Find Regression line equations from `sum x, sum y, sum x^2, sum y^2, sum xy, n` 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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