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. xlsx represent the height (in feet) and diameter (in inches) at the breast height of a person for a sample of 21 California redwood trees. Summary Output
Regression Statistics
Multiple R 0.886444087
R Square 0.78578312
Adjusted R Square 0.761981244
Standard Error 22.59816752
Observations 21
ANOVA
df SS MSF Significance F
Regression 2 33718.47752 16859.23876 33.01349577 9.50E-07
Residual 18 9192.189151 510.6771751
Total 20 42910.66667
Coefficients Standard error t-stat P-value lower 95%
Intercept 62.14112783 13.50306426 4.602001934 0.000221273 33.77224256
Diameter
at breast
height 2.05671274 0.442797529 4.644815303 0.000201409 1.126429653
Bark
thickness 15.64180216 7.148285403 2.188189374 0.042086628 0.623811831
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 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.