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ps233.lecture2 2

# ps233.lecture2 2 - PS 233 Lecture 2 The Simple Linear...

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PS 233 Lecture 2 The Simple Linear Regression Model

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What is Ordinary Least Squares? Ordinary Least Squares (OLS) finds the linear model that minimizes the sum of the squared errors . Such a model provides the best explanation/prediction of the data. Later we’ll show that OLS is the “Best Linear Unbiased Estimator” (BLUE)
“Explained” and “Unexplained” Variation

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Minimizing the Sum of Squared Errors How to put the Least in OLS? In mathematical jargon we seek to minimize the Unexplained Sum of Squares (USS), where: U S S Y Y e i i i = - = ( ) 2 2
Picking the Parameters To Minimize USS , we need parameter estimates. In calculus, if you wish to know when a function is at its minimum, you take the first derivative. In this case we must take partial derivatives since we have two parameters (a & b) to worry about.

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Parameters that Minimize USS
Minimize the Squared Errors The Unexplained Sum of Squared Errors Function is: - - = - = = 2 2 2 ) ( USS ) ˆ ( USS USS bX a Y Y Y e i i i i

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Partial Derivatives for a and b First equation is the partial derivative with respect to a Second equation is with respect to b U S S a Y a b X U S S b Y a b X X i i i i i = - - - = - - - 2 1 2 ( ) ( ) ( ) ( )
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ps233.lecture2 2 - PS 233 Lecture 2 The Simple Linear...

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