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Question
The equations of the two lines of regression are 6x + y − 31 = 0 and 3x + 2y – 26 = 0. Calculate the mean values of x and y
Solution
Given equations of regression are
3x + 2y – 26 = 0
i.e., 3x + 2y = 26 ......(i)
and 6x + y – 31 = 0
i.e., 6x + y = 31 ......(ii)
By (i) – 2 × (ii), we get
3x + 2y = 26
12x + 2y = 62
– – –
– 9x = – 36
∴ x = `(-36)/(-9)` = 4
Substituting x = 4 in (ii), we get
6 × 4 + y = 31
∴ 24 + y = 31
∴ y = 31 – 24
∴ y = 7
Since the point of intersection of two regression lines is `(bar(x), bar(y))`,
`bar(x)` = mean of X = 4,
and
`bar(y)` = mean of Y = 7
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