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Q) A study is performed on a sample of residential homes to discover whether the size of the monthly heating bill depends on the type of fuel or the type of home. In particular, three types of fuel are examined: electric, natural gas, and oil. Also, all homes are classified into two types: those on a single level and those with at least two stories.

What might an interaction effect look like in this situation? Intuitively, do you think there is any reason to expect an interaction effect?

An interaction effect is the simultaneous effect of two or more independent variables on at least one dependent variable in which their joint effect is significantly greater (or significantly less) than the sum of the parts (Lavrakas, 2008).

The main effect is the effect of one of just one of the independent variables on the dependent variable (Chesnutt, 2020). An interaction effect occurs if there is an interaction between the independent variables that affect the dependent variable (Chesnutt, 2020).

Here the independent variable is the monthly heating bill and dependent variables are types of homes (single-level and at least two stories) and type of fuel (electric, natural gas, and oil). Here the main effects are the effect of types of fuel on the monthly bill and the effect of the types of homes on the monthly heating bills. In this case, we can assume that the larger the houses the more will be the heating expenses.

There is not any combined effect of the types of heat and the type of the house on the monthly bill of different heating systems i.e. electric, natural gas, and oil.

We can expect an interaction effect in this case. The type of fuel that a household uses for heating definitely depends on the type of home, which in turn will be a function of the income level of the homeowners. But in reality, there is not any interaction effect in this scenario. However, if we try to plot the interaction between the different houses and the different types of heating systems, then it is expected to have parallel lines. This shows that there is no interaction effect on the monthly size of the heating bill and the types of houses.