Applied Mathematics for Electrical Engineering (3130908)

Question-1c ( ii )

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

Q1) (c ( ii ))

The normal equations for the straight line

y = A + B x

are

\sum_{} y = n A + B \sum_{} x

\underset{}{\sum x} y = A \sum_{} x + B \sum_{} x^{2}

So, we need to find the value of

\sum_{} x, \sum_{} y, \sum_{} x y

and

\sum_{} x^{2}

to find the value of A and B.

$x$	$y$	$x y$	$x^{2}$
1	1	1	1
2	3	6	4
3	5	1	9
4	6	24	16
5	5	25	25
$\sum_{} x = 15$	$\sum_{} y = 20$	$\sum_{} x y = 71$	$\sum_{} x^{2} = 55$

The normal equations for the straight line are

\sum_{} y = n A + B \sum_{} x \Rightarrow 20 = 5 A + 15 B . . . . . . . . . (1)

\underset{}{\sum x} y = A \sum_{} x + B \sum_{} x^{2} \Rightarrow 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