FRM Exam Part I · Linear Regression

Dummy Variable Regression Interpretation for FRM Part I

Updated 11 October 2026 · Fact-checked

A dummy variable is a 0/1 regressor that flags a category. Its coefficient is the average difference in Y between that category and the omitted base group, holding other regressors fixed. To interpret output, read the units of Y and X, the functional form, the sign, and the t-statistic.

Understand Dummy Variables and Regression Interpretation

A dummy variable (binary regressor) takes the value 1 if an observation is in a category and 0 if not. Examples: a crisis period, a bank with a high rating, or a month such as January. It lets a regression handle qualitative information.

In Y = b0 + b1·D + e, b0 is the mean of Y when D = 0 (the base group). b1 is the difference in mean Y between D = 1 and D = 0. The dummy shifts the intercept. It does not change the slope on other variables.

If a variable has k categories, include only k − 1 dummies when the model has an intercept. Including all k creates perfect multicollinearity, the dummy variable trap, because the dummies sum to the intercept column. OLS cannot be estimated. Each dummy coefficient is then measured against the omitted category.

An interaction term multiplies two regressors, for example Y = b0 + b1·X + b2·D + b3·(D·X) + e. Now the slope on X is b1 when D = 0 and b1 + b3 when D = 1. The intercept is b0 when D = 0 and b0 + b2 when D = 1. The coefficient b3 tests whether the slopes differ between groups.

Interpretation depends on units and functional form. In a linear model, a one-unit rise in X changes Y by b1 units. In a log-linear model (ln Y on X), a one-unit rise in X changes Y by about 100·b1 percent. In a linear-log model (Y on ln X), a 1% rise in X changes Y by about b1/100 units. In a log-log model, b1 is an elasticity: a 1% rise in X changes Y by about b1 percent. Always add the phrase 'holding other variables constant' in multiple regression.

Key formulas to remember

Dummy regression: Y = b0 + b1·D + e; b0 = mean of Y for D = 0 (base group); b1 = difference in mean Y, D = 1 minus D = 0.
Dummy trap rule: Number of dummies = k − 1 (with an intercept); Using k dummies plus an intercept gives perfect multicollinearity.
Interaction model: Y = b0 + b1·X + b2·D + b3·(D·X) + e; Slope on X: b1 if D = 0, b1 + b3 if D = 1. Intercept: b0 if D = 0, b0 + b2 if D = 1.
Linear model: ΔY = b1 × ΔX; Units of b1 are units of Y per unit of X.
Log-linear model: ln Y = b0 + b1·X; %ΔY ≈ 100 × b1 × ΔX; Approximation is good for small b1. Exact change is e^(b1·ΔX) − 1.
Linear-log model: Y = b0 + b1·ln X; ΔY ≈ b1 × (%ΔX ÷ 100); A 1% rise in X changes Y by about b1/100 units.
Log-log model: ln Y = b0 + b1·ln X; %ΔY ≈ b1 × %ΔX; b1 is an elasticity.
t-statistic for a coefficient: t = (b̂ − hypothesized value) ÷ SE(b̂); Usually tests whether the coefficient is zero. About |t| > 1.96 is significant at 5% for large samples.

How to solve Dummy Variables and Regression Interpretation questions

Use this routine for any question that gives a regression equation or an output table and asks what a coefficient means or what the model predicts.

1Write the model and identify the form: level, log-linear, linear-log or log-log. Note the units of Y and each X.
2Identify every dummy and its base group (the category with all dummies equal to 0).
3Check for the dummy trap: with an intercept, k categories should have k − 1 dummies.
4Interpret the coefficient of interest using the form rule, and add 'holding other variables constant'.
5If an interaction is present, compute the slope or intercept for each group by adding the relevant coefficients.
6For significance, compute t = coefficient ÷ standard error and compare with the critical value, or use the p-value given.
7For prediction, substitute 0 or 1 for the dummies and the given X values, then compute Y (or convert from ln Y using the exponential).
8Check that the answer carries the right units and sign before choosing an option.

Quickest way: Plug in the groups and read the form

When to use it: When the question gives an equation with dummies or interactions and asks for a difference, a slope, or a prediction.

