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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 .
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.
Third, a zero Pearson product-moment correlation coefficient does not necessarily mean independence, because only the two first moments are considered. For example, = (y ≠ 0) will lead to Pearson correlation coefficient of zero, which is arguably misleading. [2]
The economics of happiness or happiness economics is the theoretical, qualitative and quantitative study of happiness and quality of life, including positive and negative affects, well-being, [1] life satisfaction and related concepts – typically tying economics more closely than usual with other social sciences, like sociology and psychology, as well as physical health.
For example, in the chart at right, US income share of top earners was approximately constant from the mid-1950s to the mid-1980s, then increased from the mid-1980s through 2000s; this increased inequality was reflected in the Gini coefficient. For example, in 2007 the top decile (10%) of US earners accounted for 49.7% of total wages (times ...
Popular budgeting app YNAB has a cult-like following, and its founder credits the net positive created by viewing money as self-care. Money can’t buy happiness, but a well-crafted budget might ...
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 ...
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).