Agents at a call center get a score of 1 if a caller was satisfied with a particular call and a score of O if not. The company wants to see if it can accurately predict, including generating a probability estimate for the prediction, whether customers will be satisfied with a call based on relevant predictors involved such as, for example, length of the call, number of months of experience of the agent, time of day that the caller calls, etc. What is a natural regression method to use to build such a predictive model? Please first describe in detail (without any R or other software code) how you would algorithmically/mathematically set up a regression-based model to solve this problem, including how you could generate probability value estimates. You can assume there are M predictor variables. Then describe how you could solve the problem in practice using R. For this part, do include the R code. You can use the built-in mtcars dataset, which does include 0/1-valued variables, as a stand-in dataset for this part of the problem. In your proposed model, use the "vs" variable -- a 0/1-valued variable -- as the response variable to serve as a stand-in for the score of a call-center call. Taking M=2, you should use "wt" and "disp" as the stand-in predictor variables. What estimates for the intercept and the coefficients of wt and disp do you get?
What probability values for 0 and 1 do you get from this model when wt = 2.8, disp = 160?