Logistic Regression: A Comprehensive Guide for PhD Students

Question 1

In logistic regression, the logit transformation is applied to the probability of an event occurring. What is the formula for the logit?

Accepted Answer

logit(p) = β₀ + β₁x₁ + β₂x₂

Answer

p = e^(β₀ + β₁x₁ + β₂x₂)

Answer

x₁ + x₂ = β₀ + β₁

Answer

p = 1 - e^(β₀ + β₁x₁ + β₂x₂)

Question 2

How are the logit and the log-odds related in logistic regression?

Accepted Answer

The logit is the output of the sigmoid function, while the log-odds is the input

Answer

The log-odds is the output of the sigmoid function, while the logit is the input

Answer

The logit and the log-odds are the same

Answer

The logit is a measure of the probability of the dependent variable being 1, while the log-odds is a measure of the odds of the dependent variable being 1

Question 3

What is the objective of the maximum likelihood estimation method in logistic regression?

Accepted Answer

To find the values of the model parameters that maximize the probability of the observed data

Answer

To minimize the mean squared error of the model

Answer

To ensure that the model is unbiased

Answer

To find the values of the model parameters that minimize the log-loss

Question 4

Which assumption is NOT required for the valid use of logistic regression?

Accepted Answer

Normally distributed residuals

Answer

Linearity in log odds

Answer

Homoscedasticity of errors

Answer

Independence of observations

Question 5

In logistic regression, the dependent variable is:

Accepted Answer

Binary or categorical

Answer

Quantitative and continuous

Answer

Ordinal and bounded

Answer

Continuous and skewed

Question 6

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

Accepted Answer

AIC

Answer

R-squared

Answer

MAE

Answer

F-statistic

Question 7

What do the coefficients in logistic regression represent?

Accepted Answer

The change in log odds of the event for a one-unit increase in the predictor

Answer

The probability of the event for a one-unit increase in the predictor

Answer

The odds ratio of the event for a one-unit increase in the predictor

Answer

The slope of the logistic function

Question 8

The link function in logistic regression is used to:

Accepted Answer

Transform the linear combination of predictors into a probability

Answer

Reduce the variance of the residuals

Answer

Make the model more interpretable

Answer

Improve the accuracy of the model

Question 9

What do the coefficients in a logistic regression model represent?

Accepted Answer

The change in the log odds of the dependent variable for a one-unit increase in the corresponding independent variable.

Answer

The change in the probability of the dependent variable for a one-unit increase in the corresponding independent variable.

Answer

The effect of the corresponding independent variable on the dependent variable, holding all other variables constant.

Answer

The correlation between the corresponding independent variable and the dependent variable.

Question 10

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

Accepted Answer

To evaluate the goodness-of-fit of the model.

Answer

To assess the statistical significance of the coefficients.

Answer

To compare the predictive power of multiple logistic regression models.

Answer

To detect influential observations that may affect the model's stability.

Question 11

What is the key difference between logistic and linear regression in terms of their primary application?

Accepted Answer

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

Answer

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

Answer

Both logistic and linear regression predict binary outcomes.

Answer

Both logistic and linear regression predict continuous outcomes.

Question 12

What is the primary purpose of the sigmoid function in logistic regression?

Accepted Answer

To transform the linear combination of independent variables into a probability value between 0 and 1.

Answer

To estimate the mean of the dependent variable.

Answer

To calculate the standard deviation of the errors.

Question 13

Which metric is NOT commonly used to evaluate logistic regression models?

Accepted Answer

Root Mean Squared Error (RMSE)

Answer

Accuracy

Answer

Precision

Answer

Area Under the Receiver Operating Characteristic Curve (AUC-ROC)

Question 14

What is the main objective of maximum likelihood estimation in logistic regression?

Accepted Answer

To identify the set of parameters that maximizes the likelihood of observing the given data.

Answer

To minimize the sum of squared errors.

Answer

To estimate the mean and standard deviation of the dependent variable.

Question 15

Identify a potential limitation of logistic regression models.

Accepted Answer

Logistic regression models can only handle binary dependent variables.

Answer

Logistic regression models require a very large sample size.

Answer

Logistic regression models are computationally demanding.

Answer

Logistic regression models are highly sensitive to outliers.

Question 16

What is the mathematical formula for the logistic function used in logistic regression?

Accepted Answer

p = 1 / (1 + exp(-(b0 + b1x)))

Answer

p = exp(-(b0 + b1x))

Answer

p = b0 + b1x

Answer

p = (1 + exp(-(b0 + b1x))) / 2

Question 17

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

Accepted Answer

To linearize the relationship between the independent variables and the log-odds of the dependent variable.

Answer

To transform the dependent variable to a normal distribution.

Question 18

Which evaluation metric is commonly used for logistic regression models?

Accepted Answer

Area Under the Receiver Operating Characteristic Curve (AUC-ROC)

Answer

Mean Absolute Error (MAE)

Answer

Root Mean Squared Error (RMSE)

Question 19

What is the purpose of regularization in logistic regression?

Accepted Answer

To reduce overfitting and improve the generalization performance of the model.

Answer

To increase the variance of the model's predictions

Answer

To make the model more interpretable

Question 20

In a logistic regression model, the coefficient for an independent variable represents:

Accepted Answer

The change in the log-odds of the dependent variable for a one-unit increase in the independent variable

Answer

The probability of the dependent variable being 1 for a given value of the independent variable

Question 21

What is the difference between logistic regression and linear regression?

Accepted Answer

Logistic regression is used for binary classification, while linear regression is used for continuous prediction.

Answer

Logistic regression uses a linear function, while linear regression uses a non-linear function.

Question 22

What is the purpose of using a threshold value in logistic regression for binary classification?

Accepted Answer

To determine the probability cutoff for classifying observations as 0 or 1

Answer

To improve the model's accuracy

Answer

To reduce the model's bias