# regression coefficients

regression coefficients 150 150 Affordable Capstone Projects Written from Scratch

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 represent the height (in feet) and diameter (in inches) at the breast height of a person for a sample of 21 California redwood trees.

1. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b 0 and b 1. State the regression equation that predicts the height of a tree based on the tree’s diameter at breast height of a person.
2. Interpret the meaning of the slope in this equation.
3. Predict the height for a tree that has a breast height diameter of 25 inches.
4. Interpret the meaning of the coefficient of determination in this problem.
5. Perform a residual analysis on the results and determine the adequacy of the model.
6. 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.

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