01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of...
-
Upload
audra-beasley -
Category
Documents
-
view
218 -
download
0
Transcript of 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of...
![Page 1: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/1.jpg)
01.12.08 1
Chemometric functions in Excel Chemometric functions in Excel
Oxana Rodionova & Alexey PomerantsevOxana Rodionova & Alexey Pomerantsev
Semenov Institute of Chemical PhysicsSemenov Institute of Chemical Physics
[email protected]@chph.ras.ru
![Page 2: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/2.jpg)
01.12.08 2
Distance Learning Course in Chemometrics Distance Learning Course in Chemometrics for Technological and Natural-Science for Technological and Natural-Science Mastership EducationMastership Education
3000 km
4000 km
• Unfulfilled need in chemometric education in Russia
• Low number of qualified specialists in chemometrics
• Large distances, e.g. Moscow – Barnaul is about 3000 km
• No modern chemometrics books in Russian
• No available chemometric software
• No support from officials: government, Academy, etc
Barnaul
• Easy available everywhere => INTERNET
• Interactive layout: all calculations should be clear and repeatable
• Web friendly environment for the calculations => EXCEL
• Necessity to make and use our own (free) software => EXCEL Add-In
![Page 3: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/3.jpg)
01.12.08 3
Chemometric Chemometric calculations in calculations in Excel Excel
Excel UserInterface
VBAFunctions
С++DLL
DA
TAR
es
ults
Input
Calculations
Provides user with all possibilities of Excel interface, worksheet calculations, worksheet functions, charts, etc.
VBA helps to simplify routine work
All calculations are made "on the fly“ and very fast
![Page 4: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/4.jpg)
01.12.08 4
InstallationInstallation
http://rcs.chph.ras.ru/down/sacs.ziphttp://rcs.chph.ras.ru/down/sacs.zip
Chemometrics. xlaChemometrics. xla put in the AddInn folderput in the AddInn folder
(C:\Documents and Settings\ (C:\Documents and Settings\ <User>\Application Data\ <User>\Application Data\ Microsoft\AddIns\)Microsoft\AddIns\)
Chemometrics.dllChemometrics.dll
put in your Windows folderput in your Windows folder (C:\WINDOWS\)(C:\WINDOWS\)
Load Chemometrics.xla by < Excel Options> <Add-Ins> in the open Workbook
![Page 5: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/5.jpg)
01.12.08 5
Matrix calculations in ExcelMatrix calculations in Excel
={TRANSPOSE(B6:F10)}
={MMULT(B6:F10,TRANSPOSE(Barr))}
B6:F10
Barr
Ctrl-Shift-Enter
![Page 6: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/6.jpg)
01.12.08 6
Principal Component Analysis (PCA)Principal Component Analysis (PCA)
Initial data
Loading matrix
XI
J A
Score matrix
TI= +
×
Error matrix
EI
J
PT
J
A
PJ
A
X=TPT+E
![Page 7: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/7.jpg)
01.12.08 7
Chemometrics XLA. PCA ScoresChemometrics XLA. PCA Scores
={ScoresPCA(Xcal,5,1,Xtst)}
CenteringAND/ORweighting
nPC
XcalXcal
XtstXtst
![Page 8: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/8.jpg)
01.12.08 8
Chemometrics XLA. PCA LoadingsChemometrics XLA. PCA Loadings
=TRANSPOSE(LoadingsPCA(Xcal,5,1))}CenteringAND/ORweighting
nPCExcel worksheet function
XcalXcal
![Page 9: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/9.jpg)
01.12.08 9
List of chemometric functionsList of chemometric functionsPCA ScoresPCA <for calibration or test samples>
LoadingsPCA
PLS ScoresPLS <X-scores for calibration or test samples>
UScoresPLS <Y-scores for calibration or test samples>
LoadingsPLS <P-loadings>
WLoadingsPLS
QLoadingsPLS
PLS2 ScoresPLS2 <X-scores for calibration or test samples>
