1. 1 9. Logistic Regression ECON 251 Research Methods

2. 2 Logistic regression  So far, our dependent variable was a continuous variable. The question is how would we analyze data when the dependent variable is a dichotomous variable taking a value of either 0 or 1.  For instance, a person can vote for a democratic party or some other party in an election. If a person votes democratic, we can code this as y = 1 and if it does not, we code this as y = 0.  Then, we can estimate the probability that a person will vote for democrats given a particular set of valued for the chosen independent variables  OLS regression is inappropriate in this case

3. 3 Logistic regression  OLS regression  logistic regression estimating probabilities instead of coefficients  logit regression

4. 4 Example – Buying a car  What is the probability that a person will purchase a car given the level of income?  Data file: Buying a car.xls  CAR: 1 if car was purchased and 0 otherwise  INCOME: person’s income in $1000  run OLS regression:  and you get:

5. 5 Example – Buying a car  What is the probability that a person will buy a car if her income is 40,000?  What is the probability that a person will buy a car if her income is 15,000?  Does this make sense? What is the problem? How do we fix this?

6. 6 Example – Buying a car  open Minitab  copy data from Excel  go to Stat  Regression  Binary Logistic Regression  click into the Response box, click on CAR, and click Select  click into the “Continuous predictor” box, click on INCOME, and click Select  hit OK

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8. 8 Example – Buying a car Income positively effects the probability of buying a car, but we cannot tell by how much. Need to estimate probabilities. a significant variable the model is good

9. 9 Example – Buying a car  If we want to estimate the probability that a person with income of $40,000 will buy a car 1. estimate 2. calculate

10. 10 Example – Buying a car  If income is $15,000, the probability that the person will buy a car is: 1. estimate 2. calculate

11. 11 Example – Buying a car  We can compute probabilities for all levels of income. This is presented in the logit regression graph:

12. 12 Application: Voting  Suppose that you are working for the Republican party and you are trying to see how voters’ characteristics will impact who will vote for the Republican party in the elections.  You carry out a survey and collect information on 30 voters and you asked them whether they will vote for the Republican party  You believe that income, age and gender might have an impact on voting and you collect this information from each survey respondent.

13. 13 Application: Voting  Variables: REPUBLICAN : 1 if they will vote Republican INCOME : individual’s income in $1,000 AGE MALE : 1 if the respondent is male and 0 if female  Data: Voting.xls  Which variable is our dependent variable?  Which regression model do we have to perform?

14. Application: Voting 14 Are all the individual variables significant?

15. Application: Voting 15 How do we interpret the coefficients? INCOME: positive coefficient  the estimated probability of a person voting for the Republican party increases with income AGE: positive coefficient  the estimated probability of a person voting for the Republican party increases with age

16. 16 Application: Voting  Estimating probabilities: what is the probability that a 23 year old person with an income of $40,000 will vote republican?

17. 17 Application: Voting  How about if the income is $60,00 instead of $40,000?