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 analysis represent the height, diameter at breast height of a person, and bark thickness for a sample of 21 California redwood trees. a.) State the multiple regression equation.
b.) Briefly explain your interpretation of the two slopes in this equation.
c.) Interpret the findings. Detail the meaning of all the p-values (for each independent variable and F statistic), r square, and adjusted r square.
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