# Max and min value of coefficient of determination

I have two questions: 1) What is the maximum and minimum possible values of $R^{2}$ for fitting a straight line? and 2) List all possible cases such that $R^{2}$ achieve max/min . I know $0\leq R^{2}\leq 1$. So max = 1 and min = 0. But how can i find all possible cases that makes $R^{2}$ achieve max or min? thanks

• What do you mean by 'all possible cases'? My interpretation of the term would suggest an infinite number of cases in each. Is it that you need to figure out how it relates to the correlation? – Glen_b Feb 16 '13 at 9:46
• thanks. seriously i am also lost on the question. maybe can you suggest your own best possible answer? thanks – dorothy Feb 16 '13 at 9:58
• Are your max and min constrained by a particular set of x values or are you asking about a universal max and min, regardless of x values? The latter case is particularly simple--you need to understand only the most basic properties of R^2 (or of correlation). The former is not much more difficult but requires some knowledge of ordinary least squares theory. – whuber Feb 16 '13 at 11:35
• is there any good reading materials regarding R^2 and R that I can research on, particularly going in depth on the maths behind R^2, R? thanks – dorothy Feb 17 '13 at 3:09