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Unformatted text preview: ient of correlation. Symbolically
≥r
2
225 7. If r=0, the variables are uncorrelated , the lines of regression
become perpendicular to each other.
8. If r= +1, the two lines of regression either coincide or parallel to
each other m − m2 9. Angle between the two regression lines is θ = t an1 1 1 + m1m2 where m1 and,m2 are the slopes of the regression lines X on Y
and Y on X respectively.
10.The angle between the regression lines indicates the degree of
dependence between the variables.
Example 2:
If 2 regression coefficients are b1= 4
9
and b2 =
.What would be
5
20 the value of r?
Solution:
The correlation coefficient , r = ± b1b2
49
x
5 20 =
= 36
6
=
= 0.6
100 10 Example 3:
15
3
and b2 = , Find r
Given b1 =
8
5
Solution:
r = ± b1b2
= 15 3
x
85 9
=1.06
8
It is not possible since r, cannot be greater than one. So the given
values are wrong
= 226 9.6 Why there are two regression equations?
The regression equation of Y o n X is
σ
Ye = Y + r y ( X − X )
σx
(1)
(or)
Ye = Y + b1 ( X − X )
The regression equation of X on Y is
σ
X e = X + r x (Y − Y )
σy
X e = X + b2 (Y − Y )
These two regression equations represent entirely two
different lines. In other words, equation (1) is a function of X,
which can be written as Ye = F(X) and equation (2) is a function of
Y, which can be written as Xe = F(Y).
The variables X and Y are not inter changeable. It is mainly
due to the fact that in equation (1) Y is the dependent variable, X is
the independent variable. That is to say for the given values of X
we can find the estimates of Ye of Y only from equation (1).
Similarly, the estimates Xe of X for the values of Y can be obtained
only from equation (2).
Example 4:
Compute the two regression equations from the following data.
X
1
2
34
5
Y
2
3
5
4
6
If x =2.5, what will be the value of y?
Solution:
X
Y
x2
y2
xy
x = X − X y = Y −Y
1
2
2
2
4
4
4
2
3
1
1
1
1
1
3
5
0
1
0
1
0
4
4
1
0
1
0
0
5
6
2
2
4
4
4
15
20
20
10
10
9
227 ∑ X 15
= =3
n
5
∑ Y 20
Y=
=
=4
n
5...
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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.
 Winter '08
 Moshiri
 Business

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