Question

(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 |

Answer #1

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.

ANSWER:0.34

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**

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