Hi Regina,
On 20180506 03:41 PM, Regina Henschel
wrote:
Hi
Andreas,
I think the index of y in R² is still wrong. It should be i but it
is k.
And I have noticed an element x12 instead of x21 in the matrix X,
which I have overseen before.
"indeed" to both of these observations.
Andreas J Guelzow schrieb am 06.05.2018 um 20:51:
Hi,
I was asked to review the LINEST description with a special view
of the
correct use of the subscripts. I have attached the changes as an
odf
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
is the
sequence 1 through k. Since knownX has to be a correctly sized
array for
the rest of the description to make sense, there are two natural
possibilities: the entries could be given in columnmajor or
rowmajor
order. I have specified them as rowmajor. That is what Excel
2016 and
Gnumeric 1.12.40 are doing. Libreoffice 5.1.6.2 appears to use
column
major order instead.
Alternatively we could specify "columnmajor or rowmajor order
with the
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
28LINEST'.
Whether this is done in columnmajor, rowmajor or any other order
is meaningless since addition is commutative.
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
"knownX:.."
This is anything but "not needed". Try the following: Take the 2 by
2 matrix A1:B2 with entries in row major order 1,2, 3, 3.5 and
evaluate LINEST(A1:B2). You will get one answer in Excel/Gnumeric
and another in LibreOffice. IN this part of the description knownX
is still an array, not a sequence! So saying that if it is omitted
or an empty parameter to be a sequence is nonsensical. We need to
know how these values match with the yvalues in the array.
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
sentence:
In case knownX are omitted or an empty parameter, n=1 and the
above mentioned sequence 1,2,..,k is used as ersatz for
x11,x21,..,xk1.
This would change the specification of the LINEST function (that is
currently misspecified) in a way that is incompatible with at least
2 implementations.
That fits to all three cases.
The omitted knownX case always results in a linear, not a multiple
regression.
Andreas
I have added a document with these changes.
Kind regards
Regina

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