Factor score regression (FSR) is a popular alternative for structural equation modeling. Naively applying FSR induces bias for the estimators of the regression coefficients. Croon proposed a method to correct for this bias. Next to estimating effects without bias, interest often lies in inference of regression coefficients or in the fit of the model. In this article, we propose fit indices for FSR that can be used to inspect the model fit. We also introduce a model comparison test based on one of these newly proposed fit indices that can be used for inference of the estimators on the regression coefficients. In a simulation study we compare FSR with Croon's corrections and structural equation modeling in terms of bias of the regression coefficients, Type I error rate and power.