what is coefficient of determination

The coefficient of determination, denoted as R² or r², is a statistical measure used in regression analysis to assess how well the independent variable(s) explain the variability of the dependent variable. It represents the proportion of the variance in the dependent variable that can be predicted or explained by the independent variable(s). The coefficient of determination ranges between 0 and 1, where 0 indicates that the model does not predict the outcome, and 1 indicates a perfect prediction. In other words, an R² of 1 means that the regression predictions perfectly fit the data. It is a measure of the goodness of fit of a model, with a higher coefficient indicating a better fit for the model. However, its important to note that the coefficient of determination does not provide information about the causation relationship between the independent and dependent variables, nor does it indicate the correctness of the regression model. Therefore, it should be analyzed together with other variables in a statistical model to draw accurate conclusions about the models performance.