In a multiple regression model used for ANOVA with four populations, how many dummy variables are needed to indicate treatments?

In a multiple regression model designed to analyze variance (ANOVA) with four populations, dummy variables are employed to represent the categorical treatments. The general rule for the number of dummy variables needed is to take one less than the number of categories or groups being compared. This is because the last category can be represented as a baseline or reference group, which does not require a separate dummy variable.

In this scenario, there are four populations. By using the formula of one less than the number of groups, we find that three dummy variables are sufficient to represent the four populations. Each dummy variable indicates the presence or absence of one of the populations, allowing the model to assess the impact of the treatments across the groups while avoiding redundancy and multicollinearity.

Thus, the correct answer is based on the reasoning that to capture all four treatments, only three dummy variables are necessary in addition to the intercept, which stands in for the omitted fourth group's baseline level.