From Mary Jannausch · University of Michigan on researchgate.net
#R^2#, the coefficient of multiple determination, is defined as #(SS_(REG))/(SS_(TOTAL))# or, equivalently, #1 - (SSE)/(SSTO)#. #R^2# measures the proportionate reduction in variation of Y, associated with the set of X predictors. #R^2# will be inflated as more X variables are added. The adjusted #R^2# was therefore derived, as #R_(adj)^2 = 1 - {[(n-1)/(n-p)][(SSE)/(SSTO)]}#.
[If] (...), n=60, p=10. so, (n-1)/(n-p) = 59/50 = 1.18, and you have
#R_(adj)^2 = 1 - (1.18)(SSE)/(SSTO)#. If the ratio #(SSE)/(SSTO)# is close enough to 1, then you can see how the #R_(adj)^2#. can be negative. [In which case it can be interpreted as zero.]
[If negative] (...); you have too many predictors chasing too little information (a la small n). Just because one can run a model with n=60, and 10 predictors, does not mean that one should.