Set the dummy to 0 and write the resulting equation. Set it to 1 and write the second equation.
Subtract the two equations. The difference is the dummy effect (plus any interaction times X).
Read the log form: a log Y means percent change in Y; a log X means percent change in X.
Divide the coefficient by its standard error to get t. Compare with about 2 for a quick significance call.

Common mistakes in Dummy Variables and Regression Interpretation

Including a dummy for every category along with an intercept.
It feels complete to code every group.
Fix: Drop one category as the base group. With k categories use k − 1 dummies. Interpret each against the base.
Reading a dummy coefficient as an absolute level instead of a difference.
Students forget the omitted group sets the intercept.
Fix: State it as 'average Y is b1 higher than the base group, other variables fixed'.
Using only b1 as the slope when an interaction is present.
The interaction coefficient is easy to overlook.
Fix: Slope for the D = 1 group is b1 + b3. Test b3 to see whether slopes differ.
Treating a log-linear coefficient of 0.04 as a 0.04 unit change in Y.
Ignoring that Y is in logs.
Fix: Multiply by 100: about a 4% change in Y per one-unit rise in X.
Confusing the log-linear and linear-log rules.
Both have one log, and the rules sound alike.
Fix: The logged variable is measured in percent. Log Y means percent change in Y; log X means percent change in X.
Calling a coefficient significant because it is large.
Size is mistaken for precision.
Fix: Judge significance with t = coefficient ÷ standard error or the p-value, not the coefficient's size.

Worked examples

Example 1

A regression of monthly bond fund return (in %) on a dummy for a crisis month (1 = crisis, 0 = otherwise) gives: Return = 0.60 − 1.90·Crisis. The standard error of the crisis coefficient is 0.80. (a) What is the mean return in crisis months? (b) Is the crisis effect significant at 5% (critical value about 1.96)?

Show the solution

Crisis = 0 gives mean return = 0.60%.
Crisis = 1 gives 0.60 − 1.90 = −1.30%.
t = −1.90 ÷ 0.80 = −2.375.
|−2.375| > 1.96, so reject the null that the effect is zero.

Answer: (a) Mean crisis-month return is −1.30%. (b) Yes, t = −2.375 is significant at 5%.

Example 2

A model of loan spread in basis points on loan size in USD millions (Size) and a dummy for secured loans (Sec = 1 if secured) is: Spread = 150 + 4·Size − 30·Sec − 2·(Sec·Size). What is the predicted spread for an unsecured USD 10 million loan and for a secured USD 10 million loan, and what is the slope on Size for secured loans?

Show the solution

Unsecured (Sec = 0): Spread = 150 + 4 × 10 = 190 bp.
Secured (Sec = 1): Spread = 150 + 4 × 10 − 30 − 2 × 10 = 150 + 40 − 30 − 20 = 140 bp.
Slope on Size for secured loans = 4 + (−2) = 2 bp per USD million.

Answer: Unsecured: 190 bp. Secured: 140 bp. The slope on Size for secured loans is 2 bp per USD million.

Exam tips

Always find the base group first. Most dummy questions turn on what the omitted category is.
If a question lists dummies for every category plus an intercept, the answer is usually perfect multicollinearity.
For log models, locate which variable is logged before touching the numbers. Then apply the percent rule.
In interaction questions, write out the two group equations. It takes ten seconds and avoids sign errors.
When reading an output table, compute t = coefficient ÷ standard error yourself if the t-statistic is not shown.

Practice questions from Linear Regression

Dummy Variables and Regression Interpretation in other exams

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

CFA Level IIDummy Variables in Multiple Regression

Dummy Variables and Regression Interpretation: frequently asked questions

What is the dummy variable trap?

It is perfect multicollinearity caused by including a dummy for every category along with an intercept. The dummies add up to the constant column, so OLS cannot separate them. Drop one category to fix it.

How do I interpret a dummy variable coefficient?

It is the average difference in Y between the group coded 1 and the base group coded 0, holding other regressors constant. Its t-statistic tests whether that difference is zero.

How do I interpret a log-linear regression?

When ln Y is regressed on X, a one-unit rise in X changes Y by about 100 × b1 percent. The approximation works best when b1 is small.

What does an interaction term tell me?

It shows that the effect of one variable depends on another. With a dummy interaction, the coefficient is the difference in slope between the two groups.