Lecture Slides 21

# Lecture Slides 21 - AMS 210 Applied Linear Algebra December...

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AMS 210: Applied Linear Algebra December 1, 2009 AMS 210

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Topics Today Midterm 2 Final Exam Approximate Solutions Linear Regression: Previous Method Linear Regression, Reprise Linear Regression as Projection General Linear Regression using Pseudoinverses A Theorem on Pseudoinverses Least-Squares Polynomial Fitting Angles Between Vectors AMS 210
Midterm 2 All scores out of 100. Mean of 59, median of 58, and standard deviation of 24. AMS 210

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Final Exam December 15, 5:15pm to 7:45pm. See http://www.sunysb.edu/registrar/finals.shtml for general ﬁnal exam schedule information. May contain material from any problem sets assigned and either of the two midterms. Last two classes (they end on Dec 11 generically) on Dec 8/10 are ﬁnal exam reviews. No new material during them. Same calculator policy as midterm 2: scientiﬁc calculators and TI-83/84/85/86 acceptable. TI-89/92 and HP-48/49/50 disallowed. Any others please ask; by default, disallowed. If caught cheating, your exam may be removed. AMS 210
Linear Regression, Reprise Linear Regression a method to ﬁnd approximate (least-squares) solution to Ax = b when more equations than variables exist. That is, one has lots of rows of data. Gaussian elimination/etc tend to produce inconsistent solutions unless (very rare) an exact solution is possible. ‘Solving’ requires breaking equality constraints to best-eﬀort approximations. Oil reﬁnery example: [20,4,4,500], [10,14,5,850], [5,5,12,1000]. Can solve exactly as x = A - 1 b , but matrix inverse only deﬁned for square matrices. Linear regression approach: minimize | b - Aw | rather than aiming for b = Aw . AMS 210

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Minimizing SSE in ˆ y = qx Let x be x-values, y be the y-values, and ˆ y be estimated y values: then want to minimize Euclidean norm between y and ˆ y , that is between y and q x .
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Lecture Slides 21 - AMS 210 Applied Linear Algebra December...

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