UScoresPLS2 <Y-scores for calibration or test samples>
LoadingsPLS2 <P-loadings>
WLoadingsPLS2
QLoadingsPLS2
Options:
• Centering AND/OR scaling
• Number of PCs
![Page 10: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/10.jpg)
01.12.08 10
ScoresPCAScoresPCA
ScoresPCA (rMatrix [, nPCs] [,nCentWeightX] [, rMatrixNew] )
X data (calibration set)
Number of PC (A)
centering and/or scaling
1 centering
2 scaling
3 both
Test set
X[IJ] T[I A]
![Page 11: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/11.jpg)
01.12.08 11
Validation RulesValidation Rules
If rMatrixNew is omitted then only calibration scores are calculated
If rMatrixNew is specified then only test scores are calculated
If rMatrixNew coincides with rMatrix then cross-validation is
calculated10% -out
cross-validation
![Page 12: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/12.jpg)
01.12.08 12
LoadingsPCALoadingsPCA
LoadingsPCA (rMatrix [, nPCs] [,nCentWeightX])
X data (calibration set)
Number of PC (A)
centering and/or scaling
1 centering
2 scaling
3 both
X[IJ] P[J A]
![Page 13: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/13.jpg)
01.12.08 13
Explorative Data AnalysisExplorative Data Analysis
Case study 1: People
![Page 14: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/14.jpg)
01.12.08 14
PeoplePeople
![Page 15: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/15.jpg)
01.12.08 15
Dataset in Excel Workbook (People.xls)Dataset in Excel Workbook (People.xls)
Number of objects (n) = 32
Number of variables (m) = 12
![Page 16: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/16.jpg)
01.12.08 16
Data PreprocessingData Preprocessing
Aim: to transform the data into the most suitable form for data analysis
![Page 17: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/17.jpg)
01.12.08 17
AutoscalingAutoscaling
mean centering scaling
autoscaling
+
=
![Page 18: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/18.jpg)
01.12.08 18
PeoplePeople: : Scores & Loadings (PC1 vs. PC2)Scores & Loadings (PC1 vs. PC2)
-2
0
2
4
-4 -2 0 2 4 6
t1
t2
FSFS
FS
FS
FS
FS
FS
FS
FN
FN
FNFN
FN
FN
FN
FN
MS
MSMS
MS
MSMS
MSMS
MN
MN
MNMN
MN
MN
MNMN
-2
0
2
4
-4 -2 0 2 4 6
t1
t2
Height
Weight
Hairs
Shoes
Age
IncomeBeer
Wine
Sex
Strength
Region
IQ
-0.3
0.0
0.3
0.6
-0.4 -0.2 0.0 0.2 0.4
P1
P2 a)
“Map of Samples” “Map of Variables”
![Page 19: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/19.jpg)
01.12.08 19
PeoplePeople: : Scores & Loadings (PC1 vs. PC3)Scores & Loadings (PC1 vs. PC3)
MNMN
MN
MN
MNMN
MN
MN
MSMS
MS MS
MS
MSMS
MS
FN
FN
FN
FN
FNFN
FN
FN
FS
FS
FS
FS
FS
FS
FSFS
-3
-1
1
3
-4 -2 0 2 4 6
t1
t3
Score plot Loading plot
IQ
Region
StrengthSex
Wine
Beer
Income
Age
ShoesHairs
Weight
Height
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
-0.4 -0.2 0.0 0.2 0.4
P1
P3 a)
18
20
21
2627
26
30
33
2324
2427
30
36
32
35
36
4240
41
32 3337
41
40
49
37
50
43
55
4648
-3
-2
-1
0
1
2
3
-4 -2 0 2 4 6
t1
t3
![Page 20: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/20.jpg)
01.12.08 20
Case study 2: HPLC-DADCase study 2: HPLC-DAD
![Page 21: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/21.jpg)
01.12.08 21
MeasurementsMeasurements
15
913
1721
2529
220
249
277
306
334
0.0
0.2
0.4
0.6
0.8
1.0
1.2
AU
time
wavelength
![Page 22: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/22.jpg)
01.12.08 22
Dataset in Excel WorkbookDataset in Excel Workbook
X(3028)
![Page 23: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/23.jpg)
01.12.08 23
Pure compoundsPure compounds A andA and BB
X=CST+E
0.0
0.2
0.4
0.6
0.8
1.0
220 240 260 280 300 320 340
l, nm
AU A
BC (t )
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 5 10 15 20 25 30
time
A
B
If we observe X can we predict C and S ?
