Master Logistic Regression: A Guide for Psychology Students

Question 1

What is the purpose of the logit transformation in logistic regression?

Accepted Answer

To ensure that the predicted probabilities fall between 0 and 1.

Answer

To convert the dependent variable to a continuous scale.

Answer

To make the relationship between the independent variables and the dependent variable linear.

Answer

To improve the interpretability of the model.

Question 2

What is the purpose of a Hosmer-Lemeshow test in logistic regression?

Accepted Answer

To test the calibration of the model.

Answer

To identify influential observations.

Answer

To compare nested models.

Answer

To determine the significance of individual coefficients.

Question 3

What is the role of regularization in logistic regression?

Accepted Answer

To reduce overfitting and improve model performance.

Answer

To improve model interpretability.

Answer

To handle missing data.

Answer

To increase model accuracy.

Question 4

What is a fundamental assumption of logistic regression?

Accepted Answer

The log-odds of the dependent variable are linearly related to the independent variables.

Answer

The dependent variable is continuous.

Answer

The independent variables are normally distributed.

Answer

The residuals are homoscedastic.

Question 5

Which assumption is violated in logistic regression when there is a curvilinear relationship between the independent and dependent variables?

Accepted Answer

Linear relationship between independent and dependent variables

Answer

No multicollinearity among independent variables

Answer

Independence of observations

Answer

Normal distribution of residuals

Question 6

Which measure is most commonly used to evaluate the overall fit of a logistic regression model?

Accepted Answer

Likelihood ratio chi-square

Answer

R-squared

Answer

Adjusted R-squared

Answer

Akaike Information Criterion (AIC)

Question 7

How does the number of independent variables in a logistic regression model affect its complexity?

Accepted Answer

Increases the likelihood of multicollinearity

Answer

Decreases the likelihood of overfitting

Answer

Reduces the variance of the coefficient estimates

Answer

Improves the predictive accuracy of the model

Question 8

In a logistic regression model, what information does the coefficient for an independent variable provide?

Accepted Answer

The change in the log odds of the outcome for a one-unit increase in that variable, holding all other variables constant

Answer

The probability of the outcome for a one-unit increase in that variable

Answer

The proportion of variance in the outcome explained by that variable

Answer

The expected value of the outcome for a one-unit increase in that variable

Question 9

What is the primary purpose of using logistic regression in statistical analysis?

Accepted Answer

To predict the likelihood of an event occurring based on a set of predictor variables

Answer

To determine the causal relationship between independent and dependent variables

Answer

To identify the most important predictors of an outcome

Answer

To test the significance of individual coefficients

Question 10

Which type of research question is best suited for analysis using logistic regression?

Accepted Answer

Can certain factors predict the likelihood of developing a disease?

Answer

What is the average age of individuals in a population?

Answer

How many times per week does a person engage in physical activity?

Answer

Is there a relationship between height and weight?

Question 11

What is the primary function of logistic regression in predicting binary or multinomial outcomes?

Accepted Answer

Estimating the log odds of an event occurring based on independent variables

Answer

Categorizing observations into positive or negative outcomes using a binary classifier

Answer

Measuring the strength of the relationship between independent and dependent variables

Answer

Determining that an event cannot occur

Question 12

What is the main purpose of logistic regression?

Accepted Answer

To predict the probability of an event occurring

Answer

To estimate the mean of a distribution

Answer

To test the significance of a relationship

Question 13

Which of the following is a key difference between logistic regression and linear regression?

Accepted Answer

Linear regression uses a linear function, while logistic regression uses a non-linear function.

Answer

Logistic regression predicts continuous outcomes, while linear regression predicts binary outcomes.

Answer

Logistic regression is more sensitive to outliers than linear regression.

Question 14

What is the role of the intercept in a logistic regression model?

Accepted Answer

To predict the probability of the outcome occurring when all independent variables are equal to 0

Answer

To estimate the effect of each independent variable on the outcome

Answer

To test the significance of the model

Question 15

What is the formula for the odds ratio in a logistic regression model?

Accepted Answer

Exp(coefficient)

Answer

1 / Exp(coefficient)

Question 16

What does an odds ratio greater than 1 indicate in logistic regression?

