Least_Square_Curve_Fitting_Handout

Least_Square_Curve_Fitting_Handout - Outlines Least Squares...

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Outlines Least Squares Curve Fitting Use of Software ME 3023 Measurements in Mechanical Systems Fall 2010 Dr. Gautam Chandekar Prepared on: October 6, 2009 ME 3023 Measurements in Mechanical Systems Fall 2010 Least Squares Curve Fitting Use of Software
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Outlines Least Squares Curve Fitting Use of Software Least Squares Curve Fitting Least-Squares Curve Fitting Linear Regression Linear Regression Example Non-linear Regression ME 3023 Measurements in Mechanical Systems Fall 2010 Least Squares Curve Fitting Use of Software
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Outlines Least Squares Curve Fitting Use of Software Use of Software Use of Software Excel MATLAB ME 3023 Measurements in Mechanical Systems Fall 2010 Least Squares Curve Fitting Use of Software
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Least-Squares Curve Fitting Part I Least-Squares Curve Fitting ME 3023 Measurements in Mechanical Systems Fall 2010 Least Squares Curve Fitting Use of Software
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Least-Squares Curve Fitting Linear Regression Linear Regression Example Non-linear Regression Least-Squares Curve Fitting Experimental data always has a finite amount of error included in it, due to both accumulated instrument inaccuracies and also imperfections in the physical system being measured. Even data describing a linear system won’t all fall on a single straight line. Least-squares curve fitting is a method to find parameters that fit the error-laden data as best we can. ME 3023 Measurements in Mechanical Systems Fall 2010 Least Squares Curve Fitting Use of Software
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Least-Squares Curve Fitting Linear Regression Linear Regression Example Non-linear Regression Linear Regression Linear regression is the method of finding the slope and y intercept of a line that best fits a set of data, and is the most common least-squares method used in mechanical engineering. Consider a series of data points ( x 1 , y 1 ), ( x 2 , y 2 ), · · · , ( x n , y n ). A linear function that attempts to fit this data would be y = a 0 + a 1 x , where a 0 and a 1 are constants not yet determined. After plugging each known value x i into the equation, we’ll find some amount of error between the y i points in the original data the the predicted y value from the linear model. This error e i is found with the relationship e i = y i - a 0 - a 1 x i . ME 3023 Measurements in Mechanical Systems Fall 2010 Least Squares Curve Fitting Use of Software
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Least-Squares Curve Fitting Linear Regression Linear Regression Example Non-linear Regression Linear Regression (continued) The error e i at each point may be positive or negative, large or small. One way to quantify how good a fit a particular line is would be to: Treat negative and positive errors the same.
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Least_Square_Curve_Fitting_Handout - Outlines Least Squares...

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