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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 21 Dec 2016 17:19:26 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/21/t1482337186j87m2w0jjuzofv8.htm/, Retrieved Mon, 06 May 2024 18:30:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302414, Retrieved Mon, 06 May 2024 18:30:39 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact53
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Backward Selection] [arima backward ] [2016-12-21 09:55:50] [3b3f8501f11153ebb77cc78b956c8d99]
- RMP     [Exponential Smoothing] [] [2016-12-21 16:19:26] [bd7223969ac5b08f41438741a34686d6] [Current]
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Dataseries X:
7732.01
7905.27
8098.32
9143.32
9283.07
9480.25
9720.24
9765.41
9724.25
9207.97
9015.39
7244.45
6243.13
6218.68
6251.37
6088.65
6265.25
6146.75
5846.79
4839.25
4744.82
4581.5
4534.04
4678.62
4607.46
4808.33
4944.31
5157.91
5280.66
5405.02
5609.6
5930.32
5855.98
6069.38
6135.39
5949.96




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302414&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302414&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302414&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.448569230586372
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.448569230586372 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302414&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.448569230586372[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302414&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302414&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.448569230586372
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
38098.328078.5319.7899999999991
49143.328280.4571850733862.862814926695
59283.079712.51089406656-429.440894066563
69480.259659.6269226328-179.3769226328
79720.249776.34395446245-56.1039544624546
89765.419991.16744677638-225.757446776379
99724.259935.06960257675-210.819602576754
109207.979799.34241565637-591.372415656375
119015.399017.79094617539-2.40094617539035
127244.458824.13395559682-1579.68395559682
136243.136344.59633906512-101.466339065116
146218.685297.76166142026920.918338579739
156251.375686.40729198986564.962708010145
166088.655972.52217923196116.127820768042
176265.255861.89354644355403.356453556449
186146.756219.42684046741-72.6768404674149
195846.796068.3262460575-221.536246057498
204839.255668.99190261649-829.741902616493
214744.824289.25521577454455.564784225459
224581.54399.1775605168182.322439483199
234534.044317.64179691441216.39820308559
244678.624367.25137237279311.368627627213
254607.464651.50175809626-44.0417580962603
264808.334560.58598055335247.74401944665
274944.314872.5863247389171.7236752610916
285157.915040.7393585656117.170641434396
295280.665306.89850304114-26.2385030411424
305405.025417.87871792024-12.8587179202386
315609.65536.4706927164373.1293072835697
325930.325773.85424981794156.465750182064
335855.986164.75997099022-308.779970990224
346069.385951.91077698266117.469223017344
356135.396218.00385596913-82.6138559691253
365949.966246.95582216128-296.995822161282

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 8098.32 & 8078.53 & 19.7899999999991 \tabularnewline
4 & 9143.32 & 8280.4571850733 & 862.862814926695 \tabularnewline
5 & 9283.07 & 9712.51089406656 & -429.440894066563 \tabularnewline
