slide6 - MLR(example house price size Lot size 1 2 3 4 5 6...

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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
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2 MLR: General Model y depends linearly on the k factors x 1 , …, x k y =  β 0  +  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 represent? Which is the dependent variable?  
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3 MLR: General Model The model fitting in MLR can be thought of as fitting  a k-dimensional  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? 
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4 Vector and Matrix Notation = = k 1 0 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
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5 The Transpose [ ] k nk k k n n x x x x x x x x x X β β β β 1 0 2 1 2 22 12 1 21 11 ' 1 1 1 ' =
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