Page 192 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 9: Regression Analysis

9.1.2 Line of Regression of X on Y Notes

The general form of the line of regression of X on Y is X = c + dY , where X denotes the
Ci i Ci
predicted or calculated or estimated value of X for a given value of Y = Y and c and d are
i
constants. d is known as the regression coefficient of regression of X on Y.
Figure 9.2

In this case, we have to calculate the value of c and d so that
S' = (X - X ) is minimised.
2
i Ci
As in the previous section, the normal equations for the estimation of c and d are
X = nc + d Y .... (13)
i i
and X Y = c Y + d Y 2 .... (14)
i i i i
Dividing both sides of equation (13) by n, we have X = c +dY .
Graphing Regression Lines

This shows that the line of regression also passes through the point X,Y . Since both the lines
of regression passes through the point X,Y , therefore X,Y is their point of intersection as
shown in Figure 9.3.

Figure 9.3

We can write c = X - dY .... (15)

As before, the various expressions for d can be directly written, as given below.

X Y nXY
i i
d .... (16)
2 2
Y i nY
X i X Y i Y
or d 2 .... (17)
Y i Y

LOVELY PROFESSIONAL UNIVERSITY 187