Let X and Y be two related variables. The two regression lines are given by x - y + 1 = 0 and 2x - y + 4 = 0. The two regression lines pass through the point:

  1. (-4, -3)
  2. (-6, -5)
  3. (3, -2)
  4. (-3, -2)

Answer (Detailed Solution Below)

Option 4 : (-3, -2)
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Detailed Solution

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Concept:

The two lines of regression coincide and both pass through the common point (x̅, y̅). 

Where (x̅, y̅) is the point of intersection of the two regression lines.

 

Calculation:

Given two regression lines are

x - y + 1 = 0               .... (1)

2x - y + 4 = 0             .... (2)

Subtracting equation (2) from (1), we get

⇒ (2x - y + 4) - (x - y + 1) = 0 - 0

⇒ x + 3 = 0

∴ x = -3

Put the value of x in equation (1), we get

⇒ -3 - y + 1 = 0

∴ y = -2

Hence two regression lines pass through the point: (-3, -2)

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