Measuring the height of a California redwood tree is a very difficult undertakin
ID: 3368776 • Letter: M
Question
Measuring the height of a California redwood tree is a very difficult undertaking, It is understood 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 (dbh) of a person. The following data represent the height and dbh for a sample of 21 California redwood trees. A partial excel output for this problem's solution is shown on page (35 pts) 1. Obs No. Obs. No. Height Diameter at Breast Height Diameter at Breast Height (dbh) Height (dbh 164 203.25 174 159 205 223.5 195 232.5 190.5 40 52 30 12 13 14 15 16 17 18 19 20 21 122 20 2 193.5 166.5 36 18 10 2 1 29 5 1 82 133.5 4 5 42 156 172.5 45 54 39 7 8 8 1 148 113 84 36 26 12 13 9 10 100 8 What is the regression equation? (Give the values for the slope and intercept, not just the variable names.) a. Predict the height for a redwood tree that has a dbh of 40 inches and calculate its residual. b. c. Interpret the meaning of bo and bi for this problem.Explanation / Answer
Solution:
Data >Dataanalysis>Regression
Regression equation is
height=78.78851+2.263604*diameter
Solutionb:
predicted height for diamter=40 is
height=78.78851+2.263604*diameter
=78.78851+2.263604*40
predicted height=169.33267
Observed height for x=40 is 164
residual=observed-predicted
=164-169.33267
=
Solutionc:
slope=b0=
2.673604
y intercept =b1=
SUMMARY OUTPUT Regression Statistics Multiple R 0.853753 R Square 0.728894 Adjusted R Square 0.714625 Standard Error 24.74631 Observations 21 ANOVA df SS MS F Significance F Regression 1 31282.38 31282.38 51.08327 8.57E-07 Residual 19 11635.22 612.3801 Total 20 42917.6 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 78.78851 12.21366 6.450849 3.49E-06 53.22502 104.352 Diameter 2.673604 0.374074 7.147256 8.57E-07 1.890657 3.45655