2. Find Regression line equations from the following data
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`
This material is intended as a summary. Use your textbook for detail explanation.
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