6 & 9480.25 & 9659.6269226328 & -179.3769226328 \tabularnewline
7 & 9720.24 & 9776.34395446245 & -56.1039544624546 \tabularnewline
8 & 9765.41 & 9991.16744677638 & -225.757446776379 \tabularnewline
9 & 9724.25 & 9935.06960257675 & -210.819602576754 \tabularnewline
10 & 9207.97 & 9799.34241565637 & -591.372415656375 \tabularnewline
11 & 9015.39 & 9017.79094617539 & -2.40094617539035 \tabularnewline
12 & 7244.45 & 8824.13395559682 & -1579.68395559682 \tabularnewline
13 & 6243.13 & 6344.59633906512 & -101.466339065116 \tabularnewline
14 & 6218.68 & 5297.76166142026 & 920.918338579739 \tabularnewline
15 & 6251.37 & 5686.40729198986 & 564.962708010145 \tabularnewline
16 & 6088.65 & 5972.52217923196 & 116.127820768042 \tabularnewline
17 & 6265.25 & 5861.89354644355 & 403.356453556449 \tabularnewline
18 & 6146.75 & 6219.42684046741 & -72.6768404674149 \tabularnewline
19 & 5846.79 & 6068.3262460575 & -221.536246057498 \tabularnewline
20 & 4839.25 & 5668.99190261649 & -829.741902616493 \tabularnewline
21 & 4744.82 & 4289.25521577454 & 455.564784225459 \tabularnewline
22 & 4581.5 & 4399.1775605168 & 182.322439483199 \tabularnewline
23 & 4534.04 & 4317.64179691441 & 216.39820308559 \tabularnewline
24 & 4678.62 & 4367.25137237279 & 311.368627627213 \tabularnewline
25 & 4607.46 & 4651.50175809626 & -44.0417580962603 \tabularnewline
26 & 4808.33 & 4560.58598055335 & 247.74401944665 \tabularnewline
27 & 4944.31 & 4872.58632473891 & 71.7236752610916 \tabularnewline
28 & 5157.91 & 5040.7393585656 & 117.170641434396 \tabularnewline
29 & 5280.66 & 5306.89850304114 & -26.2385030411424 \tabularnewline
30 & 5405.02 & 5417.87871792024 & -12.8587179202386 \tabularnewline
31 & 5609.6 & 5536.47069271643 & 73.1293072835697 \tabularnewline
32 & 5930.32 & 5773.85424981794 & 156.465750182064 \tabularnewline
33 & 5855.98 & 6164.75997099022 & -308.779970990224 \tabularnewline
34 & 6069.38 & 5951.91077698266 & 117.469223017344 \tabularnewline
35 & 6135.39 & 6218.00385596913 & -82.6138559691253 \tabularnewline
36 & 5949.96 & 6246.95582216128 & -296.995822161282 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302414&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]8098.32[/C][C]8078.53[/C][C]19.7899999999991[/C][/ROW]
[ROW][C]4[/C][C]9143.32[/C][C]8280.4571850733[/C][C]862.862814926695[/C][/ROW]
[ROW][C]5[/C][C]9283.07[/C][C]9712.51089406656[/C][C]-429.440894066563[/C][/ROW]
[ROW][C]6[/C][C]9480.25[/C][C]9659.6269226328[/C][C]-179.3769226328[/C][/ROW]
[ROW][C]7[/C][C]9720.24[/C][C]9776.34395446245[/C][C]-56.1039544624546[/C][/ROW]
[ROW][C]8[/C][C]9765.41[/C][C]9991.16744677638[/C][C]-225.757446776379[/C][/ROW]
[ROW][C]9[/C][C]9724.25[/C][C]9935.06960257675[/C][C]-210.819602576754[/C][/ROW]
[ROW][C]10[/C][C]9207.97[/C][C]9799.34241565637[/C][C]-591.372415656375[/C][/ROW]
[ROW][C]11[/C][C]9015.39[/C][C]9017.79094617539[/C][C]-2.40094617539035[/C][/ROW]
[ROW][C]12[/C][C]7244.45[/C][C]8824.13395559682[/C][C]-1579.68395559682[/C][/ROW]
[ROW][C]13[/C][C]6243.13[/C][C]6344.59633906512[/C][C]-101.466339065116[/C][/ROW]
[ROW][C]14[/C][C]6218.68[/C][C]5297.76166142026[/C][C]920.918338579739[/C][/ROW]
[ROW][C]15[/C][C]6251.37[/C][C]5686.40729198986[/C][C]564.962708010145[/C][/ROW]
[ROW][C]16[/C][C]6088.65[/C][C]5972.52217923196[/C][C]116.127820768042[/C][/ROW]
[ROW][C]17[/C][C]6265.25[/C][C]5861.89354644355[/C][C]403.356453556449[/C][/ROW]
