![]() ![]() Polynomials are one of the most commonly used types of curves in regression. According to the method of least squares, the best fitting curve has the property that: ![]() The fitting curve has the deviation (error) from each data point, i.e.,,. , where is the independent variable and is the dependent variable. The method of least squares assumes that the best-fit curve of a given type is the curve that has the minimal sum of the deviations squared ( least square error) from a given set of data. This best-fitting curve can be obtained by the method of least squares. Thus, a curve with a minimal deviation from all data points is desired. ![]() Nevertheless, for a given set of data, the fitting curves of a given type are generally NOT unique. The curve fitting process fits equations of approximating curves to the raw field data. A process of quantitatively estimating the trend of the outcomes, also known as regression or curve fitting, therefore becomes necessary. Even though all control parameters (independent variables) remain constant, the resultant outcomes (dependent variables) vary. Field data is often accompanied by noise.
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