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Data Analysis

Data Analysis. or why I like to draw straight lines. Engineers like Lines. What are the two parameters for a line m slope of the line b the y intercept. b = 5 m = (-5/2.5) = -2 y = -2x +5. How Do We Make Lines?. How do we make lines?. e 6. e 5. e 4. e 3. e 2. e 1.

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Data Analysis

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  1. Data Analysis or why I like to draw straight lines

  2. Engineers like Lines • What are the two parameters for a line • m slope of the line • b the y intercept b = 5 m = (-5/2.5) = -2 y = -2x +5

  3. How Do We Make Lines?

  4. How do we make lines? e6 e5 e4 e3 e2 e1

  5. How do we evaluate lines? One of these things is not like the other, one of these things does not belong

  6. Plot ei vs xi e6 e5 e4 e3 e2 e1 Good lines have random, uncorrelated errors

  7. Residual Plots

  8. Why do we plot lines?

  9. Why do we plot lines? y = mx + b

  10. Why do we plot lines? y = Aebx

  11. Why do we plot lines? y = Ax2 + Bx + C

  12. Why do we plot lines? • Lines are simple to comprehend and draw • We are familiar with slope and intercept as parameters • We can linearize many functions and plot them as lines

  13. Linearizing equations • We have non linear function v = f(u) • v = u3 • v = 3*log (u)+2 • v = u/(u-4) • We want to transform equation into y = mx+b

  14. Linearizing equations y = v x = u3 m = 1 b = 1 v =2 u3+1 y = mx + b

  15. Linearizing equations y = v x = (u-0.5)2 m = 3 b = 2 v = 3(u-0.5)2 + 2 y = mx + b

  16. Linearizing equations y = ln(v/(5u)) x = u m = ln(2) b = -.5 ln(2) v = 5*u*2u-0.5+1+1 y = mx + b

  17. What are logarithms? • Logab = x  b = ax • Logarithms are the inverse properties of exponentials

  18. Most important log bases • log10 = log • We like to count in powers of 10 • loge = ln • Nature likes to count in powers of e And maybe … • log2 • Computers like bits

  19. What are the important properties of logs? • log(a*b) = log(a) +log(b) • log(ab) = b*log(a)

  20. Why do we care about logs? • Nature likes power law relationships • y = k*uavbwc • For some reason a,b,c are usually either integers, or nice fractions • log(y) = log(k)+a*log(u)+b*log(v)+c*log(w) • Pretty close to linear - we can use linear regression

  21. Buckling in the Materials Lab • From studying the problem we expect that buckling load (P) is a function of Young’s Modulus E, Radius R, and Length L

  22. How would you design an experiment for the pendulum? L M g Keep Mass constant – vary L Keep Length constant – vary M Keep mass and length constant – vary g

  23. Where do log-log plots break down? • Two or more power laws • y=k1*uavb + k2ucvd • Ergun Equation for flow through a packed bed • Flow of fluid through a pipe • For Re < 2100 f=16/Re • For Re > 2100 f=0.0701/Re1/4 • Re=(r v D) / m

  24. Extra Stuff on Lines

  25. Extra Stuff on Lines

  26. More Extra Stuff on Lines

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