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Non-linear regression

Non-linear regression. Exponential relationships and power r elationships. Does this look linear?. Regression line and correlation coefficient. r =0.799. Natural log of y. If x and ln (y) are linear, then x and y have an exponential relationship -> y=a* b x. Log-linear graph (or semi-log).

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Non-linear regression

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  1. Non-linear regression Exponential relationships and power relationships

  2. Does this look linear?

  3. Regression line and correlation coefficient r=0.799

  4. Natural log of y If x and ln(y) are linear, then x and y have an exponential relationship -> y=a*bx

  5. Log-linear graph (or semi-log) We scaled the y-axis (logarithmic scale). On the previous slide scaled the values of y (the result is the same). --here we used log10 scale, but it doesn’t matter!

  6. Proof on chalkboard

  7. Does this look linear? Or Exponential?

  8. Does this look linear? r=0.963

  9. Does this look exponential? Log-linear graph Log-linear (log10) graph is NOT linear. So x and y do NOT have an exponential relationship!!

  10. ln x by ln y If ln(x) and ln(y) are linear, then x and y have an power relationship. y=a*x^b

  11. Log-log graph Here we scaled both the x-axis and the y-axis (both on logarithmic scales). In the previous slide we scaled the values of x and y (result is the same).

  12. Proof on chalkboard

  13. Conclusions • Humans are good at identifying linear relationships visually. • Distinguishing between exponential and power (or other) is very difficult just by looking at data. • So if in doubt, try the semi-log plot and log-log plot to see if either of them are linear.

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