(3 points) Timber yield is approximately equal to the volume of a tree, however,
ID: 3059891 • Letter: #
Question
(3 points) 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 32 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.
(a) Calculate a 95.16 % confidence interval for the coefficient of height.
The lower end of the confidence interval is:
The upper end of the confidence interval is:
(b) One tree in this sample is 79 feet tall, has a diameter of 10.1 inches, and is 24.5 cubic feet in volume. Determine if the model overestimates or underestimates the volume of this tree. (enter either OVERESTIMATES or UNDERESTIMATES):
How much does it overestimate or underestimate by?
(c) Fill in the blanks in the sentence to show your contextual understanding of the confidence interval you calculated in part (a):
For a given diameter, we are % confident that for each foot increase in the height of a tree, the is expected to (enter either INCREASE or DECREASE) on average by to cubic feet.
Explanation / Answer
a)
The confidence intervals would be calculated as Estimate+/-ta/2*SE, where ta/2 would be for n-2 degrees of freedom. In this case, it is 30
It is 2.04
0.49+/-2.04*0.3
Lower Interval=-0.122
Upper Interval=1.102
b)
Volume=-59.87+0.49*height+4.2*diameter
=-59.87+0.49*79+4.2*10.1
=21.26
Actual is 24.5 cubic feet. Hence, it underestimates.
c)
95%, volume, INCREASE, -0.122 to 1.102
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