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Normal Equations

Normal Equations. Quantity: number & unit & more. Name Procedural statement that defines its measurement Numbers Units Symbol. Partition of Variance. Matrix approach to Regression. Matrix algebra offers a convenient, and eventually necessary, toolbox for traditional statistics.

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Normal Equations

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  1. Normal Equations AGR206

  2. Quantity: number & unit & more • Name • Procedural statement that defines its measurement • Numbers • Units • Symbol AGR206

  3. Partition of Variance AGR206

  4. Matrix approach to Regression Matrix algebra offers a convenient, and eventually necessary, toolbox for traditional statistics. The approach is only different in the way equations are written and in the use of more succinct formulas and mathematical results. AGR206

  5. Linear functions of parameters • v’s are parameters or random variables such as estimated parameters • l’s are coefficients that can have any shape and form for as long as they do not involve the v’s. AGR206

  6. Linear on the parameters! AGR206

  7. Matrices and transposes AGR206

  8. Matrix operations AGR206

  9. Familiar matrix products AGR206

  10. Inverse and Determinant • The inverse involves the reciprocal of the determinant det(A)=|A|, which depends on all values of A. • If det(A)=0 there is no inverse. AGR206

  11. Simple Linear Regression AGR206

  12. Normal Equations AGR206

  13. Estimation and Prediction AGR206

  14. AGR206

  15. Estimation and prediction AGR206

  16. AGR206

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