This study focuses on regression estimation and variable selection based on target data, while incorporating information from coefficient estimates obtained in related studies. A weighted combination of these estimates may agree with some target effects but differ from others. We propose Transfer Regression with Adaptive Credibility Estimation (TRACE), a Bayesian method requiring only fitted coefficients and sample sizes from source studies. TRACE learns simplex-constrained source weights shared across variables. Separate latent indicators determine target inclusion and whether each coefficient is guided by the weighted source estimate. We develop an approximate collapsed variational expectation-maximization algorithm with robust source-weight initialization. Under suitable conditions, consistency of variable selection, transfer decisions, and source-weight estimation is established. These results hold at every prespecified fixed iteration in fixed dimension and at global mean-field optima of the exact collapsed variational objective as the dimension grows. Simulations show that TRACE achieves competitive variable-selection performance under different patterns of source heterogeneity. An application to data from the Genotype-Tissue Expression project illustrates its use in cross-tissue gene-expression prediction.

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