Lecture 6: Logistic Regression (original) Flashcards
(32 cards)
What type of outcome does linear regression model?
Continuous outcome
What does a slope coefficient represent in linear regression?
a slope coefficient represents the expected change in the dependent variable (Y) for a one-unit increase in the independent variable (X), assuming all other variables in the model are held constant.
It captures the direction and strength of the relationship between the predictor and outcome.
What are residuals in linear regression?
Errors between predicted and actual values
What does linear regression assume about the predictor-outcome relationship?
That it is linear
What type of outcome does logistic regression model?
Categorical outcome
Why can’t linear regression be used for binary outcomes?
- Predicted values aren’t bounded between 0 and 1
- Linear regression can predict values below 0 or above 1, which makes no sense for probabilities.
- Non-constant error variance (heteroskedasticity)
- Binary outcomes lead to error terms that are not normally distributed and have non-constant variance, violating regression assumptions.
- Non-linearity of the probability relationship
- The relationship between the predictor and the probability of the outcome is typically non-linear, which linear regression cannot model properly.
For these reasons, logistic regression is used instead. It models the log odds of the outcome and ensures predictions are valid probabilities (between 0 and 1).
What function does logistic regression use to constrain predictions between 0 and 1?
Logistic function
What is the shape of the curve produced by the logistic function?
S-shaped (sigmoidal)
What do odds represent in logistic regression?
The ratio of event to non-event likelihood
What are log odds?
The natural log of odds
What does the coefficient B indicate in logistic regression?
Change in log odds per unit increase in the predictor
What does exp(B) represent in logistic regression?
Odds ratio
How are probabilities and odds related?
Non-linearly
What happens to probability as odds increase near 0 or 1?
It increases more slowly
What is the effect of odds ratios near the extremes of probability?
Diminishing effect on probability
What test checks if a coefficient differs from zero in logistic regression?
Wald test
What does a significant Wald test result indicate?
The predictor significantly affects the outcome
What does a confidence interval around an odds ratio show?
Reliability of the estimate
What are Cox & Snell and Nagelkerke examples of?
Pseudo-R² statistics
What does classification accuracy measure?
Correctness of predicted outcomes
What does a significant Hosmer-Lemeshow test suggest?
Poor model fit
What does the omnibus test assess?
Whether all predictors improve prediction
What method enters all predictors at once in logistic regression?
Direct method
What method adds predictors in blocks for hypothesis testing?
Sequential (hierarchical) method
