R^2 of 10% means 10% of the variance in one variable is accounted for by the linear regression on the other variable. That is, the expectation of the conditiona

R^2 of 10% means 10% of the variance in one variable is accounted for by the linear regression on the other variable. That is, the expectation of the conditional variance (the amount of variance left after using the information from the linear regression) is 90% of the unconditional variance. A p-value of 0.01 means that under the null hypothesis (generally that the variables are independent), a result at least this extreme (in this case, with at least this large a correlation) would be seen 1% of the time. Note in general that R^2 = 10% does not imply p = 0.01, nor the converse. They are largely unrelated measures. In principle one could have a small correlation with high significance, or a large correlation with low significance.