9.6 Cherry trees. Timber yield is approximately equal to the volume of a tree, however, this value is difficalt. to measure without first cutting the tree down. Instead, other variables, such as beight and diameter, may be used to predict a tree's volume and yield. Researchers wanting to tnderstand the relationship between these variables for black cherry trees collected data from 31 such tries in the Allegheny National Forest, Pennsylvania. Height is meastured in feet, dinmeter in inches (at 54 inches above ground), and wolame in cubic feet. (a) Calculate a 95% confidence interval for the coeflicient of hejght, and interpret it in the context of tbe dath. (b) One tree in this sample is 79 feet tall, has a diameter of 11.3 inches, and is 24.2 cubic foet in volume: Determine if the model everestimates or underestimates the volume of this tree, and by how mnich..