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1 9. Logistic Regression ECON 251 Research Methods

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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

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

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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:

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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?

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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 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

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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

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

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

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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.

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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?

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Application: Voting 14 Are all the individual variables significant?

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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

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

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

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Multiple Regression David A. Kenny January 12, 2014.

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