Chapter 7 Hypothesis Tests and Confidence Intervals in
- Slides: 44
Chapter 7 Hypothesis Tests and Confidence Intervals in Multiple Regression
Outline 2
Hypothesis Tests and Confidence Intervals for a Single Coefficient in Multiple Regression (SW Section 7. 1) 3
Example: The California class size data 4
Standard errors in multiple regression in STATA 5
Tests of Joint Hypotheses (SW Section 7. 2) 6
Tests of joint hypotheses, ctd. 7
Why can’t we just test the coefficients one at a time? 8
Suppose t 1 and t 2 are independent (for this calculation). 9
10
The F-statistic 11
The F-statistic testing 1 and 2: 12
Large-sample distribution of the F-statistic 13
14
Computing the p-value using the F-statistic: 15
F-test example, California class size data: 16
17
The “restricted” and “unrestricted” regressions 18
Simple formula for the homoskedasticity-only F-statistic: 19
Example: 20
The homoskedasticity-only F-statistic – summary 21
Digression: The F distribution 22
The Fq, n–k– 1 distribution: 23
Another digression: A little history of statistics… 24
A little history of statistics, ctd… 25
Summary: the homoskedasticity-only Fstatistic and the F distribution 26
Summary: testing joint hypotheses 27
Testing Single Restrictions on Multiple Coefficients (SW Section 7. 3) 28
Testing single restrictions on multiple coefficients, ctd. 29
Method 1: Rearrange (“transform”) the regression 30
Rearrange the regression, ctd. 31
Method 2: Perform the test directly 32
Confidence Sets for Multiple Coefficients (SW Section 7. 4) 33
Joint confidence sets ctd. 34
35
Confidence set based on inverting the F-statistic 36
An example of a multiple regression analysis – and how to decide which variables to include in a regression… 37
A general approach to variable selection and “model specification” 38
Digression about measures of fit… 39
Back to the test score application: 40
More California data… 41
Digression on presentation of regression results 42
43
Summary: Multiple Regression 44
- Chapter 20 more about tests and intervals
- Confident
- Critical value for 90 confidence interval
- Chapter 18 confidence intervals for proportions
- Chapter 19 confidence intervals for proportions
- Importance of confidence interval
- How to interpret confidence intervals example
- Reporting confidence intervals
- What is the interpretation of a 96 confidence level
- Confidence interval excel
- Estimating a population proportion
- How to find confidence level on ti 84
- Confidence intervals minitab
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- Confidence interval vs confidence level
- Duality of confidence interval and hypothesis test
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- What is an alternative hypothesis
- Examples of null hypothesis
- Weakness of protoplanet hypothesis
- Developing null and alternative hypothesis
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- Increasing intervals
- Increasing intervals
- How to make histogram with unequal class widths
- Increasing and decreasing intervals
- Error interval questions
- Characteristics of parabola
- Chapter 2 building confidence
- Chapter 8 estimating with confidence
- Suppose your class is investigating the weights of snickers
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- Error intervals
- What is an error interval
- Pr interval normal
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- Statistical intervals for a single sample
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