In order to perform local regression, we use the loess() function.

plot(age, wage, xlim = agelims, cex = .5, col = "darkgrey")
title("Local Regression")
fit <- loess(wage ~ age, span = .2, data = Wage)
fit2 <- loess(wage ~ age, span = .5, data = Wage)
lines(age.grid, predict(fit, data.frame(age = age.grid)), col = "red", lwd = 2)
lines(age.grid, predict(fit2, data.frame(age = age.grid)), col = "blue", lwd = 2)
legend("topright", legend = c("Span=0.2", "Span=0.5"), col = c("red", "blue"), lty = 1, lwd = 2, cex = .8)

Here we have performed local linear regression using spans of 0.2 and 0.5: that is, each neighborhood consists of 20% or 50% of the observations. The larger the span, the smoother the fit. The locfit library can also be used for fitting local regression models in R.

Questions

• Fit a local regression on the Boston dataset with medv as dependent variable and rm as independent variable. Use a span of 0.4. Store the result in the variable fit.
• Calculate the predictions of medv for a series of values of rm, ranging from 4 to 8, in steps of 0.1. Store the results in variable preds.
• MC1: Imagine that we decrease the span to 0.2, what would happen to the fit?
  • 1: The fit is less smooth
  • 2: The fit is more smooth
  • 3: The fit is equally smooth

Assume that:

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