10th Edition

ISBN: 9780321989178

Author: Neil A. Weiss

Publisher: PEARSON

Concept explainers

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of tw…

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Z-Scores

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Textbook Question

Chapter A.3, Problem 74E

Use the regression identity for multiple linear regression to show that

R 2 = 1 − S S E S S T .

a. Explain why this formula shows that the coefficient of multiple determination can also be interpreted as the percentage reduction in the total squared error obtained by using the regression equation instead of the mean, y ¯ , to predict the observed values of the response variable.
b. Referring to Exercise A.65, what percentage reduction in the total squared error is obtained by using the regression equation instead of the mean of the observed prices to predict the observed prices?
c. Referring to Exercise A.66, what percentage reduction in the total squared error is obtained by using the regression equation instead of the mean of the observed graduation rates to predict the observed graduation rates?

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 A.3, Problem 73E

Chapter A.4, Problem 75E

Chapter A Solutions

Introductory Statistics (10th Edition)

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Solution Summary: The author explains that the coefficient of multiple determination can be interpreted as the percentage reduction in the total squared error obtained by using the regression instead of the mean.

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