標題:
Linear Regression
You observe n data pairs (Xi, Yi), i=1,..,n from simple linear regression model Yi=Bo+B1Xi+ei where ei's satisfy Gauss Markov Theorem. Let bo and b1 be least square estimates. Now let Yi' = (Yi-a)/c, where a,c are constants. Show that:a) slope estimate b1' = b1/c for data (Xi,Yi), i=1,..,nb)... 顯示更多 You observe n data pairs (Xi, Yi), i=1,..,n from simple linear regression model Yi=Bo+B1Xi+ei where ei's satisfy Gauss Markov Theorem. Let bo and b1 be least square estimates. Now let Yi' = (Yi-a)/c, where a,c are constants. Show that: a) slope estimate b1' = b1/c for data (Xi,Yi), i=1,..,n b) intercept estimate bo'=(bo-a)/c for data (Xi,Yi), i=1,..,n
最佳解答:
============================================================ 圖片參考：http://img838.imageshack.us/img838/8177/84049904.png 2010-10-20 22:47:02 補充： http://img838.imageshack.us/img838/8177/84049904.png
其他解答:
Given two upper triangular matrices, A = [ a1 * . . * ], B = [ b1 * . . * ] 0 a2 . . * 0 b2 . . * : : : : : : 0 0 . . an 0 0 . . bn their multiplication is still upper triangular, with the diagonal entries simply multiplied together (the other entries are more complicated). AB = [ a1b1 * . . * ] 0 a2b2 . . * : : : 0 0 . . anbn The similar statement is true for the multiplication of two lower triangular matrices. For two diagonal matrices, A = [ a1 0 . . 0 ], B = [ b1 0 . . 0 ] 0 a2 . . 0 0 b2 . . 0 : : : : : : 0 0 . . an 0 0 . . bn their multiplication is still diagonal, with the diagonal entries simply multiplied together. AB = [ a1b1 0 . . 0 ] 0 a2b2 . . 0 : : : 0 0 . . anbn
Linear Regression
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發問:You observe n data pairs (Xi, Yi), i=1,..,n from simple linear regression model Yi=Bo+B1Xi+ei where ei's satisfy Gauss Markov Theorem. Let bo and b1 be least square estimates. Now let Yi' = (Yi-a)/c, where a,c are constants. Show that:a) slope estimate b1' = b1/c for data (Xi,Yi), i=1,..,nb)... 顯示更多 You observe n data pairs (Xi, Yi), i=1,..,n from simple linear regression model Yi=Bo+B1Xi+ei where ei's satisfy Gauss Markov Theorem. Let bo and b1 be least square estimates. Now let Yi' = (Yi-a)/c, where a,c are constants. Show that: a) slope estimate b1' = b1/c for data (Xi,Yi), i=1,..,n b) intercept estimate bo'=(bo-a)/c for data (Xi,Yi), i=1,..,n
最佳解答:
============================================================ 圖片參考：http://img838.imageshack.us/img838/8177/84049904.png 2010-10-20 22:47:02 補充： http://img838.imageshack.us/img838/8177/84049904.png
其他解答:
Given two upper triangular matrices, A = [ a1 * . . * ], B = [ b1 * . . * ] 0 a2 . . * 0 b2 . . * : : : : : : 0 0 . . an 0 0 . . bn their multiplication is still upper triangular, with the diagonal entries simply multiplied together (the other entries are more complicated). AB = [ a1b1 * . . * ] 0 a2b2 . . * : : : 0 0 . . anbn The similar statement is true for the multiplication of two lower triangular matrices. For two diagonal matrices, A = [ a1 0 . . 0 ], B = [ b1 0 . . 0 ] 0 a2 . . 0 0 b2 . . 0 : : : : : : 0 0 . . an 0 0 . . bn their multiplication is still diagonal, with the diagonal entries simply multiplied together. AB = [ a1b1 0 . . 0 ] 0 a2b2 . . 0 : : : 0 0 . . anbn
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