Excel has no built-in functionality for non-linear least squares.
If you only need approximate coefficient estimates, enter trial values for
the parameters in a contiguous block of cells. Calculate predicted values in
a range of cells using formulas that depend on the parameter cells. In
another cell, calculate the sum of square differences of predicted from
observed values. Use Solver to approximately minimize that sum of squared
differences by changing the parameter cells.
Note that with Solver's default convergence criteria it may declare a
"solution" that is far from the real minimum. Try either tweekin Solver's
options or minimizing a large multiple (say 1E8) times the sum of squared
differences to see if you can get some improvement in Solver's "solution".
If you know calculus, you can calculate the Jacobian matrix of partial
derivatives evaluated at a trial solution and use LINEST to regress the (not
squared) differences observed-predicted vs the Jacobian, to get a vector
parameter shift. The next guess is that guess plus the shift; recalculate
the Jacobian and repeat until convergence
http://en.wikipedia.org/wiki/Nonlinear_least_squares
At the least squares solution, use LINEST to regress the original
observations vs the Jacobian to get 1st order Taylor series approximate
standard errors of the parameter estimates.
Jerry
