1. or why I like to draw straight lines
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?

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 continuedy x

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

17. Linearizing Data continuedy 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?
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