors for your coefficients differ from the corresponding ones in the full model of (a)? 4 a. Starting with the same full model as in (3a) run step (fullmodel) to do backward elimination in a way that achieves the best AIC. Show a summary of your final model. How does it compare to the model found in (3b)? b. Now run step() using forward selection. Show a summary of your final model and if it is different from the model of 4a, compare the AIC values. 5. Parts 3 and 4 used stepwise techniques but different rules for adding or eliminating variables and different stopping rules. Ideally when using criterion based measures like AIC, you would fit every model with at least one predictor and pick the one with the best AIC. a. How many possible models are there that include at least one of the predictors? Explain. b. Let's say we allow two-way interactions as well as main effects. By this I mean construct extra predictors Xi = XX, where i / j. How many possible models are there if we also consider two-way interactions as well as the main effects