Example – Black Cherry TreesExample – Black Cherry Trees

Example – Black Cherry TreesExample – Black Cherry Trees

The data frame trees is made available in R with

>data(trees)

and contains the well-known black cherry trees data. These record the girth in inches, height in feet and volume of timber in cubic feet of each of a sample of 31 felled black cherry trees in Allegheny National Forest, Pennsylvania. Note that girth is the diameter of the tree (in inches) measured at 4 ft 6 in above the ground.

We treat volume as the (continuous) response variable y and seek a reasonablemodel describing its distribution conditional on the explanatory variables girth and height.

This might be a first step to prediction of volume based on further observations ofthe explanatory variables.

Consider the R command

>pairs(trees, main = "trees data")

The relationship between girth and volume is especially noticeable.We therefore consider first a linear model

Yi=a + bxi +εi

where Y is volume and x is girth

The R command for fitting linear models by least squares is lm. We have

> trees.model.1 = lm(Volume~Girth, data=trees)> summary(trees.model.1)

The fitted model is

volume = −36.9 + 5.07 × girth + residual

Now try:

> plot(Volume~Girth, data=trees)> abline(coef(trees.model.1))> plot(resid(trees.model.1)~Girth, data=trees,ylab="residuals from Model 1")