The coefficient of determination indicates how well data points fit a line or curve. It is denoted by R2 and pronounced R squared. It is a statistic used in the context of statistical models whose main purpose is either to prediction of future outcomes or the testing of hypotheses on the basis of other related information. It is a statistic used in the context of statistical models whose main purpose is either the prediction of future outcomes or the testing of hypotheses, on the basis of other related information. The coefficient of determination provides a measure of how well observed outcomes are replicated by the model as the proportion of total variation of outcomes explained by the model.
There are many definitions of R2 which are only sometimes equivalent; for example linear regression. If an intercept is included then R2 is simply the square of the sample correlation coefficient between the outcome and their predicted values. If an intercept is included and the number of explanators is more than one, R2 is the square of the coefficient of multiple correlations. In these cases, the coefficient of determination ranges from 0 to 1.
R2 is a statistic that will give some information about the goodness of fit of a model. In regression, the R2 coefficient of determination is a statistical measure of how well the regression line approximates the real data points. An R2 of 1 indicates that the regression line perfectly fits the data. However, the R2 value can range outside 0 to 1 where it is used to measure the agreement between observed and modeled values, where the modeled values are not obtained by linear regression.© BrainMass Inc. brainmass.com June 24, 2018, 8:32 pm ad1c9bdddf