R² After Scaling the Data
R squared after scaling data is an easy quant interview question on Linear Regression, reported to have been seen at Squarepoint Capital and Two Sigma.
MyQuantPartner is not affiliated with, endorsed by, or sponsored by these companies, and all trademarks belong to their respective owners.
This quant interview question lives in the core of linear regression: how goodness-of-fit behaves when you rescale your data. It asks you to reason about what happens to a fit statistic when all inputs and outputs are uniformly scaled, without re-deriving the full model. For candidates doing quant prep, it checks whether you really understand what a performance metric represents, beyond just memorizing formulas.
It trains your intuition about variance, sums of squares, and proportions of explained variance in regression. You need to connect geometric thinking about distances from a line with probabilistic ideas like variance decomposition. It also reinforces comfort with transformations of data and their effect on model diagnostics, a crucial part of rigorous quant interviews.
This matters because top trading firms expect you to know which quantities are invariant under scaling and why. In real quant research, you constantly normalize, rescale, and standardize features. Misunderstanding what changes and what stays the same can lead to wrong model comparisons, bad backtests, or incorrect risk assessments. A small, clean question like this reveals whether your linear regression knowledge is deep enough for demanding quant interviews.
What it tests
The core structure of problems involving regression metrics under linear transformations is invariance under scaling. When both the dependent and independent variables in a dataset are scaled by a constant factor, all deviations (both from the regression line and from the mean) are multiplied by that factor, so their squares are multiplied by the square of the factor. Since $R^2$ is a ratio of two sums of squares (the explained and total variance), both the numerator and denominator scale identically, leaving the ratio unchanged. This invariance arises because $R^2$ measures the proportion of variance explained, not the absolute magnitude of errors or deviations. Thus, $R^2$ captures the relative fit quality, which is unaffected by uniform scaling of the data.
Practise this question with written feedback, or hear it in a spoken mock interview.
Get started free