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Question
Find the equation of the line of regression of Y on X for the following data:
n = 8, `sum(x_i - barx).(y_i - bary) = 120, barx = 20, bary = 36, sigma_x = 2, sigma_y = 3`
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Solution
Given, n = 8, `sum(x_i - barx)(y_i - bary)` = 120,
`barx` = 20, `bary` = 36, `sigma_x` = 2, `sigma_y` = 3
∴ Var (X) = `sigma_"X"^2` = 4
Since Var (X) = `(sum (x_i - bar x))/"n"`,
4 = `(sum (x_i - bar x))^2/8`
∴ `sum (x_i - bar x)^2` = 32
Now, `"b"_"YX" = (sum ("x"_"i" - bar"x")("y"_"i" - bar"y"))/(sum("x"_"i" - bar"x")^2) = 120/32` = 3.75
∴ The regression equation of Y on X is
`("Y" - bar y) = "b"_"YX" ("X" - bar x)`
∴ (Y – 36) = 3.75 (X – 20)
∴ Y – 36 = 3.75X – 75
∴ Y = 3.75X – 75 + 36
∴ Y = 3.75 X – 39
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