FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 6.23Regression equation of Yon X is given by
Y = a + bX
Where constants a and b can be found out by solving the following 2 normal equations simultaneously—
∑Y = Na+b∑X
∑XY = a∑X+b∑X^2
Substituting the value obtained from the above table, we get
120 = 6a + 96b ....(1)
2188 = 96a +1758b....(2)
Multiply e.g. 1 by 16 & subtract equation 2 from it
1920 = 96a + 1536
2188 = 96a + 1758
-268 = 0 + -222b
b =^268222 =1.21
Put the value of b in equation 1
120 = 6a+ 96×1.21
120 = 6a+116.16
6a = 120 -116.16
6a = 3.84
a =^3 .84 6 =0.64
Put the value of a and 6 in the regression equation of Y on X
Y = a + bX
Y = 0.64 + 1.21X
There is an alternative method of finding the regression equations. Instead of the normal equations, deviations
from the respective arithmetic mean or assumed mean are considered :
6.2.6. METHOD II WHEN DEVIATIONS ARE TAKEN FROM ACTUAL MEAN
Regression equation of X and Y is given by
X X b (Y Y)− = XY −where X, Y are actual mean of X & Y series respectively
XY 2
b XY
= Y∑XY = Sum of product of deviations taken from actual mean of X & Y.
∑Y^2 = Sum of sequare of deviations from actual mean of Y.
Regression equation of Y and X is given by