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Solution given x 65 y 67 x 25 y 35 r 08 the

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Unformatted text preview: Regression Co efficient of Y on X ∑ xy 9 byx = = = 0.9 ∑ x 2 10 X= Hence regression equation of Y on X is Y = Y + byx ( X − X ) = 4 + 0.9 ( X – 3 ) = 4 + 0.9X – 2.7 =1.3 + 0.9X when X = 2.5 Y = 1.3 + 0.9 × 2.5 = 3.55 Regression co efficient of X on Y ∑ xy 9 = = 0.9 bxy = ∑ y 2 10 So, regression equation of X on Y is X = X + bxy (Y − Y ) = 3 + 0.9 ( Y – 4 ) = 3 + 0.9Y – 3.6 = 0.9Y - 0.6 Short-cut method Example 5: Obtain the equations of the two lines of regression for the data given below: X Y 45 40 42 38 44 36 43 35 41 38 228 45 39 43 37 40 41 Solution: X 46 42 44 A 43 41 45 43 40 Y 40 38 B 36 35 38 39 37 41 u = X-A 3 -1 1 0 -2 2 0 -3 0 u2 9 1 1 0 4 4 0 9 28 v = Y-B 2 0 -2 -3 0 1 -1 3 0 ∑u n 0 = 43 = 43 + 8 ∑u Y = B+ n 0 = 38 = 38 + 8 The regression Co-efficient of Y on X is n uv − ∑ u ∑ v b1 = byx = ∑ 2 n∑ u 2 − ( ∑ u ) X = A+ 8(−3) − (0)(0) −24 = = -0.11 2 8(28) − (0) 224 The regression coefficient of X on Y is n uv − ∑ u ∑ v b2 = bxy = ∑ 2 n∑ v 2 − ( ∑ v ) = 8(−3) − (0)(0) 8(28) − (0) 2 −24 = = - 0.11 224 = 229 V2 4 0 4 9 0 1 1 9 28 uv 6 0 -2 0 0 2 0 -9 -3 Hence the reression equation of Y on X is Ye = Y + b1 ( X − X ) = 38 – 0.11 (X-43) = 38 – 0.11X + 4.73 = 42.73 – 0.11X The regression equation of X on Y is X e = X + b1 (Y − Y ) = 43 – 0.11 (Y-38) = 43 – 0.11Y + 4.18 = 47.18 – 0.11Y Example 6: In a correlation study, the following values are obtained Mean S.D X 65 2.5 Y 67 3.5 Co-efficient of correlation = 0.8 Find the two regression equations that are associated with the above values. Solution: Given, X = 65, Y = 67, σx = 2.5, σy= 3.5, r = 0.8 The regression co-efficient of Y on X is σ byx= b1 = r y σx 3.5 = 0.8 × = 1.12 2.5 The regression coefficient of X on Y is σ bxy = b2 = r x σy 230 2.5 = 0.57 3.5 Hence, the regression equation of Y on X is Ye = Y + b1 ( X − X ) = 67 + 1.12 (X-65) = 67 + 1.12 X - 72.8 = 1.12X – 5.8 The regression equation of X on Y is X e = X + b2 (Y − Y ) = 65 + 0.57...
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This note was uploaded on 01/18/2014 for the course BUS 100 taught by Professor Moshiri during the Winter '08 term at UC Riverside.

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