Note: The coefficient of determination is always positive, even when the correlation is negative. In other words, most points are close to the line of best fit: You can see in the first dataset that when the R 2 is high, the observations are close to the model’s predictions. The distance between the observations and their predicted values (the residuals) are shown as purple lines.The model’s predictions (the line of best fit) are shown as a black line.For example, the graphs below show two sets of simulated data: Graphing your linear regression data usually gives you a good clue as to whether its R 2 is high or low. It is the proportion of variance in the dependent variable that is explained by the model. More technically, R 2 is a measure of goodness of fit. If the R 2 is 1, the model allows you to perfectly predict anyone’s exam score.The model’s estimates are not perfect, but they’re better than simply using the average exam score. If the R 2 is between 0 and 1, the model allows you to partially predict exam scores.If the R 2 is 0, the linear regression model doesn’t allow you to predict exam scores any better than simply estimating that everyone has an average exam score.Example: Coefficient of determinationImagine that you perform a simple linear regression that predicts students’ exam scores (dependent variable) from their time spent studying ( independent variable). Put simply, the better a model is at making predictions, the closer its R² will be to 1. The lowest possible value of R² is 0 and the highest possible value is 1. The outcome is represented by the model’s dependent variable. The coefficient of determination ( R²) measures how well a statistical model predicts an outcome. What is the coefficient of determination? Frequently asked questions about the coefficient of determination.Reporting the coefficient of determination.Interpreting the coefficient of determination.Calculating the coefficient of determination.What is the coefficient of determination?.
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