Accepted Answer

The odds of the dependent variable occurring increase with each unit increase in the independent variable.

Answer

The odds of the dependent variable occurring decrease with each unit increase in the independent variable.

Answer

The relationship between the independent variable and the dependent variable is negative.

Answer

The independent variable has no effect on the dependent variable.

Question 17

What is the role of the intercept in a logistic regression model?

Accepted Answer

It represents the log odds of the dependent variable occurring when all independent variables are equal to 0.

Answer

It represents the slope of the regression line.

Answer

It measures the strength of the relationship between the independent variables and the dependent variable.

Answer

It is not present in logistic regression models.

Question 18

What is the key difference between binary and multinomial logistic regression?

Accepted Answer

Binary logistic regression predicts a binary outcome, while multinomial logistic regression predicts a categorical outcome with more than two categories.

Answer

Binary logistic regression uses a linear function, while multinomial logistic regression uses a non-linear function.

Answer

Binary logistic regression is more computationally complex than multinomial logistic regression.

Answer

There is no difference between binary and multinomial logistic regression.

Question 19

Which of the following is NOT a type of regularization technique used in logistic regression?

Accepted Answer

Support Vector Machines

Answer

L1 regularization (Lasso)

Answer

L2 regularization (Ridge)

Answer

Elastic Net regularization

Question 20

Which assumption of logistic regression ensures that the relationship between the independent variables and the log odds of the outcome is linear?

Accepted Answer

Linearity

Answer

Independent observations

Answer

Binary dependent variable

Answer

Normal distribution of residuals

Question 21

In a logistic regression model, the linear predictor is used to calculate which of the following?

Accepted Answer

The log odds of the outcome being 1

Answer

The odds of the outcome being 1

Answer

The probability of the outcome being 1

Answer

The variance of the outcome

Question 22

How do you interpret the numerical value of the odds ratio in a logistic regression model?

Accepted Answer

It represents the increase in the odds of the outcome for each unit increase in the corresponding independent variable

Answer

It represents the decrease in the odds of the outcome for each unit increase in the corresponding independent variable

Answer

It represents the difference in the odds of the outcome between two groups

Answer

It represents the probability of the outcome for each unit increase in the corresponding independent variable

Question 23

What is a key advantage of using multinomial logistic regression over binary logistic regression?

Accepted Answer

It can predict outcomes with more than two categories.

Answer

It needs fewer independent variables.

Answer

It assumes a linear relationship between the independent variables and the outcome.

Answer

It is easier to interpret than binary logistic regression.

Question 24

Primary purpose of the logit transformation in logistic regression is to:

Accepted Answer

Linearize the relationship between the independent variables and the probability of the outcome.

Answer

Transform the outcome into a continuous variable.

Answer

Make the model more interpretable.

Answer

Reduce computational complexity of the model.

Question 25

The intercept in a logistic regression model represents:

Accepted Answer

The log odds of the outcome occurring when all independent variables are zero.

Answer

The probability of the outcome occurring when all independent variables are zero.

Answer

The odds of the outcome occurring when all independent variables are zero.

Answer

The risk of the outcome occurring when all independent variables are zero.

Question 26

A key purpose of a ROC curve in logistic regression is to:

Accepted Answer

Evaluate the sensitivity and specificity of the model at different probability thresholds.

Answer

Determine the optimal cutoff point for classifying outcomes.

Answer

Assess the goodness-of-fit of the model.

Answer

Compare multiple logistic regression models.

Question 27

Which of the following is an assumption of logistic regression?

Accepted Answer

The relationship between the independent variables and the logit of the dependent variable is linear.

Answer

The errors are normally distributed.

Question 28

What is the purpose of the logit transformation in logistic regression?

Accepted Answer

To convert the non-linear relationship between the independent variables and the dependent variable into a linear relationship.

Answer

To normalize the distribution of the dependent variable.

Question 29

Which of the following is a typical application of logistic regression in psychological research?

Accepted Answer

Predicting the probability of developing a mental disorder based on demographic and clinical characteristics.

Answer

Estimating the mean score on a cognitive test.

Question 30

What is the advantage of using maximum likelihood estimation to fit a logistic regression model?

