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# note5 - STAT5044 Regression and Anova Inyoung Kim Outline 1...

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STAT5044: Regression and Anova Inyoung Kim

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Outline 1 Prediction
Prediction Two meaning Predict conditional mean of Y given a x new Point estimation for conditional mean is ˆ β 0 + ˆ β 1 x new . Predict a new observation Y * given a x new Y * = β 0 + β 1 x new + ε * ε * N ( 0 , σ 2 ) what is the point estimation for this?

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Prediction Two meaning Predict conditional mean of Y given a x new Point estimation for conditional mean is ˆ β 0 + ˆ β 1 x new . Predict a new observation Y * given a x new Y * = β 0 + β 1 x new + ε * ε * N ( 0 , σ 2 ) what is the point estimation for this? ˆ β 0 + ˆ β 1 x new
Two meaning Conditional means: E ( ˆ Y | x new ) = β 0 + β 1 x new , where x new is given. This is a new parameter Predict β 0 + β 1 x new + ε * This is a new random observation

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Distribution of ˆ β 0 + ˆ β 1 x new What is the distribution of ˆ β 0 + ˆ β 1 x new ? ˆ β = ˆ β 0 ˆ β 1 ! and X new = ( 1 x new ) ˆ β 0 + ˆ β 1 x new = X new ˆ β = [ X new ( X t X ) - 1 X t ] y = By : a linear function of Y
Distribution of ˆ β 0 + ˆ β 1 x new E ( ˆ β 0 + ˆ β 1 x new ) = β 0 + β 1 x

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note5 - STAT5044 Regression and Anova Inyoung Kim Outline 1...

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