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=== Expanded
The above equations are efficient to use if the mean of the x and y variables (<math>\bar{x} \text{ and } \bar{y}</math>) are known. If the means are not known at the time of calculation, it may be more efficient to use the expanded version of the <math>\widehat\alpha\text{ and }\widehat\beta</math> equations. These expanded equations may be derived from the more general [[polynomial regression]] equations<ref name=":1" /><ref>{{Cite web |title=Mathematics of Polynomial Regression |url=http://polynomialregression.drque.net/math.html |website=Polynomial Regression, A PHP regression class}}</ref> by defining the regression polynomial to be of order 1, as follows.
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