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# Multiple Regression Analysis in Minitab

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BC LUMBER is trying to obtain a better prediction on the volume of its trees. A
sample of trees of various diameters were cut and the diameters, heights and volumes were recorded. The results are given below.

DIAMETER: Diameter in inches at 4.5 feet above ground level

HEIGHT: Height of the tree in feet

VOLUME: Volume of tree in cubic feet

DIAMETER HEIGHT VOLUME

8.3 70 10.3
8.6 65 10.3
8.8 63 10.2
10.5 72 16.4
10.7 81 18.8
10.8 83 19.7
11.0 66 15.6
11.0 75 18.2
11.1 80 22.6
11.2 75 19.9
11.3 79 24.2
11.4 76 21.0
11.4 76 21.4
11.7 69 21.3
12.0 75 19.1
12.9 74 22.2
12.9 85 33.8
13.3 86 27.4
13.7 71 25.7
13.8 64 24.9
14.0 78 34.5
14.2 80 31.7
14.5 74 36.3
16.0 72 38.3
16.3 77 42.6
17.3 81 55.4
17.5 82 55.7
17.9 80 58.3
18.0 80 51.5
18.0 80 51.0
20.6 87 77.0

Using MINITAB perform the regression and correlation analysis for the data on
VOLUME and DIAMETER and HEIGHT by answering the following:

1. Determine the regression equation which describes the relationship between
VOLUME, DIAMETER and HEIGHT.

2. Test the utility of this regression model using the F-test. Interpret the observed
p-value for this test.

3. Test the utility of each component of the model (i.e, is DIAMETER useful in
predicting VOLUME, and is HEIGHT useful in predicting VOLUME). Perform the
t-tests on Ã?²1 and Ã?²2 , report the t-values and observed p values and
interpret.

4. Determine the correlation matrix for VOLUME, HEIGHT and DIAMETER.

5. Find and interpret the multiple index of determination (R-Squared).

6. Find and interpret the 95% prediction interval for volume of a tree having
diameter of 15 inches and height 80 feet.

7. Find and interpret the 95% confidence interval for the mean volume for trees
having diameter of 15 inches and height 80 feet.

8. What volume would you predict for a tree having diameter 15 inches and height
120 feet?

9. What volume would you predict for a tree having diameter 30 inches and height
120 feet?

10. Based on your findings in 1-11 and your work in CASE #9, what is your opinion about using diameter and height to predict volume of trees? Explain.

11. Based on your analysis can you conclude that the diameter and the height cause the volume? Explain.