Hi Regina,
On 2018-05-06 03:41 PM, Regina Henschel
wrote:
Hi Andreas,"indeed" to both of these observations.
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.
Whether this is done in column-major, row-major or any other order is meaningless since addition is commutative.
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 column-major or row-major
order. I have specified them as row-major. 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 "column-major or row-major 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 28-LINEST'.
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 y-values in the array.
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 would change the specification of the LINEST function (that is currently mis-specified) in a way that is incompatible with at least 2 implementations.
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.
The omitted knownX case always results in a linear, not a multiple regression.
That fits to all three cases.
Andreas
I have added a document with these changes.
Kind regards
Regina
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