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 + bΣx^{2}
Whereas Σy = Sum of y values
Σxy = sum of the product of x and y
Σx = sum of x values
Σx^{2}= 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.