I Bias in Linear Regression (x-intercept) vs Statistics

AI Thread Summary
In simple regression, the bias represented by the intercept (b) differs from the statistical definition of bias in estimators, which is the difference between the expected value and the true parameter. The model Y = mx + b can produce an unbiased estimator for the population parameter Y, leading to confusion about the term "bias." The terminology used in machine learning may borrow from statistics but does not align perfectly, creating a disparity in understanding. This discrepancy highlights the need for clarity in the use of terms across different fields. The discussion emphasizes that while the concepts may be related, they are not interchangeable.
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TL;DR Summary
Trying to Reconcile two apparently/superficially different usages of the tern "Bias"
Hi,
In simple regression for machine learning , a model :

Y=mx +b ,

Is said AFAIK, to have bias equal to b. Is there a relation between the use of bias here and the use of bias in terms of estimators

for population parameters, i.e., the bias of an estimator P^ for a population parameter P is defined as the difference E[P^]- P?

The two do not seem to coincide as Y^= mx^ +b^ is an unbiased estimator of the population parameter Y . Can anyone explain the

disparity?
 
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Words have more than one meaning. I have never seen bias used with the first meaning, so that appears to be a specialized field of study just “hijacking” terminology from other fields of study. It happens often. I am afraid there is not much justification needed or provided for that type of thing.
 
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I think that the two uses are only logically similar in the context of a model where X and Y are known or assumed to be proportional (Y = mx). In that case, b would be a bias due to something.
 
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I'm taking a look at intuitionistic propositional logic (IPL). Basically it exclude Double Negation Elimination (DNE) from the set of axiom schemas replacing it with Ex falso quodlibet: ⊥ → p for any proposition p (including both atomic and composite propositions). In IPL, for instance, the Law of Excluded Middle (LEM) p ∨ ¬p is no longer a theorem. My question: aside from the logic formal perspective, is IPL supposed to model/address some specific "kind of world" ? Thanks.
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