See attached data file.
BC LUMBER harvests trees throughout the U.S. and Canada. They need to be able to estimate the amount of timber in a given area of forest. More specifically they need a quick and easy way to determine the volume of any given tree. Unfortunately, it is difficult to measure the volume of a tree directly. However, it is not difficult to measure the diameter of the tree. Thus, BC LUMBER would like to be able to arrive at a relationship between volume of a tree and the diameter of a tree, and determine whether the volume may be predicted on the basis of the diameter. A sample of trees of various diameters were cut and the diameters and volumes were recorded. The results are given below. (This sample is for black cherry trees in Allegheny National Forest, Pennsylvania. Of course, different varieties of trees and different locations will yield different results. So separate tables of data are prepared for each species and each location.)
DIAMETER: Diameter in inches at 4.5 feet above ground level
VOLUME: Volume of tree in cubic feet
Using MINITAB perform the regression and correlation analysis for the data on VOLUME and DIAMETER by answering the following:
1. Generate a scatterplot for VOLUME vs. DIAMETER. Interpret.
2. Determine the equation of the "best fit" line which describes the relationship between VOLUME and DIAMETER.
3. Generate the the graph of the "best fit" line on your scatterplot in 1.
Discuss 1-3, and specifically what does the scatter plot and best fit line show you in this case?
Step by step method for regression analysis in Minitab is given in the answer.