Lecture Slides 16

# Lecture Slides 16 - AMS 210 Applied Linear Algebra AMS 210...

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AMS 210: Applied Linear Algebra November 10, 2009 AMS 210

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Topics Today Problem Set 7 Linear Regression: ˆ y = qx and ˆ y = qx + r Nonlinear Regression Linear Models in Chemistry AMS 210
Problem Set 7 Grades and solution available on Blackboard. Mean of 74, median of 78, and standard deviation of 18. AMS 210

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Linear Regression Method of fitting parameters of a linear model based on data. Linear Regression Model: Given a set of points ( x 1 , y 1 ) , ( x 2 , y 2 ) , . . . , ( x n , y n ), find constants q and r such that the linear relation ˆ y i = qx i + r gives the best possible fit for these points. Notationally, ( x i , ˆ y i ) is the estimate for ( x i , y i ). Multilinear regression finds several q i s corresponding to different variables (that is, multivariable linear regression); nonlinear regression fits to equations that aren’t linear. This course describes only simple, linear regression, which corresponds to the equation above. However, some nonlinear problems can be transformed to become linear problems. AMS 210
Using the Model ˆ y = qx A restricted linear regression model: given a set of points ( x 1 , y 1 ) , ( x 2 , y 2 ) , . . . , ( x n , y n ), find a constant q such that the linear relation ˆ y i = qx i gives the best possible fit for these points.

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