Note that we could have directly computed the probabilities by selecting the type="response" option in the predict() function.

preds <- predict(fit, newdata = list(age = age.grid), type = "response", se = TRUE)

However, the corresponding confidence intervals would not have been sensible because we would end up with negative probabilities!

Questions

• Create the same model as in the previous exercise (medv as dependent variable and a degree-3 polynomial of dis as independent variable). Store the result in fit.
• Calculate the predictions of medv for a series of values of dis, ranging from 1 mile to 12 miles, in steps of 0.1 mile. This time, use the type="response" option. Store the results in the variable preds.
• Calculate the confidence intervals with z-value 2.0. Store the results in variable se.bands. Make use of the cbindfunction in order to column bind the two vectors.
• MC1: Interpret the regression coefficients and decide which order polynomial is sufficient to explain the data.
  • 1: Degree-1 for dis
  • 2: Degree-2 for dis
  • 3: Degree-3 for dis

Assume that:

• The MASS library has been loaded
• The Boston dataset has been loaded and attached