Lecture Slides 21

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

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
AMS 210: Applied Linear Algebra December 1, 2009 AMS 210
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Background image of page 2
Midterm 2 All scores out of 100. Mean of 59, median of 58, and standard deviation of 24. AMS 210
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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 .
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 17

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

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online