Statistics for Business and Economics (13th Edition)

13th Edition

ISBN: 9780134506593

Author: James T. McClave, P. George Benson, Terry Sincich

Publisher: PEARSON

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Textbook Question

Chapter 12.8, Problem 12.93ACI

Chemical plant contamination. Refer to Exercise 12.180 (p. 701) and the model relating the mean DDT level E(y) of contaminated fish to x₁ = miles captured upstream, x₂ = length, and x₃ = weight. Now consider a model for E(y) as a function of both weight and species (channel catfish, largemouth bass, and smallmouth buffalo).

a. Set up the appropriate dummy variables for species.
b. Write the equation of a model that proposes parallel straight-line relationships between mean DDT level E(y) and weight, one line for each species.
c. Write the equation of a model that proposes nonparallel straight-line relationships between mean DDT level E(y) and weight, one line for each species.
d. Fit the model, part b_f to the data saved in the file. Give the least squares prediction equation.
e. Refer to part d. Interpret the value of the least squares estimate of the beta coefficient multiplied by weight.
f. Fit the model, part c, to the data saved in the file. Give the least squares prediction equation.
g. Refer to part f. Find the estimated slope of the line relating DDT level (y) to weight for the channel catfish species.

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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Chapter 12.8, Problem 12.92ACI

Chapter 12.8, Problem 12.94ACI

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Chapter 12 Solutions

Statistics for Business and Economics (13th Edition)

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Solution Summary: The author explains how a model proposes parallel straight-line relationships between mean DDT level E(y) and weight, one line for each species.

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