Sample Question #66 (statistics)

We have a simple univariate linear regression model which we estimate by OLS:

*y = α + βx + ε*

Now, what would be the reason why we don’t run a reverse regression like this:

*x = η + φy + μ* ?

In other words, if the first equation is valid, why isn’t the second equation?

(Comment: this is a relatively easy question, but many people are confused about why and when a variable should be the dependent variable and why and when another variable should be an independent variable)

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If the 1st equation is valid, that means x and ε satisfy the OLS conditions. When you revert the relationship, y and μ cannot also satisfy the OLS conditions. More specifically, y is not an exogenous variable, so you can’t have the 2nd relationship.