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Question
Out of the two regression lines x + 2y – 5 = 0 and 2x + 3y = 8, find the line of regression of y on x.
Solution
Given the lines of regression are
x + 2y – 5 = 0 ...(1)
and 2x + 3y = 8 ...(2)
Assume that (1) is the regression line of y on x
i.e., y = `(-1)/2x + 5/2`
`\implies` byx = `(-1)/2`
and line (2) is the regression line of x on y
i.e., x = `(-3)/2y + 4`
`\implies` bxy = `(-3)/2`
Now byx · bxy = `(-1)/2 xx (-3)/2 = 3/4 < 1`
Therefore, our assumption is correct and line (1)
i.e., x + 2y – 5 = 0 is the regression line of y on x.
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