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Lecture 8 Typeset Notes(1)

# Lecture 8 Typeset Notes(1) - ME 218 ENGINEERING...

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ME 218: ENGINEERING COMPUTATIONAL METHODS Fall 2011 Lecture #8 Curve Fitting: Curve fitting is an important statistical tool for analyzing discrete data points and obtaining the governing relation. Linear Curve Fitting : When the given set of data points is fit so as to yield a linear relationship ( y = mx + c) , the process is called linear regression or linear curve fitting. For instance, from experiment, one might have the data points: Y 1 , Y 2 , Y 3 , …. .Y n . From theoretical considerations, it might be known that these points must lie on a straight line with respect to a given parameter, x . Hence, ideally, y = mx + c . A way to obtain the best fit line, is by the Least Squares method. In this method, the error or residual, e i , at each data point is defined as the difference between the actual value, Y i , and the desired value, y i = mx i + c . The idea is to minimize the sum of the y x y = mx + c Y i

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squares of the errors for all data points. Thus: e i = Y i – y i = Y i – (mx
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Lecture 8 Typeset Notes(1) - ME 218 ENGINEERING...

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