<p>The aim of this paper is to develop a transformed function on the scalar regression model, using the functional principal components to account for random distribution. This framework allows us to model functions transformed from random distributions by using the functional principal components approach in a transformed functional space, and then to regress functional principal component scores on multiple sets of predictors in their projected space. Thereby, we can estimate the underlying model parameters as well as the effect of the covariates in the projected space. Then, these parameters are transformed back to the original distributional space to understand the subject-specific random distributions. We also conduct hypothesis testing and predict random distributions for any given predictors. We demonstrate the advantages of our proposed approach through simulation studies, as well as through application to daily observed temperatures contained in Canadian climate dataset, relating annual temperature distributions to predictors for obtaining various summary of temperatures over many years and sites.</p>