Lecture 6: Logistic Regression (Alt 3)

Question 1

What type of outcome variable does linear regression model?

Answer 1

A continuous outcome (e.g., liking a person).

Question 2

What assumption underlies the equation used in linear regression?

Answer 2

A linear relationship that incorporates an intercept and slope coefficient.

Question 3

What are residuals in the context of linear regression?

Answer 3

Deviations from the predicted line, reflecting model imperfection.

Question 4

Why is logistic regression introduced as an alternative to linear regression?

Answer 4

Because linear regression fails with dichotomous outcomes.

Question 5

What kind of outcome variable necessitates the use of logistic regression?

Answer 5

A categorical outcome (e.g., labeling someone as a boyfriend/girlfriend).

Question 6

What are two key differences between logistic and linear regression?

Answer 6

Predictors are not assumed to be normally distributed, and logistic regression can deal with non-linear relationships among variables.

Question 7

What function does logistic regression use to model probabilities?

Answer 7

A logistic function that transforms continuous predictions into a 0–1 probability range.

Question 8

What does it mean for outcome categories in logistic regression to be mutually exclusive?

Answer 8

Each observation fits into only one category.

Question 9

What does it mean for outcome categories in logistic regression to be exhaustive?

Answer 9

All possible outcome categories are represented.

Question 10

What happens if outcomes are not mutually exclusive or exhaustive in logistic regression?

Answer 10

The probabilities won’t sum to 1, the model cannot correctly classify or predict the outcome for each case, and the likelihood function will break down.

Question 11

What is the shape of the curve produced by the logistic function?

Answer 11

S-shaped (sigmoidal).

Question 12

What does the logistic regression equation do to convert linear predictions into probabilities?

Answer 12

Exponentiates a linear combination of predictors to yield probabilities bounded between 0 and 1.

Question 13

What do odds express in logistic regression?

Answer 13

The ratio of event likelihood to non-event likelihood.

Question 14

What mathematical scale is used for logistic regression coefficients?

Answer 14

Log odds (the natural logarithm of odds).

Question 15

What does each unit increase in a predictor change in terms of log odds?

Answer 15

It changes the log odds by the coefficient B.

Question 16

What does exponentiating the coefficient B yield in logistic regression?

Answer 16

The odds ratio.

Question 17

How do odds differ from probabilities in logistic regression?

Answer 17

Odds and probabilities have a non-linear relationship.

Question 18

Why is the change in probability not constant across the logistic curve?

Answer 18

Because changes in probability are largest near 0.5 and smaller as the predicted probability approaches 0 or 1, reflecting the flattening of the logistic curve at its extremes.

Question 19

In logistic regression, how is a one-unit increase in the predictor variable reflected in odds?

Answer 19

As a consistent multiplicative change in odds determined by exp⁡(b).

Question 20

What are the two ways to interpret logistic regression coefficients?

Answer 20

As log odds (the raw b coefficients) and as odds ratios (the exponentiated b, or exp⁡(b)).

Question 21

What is the null hypothesis (H₀) when interpreting logistic regression coefficients?

Answer 21

That the predictor has no effect on the outcome.

Question 22

What does b=0 imply in terms of log odds?

Answer 22

There is no change in log odds as the predictor increases.

Question 23

What does exp⁡(b)=1 imply in terms of odds ratios?

Answer 23

There is no multiplicative change in odds with each unit increase in the predictor.

Question 24

What test evaluates whether a logistic regression coefficient b is significantly different from 0?

Answer 24

The Wald Test.

Question 25

What does a significant Wald Test result indicate?

Answer 25

That the predictor has statistical utility.

Question 26

What does a 95% confidence interval (CI) for exp⁡(b) assess?

Answer 26

The odds ratio.

Question 27

What does it mean if the 95% CI for exp⁡(b) does not include 1?

Answer 27

The predictor significantly affects the odds.

Question 28

What does it mean if the 95% CI for exp⁡(b) includes 1?

Answer 28

The odds are not significantly changed by the predictor.

Question 29

What pseudo-R² statistics are used to assess model fit in logistic regression?

Answer 29

Cox & Snell (conservative) and Nagelkerke (liberal).

Question 30

What statistic evaluates classification performance and model fit in logistic regression?

Answer 30

The Hosmer-Lemeshow test.

Question 31

What does a significant result on the Hosmer-Lemeshow test imply?

Answer 31

Poor fit.

Question 32

What test can assess whether all predictors collectively improve prediction beyond chance?

Answer 32

An omnibus test.

Question 33

What is the Direct (Enter) Method in logistic regression?

Answer 33

All predictors are entered into the model at the same time.

Question 34

When is the Direct Method not suitable?

Answer 34

When testing hypotheses about the order or theoretical importance of variables.

Question 35

What is Sequential (Hierarchical) Logistic Regression used for?

Answer 35

To assess whether adding predictors improves model fit beyond those already included.

Question 36

What guides the order of predictor entry in Sequential Logistic Regression?

Answer 36

The order is determined by the researcher.

Question 37

What is the purpose of Stepwise Logistic Regression?

Answer 37

To identify promising predictors based on statistical criteria.

Question 38

What are the two main types of stepwise logistic regression?

Answer 38

Forward Stepwise and Backward Stepwise.

Question 39

What is the procedure in Forward Stepwise regression?

Answer 39

Start with no predictors and add them one by one based on their contribution.

Question 40

What is the procedure in Backward Stepwise regression?

Answer 40

Start with all predictors and remove them one by one based on least contribution.

Question 41

What is assessed at each step in stepwise regression methods?

Answer 41

Whether adding or removing a predictor significantly improves or reduces model fit.

Question 42

What is multinomial logistic regression used for?

Answer 42

Outcomes with more than two categories.

Question 43

How does SPSS implement multinomial logistic regression?

Answer 43

By decomposing multicategory outcomes into binary comparisons using dummy coding.