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9.3 In this section we shall use results about orthogonal projections in inner
product spaces to obtain a technique for fitting a line or other polynomial
LEAST SQUARES curve to a set of experimentally determined points in the plane.
FITTING TO DATA
Fitting a Curve to Data
A common problem in experimental work is to obtain a mathematical relationship between two variables x and y
by “fitting” a curve to points in the plane corresponding to various experimentally determined values of x and y, say
On the basis of theoretical considerations or simply by the pattern of the points, one decides on the general form of the curve
to be fitted. Some possibilities are (Figure 9.3.1)
(a) A straight line:
(b) A quadratic polynomial:
(c) A cubic polynomial:
