Dear Stephen,

thank you for your answer. However, I of course did the hierarchical regression analysis first, and then normal linear regression with just these 2 variables (X and M) and criterion (Y). I even tried with Bootstraping method, since it's used in mediation analysis. And X doesn't contribute to the explanation of the criterion, just the M. That should indicate that direct effect (X and Y) is insignificant, but is quite large I would say.

Should I neglect the results of bivariate correlation and regression analysis?

Both variables interact with the third variable which lacks in bivariate correlation

Beta ponder is insignificant in case of the first variable, but significant in case of other (which was later used as a mediator). I also created an interaction variable and its beta ponder wasn't significant.

Yes, hierarchical regression analysis, in three steps.

It's probably very late but here is an answer from Zhao X et al. Reconsidering Baron and Kenny: Myths and Truths about Mediation Analysis. Journal of Consumer Research. 2010;37(2):197–206.

https://www.jstor.org/stable/10.1086/651257?seq=1#metadata_info_tab_contents

NO NEED FOR AN “EFFECT TO BE MEDIATED” The starting point for Baron and Kenny’s (1986) analysis is to establish first that there is a significant zero-order effectof the independent variableX(often an experimental ma-nipulation) on the dependent variableYin equation 2. This“X-Ytest” has been labeled the “effect to be mediated”(Collins, Graham, and Flaherty 1998; Judd and Kenny 1981;Kenny 2003; Kenny, Kashy, and Bolger 1998; Preacher andHayes 2004). It seems intuitive that, without an effect to be mediated, there is no point in further investigating whether the effect of X on Y is in fact mediated by M. It is for thisreason that advisors think they are helping their students by telling them to wait until they have established a zero-ordereffect ofXonYbefore hunting for mediation.This intuition is wrong. There need not be a significantzero-order effect ofXonY,rXY, to establish mediation. WhatBaron and Kenny (1986) and most users of their tests there-after have missed is that the zero-order effect ofXonYisin fact mathematically equivalent to the “total effect” ofXonYin figure 1.′cp(a#b)+c.(5)That is, it exactly equals the sum of the “indirect path” (patha#pathb, usually hypothesized) and the “direct path”(pathc, usually not hypothesized, as just discussed).Ifcanda#bare of the same sign,will have the′csame sign. We call this complementary mediation if boththe indirect patha#band the direct pathcare significant.In such a situation, theX-Ytest is superfluous since it willpass any timea#bandcare significant.But ifcanda#bare of opposite signs—what we willcall competitive mediation if both paths are signifi-cant—thencan be close to zero and theX-Ytest may fail.