The Least Squares Method

 

Least square method estimates ί1 and ί0 so that the sum of squares of the residuals is minimized.

            Min or ΆSSres = 0

 

This method is a well-known method that already be a routing of most applications and statistical software’s. Some scientific calculators also have this function on them. We can easily use this method by just plugging the data on the worksheet and clicking the functions. In case away from a computer and just having an ordinary calculator, we can still calculate least square coefficients easily by using a provided table below:

 

Least Square Table

i

xi

yi

(xi)2

xi * yi

1

2

3

…

 

…

n

x1

x2

…

 

 

…

xn

y1

y2

…

 

 

…

yn

(x1)2

(x2)2

….

 

 

…

(xn)2

x1 * y1

x2 * y2

…

 

 

…

xn * yn

 

S xi = …..

S yi = …..

S (xi)2 = …..

S xi * yi = …..

 

b1 and b0 are calculated using steps as follow:

  1. Fill the least square table with pairs of data (xi, yi) and calculate the corresponding columns.
  2. Calculate:  and
  3. Plug the number form the table to calculate:

 

 and

 

  1. To get b1 calculate:

 

 …. this is our estimate slope

 

 … this is our y intercept.