Regression Basics: Linear u0026 Logistic Quiz Quiz

Explore key concepts of linear and logistic regression with practical questions designed to strengthen your understanding of model assumptions, variable interpretations, and real-world applications. This quiz helps learners distinguish between regression types, predictors, and statistical outputs while avoiding common misconceptions.

1. Linear vs Logistic Regression Application

   When predicting whether a student will pass or fail an exam based on study hours, which type of regression should be used?

   1. Stepwise regression
   2. Polynomial regression
   3. Linear regression
   4. Logistic regression

   Explanation: Logistic regression is appropriate when the outcome is binary, such as pass or fail. Linear regression is suited for predicting continuous numerical values, not classifications. Polynomial regression models nonlinear relationships but is not used for classification problems. Stepwise regression is a variable selection method, not a classification technique.

2. Assumptions of Linear Regression

   Which of the following is an assumption of linear regression when modeling house prices based on square footage?

   1. Multicollinearity
   2. Non-binary response
   3. Multinomial outcome
   4. Homoscedasticity

   Explanation: Homoscedasticity refers to constant variance of errors, a key assumption in linear regression. Multicollinearity refers to highly correlated predictors and is a condition to be avoided, not assumed. Multinomial outcomes require other types of models, not linear regression. Non-binary response is a property of the outcome, not an assumption.

3. Interpreting Logistic Regression Output

   In logistic regression, what does the coefficient for an independent variable represent?

   1. The change in the log odds of the outcome per unit increase in the variable
   2. Direct effect size measured in percent
   3. The change in predicted probability per unit increase in the variable
   4. The mean difference of outcomes for each group

   Explanation: Coefficients in logistic regression describe how the log odds of the outcome change with each unit increase in the independent variable. They do not show direct changes in probability, which requires further transformation. The mean difference option pertains more to t-tests, not logistic regression. The direct effect in percent is not the interpretation of the raw coefficient.

4. Evaluating Linear Regression Models

   Which metric is commonly used to assess the goodness-of-fit in a linear regression model predicting car prices?

   1. Gini coefficient
   2. R-squared
   3. Confusion matrix
   4. F-measure

   Explanation: R-squared quantifies how well the model explains the variance in the dependent variable. The Gini coefficient is used for inequality measurements and classification performance, not regression fit. Confusion matrices and F-measure apply to classification tasks, not regression models.

5. Predictor Suitability in Regression

   If a categorical variable with three categories is to be included in a linear regression model, what must be done before including it?

   1. Sum the categories into one numeric value
   2. Enter it as text without changes
   3. Convert it into dummy variables
   4. Ignore the variable completely

   Explanation: Linear regression requires numeric predictors, so categorical variables must be converted to dummy (indicator) variables before modeling. Ignoring the variable leads to information loss. Summing categories is inappropriate as it imposes a non-existent order. Entering as text will cause errors since the model cannot process text data.