Question

Fit a straight line y=a+bx into the given data:

(x,y):(5,12)(10,13)(15,14)(20,15)(25,16).

(a) y=11

(b) y=0.2x

(c) y=11+0.2x

(d) y=1.1+0.2x

The question was posed to me in exam.

My doubt is from Curve Fitting topic in portion Matrices of Engineering Mathematics

Answer 1

Right choice is (c) y=11+0.2x

To elaborate: Here, N=5

Calculations of ∑x and ∑x^2

x y x2 xy

5 12 25 60

10 13 100 130

15 14 225 210

20 15 400 300

25 16 625 400

∑x=75 ∑y=70 ∑x2=1375 ∑xy=1100

We know that,

∑y=Na+b∑x

∑xy=a∑x+b∑x2

Substituting the values from the table into the equations-

70=(5)a+b(75) – (1)

1100=(a)75+b(1375) – (2)

Solving equations (1) and (2) simultaneously

a=11 and b=0.2

Thus the equation of the line is given by y=a+bx

Thus, the equation of the line is y=11+0.2x.