Coarse-grained molecular dynamics (CG-MD) simulations and subsequent persistent homology (PH) analysis were performed to correlate the structure and stress-strain behavior of polymer films. During uniaxial tensile MD simulations, the first principal component of the persistence diagram obtained by principal component analysis (PCA) was in good agreement with the stress-strain curve. This indicates that PH + PCA can identify critical ring structures relevant to the dynamic changes in MD simulations without requiring any prior knowledge. Inverse analysis of the persistence diagram revealed that smaller rings with ten or fewer CG beads mainly contribute to changes in the first principal component of the persistence diagram. This is due to the properties of the poly(ethylene oxide) chain, which favors the formation of a seven-membered helical structure during the self-entanglement process. The PH + PCA approach successfully reproduced the stress-strain curves for polymers with different nonbonding interactions and bond lengths. Moreover, the changes in the yield stress of each polymer film were qualitatively explained by the ring distribution in the persistence diagram. These results suggest that persistent homology analysis followed by PCA provides a versatile and powerful framework for correlating structural features with physical properties, such as ring distribution and stress-strain behavior in polymer films.