Question

1. How does a simple linear model using one continuous predictor change if we add an interaction term with an indicator variable, but don’t include the indicator variable on its own?

Answer 1

Let us define

y:Dependent variable

x:Independent continuous variable

w:Indicator variable

So let model 1 be the model with just continuous variable

Now let model 2 be model with continuous variable as well as interaction term

Where w is the indicator term that it it takes only 2 values 0 and 1

When w=1 model 2 reduces to

And when w=0, model 2 reduces to

It can be observed that in case when w=0 model 2 is reduced to model 1.

But in case when w=1 model 2 has the same intercept as that of model 1 but the slope has changed.

So model two will have 2 lines with sae intercept but different slope, 1 of them being same as that of model 1.

Hence this is how the model changes when an interaction term is added to it.