The Big R-Book

♣ 21 ♣Regression Models

21.1 Linear Regression

Linear Regression

With a linear regression we try to estimate an unknown variable y based on a known variable x and some constants (a and b). Its form is

regression – linear linear regression

To illustrate the linear regression, we will use data of the dataset survey from the package MASS. This dataset contains some physical measures, such as the span of the hand (variable Wr.Hand), the height of the person (variable Height, and the gender (variable Sex). Let us first illustrate the data by plotting the hand size in function of the height (results in Figure 21.1 on page 376):

library(MASS)

# Explore the data: 
plot(survey$Height, survey$Wr.Hnd) 

The package stats, that is loaded at start of R, has a function called lm() that can handle a linear regression. Its use is not difficult: we provide a data-frame (argument data) and a formula (argument formula). The formula has the shape of

lm()

< dependent variable> tilde <sum of independent variables> 

# Create the model: 
lm1 <- lm (formula = Wr.Hnd ~ Height, data = survey) 
summary(lm1) 
## 
## Call: 
## lm(formula = Wr.Hnd ~ Height, data = survey) 
## 
## Residuals: 

Figure 21.1: A scatter-plot generated by the line “plot(survey$Height, survey$Wr.Hnd).”