1. Measuring the height of a California redwood tree

1. 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.
a. Assuming a linear relationship, use the least-squares method to compute the regression of confidence 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 of this equation
c. Predict the 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