4. Find Regression line equations from ∑x = 130, ∑y = 220, ∑x² = 2288, ∑y² = 8822, ∑xy = 3467, n = 10

Solution:
Mean `bar x = (sum x)/n`

`=130/10`

`=13`


Mean `bar y = (sum y)/n`

`=220/10`

`=22`


`byx = (n * sum xy - sum x * sum y)/(n * sum x^2 - (sum x)^2)`

`=(10 * 3467 - 130 * 220 )/(10 * 2288 - (130)^2)`

`=(34670 - 28600 )/(22880 - 16900)`

`=6070/5980`

`=1.02`


Regression Line y on x
`y - bar y = byx (x - bar x)`

`y - 22 = 1.02 (x - 13)`

`y - 22 = 1.02 x - 13.2`

`y = 1.02 x - 13.2 + 22`

`y = 1.02 x + 8.8`


`bxy = (n * sum xy - sum x * sum y)/(n * sum y^2 - (sum y)^2)`

`=(10 * 3467 - 130 * 220 )/(10 * 8822 - (220)^2)`

`=(34670 - 28600 )/(88220 - 48400)`

`=6070/39820`

`=0.15`


Regression Line x on y
`x - bar x = bxy (y - bar y)`

`x - 13 = 0.15 (y - 22)`

`x - 13 = 0.15 y - 3.35`

`x = 0.15 y - 3.35 + 13`

`x = 0.15 y + 9.65`

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