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Solve the following.
For the lines of regression 4x - 2y = 4 and 2x - 3y + 6 = 0, find the mean of ‘x’ and the mean of…
For the lines of regression $4x - 2y = 4$ and $2x - 3y + 6 = 0$, find the mean of ‘$x$’ and the mean of ‘$y$’.
Answer
Answer
Mean of x: 3
Mean of y: 4
Both regression lines pass through $(\bar x, \bar y)$, so solve $4x - 2y = 4$ and $2x - 3y = -6$ together.
From the first, $y = 2x - 2$. Substituting: $2x - 3(2x - 2) = -6$, so $-4x + 6 = -6$ and $x = 3$; then $y = 4$.
Hence $\bar x = 3$ and $\bar y = 4$.