--- title: "Exploration 2.3" output: word_document --- ```{r setup, include=FALSE} knitr::opts_knit$set(global.par = TRUE) #knitr::opts_chunk$set(fig.width=4, fig.height=2.67) load(url("http://www.isi-stats.com/isi2/ISI.RData")) ``` ```{r, echo=FALSE} par(mar=c(4.1, 4.1, 1.1, 1.1)) ``` **Load the carmpg dataset, e.g.,** ```{r} carmpg= read.delim("http://www.isi-stats.com/isi2/data/carmpg.txt", stringsAsFactors=T) head(carmpg) ``` **Acceleration vs. weight** ```{r} with(carmpg, plot(acceleration ~ weight)) with(carmpg, summary(lm(acceleration ~ weight))$r.squared) ``` **ANOVA table** ```{r} with(carmpg, summary(aov(acceleration ~ weight))) ``` **Acceleration vs. Horsepower** ```{r} with(carmpg, plot(acceleration ~ horsepower)) with(carmpg, summary(lm(acceleration ~ horsepower))$r.squared) with(carmpg, summary(aov(acceleration ~ horsepower))) ``` **Acceleration vs. Weight equation, with effect coding** ```{r} with(carmpg, summary(lm(acceleration ~ weight, contrasts = list(weight="contr.sum")))) ``` **adjusting for horsepower** ```{r} ##Create -1/1 version of weight weightEffect = 2*as.numeric(carmpg$weight)-3 with(carmpg, plot(acceleration ~ weightEffect, col = horsepower)) #see also boxplot(acceleration ~ horsepower:weight, data = carmpg, col=c("blue", "red"), varwidth=T) ``` **Adjusting for horsepower** ```{r} horsepowerEffect = 2*as.numeric(carmpg$horsepower)-3 model1=lm(acceleration ~ horsepowerEffect + weightEffect, data = carmpg) summary(model1) acceleration.adj=carmpg$acceleration - 1.87147*(2*as.numeric(carmpg$horsepower)-3) plot(acceleration.adj ~ carmpg$weight) isisummary(acceleration.adj, carmpg$weight) model2 = lm(acceleration.adj ~ weightEffect) summary(model2) #see also coplot(acceleration ~ weight | horsepower, data = carmpg, panel = panel.smooth) ``` **ANOVA** ```{r} anova(model1) #to get adjusted sums of squares (p-values match the t-tests) ##first install the car package car::Anova(model1, type = "III") summary(model1) ```