Data Analysis

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Data Analysis

• or why I like to draw straight lines

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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
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How Do We Make Lines?
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How do we make lines?
e6
e5
e4
e3
e2
e1
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How do we evaluate lines?
One of these things is not like the other, one of
these things does not belong
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Plot ei vs xi
e6
e5
e4
e3
e2
e1
Good lines have random, uncorrelated errors
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Residual Plots
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Why do we plot lines?
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Why do we plot lines?
y mx b
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Why do we plot lines?
y Aebx
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Why do we plot lines?
y Ax2 Bx C
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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

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Linearizing equations

• We have non linear function v f(u)
• v u3
• v 3log (u)2
• v u/(u-4)
• We want to transform equation into y mxb

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Linearizing equations
y v x u3 m 1 b 1
v 2 u31
y mx b
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Linearizing equations
y v x (u-0.5)2 m 3 b 2
v 3(u-0.5)2 2
y mx b
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Linearizing equations
y ln(v/(5u)) x u m ln(2) b -.5 ln(2)
v 5u2u-0.511
y mx b
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What are logarithms?

• Logab x ?? b ax
• Logarithms are the inverse properties of
  exponentials

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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

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What are the important properties of logs?

• log(ab) log(a) log(b)
• log(ab) blog(a)

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Why do we care about logs?

• Nature likes power law relationships
• y kuavbwc
• For some reason a,b,c are usually either
  integers, or nice fractions
• log(y) log(k)alog(u)blog(v)clog(w)
• Pretty close to linear - we can use linear
  regression

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Buckling in the Materials Lab

• From studying the problem we expect that buckling
  load (P) is a function of Youngs Modulus E,
  Radius R, and Length L

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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
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Where do log-log plots break down?

• Two or more power laws
• yk1uavb k2ucvd
• Ergun Equation for flow through a packed bed
• Flow of fluid through a pipe
• For Re lt 2100 f16/Re
• For Re gt 2100 f0.0701/Re1/4
• Re(r v D) / m

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Extra Stuff on Lines
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Extra Stuff on Lines
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More Extra Stuff on Lines