- 11-8.11-42: Refer to the NFL team performance data in Exercise 11-4. (a) Calcul...
- 11-8.11-43: 11-43. Refer to the data in Exercise 11-5 on house selling price y ...
- 11-8.11-44: . Exercise 11-6 presents data on y steam usage and x average monthl...
- 11-8.11-45: Refer to the gasoline mileage data in Exercise 11-7. (a) What propo...
- 11-8.11-46: . Consider the data in Exercise 11-8 on y green liquor Na2S concent...
- 11-8.11-47: 11-47. Refer to Exercise 11-9, which presented data on blood pressu...
- 11-8.11-48: Exercise 11-10 presents data on wear volume y and oil viscosity x. ...
- 11-8.11-49: 11-49. Refer to Exercise 11-11, which presented data on chloride co...
- 11-8.11-50: Consider the rocket propellant data in Exercise 11-12. (a) Calculat...
- 11-8.11-51: Show that an equivalent way to define the test for significance of ...
- 11-8.11-52: Suppose that a simple linear regression model has been fit to n 25 ...
- 11-8.11-53: . Consider the rocket propellant data in Exercise 11- 12. Calculate...
- 11-8.11-54: Studentized Residuals. Show that the variance of the ith residual i...
Solutions for Chapter 11-8: ADEQUACY OF THE REGRESSION MODEL
Full solutions for Applied Statistics and Probability for Engineers | 3rd Edition
a-error (or a-risk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).
All possible (subsets) regressions
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
Analysis of variance (ANOVA)
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
Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
Central limit theorem
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.
Chi-square (or chi-squared) random variable
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.
The mean of the conditional probability distribution of a random variable.
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
Formulas used to determine the number of elements in sample spaces and events.
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 .
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.
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.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
Another name for a probability density function
Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).
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.
Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.
Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.