I am not sure how much you understand about curve fitting so please excuse me if I simplify this too much.
In general, curve fitting does not generate an equation that will exactly place a curve through every data point. The objective of curve fitting is to create a curve that is a "best fit". The technique seeks to minimize the error between the data points and the curve (equation) that approximates the data. To place a curve exactly though a set of data with a polynomial the order of the polynomial will usually need to be one less than the number of data points. For example, a straight line (order 1) can exactly pass through any 2 points, a parabola (order 2) through 3 points. A 14th order polynomial can pass through 13 points but it may have a lot of ripples in it so in general it is best to use the lowest order polynomial possible when curve fitting if you want a "nice" smooth curve.
The Excel Trendline feature does curve fitting and gives you several options for the type of curve to fit to the data including linear, polynomial, exponential and others. It also gives you the coefficients of the resulting fit and a measure of how well the curve fits the data.
Assuming that you have more than 5 data points and you want to fit a 4th order polynomial, as you stated, to the data the resulting curve will not pass through every data point. Once you have determined the equation of the curve using Trendline you would then generate a series of points in Excel that reference the curve fit equation. You can then transfer those points to AutoCAD with a simple script to generate a polyline of the fit curve. Since the "curve" in AutoCAD is a polyline it will be a series of straight line segments that have, to whatever precision you need, the shape of the curve.
AutoCAD does not have a feature for directly entering the coefficients of an equation to generate a curve. AutoCAD splines (NURBS) can exactly represent any shaped curve but it can be difficult to go from a polynomial expression to the equivalent NURBS. It is interesting to note that the polyline splines created by splining a polyline will yield a 3rd order B-spline that can exactly duplicate a parabola if the polyline had 4 control vertices but not a circle, ellipse or hyperbola since a parabola is the only conic section that can be expressed as a polynomial.
If you would like to post the data you would like to fit with a curve I will take a stab at doing the curve fit and transferring it to AutoCAD.
~Lee
lee.minardi
