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# Solutions for Chapter 12.4: An Analysis of Variance for Linear Regression ## Full solutions for Introduction to Probability and Statistics 1 | 14th Edition

ISBN: 9781133103752 Solutions for Chapter 12.4: An Analysis of Variance for Linear Regression

Solutions for Chapter 12.4
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##### ISBN: 9781133103752

This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Introduction to Probability and Statistics 1, edition: 14. Chapter 12.4: An Analysis of Variance for Linear Regression includes 18 full step-by-step solutions. Since 18 problems in chapter 12.4: An Analysis of Variance for Linear Regression have been answered, more than 9180 students have viewed full step-by-step solutions from this chapter. Introduction to Probability and Statistics 1 was written by and is associated to the ISBN: 9781133103752.

Key Statistics Terms and definitions covered in this textbook
• `-error (or `-risk)

In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).

• Acceptance region

In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion

• Additivity property of x 2

If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.

• Axioms of probability

A set of rules that probabilities deined on a sample space must follow. See Probability

• Biased estimator

Unbiased estimator.

• Categorical data

Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

• Central composite design (CCD)

A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.

• Central tendency

The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

• Chance cause

The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.

• Conditional variance.

The variance of the conditional probability distribution of a random variable.

• Control limits

See Control chart.

• Deining relation

A subset of effects in a fractional factorial design that deine the aliases in the design.

• Discrete distribution

A probability distribution for a discrete random variable

• Discrete uniform random variable

A discrete random variable with a inite range and constant probability mass function.

• Dispersion

The amount of variability exhibited by data

• Erlang random variable

A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

• Error variance

The variance of an error term or component in a model.

• Experiment

A series of tests in which changes are made to the system under study

• Frequency distribution

An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on

• Generating function

A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function

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