Solutions for Chapter 6: Descriptive Statistics

A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

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.

The probability of an event given that the random experiment produces an outcome in another event.

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

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

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.

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 .

A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t

W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.

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

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

A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

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

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

A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

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

A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function

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.

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 .