3 Diagnostics for Simple Regression

3 Diagnostics for Simple Regression - Statistics 191:...

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Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Statistics 191: Introduction to Applied Statistics Diagnostics for simple linear regression Jonathan Taylor Department of Statistics Stanford University January 26, 2010 1 / 1
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Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Outline Diagnostics for simple regression Goodness of fit of regression: analysis of variance. F -statistics. Residuals. Diagnostic plots. 2 / 1
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Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Geometry of Least Squares 3 / 1
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Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Goodness of fit Sums of squares SSE = n X i =1 ( Y i - b Y i ) 2 = n X i =1 ( Y i - b β 0 - b β 1 X i ) 2 SSR = n X i =1 ( Y - b Y i ) 2 = n X i =1 ( Y - b β 0 - b β 1 X i ) 2 SST = n X i =1 ( Y i - Y ) 2 = SSE + SSR R 2 = SSR SST = 1 - SSE SST = d Cor ( X , Y ) 2 . Basic idea: if R 2 is large: a lot of the variability in Y is explained by X . 4 / 1
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Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Total sum of squares R code 5 / 1
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Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Error sum of squares R code 6 / 1
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Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Regression sum of squares R code 7 / 1
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Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University F -statistics What is an F -statistic? An
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3 Diagnostics for Simple Regression - Statistics 191:...

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