This value can be used to calculate the coefficient of determination ( R²) using Formula 1:įormula 2: Using the regression outputs Formula 2:Įxample: Calculating R² using regression outputsAs part of performing a simple linear regression that predicts students’ exam scores (dependent variable) from their study time (independent variable), you calculate that: Where r = Pearson correlation coefficient Example: Calculating R² using the correlation coefficientYou are studying the relationship between heart rate and age in children, and you find that the two variables have a negative Pearson correlation: Formula 1: Using the correlation coefficient Formula 1: The first formula is specific to simple linear regressions, and the second formula can be used to calculate the R² of many types of statistical models. You can choose between two formulas to calculate the coefficient of determination ( R²) of a simple linear regression. In other words, when the R 2 is low, many points are far from the line of best fit:ĭiscover proofreading & editing Calculating the coefficient of determination In contrast, you can see in the second dataset that when the R 2 is low, the observations are far from the model’s predictions. 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.
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