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In statistics, explained variation measures the proportion to which a mathematical model accounts for the variation of a given data set. Often, variation is quantified as variance; then, the more specific term explained variance can be used. The complementary part of the total variation is called unexplained or residual variation; likewise ...
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 ...
The coefficient of variation should be computed only for data measured on scales that have a meaningful zero (ratio scale) and hence allow relative comparison of two measurements (i.e., division of one measurement by the other). The coefficient of variation may not have any meaning for data on an interval scale. [2]
Common measures of statistical dispersion are the standard deviation, variance, range, interquartile range, absolute deviation, mean absolute difference and the distance standard deviation. Measures that assess spread in comparison to the typical size of data values include the coefficient of variation.
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).
A measure of statistical dispersion is a nonnegative real number that is zero if all the data are the same and increases as the data become more diverse. Most measures of dispersion have the same units as the quantity being measured. In other words, if the measurements are in metres or seconds, so is the measure of dispersion.
The general regression model with n observations and k explanators, the first of which is a constant unit vector whose coefficient is the regression intercept, is = + where y is an n × 1 vector of dependent variable observations, each column of the n × k matrix X is a vector of observations on one of the k explanators, is a k × 1 vector of true coefficients, and e is an n × 1 vector of the ...
While a simple measure, it is notable in that some texts and guides suggest or imply that the dispersion of nominal measurements cannot be ascertained. It is defined for instance by ( Freeman 1965 ). Just as with the range or standard deviation , the larger the variation ratio, the more differentiated or dispersed the data are; and the smaller ...
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