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January 16th, 2015, 08:09 PM   #1
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Least Squares Problem

These values:
r |V(r)
1 |2.0844
1.04 |0.7748
1.09 |0.0074
1.19 |-0.3653
1.39 |-0.2967
1.6 |-0.1349
2 |0.0265
2.4 |0.0623

have the relationship:

v(r) = A/r^12 - B/r^6

I am trying to find the values of A and B by minimising the residuals of f(A,B)=āˆ‘_(i=1)^nā–’怖(w_i-(A/r^12 -B/r^6 ))^2.怗

Using the data given in above table, formulate a linear system (Mx=b) where A and B are the unknown variables, and hence use the normal equation to find the least-squares solution to the linear system. Plot the function V(r) using your values of A and B, together with the data I have given above in the Table.

My main problem is producing the least squares equation
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January 21st, 2015, 01:27 AM   #2
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What plotting program are you using? Most plotting programs have some means of calculating a least-squares fit to a general formula.
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January 27th, 2015, 12:15 AM   #3
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Hey ALLIRIX.

Just make sure you calculate two number variables - one is 1/r^6 and the other 1/r^12 and do the regression on those variables. If you don't have a function that does non-linear regression then you can feed these in for linear regression.
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