Page 335 - DMTH404_STATISTICS

Unit 23: Regression Analysis

and the predicted value of Y when X = 50, is given by Notes

Y = 20.24 + 0.69 ´ 50 = 54.74.
C
(b) Regression of X on Y

s X 10.8
r
Regression coefficient d = × = 0.42 ´ = 0.25
s Y 17.8
-
-
´
and c = X dY = 39.5 0.25 47.5 = 27.62
 The line of regression of X on Y is X = 27.62 + 0.25Y
C
and the predicted value of X when Y = 30 is given by
X = 27.62 + 0.25 ´ 30 = 35.12
C

Example 7:
For a bivariate data, you are given the following information :
2
(X - 58) = 46 (X - 58) = 3086
(Y - 58) = 9 (Y - 58) = 483
2
(X - 58)(Y - 58) = 1095.
Number of pairs of observations = 7. You are required to determine (i) the two regression
equations and (ii) the coefficient of correlation between X and Y.

Solution.
Let u = X - 58 and v = Y - 58. In terms of our notations, we are given u = 46, u = 3086, v = 9,
2
2
v = 483, uv = 1095 and n = 7.
46 9
Now X = 58 + = 64.7 and Y = 58 + = 59.29
7 7
(a) For regression equation of Y on X, we have

7 1095 46 9
-
´
´
b = 2 = 0.37
46
´
7 3086 - ( )
and a = Y bX = 59.29 0.37 64.57 = 35.40
´
-
-
 The line of regression of Y on X is given by
Y = 35.40 + 0.37X
C
(b) For regression equation of X on Y, we have
7 1095 46 9
´
´
-
d = 2 = 2.20
´
7 483 - ( ) 9
and c = X dY = 64.57 2.2 59.29 = - 65.87
-
-
´
 The line of regression of X on Y is given by
X = - 65.87 + 2.2Y
C
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