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Question
Find the line of regression of X on Y for the following data:
n = 8, `sum(x_i - bar x)^2 = 36, sum(y_i - bar y)^2 = 44, sum(x_i - bar x)(y_i - bar y) = 24`
Solution
Given, n = 8, `sum(x_i - bar x)^2 = 36`
`sum(y_i - bar y)^2 = 44, sum(x_i - bar x)(y_i - bar y) = 24`
∴ `"b"_"XY" = (sum(x_i - bar x)(y_i - bar y))/(sum(y_i - bar y)^2) = 24/44 = 6/11`
Now, the regression equation of X on Y is
`("X" - bar x) = "b"_"XY" ("Y" - bar y)`
i.e., `("X" - bar x) = 6/11 ("Y" - bar y)`
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