Use the following information to answer questions 6-10 Timber yield is approxima
ID: 3319073 • Letter: U
Question
Use the following information to answer questions 6-10 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 tStat P-value Intercept -57.99 height0.34 diameter4.71 8.64 0.13 0.26 6.71 0.00 2.61 0.01 17.82 0.00 6. What is the estimated regression equation used to predict volume? 7. What would you conclude about the relationship, if any, between height and diameter? 8. Interpret the slope of the diameter. 9. One tree in this sample is 79 feet tall, has a diameter of 11.3 inches, and is 24.2 cubic feet in volume. Determine if the model overestimates or underestimates the volume of this tree. 10. By how much does it over or underestimate the volume (to 2 decimal places)?Explanation / Answer
6) Estimated Regression equation used to predict volume is
Y(hat)= 0.34x1+4.71x2-57.99
7) It is difficult To conclude any relationship between two independence variabled. But the coefficient of diameter is greater than the height we can say as more diameter, more will be height.
9) on putting the value in regression equation
Y(hat)= 0.34x1+4.71x2-57.99
Y(hat)= 0.34*71+4.71*11.3-57.99= 19.373
The model underestimated the volume of this tree.
10) Difference= Actual- underestimated= 24.2-19.373= 4.83
By 4.83 it underestimate the volume.