Question

how can regression analysis be used to determine causality?

Answer 1

Causality- This means the cause and effect relation. For example, An egg is dropped from table(it is cause) and due to to fall from table egg is broken(that is effect).And in the world of modern physics many theories are actually based on the causality.

Now, when it comes to be determine the causality in the regression analysis.It is very simple to identify/determine the cause and effect in regression equation.

We know the regression equation is something like given below:

y=b₀+b₁x+e ; where, e is considered as error term and b₀ & b₁ be coefficients.

And y be the dependent variable as you can see in the equation.

Now, here comes to determine the causality in the regression , it is simply define as that if any thing occurs with x(cause) then it will affect the y(effect).

But it is not necessary that causality always be determine by using regression analysis because causality is cause and effect relation and if x wouldn't occur then y will also be not occur which is not applicable in real life.

Now, there's a fun fact and this could be explain with many examples but this one i am going to explain is deeply into the laws of physics,

Have you ever heard of time travel,of course in sci-fi movies but is it possible according to physics it broke many laws of physics which we know if the theory of time travel could be true.

Time travel could be possible if you can travel with the speed of light but there's a catch that nothing in the universe faster than light.

Simply come to the point, the one of the law it will break is the causality (that cause and effect relation).Now the question arises that how is it even related to the determining the causality through regression, yes it is. Just like i have explained above that if x never occur then y will not be occur as well, so if time travel is possible(theory of general relativity proves that it is possible) then consider y be your future and x be your present.

So, according to regression analysis generally if x occur then y will be affected but in our case we can do time travel so anything we do in future can also be affected the x but when y occurs at that x didn't occured which broke the causality rule.This can also happen due to time dilation, there are many examples in physics like that which represents that regression doesn't always imply the causality.