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QMB Exam 3
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Gravity
Terms in this set (53)
Treatments
Different levels of a factor.
Response variable
Another word for the dependent variable of interest.
Factor
Another word for the independent variable of interest.
ANOVA table
A table used to summarize the analysis of variance computations and results. It contains columns showing the source of variation, the sum of squares, the degrees of freedom, the mean square, the F value(s), and the p-value(s).
Experimental units
The objects of interest in the experiment.
Completely randomized design:
An experimental design in which the treatments are randomly assigned to the experimental units.
Single-factor experiment
An experiment involving only one factor with k populations or treatments.
F distribution
A probability distribution based on the ratio of two independent estimates of the variance of a normal population. The F distribution is used in hypothesis tests about the equality of k population means.
Matched samples
One simple random sample of elements is selected and two data values are obtained for each element. For example, to compare two production methods, one simple random sample of n workers is selected. Each worker first uses one method and then the other method. The order of the two methods is assigned randomly.
Independent random samples
Samples selected from two populations in such a way that the elements making up one sample are chosen independently of the elements making up the other sample.
Partitioning
The process of allocating the total sum of squares and degrees of freedom to the various components.
Contingency tables:
A table used to summarize observed and expected frequencies for a test of independence.
Multinomial population
A population in which each element is assigned to one and only one of several categories. The multinomial distribution extends the binomial distribution from two to three or more outcomes.
Contingency table
A table used to summarize observed and expected frequencies for a test of independence.
Test of independence
A method of assessing whether two categorical variables are associated or dependent.
Pooled estimator of p
An estimator of a population proportion obtained by computing a weighted average of the sample proportions obtained from two independent samples.
Independent variables
The variable that is doing the predicting or explaining. It is denoted by x.
Dependent variable
The variable that is being predicted or explained. It is denoted by y.
Regression model
The equation that describes how y is related to x and an error term; in simple linear regression, the regression model is y=β0+β1x+ϵ.
Scatter diagram
A graph of bivariate data in which the independent variable is on the horizontal axis and the dependent variable is on the vertical axis.
Residual analysis
The analysis of the residuals used to determine whether the assumptions made about the regression model appear to be valid. Residual analysis is also used to identify outliers and influential observations.
Coefficient of determination
A measure of the goodness of fit of the estimated regression equation. It can be interpreted as the proportion of the variability in the dependent variable y that is explained by the estimated regression equation.
Simple linear regression
Regression analysis involving one independent variable and one dependent variable in which the relationship between the variables is approximated by a straight line.
Residual plot
Graphical representation of the residuals that can be used to determine whether the assumptions made about the regression model appear to be valid.
ANOVA table
The analysis of variance table used to summarize the computations associated with the F test for significance.
Influential observation
An observation that has a strong influence or effect on the regression results.
Outlier
A data point or observation that does not fit the trend shown by the remaining data.
Standardized residual
The value obtained by dividing a residual by its standard deviation.
Prediction interval
The interval estimate of an individual value of y for a given value of x.
Confidence interval
The interval estimate of the mean value of y for a given value of x.
Least squares method
A procedure used to develop the estimated regression equation. The objective is to minimize Σ(yi-y^i)2.
Scatter diagrams
A graph of bivariate data in which the independent variable is on the horizontal axis and the dependent variable is on the vertical axis.
Estimated regression equation
The estimate of the regression equation developed from sample data by using the least squares method. For simple linear regression, the estimated regression equation is y^=b0+b1x.
Regression equation
The equation that describes how the mean or expected value of the dependent variable is related to the independent variable; in simple linear regression, E(y)=β0+β1x.
ith residual
The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation; for the ith observation the ith residual is yi-y^i.
For the ith observation, the ith residual is what equation?
yi-y^i
Correlation coefficient
A measure of the strength of the linear relationship between two variables (previously discussed in Chapter 3).
Mean square error (MSE)
The unbiased estimate of the variance of the error term σ2. It is denoted by MSE or s2.
Standard error of the estimate
The square root of the mean square error, denoted by s. It is the estimate of σ, the standard deviation of the error term ϵ.
Mean square error
The unbiased estimate of the variance of the error term σ2. It is denoted by MSE or s2.
Multiple regression analysis
Regression analysis involving two or more independent variables.
Dummy or indicator variable
A variable used to model the effect of categorical independent variables. A dummy variable may take only the value zero or one.
Categorical independent variable
An independent variable with categorical data.
Adjusted multiple coefficient of determination
A measure of the goodness of fit of the estimated multiple regression equation that adjusts for the number of independent variables in the model and thus avoids overestimating the impact of adding more independent variables.
Multiple coefficient of determination
A measure of the goodness of fit of the estimated multiple regression equation. It can be interpreted as the proportion of the variability in the dependent variable that is explained by the estimated regression equation.
Dummy variable
A variable used to model the effect of categorical independent variables. A dummy variable may take only the value zero or one.
Categorical independent variables
An independent variable with categorical data.
Multicollinearity
The term used to describe the correlation among the independent variables.
Multiple regression model
The mathematical equation that describes how the dependent variable y is related to the independent variables x1,x2,...,xp and an error term ε.
Multiple regression equation
The mathematical equation relating the expected value or mean value of the dependent variable to the values of the independent variables; that is, E(y)=β0+β1x1+β2x2+⋯+βpxp.
Estimated multiple regression equation
The estimate of the multiple regression equation based on sample data and the least squares method; it is y^=b0+b1x1+b2x2+⋯+bpxp.
Least squares method
The method used to develop the estimated regression equation. It minimizes the sum of squared residuals (the deviations between the observed values of the dependent variable, yi, and the estimated values of the dependent variable, y^i).
We would like the mean difference to be what?
Zero.
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