Residual Analysis and Error Diagnostics Quiz

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3. Which method addresses heteroscedasticity by transforming the response variable?

Weighted Least Squares

Log transformation

Ridge regression

Robust regression

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5. If residuals display a curved pattern in a residual plot, what does this suggest?

Violation of linearity assumption

Non-constant variance

Autocorrelation present

Model is properly specified

6. High leverage points are identified by values of which diagnostic measure?

Hat values or diagonal of hat matrix

Residual sum of squares

R-squared statistic

Mean squared error

7. What does a studentized residual equal to ±2 approximately represent?

A value at the 68% confidence level

A value at the 95% confidence level

An outlier requiring removal

A perfectly normal observation

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9. The Breusch-Pagan test is used to detect which type of model violation?

Non-normality

Heteroscedasticity

Autocorrelation

Multicollinearity

10. Which test statistic is used to formally test normality of residuals?

Shapiro-Wilk Test

Breusch-Pagan Test

Variance Inflation Factor

Akaike Information Criterion

11. What do residuals represent in a regression model?

The difference between observed and predicted values

The slope of the regression line

The correlation coefficient between variables

The variance explained by the model

12. What is the purpose of a Scale-Location plot?

Test normality of residuals

Detect heteroscedasticity and spread patterns

Identify autocorrelation

Find multicollinearity

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14. Which diagnostic tool identifies influential points that disproportionately affect model coefficients?

Cook's Distance

Leverage Plot

Scale-Location Plot

Both a and b

15. Autocorrelation in residuals violates which regression assumption?

Independence of errors

Normality of errors

Homogeneity of variance

Linearity of relationship

16. A Durbin-Watson statistic near 2 suggests what about autocorrelation?

Strong positive autocorrelation

Little to no autocorrelation

Strong negative autocorrelation

Cannot be determined

17. What does the Durbin-Watson test diagnose?

Normality of residuals

Autocorrelation in residuals

Multicollinearity among predictors

Outliers in the dataset

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19. A Q-Q plot is primarily used to assess which assumption?

Linearity

Normality of residuals

Independence

Homoscedasticity

20. Which plot is most useful for detecting heteroscedasticity?

Residuals vs. Fitted Values

Q-Q Plot

Histogram of Residuals

Time Series Plot

DataAI Residual Analysis and Error Diagnostics Quiz

1. Standardized residuals that exceed ±3 typically indicate potential ____ in the data.

2.

What first name or nickname would you like us to use?

2. When a residual plot shows points randomly scattered around zero with no pattern, the model assumptions are likely ____.

3. Which method addresses heteroscedasticity by transforming the response variable?

4. The variance of residuals should be ____ across all fitted values in a properly specified model.

5. If residuals display a curved pattern in a residual plot, what does this suggest?

6. High leverage points are identified by values of which diagnostic measure?

7. What does a studentized residual equal to ±2 approximately represent?

8. When residuals show a clear funnel pattern in a residual plot, this indicates ____.

9. The Breusch-Pagan test is used to detect which type of model violation?

10. Which test statistic is used to formally test normality of residuals?

11. What do residuals represent in a regression model?

12. What is the purpose of a Scale-Location plot?

13. A Cook's Distance value greater than 4/n suggests a point is ____ for the model.

14. Which diagnostic tool identifies influential points that disproportionately affect model coefficients?

15. Autocorrelation in residuals violates which regression assumption?

16. A Durbin-Watson statistic near 2 suggests what about autocorrelation?

17. What does the Durbin-Watson test diagnose?

18. Heteroscedasticity occurs when residual variance is ____ across predictor values.

19. A Q-Q plot is primarily used to assess which assumption?

20. Which plot is most useful for detecting heteroscedasticity?