1. Fora sample of 12 trees, the volume of lumber (in m3 ) and the diameter (in cm) at a fixed height above ground level was measured. The results were as follows.
|
Diameter
|
Volume
|
Diameter
|
Volume
|
|
35.1
|
0.81
|
33.8
|
0.80
|
|
48.4
|
1.39
|
45.3
|
1.69
|
|
47.9
|
1.31
|
25.2
|
0.30
|
|
35.3
|
0.67
|
28.5
|
0.19
|
|
47.3
|
1.46
|
30.1
|
0.63
|
|
26.4
|
0.47
|
30.0
|
0.64
|
a. Construct a scatterplot of volume (y) versus diameter (x).
b. Compute the least-squares line for predicting volume from diameter.
c. Compute the fitted value and the residual for each point.
d. If two trees differ in diameter by 8 cm, by how much would you predict their volumes to differ?
e. Predict the volume for a tree whose diameter is 44 cm.
f. For what diameter would you predict a volume of 1 m3 ?