lecture_E7_10_regression_2p - Lecture 10: Regression Issues...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Issues of noise in experimental data: illustration Projection operator Writing the regression equations Lecture 10: Regression Getting the pseudo inverse An example: computing pi A least square error justification Example of taxi data
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 Example of taxi data Example of taxi data
Background image of page 2
3 Example of taxi data Example of taxi data
Background image of page 3

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

View Full DocumentRight Arrow Icon
4 Example of taxi data Main problem of noisy data: regression If I have a set of data points, and I try to ‘fit’ a line through the cloud of points, what is the best way to fit that line?
Background image of page 4
5 Main problem of noisy data: regression If I have a set of data points, and I try to ‘fit’ a line through the cloud of points, what is the best way to fit that line? Main problem of noisy data: regression If I have a set of data points, and I try to ‘fit’ a line through the cloud of points, what is the best way to fit that line?
Background image of page 5

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

View Full DocumentRight Arrow Icon
6 Main problem of noisy data: regression Main question: “what does good mean”, i.e. what is the criterion for being a “good” approximation. Avector Y of “data” ˆ Y projected along the red line Main problem of noisy data: regression What does “projected” mean? It means that ˆ Y Y is orthogonoal to ˆ Y ˆ Y This means that from all the points along the red line, the point is the one which minimizes the distance to Y
Background image of page 6
7 Main problem of noisy data: regression What does “projected” mean? It means that ˆ Y Y is orthogonoal to ˆ Y ˆ Y This means that from all the points along the red line, the point is the one which minimizes the distance to Y Orthogonality of vectors? Vectors are orthogonal if their dot product is zero ˆ Y Y is orthogonoal to ˆ Y Means that dot( ˆ Y Y , ˆ Y )=0 In other words: ˆ Y T ˆ Y Y = 0 ( ) = 0 Where as in the previous chapter on linear algebra, the superscript T means transpose
Background image of page 7

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

View Full DocumentRight Arrow Icon
8 So in summary: to find the projection In order to find the projection of a vector on the red line, one needs to check the following formula: ˆ Y T ˆ Y Y = 0 ˆ Y Y ( ) = 0 Now we can define regression We consider data points ( x i ,y i ) We want to construct an estimator, which describes the data as a linea combination o functions y i which describes the data as a linear combination of functions with coefficients x i
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/07/2011 for the course ENGIN 7 taught by Professor Horowitz during the Spring '08 term at University of California, Berkeley.

Page1 / 23

lecture_E7_10_regression_2p - Lecture 10: Regression Issues...

This preview shows document pages 1 - 9. Sign up to view the full document.

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