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Ordinary least squares regression of Okun's law.Since the regression line does not miss any of the points by very much, the R 2 of the regression is relatively high.. In statistics, the coefficient of determination, denoted R 2 or r 2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s).
In the words of one critic: "Thus gives the 'percentage of variance explained' by the regression, an expression that, for most social scientists, is of doubtful meaning but great rhetorical value. If this number is large, the regression gives a good fit, and there is little point in searching for additional variables.
In probability theory and statistics, the index of dispersion, [1] dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR), like the coefficient of variation, is a normalized measure of the dispersion of a probability distribution: it is a measure used to quantify whether a set of observed occurrences are clustered or dispersed compared to a standard ...
The formula for the one-way ANOVA F-test statistic is =, or =. The "explained variance", or "between-group variability" is = (¯ ¯) / where ¯ denotes the sample mean in the i-th group, is the number of observations in the i-th group, ¯ denotes the overall mean of the data, and denotes the number of groups.
The explained sum of squares (ESS) is the sum of the squares of the deviations of the predicted values from the mean value of a response variable, in a standard regression model — for example, y i = a + b 1 x 1i + b 2 x 2i + ... + ε i, where y i is the i th observation of the response variable, x ji is the i th observation of the j th ...
Variance (the square of the standard deviation) – location-invariant but not linear in scale. Variance-to-mean ratio – mostly used for count data when the term coefficient of dispersion is used and when this ratio is dimensionless, as count data are themselves dimensionless, not otherwise. Some measures of dispersion have specialized purposes.
For any index, the closer to uniform the distribution, the larger the variance, and the larger the differences in frequencies across categories, the smaller the variance. Indices of qualitative variation are then analogous to information entropy , which is minimized when all cases belong to a single category and maximized in a uniform distribution.
The ratio estimator is a statistical estimator for the ratio of means of two random variables. Ratio estimates are biased and corrections must be made when they are used in experimental or survey work. The ratio estimates are asymmetrical and symmetrical tests such as the t test should not be used to generate confidence intervals.