![Page 24: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/24.jpg)
01.12.08 24
30292827262524232221201918
1716
1514
1312 11
10
9
8
7
6
54
3
2
1
t 1
t 2
Score plotScore plot
B
A
C (t )
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 5 10 15 20 25 30
time
A
B
![Page 25: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/25.jpg)
01.12.08 25
Conclusions from the Score PlotConclusions from the Score Plot
1. Linear regions = Pure compounds
2. Curved line= Co-elution
3. Closer to the origin = Lower intensity
4. Number of bends = Number of different compounds
![Page 26: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/26.jpg)
01.12.08 26
Factor analysis vs. PCA analysisFactor analysis vs. PCA analysis
X
E1
+
=
CST×
2
J
I
I
J
X
E2
+
=
TPT×
A
J
I
I
J
![Page 27: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/27.jpg)
01.12.08 27
Scores and LoadingsScores and Loadings
S , P
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
220 240 260 280 300 320 340
wave length
A
B
p1
p2
C , T
-0.8
0.2
1.2
2.2
3.2
0 5 10 15 20 25 30
time
A
B
t1
t2
![Page 28: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/28.jpg)
01.12.08 28
Procrustes transformationProcrustes transformation
X ≈ CST
X ≈ TPT
I = RRT = Identity matrix
X ≈ T(RRT)PT = (TR)(PR)T
C ≈ TR S ≈ PR
R = Rstretch ×Rrotation
^ ^
![Page 29: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/29.jpg)
01.12.08 29
Scores TransformationScores Transformation
3029282726252423222120191817 16 15 1413 12 11 10
9
8
7
6
54
3
21
t 1
t 2
12
3
4 5
6
7
8
9
10111213
1415161718192021222324252627282930
t 1
t 2
Stretching
12
3
45
6
7
8
9
101112131415161718192021222324252627282930
t 1
t 2
![Page 30: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/30.jpg)
01.12.08 30
Procrustes analysis resultsProcrustes analysis results
C (t )
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 5 10 15 20 25 30
time
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0C hat(t )
A
B
Ahat
Bhat
0.0
0.2
0.4
0.6
0.8
1.0
220 240 260 280 300 320 340
wavelength l, nm
S(l)
0.0
0.2
0.4
0.6
0.8
1.0
1.2S hat(l)
A
B
Ahat
Bhat
![Page 31: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/31.jpg)
01.12.08 31
Conclusions Conclusions
1. Scaling and centering is problem dependent
2. In this example number of PCs = Number of
different compounds
![Page 32: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/32.jpg)
01.12.08 32
RegressionRegression
![Page 33: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/33.jpg)
01.12.08 33
Principal Component Regression (PCR)Principal Component Regression (PCR)
Xp1
t
pAt...
tAt1
...
P
T
a = + e yT
1) PCA
2) MLR
![Page 34: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/34.jpg)
01.12.08 34
Projection on Latent Structures (PLS)Projection on Latent Structures (PLS)
w1 t
wA t...
Xp1
t
pAt...
tAt1
... Yu1 uA
...
