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</math>
The above [[System of linear equations|linear equations]] may be solved directly, or stand-alone equations for <math>\widehat\alpha\text{ and }\widehat\beta</math> may be derived by expanding the matrix equations above. The resultant equations are algebraically equivalent to the ones shown in the prior paragraph, and are shown below without proof.<ref>{{Cite web |title=Numeracy, Maths and Statistics - Academic Skills Kit, Newcastle University |url=https://www.ncl.ac.uk/webtemplate/ask-assets/external/maths-resources/statistics/regression-and-correlation/simple-linear-regression.html |url-status=live |access-date=30 Jan 2024 |website=Simple Linear Regression}}</ref><ref name=":1">{{Cite web |last=Muthukrishnan |first=Gowri |date=17 Jun 2018 |title=Maths behind Polynomial regression, Muthukrishnan |url=https://muthu.co/maths-behind-polynomial-regression/ |url-status=live |access-date=30 Jan 2024 |website=Maths behind Polynomial regression}}</ref>
<math>\begin{align}
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