Which of these is NOT an assumption of Linear Regression?

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BlackTom AI · Accepted Answer

When evaluating assumptions of Linear Regression, it helps to recall the standard requirements for the model to provide reliable estimates.
Option 1: Constant Variance Errors. This corresponds to homoscedasticity, meaning the residuals (errors) have constant variance across all levels of the predictor. This is indeed an assumption of linear regression, so this statement describes a valid assumption.
Option 2: Independent Errors. The assumption is that the residuals are uncorrelated with each other (no autocorrelation). This is another core assumption, so this statement correctly describes an assumption.
Option 3: Linearity Errors. Here, the phrase implies that there are errors in the assumption of linearity. However, linear regression assumes a linear relationship between predictors and the outcome, not “linearity errors.” In other words, Linearity is an assumption; saying there are Linearity Errors is describing a violation or mis-specification, not an assumption itself. Therefore this option is not an assumption of linear regression.
Option 4: Normally Distributed Errors. For inference (confidence intervals, hypothesis tests) the residuals are assumed to be normally distributed (especially important in small samples). Hence, this is indeed an assumption.
Thus, among the options, the statement that is NOT an assumption of Linear Regression is the one that talks about Linearity Errors, since it suggests an error rather than a foundational assumption. The others correctly reflect standard assumptions of the model.

ERMCPS5350_003_2025_3 - INTRO TO QUANTITATIVE RISK MANAGEMENT 11. Quiz for Class 11

Which of these is NOT an assumption of Linear Regression?

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