2. Find Regression line equations from ∑x = 100, ∑y = 200, ∑x² = 2000, ∑y² = 8000, ∑xy = 3000, n = 10

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

`=100/10`

`=10`


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

`=200/10`

`=20`


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

`=(10 * 3000 - 100 * 200 )/(10 * 2000 - (100)^2)`

`=(30000 - 20000 )/(20000 - 10000)`

`=10000/10000`

`=1`


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

`y - 20 = 1 (x - 10)`

`y - 20 = x - 10`

`y = x - 10 + 20`

`y = x + 10`


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

`=(10 * 3000 - 100 * 200 )/(10 * 8000 - (200)^2)`

`=(30000 - 20000 )/(80000 - 40000)`

`=10000/40000`

`=0.25`


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

`x - 10 = 0.25 (y - 20)`

`x - 10 = 0.25 y - 5`

`x = 0.25 y - 5 + 10`

`x = 0.25 y + 5`

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