Negative \(R^2\): Practice
Can \(R^{2}\) ever be negative? Explain why practically (linear regression case).
Answer
Practically, this can happen when there are constraints on the model, for example, if the intercept is fixed at a specific value (such as 140) or forced to be 0 (no intercept parameter). Such constraints can cause the model to estimate a slope that does not follow the actual direction of the trend in the data, leading to predictions that are worse than simply using the average of \(Y\).
If no such constraints exist, the OLS method will estimate parameters s.t. \(R^{2}\) is always non-negative .