Measuring the height of a California redwood tree is very difficult because these trees grow to heights of over 300 feet. People familiar with these trees understand that the height of a California redwood tree is related to other characteristics of the tree, including the diameter of the tree at the breast height of a person. The data in the table represent the height (in feet) and diameter (in inches) at the breast height of a person for a sample of 21 California redwood trees.Assuming a linear relationship, use the least- squares method to compute the regression coefficients b0 and b1. State the regression equation that predicts the height of a tree based on the tree’s diameter at breast height of a person.Interpret the meaning of the slope in this equation.Predict the mean height for a tree that has a breast height diameter of 25 inches.HeightDiameter at breast heightBark thickness122.0201.1193.5362.8166.5182.082.0101.2133.5212.0156.0291.4172.5511.881.0111.1148.0262.5113.0121.584.0131.4164.0402.3203.3522.0174.0302.5159.0223.0205.0422.6223.5454.3195.0544.0232.5392.2190.5363.5100.081.4

1.Step-by-step procedure to obtain the regression equation using Excel:In Excel sheet, enter Height…

Answered: Measuring the height of a California…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Measuring the height of a California redwood tree is very difficult because these trees grow to heights of over 300 feet. People familiar with these trees understand that the height of a California redwood tree is related to other characteristics of the tree, including the diameter of the tree at the breast height of a person. The data in the table represent the height (in feet) and diameter (in inches) at the breast height of a person for a sample of 21 California redwood trees.

Assuming a linear relationship, use the least- squares method to compute the regression coefficients b0 and b1. State the regression equation that predicts the height of a tree based on the tree’s diameter at breast height of a person.
Interpret the meaning of the slope in this equation.
Predict the mean height for a tree that has a breast height diameter of 25 inches.

Height	Diameter at breast height	Bark thickness
122.0	20	1.1
193.5	36	2.8
166.5	18	2.0
82.0	10	1.2
133.5	21	2.0
156.0	29	1.4
172.5	51	1.8
81.0	11	1.1
148.0	26	2.5
113.0	12	1.5
84.0	13	1.4
164.0	40	2.3
203.3	52	2.0
174.0	30	2.5
159.0	22	3.0
205.0	42	2.6
223.5	45	4.3
195.0	54	4.0
232.5	39	2.2
190.5	36	3.5
100.0	8	1.4

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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