It does show you a postivepositive correlation, since \hat{\beta} = cov(y,x) / var(x) $\hat{\beta} = cov(y,x) / var(x)$ and var(x) can neven benever be negative. (Replace x with a partialled out x in case you have a multivariate linear regression.)
I heavily advise to recapreview the basics of linear regression.