The line of regression of y on x is, 4x − 5y + 33 = 0 and the line of regression of x on y is, 20x − 9y − 107 = 0, then the value of x when y = 7 is ______.

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The line of regression of y on x is, 4x − 5y + 33 = 0 and the line of regression of x on y is, 20x − 9y − 107 = 0, then the value of x when y = 7 is 8.5. Explanation: The regression line of x on y is 20x − 9y − 107 = 0 We can write it as, 20x = 9y + 107 $\Rightarrow$ x = $\frac{9}{20}$y + $\frac{107}{20}$ x = (9 $\times$ 7)/20 + $\frac{107}{20}$ ...[∵ y = 7] x = 8.5 $\therefore$ Option 8.5 is correct.

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