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DON’T TAKE NOTES! MUCH OF THE FOLLOWING IS IN THE COURSEPACK!
Just follow the discussion and try to interpret the statistical results that follow.
Variable Association - 1
We often want to see the degree to which two variables are associated with each other. For example, is there a relationship between a person’s level of education and the likelihood t they smoke? Yes! The association is negative: the more educated a person is the less likely they are to smoke. Had the association been positive it would have meant the more educated a person the more likely they are to smoke.
Variable Association - 2
We frequently use what is termed a “measure of association” to assess the degree to which two variables are associated. Typically, such measures range between -1.0 (strongest negative association) and +1.0 (strongest positive association). A score of “0” means there is no association between the variables.
Variable Association - 3
If variables are measured with a low degree of measurement error:
0 to plus/minus .25 = weak association
.26 to plus/minus .49 = moderate assoc.
.50 to plus/minus .69 = strong association
.70 to plus/minus 1.0 = very strong assoc.
Social Science Models and Regression
What must we have in order to have a “social science model”?
Why do we typically use regression rather than measures of association?
Examining Variable Relationships - 1
Tax Conservatism
1 2 3
1 12.3% 76.2% 95.5%
2 40.4% 23.8% 4.5%
3 47.3% 0.0% 0.0%
What does the above data tell us?
Examining Variable Relationships - 2
Association between Tax and Conservatism
Pearson’s Correlation: -.69
NOTE: if percentages rather than 1-3 scale are used Pearson’s Correlation is -.80. Not using all the information reduces the association.
Why Regression? - 1
Measures of Association (e.g., correlation) only tell us the strength of the relationship between X and Y, NOT the MAGNITUDE of the relationship. Regression tells us the MAGNITUDE of the relationship (i.e., how MUCH the dependent variable changes for a specified amount of change in the independent variable).
Why Regression? - 2
California Election 2010 - 1
Correlation of the Percent of the Countywide Vote for Barbara Boxer and Jerry Brown in 2010 with the Percentage of those 25, and Older, Who Have at Least a Bachelor’s Degree in 2000 and Median Household Income in 2008.
correlate boxer10 brown10 coll00 medinc08
(obs=58)
| boxer10 brown10 coll00 medinc08
-------------+------------------------------------
boxer10 | 1.0000
brown10 | 0.9788 1.0000
coll00 | 0.7422 0.6885 1.0000
medinc08 | 0.6022 0.5401 0.8321 1.0000
Graph of .97 Correlation of Brown10 and Boxer10
2040
6080
20 40 60 80brown10
Fitted values boxer10
Graph of .74 Correlation of Coll00 and Boxer10
2040
6080
10 20 30 40 50coll00
Fitted values boxer10
Graph of -.58 Correlation of %White in 2005 and Boxer10
2040
6080
60 70 80 90 100white05
Fitted values boxer10
Graph of -.23 Correlation of %Senior in 2005 and Boxer10
2040
6080
8 10 12 14 16 18senior05
Fitted values boxer10
California Election 2010 - 1
Given the correlations below, what should you expect
in the regression table on the next slide where the dependent variable is “boxer 10” (percent
of county vote for Boxer in 2010)?
correlate boxer10 brown10 coll00 medinc08
(obs=58)
| boxer10 brown10 coll00 medinc08
-------------+------------------------------------
boxer10 | 1.0000
brown10 | 0.9788 1.0000
coll00 | 0.7422 0.6885 1.0000
medinc08 | 0.6022 0.5401 0.8321 1.0000
Probit – State Adoption of TRAP Abortion Laws
DON’T WRITE THE NUMBERS!
Ind. Var. Coefficient St. Error
Dem. Control -.555 .260
State Ideology .003 .010
% Catholic .009 .010
% Fundamental .029 .009
Public Opinion -.825 .465
about Abortion
Probit – State Adoption of an Income Tax Over 1916-1937
DON’T WRITE THE NUMBERS!
Ind. Var. Coefficient St. Error
Liberal Control .788 .318
Real Per Capita -1.802 .892
Income
Governor -.925 .301
Election Year
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