Redwood scenario. A forest management company wished to develop a model to assist in estimating the heights of the trees in a tract of Califomia redwood trees. For a random sample of 21 redwood trees in the tract were determined the height (in feet), diameter (in inches) five feet from the base of the tree, and the bark thickness (in inches) five feet from the base of the tree. Below are the results of a regression analysis on this data using a model specification of Height = ,+B,Diameter + ,Bark Thickness + E. [source: Adapted from Berenson et al (2006)] 12 Regression Statistics Multiple R 0.8864 R Square 0.7858 Adjusted R Squ 0.7620 Standard Error 22.5982 Observations 21 ANOVA df SS Regression 2 Residual 18 Total 20 33718.478 16859.24 9192.189 510.6772 42910.667 MS F 33.0135 Significance F 9.4991E-07 Coefficients Intercept Diameter Bark Thickness 62.141 2.057 15.642 Standard Error 13.503 0.443 7.148 t Stat P-value 4.602 0.000221 4.645 0.000201 2.188 0.042087 Lower 95% Upper 95% 33.772 90.510 1.126 2.987 0.624 30.660 To assess whether there is evidence that height is linearly related to at least one of diameter and bark thickness, the appropriate null and alternate hypotheses are: