The diameter height and volume of 31 black cherry trees in A

The diameter, height, and volume of 31 black cherry trees in Allegheny National Forest are recorded:

Col

Name

Count

Description

C1

Diameter

31

Diameter of tree in inches (measured at 4.5 feet above ground)

C2

Height

31

Height of tree

C3

Volume

31

Volume of tree in cubic feet

Using Minitab to answer the following questions:

a) Fit the least squares regression line to predict Volume from Diameter using Minitab.

b) Test the significance for the slope coefficient in the above fitted line.

c) Do a scatter plot of the Volume and the Diameter with the regression line plotted on the same graph.

d) What percentage of the total variation of Volume is explained by the Diameter?

e) Find a 95% confidence interval for the mean Volume when the Diameter = 10.

f) Find a 95% prediction interval for the Volume when the Diameter = 10.

g) Calculate the correlation coefficients between Volume and the Diameter using Minitab. Test the hypothesis that the variables are uncorrelated for this pair of variables.

Solution