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# Solutions for Chapter 11.3: Linear Statistical Models

## Full solutions for Probability and Statistics | 4th Edition

ISBN: 9780321500465

Solutions for Chapter 11.3: Linear Statistical Models

Solutions for Chapter 11.3
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##### ISBN: 9780321500465

This textbook survival guide was created for the textbook: Probability and Statistics, edition: 4. Probability and Statistics was written by and is associated to the ISBN: 9780321500465. Chapter 11.3: Linear Statistical Models includes 25 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 25 problems in chapter 11.3: Linear Statistical Models have been answered, more than 15735 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
• All possible (subsets) regressions

A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

• Analysis of variance (ANOVA)

A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

• Backward elimination

A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain

• Bivariate distribution

The joint probability distribution of two random variables.

• Cause-and-effect diagram

A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

• Comparative experiment

An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.

• Conditional probability density function

The probability density function of the conditional probability distribution of a continuous random variable.

• Consistent estimator

An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.

• Continuous uniform random variable

A continuous random variable with range of a inite interval and a constant probability density function.

• Contour plot

A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

• Contrast

A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.

• Convolution

A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

• Correlation matrix

A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .

• Covariance

A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .

• Crossed factors

Another name for factors that are arranged in a factorial experiment.

• Degrees of freedom.

The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.

• Designed experiment

An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

• Discrete uniform random variable

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

• Distribution function

Another name for a cumulative distribution function.

• Fraction defective

In statistical quality control, that portion of a number of units or the output of a process that is defective.

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