Linear Regression Questions and Answers for Viva

Answer-1: The F-test in linear regression tests the overall significance of the regression model, checking if at least one predictor variable has a non-zero coefficient.

Answer-2: A confidence interval provides a range of values for the regression coefficients within which we are confident the true coefficient lies, typically at a 95% confidence level.

Answer-3: Multicollinearity can be addressed by removing highly correlated predictors, combining variables, or using techniques like Ridge or Lasso regression.

Answer-4: Residual Sum of Squares (RSS) is the sum of squared residuals, representing the portion of the variance not explained by the model. A lower RSS indicates a better-fitting model.

Answer-5: Feature scaling ensures that all predictors have similar scales, which is especially important for regularized regression methods like Ridge and Lasso.

Answer-6: Cross-validation helps assess the performance and generalization ability of a linear regression model by splitting the data into training and validation sets multiple times.

Answer-7: Stepwise regression is a method of building a linear model by automatically adding or removing predictors based on certain criteria like the AIC or p-value.

Answer-8: Standardizing variables ensures that all predictors have the same scale, which helps prevent certain variables from dominating the regression model, especially in regularized models.

Answer-9: Linear regression predicts continuous outcomes, while logistic regression is used for binary or categorical outcomes by applying a logistic function to the predicted value.

Answer-10: Limitations of linear regression include sensitivity to outliers, assumptions of linearity, homoscedasticity, and normality, and the inability to model complex non-linear relationships.

Answer-11: Overfitting occurs when a linear regression model becomes too complex and captures noise in the data, leading to poor generalization to new data. Regularization methods help address overfitting.

Answer-12: Underfitting occurs when the linear regression model is too simple to capture the underlying patterns in the data, leading to poor performance.

Answer-13: Residual plots help check the assumptions of linear regression by visualizing the residuals and identifying patterns like non-linearity, heteroscedasticity, and outliers.

Answer-14: The fitted values in linear regression are calculated by applying the estimated regression coefficients to the independent variables. The formula is y^=?0+?1x1+?+?nxn\hat{y} = \beta_0 + \beta_1 x_1 + \dots + \beta_n x_ny^?=?0?+?1?x1?+?+?n?xn?.

Answer-15: The standard error of regression coefficients measures the precision of the estimated coefficients. A larger standard error indicates less precision and greater uncertainty in the estimates.

Answer-16: OLS is a direct method that minimizes the sum of squared residuals to estimate coefficients, while gradient descent is an iterative optimization method used to minimize the cost function, often used for large datasets.

Answer-17: Outliers can heavily impact the results of linear regression by skewing the coefficients, inflating the error term, and distorting model predictions.

Answer-18: In multiple linear regression, the coefficients represent the change in the dependent variable for a one-unit change in the corresponding independent variable, holding all other predictors constant.

Answer-19: Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to the observed data.

Answer-20: The two main types of linear regression are Simple Linear Regression (with one predictor) and Multiple Linear Regression (with two or more predictors).

Answer-21: The equation of a linear regression model is: y=?0+?1x1+?2x2+?+?nxn+?y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \dots + \beta_n x_n + \epsilony=?0?+?1?x1?+?2?x2?+?+?n?xn?+?, where yyy is the dependent variable, xix_ixi? are independent variables, ?i\beta_i?i? are coefficients, and ?\epsilon? is the error term.

Answer-22: The purpose of linear regression is to predict the value of a dependent variable based on the values of independent variables, and to determine the strength and direction of their relationship.

Answer-23: The dependent variable is the variable that we are trying to predict or explain (e.g., house prices), while independent variables are the predictors or factors that influence the dependent variable (e.g., size, location).

Answer-24: Assumptions in linear regression include linearity, independence, homoscedasticity, normality of errors, and no multicollinearity.

Answer-25: The least squares method is used to estimate the coefficients of a linear regression model by minimizing the sum of the squared differences between the observed and predicted values.

Answer-26: The coefficients represent the impact of each independent variable on the dependent variable. For instance, the coefficient ?1\beta_1?1? represents the change in yyy for a one-unit change in x1x_1x1?, keeping all other variables constant.

Answer-27: The cost function in linear regression is typically the Mean Squared Error (MSE), which measures the average of the squared differences between the predicted and actual values.

Answer-28: The formula for MSE is: MSE=1n?i=1n(yi?yi^)2\text{MSE} = \frac{1}{n} \sum_{i=1}^n (y_i - \hat{y_i})^2MSE=n1??i=1n?(yi??yi?^?)2, where yiy_iyi? are the actual values and yi^\hat{y_i}yi?^? are the predicted values.

Answer-29: A linear regression model can be evaluated using metrics like R-squared, Adjusted R-squared, Mean Squared Error (MSE), and Root Mean Squared Error (RMSE).

Answer-30: R-squared is a statistical measure that represents the proportion of the variance in the dependent variable that is predictable from the independent variables. It ranges from 0 to 1.

Answer-31: Adjusted R-squared adjusts R-squared for the number of predictors in the model, providing a more accurate measure of model performance when multiple independent variables are used.

Answer-32: Multicollinearity occurs when two or more independent variables in a linear regression model are highly correlated, making it difficult to assess the individual effect of each variable.

Answer-33: Multicollinearity can be checked using Variance Inflation Factor (VIF). A VIF greater than 10 indicates high multicollinearity.

Answer-34: The intercept term ?0\beta_0?0? in linear regression represents the predicted value of the dependent variable when all independent variables are zero.

Answer-35: Heteroscedasticity refers to the situation where the variance of errors is not constant across all values of the independent variables, violating one of the key assumptions of linear regression.

Answer-36: Heteroscedasticity can be detected using graphical methods like residual plots or statistical tests like Breusch-Pagan or White?s test.

Answer-37: Homoscedasticity refers to the assumption that the variance of the errors is constant across all values of the independent variables.

Answer-38: Outliers can be handled by using robust regression techniques, transforming the data, or removing extreme outliers if they significantly impact model performance.

Answer-39: A residual is the difference between the actual and predicted values in a regression model. It represents the error in the prediction for each data point.

Answer-40: The p-value in linear regression tests the null hypothesis that the coefficient is equal to zero (no effect). A p-value less than 0.05 typically indicates that the variable is statistically significant.

Answer-41: The normality assumption ensures that the error terms are normally distributed, which is important for hypothesis testing and confidence intervals in linear regression.

Answer-42: Missing data can be handled using techniques like mean imputation, median imputation, or more advanced methods like regression imputation or multiple imputation.

Answer-43: Ridge regression is a type of linear regression that applies L2 regularization to penalize large coefficients, helping to prevent overfitting and improve model generalization.

Answer-44: Lasso regression is a type of linear regression that applies L1 regularization to the model, which can shrink some coefficients to zero, effectively performing feature selection.

Answer-45: ElasticNet is a regularized linear regression model that combines both L1 (Lasso) and L2 (Ridge) regularization, useful when there are many correlated features.

Answer-46: Ridge regression uses L2 regularization to penalize large coefficients, while Lasso regression uses L1 regularization, which can reduce some coefficients to zero and perform feature selection.

Answer-47: Linear regression and correlation both measure relationships between variables, but regression models the functional relationship between variables, while correlation measures the strength and direction of a linear relationship.

Answer-48: Categorical variables can be handled in linear regression by using techniques like one-hot encoding or label encoding to convert them into numerical form.

Answer-49: Simple linear regression involves one independent variable, while multiple linear regression involves two or more independent variables to predict the dependent variable.

Answer-50: R-squared indicates how well the independent variables explain the variability in the dependent variable. A higher R-squared value indicates a better fit of the model.