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:<math> E[Y|X] = \Pr(Y=1|X) =x'\beta,</math>
and hence the vector of parameters β can be estimated using [[least squares]]. This method of fitting would be inefficient,<ref name=Cox /> and can be improved by adopting an iterative scheme based on [[weighted least squares]],<ref name=Cox/> in which the model from the previous iteration is used to supply estimates of the conditional variances, <math>\operatorname{Var}(Y|X=x)</math>, which would vary between observations. This approach can be related to fitting the model by [[maximum likelihood]].<ref name=Cox/>
Horace and Oaxaca (2006) shows that estimating such a model using OLS leads to biased and inconsistent parameter estimates. THey propsed a trimmed 2SLS estimation technique to correct the effects.
A drawback of this model is that, unless restrictions are placed on <math> \beta </math>, the estimated coefficients can imply probabilities outside the [[unit interval]] <math> [0,1] </math>. For this reason, models such as the [[logit model]] or the [[probit model]] are more commonly used.
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