Solutions for Chapter 5: Continuous Random Variables

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

A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.

A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.

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.

A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.

The probability mass function of the conditional probability distribution of a discrete random variable.

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

A continuous random variable with range of a inite interval and a constant probability density function.

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.

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 .

Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

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.

A random variable with a inite (or countably ininite) range.

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 method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

In statistical quality control, that portion of a number of units or the output of a process that is defective.

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

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 .