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Question
If Σx1 = 56 Σy1 = 56, Σ`x_1^2` = 478,
Σ`y_1^2` = 476, Σx1y1 = 469 and n = 7, Find
(a) the regression equation of y on x.
(b) y, if x = 12.
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Solution
Σx1 = 56 Σy1 = 56, Σ`x_1^2` = 478,
Σ`y_1^2` = 476, Σx1y1 = 469 and n = 7,
`barx = Σ_(x1)/n = 56/7 = 8 and bary = Σ_(y1)/n = 56/7 = 8`
Now regression coefficient of y on x is,
`b_(yx) = (Σx_1y_1 -n barx bary)/(Σ_1^2 - nx^-2)`
= `(469 - (7 xx 8 xx 8))/(476 - (7 xx (8)^2)`
= `(469 - 448)/(476 - 448)`
= `21/28`
= `3/4`
= 0.75
(a) Equation of regression of line of income on year service is
`y - bary = b_(yx) (x - barx)`
y - 8 = 0.75 ( x - 8)
y = 2 + 0.75x
(b) When x = 12, y = ?
y =2 + 0.75 x 12
y = 11
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