Question

Consider Regressions I and II. Regression I: Heating Cost = a + b1*House Size + b2*Insulation + e. Regression II: Heating Cost = a + bInsul*Insulation + e. Suppose the true regression equation (for this question) is Regression I. However, suppose House Size and Insulation are correlated, and we run Regression II. The estimator for our slope coefficient bInsul consists of what two specific effects? (Use actual variable names. This is not an “interpret the slope” question.)

Answer 1

Regression 1:

Regression 2:

Now, the true regression equation is regression 1.

However, as house size and insulation are correlated, we can run regression 2.

So, the estimator for our slope coefficient binsul, consists of two specific effects. They are

i) Main effect of insulation

ii) Interaction effect of house size and insulation

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