12. To estimate ages of trees, forest rangers use a linear model that relates tree diameter (in inches) to age (in years). The model is useful because tree diameter is much easier to measure than tree age, which requires special tools for extracting a representative cross section of the tree and counting the rings. Use the Excel output below collected for a certain variety of oaks to answer the following items. Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total 0.987245589 0.974653853 0.973245734 9.856485308 df 20 SS MS F 1 67244.24455 67244.24455 692.1671136 18 1748.705447 97.15030262 19 68992.95 Coefficients Standard Error t Stat P-value Intercept 2.324650035 3.532378821 0.658097503 0.518804417 Diameter (inches) 5.812352938 0.220925831 26.30906904 8.10017E-16 Significance F 8.10017E-16 Lower 95% Upper 95% Lower 95.0% Upper 95.0% -5.096602484 9.745902554 -5.096602484 9.745902554 5.348204991 6.276500886 5.348204991 6.276500886 a. Compute for the Pearson's r. Interpret. b. Write the equation of the estimated regression line. c. Interpret the regression coefficients. d. How much variability of age of the oak trees can be attributed to their diameter? e. If the scope of diameter data is from 2.2 to 38.1, predict the age of the tree with a diameter of 3 feet (36 inches).
12. To estimate ages of trees, forest rangers use a linear model that relates tree diameter (in inches) to age (in years). The model is useful because tree diameter is much easier to measure than tree age, which requires special tools for extracting a representative cross section of the tree and counting the rings. Use the Excel output below collected for a certain variety of oaks to answer the following items. Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total 0.987245589 0.974653853 0.973245734 9.856485308 df 20 SS MS F 1 67244.24455 67244.24455 692.1671136 18 1748.705447 97.15030262 19 68992.95 Coefficients Standard Error t Stat P-value Intercept 2.324650035 3.532378821 0.658097503 0.518804417 Diameter (inches) 5.812352938 0.220925831 26.30906904 8.10017E-16 Significance F 8.10017E-16 Lower 95% Upper 95% Lower 95.0% Upper 95.0% -5.096602484 9.745902554 -5.096602484 9.745902554 5.348204991 6.276500886 5.348204991 6.276500886 a. Compute for the Pearson's r. Interpret. b. Write the equation of the estimated regression line. c. Interpret the regression coefficients. d. How much variability of age of the oak trees can be attributed to their diameter? e. If the scope of diameter data is from 2.2 to 38.1, predict the age of the tree with a diameter of 3 feet (36 inches).
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Transcribed Image Text:12. To estimate ages of trees, forest rangers use a linear model that relates tree diameter (in
inches) to age (in years). The model is useful because tree diameter is much easier to
measure than tree age, which requires special tools for extracting a representative cross
section of the tree and counting the rings. Use the Excel output below collected for a
certain variety of oaks to answer the following items.
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
ANOVA
Regression
Residual
Total
0.987245589
0.974653853
0.973245734
9.856485308
df
20
SS
MS
F
67244.24455 67244.24455 692.1671136
1
18 1748.705447 97.15030262
19
68992.95
Significance F
8.10017E-16
t Stat
P-value
Lower 95%
Upper 95%
Coefficients Standard Error
Lower 95.0% Upper 95.0%
2.324650035 3.532378821 0.658097603 0.518804417 -5.096602484 9.745902554 -5.096602484 9.745902554
Diameter (inches) 5.812352938 0.220925831 26.30906904 8.10017E-16 5.348204991 6.276500886 5.348204991 6.276500886
Intercept
a. Compute for the Pearson's r. Interpret.
b. Write the equation of the estimated regression line.
c. Interpret the regression coefficients.
d. How much variability of age of the oak trees can be attributed to their diameter?
e. If the scope of diameter data is from 2.2 to 38.1, predict the age of the tree with a
diameter of 3 feet (36 inches).
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VIEWStep 5: Compute the variability of age which is explained by the diameter of tree.
VIEWStep 6: Find the predicted age.
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