Accepted Answer

It provides unbiased and efficient estimates of the model parameters.

Answer

It can handle missing data more effectively than other estimation methods.

Answer

It is computationally simple and fast to implement.

Question 31

Which of the following statistics is used to assess the overall goodness-of-fit of a logistic regression model?

Accepted Answer

Likelihood ratio test

Answer

R-squared

Answer

Chi-square test

Answer

F-test

Question 32

What is the purpose of the Wald test in logistic regression?

Accepted Answer

To test the significance of individual regression coefficients.

Answer

To assess the presence of multicollinearity among the independent variables.

Answer

To compare the overall fit of two nested models.

Question 33

What is the difference between a logit model and a probit model?

Accepted Answer

The logit model uses the logistic function, while the probit model uses the cumulative normal distribution function.

Answer

The logit model is more accurate than the probit model.

Question 34

What is the role of the intercept in a logistic regression model?

Accepted Answer

It represents the logit of the probability of the event occurring when all the independent variables are equal to zero.

Answer

It represents the probability of the event occurring when all the independent variables are equal to one.

Question 35

Which of the following is a key assumption of logistic regression?

Accepted Answer

The outcome variable must be binary or multinomial.

Answer

The sample size must be large.

Answer

The relationship between the variables must be linear.

Answer

The independent variables must be normally distributed.

Question 36

What is the purpose of the logit function in logistic regression?

Accepted Answer

To transform the probability of the outcome into a linear function, making it easier to estimate the relationship between the independent variables and the outcome.

Answer

To predict the exact probability of the outcome.

Answer

To calculate the odds of the outcome.

Question 37

Which measure is used to assess the goodness-of-fit of a logistic regression model?

Accepted Answer

Pseudo R-squared, which indicates the proportion of variance in the outcome variable explained by the model.

Answer

Coefficient of determination, which measures the strength of the relationship between the independent and dependent variables in linear regression.

Answer

F-statistic, which tests the overall significance of the model.

Answer

Mean squared error, which measures the average squared difference between the predicted and observed values.

Question 38

What is the effect of increasing a continuous independent variable on the log odds of the outcome in logistic regression?

Accepted Answer

It either increases or decreases the log odds, depending on the sign of the coefficient associated with that variable.

Answer

It always decreases the log odds.

Answer

It always increases the log odds.

Question 39

Which type of independent variable is represented by the intercept term in a logistic regression model?

Accepted Answer

Constant, representing the log odds of the outcome when all other variables are set to zero.

Answer

Categorical, representing different categories of a variable.

Answer

Continuous, representing variables that can take on any numerical value.

Answer

Interaction, representing the combined effect of two or more variables.

Question 40

What is the purpose of using maximum likelihood estimation in logistic regression?

Accepted Answer

To find the values of the model parameters that maximize the likelihood of observing the data, given the specified model.

Answer

To test the significance of the model.

Question 41

Which of the following is a potential violation of the assumptions of logistic regression?

Accepted Answer

Non-linear relationship between the variables, which can lead to biased parameter estimates and inaccurate predictions.

Answer

Binary outcome variable, which is a fundamental assumption of logistic regression.

Answer

Large sample size, which is typically not a concern in logistic regression as long as the sample is representative.

Answer

Normally distributed independent variables, which is not a strict requirement for logistic regression as long as the sample size is sufficient.

Question 42

What is the difference between the odds ratio and the risk ratio in logistic regression?

Accepted Answer

The odds ratio compares the odds of the outcome between two groups, while the risk ratio compares the probability of the outcome between two groups.

Answer

They are the same measure.

Question 43

Which of the following is an application of logistic regression in psychological research?

Accepted Answer

Predicting the likelihood of developing a specific psychological disorder based on a combination of risk factors.

Answer

Estimating the population mean of a continuous variable, which is typically done using linear regression.

Answer

Testing the difference between two means, which is typically done using t-tests or ANOVA.

Question 44

What is the role of the Wald test in logistic regression?

Accepted Answer

To test the statistical significance of individual model coefficients, determining whether they are significantly different from zero.

Answer

To test the overall significance of the model.

Answer

To calculate the odds ratio.