IEOR 165 Lecture 13 June 23 2009

# IEOR 165 Lecture 13 - Chapter 9 Regression Sample data x1.xn corresponding y1.yn We use the most basic linear regression Y=A Bx Objective we want

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Chapter 9 Regression Sample data x1…xn corresponding y1…yn We use the most basic linear regression: = + Y A Bx Objective: we want to estimate A and B from sample data Process: Use Least Square Estimator - Square Error: = - - SSR Y A Bx2 - We want to find A and B that minimizes SSR = = - * * = - B i 1nxiYi n xbar ybari 1nxi2 nxbar2 = - * A Ybar B xbar Substitute back into SSr: = = - = - - = - * * = - SSR i 1nxi2 nxbar2i 1nYi2 nYbar2 i 1nxiYi n xbar ybar2i 1nxi2 nxbar2 - - ~ , Yi A Bxi2 N0 σ2 : ~ - Therefore SSRσ2 χn 22 After doing this test, we can do either Hypothesis Testing or Confidence Interval: - Confidence Interval: = + Y α βx a. : = : ≠ H0 B 0 H1 B 0 This tests whether x and y are independent because if B=0, then x = 0. b. - % . Find 1 α100 CI for β ~ , ~ - B Nβ σ2Sxx whereσ2Sxx χn 22 = = - Sxx i 1nxi2 nxbar2 = tn zχn2n c. ~ - - - = - - ~ - SSRσ2 χn 22B βσ2SxxSSRσ2n 2 B β1SxxSSR1n 2 tn 2 - , - ≤ - * - ≤ , - = - P tα2 n 2 SxxSSRn 2 B β tα2 n 2 1 α d. Confidence interval for Beta:

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## This note was uploaded on 07/22/2009 for the course IEOR 165 taught by Professor Shanthikumar during the Summer '08 term at University of California, Berkeley.

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IEOR 165 Lecture 13 - Chapter 9 Regression Sample data x1.xn corresponding y1.yn We use the most basic linear regression Y=A Bx Objective we want

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