January 16th, 2015, 08:09 PM  #1 
Newbie Joined: Jan 2015 From: Brisbane Posts: 1 Thanks: 0  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)=ā_(i=1)^nāć(w_i(A/r^12 B/r^6 ))^2.ć 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 leastsquares 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 
January 21st, 2015, 01:27 AM  #2 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,119 Thanks: 710 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
What plotting program are you using? Most plotting programs have some means of calculating a leastsquares fit to a general formula.

January 27th, 2015, 12:15 AM  #3 
Senior Member Joined: Aug 2012 Posts: 229 Thanks: 3 
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 nonlinear regression then you can feed these in for linear regression. 

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