Solutions for Chapter 11.8: HIGHERDIMENSIONAL LEASTSQUARES FIT
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications  2nd Edition
ISBN: 9781119285427
Solutions for Chapter 11.8: HIGHERDIMENSIONAL LEASTSQUARES FIT
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2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

Adjusted R 2
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.

Alias
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.

Average
See Arithmetic mean.

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.

Confounding
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

Conidence coeficient
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.

Contingency table.
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria

Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.

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.

Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.

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

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.

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

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

Fisherâ€™s least signiicant difference (LSD) method
A series of pairwise hypothesis tests of treatment means in an experiment to determine which means differ.

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