This question is from a book (Active Portfolio Management), but unfortunately there are no provided solutions.
"Assume that residual returns are uncorrelated across stocks. Stock A has a beta of 1.15, volatility=35%. Stock B has beta of 0.95 and a volatility of 33%. If the market volatility=20%, what is the correlation of stock A with stock B? Which has higher residual volatility?"
The slope is related to the correlation coefficient by, m = r( s_B / s_A ), (for s=standard deviation, r is correlation coef), but that's the extent of my knowledge here :-|