2. Find Regression line equations from the following data

X	Y
0	1
1	5
2	10
3	6
4	3

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

` = (0+1+2+3+4)/5`

` = 10/5`

` = 2`

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

` = (1+5+10+6+3)/5`

` = 25/5`

` = 5`

`x`	`y`	`X=x-bar x=x-2`	`Y=y-bar y=y-5`	`X^2`	`Y^2`	`X*Y`
0	1	-2 `-2=0-2`	-4 `-4=1-5`	4 `4=(-2)^2`	16 `16=(-4)^2`	8 `8=-2 xx -4`
1	5	-1 `-1=1-2`	0 `0=5-5`	1 `1=(-1)^2`	0 `0=(0)^2`	0 `0=-1 xx 0`
2	10	0 `0=2-2`	5 `5=10-5`	0 `0=(0)^2`	25 `25=(5)^2`	0 `0=0 xx 5`
3	6	1 `1=3-2`	1 `1=6-5`	1 `1=(1)^2`	1 `1=(1)^2`	1 `1=1 xx 1`
4	3	2 `2=4-2`	-2 `-2=3-5`	4 `4=(2)^2`	4 `4=(-2)^2`	-4 `-4=2 xx -2`
---	---	---	---	---	---	---
`10`	`25`	`sum X=0`	`sum Y=0`	`sum X^2=10`	`sum Y^2=46`	`sum X*Y=5`

`byx = (sum XY)/(sum X^2)`

`=5/10`

`=0.5`


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

`y - 5 = 0.5 (x - 2)`

`y - 5 = 0.5 x - 1`

`y = 0.5 x - 1 + 5`

`y = 0.5 x + 4`


`bxy = (sum XY)/(sum Y^2)`

`=5/46`

`=0.1087`


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

`x - 2 = 0.1087 (y - 5)`

`x - 2 = 0.1087 y - 0.5435`

`x = 0.1087 y - 0.5435 + 2`

`x = 0.1087 y + 1.4565`

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