0. Although β1^ is unbiased, it is clearly inferior to the biased β2^.-->
In statistics, the bias (or bias function) of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased. Otherwise the estimator is said to be biased.
In ordinary English, the term bias is pejorative. In statistics, there are problems for which it may be good to use an estimator with a small, but nonzero, bias. In some cases, an estimator with a small bias may have lesser mean squared error or be median-unbiased (rather than expected value|mean-unbiased, the standard unbiasedness property). The property of median-unbiasedness is invariant under monotone transformations, while the property of mean-unbiasedness may be lost under nonlinear transformations.