the attached file also fixes the 4 more places pointed out by
Regina to have incorrect indices. This file specifies the default
for the second parameter as used by Excel & Gnumeric.
On 2018-05-06 03:41 PM, Regina Henschel
I think the index of y in R² is still wrong. It should be i but it
And I have noticed an element x12 instead of x21 in the matrix X,
which I have overseen before.
Andreas J Guelzow schrieb am 06.05.2018 um 20:51:
I was asked to review the LINEST description with a special view
correct use of the subscripts. I have attached the changes as an
file containing the LINEST description with the required
changes. I have
enabled track changes so that the changes are easier viewable.
I have made one, likely controversial, change:
knownX is optional and we currently just say that by default it
sequence 1 through k. Since knownX has to be a correctly sized
the rest of the description to make sense, there are two natural
possibilities: the entries could be given in column-major or
order. I have specified them as row-major. That is what Excel
Gnumeric 1.12.40 are doing. Libreoffice 126.96.36.199 appears to use
major order instead.
Alternatively we could specify "column-major or row-major order
choice being implementation defined".
In case "COLUMNS(knownY)<>1 and ROWS(knownY)<>1" the
knownX and the knownY both are arranged in column major order to
x1n, x2n,..,xkn and y1, y2, ... yk in the specification. The
notation x1n, x2n,..,xkn is effectively x11,x21,..,xk1 because,
n=1 in that case. You find this in the paragraph below 'Table
In case "ROWS(knownY)=1" the description contains a transpose of
the knownX matrix, so that the first row of the knownX values
becomes x11,x21,..,xk1 notation.
In case "COLUMN(knownY)=1" the knownX matrix are denoted in
mathematical way directly with first column as x11,x21,..xk1.
I dislike to introduce an arrangement of the ersatz values
1,2,..,k. It is not needed. Keep the sentence "If omitted or an
empty parameter, it is set to the sequence .." in the paragraph
In case you want a more precise description, we can add before the
paragraph starting with "We denote 'x_i quer ..' and 'y quer' the
In case knownX are omitted or an empty parameter, n=1 and the
above mentioned sequence 1,2,..,k is used as ersatz for
That fits to all three cases.
I have added a document with these changes.
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