Measuring the height of a California redwood tree is verydifficult because these trees grow to heights of over 300 feet.People familiar with these trees understand that the height of aCalifornia redwood tree is related to other characteristics of thetree, including the diameter of the tree at the breast height of aperson. The data in Redwood represent the height ( in feet) anddiameter ( in inches) at the breast height of a person for a sampleof 21 California redwood trees.
a. Assuming a linear relationship, use the least- squares methodto compute the regression coefficients b0 and b1. State theregression equation that predicts the height of a tree based on thetree’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 heightdiameter of 25 inches.
d. Interpret the meaning of the coefficient of determination inthis problem.
e. Perform a residual analysis of the results and determine theadequacy of the model.
f. Determine whether there is a significant relationship betweenthe height of redwood trees and the breast height diameter at the0.05 level of significance.
g. Construct a 95% confidence interval estimate of thepopulation slope between the height of the redwood trees and breastheight diameter.
h. What conclusion can you reach about the relationship betweenthe diameter of the tree and its height?
| Height | Diameter at breast height | Bark thickness |
| 122.0 | 20 | 1.1 |
| 193.5 | 36 | 2.8 |
| 166.5 | 18 | 2.0 |
| 82.0 | 10 | 1.2 |
| 133.5 | 21 | 2.0 |
| 156.0 | 29 | 1.4 |
| 172.5 | 51 | 1.8 |
| 81.0 | 11 | 1.1 |
| 148.0 | 26 | 2.5 |
| 113.0 | 12 | 1.5 |
| 84.0 | 13 | 1.4 |
| 164.0 | 40 | 2.3 |
| 203.3 | 52 | 2.0 |
| 174.0 | 30 | 2.5 |
| 159.0 | 22 | 3.0 |
| 205.0 | 42 | 2.6 |
| 223.5 | 45 | 4.3 |
| 195.0 | 54 | 4.0 |
| 232.5 | 39 | 2.2 |
| 190.5 | 36 | 3.5 |
| 100.0 | 8 | 1.4 |
