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Question
| x | y | xy | x2 | y2 |
| 6 | 9 | 54 | 36 | 81 |
| 2 | 11 | 22 | 4 | 121 |
| 10 | 5 | 50 | 100 | 25 |
| 4 | 8 | 32 | 16 | 64 |
| 8 | 7 | `square` | 64 | 49 |
| Total = 30 | Total = 40 | Total = `square` | Total = 220 | Total = `square` |
bxy = `square/square`
byx = `square/square`
∴ Regression equation of x on y is `square`
∴ Regression equation of y on x is `square`
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Solution
| x | y | xy | x2 | y2 |
| 6 | 9 | 54 | 36 | 81 |
| 2 | 11 | 22 | 4 | 121 |
| 10 | 5 | 50 | 100 | 25 |
| 4 | 8 | 32 | 16 | 64 |
| 8 | 7 | 56 | 64 | 49 |
| Total = 30 | Total = 40 | Total = 214 | Total = 220 | Total = 340 |
From the table, we have
n = 5, ∑x = 30, ∑y = 40, ∑xy = 214, ∑x2 = 220, ∑y2 = 340
`barx = (sumx_"i")/"n" = 30/5` = 6
`bary = (sumy_"i")/"n" = 40/5` = 8
bxy = `(sumxy - "n" bar(x) bar(y))/(sumy^2 - "n" bary^2)`
= `(214 - 5 xx 6 xx 8)/(340 - 5(8)^2`
= `(214 - 240)/(340 - 320)`
= `(-26)/20`
bxy = `(-13)/10`
byx = `(sumxy - "n" bar(x) bar(y))/(sumx^2 - "n" barx^2)`
= `(214 - 5 xx 6 xx 8)/(220 - 5(6)^2`
= `(214 - 240)/(220 - 180)`
= `(-26)/40`
byx = `(-13)/20`
∴ Regression equation of x on y is x = – 1.3y + 16.4
∴ Regression equation of y on x is y = – 0.65x + 11.9
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| 1 | 5 | – 2 | – 4 | 8 | 4 | 16 |
| 2 | 7 | – 1 | – 2 | `square` | 1 | 4 |
| 3 | 9 | 0 | 0 | 0 | 0 | 0 |
| 4 | 11 | 1 | 2 | 2 | 4 | 4 |
| 5 | 13 | 2 | 4 | 8 | 1 | 16 |
| Total = 15 | Total = 45 | Total = 0 | Total = 0 | Total = `square` | Total = 10 | Total = 40 |
Mean of x = `barx = square`
Mean of y = `bary = square`
bxy = `square/square`
byx = `square/square`
Regression equation of x on y is `(x - barx) = "b"_(xy) (y - bary)`
∴ Regression equation x on y is `square`
Regression equation of y on x is `(y - bary) = "b"_(yx) (x - barx)`
∴ Regression equation of y on x is `square`
Mean of x = 53
Mean of y = 28
Regression coefficient of y on x = – 1.2
Regression coefficient of x on y = – 0.3
a. r = `square`
b. When x = 50,
`y - square = square (50 - square)`
∴ y = `square`
c. When y = 25,
`x - square = square (25 - square)`
∴ x = `square`
The following results were obtained from records of age (x) and systolic blood pressure (y) of a group of 10 women.
| x | y | |
| Mean | 53 | 142 |
| Variance | 130 | 165 |
`sum(x_i - barx)(y_i - bary)` = 1170
