b.lect22 - Outline Fitting Regression Models: The Method of...

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Unformatted text preview: Outline Fitting Regression Models: The Method of Least Squares * The Method of Maximum Likelihood (ML) Lecture 22 Chapter 7: Point Estimation: Fitting Models to Data Michael Akritas Michael Akritas Lecture 22 Chapter 7: Point Estimation: Fitting Models to Dat Outline Fitting Regression Models: The Method of Least Squares * The Method of Maximum Likelihood (ML) Fitting Regression Models: The Method of Least Squares Estimation of the Intercept and the Slope Regression Jargon The Intrinsic Error Variance * The Method of Maximum Likelihood (ML) Michael Akritas Lecture 22 Chapter 7: Point Estimation: Fitting Models to Dat Outline Fitting Regression Models: The Method of Least Squares * The Method of Maximum Likelihood (ML) Estimation of the Intercept and the Slope Regression Jargon The Intrinsic Error Variance Michael Akritas Lecture 22 Chapter 7: Point Estimation: Fitting Models to Dat Outline Fitting Regression Models: The Method of Least Squares * The Method of Maximum Likelihood (ML) Estimation of the Intercept and the Slope Regression Jargon The Intrinsic Error Variance Let ( X 1 , Y 1 ) , . . . , ( X n , Y n ) be a s.r.s. from a bivariate population ( X , Y ), and assume that Y | X ( x ) = E ( Y | X = x ) = 1 + 1 x Michael Akritas Lecture 22 Chapter 7: Point Estimation: Fitting Models to Dat Outline Fitting Regression Models: The Method of Least Squares * The Method of Maximum Likelihood (ML) Estimation of the Intercept and the Slope Regression Jargon The Intrinsic Error Variance Let ( X 1 , Y 1 ) , . . . , ( X n , Y n ) be a s.r.s. from a bivariate population ( X , Y ), and assume that Y | X ( x ) = E ( Y | X = x ) = 1 + 1 x The method of least squares (LS) finds the line that achieves the least sum of square vertical distances from the data points. Michael Akritas Lecture 22 Chapter 7: Point Estimation: Fitting Models to Dat Outline Fitting Regression Models: The Method of Least Squares * The Method of Maximum Likelihood (ML) Estimation of the Intercept and the Slope Regression Jargon The Intrinsic Error Variance Let ( X 1 , Y 1 ) , . . . , ( X n , Y n ) be a s.r.s. from a bivariate population ( X , Y ), and assume that Y | X ( x ) = E ( Y | X = x ) = 1 + 1 x The method of least squares (LS) finds the line that achieves the least sum of square vertical distances from the data points. } Vertical Distance from Line 1 Line 1 Line 2 Figure: Illustration of Vertical Distance Michael Akritas Lecture 22 Chapter 7: Point Estimation: Fitting Models to Dat Outline Fitting Regression Models: The Method of Least Squares * The Method of Maximum Likelihood (ML) Estimation of the Intercept and the Slope Regression Jargon The Intrinsic Error Variance The Least Squares Estimators Michael Akritas Lecture 22 Chapter 7: Point Estimation: Fitting Models to Dat Outline Fitting Regression Models: The Method of Least Squares * The Method of Maximum Likelihood (ML) Estimation of the Intercept and the Slope Regression Jargon The Intrinsic Error Variance...
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b.lect22 - Outline Fitting Regression Models: The Method of...

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