Example Method of Least Squares
The given example explains how to find the equation of a straight line or a 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 for the following data. Also find the 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 from equation (2). Thus we get the values of and .
Here and , the equation of least square line becomes .
For the trends values, put the values of in the above equation (see column 4 in the table above).