Homework Assignment 3: Old Heteroskedastic
36-402, Advanced Data Analysis, Spring 2011
SOLUTIONS
# Setup
library(MASS)
data(geyser)
summary(geyser)
1. Answer:
# Plot the data points
plot(geyser$duration, geyser$waiting, cex = 0.5, pch = 16,
main = "Waiting time as function of geyser duration",
xlab = "Duration (minutes)", ylab = "Waiting time (minutes)")
mtext("Black line = LS regression line")
# Build linear model:
lm.1 = lm(waiting ~ duration, data = geyser)
# Add the regression line to the plot
abline(lm.1)
See Figure 1. Values of duration seem to cluster around 2 minutes and
4-5 minutes. The cluster on the right has more variation in waiting times
compared to the cluster on the left.
2. Answer:
# Plot the squared residuals against duration
plot(geyser$duration, lm.1$residuals^2, cex = 0.5, pch = 16,
main = "Squared residuals versus geyser duration",
xlab = "Geyser duration", ylab = "Squared residuals from linear model")
See Figure 2. The squared residuals seem to be largest, on average, near
duration = 4.5, and substantially smaller for the cluster of observations
near duration = 2.
3. Answer:
# To estimate the variance, I will use the same kernel regression function
# from HW Assignment 2:
1
