Which of the following sentences regarding bias and variance of an estimator are true?

I Bias measures the expected deviation from the actual value to be estimated.
II The ideal situation for a machine model is to have high bias and low variance.
III There is a known tradeoff regarding bias and variance in machine learning.
IV Variance calculates the deviation from the expected estimation.

Question

Which of the following sentences regarding bias and variance of an estimator are true?

I	Bias measures the expected deviation from the actual value to be estimated.
II	The ideal situation for a machine model is to have high bias and low variance.
III	There is a known tradeoff regarding bias and variance in machine learning.
IV	Variance calculates the deviation from the expected estimation.

BlackTom AI · Accepted Answer

To evaluate the truth of each statement, I will parse what bias and variance mean in the context of an estimator and how they relate to model performance.
Option I: 'Bias measures the expected deviation from the actual value to be estimated.' This aligns with the formal definition of bias for an estimator: bias = E[Estimator] − TrueValue. It captures the systematic error in the estimation, i.e., the average error across many samples. Therefore, this statement is correct.
Option II: 'The ideal situation for a machine model is to have high bias and low variance.' This is inconsistent with common modeling goals. High bias typically means the model is too simplistic (underfitting) and misses the underlying pattern, while low variance means stable predictions across samples. In practice, we strive for low bias and low variance; thus, high bias is undesirable. This statement is incorrect.
Option III: 'There is a known tradeoff regarding bias and variance in machine learning.' Indeed, the bias–variance tradeoff describes how reducing one often increases the other, affecting generalization. This statement is correct.
Option IV: 'Variance calculates the deviation from the expected estimation.' In statistical terms, variance measures how much the estimator varies around its own expected value (its mean). It quantifies the dispersion of the estimator across different samples. While the wording is somewhat concise, it captures the core idea that variance concerns deviation from the estimator’s expectation, making this statement correct.
Summarizing the assessment across options, the statements that hold true are I, III, and IV, while II is false due to promoting a goal of high bias, which contradicts the objective of good generalization.

FINTECH 540.01.Fa25 Final Exam

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