- 8.1.1E: In an experiment to determine the factors affecting tensile strengt...
- 8.1.2E: Refer to Exercise 1.a. Find a 95% confidence interval for the coeff...
- 8.1.3E: The data used to fit the model in Exercise 1 are presented in the f...
- 8.1.4E: The article “Application of Analysis of Variance to Wet Clutch Enga...
- 8.1.5E: In the article “Application of Statistical Design in the Leaching S...
- 8.1.6E: The article “Earthmoving Productivity Estimation Using Linear Regre...
- 8.1.7E: In a study of the lung function of children, the volume of air exha...
- 8.1.8E: Refer to Exercise 7.a. Find a 95% confidence interval for the coeff...
- 8.1.9E: The article “Drying of Pulps in Sprouted Bed: Effect of Composition...
- 8.1.10E: A scientist has measured quantities y, x1 and x2. She believes that...
- 8.1.11E: The following MINITAB output is for a multiple regression. Somethin...
- 8.1.12E: The following MINITAB output is for a multiple regression. Some of ...
- 8.1.13E: The article “Evaluating Vent Manifold Inerting Requirements: Flash ...
- 8.1.14E: In the article “Low-Temperature Heat Capacity and Thermodynamic Pro...
- 8.1.15E: The following data were collected in an experiment to study the rel...
- 8.1.16E: The following data were collected in an experiment to study the rel...
- 8.1.17E: The November 24. 2001, issue of The Economist published economic da...
- 8.1.18E: The article “Multiple Linear Regression for Lake Ice and Lake Tempe...
- 8.1.19E: In an experiment to estimate the acceleration of an object down an ...
Solutions for Chapter 8.1: Statistics for Engineers and Scientists 4th Edition
Full solutions for Statistics for Engineers and Scientists | 4th Edition
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.
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
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain
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.
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .
In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).
Formulas used to determine the number of elements in sample spaces and events.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
An expression sometimes used for nonlinear regression models or polynomial regression models.
The amount of variability exhibited by data
A study in which a sample from a population is used to make inference to the population. See Analytic study
Error mean square
The error sum of squares divided by its number of degrees of freedom.
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.
Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.
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.
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.