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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).
A related effect size is r 2, the coefficient of determination (also referred to as R 2 or "r-squared"), calculated as the square of the Pearson correlation r. In the case of paired data, this is a measure of the proportion of variance shared by the two variables, and varies from 0 to 1.
All have the same trend, but more filtering leads to higher r 2 of fitted trend line. The least-squares fitting process produces a value, r-squared (r 2), which is 1 minus the ratio of the variance of the residuals to the variance of the dependent variable. It says what fraction of the variance of the data is explained by the fitted trend line.
Commonly used checks of goodness of fit include the R-squared, analyses of the pattern of residuals and hypothesis testing. Statistical significance can be checked by an F-test of the overall fit, followed by t-tests of individual parameters. Interpretations of these diagnostic tests rest heavily on the model's assumptions.
R 2 or r 2 (pronounced R-squared), the coefficient of determination of a linear regression in statistics; R 2, the two-dimensional real coordinate space in mathematics; R2: Risk of explosion by shock, friction, fire or other sources of ignition, a risk phrase in chemistry
R 2 N, proposed by Nico Nagelkerke in a highly cited Biometrika paper, [4] provides a correction to the Cox and Snell R 2 so that the maximum value is equal to 1. Nevertheless, the Cox and Snell and likelihood ratio R 2 s show greater agreement with each other than either does with the Nagelkerke R 2. [1]
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 ...
A plot of the absolute or squared residuals versus the predicted values (or each predictor) can also be examined for a trend or curvature. Formal tests can also be used; see Heteroscedasticity . The presence of heteroscedasticity will result in an overall "average" estimate of variance being used instead of one that takes into account the true ...