Measuring the height of a California redwood tree is very difficult 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 mean height for a tree that has a breast height 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 height diameter.