ECO375H_Slides_5

# ECO375H_Slides_5 - Lecture 5 Multiple Regression Inference...

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Lecture 5 Multiple Regression: Inference Junichi Suzuki University of Toronto October 8th, 2009

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Announcement I 2nd problem set is due October 16th. I Start early! I Sacha is going to hold an o¢ ce hour I Place: Max Gluskin House GE313 I Time: October 14th (Wed): 10:30am-12:30pm I Information Session on Applying to Graduate School I October 15th (Th) 4:10-5:30pm I SS2118
I Goal: Wrap up Chapter 3 and get into Chapter 4. I Chapter 3 I Multicollinearity I Estimating the variance and standard error I Gauss-Markov Theorem I Chapter 4: Inference I Testing hypothesis on an individual parameter (e.g., β 1 = 0) I Con±dence interval

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Chapter 4 Multiple Regression Analysis: Inference
Motivation I Want to examine whether data are consistent with particular hypotheses I e.g., 1: Should I include a variable as a regressor? I Want to know if data support β 6 = 0 I e.g., 2: Does data suggest constant returns to scale? I Want to test if data support β 1 + β 2 = 1 I Need to conduct hypothesis tests

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Quick Review of Hypothesis Test: Big Picture I Consider two mutually exclusive hypotheses: I Null hypothesis (e.g., H 0 : β 1 = 0) I Alternative hypothesis (e.g., H 1 : β 1 6 = 0) I Hypothesis test examines whether data are considerably against the null hypothesis ( H 0 ) I alternative I Two possible outcomes I Reject the null I Cannot reject the null (not so strong evidence for the null)
Quick Review of Hypothesis Test: Errors I Tests based on a sample data are always subject to errors I Type I error: Does reject H 0 when one should not (i.e., β 1 = 0) I Type II error: Does not reject H 0 when one should (i.e., β 1 6 = 0) I Making Type I error is more serious I Trade-o/ between these two types of errors I Can and should design the hypothesis test by taking into account this trade-o/ I I Power of the test: 1 Chance of making a Type II error

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Quick Review of Hypothesis Test: Implementation I Obtain ˆ β 1 , an estimate of β 1 from the given sample and convert it to a test statistic (e.g., t-value) I Characterize the distribution of the test statistic under H
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ECO375H_Slides_5 - Lecture 5 Multiple Regression Inference...

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