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Question
X and Y are a pair of correlated variables. Ten observations of their values (X, Y) have the following results. ∑X = 55, ∑XY = 350, ∑X2 = 385, ∑Y = 55, Predict the value of y when the value of X is 6.
Solution
Given ∑X = 55, ∑XY = 350, ∑X2 = 385, ∑Y = 55
Regression coefficient of Y on X is
byx = `("N"sum"XY" - (sum"X")(sum"Y"))/("N".sum"X"^2 - (sum"X")^2)`
= `(10(350) - (55)(55))/(10(385) - (55)^2)`
= `(3500 - 3025)/(3850 - 3025)`
= `475/825`
= 0.576
∴ Regression line of Y on X is
`"Y" - bar"Y" = "b"_"yx"("X" - bar"X")`
Y − 5.5 = 0.576 (X − 5.5) .....`[∵ bar"X" = (sum"X")/"n" = 55/10 = 5.5; bar"Y" = (sum"Y")/"n" = 55/10 = 5.5]`
Y − 5.5 = 0.576X − 3.168
Y = 0.576X + 2.332
When X = 6, Y = 0.576(6) + 2.332
Y = 3.456 + 2.332
Y = 5.788
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