Regression analysis curve fitting

In general, regression analysis of reference designs can be linear, i.e. we draw a straight line through the cloud of points. The line can be represented by the equation:

y = a ■ x + b where the coefficients a and b have to be determined so as to give a 'best fit' through the cloud of points.

Linear least square curve fitting means that we determine the coefficients a and b such that the sum of the squares of the deviations of the points from the regression line is at its minimum.

For n points, having coordinates (xm,ym), m = 1, 2,..., n, this sum, S, is:

The values for a and b that minimise S are those that satisfy the conditions dS/da = 0 and dS/db = 0. Differentiating (8.6) with respect to a and b yields (after rearranging terms and substitution):

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