Linear Regression Quiz: Test Yourself Before Final Interview

Linear Regression Quiz

1. What is the primary goal of Linear Regression in machine learning?

   Minimize the number of features
   Maximize the accuracy of the model
   Minimize the mean squared error
   Maximize the regularization term
   

2. Which of the following assumptions is NOT required for simple linear regression?

   Linearity
   Homoscedasticity
   Independence of errors
   Multicollinearity
   

3. What does the slope coefficient in simple linear regression represent?

   The predicted value of the dependent variable
   The correlation between independent variables
   The change in the dependent variable for a one-unit change in the independent variable
   The standard error of the regression
   

4. What is multicollinearity in multiple linear regression?

   The presence of outliers in the data
   The assumption of normality in the error terms
   High correlation between independent variables
   The violation of linearity assumption
   

5. What does the p-value associated with an independent variable in linear regression indicate?

   The importance of the variable
   The correlation between the variable and the dependent variable
   The probability that the variable has no effect on the dependent variable
   The number of observations in the dataset
   

6. In linear regression, what does the residual represent?

   The dependent variable
   The difference between the observed and predicted values
   The independent variable
   The coefficient of determination (R-squared)
   

7. What is the coefficient of determination (R-squared) in linear regression?

   A measure of model complexity
   A measure of the correlation between independent variables
   A measure of the goodness of fit of the model
   A measure of the bias in the model
   

8. What is the purpose of the Ridge Regression technique in linear regression?

   To reduce the number of features
   To increase model interpretability
   To handle multicollinearity
   To remove outliers from the data
   

9. Which of the following statements about the assumptions of linear regression is true?

   The assumption of independence of errors can be violated without consequences
   The assumption of homoscedasticity implies that the variance of errors is constant across all levels of the independent variable
   The assumption of linearity requires that the relationship between the independent and dependent variables is always linear
   The assumption of normality in the error terms is not required for the OLS method
   

10. What is the formula for the mean squared error (MSE) in linear regression?

    MSE = (1 / n) Σ(yi - ŷi)²
    MSE = Σ(yi - ŷi)²
    MSE = (1 / n) Σ(yi - ŷi)³
    MSE = Σ(yi - ŷi)³
    

11. What is the purpose of the Durbin-Watson statistic in linear regression?

    To assess the linearity of the relationship between variables
    To check for the presence of outliers in the data
    To test for homoscedasticity
    To detect autocorrelation in the error terms
    

12. What is the primary purpose of cross-validation in linear regression?

    To reduce the computational complexity of the model
    To prevent overfitting and assess model generalization
    To remove outliers from the dataset
    To increase the interpretability of the model
    

13. What is the formula for the adjusted R-squared in multiple linear regression?

    Adjusted R-squared = 1 - (SSE / SSTO)
    Adjusted R-squared = 1 - (SST / SSE)
    Adjusted R-squared = 1 - (1 - R-squared)
    Adjusted R-squared = 1 - (n / (n - k - 1)) * (1 - R-squared)
    

14. What is the purpose of the Lasso Regression technique in linear regression?

    To remove outliers from the dataset
    To increase the interpretability of the model
    To handle multicollinearity and perform feature selection
    To reduce the computational complexity of the model
    

15. What is the formula for the residual sum of squares (SSE) in linear regression?

    SSE = Σ(yi - ŷi)²
    SSE = (1 / n) Σ(yi - ŷi)²
    SSE = (1 / n) Σ(yi - ŷi)³
    SSE = Σ(yi - ŷi)³
    

16. What does the F-statistic in linear regression measure?

    The strength of the relationship between the dependent and independent variables
    The overall significance of the model
    The variance of the error terms
    The normality of the residuals
    

17. Which of the following statements about the coefficient of determination (R-squared) is true?

    R-squared can be negative when the model is a poor fit to the data
    R-squared ranges from -1 to 1, where 1 indicates a perfect fit
    R-squared measures the total variability in the dependent variable
    R-squared is independent of the number of independent variables in the model
    

18. What is the purpose of the Breusch-Pagan test in linear regression?

    To check for autocorrelation in the error terms
    To test the linearity of the relationship between variables
    To assess the normality of the residuals
    To detect heteroscedasticity in the error terms
    

19. What is the formula for the coefficient of determination (R-squared) in linear regression?

    R-squared = 1 - (SSE / SSTO)
    R-squared = 1 - (SST / SSE)
    R-squared = 1 - (1 - R-squared)
    R-squared = 1 - (n / (n - k - 1)) * (1 - R-squared)
    

20. What is the primary purpose of the Elastic Net technique in linear regression?

    To remove outliers from the dataset
    To increase the interpretability of the model
    To handle multicollinearity, perform feature selection, and reduce overfitting
    To reduce the computational complexity of the model