Representing Data by Continuous Functions Regression Analysis

Representing Data by Continuous Functions Regression Analysis 

In the simplest cases, the data is fitted to a linear relationship, y - mx + b. 

The technique of obtaining the best fit for the data i s referred to as L inear Least Squares (LS) since it represents a minimum in the sum of the squares of the deviations of each data point from that calculated from the best line. As recently as 20 years ago, such problems were solved without computer assistance. Today, many inexpensive hand calculators are equipped for relatively simple LS computation. Quattro provides us with a still easier method. 

When you use this equation to calculate A in column C and calculate the difference (C2-B2) or the % difference (100(C2-B2)/B2), a clear estimate of the reliability of the calibration can be obtained. 

This simple linear regression can be readily adapted to multiple regression, i.e., to develop the best fit to an equation involving more than one variable, as in multicomponent spectrophotometric analysis (see Chapter 13), or in most complex curve fitting where the results are related to the independent variable but not in a linear fashion. The well-known Taylor, McLauren, or related theorems about infinite series state that most mathematical functions, f(x), can be expressed as the sum of series of terms in x . Many of these result in converging series, i.e., only several terms are necessary to represent the function with reasonable precision. 

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