The volume (in cubic feet) of a black cherry tree can be modeled by the equation y = - 50.7 + 0.4x, +5.3x2, where x, is the tree's height (in feet) and x, is the tree's diameter (in inches). Use the multiple regression equation to predict the y-valuesfor the values of the independent variables.(a) x, = 71, x2 = 8.7(b) x, = 65, x2 = 10.6(c) X4 = 82, x2 = 17.8(d) x1 = 92, x2 = 20.2%3D(a) The predicted volume is 23.8 cubic feet.(Round to one decimal place as needed.)(b) The predicted volume is cubic feet.(Round to one decimal place as needed.)

Answered: The volume (in cubic feet) of a black…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.5: Mathematical Modeling And Variation

Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...

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The volume (in cubic feet) of a black cherry tree can be modeled by the equation y = - 50.7 + 0.4x, +5.3x2, where x, is the tree's height (in feet) and x, is the tree's diameter (in inches). Use the multiple regression equation to predict the y-values
for the values of the independent variables.
(a) x, = 71, x2 = 8.7
(b) x, = 65, x2 = 10.6
(c) X4 = 82, x2 = 17.8
(d) x1 = 92, x2 = 20.2
%3D
(a) The predicted volume is 23.8 cubic feet.
(Round to one decimal place as needed.)
(b) The predicted volume is cubic feet.
(Round to one decimal place as needed.)

Expert Solution

Step 1

Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a time so we are answering the first three as you have not mentioned which of these you are looking for. Please re-submit the question separately for the remaining sub-parts.

Given:

The regression line is as follows

$\hat{y} = - 50.7 + 0.4 x_{1} + 5.3 x_{2}$

x₁ is the tree's height

x₂ is the tree's diameter

y is the volume in cubic feet.

Step 2

$x_{1} = 71 x_{2} = 8.7$

Substituting the values in the given equation

$\hat{y} = - 50.7 + 0.4 \times 71 + 5.3 \times 8.7 = 23.81$

The required answer is 23.81

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