11/19 201 LEC

Focus on logistic regression and its differences from ordinary least squares (OLS) regression.
Summary of assignments and expectations.

Chapter 11:
- Focus on correlation and measures of association.
- Introduction to binary regression with functions and plotting.
- Emphasis on interpretation of binary regression results.
Chapter 12:
- Continues ordinary least squares regression.
- Introduction to multiple regression (multiple independent variables).
- Tasks include running the regression, generating predictions, and plotting the model.
- Creation of interaction terms and visualization of relationships among categorical and interval independent variables.

Complete all practice exercises from chapters 11 and 12 before attempting survey practice.
First survey practice divided into two parts: part one focuses on Chi Square and regression, due on Friday.
Instructor available for online office hours during travel week (Monday).
Upcoming: Survey practice two focuses on multiple regression and logistic regression.

Availability: All materials for final projects available in the survey folder (including rubric and examples of prior projects).
Continue homework for chapter 14 focused on logistic analysis, available for work during Thanksgiving break.
Instructor will cover additional topics and expectations for final project after the break.

Logistic regression is used for binary dependent variables.
Key difference from OLS regression:
- Logistic regression does not assume a linear relationship for changes in the dependent variable.
Importance of understanding logistic regression’s internal workings for application.

Commonly used in fields such as political science to answer binary questions:
- Why do some individuals vote while others do not?
- Why do some democracies exist while some are autocracies?

Definition of Odds: A way to express probabilities, calculated as:
- $Odds = \frac{Probability}{1 - Probability}$
Conversion between odds and probabilities:
- From probability to odds: If probability = 0.8, then odds = 4 to 1.
- From odds to probability: If odds = 4 to 1, then probability = 0.8.

Essential for interpreting coefficients in logistic regression.
Key Points:
- Probabilities < 0.5 yield negative log odds.
- Probabilities = 0.5 yield log odds = 0.
- Probabilities > 0.5 yield positive log odds.
The switchover point of log odds occurs at a probability of 0.5 where outcomes transition from less likely to more likely.

Unlike OLS, logistic regression represents changes in probability in a non-linear manner, which causes differences in interpretation:
- Linear relationship seen with OLS doesn’t apply to logistic regression; behavior changes based on the level of the independent variable.

Regression Output Includes: Intercept, coefficients, standard error, z-statistic, p-value.
To interpret coefficients:
- Exponentiate the coefficient to obtain odds.
- From odds, calculate probabilities for substantive interpretation.
Example of interpreting coefficients:
- If coefficient for partisan preference towards GOP = 0.07, the exponentiation gives odds of 1.07, indicating a 7% increase in likelihood of voting for Trump.

Similar methods to OLS for testing significance:
- Hypothesis testing with t-statistic, p-value, and confidence intervals.
Steps for interpretation:
- Standard errors can be doubled to determine if a confidence interval crosses zero, confirming if a coefficient is statistically significant.

Logistic regression coefficients report logged odds, which require transformation for interpretation.
Overall association and statistical significance are interpreted similarly to OLS.
Familiarity with transformations is critical for accurate reporting and interpretation of effects in logistic regression.

Emphasis on logistic regression as a continuation of regression study.
Importance of engagement over the break with chapter 14 materials to prepare for practical applications and final project.
Instructor availability during travel week for student support and clarification of topics.