Straight Line Fit - Classical Derivation

Earlier, we promised an explicit solution for the determination of linear parameters. We first change the original notation introduced in equation (4.3)  

It is more efficient to use ai and 02 as parameters rather than intercept and slope. More importantly, in 4.2.3, Generalised Matrix Notation we will be able to extend the vector containing the a-values to any higher dimension. 

This represents a system of 2 equations with 2 unknowns, ai and 02. After division by 2 and introducing a short notation for the sums 

Inserting (4.12) into the matrix product of (4.11) results in a set of two explicit equations for the two parameters  

Rather than writing a short program in Matlab for this result, we demonstrate how to perform the task of a straight line fit in Excel. Excel actually provides several ways of performing the job of fitting the best line through a set of data pairs. The most convenient is probably the Add Trendline. .. tool which delivers the result in a few clicks. 

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