Cell phones, nowadays, are used for not only making phone calls and sending messages but also for entertainment. Mobile-based games of various kinds are instrumental in acting as a source of entertainment. Player enjoyment is one of the major motivations in playing any kind of mobile game. The first model proposed for player enjoyment was Flow, which used eight different elements of enjoyment. GameFlow, a later model, was derived through mapping with the Flow model. Each element of GameFlow consists of a set of criteria for experiencing enjoyment while playing mobile games. Prediction of mobile games' rating using aspects of player enjoyment can be extremely beneficial to mobile game designers. This work first provides a Regression-Based Rating Prediction Model (RBRPM) for Android-based puzzle games using elements of the GameFlow model. RBRPM is derived by applying Forward Stepwise Multiple Linear Regression on a data set consisting of 80 puzzle games. The data set is compiled by playing these games considering the criteria of all elements of the GameFlow model. RBRPM relies on five predictors, namely feedback, social interaction, concentration, clear goals, and player skills for predicting a games' rating. Next, this work extends RBRPM by including not only additional criteria in the already identified elements but also adds three new elements i.e. fantasy, mystery, and thrill. The improved model (IRBRPM) uses 8 predictors. MMRE and PRED(x) are used as prediction accuracy metrics for assessing this model and K-fold cross-validation is used for model validation. These two steps provide encouraging results.