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Making a curved line straight

Making a curved line straight. Data Transformation & Regression. Last Class. Predicting the dependant variable and standard errors of predicted values. Outliers. Need to visually inspect data in graphic form. Making a curved line straight. Transformation. Early Growth Pattern of Plants.

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Making a curved line straight

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  1. Making a curved line straight Data Transformation & Regression

  2. Last Class • Predicting the dependant variable and standard errors of predicted values. • Outliers. • Need to visually inspect data in graphic form. • Making a curved line straight. • Transformation.

  3. Early Growth Pattern of Plants

  4. Early Growth Pattern of Plants y = Ln(y)

  5. Early Growth Pattern of Plants y = y

  6. Homogeneity of Error Variance

  7. Homogeneity of Error Variance y =Ln(y)

  8. Growth Curve Y = ex

  9. Growth Curve Y = Log(x)

  10. Sigmoid Growth Curve

  11. Sigmoid Growth Curve Accululative Normal Distribution 

  12. Sigmoid Growth Curve ƒ(dd  T - Accululative Normal Distribution T 

  13. Sigmoid Growth Curve ƒ(dd  T - Accululative Normal Distribution T 

  14. Probit Analysis • Group of plants/insects exposed to different concentrations of a specific stimulant (i.e. insecticide). • Data are counts (or proportions), say number killed. • Usually concerned or interested in concentration which causes specific event (i.e. LD 50%).

  15. Probit Analysis ~ Example

  16. Probit Analysis ~ Example

  17. Estimating the Mean y= 50% Killed x ~ 2.8

  18. Estimating the Standard Deviation 2.8

  19. Estimating the Standard Deviation 2 2.8

  20. Estimating the Standard Deviation 95% values 2 2.8

  21. Estimating the Standard Deviation  = 1.2 95% values 2 2.8

  22. Probit Analysis

  23. Probit Analysis

  24. Probit Analysis Probit () =  +  . Log10(concentration)  = -1.022 + 0.202  = 2.415 + 0.331 Log10 (conc) to kill 50% (LD-50) is probit 0.5 = 0 0 = -1.022 + 2.415 x LD-50 LD-50 = 0.423 100.423 = 2.65%

  25. Problems • Obtaining “good estimates” of the mean and standard deviation of the data. • Make a calculated guess, use iteration to get “better fit” to observed data.

  26. Where Straight Lines Meet

  27. Optimal Assent

  28. Optimal Assent Y1=a1+b1x

  29. Optimal Assent Y2=a2+b2x Y1=a1+b1x

  30. Optimal Assent t =[b1-b2]/se(b) = ns Y2=a2+b2x Y1=a1+b1x

  31. Optimal Assent Y3=a3+b3x Y1=a1+b1x

  32. Optimal Assent Y3=a3+b3x t =[b1-b3]/se(b) = *** Y1=a1+b1x

  33. Optimal Assent Y3=a3+b3x Y1=a1+b1x

  34. Optimal Assent t =[b1-bn]/se(b) = *** Yn=an+bnx Y3=a3+b3x Y1=a1+b1x

  35. Optimal Assent Y3=a3+b3x Y3=a3+b3x Y1=a1+b1x

  36. Yield and Nitrogen

  37. What application of nitrogen will result in the optimumyield response?

  38. Intersecting Lines

  39. Intersecting Lines Y = 9.01x + 466.60 Y = 2.81x + 1055.10

  40. Intersecting Lines t = [b11 - b21]/average se(b) 6.2/0.593 = 10.45 * , With 3 df Intersect = same value of y b10 + b11x = y = b20 + b21x x = [b20 - b10]/[b11 - b21] = 94.92 lb N/acre with 1321.83 lb/acre seed yield

  41. Intersecting Lines Y = 9.01x + 466.60 1321.83 lb/acre Y = 2.81x + 1055.10 94.92 lb N/acre

  42. Linear Y = b0 + b1x Quadratic Y = b0 + b1x + b2 x2 Cubic Y = b0 + b1x + b2 x2 + b3 x3 Bi-variate Distribution Correlation

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