Regression


Once a positive correlation between two variables has been established, we can proceed to graph this statistical relationship in the form of a linear equation.  This equation is valuable in predicting the value of one variable given the value of its counterpart.  The equation is known as a regression line, or line of least-squares.

To construct this line, we must interpret our data in terms of that familiar equation, y=m x+b .  This Equation represents the line of least-squares of our sample data.  (The true regression line for the Population, the line we are attempting to approximate, is represented by the equation y= Mx+ B.)  Let's begin by solving for the slope of the line.  Here is the equation for m :

As you can see, many of the values used to solve for r  are used to find the slope. Once the slope is calculated there are several methods for calculating the y-intercept.


 

6:8