Answered: 15.3 #6 The authors of the article…

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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15.3 #6

The authors of the article "Age, Spacing and Growth Rate of Tamarix as an Indication of Lake Boundary Fluctuations at Sebkhet Kelbia, Tunisia"† used a simple linear regression model to describe the relationship between y = vigor (average width in centimeters of the last two annual rings) and x = stem density (stems/m²). The estimated model was based on the following data. Also given are the standardized residuals.

x	4	5	6	9	14	15	15	19	21	22
y	0.75	1.20	0.55	0.60	0.65	0.55	0.00	0.35	0.45	0.40
Std resid	−0.28	1.92	−0.90	−0.28	0.54	0.24	−2.05	−0.12	0.60	0.52

(a)

What assumptions are required for the simple linear regression model to be appropriate? (Select all that apply.)

A) The random errors associated with different observations are dependent on one another.

B) The distribution of e at any given x is not normal.

C) The distribution of e at any given x is normal.

D) The distribution of e at any particular x value has mean value 0.

E) The random errors associated with different observations are independent of one another.

F) The standard deviation of e varies across values of x.

G) The standard deviation of e is the same across values of x.

H)The distribution of e at any particular x value has mean value 1.

Are there any points with unusually large residuals? (Select all that apply.)

A) (x, y) = (4, 0.75)

B) (x, y) = (15, 0.00)

C) (x, y) = (14, 0.65)

D) (x, y) = (5, 1.20)

E) (x, y) = (15, 0.55)

F) (x, y) = (9, 0.60)

G) (x, y) = (6, 0.55)

H)none of the above

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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