The adjusted R^2 is not what indicates the quality of a result, but rather the p-value...R^2 indicates an effect size, whereas p-value indicates significance. A small R^2 just means there are other things that should be in the model.

- P-value is the result of a hypothesis test with the question being "is this effect size 0". The p-value is the probability of seeing the observed data under the assumption of the effect being zero.

- The R^2 is a measure of how well the regression model 'explains' the observed data so to speak.

- The effect size is contained in the coefficients assuming near perfect independence between the variables