This chapter is focused on the study application of central composite design, in response surface methodology. We have reviewed this concept and applied it to optimize Biodiesel yield from transesterification of methanol and vegetable oil with a catalyst derived from eggshell using design expert 13. This optimization was carried out with reaction conditions of reaction time, methanol to oil ratio, catalyst loading, and reaction temperature. Data used as an instance was collected and analyzed from the work of Tshizanga et al. and the result obtained for a randomized experiment showed at a 95% confidence level that all the factors affected the product’s output. About 91% yield was obtained and operating parameters were optimized at a temperature of around 61%. Methanol to oil ratio of 22.13, and catalyst loading of around 3.7 wt%. This chapter provided a step-by-step guide on how to carry out this experiment using design expert 13, a reduced Quadratic model with a significant P-value of 0.0325 shows the model is significant, as indicated by an f-value of 3.57. An F-value might be caused by noise only in 3.25% of cases. The run was reduced to 18 compared to the 20 runs originally used by Tshizanga et al.