[ROW][C]18[/C][C]6146.75[/C][C]6219.42684046741[/C][C]-72.6768404674149[/C][/ROW]
[ROW][C]19[/C][C]5846.79[/C][C]6068.3262460575[/C][C]-221.536246057498[/C][/ROW]
[ROW][C]20[/C][C]4839.25[/C][C]5668.99190261649[/C][C]-829.741902616493[/C][/ROW]
[ROW][C]21[/C][C]4744.82[/C][C]4289.25521577454[/C][C]455.564784225459[/C][/ROW]
[ROW][C]22[/C][C]4581.5[/C][C]4399.1775605168[/C][C]182.322439483199[/C][/ROW]
[ROW][C]23[/C][C]4534.04[/C][C]4317.64179691441[/C][C]216.39820308559[/C][/ROW]
[ROW][C]24[/C][C]4678.62[/C][C]4367.25137237279[/C][C]311.368627627213[/C][/ROW]
[ROW][C]25[/C][C]4607.46[/C][C]4651.50175809626[/C][C]-44.0417580962603[/C][/ROW]
[ROW][C]26[/C][C]4808.33[/C][C]4560.58598055335[/C][C]247.74401944665[/C][/ROW]
[ROW][C]27[/C][C]4944.31[/C][C]4872.58632473891[/C][C]71.7236752610916[/C][/ROW]
[ROW][C]28[/C][C]5157.91[/C][C]5040.7393585656[/C][C]117.170641434396[/C][/ROW]
[ROW][C]29[/C][C]5280.66[/C][C]5306.89850304114[/C][C]-26.2385030411424[/C][/ROW]
[ROW][C]30[/C][C]5405.02[/C][C]5417.87871792024[/C][C]-12.8587179202386[/C][/ROW]
[ROW][C]31[/C][C]5609.6[/C][C]5536.47069271643[/C][C]73.1293072835697[/C][/ROW]
[ROW][C]32[/C][C]5930.32[/C][C]5773.85424981794[/C][C]156.465750182064[/C][/ROW]
[ROW][C]33[/C][C]5855.98[/C][C]6164.75997099022[/C][C]-308.779970990224[/C][/ROW]
[ROW][C]34[/C][C]6069.38[/C][C]5951.91077698266[/C][C]117.469223017344[/C][/ROW]
[ROW][C]35[/C][C]6135.39[/C][C]6218.00385596913[/C][C]-82.6138559691253[/C][/ROW]
[ROW][C]36[/C][C]5949.96[/C][C]6246.95582216128[/C][C]-296.995822161282[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302414&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302414&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
38098.328078.5319.7899999999991
49143.328280.4571850733862.862814926695
59283.079712.51089406656-429.440894066563
69480.259659.6269226328-179.3769226328
79720.249776.34395446245-56.1039544624546
89765.419991.16744677638-225.757446776379
99724.259935.06960257675-210.819602576754
109207.979799.34241565637-591.372415656375
119015.399017.79094617539-2.40094617539035
127244.458824.13395559682-1579.68395559682
136243.136344.59633906512-101.466339065116
146218.685297.76166142026920.918338579739
156251.375686.40729198986564.962708010145
166088.655972.52217923196116.127820768042
176265.255861.89354644355403.356453556449
186146.756219.42684046741-72.6768404674149
195846.796068.3262460575-221.536246057498
204839.255668.99190261649-829.741902616493
214744.824289.25521577454455.564784225459
224581.54399.1775605168182.322439483199
234534.044317.64179691441216.39820308559
244678.624367.25137237279311.368627627213
254607.464651.50175809626-44.0417580962603
264808.334560.58598055335247.74401944665
274944.314872.5863247389171.7236752610916
285157.915040.7393585656117.170641434396
295280.665306.89850304114-26.2385030411424
305405.025417.87871792024-12.8587179202386
315609.65536.4706927164373.1293072835697
325930.325773.85424981794156.465750182064
335855.986164.75997099022-308.779970990224
346069.385951.91077698266117.469223017344
356135.396218.00385596913-82.6138559691253
365949.966246.95582216128-296.995822161282







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
375928.302634727035045.306803928316811.29846552575
385906.645269454064352.383774057627460.9067648505
395884.987904181093599.838510490238170.13729787194
405863.330538908112779.179962437748947.48111537848
