Lecture 13: Simple Linear Regression in Matrix Format
11:55 Wednesday 14thOctober, 2015See updates and corrections ~cshalizi/mreg/ Lecture 13: Simple Linear Regression in MatrixFormat36-401, Section B, Fall 201513 October 2015Contents1 Least Squares in Matrix The Basic Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . Mean Squared Error . . . . . . . . . . . . . . . . . . . . . . . . . Minimizing the MSE . . . . . . . . . . . . . . . . . . . . . . . . .42 Fitted Values and Residuals.
2)y x(c XY + xy ) c XY (32) = 1 s2 X s2 x y+ x2y xc XY 2 y c XY (33) = " y c XY s2 X x c XY s2 X # (34) which is what it should be. So: n 1xTy is keeping track of yand xy, and n xTx keeps track of x and x2. The matrix inversion and multiplication then handles all the book-keeping to put these pieces together to get the appropriate (sample ...
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