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Data Analysis

Data Analysis. or why I like to draw straight lines. Engineers like Lines. 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 Trend Lines?. How Do We Make Trend 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 • 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 Trend Lines?

  4. How Do We Make Trend 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 • Many functions can be expressed as Taylor Series

  13. Taylor Series

  14. Linearizing Equations • We have non linear function v = f(u) • v = u3 • v = 2eu+5u • v=u/(u-4) • We want to transform the equation into y=mx+b

  15. Linearizing Data continued y x

  16. Linearizing Data continued ln(y) ln(x)

  17. Linearizing Data continued y x

  18. Linearizing Data ln(y+5) x

  19. Enzyme Kinetics

  20. Enzyme Production Michaelis - Menten Vmax Vmax = 10 Km = 1 ½*Vmax Km

  21. Linearization of Enzyme Kinetics

  22. Engineers often use logarithms to solve problems • What is a Log? • logab = x  b = ax • Logarithms are the inverse functions of exponential functions

  23. 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 count in bits

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

  25. 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

  26. Buckling in the Materials Lab • From studying the problem we expect that buckling load (P) is a power law function of Radius R, and Length L

  27. 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

  28. Where do log-log plots break down? • Two or more power laws • y=k1*uavb + k2ucvd • s(t)=-g/2*t2+v0t+s0 • E=mgh+1/2*mv2

  29. Extra Stuff on Lines

  30. Extra Stuff on Lines

  31. More Extra Stuff on Lines

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