How are Regression Equations derived? Explain.
Computation of Regression Equations : Algebraic expression of regression lines is called regression equations. Like lines equations are also two :
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Regression Equation X on Y |
Regression Equation Y on X |
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Original Form : X = a + by Formula :
X - X = bxy (Y - Y) Here - X à Mean of x series. Y à Mean of y series. bxy àRegression coefficient X on Y |
Original Form : Y = a + bx Formula :
Y - Y = byx (X - X) Here - X à Mean of x series. Y à Mean of y series. byx àRegression coefficient Y on X |
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Computation of Regression Coefficients : |
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1. Direct Method : |
1. Direct Method : |
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bxy = Σxy Σy2 or bxy = r σx σy |
byx = Σxy Σx2 or byx = r σy σx |
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2. Short Cut Method : |
2. Short Cut Method : |
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bxy = N. Σdxdy – (Σdx . Σdy) N.Σd2y – (Σdy)2 Here - dx = X - A dy =Y - A |
bxy = N. Σdxdy – (Σdx . Σdy) N.Σd2x – (Σdx)2 Here - dx = X - A dy =Y - A |
