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Parabola Curve Fitting Guide

This document discusses curve fitting, specifically fitting parabolas and higher degree curves to data. It explains that fitting a parabola involves finding the coefficients a and b of the equation y=ax^2 + bx + c that best fits the data using a system of normal equations. The document provides example problems of fitting second degree parabolas to various data sets and notes that the number of normal equations needed equals the degree of the curve plus one.

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119 views4 pages

Parabola Curve Fitting Guide

This document discusses curve fitting, specifically fitting parabolas and higher degree curves to data. It explains that fitting a parabola involves finding the coefficients a and b of the equation y=ax^2 + bx + c that best fits the data using a system of normal equations. The document provides example problems of fitting second degree parabolas to various data sets and notes that the number of normal equations needed equals the degree of the curve plus one.

Uploaded by

Zaheen00 Fatima
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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4/16/2020

CURVE FITTING

Muhammad Atique ur Rehman


Assistant Professor
YIPS

Biostatistics

Fitting of Parabola
 What is Parabola?
 It a set of all points in a plane that are equidistant from a
fixed line (Directrix) and a fixed point (Focus) in the plane.

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Fitting of Parabola
 Problem: We will be provided with data table of two
variables and we have to find a relation of degree 2 that best
fits the given data.
 We will perform the following steps in order to obtain the
required relation.
 Step-I: Let the equation of
Parabola.

Fitting of Parabola…
Step-II: Write the normal equations:-

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Fitting of Parabola…
 Where : n = Number of data values
 Step-III: Find the values of all above sums in the same way as in
the previous section.
 Step-IV: Substitute all the above calculated values in normal
equations.
 Step-V:We will have now two equations in two unknowns ‘a’ and
‘b’. We will solve these equations to find the values of ‘a’ and ‘b’.
 Step-VI: Substitute the values of ‘a’ and ‘b’ in equation in step-I
to have the required equation of straight line that fits the curve
best and can also predict about the unknown values.

For Higher Degree Curve


 One can use the following relation for finding the normal
equations for higher order curves.

 Where : A is the constant arising with respect to the term


and degree of the curve to be fitted.
nd
 For 2 degree we have seen that we require three normal
equations and in the same way we will remember that the
number of normal equations will be one more than the
degree of the curve.

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For Higher Degree Curve…


 The rest of the required equation in a short way can also be
found by simply replacing ‘n’ and multiplying the both sides
by .

Assignment
Q.1. Find a second degree curve that best fits the following data.

x 1 2 3 4
y 6 11 18 27
Q.2. Fit the a second degree parabola to the following data taking x
as the independent variable.
x 1 2 3 4 5 6 7 8 9
y 2 6 7 8 10 11 11 10 9

Q.3. Fit the second degree parabola to the following data.


x 1929 1930 1931 1932 1933 1934 1935 1936 1937
y 352 356 357 358 360 361 361 360 359

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