As described, a regression line was fitted through 30 data points in the trees30.rda data set.

The formula of the line is found by:

*fit<-lm(Mass~Girth,data=TreeGirthMass)*

*fit*

*Call:*

*lm(formula = Mass ~ Girth, data = TreeGirthMass)*

*Coefficients:*

*(Intercept) Girth *

* -411.62 3.24 *

Therefore the equation of the regression line is:

Mass = 3.24×Girth -411.62

This is the equation of the line showing the relation between girth and mass of a tree. In the example, the tree had to be chopped down to measure its mass. It would be nice to estimate the mass of a tree by only measuring its girth (without chopping it down; so the profit margin could be estimated)! From the equation we can estimate the mass of a tree with a girth of 280 centimetres:

Mass = 3.24×280 -411.62 = 495.58 kg

The estimation we made is ** within the range we have measured**. This process is called interpolation. Of course, it is also possible to let R do this directly using the predict function. The predict function takes the model (fit) as first argument and a data frame with the value(s) of the Girth:

*predict(fit, data.frame(Girth = 280))*

* 1 *

*495.7158*

The difference with the manual method above is due to rounding error.

Similarly, we can estimate the mass of a tree ** outside the range we have measured**. This process is called extrapolation. For example, to estimate the mass of a tree with a girth of 500 cm:

Mass = 3.24×500 -411.62 = 1208.38 kg

Or in R:

*predict(fit, data.frame(Girth = 500))*

*1 *

*1208.622 *

Obviously, one has to be far more cautious with estimations found by means of extrapolation than with interpolation.

It is also possible to predict a range of value in R:

*predict(fit, data.frame(Girth = c(280, 500)))*

*1 2 *

* 495.7158 1208.6223*