Folks, In linear regression, I am looking to understand why the coefficients of a given independent variable (HS_ENGL in this example) would change as other independent variables are added (SAT_VERB SAT_QUAN).

So if I create a model with just HS_ENGL as the predictor, it comes up as significant. As I add additional variables, its coefficient drops + it becomes less significant.

I think if the 3 independent variables had been perfectly orthogonal, then HS_ENGL would have remained the same through the models. So the first thing I did was compute the VIF and got the following. All low values.

HS_ENGL SAT_VERB SAT_QUAN 1.839065 1.300852 1.918336

Next I plotted the correlation between them as below; focus on bottom 3 variables. Hence despite the fact that the VIF were low, the variables are correlated as shown below.

Is this the reason for change in the coefficient of HS_ENGL? Also could there be other possible reasons like 'interaction terms'?...I have not learned about these in any detail yet.


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