When More Data Doesn't Help: Bias, Consistency, and the Experiment

The viewer can (1) define bias and consistency, (2) explain why LS is inconsistent for S2 (ε is coloured and correlated with y(t−1)), (3) use the bias formula â = a₀ − c₀(1 − a₀²)λ² / (b₀²σ² + (1 + c₀² − 2a₀c₀)λ²) and get −0.588 for S2, (4) explain how the input choice changes the S2 model (step: â ≈ 0, b̂ ≈ 5 but right gain), why an impulse fails (not persistently exciting), and why pure feedback u = −ky makes a, b unidentifiable.