Hi Sourav,

the p-value measures the difference of the regression coefficient B from zero. If the p-value gets smaller, hence, B has become larger. If B is positive this happens because either a) the correlation between X1 and X2 [X3] is negative and the X2-effect [X3 effect] is positive or b) the other way around. Chains of coefficients form "paths" and their magntitude is the product of all parts of the chain. If you remove X2 [X3] then the magnitude of their path is added to the B of X1.

Search for path tracing.

HTH

Holger

When you add control variables to your regression (x2, x3, say), the coefficient for x1 will (most probably) change in magnitude if x1 is correlated with x2 and x3 and x2 and x3 has an effect on y. For this reason, the standard error of x1's coefficient will change and so will x1's t-value and p-value. BR, Chris

You should not compare p-values of variables that are part of different models. If you include or exclude variables, you change the entire model and with this also the interpretation of the estimates in the model. This, by the way, is one reason why all these automated variable-selection precedures (foreward, backward and whatever) are not good, because they don't do at all what you (usually) expect them to do.

But even if it would make some sense in your case that the estimate of X1, given X2, X3, and X4 are in the model and are all zero, is comparable to the estimate of X1 in a different model, given X2, X3, X4 and also X5 are in the model and are all zero, X5 may explain some variance of Y that can also be explained by X1. This is called co-linearity. The model can not decide which variable is reponsible for the total amount of variance explained, so it "shares" the (un-)certainty between both variables. Another reason not to judge the importance of a variable in a model by its p-value (like in variable selection procedures).