Quiz on Linear Regression in Machine Learning

Introduction to Linear Regression Answers 1. What is the purpose of adjusted R-squared in model evaluation? A. To increase the model's accuracy by adding more variables. B. To measure the correlation between dependent variables. C. To determine the proportion of variance explained by the model while accounting for the number of independent variables. D. To evaluate the model using a training dataset only. Answer: To determine the proportion of variance explained by the model while accounting for the number of independent variables. (C) Adjusted R-squared provides a more accurate measure of model performance by adjusting for the number of predictors used, preventing overfitting. 2. Which assumption is violated if the residuals of a regression model display a systematic pattern? A. Homoscedasticity B. Linearity C. Independence of Errors D. Normality of Errors Answer: Linearity (B) A systematic pattern in residuals indicates that the relationship may not be linear, violating the linearity assumption of the model. 3. What does cross-validation primarily help assess? A. The generalization ability of the model on unseen data. B. The model's performance on seen data. C. The variance of the training data. D. The bias of the model. Answer: The generalization ability of the model on unseen data. (A) Cross-validation provides a more reliable estimate of a model's ability to generalize by testing it on multiple subsets of the data. 4. Which of the following best describes homoscedasticity in a linear regression model? A. The errors are normally distributed. B. The dependent variable is a linear combination of independent variables. C. The independent variables are not correlated. D. The errors have constant variance across all levels of the independent variable. Answer: The errors have constant variance across all levels of the independent variable. (D) Homoscedasticity refers to the condition where the error terms in a regression model have constant variance, which is crucial for making valid statistical inferences. 5. In predictive modeling, which of the following is a common application? A. Identifying the distribution of independent variables. B. Predicting the probability of a customer making a purchase. C. Establishing causal relationships between variables. D. Determining the historical trends of data points. Answer: Predicting the probability of a customer making a purchase. (B) Predictive modeling often focuses on forecasting future outcomes, such as a customer's likelihood to make a purchase based on historical data. 6. What is the primary purpose of linear regression? A. To model the relationship between dependent and independent variables. B. To generate random data for testing. C. To classify data into categories. D. To reduce the dimensionality of data. Answer: To model the relationship between dependent and independent variables. (A) Linear regression is primarily used to model the relationship between dependent and independent variables. 7. Which equation represents simple linear regression? A. y = m + bx^2 B. y = mx + b C. y = bx + m D. y = mx^2 + b Answer: y = mx + b (B) The correct equation for simple linear regression is y = mx + b, which describes a straight line. 8. In multiple linear regression, how does the relationship between variables differ from simple linear regression? A. It only has one independent variable. B. It always results in a curve. C. It uses a hyperplane to represent relationships. D. It cannot provide predictions. Answer: It uses a hyperplane to represent relationships. (C) Multiple linear regression represents relationships using a hyperplane due to the involvement of multiple independent variables. 9. What does the slope (m) in the equation y = mx + b indicate? A. The total number of independent variables. B. The change in the dependent variable for a unit change in the independent variable. C. The starting point of the dependent variable. D. The error term in the model. Answer: The change in the dependent variable for a unit change in the independent variable. (B) The slope (m) indicates how much the dependent variable changes with a unit change in the independent variable. 10. Which of the following best describes the term 'residuals' in linear regression? A. The total number of independent variables chosen. B. The difference between observed values and predicted values. C. The coefficients assigned to the independent variables. D. The predicted values of the dependent variable. Answer: The difference between observed values and predicted values. (B) Residuals represent the differences between the observed values and the predicted values in a dataset. 11. What is considered a good measure of 'goodness of fit' in a regression model? A. Maximizing the number of independent variables. B. Minimizing residuals. C. Achieving high R-squared values. D. Using random data points. Answer: Achieving high R-squared values. (C) Higher values of R-squared indicate a better fit of the regression line to the data. 12. What is the purpose of Ordinary Least Squares (OLS) in linear regression? A. To estimate the coefficients by minimizing errors. B. To classify data points. C. To increase the number of independent variables. D. To create a non-linear model. Answer: To estimate the coefficients by minimizing errors. (A) OLS is a technique used to estimate the coefficients in linear regression by minimizing the sum of squared errors. 13. Which of the following operations is NOT part of data preparation for linear regression? A. Transforming data. B. Scaling features. C. Handling missing values. D. Performing classification. Answer: Performing classification. (D) Classification is not part of data preparation for linear regression; the focus is on cleaning and transforming the data.