SlideServe
Télécharger Obtenir Pro
Menu
Accueil Pro
Préférences
ApparenceLight Aide et commentaires
© SlideServe · v2026

Understanding Linear Relationships: From Trend Lines to Logarithmic Functions

zephania-branch avatar
zephania-branch
31 diapositives · 488 Views · Nov 28, 2014

This text explores the significance of linear relationships in data analysis, emphasizing the role of trend lines, slope, and y-intercepts. It discusses linearizing complex functions, the importance of residual plots, and how logarithms are used in engineering and scientific contexts. The discussion extends to enzyme kinetics, power-law relationships, and the application of logarithms in analyses. Ultimately, engineers leverage these techniques to simplify problems and extract meaningful insights from data, demonstrating the utility of linear models in diverse scenarios.

#understanding linear relationships: from trend lines to logarithmic functions #understanding linear relationships: from trend lines to logarithmic functions ppt #powerpoint #presentation
Understanding Linear Relationships: From Trend Lines to Logarithmic Functions - slide 1
01 / 31Understanding Linear Relationships: From Trend Lines to Logarithmic Functions
1 / 17

Télécharger la présentation

Understanding Linear Relationships: From Trend Lines to Logarithmic Functions
Une image / un lien ci-dessous est fourni (tel quel) pour télécharger la présentation

Politique de téléchargement : le contenu du site vous est fourni TEL QUEL pour votre information et votre usage personnel ; il ne peut être vendu, concédé sous licence ni partagé sur d’autres sites sans l’accord de son auteur.Le contenu vous est fourni TEL QUEL, pour votre information et votre usage personnel uniquement. Téléchargez la présentation en cliquant sur ce lien. Lors du téléchargement, si vous ne parvenez pas à télécharger une présentation, l’éditeur a peut-être supprimé le fichier de son serveur.Pendant le téléchargement, si vous ne parvenez pas à obtenir une présentation, le fichier a peut-être été supprimé par l’éditeur.

F I N

Plus de contenu associé

Transcription de la présentation

  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