Linear Regression Assumptions and Residual Analysis Quiz

Answers and explanations appear as you take the quiz.

1. A residual-versus-fitted plot bends into a clear U shape. Which concern does this pattern raise first?
   • The mean relationship may need a nonlinear term
   • The residual spread may change across fitted values
   • The residual distribution may have heavy tails
   • Residuals may remain correlated across time
2. As fitted values increase, residual spread grows into a fan. Which classical condition is most directly questioned?
   • Predictor measurements are exact
   • Errors have constant conditional variance
   • The conditional mean equals zero everywhere
   • Predictors are normally distributed
3. Why is normally distributed error not required merely to calculate the ordinary least-squares coefficients?
   • OLS coefficients are calculated by minimizing squared residuals
   • Gaussian errors are required to calculate the least-squares coefficients
   • Constant variance is required for the least-squares minimizer to exist
   • Independent errors are required to compute fitted values
4. Daily demand residuals stay positive for a week after a spike. What should an analyst examine?
   • A missing time pattern may shift the conditional mean
   • The residual variance may vary by period
   • Whether consecutive errors are dependent over time
   • A few outliers may account for the sequence
5. A point has predictors far from the rest but a modest residual. Which description may still apply?
   • It has high leverage
   • It must have zero influence
   • It proves heteroscedasticity
   • It is a response outlier by definition
6. An influential observation changes the fitted slope. What is the sound first response?
   • Delete it immediately because influence proves the record is invalid
   • Inspect its source and report how the fit changes with and without it
   • Replace its response with the fitted value before checking the record
   • Keep it automatically because the complete sample is always preferable
7. Which plot is most directly used to compare residual quantiles with a normal distribution?
   • Residuals against time
   • A normal Q-Q plot
   • A fitted-versus-observed plot
   • A predictor correlation matrix
8. A residual plot looks patternless on training data. What evidence is still needed before relying on predictions?
   • Independent or later data reflecting intended use
   • A normal Q-Q plot on the same training residuals
   • A lower training squared error than a simpler model
   • A robust covariance estimate for the fitted coefficients