Kavana Sarma Kaburlu

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Statistics for Beginners

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CURVE FITTING FOR BEGINNERS:

We have derived the folloing equation for distance Y from a point ( Other than starting Point) at a time X ( measured from the commence ment of motion)

Y = A +BX +o.5 CX^2

A is the value of Y at X=0 ,B is the Velocity at X=0 andC is the Acceleration If we know A= 3m B= 2 m/s and C= 2m/s^2 we can calculate Y values at X= 1,2 and 3 .The paired values are (1,6) ,(2,11) and (3,18)

We can determine the values of A,B,C if we knw 3 paired values of X and Y From the above 3 pairs we can determine A as 3 B as 2m/s and C as 2m/s^2

We need 3 indepent equqtions to determine the 3 unknowns .

But when we do experiments some errors will creep in .Let us say we have measured 10 values of Y for 10 values of X To determine 3 unkowns we hve now 10 equqtions .This poses a problem So from experiments we estimate the best values of A,B and C by amethod known as curve fitting .. The values are so determined that the the sum of squares of errors is minimised

( y1-A-BX1-0.5 c X62) ^2 = Ei( Error !) ^2

Sum of (E1^2 +E2^2 +E3^2 … E10^2) = E^2

We can minimise E^2 with respect to A,B and C by differentiating it partially with A, B and C and equating each with a Zero .We thus get 3 independent equations for A,B and C. We can then solve for the best values for the 3 unknowns

Here we know the shape of the curve ( A parabola ) .There is an implied assumption that errors are normlly distributed

Next post is about the shape of the curve ( may be tomorrow )

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Written by kavanasarma

July 24, 2018 at 2:23 am

Posted in Uncategorized

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