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Solutions for Chapter 12.1: The Simple Linear Regression Model
Full solutions for Probability and Statistics for Engineering and the Sciences  9th Edition
ISBN: 9781305251809
Solutions for Chapter 12.1: The Simple Linear Regression Model
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Probability and Statistics for Engineering and the Sciences was written by and is associated to the ISBN: 9781305251809. Chapter 12.1: The Simple Linear Regression Model includes 11 full stepbystep solutions. Since 11 problems in chapter 12.1: The Simple Linear Regression Model have been answered, more than 98892 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Probability and Statistics for Engineering and the Sciences, edition: 9.

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

Arithmetic mean
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

Backward elimination
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 .

Combination.
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.

Conditional variance.
The variance of the conditional probability distribution of a random variable.

Contour plot
A twodimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

Control chart
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the incontrol 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 incontrol, or free from assignable causes. Points beyond the control limits indicate an outofcontrol process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

Cook’s distance
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.

Correlation coeficient
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).

Curvilinear regression
An expression sometimes used for nonlinear regression models or polynomial regression models.

Decision interval
A parameter in a tabular CUSUM algorithm that is determined from a tradeoff 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.

Empirical model
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.

F distribution.
The distribution of the random variable deined as the ratio of two independent chisquare random variables, each divided by its number of degrees of freedom.

Ftest
Any test of signiicance involving the F distribution. The most common Ftests 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.