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Lab 4 slides - x ˆ y x ± t α 2,n-p r s 2 s 2 x t X t X-1...

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Prediction Intervals Like with simple linear regression, we can build confidence intervals for the predicted mean value and for a new prediction, now for a covariate vector x 0 = (1 , x 01 , x 02 , ..., x 0 p ) Var y | x 0 ) = Var ( x 0 t ˆ β ) = x 0 t Var ( ˆ β ) x 0 = σ 2 x 0 t ( X t X ) - 1 x 0 Lecture 9 – p. 1/
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Prediction Intervals Again estimate σ 2 with s 2 Two types of intervals Confidence interval for the mean value at x 0 ˆ y ( x 0 ) ± t α/ 2 ,n - p radicalBig s 2 x 0 t ( X t X ) - 1 x 0 Lecture 9 – p. 2/
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Prediction Intervals Confidence interval for a predicted value at
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Unformatted text preview: x ˆ y ( x ) ± t α/ 2 ,n-p r s 2 + s 2 x t ( X t X )-1 x Lecture 9 – p. 3/ 5 Prediction Intervals Back to R for examples of prediction Lecture 9 – p. 4/ 5 Coming up next Class 12 Multiple Linear Reg (cont.) Sec 3.8, 3.9 Class 13 Model Select Sec. 4.1 - 4.2 Class 14 Midterm Review Class 15 In-class Midterm (Oct 30) Lecture 9 – p. 5/ 5...
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