If r is the coefficient of correlation between x and y, then what is the correlation coefficient between (3x+4) and (-3y+3)?

Explanation

If a new set of variables is defined as u = ax+b and v = cy+d, the correlation coefficient between u and v is given by r_{uv} = \frac{ac}{|ac|} r_{xy}. Here a = 3 and c = -3. Since ac = -9 is negative, the sign of the correlation coefficient is reversed. Thus, the new correlation coefficient is -r.

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