Problem 4e: A forester has a unique ability to estimate the volume (in cubic feet) of trees prior to a timber sale. The timber company wants him to train other employees in his technique of estimation. The forrester's assistant estimates the cubic-foot volume of each tree. After the tree has been chopped down, the forresters obtains the actual cubic-foot volume for a total of 26 trees. A regression model was fitted to the data, with the Estimated Volume y fitted against the Actual Volume x of each tree. The results of the regression are shown below: Analysis of Variance Coefficients Model Summary DF Adj SS Adj MS F-Value P-Value 0.000 Source Term Coef SE Coef T-Value P-Value S R-sq R-sq(adj) Regression 1 234.31 234.315 294.81 24 19.08 Constant 1.845 0.856 2.15 0.041 חרF וonח 0 795 02 166

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QUESTION 18
Problem 4e:
A forester has a unique ability to estimate the volume (in cubic feet) of trees prior to a timber sale. The timber company wants him to train other
employees in his technique of estimation. The forrester's assistant estimates the cubic-foot volume of each tree. After the tree has been chopped down,
the forresters obtains the actual cubic-foot volume for a total of 26 trees.
A regression model was fitted to the data, with the Estimated Volume y fitted against the Actual Volume x of each tree. The results of the regression are
shown below:
Analysis of Variance
Coefficients
Model Summary
DF Adj SS Adj MS F-Value P-Value
1 234.31 234315 294.81
Source
Term
Coef SE Coef T-Value P-Value
0.000
R-sq R-sq(adj)
92.16%
Regression
Constant 1.845
0.856
2.15
0.041
0.891520 92.47%
Error
24 19.08
0.795
Act vol 0.7830 0.0456
17.17
0.000
Total
25 253.39
e) A prediction of y for x-15 was performed based on the fitted regression, with the following results:
Settings
Prediction
Variable Setting
Fit SE Fit
95% CI
95% PI
Act_vol
15
13.5906 0.233225 (13.1093, 14.0720) (11.6887, 15.4925)
Determine the standard error for individual outcomes [s.e.(v)l for the estimated volume when the actual volume is 15 cubic feet. Use 3
decimals in your answer.
Transcribed Image Text:QUESTION 18 Problem 4e: A forester has a unique ability to estimate the volume (in cubic feet) of trees prior to a timber sale. The timber company wants him to train other employees in his technique of estimation. The forrester's assistant estimates the cubic-foot volume of each tree. After the tree has been chopped down, the forresters obtains the actual cubic-foot volume for a total of 26 trees. A regression model was fitted to the data, with the Estimated Volume y fitted against the Actual Volume x of each tree. The results of the regression are shown below: Analysis of Variance Coefficients Model Summary DF Adj SS Adj MS F-Value P-Value 1 234.31 234315 294.81 Source Term Coef SE Coef T-Value P-Value 0.000 R-sq R-sq(adj) 92.16% Regression Constant 1.845 0.856 2.15 0.041 0.891520 92.47% Error 24 19.08 0.795 Act vol 0.7830 0.0456 17.17 0.000 Total 25 253.39 e) A prediction of y for x-15 was performed based on the fitted regression, with the following results: Settings Prediction Variable Setting Fit SE Fit 95% CI 95% PI Act_vol 15 13.5906 0.233225 (13.1093, 14.0720) (11.6887, 15.4925) Determine the standard error for individual outcomes [s.e.(v)l for the estimated volume when the actual volume is 15 cubic feet. Use 3 decimals in your answer.
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