415841.673173635141892.024309300999791.32203796929
425820.01580836217941.60437163814710698.4272450862
435798.3584430892-68.776039476131711665.4929256545
445776.70107781623-1136.0841132678812689.4862689003
455755.04371254326-2257.6125639699913767.6999890565
465733.38634727029-3430.9585738807514897.7312684213
475711.72898199731-4653.985516183916077.4434801785
485690.07161672434-5924.7845835207917304.9278169695

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
37 & 5928.30263472703 & 5045.30680392831 & 6811.29846552575 \tabularnewline
38 & 5906.64526945406 & 4352.38377405762 & 7460.9067648505 \tabularnewline
39 & 5884.98790418109 & 3599.83851049023 & 8170.13729787194 \tabularnewline
40 & 5863.33053890811 & 2779.17996243774 & 8947.48111537848 \tabularnewline
41 & 5841.67317363514 & 1892.02430930099 & 9791.32203796929 \tabularnewline
42 & 5820.01580836217 & 941.604371638147 & 10698.4272450862 \tabularnewline
43 & 5798.3584430892 & -68.7760394761317 & 11665.4929256545 \tabularnewline
44 & 5776.70107781623 & -1136.08411326788 & 12689.4862689003 \tabularnewline
45 & 5755.04371254326 & -2257.61256396999 & 13767.6999890565 \tabularnewline
46 & 5733.38634727029 & -3430.95857388075 & 14897.7312684213 \tabularnewline
47 & 5711.72898199731 & -4653.9855161839 & 16077.4434801785 \tabularnewline
48 & 5690.07161672434 & -5924.78458352079 & 17304.9278169695 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302414&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]37[/C][C]5928.30263472703[/C][C]5045.30680392831[/C][C]6811.29846552575[/C][/ROW]
[ROW][C]38[/C][C]5906.64526945406[/C][C]4352.38377405762[/C][C]7460.9067648505[/C][/ROW]
[ROW][C]39[/C][C]5884.98790418109[/C][C]3599.83851049023[/C][C]8170.13729787194[/C][/ROW]
[ROW][C]40[/C][C]5863.33053890811[/C][C]2779.17996243774[/C][C]8947.48111537848[/C][/ROW]
[ROW][C]41[/C][C]5841.67317363514[/C][C]1892.02430930099[/C][C]9791.32203796929[/C][/ROW]
[ROW][C]42[/C][C]5820.01580836217[/C][C]941.604371638147[/C][C]10698.4272450862[/C][/ROW]
[ROW][C]43[/C][C]5798.3584430892[/C][C]-68.7760394761317[/C][C]11665.4929256545[/C][/ROW]
[ROW][C]44[/C][C]5776.70107781623[/C][C]-1136.08411326788[/C][C]12689.4862689003[/C][/ROW]
[ROW][C]45[/C][C]5755.04371254326[/C][C]-2257.61256396999[/C][C]13767.6999890565[/C][/ROW]
[ROW][C]46[/C][C]5733.38634727029[/C][C]-3430.95857388075[/C][C]14897.7312684213[/C][/ROW]
[ROW][C]47[/C][C]5711.72898199731[/C][C]-4653.9855161839[/C][C]16077.4434801785[/C][/ROW]
[ROW][C]48[/C][C]5690.07161672434[/C][C]-5924.78458352079[/C][C]17304.9278169695[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302414&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302414&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
375928.302634727035045.306803928316811.29846552575
385906.645269454064352.383774057627460.9067648505
395884.987904181093599.838510490238170.13729787194
405863.330538908112779.179962437748947.48111537848
415841.673173635141892.024309300999791.32203796929
425820.01580836217941.60437163814710698.4272450862
435798.3584430892-68.776039476131711665.4929256545
445776.70107781623-1136.0841132678812689.4862689003
455755.04371254326-2257.6125639699913767.6999890565
465733.38634727029-3430.9585738807514897.7312684213
475711.72898199731-4653.985516183916077.4434801785
485690.07161672434-5924.7845835207917304.9278169695



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')