In order to instead fit a natural spline, we use the ns() function. Here we fit a natural spline with four degrees of freedom.

fit2 <- lm(wage ~ ns(age, df = 4), data = Wage)
pred2 <- predict(fit2, newdata = list(age = age.grid), se = TRUE)
lines(age.grid, pred2$fit, col = "red", lwd = 2)

As with the bs() function, we could instead specify the knots directly using the knots option.

Questions

• Fit a natural spline on the Boston dataset with medv as dependent variable and lstat as independent variable. The spline should have 5 degrees of freedom. Store the result in the variable fit.
• Calculate the predictions of medv for a series of values of lstat, ranging from 0 to 50, in steps of 1. Store the point predictions in the variable preds. If you use SE = FALSE in predict(), the outputs are point predictions; if you use SE = TRUE, the point predictions are in the attribute fit.
• MC1: How many interior knots does this natural spline have?
  • 1: 3 knots
  • 2: 4 knots
  • 3: 5 knots
  • 4: 6 knots

Assume that:

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