Homework Set 8

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University of Florida *

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3344

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Mechanical Engineering

Date

Dec 6, 2023

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pdf

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15

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Problem Set 8 Problems Completed: 14.1, 14.5, 14.8, 14.18, 15.3, 15.6, 15.15
Problem 14.1 Given the data: 0.90 1.42 1.30 1.55 1.63 1.32 1.35 1.47 1.95 1.66 1.96 1.47 1.92 1.35 1.05 1.85 1.74 1.65 1.78 1.71 2.29 1.82 2.06 2.14 1.27 Determine (a) the mean, (e) standard deviation, (f) variance, and (g) coefficient of variation. Solution: a) 1.6244 e) 0.339388 f) 0.115184 g) 20.89%
Problem 14.5 Use least-squares regression to fit a straight line Along with the slope and intercept, compute the standard error of the estimate and the correlation coefficient. Plot the data and the regression line. Then repeat the problem, but regress x versus y that is, switch the variables. Interpret your results. Solution: MATLAB Code: see file: EGM3344_HW8_145a.m Output:
- MATLAB Code: see file: EGM3344_HW8_145b.m - Output: y vs x x vs y Slope 0.3591455 2.486137 Y- Intercept 4.88812 -11.1349 Best fit equation y=4.88812+0.3591455x x =-11.1349 + 2.486137 y Standard error 0.851097 2.23927 Correlation coefficient 0.9449 0.9449 The x values are greater than y values when matrices are switched, so the standard error is greater for x vs y compared to y vs x.
Problem 14.8 Beyond the examples in Fig. 14.13, there are other models that can be linearized using transformations. For example, 4 4 x x y e = Linearize this model and use it to estimate a4 and b4 based on the following data. Develop a plot of your fit along with the data. Solution: - MATLAB Code: see file: EGM3344_HW8_148.m - Output: Plot of linearized data with linear regression fit:
Plot of original data with nonlinear model fit: α 4 = 9.661786 β 4 = -2.4733
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