See this answer by amoeba.
This site and this site make it clear that the partial R-squared (also known as the coefficient of partial determination) can be used to assess the goodness of fit of a reduced multiple linear regression model as compared to a full(er) model.
The partial R-squared gives the proportion of variation explained by the explanatory variables in the full(er) model that cannot be explained by the explanatory variables in the reduced model. If the reduced model is a good fit compared to the full(er) model, then it will have a low partial R-squared.
EDIT: Please note that I just learned about this topic to answer this question because I had never heard of it before.