Numerical method (curve fitting) ***TOPICS ARE**** Linear Regression Multiple Linear Regression Polynomial Regression Example of Newton’s Interpolation Polynomial And example Example of Newton’s Interpolation Polynomial And example

1. Name:Sujit Kumar Saha
Lecturer at Varendra University
Rajshahi
Name: Istiaque Ahmed Shuvo
Id: 141311057
5th batch, 7th Semester
Sec-B
Dept. Of Cse
Varendra University, Rajshahi
Submitted By: Submitted To
11-Apr-16 1

3. TOPICS ARE
 Linear Regression
 Multiple Linear Regression
 Polynomial Regression
 Example of Newton’s Interpolation
Polynomial And example
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4. Fitting a straight line to a set of paired
observations: (x1, y1), (x2, y2),…,(xn, yn).
y = a0+ a1 x + e
a1 - slope
a0 - intercept
e - error, or residual, between the model and
the observations
Linear Regression
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2
10
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0)(2
iiii
ii
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r
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a
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iiii
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xaxaxy
yaxna
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2 equations with 2
unknowns, can be solved
simultaneously
Linear Regression:
Determination of ao and a1
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7.   
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Linear Regression:
Determination of ao and a1
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8. • Another useful extension of linear
regression is the case where y is a
linear function of two or more
independent variables:
• Again, the best fit is obtained by
minimizing the sum of the squares
of the estimate residuals:
Multiple Linear Regression

9. • The least-squares procedure
from Chapter 13 can be
readily extended to fit data
to a higher-order
polynomial. Again, the idea
is to minimize the sum of the
squares of the estimate
residuals.
• The figure shows the same
data fit with:
a) A first order polynomial
b) A second order polynomial
Polynomial Regression
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10. Many times, data is given only at discrete points such as (x0, y0), (x1, y1), ......, (xn−1, yn−1),
(xn, yn). So, how then does one find the value of y at any other value of x ? Well, a
continuous function f (x) may be used to represent the n +1 data values with f (x)
passing through the n +1 points (Figure 1). Then one can find the value of y at any
other value of x . This is called interpolation.
Of course, if x falls outside the range of x for which the data is given, it is no
longer interpolation but instead is called extrapolation.
So what kind of function f (x) should one choose? A polynomial is a common
choice for an interpolating function because polynomials are easy to
(A) evaluate,
(B) differentiate, and
(C) integrate,
relative to other choices such as a trigonometric and exponential series.
Polynomial interpolation involves finding a polynomial of order n that passes
through the n +1 points. One of the methods of interpolation is called Newton’s divided
difference polynomial method. Other methods include the direct method and the
Lagrangian interpolation method. We will discuss Newton’s divided difference
polynomial method in this
What is interpolation?
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11. Newton’s Divided-Difference Interpolating Polynomials?
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12. Example of Newton’s Interpolation Polynomial
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13. 11-Apr-16 13