I am given 2 columns of different numbers. How do I find the "mathmatical relationship" between the two. For example:
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Rearrange the data as follows:
x values y values xdiff ydiff slope=ydif/xdiff
x1=612 2052 =y1
x2=693 2779=y2 81 727 8.9753
x3=721 2170=y3 28 -609 -12.7747
It is possible to fit (i) a line of best fit of the form y=mx+c , but here as the y difference/xdifference is too much diffrent the slope is not constant and so the linear relationship is not suitable. (ii) a prarabola of 2nd degree of the form y=ax^2+bx+c between x and y.So, I chose the second form to fit here that establish the relation between x and y.
Since there are 3 pairs of entries we can find a solution of the form y=ax^2+bx+c. Then we get 3 equations if we substitute x=xi and y=yi for i=1,2 and 3 and i is a suffix to x or y.
axi^2+bxi+ c = yi for i =1,2 and 3
Solve the 3 simultaneous equations and determine the values of a,b and c. Substituting the values for xi's and yi's we get:
a(693)^2+b(693)+c= 2779 (2)
(2)-(1) eliminates c and (3)-(2) also eliminates c. We get 2 equation with 2 unkwons in a,b to be determined.:
Equations reduces to after dividing the former by (693-612) and the latter by (721-693):
(5)-(4) eliminates b , giving an equation with only a to be determined:
Substiture a=-0.281881526 in equation (5) to get b and
Having known a and b ,substitute the values of them in any of the original equations flagged at (1 ) or (2) or (3), to obtain c. So you will get the requred relation once you know all a,b and c determined:
From equatio (1)
Therefore the relation required is:
Hope this helps.
mathmatical relationship is;
the value of each number is=6+1+2=9
7=2+1=10 , 2+1+7+0=10
both are totally divided by "7".
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