# RPD -- Examples 1.1+ -- Soybean Yield vs. Ozone Level

yld.oz <- data.frame(ozone = c(0.02, 0.07, 0.11, 0.15),
                     yield = c(242, 237, 231, 201))

yld.oz.model <- lm(yield ~ ozone, data=yld.oz)

summary(yld.oz.model)
confint(yld.oz.model)                         # CIs for beta
anova(yld.oz.model)
predict(yld.oz.model, se.fit=TRUE)            # standard errors
residuals(yld.oz.model)
predict(yld.oz.model, interval="confidence")  # CIs for means
predict(yld.oz.model, interval="prediction")  # prediction intervals

plot(yield ~ ozone, pch="x", xlim=c(0,0.16), ylim=c(170,290), data=yld.oz)
abline(yld.oz.model)

# Approximation to confidence bands for the mean:
lines(yld.oz$ozone, predict(yld.oz.model,interval="confidence")[,"lwr"], lty=2)
lines(yld.oz$ozone, predict(yld.oz.model,interval="confidence")[,"upr"], lty=2)