https://file.aiquickdraw.com/mathbot/file/17205621249798rmrru8s.png

https://file.aiquickdraw.com/mathbot/file/1720562124979ugb82bql.png

Based on the residual plot below, which, if any, linear regression assumption was violated?

residual plot assp variance.PNG

Group of answer choices

None of the assumptions are violated.

The errors are not independent

The relationship between the variables is not linear

The errors do not have constant variance

The errors are not normally distributed

Based on the provided residual plot, the assumption of constant variance (homoscedasticity) appears to be violated. This is evidenced by the "fan shape" pattern in the residuals, where the spread of residuals increases with the fitted values.

Therefore, the correct answer is:

- The errors do not have constant variance

Would you like to ask for more details or have any other questions? Here are some additional questions you might consider:

1. What are the key assumptions of linear regression?
2. How can you test for homoscedasticity in a dataset?
3. What are some methods to correct for heteroscedasticity?
4. How does non-linearity affect regression analysis?
5. What steps can you take if the residuals are not normally distributed?

**Tip:** In regression analysis, always check the residual plots for patterns that indicate violations of assumptions, such as non-linearity, non-constant variance, and autocorrelation.

Explore how to identify violations of linear regression assumptions using residual plots. Understand why constant variance (homoscedasticity) is crucial in regression analysis with a detailed explanation and example. Ideal for advanced high school students and college learners.

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