4.74 Tree diameter and wood volume The ability to estimate the volume of a tree

Question

4.74 Tree diameter and wood volume The ability to estimate the volume of a tree based on a simple measurement, such as the tree's diameter is important to the lumber industry, ecologists, and conservationists. Data on volume, in cubic feet, and diameter at chest height, in inches for 70 shortleaf pines were reported in Bruce and Schumacher's book, Forest Mensuration.

Describe the scatterplot. Is there a pattern/association or lack thereof of the data? What does the scatterplot show? Clusters? Outliers? Is the association that is seen positive/negative/neither? Why does it appear to be strong, moderate or weak? If it isn’t linear, what is it? Give the value of the linear correlation coefficient, r, (not r2), and an explanation of how the correlation coefficient supports the description.

DIAMETER VOLUME 4.4 2.0 4.6 2.2 5.0 3.0 5.1 4.3 5.1 3.0 5.2 2.9 5.2 3.5 5.5 3.4 5.5 5.0 5.6 7.2 5.9 6.4 5.9 5.6 7.5 7.7 7.6 10.3 7.6 8.0 7.8 12.1 8.0 11.1 8.1 16.8 8.4 13.6 8.6 16.6 8.9 20.2 9.1 17.0 9.2 17.7 9.3 19.4 9.3 17.1 9.8 23.9 9.9 22.0 9.9 23.1 9.9 22.6 10.1 22.0 10.2 27.0 10.2 27.0 10.3 27.4 10.4 25.2 10.6 25.5 11.0 25.8 11.1 32.8 11.2 35.4 11.5 26.0 11.7 29.0 12.0 30.2 12.2 28.2 12.2 32.4 12.5 41.3 12.9 45.2 13.0 31.5 13.1 37.8 13.1 31.6 13.4 43.1 13.8 36.5 13.8 43.3 14.3 41.3 14.3 58.9 14.6 65.6 14.8 59.3 14.9 41.4 15.1 61.5 15.2 66.7 15.2 68.2 15.3 73.2 15.4 65.9 15.7 55.5 15.9 73.6 16.0 65.9 16.8 71.4 17.8 80.2 18.3 93.8 18.3 97.9 19.4 107.0 23.4 163.5 y = 6.8367x-41.568 R2 0.8926 Volume and Diameter 180.0 160.0 140.0 120.0 100.0 u 80.0 9 60.0 40.0 20.0 0.0 20.0 -40.0 010 10.0 15.0 20.0 25.0 Diameter

Explanation / Answer

Describe the scatterplot. this is a linear scatterplot

What does the scatterplot show? It shows the association between 2 variables

Clusters? Outliers? Is the association that is seen positive/negative/neither? it seems that has an outlier and the assocuation is positive

Why does it appear to be strong, moderate or weak? it appear to be strong because R^2 is greater than 0.50

Give the value of the linear correlation coefficient, r, (not r2), and an explanation of how the correlation coefficient supports the description.

R =0.9448

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