Engeneering Mathematics

2. Curve fitting
Curve fitting is the process of constructing a curve, or mathematical
function, that has the best fit to a series of data points, possibly subject
to constraints.
It is a statistical technique use to drive coefficient values for equations that
express the value of one(dependent) variable as a function of another
(independent variable)

3. X: 0 1 2 3 4 5
y: 3 6 8 11 13 14
Q.1. Fit a straight line into the following data.
Here given, N=6
Calculations of ∑x and ∑x2
Solution
We know that,
∑y=Na+b∑x
∑xy=a∑x+b∑x2
Substituting the values from the table into the
equations-

4. X y x2 xy
0 3 0 0
1 6 1 6
2 8 4 16
3 11 9 33
4 13 16 52
5 14 25 70
∑x=15 ∑y=55 ∑x2=55 ∑xy=177
55=(6)a+b(15) – (1)
177=(a)15+b(55) – (2)
Solving equations (1) and (2) simultaneously
a=3.52 and b=2.26
Thus the equation of the line is given by y=a+bx
Thus, the equation of the line is y=3.52+2.26x.

5. X 1 2 3 4 5 6 7
Y -5 -2 5 16 31 50 73
Q. 2 Fitting second degree parabola – Curve fitting using Least square method

7. Substituting these values in the normal equations
7a+28b+ 140c=168
28a+ 140b+ 784c = 1036
140a784b+ 4676c = 6440

8. Q.3 Using the method of least square fit a curve of the form Y= abx to the
following data:
X 2 3 4 5 6
Y 8.3 15.4 33.1 65.2 127.4
Y = abx
logy = log a +x log b
Y = log y, A= log a, B = log b (All log in base e)

9. Y =A+ Bx
Normal equations are,

11. Correlation
• In a bivariate distribution if the in one variable affect change in other variables, the
variable are said to be correlated.
• If the two variable deviate in same direction correlation is said to be positive or
direct.
• If two variable deviate in opposite directions correlation is said to be negative or
inverse

12. Correlation coefficient

13. Question 1: Calculate the linear correlation coefficient for
the following data. X = 4, 8 ,12, 16 and Y = 5, 10, 15, 20.
Solution:
Given variables are,
X = 4, 8 ,12, 16 and Y = 5, 10, 15, 20
For finding the linear coefficient of these data, we need to first
construct a table for the required values.

14. x y x2 y2 XY
4 5 16 25 20
8 10 64 100 80
12 15 144 225 180
16 20 256 400 320
Σ x = 40 Σ y =50 480 750 600
According to the formula of linear correlation we have,

16. Sol.

18. Rank correlation
It is defined as -:

19. Questions

20. Thank You