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# Solutions for Chapter 6: Stats: Data and Models 4th Edition

## Full solutions for Stats: Data and Models | 4th Edition

ISBN: 9780321986498

Solutions for Chapter 6

Solutions for Chapter 6
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##### ISBN: 9780321986498

This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Stats: Data and Models , edition: 4. Since 52 problems in chapter 6 have been answered, more than 40572 students have viewed full step-by-step solutions from this chapter. Chapter 6 includes 52 full step-by-step solutions. Stats: Data and Models was written by and is associated to the ISBN: 9780321986498.

Key Statistics Terms and definitions covered in this textbook
• 2 k p - factorial experiment

A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

• Bayes’ estimator

An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.

• Bimodal distribution.

A distribution with two modes

• Binomial random variable

A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.

• Continuity correction.

A correction factor used to improve the approximation to binomial probabilities from a normal distribution.

• Control limits

See Control chart.

• 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.

• 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.

• Crossed factors

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

• Cumulative distribution function

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

• Defects-per-unit control chart

See U chart

• Dependent variable

The response variable in regression or a designed experiment.

• Distribution function

Another name for a cumulative distribution function.

• Error variance

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

• Exhaustive

A property of a collection of events that indicates that their union equals the sample space.

• First-order model

A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model

• Gamma function

A function used in the probability density function of a gamma random variable that can be considered to extend factorials

• Gamma random variable

A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

• Goodness of fit

In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.

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