Q.If every plotted point on a scatter diagram of two variables $X$ and $Y$ lies exactly on a single straight line sloping downward from left to right, the correlation between $X$ and $Y$ is:

Every point lying exactly on a straight line is the definition of perfect correlation; the direction of the slope fixes the sign. …

Why (c) is correct: when every observed point lies exactly on a straight line, the correlation is perfect ($|r|=1$), since there is no scatter/deviation from the line at all. The line slopes downward (as $X$ increases, $Y$ decreases), which is the defining pattern of negative correlation. Perfect + negative together give exactly $r=-1$. …

Correctly identifying 'perfect correlation' but then picking $r=+1$ without checking the direction of the slope; assuming a scatter diagram can never by itself fix the exact value of $r$ (true i …