Measuring the height of a California redwood tree is a very difficult undertaking because these trees grow to heights of over 300 feet. People familiar with these trees understand that the height of a California redwood tree is related to other characteristics of the tree, including the diameter of the tree at the breast height of a person. The data in Redwood represent the height (in feet) and diameter (in inches) at the breast height of a person for a sample of 21 California redwood trees.
a. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b0 and b1. State the regression equation that predicts the height of a tree based on the tree's diameter at breast height of a person.
b. Interpret the meaning of the slope in this equation.
c. Predict the height for a tree that has a breast diameter of 25 inches.
d. Interpret the meaning of the coefficient of determination in this problem.
e. Perform a residual analysis on the results and determine the adequacy of the model.
f. Determine whether there is a significant relationship between the height of redwood trees and the breast height diameter at the 0.05 level of significance.
g. Construct a 95% confidence interval estimate of the population slope between the height of the redwood trees and breast diameter.