Which metric is minimized as a measure of how far predicted values are from observed values in regression?

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Which metric is minimized as a measure of how far predicted values are from observed values in regression?

In regression with ordinary least squares, the model is fitted by minimizing the residual sum of squares. This quantity sums the squared differences between observed values and the model’s predictions, capturing how far off the predictions are overall. Minimizing RSS selects the line (or hyperplane) that best fits the data in the least-squares sense. RMSE and MSE are derived from RSS (they are just RSS divided by n and then rooted, respectively), while MAE uses absolute errors rather than squared errors. R-squared is a goodness-of-fit statistic that compares RSS to the total variation in the data, not the optimization objective. So the quantity directly minimized during fitting is the residual sum of squares.

In regression with ordinary least squares, the model is fitted by minimizing the residual sum of squares. This quantity sums the squared differences between observed values and the model’s predictions, capturing how far off the predictions are overall. Minimizing RSS selects the line (or hyperplane) that best fits the data in the least-squares sense. RMSE and MSE are derived from RSS (they are just RSS divided by n and then rooted, respectively), while MAE uses absolute errors rather than squared errors. R-squared is a goodness-of-fit statistic that compares RSS to the total variation in the data, not the optimization objective. So the quantity directly minimized during fitting is the residual sum of squares.

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