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Unformatted text preview: 1 MLR (example) hous e 1 2 3 4 5 6 7 8 price 234 230 255 271 289 333 321 345 size 1.8 2.0 2.1 2.3 2.5 2.8 3.0 3.3 Lot size 14 12 23 18 13 28 14 15 upgra des 25 10 6 20 13 35 14 22 2 MLR: General Model y depends linearly on the k factors x 1 , …, x k y = β + β 1 x 1 +…+ β k x k + ε ε represents the random error term Each x j is a regressor variable What does each β j represent? Which is the dependent variable? 3 MLR: General Model The model fitting in MLR can be thought of as fitting a kdimensional hyperplane to n sample points that live in (p=k+1)dimensional space. Question: what is the minimum number of sample points that is needed for fitting a model uniquely? What is the minimum number of sample points that is needed for model error estimation? 4 Vector and Matrix Notation = = k 1 nk 2 n 1 n k 2 22 21 k 1 12 11 , x x x 1 x x x 1 x x x 1 X β β β β 5 The Transpose [ ] k nk k k n...
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This note was uploaded on 03/17/2008 for the course IE 121 taught by Professor Perevalov during the Spring '08 term at Lehigh University .
 Spring '08
 Perevalov

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