Tutorial Example Method of Least Squares


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.

X

1

2

3

4

5

Y

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




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