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Coefficient of Determination which is denoted as R2 is used in the context of statistical models whose main purpose is the prediction of future outcomes. The future outcomes are made on the basis of other related information where R2 is most often seen as a number between 0 and 1.0. This number is used to describe how well a regression line fits a set of data and if R2 near 1.0, it indicates that a regression line fits the data well and if an R2 value is closer to 0 it indicates that a regression line does not fit the data very well. It is the proportion of the variability in a data set that is accounted for by the statistical model which provides a measure of how well future outcomes are likely to be predicted by the model.
There are several different definitions of R2 which are only sometimes equivalent and one class of such cases includes that of linear regression in which if an intercept is included then R2 is simply the square of the sample Pearson product-moment correlation coefficient between the outcomes and their predicted values. For the simple linear regression, it is thus the squared correlation among the outcomes as well as the values of the single regressor being used for prediction. If an intercept is integrated and the number of explanations is more than one, then the R2 is also referred to as the coefficient of multiple correlation, then the coefficient of determination ranges from 0 to 1.
Important cases where the computational definition of R2 can yield negative values depend on the definition used and then the predictions which are being compared to the corresponding outcomes and this have not been derived from a model-fitting procedure using those data. Then the linear regression is conducted without including an intercept and negative values of R2 may occur when fitting non-linear trends to data. In this case the mean of the data provides a fit to the data which is superior to that of the trend under the goodness of fit analysis.
R2 is a defined as a statistic that will give some information about the Goodness of fit of a model and the R2 coefficient of determination is a statistical measure that determines how well the regression line approximates the real data points.
