which minimize the sum of the squares of the vertical
distances of observations
from the line
Hence, we need to minimize:
The Least Squares Method
We wish to find estimators forwhich minimize the sum of the squares of the vertical
distances of observationsfrom the lineHence, we need to minimize:
We therefore need to solve the two equations:
Since:
We are at a minimum and since we are summing over n observations:
We also need to solve for 
We also have a minimum and similarly, we can see that:
We can substitute 
into this expression to get:
Note that this expression may be written as:
Since the correlation coefficient r is cov(x,y)/(SDxSDy) then:
