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  2. Coefficient of determination - Wikipedia

    en.wikipedia.org/wiki/Coefficient_of_determination

    When only an intercept is included, then r 2 is simply the square of the sample correlation coefficient (i.e., r) between the observed outcomes and the observed predictor values. [4] If additional regressors are included, R 2 is the square of the coefficient of multiple correlation. In both such cases, the coefficient of determination normally ...

  3. Pearson correlation coefficient - Wikipedia

    en.wikipedia.org/.../Pearson_correlation_coefficient

    The square of the sample correlation coefficient is typically denoted r 2 and is a special case of the coefficient of determination. In this case, it estimates the fraction of the variance in Y that is explained by X in a simple linear regression .

  4. Effect size - Wikipedia

    en.wikipedia.org/wiki/Effect_size

    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.

  5. Correlation - Wikipedia

    en.wikipedia.org/wiki/Correlation

    Some correlation statistics, such as the rank correlation coefficient, are also invariant to monotone transformations of the marginal distributions of X and/or Y. Pearson/Spearman correlation coefficients between X and Y are shown when the two variables' ranges are unrestricted, and when the range of X is restricted to the interval (0,1).

  6. Spearman's rank correlation coefficient - Wikipedia

    en.wikipedia.org/wiki/Spearman's_rank_correlation...

    If F(r) is the Fisher transformation of r, the sample Spearman rank correlation coefficient, and n is the sample size, then z = n − 3 1.06 F ( r ) {\displaystyle z={\sqrt {\frac {n-3}{1.06}}}F(r)} is a z -score for r , which approximately follows a standard normal distribution under the null hypothesis of statistical independence ( ρ = 0 ).

  7. Correlation coefficient - Wikipedia

    en.wikipedia.org/wiki/Correlation_coefficient

    A correlation coefficient is a numerical measure of some type of linear correlation, meaning a statistical relationship between two variables. [ a ] The variables may be two columns of a given data set of observations, often called a sample , or two components of a multivariate random variable with a known distribution .

  8. Coefficient of multiple correlation - Wikipedia

    en.wikipedia.org/wiki/Coefficient_of_multiple...

    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 ...

  9. Regression analysis - Wikipedia

    en.wikipedia.org/wiki/Regression_analysis

    "Regression and correlation analysis," New Palgrave: A Dictionary of Economics, ... "The coefficient of determination R-squared is more informative than SMAPE, ...