Example Method of Least Squares
The given example explains you that how to find the equation of straight line or least square line by using the method of least square, which is very useful in statistics as well as in mathematics.
Example:
Fit a least square line to the following data. Also find trend values and show that .

1

2

3

4

5


2

5

3

8

7

Solution:






1

2

2

1

2.4

0.4

2

5

10

4

3.7

+1.3

3

3

9

9

5.0

2

4

8

32

16

6.3

1.7

5

7

35

25

7.6

0.6





Trend Values


The equation of least square line
Normal Equation for ‘a’  (1)
Normal Equation for ‘b’ (2)
Eliminate from equation (1) and (2), multiply equation (2) by 3 and subtract form equation (2), we get the values of and .
Here and , the equation of least square line becomes .
For the trends values, put the values of in above equation, see the above table column 4.