(A) What is the estimated regression equation used to predict volume? Use the fo
ID: 3319551 • Letter: #
Question
(A) What is the estimated regression equation used to predict volume? Use the following selections to form the equation.
["volume", "diameter", "height", "intercept"] -hat = ["-57.99", "0.26", "4.71", "8.64", "0.34", "0.13"] ["*", "-", "/", "+"] ["57.99", "8.64", "4.71", "0.34", "0.26", "0.13"] height ["/", "-", "*", "+"] ["0.26", "0.13", "57.99", "8.64", "0.34", "4.71"] ["diameter", "height", "intercept", "volume"]
(B) What would you conclude about the relationship, if any, between height and volume?
(C) Interpret the slope of the diameter.
(a) Height has a significant negative association with volume. Timber yield is approximately equal to the volume of a tree, however, this value is difficult to measure without first cutting the tree down. Instead, other variables, such as height and diameter, may be used to predict a tree's volume and yield. Researchers wanting to understand the relationship between these variables for black cherry trees collected data from 31 such trees in the Allegheny National Forest, Pennsylvania. Height is measured in feet, diameter in inches (at 54 inches above ground), and volume in cubic feet. Coefficients Standard Error Stat P-value Intercept -57.99 height 0.34 diameter 4.71 8.64 0.13 0.26 6.7 0.00 2.61 0.01 17.82 0.00Explanation / Answer
A) Volume = -57.99 + 0.34 Height + 4.71 Diameter
B) Height has a significant positive association with volume. Option b is correct.
C) Interpretation the slope of the diameter: As diameter increases by 1 inch, the volume is expected to increase by 4.71 cubic feet.
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