📚 Topic Summary
In regression analysis, it's crucial that certain assumptions hold true for our model to be valid and reliable. These assumptions include linearity, independence of errors, homoscedasticity (constant variance of errors), and normality of errors. When these assumptions are violated, the results of the regression can be misleading. This worksheet provides exercises to help you identify these violations through visual inspection of residual plots and other diagnostic tools.
🧠 Part A: Vocabulary
Match the term with its correct definition:
- Term: Linearity
- Term: Homoscedasticity
- Term: Independence of Errors
- Term: Normality of Errors
- Term: Multicollinearity
- Definition: The errors have constant variance across all levels of the independent variable.
- Definition: The errors are uncorrelated with each other.
- Definition: The relationship between the independent and dependent variables is linear.
- Definition: The errors are normally distributed.
- Definition: High correlation between independent variables in a multiple regression.
📝 Part B: Fill in the Blanks
Complete the following paragraph with the correct words:
When we observe a funnel shape in a residual plot, it suggests a violation of the assumption of __________. This means the __________ of the errors is not constant across all levels of the independent variable. Another common violation is __________, which can be detected by observing patterns in the residuals. To check the assumption of __________, we often use histograms or Q-Q plots of the residuals.
💡 Part C: Critical Thinking
Explain why it is important to check the assumptions of linear regression. What are the potential consequences of ignoring violations of these assumptions?