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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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**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?**e6 e5 e4 e3 e2 e1**How do we evaluate lines?**One of these things is not like the other, one of these things does not belong**Plot ei vs xi**e6 e5 e4 e3 e2 e1 Good lines have random, uncorrelated errors**Why do we plot lines?**y = mx + b**Why do we plot lines?**y = Aebx**Why do we plot lines?**y = Ax2 + Bx + C**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**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**Linearizing Data continued**ln(y) ln(x)**Linearizing Data**ln(y+5) x**Enzyme Production**Michaelis - Menten Vmax Vmax = 10 Km = 1 ½*Vmax Km**Engineers often use logarithms to solve problems**• What is a Log? • logab = x b = ax • Logarithms are the inverse functions of exponential functions**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**What are the important properties of logs?**• log(a*b) = log(a) +log(b) • log(ab) = b*log(a)**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**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**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**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

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