Biodiesel is a renewable, carbon neutral alternative fuel to diesel for compression ignition engine applications. Biodiesel could be produced from a large variety of feedstocks including vegetable oils, animal fats, algae, etc. and thus, vary significantly in their composition, fuel properties and thereby, engine characteristics. In the present work, the effects of biodiesel compositional variations on engine characteristics are captured using a multi-linear regression model incorporated with two new biodiesel composition based parameters, viz. straight chain saturation factor (SCSF) and modified degree of unsaturation (DUm). For this purpose, biodiesel produced from seven vegetable oils having significantly different compositions are tested in a single cylinder diesel engine at varying loads and injection timings. The regression model is formulated using 35 measured data points and is validated with 15 other data points which are not used for formulation. The predictions are found to be in good agreement with measurements with a regression coefficient of above 0.9 and an absolute average deviation of less than 5% for all the investigated performance and emission parameters except smoke. Although, the developed regression models could provide only a rough estimate of engine characteristics, they are primarily intended to establish the role of biodiesel composition on engine characteristics using SCSF and DUm. For each of the operating conditions, a correlation matrix analysis is carried out to examine the relative weightage of biodiesel composition, engine load and injection timings on engine characteristics and it is observed that the biodiesel composition effects are more pronounced near full load conditions. Furthermore, optimization studies are carried out using genetic algorithm to suggest optimal SCSF and DUm so as to reduce nitric oxide and brake specific fuel consumption simultaneously with biodiesel, which are obtained as 107.59 and 38.38 respectively. Although the developed regression model is applicable for a particular engine type, similar approach can be extended to any engine type by suitably modifying the correlation coefficients.