# How to interpret constant with different dummy interaction terms?

I would like to analyse the impact of Fund Size on Mutual Fund Performance by using quintiles (based on fund size). My approach is to look at the effect within each quintile to conclude uniformity of the potential effect among all size groups. My initial thought was to use a dummy regression (quintiles=dummies) with interaction terms (dummy*Lagged Fund Size). However, I would like to include a quadratic effect of the Lagged Fund Size as well and use interaction terms. In other words, analysing both the linear and quadratic effect in each quintile by using interaction terms. To avoid multicollinearity, I have to omit one of the quintiles (i.e. dummies) (since excluding the constant term instead results in the omission of one of the interaction terms in both Stata and SPSS).

My questions are the following:

1. How can I interpret the constant term as it includes both the linear and quadratic effect for the omitted dummy? Is it even statistically correct?
2. Ideally I would like to include all dummies hence excluding the constant term to better visualise the effect within each quintile. Is it possible to do this (by for example omitting the general (non-interaction) effect, i.e. either the dummies or the Fund Size effect in the regression)?
3. Are there any other models/regression forms that could avoid this hindrance and analyse the linear and quadratic effect in one regression?

## 1 Answer

1. The constant remains the expected outcome when all explanatory/independent/right-hand-side/x-variables equal zero. So it refers to the expected outcome for the omitted/reference category and when fund size equals and fund size squared equal zero. A potential difficulty would happen when you omitted the indicator variable for the largest quintile, i.e. the quintile that did not contain fund size = 0. So to make sense, you need to carefully center your fund size variable and choose your reference category to correspond with that choice of center.
2. You can do that. You will need to exclude the main effects of fund size and fund size squared. If you also want to include the reference category in the main effect of the quitiles you will have to omit the constant. See e.g. here.