Tumor growth is a complex process involving a large number of biological phenomena. However, at the macroscopic scale, it seems to follow relatively simple laws that have been formalized with the help of mathematical models. Based on experimental data of in vivo syngeneic tumor growth, rigorous quantitative and discriminant analysis of a wide array of these models was performed for description and prediction of tumor kinetics. Detailed analysis of the measurement error was performed that resulted in the design of an adapted statistical model of the variance error quantifying the uncertainty of the data. Combined to several goodness- of-fit criteria and to a study of the numerical identifiability of the models, it allowed quantification of the descriptive power of each model, from which we inferred insights on macroscopic tumor growth laws. Our analysis enlightens one model as particularly relevant, namely the power growth model, which suggests a novel, simple and minimal theory of neoplastic development based on a fractal dimension of the proliferative tissue. Detailed study of the predictive properties of the models reveals variable forecasting power among them and quantifies how far and how precise predictions can be made, based on a given number of data points. In situations where small number of data points is available, we studied the effect of adjunction of a priori information on the statistical distribution of the parameters during the fit procedure. This method revealed very powerful, yielding significant improvement of the forecast performances, for instance from a 14.9% to a 60.2% success rate when predicting future growth based only on three data points and using the power growth model.