The most important factors that influence biodiesel production are temperature, molar ratio, catalyst amount, time and degree of agitation. This study investigated the effects of temperature, molar ratio and degree of agitation and their interactions on the yield and purity of biodiesel produced from Jatropha oil. Factorial design and response surface methodology (RSM) were used to predict yield and purity of biodiesel as functions of the three variables. Interactions of all the factors were found to be significant on both yield and purity responses. Temperature and molar ratio main effects were found to be significant on the yield whereas only temperature main effect was significant on the purity of the biodiesel. The optimum conditions of operations were; temperature of 54 o C, molar ratio of methanol to oil of 6:1 and stirring speed of 660 rpm. Using these conditions, biodiesel yield of 95% (wt) was obtained with a purity of 97%. This model can be used to predict the yield and purity of biodiesel from jatropha oil within the ranges of temperature (30 – 60C), stirring rate (300 -900 rpm), and molar ratio (3 – 9 mol/mol) studied.