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Table of Contents

 


 

Software Output

Raw survey data

 

Evaluating the affect of age, education, sex, and race on whether or not a person voted in the 1992 presidential election.

 

 

------------------------ Logistic Regression -------------------

 

Dependent Y: VOTE92

 

Cases with Y=0:   417      28.86%      No, did not vote

Cases with Y=1:  1028      71.14%      Yes, voted

Total Cases:     1445

 

Explanatory Model

 

VOTE92 = Constant + AGE + EDUC + FEMALE + WHITE + e

 

 

Model Fit Statistics

 

Initial -2 Log Likelihood     1736.533

Model -2 Log Likelihood       1544.154    Iteration (4)

Cox & Snell Rsq                  0.125 (1)

McFadden Rsq                     0.111 (2)

Model Chi-Square               192.380    df 4     p< 0.0000 (3)

 

 

 

Interpretation

(1) This ranges from 0 to less than 1 and indicates the explanatory value of the model.  The closer the value is to 1 the greater the explanatory value.  Analogous to R2 in OLS regression.

(2)  Indicates explanatory value of the model.  Ranges from 0 to 1 and adjusts for the number of independent variables.  Analogous to Adjusted R2 in OLS regression.  In this model, the explanatory value is relatively low.

(3)  Tests the combined significance of the model in explaining the dependent (response) variable.  The significance test is based on the Chi-Square sampling distribution.  Analogous to the F-test in OLS regression. The independent variables in this model have a statistically significant combined effect on voting behavior.

 


Coefficients

 

 Variable  b Coeff.        SE       Wald        p <         OR

----------------------------------------------------------------

 Constant  -4.1620     0.4184    98.9755     0.0000

      AGE   0.0335 (4) 0.0040    69.1386 (5) 0.0000 (6) 1.0340 (7)

     EDUC   0.2809     0.0244   132.4730     0.0000     1.3243

   FEMALE  -0.1249     0.1269     0.9686     0.3250     0.8826

    WHITE   0.1000     0.1671     0.3581     0.5495     1.1052

----------------------------------------------------------------

 

Estimated Model

 

VOTE92 = -4.1620 + .0335(AGE) + .2809(EDUC) + -.1249(FEMALE)

                 + .1000(WHITE)

 

Classification Table (.50 cutpoint)

 

 

                    Predicted Y

Observed Y          0          1       % Correct

             +-----------+-----------+

         0   |       103 |       314 |    24.70 (8)

             +-----------+-----------+

         1   |        64 |       964 |    93.77 (9)

             +-----------+-----------+----------

                                Total     73.84 (10)

 

 

Interpretation                                           

(4)  A one unit increase in age (1 year) results in an average increase of .0335 in the log odds of vote equaling 1 (voted in election).

(5)  The test statistic for the null hypothesis that the b coefficient is equal to 0 (no effect).  It is calculated by (B/SE)2. 

(6)  Based on the Chi-Square sampling distribution, there is a statistically significant relationship between age and voting behavior.  The probability that one will vote increases with age, holding education, sex, and race constant.

(7)  OR=Odds Ratio.  The odds of a change in the dependent variable (vote) given a one unit change in age is 1.03.  Note:  if the OR is >1, odds increase; if OR <1, odds decrease; if OR =1, odds are unchanged by this variable.  In this example, the odds of voting increases with a one unit increase in age.

(8)  Of those who did not vote, the model correctly predicted non-voting in 24.7% of the non-voters included in the sample data.

(9)  Of those who did vote, the model correctly predicted voting in 93.8% of the voters included in the sample data.

(10)      Of those who did or did not vote, the model correctly predicted 73.8% of the voting decisions.


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