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The intercept in regression-type models is the value of the Y variable when all X variables are 0.
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intercept in manually weighed regression
The weighted vector of 1's is then included in the model as part of the x-matrix and the model is fit without an intercept. … A parameter estimate is returned for x0 that corresponds to the intercept in a weighted regression, even though this term was not constant, and even though the intercept was omitted. …