In forestry, the diameter of a tree at breast height (which isfairly easy to measure) is used to predict the height of the tree(a difficult measurement to obtain). Silviculturists working inBritish Columbia’s boreal forest conducted a series ofspacing trials to predict the heights of several species of trees. The data in the table are the breast height diameters (incentimeters) and heights (in meters) for a sample of 36 whitespruce trees.

a. Construct a scattergramfor the data.

b. Assuming the relationshipbetween the variables is best described by a straight line, use themethod of least squares to estimate the y-intercept and slope ofthe line.

c. Plot the least-squaresline on your scattergram.

d. Do the data provide sufficientevidence to indicate that the breast height diameter x contributesinformation for the prediction of tree height y? Test using α= .05

e. Use your least-squares line tofind a 90% confidence interval for the average height of whitespruce trees with a breast height diameter of 20 cm. Interpretthe interval.

BHDiameter

Height

18.9

20

16.6

18.8

15.5

16.8

15.5

16.9

19.4

20.2

13.7

16.3

20

20

27.5

21.4

29.8

20.2

20.3

19.2

19.8

18

22.9

19.8

20.3

17.8

14.1

18.5

20

19.2

10.1

12.1

22

22.3

5.8

8

23.6

18.9

20.7

17.4

14.8

13.3

17.8

18.4

22.7

20.6

11.4

17.3

18.5

19

14.4

16.6

21.5

19.2

13.4

12.9

14.8

16.1

17.8

17.5

17.7

19.9

20.7

19.4

21

20.4

13.3

15.5

15.9

17.6

22.9

19.2