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  2. Correlation - Wikipedia

    en.wikipedia.org/wiki/Correlation

    The correlation matrix is symmetric because the correlation between and is the same as the correlation between and . A correlation matrix appears, for example, in one formula for the coefficient of multiple determination , a measure of goodness of fit in multiple regression .

  3. Pearson correlation coefficient - Wikipedia

    en.wikipedia.org/wiki/Pearson_correlation...

    Pearson's correlation coefficient, when applied to a sample, is commonly represented by and may be referred to as the sample correlation coefficient or the sample Pearson correlation coefficient. We can obtain a formula for r x y {\displaystyle r_{xy}} by substituting estimates of the covariances and variances based on a sample into the formula ...

  4. 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 .

  5. 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 ...

  6. Covariance and correlation - Wikipedia

    en.wikipedia.org/wiki/Covariance_and_correlation

    Notably, correlation is dimensionless while covariance is in units obtained by multiplying the units of the two variables. If Y always takes on the same values as X , we have the covariance of a variable with itself (i.e. σ X X {\displaystyle \sigma _{XX}} ), which is called the variance and is more commonly denoted as σ X 2 , {\displaystyle ...

  7. Coefficient of determination - Wikipedia

    en.wikipedia.org/wiki/Coefficient_of_determination

    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).

  8. Regression analysis - Wikipedia

    en.wikipedia.org/wiki/Regression_analysis

    An alternative to such procedures is linear regression based on polychoric correlation (or polyserial correlations) between the categorical variables. Such procedures differ in the assumptions made about the distribution of the variables in the population.

  9. Partial correlation - Wikipedia

    en.wikipedia.org/wiki/Partial_correlation

    To prove Equation , return to the previous notation (i.e. ,,,, {,}) and start with the definition of partial correlation: ρ XY·Z is the correlation between the residuals e X and e Y resulting from the linear regression of X with Z and of Y with Z, respectively.