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Unformatted text preview: (Y67)
= 65 + 0.57Y – 38.19
= 26.81 + 0.57Y
Note:
Suppose, we are given two regression equations and we
have not been mentioned the regression equations of Y on X and X
on Y. To identify, always assume that the first equation is Y on X
then calculate the regression coefficient byx = b1 and bxy = b2. If
these two are satisfied the properties of regression coefficient, our
assumption is correct, otherwise interchange these two equations.
= 0.8 × Example 7:
Given 8X – 10Y + 66 = 0 and 40X – 18Y = 214. Find the
correlation coefficient, r.
Solution:
Assume that the regression equation of
8X 10Y + 66 = 0.
10Y = 668X
10Y = 66 + 8X
66 8 X
Y=
+
10 10
Now the coefficient attached with X is byx
8
4
i.e., byx =
=
10
5
231 Y on X is The regression equation of X on Y is
40X18Y=214
In this keeping X left side and write other things right side
i.e., 40X = 214 + 18Y
214 18
i.e., X =
+Y
40 40
Now, the coefficient attached with Y is bxy
18 9
=
40 20
Here byx and bxy are satisfied the properties of regression
coefficients, so our assumption is correct.
b yx b xy
Correlation Coefficient, r =
i.e., bxy = = 49
×
5 20 = 36
100 6
10
= 0.6 = Example 8:
Regression equations of two correlated variables X and Y
are 5X6Y+90 = 0 and 15X8Y130 = 0. Find correlation
coefficient.
Solution:
Let 5X6Y+90 =0 represents the regression equation of X
on Y and other for Y on X
6
90
Now
X= Y –
5
5
232 bxy = b2 = 6
5 For 15X8Y130 = 0
15
130
Y=
X–
8
8
byx = b1
15
=
8
r = ± b1 b2
15 6
×
85
= 2.25
= 1.5 >1
It is not possible. So our assumption is wrong. So let us take the
first equation as Y on X and second equation as X on Y.
From the equation 5x – 6y + 90 = 0,
5
90
Y=
X–
6
6
5
byx =
6
From the equation 15x  8y – 130 = 0,
8
130
X=
Y+
15
15
8
bxy =
15
Correlation coefficient, r = ± b1 b2
= = 58
×
6 15 40
90
2
=
3 = 233 = 0.67
Example 9:
The lines of regression of Y on X and X on Y are
respectively, y = x + 5 and 16X = 9Y – 94. Find the variance of X
if the variance of Y is 19. Also find the covariance of X and Y.
Solution:
From regression line Y on X,
Y =...
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 Winter '08
 Moshiri
 Business

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