In finding the correlation and regression of multivariable distribution what is the significance of R and R^2? What is the main relation between them?
https://en.wikipedia.org/wiki/Coefficient_of_determination
https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
In short:
There is nothing like "r²". It's actually R², which is the coefficient of determination. In a regression model it gives you the proportion of variance explained by the model. R²=1 means that all (100%) of the variance is explained by the model (there is no residual variance left), R²=0 means that nothing (0%) of the variance is explained by the model (the residual variance is as large as the variance).
"r" is Pearsons coefficient of correlation. It is applicable in bivariate regression models, where it is actually the signed square-root of R². r = -1 indicates a perfect negative linear relationship, r = +1 indicates a perfect positive linear relationship, and r = 0 indicates the absence of a (non-zero) linear relationship.
Jochen Wilhelm thanks for your informative answer. Question is edited.
R represents the correlation coefficient between two variables in a multivariable distribution. It measures the strength and direction of the linear relationship between the two variables. R ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.
R^2, on the other hand, represents the coefficient of determination. It measures the proportion of variance in one variable that is predictable from the other variable(s) in a multivariable distribution. R^2 ranges from 0 to 1, where 0 indicates no variance in the dependent variable is explained by the independent variable(s), and 1 indicates that all the variance in the dependent variable is explained by the independent variable(s).
The main relationship between R and R^2 is that R is the square root of R^2. In other words, R^2 is the proportion of variance in the dependent variable that is explained by the independent variable(s), and R is the correlation coefficient between the dependent variable and the predicted values based on the independent variable(s). Therefore, R^2 is a measure of how well the regression line fits the data, while R is a measure of the strength and direction of the linear relationship between two variables. R-Squared? R-squared (R2) is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model
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