Multiple linear regression

Hello friends,
I have a situation that I don't understand the results:
I'm doing a multiple linear regression with 1 dépendent variable and 4 independent variables 1 VDep e 4 VInd (A, B, C, D)

- The results are clear with them alls:
VindA β = 0.734 p<0.001
VindB β = 0.489 p<0.001
VindC β = 0.285 p<0.05

VindD β = 0.734 p = 0.062 ( so, variable VindD exclued of the model)

But when I perform a linear regression 1 to 1 with VDep and VindD the result is ViD β = 0.453 p < 0.05

Even if I put the variables VindB et VindC within the multiple linear regression with VindD, it is still significative. BUT when I put the VindA, VinD turns non-significative.

Do you have any idea?
Hello, this happens because when A,B,C are in the model what's brought by D is not significant.
Thanks Camille, but do you know why when I put B,C and D they all have significant effects and when I introduce A D becames non significant? Is it a negative moderation effect? ( I am guessing here…)
Hi Gustavo,

First I wouldn't necessarily count p = 0.062 as insignificant ...I don't really see a big difference between 0.06 or 0.05.
I know that people usually use 0.05 as alpha.
Also if you have a good theoretical reason to assume that D should be in the model you probably should keep it even if p=0.2.

But back to your main question, let's assume that p=0.2 and you don't have a good theoretical reason to assume that D should be in the model.

0.548 is a large correlation. but it doesn't necessarily say it is multicollinearity. I recommend you read the following:

A significantly predict Y (VDep ).
If the part that predicts Y in D has a high correlation to the part that predicts Y in A adding D to the model will not improve the prediction.
That why D is not significant in the model with A, B, C, D.

Or it may be more complex the part that predicts Y in D already included in the combination of A,B,C.

Is all clear now?