A machine learning team is comparing two regression models to predict customer lifetime value. Model A has an R-squared ($R^2$) value of 0.88 and a Mean Absolute Error (MAE) of $120. Model B has an $R^2$ value of 0.79 and a MAE of $95. If the primary goal of the selection is to deploy the model that explains the greatest proportion of variability in the target variable, which model should be chosen and why?
Select an answer to reveal the explanation.
Short Explanation and Infographic
Here's the deal: when you're looking at regression metrics, it's easy to get confused. R-squared and MAE tell you different stories. MAE is simple—it tells you the average error size in actual units (like dollars). But R-squared is the big picture; it tells you what percentage of the variance in your data is actually explained by your model. If the boss walks in and asks which model captures the underlying trends and variability of customer behavior best, you look at R-squared. A higher R-squared means Model A explains more of that variance (88% compared to Model B's 79%). That makes Model A the winner for explaining variability. Got it? Sweet.
Full explanation below image
Full Explanation
R-squared ($R^2$), also known as the coefficient of determination, measures the proportion of variance in the dependent variable that is predictable from the independent variables. An $R^2$ of 0.88 means that 88% of the variability in the target variable is explained by the model's features, while the remaining 12% is unexplained residual variance. Since the goal is to choose the model that explains the greatest proportion of variability, Model A is the correct choice because its $R^2$ is higher (0.88 vs. 0.79). - A is incorrect because a lower MAE (Mean Absolute Error) indicates better average accuracy in terms of prediction units (e.g., dollars), but it does not measure the proportion of explained variance. - C is incorrect because MAE is a measure of absolute error magnitude, not variance explanation, and it is not mathematically superior; they are different metrics used for different purposes. - D is incorrect because R-squared does not represent the average absolute prediction error. That is the definition of Mean Absolute Error (MAE). R-squared is a relative metric representing the ratio of explained variance to total variance.