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Question
From the two regression equations y = 4x – 5 and 3x = 2y + 5, find `bar x and bar y`.
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Solution
Given two regression equations are
y = 4x - 5
i.e., – 4x + y = –5 …(i)
and 3x = 2y + 5
i.e., 3x – 2y = 5 …(ii)
By (i) × 2 + (ii), we get
- 8x + 2y = - 10
+ 3x - 2y = 5
- 5x = - 5
∴ x = 1
Substituting x = 1 in (i)
-4(1) + y = - 5
∴ y = 4 - 5 = - 1
Since the point of intersection of two regression lines is `(bar x, bar y)`,
`bar x = 1 and bar y = - 1`
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