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Medium · Data Science · Quant Trader interview question · linear-regression, ols, beta, hedging, statistics
Let $X$ and $Y$ be column vectors in $\mathbb{R}^{n\times 1}$ with $n>1$. The scalar OLS slope in the no-intercept regression $Y=X\beta+\epsilon$ is $\hat\beta=(X^T X)^{-1}X^T Y$. A proposed implementation instead uses $(X^T X)^{-1}XY$. What is the fundamental problem with the proposed expression?