Asked at Two Sigma, Millennium, Jump Trading, Squarepoint Capital
Theory: Quant Python That Survives ReviewRead the problem, hints and solution here. The editor needs a bigger screen: open this page on a laptop to write and run your code.
Implement ols_fit(X, y). It fits ordinary least squares in numpy without a
regression library, and returns the coefficients and \( R^2 \).
X is a list of feature rows (each a list of floats), without an
intercept column. It may also be a flat list of floats for the
single-feature case.y is a list of floats, one target per row.Fit ordinary least squares with an intercept, and return a tuple
(coeffs, r2):
coeffs: the fitted coefficients as a list of floats rounded to 4
decimals, intercept first, then one coefficient per feature in input
order.r2: the coefficient of determination \( R^2 = 1 - SS_{res}/SS_{tot} \),
rounded to 4 decimals. If y is constant, define \( R^2 = 1.0 \).Columns may be collinear. Solve by least squares (numpy.linalg.lstsq),
which returns the minimum-norm solution in the degenerate case; the normal
equations with a plain inverse will crash there.
ols_fit([[1], [2], [3]], [3, 5, 7])
# ([1.0, 2.0], 1.0)
ols_fit([[1, 2], [2, 1], [3, 4], [4, 3]], [10, 11, 20, 21])
# ([3.0, 3.0, 2.0], 1.0)A hidden test runs 20,000 rows by 8 features, which any vectorised solution handles instantly.