Using Excel finding the multiple regression equation and 95% confidence
Answer the following question: 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 and the thickness of the bark of the tree. The data in the file redwood.sls attached represents the height, diameter at breast height of a person and the bark thickness for a sample of 21 California redwood trees.
a) State the multiple regression equation.
b) Interpret the meaning of the slopes in this equation.
c) Predict the mean height for a tree that has a breast diameter of 25 inches and a bark thickness of 2 inches.
d) Interpret the meaning of the coefficient of multiple 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 two independent variables (breast diameter and the bark thickness) 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 the bark thickness.
h) At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the independent variables to include in this model.
i) Construct a 95% confidence interval estimate of the mean height for trees that have a breast diameter of 25 inches and a bark thickness of 2 inches along with a prediction interval for a individual tree.
j) Compute and interpret the coefficients of partial determination.
NOTE: The answer for a is Y = 62.1411 + 2.0567X1 + 15.6418X2