Transcription of Lecture 13: Simple Linear Regression in Matrix Format
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Lecture 13: Simple Linear Regression in Matrix Format
11:55 Wednesday 14thOctober, 2015 See updates and corrections ~cshalizi/mreg/ Lecture 13: Simple Linear Regression in MatrixFormat36-401, Section B, Fall 201513 October 2015 Contents1 Least Squares in Matrix The Basic Matrices .. Mean Squared Error .. Minimizing the MSE ..42 Fitted Values and Residuals .. Expectations and Covariances ..73 Sampling Distribution of Estimators84 Derivatives with Respect to Second Derivatives .. Maxima and Minima .. 115 Expectations and Variances with Vectors and Matrices126 Further Reading1312So far, we have not used any notions, or notation, that goes beyond basicalgebra and calculus (and probability).
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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