According to the plot of $residuals$ versus $fittedvalues$, which of the following patterns would most likely indicate that the assumptions of $linearregression$ are violated?

• A. Residuals forming a horizontal band with no apparent pattern
• B. A funnel-shaped pattern where the spread of $residuals$ increases as $fittedvalues$ increase
• C. Residuals all clustered exactly at $0$
• D. A random scatter of $residuals$ with constant spread around $0$

Answer: (B)

Verified step by step guidance

1. Understand that in linear regression, one key assumption is homoscedasticity, which means the residuals (errors) should have constant variance across all levels of the fitted values.
2. Recognize that when plotting residuals versus fitted values, a horizontal band with no apparent pattern suggests constant variance and supports the assumption of homoscedasticity.
3. Identify that a funnel-shaped pattern, where the spread of residuals increases as fitted values increase, indicates heteroscedasticity, meaning the variance of residuals is not constant and the assumption is violated.
4. Note that residuals all clustered exactly at zero is unrealistic in practice and may indicate a problem with the model or data, but it is not a typical pattern for checking assumptions.
5. Conclude that a random scatter of residuals with constant spread around zero supports the assumptions of linear regression, while a funnel-shaped pattern signals a violation.