1. Copyright © 2005. The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Applied Numerical Methods With MATLAB ® for Engineers and Scientists First Edition Steven C. Chapra Chapter 12 PowerPoint to accompany

2. Wind tunnel experiment to measure how the force of air resistance depends on velocity. Figure 12.1 12-1

3. 12-2 Plot of force versus wind velocity for an object suspended in a wind tunnel. Figure 12.2

4. 12-3 Three attempts to fit a “best” curve through five data points: (a) least-squares regression, (b) linear interpolation, and (c) curvilinear interpolation. Figure 12.3

5. 12-4 A histogram used to depict the distribution of data. As the number of data points increases, the histogram often approaches the smooth, bell-shaped curve called the normal distribution. Figure 12.4

6. 12-5 Examples of some criteria for “best fit” that are inadequate for regression: (a) minimizes the sum of the residuals, (b) minimizes the sum of the absolute values of the residuals, and (c) minimizes the maximum error of any individual point. Figure 12.5

7. 12-6 Least-squares fit of a straight line to the data from Table 12.1. Figure 12.6

8. 12-7 The residual in linear regression represents the vertical distance between a data point and the straight line. Figure 12.7

9. 12-8 Regression data showing (a) the spread of the data around the mean of the dependent variable and (b) the spread of the data around the best-fit line. The reduction in the spread in going from (a) to (b), as indicated by the bell-shaped curves at the right, represents the improvement due to linear regression. Figure 12.8

10. 12-9 Examples of linear regression with (a) small and (b) large residual errors. Figure 12.9

11. 12-10 (a) The exponential equation, (b) the power equation, and (c) the saturation-growth-rate equation. Parts (d), (e), and (f) are linearized versions of these equations that result from simple transformations. Figure 12.10

12. 12-11 Least-squares fit of a power model to the data from Table 12.1. (a) The fit of the transformed data. (b) The power equation fit along with the data. Figure 12.11

13. 12-12 un 12.01

14. 12-13 un 12.02

15. 12-14 An M-file to implement linear regression. Figure 12.12

16. 12-15 Figure P12.15