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b.lect24 - Outline CIs Based on the T-Distribution...

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Unformatted text preview: Outline CIs Based on the T-Distribution Prediction Intervals Lecture 24 Chapter 8: Confidence and Prediction Intervals Michael Akritas Michael Akritas Lecture 24 Chapter 8: Confidence and Prediction Intervals Outline CIs Based on the T-Distribution Prediction Intervals CIs Based on the T-Distribution Introduction Confidence Intervals for a Normal Mean CIs for the Slope of a Regression Line CIs for the Regression Line Prediction Intervals Prediction Based on a Univariate Sample PIs for the Normal Simple Linear Regression Model Michael Akritas Lecture 24 Chapter 8: Confidence and Prediction Intervals Outline CIs Based on the T-Distribution Prediction Intervals Introduction Confidence Intervals for a Normal Mean CIs for the Slope of a Regression Line CIs for the Regression Line When sampling from normal populations, an estimator b θ of some parameter θ often satisfies b θ- θ b σ ˆ θ ∼ t ν , where b σ ˆ θ is the estimated s.e. , and t ν stands for ” t-distribution with ν degrees of freedom”. Michael Akritas Lecture 24 Chapter 8: Confidence and Prediction Intervals Outline CIs Based on the T-Distribution Prediction Intervals Introduction Confidence Intervals for a Normal Mean CIs for the Slope of a Regression Line CIs for the Regression Line When sampling from normal populations, an estimator b θ of some parameter θ often satisfies b θ- θ b σ ˆ θ ∼ t ν , where b σ ˆ θ is the estimated s.e. , and t ν stands for ” t-distribution with ν degrees of freedom”. ν , ν t p.d.f of the t-distr. with area= α α degrees of freedom Figure: PDF and Percentile of a t-distribution Michael Akritas Lecture 24 Chapter 8: Confidence and Prediction Intervals Outline CIs Based on the T-Distribution Prediction Intervals Introduction Confidence Intervals for a Normal Mean CIs for the Slope of a Regression Line CIs for the Regression Line Three Specific Examples Michael Akritas Lecture 24 Chapter 8: Confidence and Prediction Intervals Outline CIs Based on the T-Distribution Prediction Intervals Introduction Confidence Intervals for a Normal Mean CIs for the Slope of a Regression Line CIs for the Regression Line Three Specific Examples 1. If X 1 , X 2 , . . . , X n are iid N ( μ, σ 2 ), then X- μ S / √ n ∼ t n- 1 Michael Akritas Lecture 24 Chapter 8: Confidence and Prediction Intervals Outline CIs Based on the T-Distribution Prediction Intervals Introduction Confidence Intervals for a Normal Mean CIs for the Slope of a Regression Line CIs for the Regression Line Three Specific Examples 1. If X 1 , X 2 , . . . , X n are iid N ( μ, σ 2 ), then X- μ S / √ n ∼ t n- 1 2. If ( X i , Y i ), i = 1 , . . . , n , are iid satisfying the normal simple linear regression model, i.e. Y i | X i ∼ N ( a 1 + β 1 X i , σ 2 ), then Michael Akritas Lecture 24 Chapter 8: Confidence and Prediction Intervals Outline CIs Based on the T-Distribution Prediction Intervals Introduction Confidence Intervals for a Normal Mean CIs for the Slope of a Regression Line...
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b.lect24 - Outline CIs Based on the T-Distribution...

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