- 8.1.1: In an experiment to determine the factors affecting tensile strengt...
- 8.1.2: Refer to Exercise 1. a. Find a 95% confidence interval for the coef...
- 8.1.3: The data used to fit the model in Exercise 1 are presented in the f...
- 8.1.4: The article Application of Analysis of Variance to Wet Clutch Engag...
- 8.1.5: In the article Application of Statistical Design in the Leaching St...
- 8.1.6: The article Earthmoving Productivity Estimation Using Linear Regres...
- 8.1.7: In a study of the lung function of children, the volume of air exha...
- 8.1.8: Refer to Exercise 7. a. Find a 95% confidence interval for the coef...
- 8.1.9: The article Drying of Pulps in Sprouted Bed: Effect of Composition ...
- 8.1.10: A scientist has measured quantities y, x1, and x2. She believes tha...
- 8.1.11: The following MINITAB output is for a multiple regression. Somethin...
- 8.1.12: The following MINITAB output is for a multiple regression. Some of ...
- 8.1.13: The article Evaluating Vent Manifold Inerting Requirements: Flash P...
- 8.1.14: In the article Low-Temperature Heat Capacity and Thermodynamic Prop...
- 8.1.15: The following data were collected in an experiment to study the rel...
- 8.1.16: The following data were collected in an experiment to study the rel...
- 8.1.17: The November 24, 2001, issue of The Economist published economic da...
- 8.1.18: The article Multiple Linear Regression for Lake Ice and Lake Temper...
- 8.1.19: In an experiment to estimate the acceleration of an object down an ...
Solutions for Chapter 8.1: The Multiple Regression Model
Full solutions for Statistics for Engineers and Scientists | 4th Edition
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
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
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.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
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 probability of an event given that the random experiment produces an outcome in another event.
The variance of the conditional probability distribution of a random variable.
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
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.
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
Another name for factors that are arranged in a factorial experiment.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass 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).
Error of estimation
The difference between an estimated value and the true value.
Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.