Discussion
In a partially destroyed laboratory record of an analysis of correlation data, the results only are legible as variance of X = 9 and regression equations are \(8X - 10Y + 66 = 0\) and \(40X - 18Y = 214\). What is the mean values of X and Y ?
Answer: B
The means are X = 13 and Y = 17.
Both regression lines pass through the point of means \((\bar{X}, \bar{Y})\), so solve them together:
\[ \begin{aligned} 8X - 10Y &= -66 \\ 40X - 18Y &= 214 \end{aligned} \]
Multiplying the first by 5 gives \(40X - 50Y = -330\). Subtracting this from the second:
\[ \begin{aligned} 32Y &= 544 \Rightarrow Y = 17 \\ 8X &= 10(17) - 66 = 104 \Rightarrow X = 13 \end{aligned} \]
The variance of X is not needed for the means. 17 and 13 reverses the two values, and 12 and 17 does not satisfy the first equation.
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