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Curve Fitting

Curve Fitting. Source of Example. The chow/vizsla example is from “Lessons for A First Course in System Dynamics Modeling v1.0” by Diana M. Fisher . Summer Creek Press , 1998. Procedure. Given paired data points (x i ,y i ). Produce a scatterplot of the paired data points.

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Curve Fitting

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  1. Curve Fitting Introduction to Mathematical Modeling

  2. Source of Example The chow/vizsla example is from “Lessons for A First Course in System Dynamics Modeling v1.0” by Diana M. Fisher. Summer Creek Press, 1998. Introduction to Mathematical Modeling

  3. Procedure • Given paired data points (xi,yi). • Produce a scatterplot of the paired data points. • Fit a linear equationY = aX+band its graph (curve) to the data. • Evaluate the fit. • Analyze the result. Introduction to Mathematical Modeling

  4. Research Question • Can the appearance of a chow-vizsla hybrid be used to predict its disposition? • Dogs are rated based upon their chow-like and vizsla-like characteristics. • Scale 0 (most like vizsla) to 10 (most like chow). Introduction to Mathematical Modeling

  5. Table of Data Introduction to Mathematical Modeling

  6. Scatterplot of Data Introduction to Mathematical Modeling

  7. Plotting the Means (x,y)=(5,5.82) Introduction to Mathematical Modeling

  8. Adding a Trendline e2 e1 e3 Introduction to Mathematical Modeling

  9. Least Squares Fit • Minimize the error sum of squares Q =  (ei)2 • The smaller Q, the closer the correlation coefficient R2 is to 1. • A perfect fit (all points on the line) has R2=1. Introduction to Mathematical Modeling

  10. Trendline and Equation Introduction to Mathematical Modeling

  11. No Correlation • This graph shows essentially no correlation between the variables X and Y. Introduction to Mathematical Modeling

  12. High Correlation • This graph shows a high degree of correlation between X and Y. Introduction to Mathematical Modeling

  13. Outliers • Outliers affect the degree of correlation. • Outliers affect the fitted curve. Introduction to Mathematical Modeling

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