Correlation and Least-Squares Regression

The command cor computes correlations. The correlation of our height and weight variables is computed by

height<-c(165,171,169,182,176) weight<-c(70,83,78,87,85) cor(weight,height)

The command lm (whort for Linear Model) fits a least squares regression. Use the following command to fit a regression with weight as the response variable and height as the explanatory variable:

height<-c(165,171,169,182,176) weight<-c(70,83,78,87,85) lm(weight~height)

The slope of this line is $b = r * s_y / s_x$; you can check this with the command

height<-c(165,171,169,182,176) weight<-c(70,83,78,87,85) cor(weight,height) * sd(weight)/sd(height)

The intercept is $a = \overline{y} - a \overline{x}$:

height<-c(165,171,169,182,176) weight<-c(70,83,78,87,85) b<-cor(weight,height) * sd(weight)/sd(height) mean(weight)-b*mean(height)

Using the least squares line, the weights we would predict for the observed heights are computed by

height<-c(165,171,169,182,176) -80.04 + 0.9307 * height

The residuals can then be computes as Computing the residuals:

height<-c(165,171,169,182,176) weight<-c(70,83,78,87,85) weight - pred

Try some examples of your own in the work area below.

Work Area

Enter your own commands here; then click the Submit button.