Regression Analysis

What is the main goal of linear regression?

• To model the relationship between variables using a linear equation.

• To analyze text data

• To predict categorical outcomes

• To calculate the median of the data

Explain the difference between simple linear regression and multiple regression analysis.

• Simple linear regression uses multiple independent variables, while multiple regression analysis uses only one independent variable.

• Simple linear regression is used for categorical data, while multiple regression analysis is used for continuous data.

• Simple linear regression is more accurate than multiple regression analysis.

• In simple linear regression, there is only one independent variable, whereas in multiple regression analysis, there are two or more independent variables.

What are the assumptions of linear regression?

• Non-linearity, Independence, Homoscedasticity, Normality of residuals

• Linearity, Independence, Homoscedasticity, Normality of residuals

• Linearity, Dependence, Heteroscedasticity, Normality of errors

• Linearity, Independence, Heteroscedasticity, Skewness of residuals

What is the purpose of residual analysis in regression?

• To predict future outcomes based on residuals

• To calculate the mean of the residuals

• To determine the correlation between residuals and independent variables

• To assess the goodness of fit of a regression model and check if model assumptions are met.

Discuss the concept of multicollinearity in multiple regression analysis.

• Multicollinearity occurs when the dependent variable is highly correlated with the independent variables.

• Multicollinearity is only a concern in simple linear regression, not multiple regression analysis.

• Multicollinearity can be completely ignored in regression analysis.

• Multicollinearity in multiple regression analysis refers to the situation where independent variables in the regression model are highly correlated with each other.

What are some common metrics used to evaluate the performance of a regression model?

• Mean Squared Logarithmic Error

• Mean Absolute Percentage Error

• Mean Absolute Error

• Root Mean Squared Error

• MSE, RMSE, MAE, R-squared, Adjusted R-squared

How can outliers impact the results of a regression analysis?

• Outliers have no impact on regression analysis

• Outliers can skew coefficients and distort the relationship between variables in regression analysis.

• Outliers only affect the intercept term in regression analysis

• Outliers always improve the accuracy of regression results

Provide an example of a real-world application where regression analysis is used.

• Agriculture

• Medicine

• Marketing

• Finance

What is the difference between correlation and regression analysis?

• Correlation can only be positive, while regression can be positive or negative.

• Correlation measures the relationship between two variables, while regression predicts the value of one variable based on another.

• Correlation always implies causation, while regression does not.

• Correlation is used for categorical data, while regression is used for numerical data.

How can regression analysis be used in forecasting future trends?

• By asking a magic eight ball for guidance

• By analyzing the relationship between variables in historical data and using that information to make predictions.

• By flipping a coin to predict outcomes

• By analyzing the weather forecast