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Linear Regression and Correlation: Regression Lab II (edited: Teegarden)
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Statistics
Linear Regression
(m23468)
Author:
Paul E Pfeiffer
Keywords:
Correlation coefficient
,
Estimates
,
Mean square error
,
Regression line
Summary:
Consider a pair {X,Y} with a joint distribution. A value X(ω) is observed. It is desired to estimate the corresponding value Y(ω). The best that can be hoped for is some estimate based on an average of the errors, or on the average of some function of ... is considered
[Expand Summary]
Consider a pair {X,Y} with a joint distribution. A value X(ω) is observed. It is desired to estimate the corresponding value Y(ω). The best that can be hoped for is some estimate based on an average of the errors, or on the average of some function of the errors. The most common measure of error is the mean (expectation) of the square of the error. This has two important properties: it treats positive and negative errors alike, and it weights large errors more heavily than smaller ones. In general, we seek a rule (function) r such that the estimate is r(X(ω)). That is, we seek a function r such that the expectation of the square of Y  r(X) is a minimum. The problem of determining such a function is known as the regression problem. LINEAR REGRESSION: we seek the best straight line function (the regression line of Y on X) of the form u = r(t) + b, such that the mean square of Y  r(X) is a minimum. Matlab approximation procedures are compared with analytic results. More general linear regression is considered
[Collapse Summary]
Subject:
Mathematics and Statistics
Language:
English
Popularity:
56.40%
Revised:
20090918
Revisions:
6
Popularity is measured as percentile rank of page views/day over all time
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