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