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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).
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.
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
For example, least squares (including its most common variant, ordinary least squares) finds the value of that minimizes the sum of squared errors ((,)). A given regression method will ultimately provide an estimate of β {\displaystyle \beta } , usually denoted β ^ {\displaystyle {\hat {\beta }}} to distinguish the estimate from the true ...
The coefficient of multiple correlation is known as the square root of the coefficient of determination, but under the particular assumptions that an intercept is included and that the best possible linear predictors are used, whereas the coefficient of determination is defined for more general cases, including those of nonlinear prediction and those in which the predicted values have not been ...
RExcel is an add-on for Microsoft Excel that allows access to the statistics package R from within Excel. It uses the statconnDCOM server and, for certain configurations, the room package. It uses the statconnDCOM server and, for certain configurations, the room package.
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 ...
Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression, including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals.