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- 12.1.3: Bivariate data often arises from the use of two differenttechniques...
- 12.1.4: The accompanying data on y 5 ammonium concentration(mg/L) and x 5 t...
- 12.1.5: The article Objective Measurement of the Stretchabilityof Mozzarell...
- 12.1.6: One factor in the development of tennis elbow, a maladythat strikes...
- 12.1.7: The article Some Field Experience in the Use of anAccelerated Metho...
- 12.1.8: Referring to Exercise 7, suppose that the standard deviationof the ...
- 12.1.9: The flow rate y (m3/min) in a device used for air-qualitymeasuremen...
- 12.1.10: Suppose the expected cost of a production run is related tothe size...
- 12.1.11: Suppose that in a certain chemical process the reactiontime y (hr) ...
Solutions for Chapter 12.1: The Simple Linear Regression Model
Full solutions for Probability and Statistics for Engineering and the Sciences | 9th Edition
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
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
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
Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).
Coeficient of determination
See R 2 .
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
The variance of the conditional probability distribution of a 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 graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
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 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).
An expression sometimes used for nonlinear regression models or polynomial regression models.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
Degrees of freedom.
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 model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
Estimate (or point estimate)
The numerical value of a point estimator.
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.