Question

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 ______.

Options

• 8.5

• −8.5

• 0.5

• −0.5

Answer 1

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

⇒ `x = 9/20y + 107/20`

x = `(9 × 7)/20 + 107/20`      ...[∵ y = 7]

x = 8.5

∴ Option 8.5 is correct.