FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 6.21Whereas in case of regression analysis, there is a functional relationship between Y and X such that for each
value of Y there is only one value of X. One of the variables is identified as a dependent variable the other(s)
as independent valuable(s). The expression is derived for the purpose of predicting values of a dependent
variable on the basis of independent valuable(s).
6.2.3. REGRESSION LINES
A regression line is the line which shows the best mean values of one variable correspond-ing to mean
values of the other. With two series X and Y, there are two arithmetic regression lines, one showing the best
mean values of X corresponding to mean Y’s and the other showing the best mean values of Y corresponding
to mean X’s. In the context of scatter diagram, the regression line is the straight line that best fits the scatter
diagram. The most commonly used criteria is that it is the straight line that minimise the sum of the squared
deviations between the predicted and observed values of the dependent variable. In the case of two
variables X and Y, there will be two regression lines as the regression of X on Y and regression of Y on X.
6.2.4. REGRESSION EQUATIONS
There are different methods of deriving regression equations
(1) By taking actual values of X and Y
(2) By taking deviations from actual mean
(3) By taking deviations from assume mean
6.2.5. METHOD I WHEN ACTUAL VALUES ARE TAKEN
The regression equation of Y on X is expressed as follows:
Yc = a+bX
Where a and b can be found out by solving the following two normal equations simultaneously:
∑Y Na b X= + ∑
∑ ∑ ∑XY a X b X= +^2
The regression equation of X on Y is expressed as follows:
Xc = a + bY
Where a and b can be found out by solving the following two normal equations simultaneously:
∑X Na b Y= + ∑
∑ ∑ ∑XY a Y b Y= +^2
Example15 : From the following table find :
(1) Regression Equation of X on Y.
(2) Regression Equation of Y on X.
X 10 12 18 22 25 9
Y 15 18 21 26 32 8