Determination of the Regression Equation

The determination of the regression equation such given above is generally done by using a technique termed as "the method of least squares'.

Regression equation of y on x that is y = a + bx

The given sets of equations generally known as common equation are utilized to determine the equation of the above regression line when described a set of data.

Σy = an + bΣx  

Σxy = aΣx + bΣx²

Whereas Σy = Sum of y values

Σxy = sum of the product of x and y

Σx = sum of x values

Σx²= sum of the squares of the x values

a = the intercept on the y axis

b = Slope gradient line of y on x

NB: The above regression line is generally used in one way only that is used to estimate the y values when the x values are described.

Regression line of x on y that is x = a + by

- The fact that regression lines can only be utilized in one way leads to what is termed as a regression paradox

- It means that the regression lines are not ordinary mathematical line graphs such may be utilized to estimate the x and y simultaneously

- Hence one has to be careful when using regression lines as it becomes essential to develop an equation for x and y before doing the estimation.