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Enhancing STEM Education: Applications of Regression Analysis in Engineering

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This resource explores the transformative role of regression analysis in STEM education, particularly for undergraduate students. It covers both linear and nonlinear regression models, providing practical examples such as stress-strain analysis in composite materials and bone scans. The resource aims to enrich students’ understanding of regression techniques and their applications in real-world scenarios, fostering critical thinking and problem-solving skills. Relevant exercises and data manipulation strategies are included to reinforce learning.

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Enhancing STEM Education: Applications of Regression Analysis in Engineering

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  1. Regressionhttp://numericalmethods.eng.usf.eduTransforming Numerical Methods Education for the STEM undergraduate http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  2. Applications http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  3. Mousetrap Car http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  4. Torsional Stiffness of a Mousetrap Spring http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  5. Stress vs Strain in a Composite Material http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  6. A Bone Scan http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  7. Radiation intensity from Technitium-99m http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  8. Trunnion-Hub Assembly http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  9. Thermal Expansion Coefficient Changes with Temperature? http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  10. THE END http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  11. Pre-Requisite Knowledge http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  12. This rapper’s name is • Da Brat • Shawntae Harris • Ke$ha • Ashley Tisdale • Rebecca Black http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  13. Close to half of the scores in a test given to a class are above the • average score • median score • standard deviation • mean score http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  14. Given y1, y2,……….. yn,the standard deviation is defined as • . • . • . • . http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  15. THE END http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  16. Linear Regression http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  17. Given (x1,y1), (x2,y2),……….. (xn,yn), best fitting data to y=f (x) by least squares requires minimization of • ) • ) • ) • ) http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  18. The following data • -136 • 400 • 536 is regressed with least squares regression to a straight line to give y=-116+32.6x. The observed value of y at x=20 is http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  19. The following data • -136 • 400 • 536 is regressed with least squares regression to a straight line to give y=-116+32.6x. The predicted value of y at x=20 is http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  20. The following data • -136 • 400 • 536 is regressed with least squares regression to a straight line to give y=-116+32.6x. The residual of y at x=20 is http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  21. THE END http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  22. Nonlinear Regression http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  23. When transforming the data to find the constants of the regression model y=aebx to best fit (x1,y1), (x2,y2),……….. (xn,yn), the sum of the square of the residuals that is minimized is http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  24. When transforming the data for stress-strain curve for concrete in compression, where is the stress and is the strain, the model is rewritten as • ) • ) • ) • ) http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  25. Adequacy of Linear Regression Models http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  26. The case where the coefficient of determination for regression of n data pairs to a straight line is one if • none of data points fall exactly on the straight line • the slope of the straight line is zero • all the data points fall on the straight line http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  27. The case where the coefficient of determination for regression of n data pairs to a general straight line is zero if the straight line model • has zero intercept • has zero slope • has negative slope • has equal value for intercept and the slope http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  28. The coefficient of determination varies between • -1 and 1 • 0 and 1 • -2 and 2 http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  29. The correlation coefficient varies between • -1 and 1 • 0 and 1 • -2 and 2 http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  30. If the coefficient of determination is 0.25, and the straight line regression model is y=2-0.81x, the correlation coefficient is • -0.25 • -0.50 • 0.00 • 0.25 • 0.50 http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  31. If the coefficient of determination is 0.25, and the straight line regression model is y=2-0.81x, the strength of the correlation is • Very strong • Strong • Moderate • Weak • Very Weak http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  32. If the coefficient of determination for a regression line is 0.81, then the percentage amount of the original uncertainty in the data explained by the regression model is • 9 • 19 • 81 http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  33. The percentage of scaled residuals expected to be in the domain [-2,2] for an adequate regression model is • 85 • 90 • 95 • 100 http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  34. THE END http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  35. The average of the following numbers is • 4.0 • 7.0 • 7.5 • 10.0 http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  36. The following data • 27.480 • 28.956 • 32.625 • 40.000 is regressed with least squares regression to y=a1x. The value of a1 most nearly is http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  37. A scientist finds that regressing y vs x data given below to straight-line y=a0+a1xresults in the coefficient of determination, r2 for the straight-line model to be zero. • -2.444 • 2.000 • 6.889 • 34.00 The missing value for y at x=17 most nearly is http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  38. A scientist finds that regressing y vs x data given below to straight-line y=a0+a1xresults in the coefficient of determination, r2 for the straight-line model to be one. • -2.444 • 2.000 • 6.889 • 34.00 The missing value for y at x=17 most nearly is http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

  39. The average of 7 numbers is given 12.6. If 6 of the numbers are 5, 7, 9, 12, 17 and 10, the remaining number is • -47.9 • -47.4 • 15.6 • 28.2 http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for the STEM Undergraduate

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