Green beanprojectJason KohMHF4U
Under direct sun       (table)Days                  Height1                                02                             ...
Scatter plot
Linear
Quadratic
Cubic
Quartic
Quintic
Exponential
Logarithmic
Best fit functionModel                         R2Linear                        0.9592Quadratic                     0.9982C...
Graph for best fit
Properties of regressiony  = -0.0006x5 + 0.0169x4 - 0.1926x3 + 0.859x2  + 1.4509x - 2.16 R² = 0.9993     Domain: {XER|X...
3 sets of Intervals
Centered intervaly  = -0.0006x5 + 0.0169x4 - 0.1926x3 + 0.859x2  + 1.4509x - 2.16 X=5 4≤x≤6 X=4      X=6 8.7732   13.10...
Verifying the degree of the       functionDays    Height1             0 2.8                       12           2.8 3.2    ...
Predictionf(11)= 12.191f(12)= 7.2732f(13)= -1.364f(15)= -37.21f(20)= -386.3The prediction is wrong because there is no suc...
No direct sunlight(table)days           height1                         02                        0.23                    ...
Scatter plot
Linear
Quadratic
Cubic
Quartic
Quintic
Exponential
Logarithmic
Best fit functionModel                           R2Linear                          0.9577Quadratic                       0...
Graph for best fit
Properties of regressiony  = 0.0048x5 - 0.1252x4 + 1.1201x3 - 3.8987x2  + 5.6573x - 2.62 Domain: Range: X-intercept: ...
3 sets of intervals
Centered intervaly  = 0.0048x5 - 0.1252x4 + 1.1201x3 - 3.8987x2  + 5.6573x - 2.62 X=5 4≤x≤6  X=4       X=6  -43.078   -...
Verifying the degree of thefunctionDays   Height1          0.1                 0.22          0.3         0.1              ...
Predictionf(11)= 18.712f(12)= 37.634f(13)= 79.374f(15)= 292.12f(20)= 2839.8The prediction is unacceptable in real life sit...
ConclusionBased on the analysis, the quartic regressionis the best fit for the growth of the greenbean with or without dir...
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Growth of a Green Bean

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Growth of a Green Bean

  1. 1. Green beanprojectJason KohMHF4U
  2. 2. Under direct sun (table)Days Height1 02 2.83 64 95 116 13.67 158 16.89 17.610 18.4
  3. 3. Scatter plot
  4. 4. Linear
  5. 5. Quadratic
  6. 6. Cubic
  7. 7. Quartic
  8. 8. Quintic
  9. 9. Exponential
  10. 10. Logarithmic
  11. 11. Best fit functionModel R2Linear 0.9592Quadratic 0.9982Cubic 0.9992Quartic 0.9992Quintic 0.9993Exponential 0.6341Logarithmic 0.9687 The model that best fits Quintic regression
  12. 12. Graph for best fit
  13. 13. Properties of regressiony = -0.0006x5 + 0.0169x4 - 0.1926x3 + 0.859x2 + 1.4509x - 2.16 R² = 0.9993  Domain: {XER|X≥0}  Range: {YER|Y≥0}  X-intercept:  Y-intercept: -2.16
  14. 14. 3 sets of Intervals
  15. 15. Centered intervaly = -0.0006x5 + 0.0169x4 - 0.1926x3 + 0.859x2 + 1.4509x - 2.16 X=5 4≤x≤6 X=4 X=6 8.7732 13.1046 The instantaneous rate of change is 2.1657
  16. 16. Verifying the degree of the functionDays Height1 0 2.8 12 2.8 3.2 -0.8 0.2 -0.43 6 3 -1.2 3.2 -1 2.84 1.6 -6.2 9 2 0.6 -3.4 -1.8 6.85 11 2.6 -1.2 3.4 1.6 -2.46 13.6 1.4 0.4 -1 0.6 1.47 15 1.8 -1 0.48 16.8 0.8 1 09 17.6 0.810 18.4
  17. 17. Predictionf(11)= 12.191f(12)= 7.2732f(13)= -1.364f(15)= -37.21f(20)= -386.3The prediction is wrong because there is no such way thata plant can grow shorter as day passes.
  18. 18. No direct sunlight(table)days height1 02 0.23 0.54 25 4.56 9.37 10.28 129 13.610 15.8
  19. 19. Scatter plot
  20. 20. Linear
  21. 21. Quadratic
  22. 22. Cubic
  23. 23. Quartic
  24. 24. Quintic
  25. 25. Exponential
  26. 26. Logarithmic
  27. 27. Best fit functionModel R2Linear 0.9577Quadratic 0.9652Cubic 0.9853Quartic 0.9883Quintic 0.9938Exponential 0.8824Logarithmic 0.793The model that best fits is Quintic regression
  28. 28. Graph for best fit
  29. 29. Properties of regressiony = 0.0048x5 - 0.1252x4 + 1.1201x3 - 3.8987x2 + 5.6573x - 2.62 Domain: Range: X-intercept: Y-intercept:
  30. 30. 3 sets of intervals
  31. 31. Centered intervaly = 0.0048x5 - 0.1252x4 + 1.1201x3 - 3.8987x2 + 5.6573x - 2.62 X=5 4≤x≤6 X=4 X=6 -43.078 -59.9098 The instantaneous rate of change is -8.4159
  32. 32. Verifying the degree of thefunctionDays Height1 0.1 0.22 0.3 0.1 0.3 1.1 1.2 -1.33 0.6 -0.2 2.8 1.5 1.54 2.1 1 -9 2.5 1.3 2.3 -7.55 4.6 -6.2 18.5 4.8 116 -3.9 -16.9 9.4 0.9 4.8 0.9 -5.97 10.3 -1.1 -4 1.8 1.98 12.1 -0.2 0.8 1.69 13.7 0.6 2.210 15.9
  33. 33. Predictionf(11)= 18.712f(12)= 37.634f(13)= 79.374f(15)= 292.12f(20)= 2839.8The prediction is unacceptable in real life situationbecause green beans cannot grow that much in just 20days.
  34. 34. ConclusionBased on the analysis, the quartic regressionis the best fit for the growth of the greenbean with or without direct sunlight.
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