Understanding Linear Regression: Interpreting the Coefficient of Determination

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Linear regression is a powerful tool for predicting outcomes based on the relationship between variables. The coefficient of determination (R²) quantifies how much of the variance in the dependent variable can be explained by the independent variable(s). In our analysis, 40% of the variation in y is explained by the regression model, with an R² of approximately 0.41. This suggests a moderate correlation between y and x. For the blood alcohol concentration (BAC) model, 80% of the variation is explained by beer consumption, indicating a stronger predictive relationship.

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Feb 09, 2026

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Understanding Linear Regression: Interpreting the Coefficient of Determination

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Linear Regression The Science of Predicting Outcome
Is the fraction of the variation in the values of y that is explained by the least-squares regression of y on x 40% of the variation in y is explained by the least-square regression of y on x r2 :coefficient of determination a=.0987 b=2.3234 r2=.40997 r=.6502
80% of the variation in the predicted BAC is explained by the least-square regression of BAC on number of beers consumed. Your Turn Interpret the coefficient of determination generated by this computer output.