The attached data set bumpus is an excerpt from the classic data set by Bumpus (1898). It concerns the mortality of house sparrows based on several measurements. In this case survive=1 indicates the sparrow survived, survive=0 indicates it did not. The predictor variable in this case is length. [The code for conducting a logistic regression is in the handout from class.]

(1) Conduct a linear regression predicting survive from length. Show the residual plots and briefly explain how they clearly show that this is not the right analysis (just referring to the assumptions of linear regression).

(2) Conduct a logistic regression to predict the probability of surviving from length. Give the output showing the estitmated beta_0-hat and beta_1-hat.

(3) Give the equation for predicting the estimated probability of surviving from length, and the particular estimated probability for a sparrow of length 160.