I have a multi linear regression model with four variables, X1, X2,X3 and X4 that I am analysing to check how they influence Y. I have tested each of the four variables against Y and concluded that X2 is not correlated with Y.
I then tested each of the X variables against each other to check for non linearity and concluded that the only ones that are non linear correlated is X2 with X1, X2 with X3 and X2 and X4.
Now I am bit confused since in the first test I checked that X2 should be taken out the model as it is not correlated with Y, but in the non linear test the only ones that are non linear are the ones with X2, that should not be taken into account.
Can you shed a light on this? I must be doing something wrong as these results don't make sense.