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Math Foundations
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Linear Algebra
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Matrix inversion intuition
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548.
OLS and Matrix Inversion
medium
The OLS solution to linear regression is β = (XᵀX)⁻¹Xᵀy. When does this inverse fail to exist?
A
When y has nonzero mean — which causes XᵀX to become ill-conditioned and numerically unstable
B
When XᵀX is singular — which happens when features are linearly dependent or when there are more features than samples
C
When X is not square — which happens whenever the number of samples differs from the number of features
D
When Xᵀy is zero — which happens when the features are uncorrelated with the target variable in the given dataset
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