I'm not exactly sure of what you mean by this Jerry. Can you elaborate?

In addition to Jerry's adivce, Arrays passed to Linest appear to  need to be
1 based, not zero based.  

Here is a working example that returns the coefficients for a 6th degree
polynomial.

Sub abc()
 Dim v2 As Variant
 Dim v() As Double
 Dim r() As Double
 Dim v1 As Variant
 Dim i As Long, j As Long
  ReDim r(0 To 1, 0 To 6)
 v2 = Array(5, 15, 89, 851, 4677, _
 17615, 52025, 129939, 287141, _
 577967, 1080825)
 ReDim v(1 To UBound(v2) - LBound(v2) + 1, 1 To 1)
 j = LBound(v2)
 ' make v a 1-based 2-D array
 ' it will be passed as Date
 For i = 1 To UBound(v)
   v(i, 1) = v2(j)
   j = j + 1
 Next
   
 v1 = DoLinest(v, r)
 Debug.Print v1
 For i = LBound(r, 2) To UBound(r, 2)
   Debug.Print i, Application.Round(r(LBound(r), i), 0)
 Next
 End Sub
 
 
 
 
 Private Function DoLinest(Data() As Double, ByRef Result() As Double) As
Long
 
 'On Error GoTo FunctionError
 
 Dim wsf As WorksheetFunction
 
 Set wsf = Application.WorksheetFunction
 
 ' Depending on the number of samples passed to the function in DATA(),
 ' number the x values from 0 to N.
 Dim intXterms() As Long
 Dim v As Variant, r1 As Long
 Dim v1 As Variant, c1 As Long
 Dim i As Long, j As Long, k As Long
 ReDim intXterms(0 To UBound(Data))
 Dim intCounter As Integer
 For intCounter = 0 To UBound(Data)
 intXterms(intCounter) = intCounter
 Next intCounter
 
 ' The exponents are determined by the second part of the array, what
 ' would be columns in the worksheet. I am trying to get a sixth order,
 ' so this array would be {1,2,3,4,5,6}
 ' NOTE: For clarity, I should have labeled the intCoeff variable as
intExponents
 intCounter = UBound(Result, 2) - LBound(Result, 2)
 ReDim v1(LBound(Data) To UBound(Data), _
    1 To intCounter)
 k = 0
 For i = LBound(Data) To UBound(Data)
    For j = 1 To intCounter
      v1(i, j) = (i - 1) ^ j
'       Debug.Print " V1(" & i & "," & j & ")=" & v1(i, j);
    Next
'     Debug.Print
 Next
'  R1 = UBound(v1, 1) - LBound(v1, 1) + 1
'  c1 = UBound(v1, 2) - LBound(v1, 2) + 1
'  Worksheets("Sheet2").Range("A1").Resize(R1, c1).Value = v1
 v = Application.LinEst(Data, v1, , True)
 If IsError(v) Then
   MsgBox "Bad data"
   Exit Function
 End If
 j = LBound(v, 2)
 For i = LBound(Result, 2) To UBound(Result, 2)
   Result(LBound(Result, 1), i) = v(LBound(v, 1), j)
   j = j + 1
 Next
 DoLinest = 0
 Exit Function
 
FunctionError:
 Debug.Print Err.Number
 Debug.Print Err.Description
 DoLinest = -1007
 
 End Function

I've used the linest function in the worksheets on multiple sets of
data. I found that I consistently obtained an R² value that was greater
than .99 when I used the sixth order. I understand that the R² value is
a "rating" of how well the function fits the actual data and a rating
of 1 is best.

Some data sets fit fine with a third degree and some required higher
order fitting. I agree that it is probably overkill in some of the data
sets, but I need the precision at times. Thanks for the advice.