NAME:

The data set below consists of the height (H) and diameter (D) of a sample of 31 Black Cherry Trees from Allegheny Natinoal Forest, Pennsylvania. Vol is the volume of marketable lumber produced by each tree.

1. Describe the relationship between Volume and Height, and Volume and Diameter. Is there a relation between Height and Diameter? (See next page.)

2. If you could know only one thing, height or diameter, which would you prefer to know to help you predict the volume of wood a tree would produce? Explain.

 Based just on the graph, diameter would probably be the best choice, since the relationship is very clear there, and there seems to be little error (which means little variation about the regression line.)

3. On the next page you can see the printout for the regression of Volume on Diameter. The regression of Volume on Height is not shown. How will the F statistic for that regression compare to the value obtained for Volume on Diameter? Why?

 The F-statistic measures the MSR/MSE, which is the mean sum of squares due to regression divided by the mean sum of squares due to error. Because the points are much more tightly clustered about a line for Vol vs. Diameter, we would expect the F-Statistic to be higher for this regression than for Volume vs. Height. ( In fact, the F-stat for diameter is 419.36, while for vol. vs. height it is only 16.6.)

Data set = Trees, Name of Fit = L1

Normal Regression

Kernel mean function = Identity

Response = Vol

Terms = (D)

Coefficient Estimates

Label Estimate Std. Error t-value

Constant -36.9435 3.36514 -10.978

D 5.06586 0.247377 20.478

R Squared: 0.93532

Sigma hat: 4.25199

Number of cases: 31

Degrees of freedom: 29

Summary Analysis of Variance Table

Source df SS MS F p-value

Regression 1 7581.78 7581.78 419.36 0.0000

Residual 29 524.303 18.0794