F7 : 11' Curve Fitting

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F7 11. Curve Fitting

• Simple linear regression
• Method of Least Squares

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Soya bean
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Growth curve of soya beans

• Independent variable X
  age in weeks x1,...,xn
• Dependent variable Y
• hight of the plants y1,...yN
• Wanted relation between X and Y
• Y is random (biologigal varibility, measurement
  errors).
• X is fixed and known

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Soya bean data (xi,yi) i1...N(1,5), (2,13),
(3,16), (4,23), (5,33), (6,38), (7,40)
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Regressions model

• Wanted regressions function f
• Errors , independent, expected value 0
• simple linear regression f (x) alpha beta x
• Wanted alpha, beta

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Idea of Least Squares

• Take the curve with minimal avarage of squared
  differences between curve and observations !
• Gauss (1798), Legendre (1806)

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Method of Least Squares in simple linear
regression
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Residual Analysis
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Application to Soya beans
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Result for Soya beans
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SPSS-Result Soya beans
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Properties of LSE
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Inference based on LSE
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SPSS-Result Soya beans
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Confidence and Prediction
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