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Textbooks / Statistics / Applied Linear Regression Models 4

# Applied Linear Regression Models 4th Edition Solutions

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ISBN: 9780073014661

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##### ISBN: 9780073014661

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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).

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.

• Average run length, or ARL

The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

• 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.

• Binomial random variable

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

• Center line

A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.

• 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.

• Conidence interval

If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made

• Conidence level

Another term for the conidence coeficient.

• Continuous random variable.

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

• 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.

• 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 .

• Discrete uniform random variable

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

• Error propagation

An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

• Expected value

The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

• F-test

Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

• 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

• 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.

• Harmonic mean

The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .