Response surface methodology (RSM) is widely employed for experimental optimization due to its ability to provide a 

transparent quadratic surrogate constructed from a small, designed experiment, which is often suitable for laboratory and 

pilot studies. However, the standard approach of fitting a quadratic model by ordinary least squares and optimizing the 

resulting surface may produce unstable recommendations when the design is ill-conditioned, measurements are noisy, or 

the response is misspecified. In this study, we introduce an uncertainty-penalized quadratic RSM framework that preserves 

the experimental design pipeline while enhancing recommendation reliability. The surrogate model is estimated using 

ridge regression, with the regularization parameter determined by leave-one-out cross validation. A closed-form posterior 

covariance for the coefficients is derived from a Bayesian interpretation of ridge regression, leading to an analytic predictive

variance and an uncertainty estimate across the design region. The recommendation is obtained by minimizing 

a conservative objective that combines the predicted mean with a tunable multiple of the predictive standard deviation. 

Five representative scenarios, including correct specification, mild and strong misspecification, severe ill conditioning, and 

higher-dimensional designs, demonstrate consistent reductions in regret and tail risk metrics, such as the 95th percentile 

regret and conditional value at risk, compared to ordinary least squares.