I am trying to interpret the regression coefficients of a covariate in a Bayesian linear regression problem. More specifically, I am trying to determine if the regression coefficient have an important effect on the prediction of the response variable. A discsussion of this can be found here in a Bayesian context (see section 5.2.3).
From my understanding, when the posterior distribution of the estimated regression coefficient is away form the zero, its suggests an important contribution of the covariate to the prediction of the response variable.
Here is the posterior distribution from regression coefficient:
The posterior mean of this distribution is 0.018 and the 95% credible interval is -0.01 and 0.045.
My question is: Since the mean is 0.018 and away from zero, can I say this regression coefficient had an important effect on the prediction/estimation of the response variable ?
Can I say that: Since the zero value lies between the 95% credible interval of the covariate's posterior distribution, then this regression coefficinet DOES NOT have an important effect on the response variable ?
My issue is that I am not sure if to use the posterior mean or the posterior credible interval to determine the effect of a regression coefficient on the dependent variable, i.e., I am not sure which property (i.e., mean or Cred Int.) of the posterior distribution to assess this impact.