Some observed phenomena are qualitative rather than quantitative and thus cannot be measured on a continuous scale. For example, an individual's income might depend on whether the person possesses a college degree. Dummy variables are specially constructed variables that indicate the presence or absence of some characteristics. They assume a value of 1 or 0, depending upon whether a certain characteristic is present.

An intercept dummy adds to or reduces the original intercept if a specific condition is met. When the intercept dummy is 1, the regression line shifts up or down parallel to the base regression line.

A slope dummy allows for a changing slope if a specific condition is met. When the slope dummy is 1, the slope changes to (d_j + b_j) × X_j, where d_j is the coefficient on the dummy variable and bj is the slope of X_j in the original regression line.

Suppose the salaries of employees at a particular research institute depend on seniority (or number of years employed at the institute), whether the employee has a Ph. D. degree, and other random factors.

Suppose we express the relationship between the variables in terms of the following multiple regression model:

E(Y_t | X_t, Z_t) = β₀ + β₁X_t + β₂Z_t

where

• Y = salary in dollars
• X = years in seniority
• Z = 1 if individual has a Ph. D, or 0 if individual does not have a Ph.D.

Suppose the t-th individual has seniority of X_t years and does not have a Ph.D. Thus, the variable Z assumes the value 0. The expected salary would be E(Y_t | X_t, Z_t = 0) = β₀ + β₁X_t.

A person who has a Ph.D and the same seniority of Xt years would have an expected salary of E(Y_t | X_t, Z_t = 1) = β₀ + β₁X_t + β₂.

Suppose β₀ is $15,000, β₁ is $1,000, and β₂ is $2,500. The expected salary of a non-Ph.D. with X_t years of seniority would be E(Yt | Xt, Zt = 0) = 15000 + 1000Xt. The constant β0 = $15,000 represents the starting salary, and the coefficient β1 = $1,000 represents the annual salary increment.

The expected salary of a Ph.D. with Xt years of seniority would be E(Y_t | X_t, Z_t = 1) = 15000 + 1000X_t + 2500. The coefficient β₂ = $2,500 represents the effect of having the Ph.D as opposed to not having the Ph.D and indicates that a person who has a Ph.D. earns, on the average, $2,500 more per year than a person with the same seniority who does not have a Ph.D. Thus testing the hypothesis that β₂ = 0 is equivalent to testing the hypothesis that there is no difference between the salaries of Ph.D.'s and the salaries of non-Ph.D.'s.