Applied Mathematics for Electrical Engineering (3130908)

BE | Semester-3   Winter-2019 | 26-11-2019

Q1) (c ( ii ))

Using method of least square, find the best fitting straight line to the given following data.
x 1 2 3 4 5
y 1 3 5 6 5

The normal equations for the straight line y = A + B x are
 
y = n A + B  x
 
x y = A  x + B  x2
 
So, we need to find the value of  x ,  y ,  x y  and  x2 to find the value of A and B.
 
x y x y x2
1 1 1 1
2 3 6 4
3 5 1 9
4 6 24 16
5 5 25 25
x = 15 y = 20 x y = 71 x2 = 55
 
The normal equations for the straight line are
 
y = n A + B  x   20 = 5 A +15 B ......... 1 
 
x y = A  x + B  x2  71 = 15 A +55 B ......... 2 
 
By solving equation ( 1 ) and ( 2 ), we have
 
A = 0.7 and B = 1.1
 
Therefore, the best fit line is y = A + Bx = 13.6 x.