Question

In: Statistics and Probability

How does a simple linear model using one continuous predictor change if we add an interaction...

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?

Expert Solution

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.

orchestra answered 2 years ago

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