Expand linear models modules across all chapters - #7
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| function generalized_inverse_solution(X::AbstractMatrix{<:Real}, y::AbstractVector) | ||
| F = svd(X) | ||
| tol = maximum(size(X)) * eps() * maximum(F.S) | ||
| idx = F.S .> tol | ||
| Sinv = zeros(eltype(F.S), length(F.S)) | ||
| Sinv[idx] .= 1 ./ F.S[idx] | ||
| β̂ = F.Vt' * Diagonal(Sinv) * F.U' * y | ||
| κ = isempty(F.S) ? 0.0 : maximum(F.S[idx]) / minimum(F.S[idx]) | ||
| return β̂, κ |
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[P1] Guard generalized inverse against rank-zero matrices
The pseudoinverse fallback assumes at least one singular value exceeds the tolerance. When the design matrix is completely singular (all singular values ≤ tol), idx is empty and the calls to maximum(F.S[idx])/minimum(F.S[idx]) throw an error instead of returning the minimum-norm solution. This causes least_squares_estimator to fail precisely in the degenerate cases it was supposed to handle. Short-circuit the empty set before computing the condition number or return a zero vector with κ=Inf.
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| diff = C * β̂ .- d | ||
| middle = C * (design.X' * design.X) \ C' | ||
| q = rank(C) | ||
| fstat = (diff' * (middle \ diff)) / q / mse |
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[P0] F-test builds constraint quadratic form with wrong operator precedence
The matrix for the quadratic form is defined as middle = C * (design.X' * design.X) \ C'. Because \ binds tighter than *, this evaluates as (C * (design.X' * design.X)) \ C', producing a DimensionMismatch for the common case size(C,1) ≠ size(C,2) and making the hypothesis test unusable. The intended quantity is C * ((design.X' * design.X) \ C') (i.e., C * (X'X)⁻¹ * C'). Parenthesize the solve or compute the inverse explicitly so rectangular constraint matrices work.
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Summary
Testing
https://chatgpt.com/codex/tasks/task_e_68d8c8bf56ac8321bad7704f1d7b05ec