The aim of this research is to increase the accuracy of estimating environmental standards by starting to fix fixed effects by using Principal Component Analysis (PCA) as an alternative approach to analyzing the studied traits and solving the problem of multicollinearity, with the possibility of identifying an appropriate and more accurate model for predicting milk production and thus obtaining an increase in economic return. Number of records 2067 in Holstein Friesian (HF). Studied traits were Total milk yield (TMY, kg), lactation period (LP), Calving interval (CI), Dry period (DP) and Days open (DO); day. Methods: The factor program of SPSS statistical package was used for the principal component analysis (PCA). It was found that for all studied traits; the first 2 principal components(PC) explained more than 82% of the total variation . Multiple regression models were: TMY=2331.34+4.96LP+0.98CI+2.01DP+2.04DO. To predict the increase in the amount of TMY, the multiple regression (MR) model was used variables LP, CI and DP.  The obtained equations for (PCA) were written as:PC1=0.533 LP+0.272 CI- 0.226DP+ 0.407 DO, PC2 = 0.019 LP+0.551 CI+ 0.581 DP- 0.035 DO. Regression equation for PCA scores as: TMY = 4726.12+433.30 PC1+ 179.83 PC2 ,(PC1& PC2) used as predictors with (TMY); increasing TMY would be expected to increase with increasing PC. The present results showed that instead of (MR) analysis use of (PCA) in (MR) analysis might offer a good opportunity without multicollinearity problem for predicting TMY  of HF