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FRM Part I · FRM Exam Part I

Regression Diagnostics for FRM Part I: Chapter Guide

Regression diagnostics are the checks you run to see whether a fitted regression can be trusted. You test the OLS assumptions: constant error variance, uncorrelated errors, no perfect collinearity and a correct specification. For each problem, learn the symptom, the test, the effect on estimates and standard errors, and the fix.

What this chapter covers

This chapter starts from multiple regression and the OLS assumptions, then asks what happens when each assumption fails. The main problems are heteroskedasticity, multicollinearity, serial correlation and model misspecification, including omitted variables. It ends with outliers, residual plots and general diagnostics.

The questions follow a pattern. You are given a symptom or a test result, and you must name the problem, say what it does to coefficients and standard errors, and pick the remedy. Some questions need short calculations, such as a t-statistic, an adjusted R², an F-statistic or a Durbin-Watson reading. Most are conceptual.

The chapter builds on probability, hypothesis testing and simple linear regression from earlier in Quantitative Analysis. It also supports later material: time series and volatility models rely on the autocorrelation ideas here, and risk-model validation in Valuation and Risk Models uses the same logic of checking residuals and specification.

Regression is the core tool of the Quantitative Analysis topic, and this chapter is where the exam tests whether you understand its limits. The questions are usually short and can be answered quickly once you know the symptom-effect-fix pattern. That makes them a good source of reliable marks in a 100-question, 4-hour exam. The ideas also carry into time series, factor models and model risk, so time spent here pays off elsewhere. GARP publishes no pass mark, so aim for solid command of every topic instead of guessing which ones to skip.

Regression Diagnostics: topics in the order to study them

  1. 1Multiple Regression and OLS AssumptionsEvery later problem is a failure of one of these assumptions, so you need the baseline first.
  2. 2HeteroskedasticityIt is the first assumption failure to study, and it introduces the idea that standard errors can be wrong even when coefficients are fine.
  3. 3MulticollinearityIt is easy to learn next and contrasts well with heteroskedasticity, because the damage falls on precision rather than bias.
  4. 4Serial Correlation and Autocorrelation of ResidualsIt follows the same logic as heteroskedasticity and adds time-series tests such as Durbin-Watson.
  5. 5Model Specification and Omitted Variable BiasIt covers bias in the coefficients themselves, which is more serious, and you can compare it with the earlier problems.
  6. 6Outliers, Residual Plots and Model DiagnosticsIt ties everything together as a practical toolkit, so it works best as the final review.

How to prepare Regression Diagnostics

Aim to recognise each problem from a one-line description and recall its effect and fix without hesitation.

  1. Write the OLS assumptions in your own words and note which result each one supports, such as unbiasedness or valid standard errors.
  2. For each problem, build a four-line card: symptom, test, effect on coefficients and standard errors, and remedy.
  3. Practise the short calculations by hand and with your financial calculator: t-statistics, confidence intervals, adjusted R², F-tests and Durbin-Watson interpretation.
  4. Make a comparison table of the problems on paper, showing which ones bias coefficients and which ones only distort standard errors.
  5. Read residual plots and sample regression output until you can name the problem in under a minute.
  6. Do timed mixed questions and review every miss by asking which assumption you confused.
  7. Revisit the chapter a few days before the exam and recite the cards from memory.

Common mistakes in Regression Diagnostics

  • Saying heteroskedasticity or serial correlation biases the OLS coefficients.

    Fix: Remember that these problems usually leave the coefficients unbiased and mainly make standard errors and tests unreliable.

  • Treating multicollinearity as a cause of biased coefficients.

    Fix: Link it to imprecision: large standard errors, unstable estimates and insignificant t-statistics despite a good overall fit.

  • Claiming any omitted variable causes bias.

    Fix: Check both conditions: the omitted variable must affect the dependent variable and be correlated with an included regressor.

  • Using R² to compare models with different numbers of regressors.

    Fix: Use adjusted R², which penalises extra regressors, and remember that R² never falls when a variable is added.

  • Misreading the Durbin-Watson statistic direction.

    Fix: Anchor on 2 as neutral: values well below 2 suggest positive autocorrelation and values well above 2 suggest negative.

  • Deleting outliers automatically.

    Fix: Investigate first. An outlier may be a data error or a genuine observation, and removing genuine ones can hide real risk.

Last-day revision: Regression Diagnostics

  • Heteroskedasticity means non-constant error variance; OLS coefficients stay unbiased but standard errors are unreliable.
  • Robust (White) standard errors are the usual fix for heteroskedasticity.
  • Common tests for heteroskedasticity include Breusch-Pagan and White.
  • Perfect multicollinearity makes OLS impossible; imperfect multicollinearity inflates standard errors.
  • Classic multicollinearity symptom: high R² and a significant F-test but insignificant individual t-statistics.
  • A high variance inflation factor (VIF) or high pairwise correlations point to multicollinearity.
  • Positive serial correlation typically makes standard errors too small and t-statistics too large.
  • Durbin-Watson is near 2 with no first-order autocorrelation, below 2 for positive, above 2 for negative.
  • Omitted variable bias needs the omitted variable to be both correlated with an included regressor and a determinant of the dependent variable.
  • Adding regressors never lowers R², so use adjusted R² to compare models.
  • Outliers can have a large influence on coefficients; investigate before deleting.
  • Residual plots should show no pattern; a funnel suggests heteroskedasticity, a wave suggests autocorrelation.

Regression Diagnostics practice questions

Regression Diagnostics in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Regression Diagnostics: frequently asked questions

Is regression diagnostics a calculation-heavy chapter?

Not mostly. The questions are largely conceptual, asking you to identify a problem, its effect and its fix. Expect some short calculations such as t-statistics, adjusted R² or interpreting a test value.

Which problems bias the coefficients?

Omitted variable bias and other serious misspecification can bias coefficients. Heteroskedasticity, serial correlation and multicollinearity generally affect standard errors or precision instead, though details depend on the model.

How should I split study time across the six topics?

Give extra time to the OLS assumptions, since they underpin everything, and to specification and omitted variable bias, which are subtle. The others are shorter once you have a symptom-effect-fix card for each.

Do I need to memorise test names?

Learn the main ones and what each checks, such as Breusch-Pagan and White for heteroskedasticity and Durbin-Watson for autocorrelation. Understanding the purpose matters more than recalling formulas.