Multiple linear regression analysis with a lot of independent variable always makes many problems because there is a relationship between two or more independent variables. The independent variables which correlated each other are called multicollinearity. Principal component  analysis which based on variance covariance matrix is very sensitive toward the existence of outlier in the observing data. Therefore in order to overcome the problem of outlier it is needed a method of robust estimator toward outlier. ROBPCA is a robust method for PCA toward the existence of outlier in the data. In order to obtain the robust principal component is needed a combination of Projection Pursuit (PP) with Minimum Covariant Determinant (MCD). The results showed that the ROBPCA method has a bias parameter and Mean Square Error (MSE) parameter lower than Principal Component Regression method. This case shows that the ROBPCA method better cope with the multicollinearity observational data influenced by outlier.

The research was conducted at BPR in Buleleng Regency, Bali Province which is registered with the Financial Services Authority. The population of this research is BPRs that are registered and report their finances in full at the Financial Services Authority during the 2018-2020 period, as many as 7 BPRs. The number of samples used was 7 rural banks using the saturated sampling method (census). The research data uses secondary data, obtained from the publications of the Financial Services Authority. The data analysis technique used is path analysis to analyze the pattern of relationships between variables and using the Sobel test to determine the role of mediating variables. The results of the analysis and discussion of the study found that NPL and BOPO had a negative and significant effect on ROA, CAR had a positive and significant effect on ROA, NPL had a positive and insignificant effect on CAR, BOPO had a negative and significant effect on CAR, CAR was unable to mediate the effect of NPL on ROA, and CAR is able to mediate the effect of BOPO on ROA. Good management of NPL, BOPO, and CAR will bring maximum profitability, so that the bank's financial performance will be better.