# NOT RUN {
# Using the data in the built-in data frame Air.df,
# fit the cube root of ozone as a function of temperature.
# Then compute predicted values for ozone at 70 and 90
# degrees F, and compute 95% confidence intervals for the
# mean value of ozone at these temperatures.
# First create the lm object
#---------------------------
ozone.fit <- lm(ozone ~ temperature, data = Air.df)
# Now get predicted values and CIs at 70 and 90 degrees
#------------------------------------------------------
predict.list <- predict(ozone.fit,
newdata = data.frame(temperature = c(70, 90)), se.fit = TRUE)
pointwise(predict.list, coverage = 0.95)
# $upper
# 1 2
# 2.839145 4.278533
# $fit
# 1 2
# 2.697810 4.101808
# $lower
# 1 2
# 2.556475 3.925082
#--------------------------------------------------------------------
# Continuing with the above example, create a scatterplot of ozone
# vs. temperature, and add the fitted line along with simultaneous
# 95% confidence bands.
x <- Air.df$temperature
y <- Air.df$ozone
dev.new()
plot(x, y, xlab="Temperature (degrees F)",
ylab = expression(sqrt("Ozone (ppb)", 3)))
abline(ozone.fit, lwd = 2)
new.x <- seq(min(x), max(x), length=100)
predict.ozone <- predict(ozone.fit,
newdata = data.frame(temperature = new.x), se.fit = TRUE)
ci.ozone <- pointwise(predict.ozone, coverage=0.95,
simultaneous=TRUE)
lines(new.x, ci.ozone$lower, lty=2, lwd = 2, col = 2)
lines(new.x, ci.ozone$upper, lty=2, lwd = 2, col = 2)
title(main=paste("Cube Root Ozone vs. Temperature with Fitted Line",
"and Simultaneous 95% Confidence Bands",
sep="\n"))
#--------------------------------------------------------------------
# Redo the last example by creating non-simultaneous
# confidence bounds and prediction bounds as well.
dev.new()
plot(x, y, xlab = "Temperature (degrees F)",
ylab = expression(sqrt("Ozone (ppb)", 3)))
abline(ozone.fit, lwd = 2)
new.x <- seq(min(x), max(x), length=100)
predict.ozone <- predict(ozone.fit,
newdata = data.frame(temperature = new.x), se.fit = TRUE)
ci.ozone <- pointwise(predict.ozone, coverage=0.95)
lines(new.x, ci.ozone$lower, lty=2, col = 2, lwd = 2)
lines(new.x, ci.ozone$upper, lty=2, col = 2, lwd = 2)
pi.ozone <- pointwise(predict.ozone, coverage = 0.95,
individual = TRUE)
lines(new.x, pi.ozone$lower, lty=4, col = 4, lwd = 2)
lines(new.x, pi.ozone$upper, lty=4, col = 4, lwd = 2)
title(main=paste("Cube Root Ozone vs. Temperature with Fitted Line",
"and 95% Confidence and Prediction Bands",
sep="\n"))
#--------------------------------------------------------------------
# Clean up
rm(predict.list, ozone.fit, x, y, new.x, predict.ozone, ci.ozone,
pi.ozone)
# }
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