2. Example-2
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`
This material is intended as a summary. Use your textbook for detail explanation.
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