<\body> A line, however, is uniquely specified by two points. In the given problem, we have to fit a line through three points, one more than needed. A technique called helps us do just that. <\quote-env> In Least Squares Fitting, you attempt to find parameters \> specifying a line that match a given set of data ,y)> , such that <\equation*> \|f(x)-y\|\min! We would like to use linear algebra to achieve this. To that end, let's rewrite the simultaneous evaluation of at all > in matrix form: <\equation*> |>>||>>||>>>>>|\>>>|>>>>|\>\>=b+x\a>>|>>|b+x\a>>>>>=)>>|>>|)>>>>>. The error term is then <\eqnarray*> \|f(x)-y\|>||-\\|=(A\-\)(A\-\)>>|||AA\-\A\-\A\-\\>>|||AA\-2\A\-\\,>>>> where \(y,\,y)>. Since we're trying to minimize this term, we demand <\equation*> |\\>E0. Glossing over some technical issues, we write <\equation*> 0|\\>E=2AA\-2A\. This is a set of linear equations that we may write as <\equation*> AA\=Ay, yielding the solution to our fitting problem. <\initial> <\collection>