# Nonparametric Regression Exercises # 1 Scatterplot Smoothing # (a) Robey data on fertility and contraception library(car) data(Robey) attach(Robey) plot(contraceptors, tfr) abline(lm(tfr ~ contraceptors), lty=2) lines(loess.smooth(contraceptors, tfr, span=.5, family="gaussian")) # (b) SLID data detach(Robey) data(SLID) attach(SLID) hist(wages) hist(education) hist(age) plot(education, wages) lines(loess.smooth(education, wages, span=.3, family="gaussian")) abline(lm(wages ~ education), lty=2) plot(education^3, log(wages)) lines(loess.smooth(education^3, log(wages), span=.3, family="gaussian")) abline(lm(log(wages) ~ I(education^3)), lty=2) # (c) U.S. education data detach(SLID) data(States) attach(States) pairs(cbind(SATM, dollars, percent)) plot(dollars, SATM) lines(loess.smooth(dollars, SATM, span=.7, family="gaussian")) abline(lm(SATM ~ dollars), lty=2) plot(percent, SATM) lines(loess.smooth(percent, SATM, span=.5, family="gaussian")) abline(lm(SATM ~ percent), lty=2) plot(dollars, percent) lines(loess.smooth(dollars, percent, span=.7, family="gaussian")) abline(lm(percent ~ dollars), lty=2) mod.SATM <- lm(SATM ~ dollars + percent) summary(mod.SATM) cr.plots(mod.SATM) mod.SATM.2 <- lm(SATM ~ dollars + log(percent/(100 - percent))) summary(mod.SATM.2) cr.plots(mod.SATM.2)