Lanczos3.dat 2.6 KB

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  1. NIST/ITL StRD
  2. Dataset Name: Lanczos3 (Lanczos3.dat)
  3. File Format: ASCII
  4. Starting Values (lines 41 to 46)
  5. Certified Values (lines 41 to 51)
  6. Data (lines 61 to 84)
  7. Procedure: Nonlinear Least Squares Regression
  8. Description: These data are taken from an example discussed in
  9. Lanczos (1956). The data were generated to 5-digits
  10. of accuracy using
  11. f(x) = 0.0951*exp(-x) + 0.8607*exp(-3*x)
  12. + 1.5576*exp(-5*x).
  13. Reference: Lanczos, C. (1956).
  14. Applied Analysis.
  15. Englewood Cliffs, NJ: Prentice Hall, pp. 272-280.
  16. Data: 1 Response (y)
  17. 1 Predictor (x)
  18. 24 Observations
  19. Lower Level of Difficulty
  20. Generated Data
  21. Model: Exponential Class
  22. 6 Parameters (b1 to b6)
  23. y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x) + e
  24. Starting values Certified Values
  25. Start 1 Start 2 Parameter Standard Deviation
  26. b1 = 1.2 0.5 8.6816414977E-02 1.7197908859E-02
  27. b2 = 0.3 0.7 9.5498101505E-01 9.7041624475E-02
  28. b3 = 5.6 3.6 8.4400777463E-01 4.1488663282E-02
  29. b4 = 5.5 4.2 2.9515951832E+00 1.0766312506E-01
  30. b5 = 6.5 4 1.5825685901E+00 5.8371576281E-02
  31. b6 = 7.6 6.3 4.9863565084E+00 3.4436403035E-02
  32. Residual Sum of Squares: 1.6117193594E-08
  33. Residual Standard Deviation: 2.9923229172E-05
  34. Degrees of Freedom: 18
  35. Number of Observations: 24
  36. Data: y x
  37. 2.5134E+00 0.00000E+00
  38. 2.0443E+00 5.00000E-02
  39. 1.6684E+00 1.00000E-01
  40. 1.3664E+00 1.50000E-01
  41. 1.1232E+00 2.00000E-01
  42. 0.9269E+00 2.50000E-01
  43. 0.7679E+00 3.00000E-01
  44. 0.6389E+00 3.50000E-01
  45. 0.5338E+00 4.00000E-01
  46. 0.4479E+00 4.50000E-01
  47. 0.3776E+00 5.00000E-01
  48. 0.3197E+00 5.50000E-01
  49. 0.2720E+00 6.00000E-01
  50. 0.2325E+00 6.50000E-01
  51. 0.1997E+00 7.00000E-01
  52. 0.1723E+00 7.50000E-01
  53. 0.1493E+00 8.00000E-01
  54. 0.1301E+00 8.50000E-01
  55. 0.1138E+00 9.00000E-01
  56. 0.1000E+00 9.50000E-01
  57. 0.0883E+00 1.00000E+00
  58. 0.0783E+00 1.05000E+00
  59. 0.0698E+00 1.10000E+00
  60. 0.0624E+00 1.15000E+00