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# Solutions for Chapter 6.3: Statistics for Engineers and Scientists 4th Edition

## Full solutions for Statistics for Engineers and Scientists | 4th Edition

ISBN: 9780073401331

Solutions for Chapter 6.3

Solutions for Chapter 6.3
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##### ISBN: 9780073401331

Since 13 problems in chapter 6.3 have been answered, more than 262785 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Chapter 6.3 includes 13 full step-by-step solutions. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4.

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

• Attribute

A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

• Bimodal distribution.

A distribution with two modes

• Bivariate normal distribution

The joint distribution of two normal random variables

• C chart

An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.

• Central limit theorem

The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

• 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.

• Coeficient of determination

See R 2 .

• Combination.

A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.

• Cook’s distance

In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

• 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 matrix

A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

• Critical value(s)

The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. 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.

• Deming’s 14 points.

A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality

• Density function

Another name for a probability density function

• Design matrix

A matrix that provides the tests that are to be conducted in an experiment.

• Enumerative study

A study in which a sample from a population is used to make inference to the population. See Analytic study

• Finite population correction factor

A term in the formula for the variance of a hypergeometric random variable.

• Hat matrix.

In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .

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