Question

For a sample of 12 trees, the volume of lumber (in m³) and the diameter ( in cm ) at a fixed height above the ground level was measured. The results were as follows.

Use Excel sheet

Diameter	Volumes
35.1	0.81
48.4	1.39
47.9	1.31
35.3	0.67
47.3	1.46
26.4	0.47
33.8	0.8
45.3	1.69
25.2	0.3
28.5	0.19
30.1	0.63
30	0.64

a)Construct a scatterplot of volume ( y ) versus diameter ( x ). using Excel

b)Compute the least-square line for predicting volume from diameter.

c)Compute the fitted value and residual for each point. d)If two trees differ in diameter by 8 cm, by how much would you predict their volume to differ?

e)Predict the volume of a tree whose diameter is 44 cm.

f)For what diameter would you predict a volume of 1m³

Answer 1

Interpretation:

The scatter plot illustrates that there exists a positive linear relationship between the variables Diameter (X) and Volume (Y). The direction of the scattered points is upwards, and hence the relationship is positive. The strength of the positive linear relationship between the variables is very strong.

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