...q1
t
qAtQ
U
P
T
W
![Page 35: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/35.jpg)
01.12.08 35
Projection on Latent Structures (PLS)Projection on Latent Structures (PLS)
B = + e YT
![Page 36: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/36.jpg)
01.12.08 36
PLS and PLS2PLS and PLS2
b = + e yT1
1 1
B = + E YTM
M M
PLS
PLS2
![Page 37: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/37.jpg)
01.12.08 37
ScoresPLSScoresPLS
ScoresPLS (rMatrixX, rMatrixY
[, nPCs] [, nCentWeightX] [, nCentWeightY] [, rMatrixXNew])
X data (calibration set)
Number of PC (A)
centering and/or scaling of X
1 centering
2 scaling
3 both
X Test set
Y data (calibration set)
centering and/or scaling of Y
1 centering
2 scaling
3 both
X[IJ], Y[I1] T[IA]
![Page 38: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/38.jpg)
01.12.08 38
UScoresPLSUScoresPLS
UScoresPLS (rMatrixX, rMatrixY
[, nPCs] [, nCentWeightX] [, nCentWeightY] [, rMatrixXNew] [,
rMatrixYNew])
X data (calibration set)
Number of PC (A)
centering and/or scaling of X
1 centering
2 scaling
3 both
X Test set
Y data (calibration set)
centering and/or scaling of Y
1 centering
2 scaling
3 both
Y Test set
X[IJ] , Y[I1] U[I A]
![Page 39: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/39.jpg)
01.12.08 39
WLoadingsPLSWLoadingsPLS
WLoadingsPLS (rMatrixX, rMatrixY
[, nPCs] [, nCentWeightX] [, nCentWeightY])
X data (calibration set)
Number of PC (A)
centering and/or scaling of X
1 centering
2 scaling
3 both
Y data (calibration set)
centering and/or scaling of Y
1 centering
2 scaling
3 both
X[IJ] , Y[I1] W[J A]
![Page 40: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/40.jpg)
01.12.08 40
LoadingsPLSLoadingsPLS
LoadingsPLS (rMatrixX, rMatrixY
[, nPCs] [, nCentWeightX] [, nCentWeightY])
X data (calibration set)
Number of PC (A)
centering and/or scaling of X
1 centering
2 scaling
3 both
Y data (calibration set)
centering and/or scaling of Y
1 centering
2 scaling
3 both
X[IJ] , Y[I1] P[JA]
![Page 41: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/41.jpg)
01.12.08 41
QLoadingsPLSQLoadingsPLS
QLoadingsPLS (rMatrixX, rMatrixY
[, nPCs] [, nCentWeightX] [, nCentWeightY])
X data (calibration set)
Number of PC (A)
centering and/or scaling of X
1 centering
2 scaling
3 both
Y data (calibration set)
centering and/or scaling of Y
1 centering
2 scaling
3 both
X[IJ], Y[I1] Q[1 A]
![Page 42: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/42.jpg)
01.12.08 42
ScoresPLS2ScoresPLS2
ScoresPLS2 (rMatrixX, rMatrixY
[, nPCs] [, nCentWeightX] [, nCentWeightY] [, rMatrixXNew])
X data (calibration set)
Number of PC (A)
centering and/or scaling of X
1 centering
2 scaling
3 both
X Test set
Y data (calibration set)
centering and/or scaling of Y
1 centering
2 scaling
3 both
X[IJ], Y[IK] T[I A]
![Page 43: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/43.jpg)
01.12.08 43
UScoresPLS2UScoresPLS2
UScoresPLS2 (rMatrixX, rMatrixY
[, nPCs] [, nCentWeightX] [, nCentWeightY] [, rMatrixXNew] [,
rMatrixYNew])
X data (calibration set)
Number of PC (A)
centering and/or scaling of X
1 centering
2 scaling
3 both
X Test set
Y data (calibration set)
centering and/or scaling of Y
1 centering
2 scaling
3 both
Y Test set
X[IJ], Y[IK] U[I A]
![Page 44: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/44.jpg)
01.12.08 44
LoadingsPLS2LoadingsPLS2
LoadingsPLS2 (rMatrixX, rMatrixY
[, nPCs] [, nCentWeightX] [, nCentWeightY])
X data (calibration set)
Number of PC (A)
centering and/or scaling of X
1 centering
2 scaling
3 both
Y data (calibration set)
centering and/or scaling of Y
1 centering
2 scaling
3 both
WLoadingsPLS2WLoadingsPLS2
QLoadingsPLS2QLoadingsPLS2
X[IJ], Y[IK] P[J A] or W[J A] or Q[K A]
![Page 45: 01.12.08 1 Chemometric functions in Excel Oxana Rodionova & Alexey Pomerantsev Semenov Institute of Chemical Physics rcs@chph.ras.ru.](https://reader030.fdocuments.net/reader030/viewer/2022032708/56649e5d5503460f94b553a7/html5/thumbnails/45.jpg)
01.12.08 45
Seventh Winter Symposium on Seventh Winter Symposium on ChemometricsChemometrics
near Tula city, February 2010
100 km