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OLS Review
Review of Multivariate OLS
– Topics
– Data Analysis
– Questions
Exam Particulars
Lecture 11
2009
Slide #1
Regression Diagnostics Example
Problem Setup
“Bid” inserted into question
Suppose that a national advisory vote or
referendum was held today, and you
could vote to advise the federal
government on whether to create a
National Energy Research and
Development Fund, but the fund
would cost your household <insert
randomly selected cost> per year in
increased energy prices. Where would
you place yourself on a scale from
zero to 100, where zero means you
are absolutely certain that you would
vote against the creation of the Fund
and 100 means you are absolutely
certain that you would vote for it?
bid |
Freq. Percent
------------+-------------------------6|
164
7.13
12 |
162
7.05
24 |
132
5.74
48 |
156
6.79
72 |
155
6.74
96 |
165
7.18
120 |
152
6.61
240 |
151
6.57
360 |
150
6.52
480 |
146
6.35
600 |
167
7.26
960 |
142
6.18
1200 |
134
5.83
1800 |
157
6.83
2400 |
166
7.22
------------+-------------------------Total |
2,299
100.00
Lecture 11
2009
Slide #2
Model IV’s
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Bid (cost to responding household)
Ideology
Perceived GCC risk
Political Ideology
Income
Age
Gender
Experimental treatment: nuclear option
Lecture 11
2009
Slide #3
Review of Multivariate OLS
• Matrix algebra
• E.g., transpose, identity, addition & multiplication
– Regression in Matrix Notation
– Understanding the Matrix Calculation
• When X matrix has no unique X-1
• Partial Effects
– Calculating partial effects; interpretation (!)
• Variable selection and model building
– Risks in model building
Lecture 11
2009
Slide #4
More review...
• T-tests, hypotheses, etc.
• F-tests & nested models
• The evils of stepwise regression
– Why is it a problem?
• Critical OLS Assumptions
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Fixed X’s
Errors cancel out
Constant variance of the errors
Errors are uncorrelated
Errors are normally distributed
• Correctly specified models:
– Linear, correct X’s included and omitted
• Estimating dummy and interactive terms
Lecture 11
2009
Slide #5
Summary of Assumption Failures
and their Implications
Problem Biased b Biased SE
Invalid t/F
Hi Var
Non-linear
Yes
Yes
Yes
---
Omit relev. X
Yes
Yes
Yes
---
Irrel X
No
No
No
Yes
X meas. Error
Yes
Yes
Yes
---
Heterosced.
No
Yes
Yes
Yes
Autocorr.
No
Yes
Yes
Yes
X corr. error
Yes
Yes
Yes
---
Non-normal err.
No
No
Yes
Yes
Multicollinearity
No
No
No
Yes
Lecture 11
2009
Slide #6
Testing for OLS Failures
• Can’t check some assumptions
– which ones?
• Can check for:
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Linearity
Whether an X should be included
Homoscedasticity
Autocorrelation
Non-normality
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Univariate and bivariate analyses
Plots
Tolerances
Influence analyses
• Method
Lecture 11
2009
Slide #7
Autocorrelation
• Types of autocorrelation
– First order
– N-order
• Seasonality, etc
• Identifying: DW statistics
• Methods of correction
– Calculating Rho
– AR1
– ARIMA
Lecture 11
2009
Slide #8
Exam (Quiz) #2
• Posted by noon Wednesday, April 15th
• Will be due 5pm Monday April 20th
• E-mail with subject line: “Methods Exam 2”
• Questions?
• Coming up: Chapter 11: Logit Regression Analysis
Lecture 11
2009
Slide #9