Part CCSIR NET December 2024a-saturated-model-has-no-residual-degrees-of-freedom

A saturated model has no residual degrees of freedom

Consider a linear model $Y_{i} = β_{1} + β_{2} + \dots + β_{i} + ε_{i}, 1 \leq i \leq n$ , where errors $ε_{i}^{'} s$ are uncorrelated with zero mean and finite variance $σ^{2} > 0$ . Let $β$ ̂ $_{i}$ be the best linear unbiased estimator (BLUE) of $β_{i}, i = 1, 2, \dots, n$ . Then, which of the following statements are true?

A.The sum of squares residuals is strictly positive with probability 1.
B.For every $β_{i}, 1 \leq i \leq n$ , there are infinitely many linear unbiased estimators.
C. $V a r (β$ ̂ $_{1}) = σ^{2}$ ✓
D. $Y_{3} - Y_{2}$ is the BLUE of $β_{3}$ .✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

Related counterexample: OLS is the BLUE in every linear model

A saturated model has no residual degrees of freedom

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