Question

# (a) Write the regression model (please do not round coefficients): E[y]= ____ + ____ ?height +...

(a) Write the regression model (please do not round coefficients):
E[y]= ____ + ____ ?height + ______ ?diameter

(b) Keeping diameter constant, how much additional volume should we expect from an average tree if height is increased by 1 foot?

Are each of the predictors, "height" and "diameter" significant predictors of volume?

a.) Yes, since the p-values associated with each predictor are less than 0.05

b.) Only diameter is a significant predictor since it has the smallest p-value

c.) No, since the p-values associated with each predictor are less than 0.05

8.6 Cherry Trees: 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. (Hand, 1994)

Estimate Std. Error t value P(>|t|)
(Intercept) -57.99 8.64 -6.71 0.00
height 0.34 0.13 2.61 0.01
diameter 4.71 0.26 17.82

0.0

SolutonA:

Regression equation is

E(y)=-57.99+0.34*height+4.71*diameter

Solutionb:

b) Keeping diameter constant, how much additional volume should we expect from an average tree if height is increased by 1 foot?

For height coefficient=0.34

We must expect 0.34 additional volume from an average tree if height is increased by 1 foot.

Solutionc:

For height p=0.01

and for Diameter p=0.0

Both are significant variables since <0.05

a.) Yes, since the p-values associated with each predictor are less than 0.05