In forestry, the diameter of a tree at breast height (which is fairly easy to measure) is used to predict the
height of a tree (a dicult measurement ot obtain). Silviculturists working in British Columbia's boreal
forest conducted a series of spacing trials to predict the heights of several species of trees. The data in
the accompanyhing table are the breast height diameters (in cm, x) and heights (in m, y) for a sample
of 36 white spruce trees. x y x y x y x y x y x y

18.9 20.0 20.3 17.8 18.5 19.0 20.0 20.0 23.6 18.9 17.7 19.9
16.6 18.8 14.1 18.5 14.4 16.6 27.5 21.4 20.7 17.4 20.7 19.4
15.5 16.8 20.0 19.2 21.5 19.2 29.8 20.2 14.8 13.3 21.0 20.4
15.5 16.9 10.1 12.1 13.4 12.9 20.3 19.2 17.8 18.4 13.3 15.5
19.4 20.2 22.0 22.3 14.8 16.1 19.8 18.0 22.7 20.6 15.9 17.6
13.7 16.3 5.8 8.0 17.8 17.5 22.9 19.8 11.4 17.3 22.9 19.2
The data are available on the STA 113 homepage (click \exams"). Or copy the data set by typing from
your acpub account:
cp /afs/acpub/project/sta215/trees. data trees. data
a) Construct a scattergram for the data.
b) Assuming the relatinship between the variabels is best described by a straight line, use the method of
least squares to estimate the intercept and the slope of the line.
c) Plot the least squares lline on your scattergram.
d) Do the data provide sucient evidence to indicate that the breast height diamter x contributes information
for the prediction of tree height? Test using = 0:05.
e) Use your least squares line to nd a 90% condence interval for the average height of white spruce trees
with a breast diameter of 20cm. Interpret the result.