COEFFICIENT OF DETERMINATION Meaning and
Definition
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The coefficient of determination, also known as R-squared (R2), is a statistical metric that measures the proportion of the variance in the dependent variable that can be accurately predicted from the independent variable(s) in a regression model. It represents the strength of the relationship between the predictors and the response variable.
The coefficient of determination is expressed as a value between 0 and 1, where a value of 0 indicates that the independent variable(s) have no explanatory power in predicting the dependent variable, and a value of 1 indicates a perfect predictive ability. A higher coefficient of determination suggests a stronger relationship between the variables, indicating that a larger percentage of the variability in the dependent variable can be explained by the independent variable(s).
To calculate the coefficient of determination, one must first fit a regression model and determine the variation from the actual values to the fitted values (the sum of squares error) and the variation from the actual values to the mean of the dependent variable (the total sum of squares). The coefficient of determination is then computed as the ratio of the explained sum of squares to the total sum of squares.
In practical terms, the coefficient of determination helps to evaluate the accuracy and usefulness of a regression model. It is widely utilized in fields like economics, finance, and social sciences to ascertain the strength of relationships and to determine the proportion of the variation that can be attributed to certain factors.
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