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)EstimateStd. Errort valueP(>|t|)(Intercept)-57.998.6 4-6.710.00height0.340.132.610.01dia meter4.710.2617.82(c) Are each of the predictors, "height" and "diameter" significant predictors of volume? PICK ONEOnly diameter is a significant predictor since it has the smallest p-valueYes, since the p-values associated with each predictor are less than 0.05No, since the p-values associated with each predictor are less than 0.05(d) How much volume is expected from a tree that measures 79 feet tall and has a diameter of 11.3 inches?(please round to the nearest cubic foot) cubic feet(e) A tree in the data set measures 79 feet tall, has a diameter of 11.3 inches, and is 24.2 cubic feet in volume. Determine whether the model gives an overestimate or underestimate of the volume of this tree. PICK

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

(d) 22.093 cubic feet

(e) underestimate

Step-by-step explanation:

Our main objective is to determine the following

(c) Are each of the predictors, "height" and "diameter" significant predictors of volume? PICK ONE Only diameter is a significant predictor since it has the smallest p-value

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

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

Assuming our significance level ∝ = 0.05

From the data given;

p-value for height is = 0.00

p - value for diameter = 0.01

where, p-value ( = 0.01 and 0.00 ) <  ∝ (= 0.05 )

Hence, according to the rejection rule; the null hypothesis is rejected and  the predictors "height" and " diameter" are significant predictors of volume.

Thus

The answer is :

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

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

(d) How much volume is expected from a tree that measures 79 feet tall and has a diameter of 11.3 inches?(please round to the nearest cubic foot)________

(e)

A tree in the data set measures 79 feet tall, has a diameter of 11.3 inches, and is 24.2 cubic feet in volume. Determine whether the model gives an overestimate or underestimate of the volume of this tree. PICK ONE

overestimate

underestimate

We can posits that the model gives an underestimate of the volume of this tree due to the fact that the predicted value is 22.093 and which is less than the observed value of 24.2 cubic feet.

2x + 8

step-by-step explanation: