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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 computationFri, 16 Dec 2016 21:17:31 +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/16/t1481919475jqotz67bppklhbf.htm/, Retrieved Thu, 02 May 2024 17:42:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300539, Retrieved Thu, 02 May 2024 17:42:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact41
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-16 20:17:31] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataseries X:
2380
2354
2343
2362
2352
2341
2324
2362
2421
2451
2436
2444
2421
2427
2390
2369
2408
2356
2297
2262
2266
2347
2330
2331
2267
2163
2095
2006
2061
1954
1841
1837
1777
1757
1715
1691
1683
1658
1660
1669
1689
1644
1573
1535
1526
1536
1526
1498
1470
1485
1452
1442
1373
1373
1397
1352
1355
1336
1347
1323
1289
1265
1244




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=300539&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=300539&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300539&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
beta0.0117901820162066
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0117901820162066 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300539&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]0.0117901820162066[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300539&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300539&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
beta0.0117901820162066
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32343232815
423622317.1768527302444.8231472697571
523522336.7053257950915.2946742049071
623412326.8856527878514.114347212153
723242316.052063510527.94793648948144
823622299.1457711283862.8542288716171
924212337.8868339272783.1131660727328
1024512397.8667532832153.1332467167917
1124362428.493203933117.50679606688891
1224442413.581710425130.4182895749018
1324212421.94034759581-0.940347595807907
1424272398.9292607264928.0707392735053
1523902405.26021985186-15.2602198518589
1623692368.08029908220.919700917801947
1724082347.0911425234260.9088574765806
1823562386.80926903947-30.8092690394678
1922972334.44602214971-37.4460221497061
2022622275.00452673278-13.0045267327782
2122662239.8512009955626.1487990044361
2223472244.15950009533102.840499904668
2323302326.372008307853.62799169215486
2423312309.4147829902521.585217009751
2522672310.66927662765-43.6692766276533
2621632246.1544079077-83.1544079076971
2720952141.17400230302-46.1740023030156
2820062072.62960241145-66.6296024114463
2920611982.8440272713578.1559727286522
3019542038.76550041547-84.7655004154724
3118411930.76609973688-89.7660997368791
3218371816.707741082120.2922589179036
3317771812.94699050826-35.9469905082585
3417571752.523168947234.47683105276883
3517151732.5759516002-17.5759516001992
3616911690.368727931720.631272068275166
3716831666.3761707443116.6238292556884
3816581658.57216871704-0.572168717042359
3916601633.5654227437226.4345772562756
4016691635.877091221133.1229087789025
4116891645.2676163445143.7323836554931
4216441665.78322910781-21.7832291078078
4315731620.52640087173-47.5264008717261
4415351548.96605595487-13.9660559548731
4515261510.8013936131215.1986063868833
4615361501.9805879488134.0194120511894
4715261512.3816830089813.6183169910214
4814981502.54224544506-4.54224544505701
4914701474.4886915445-4.48869154449767
5014851446.4357690541738.5642309458267
5114521461.89044835634-9.89044835633968
5214421428.7738381713.2261618300035
5313731418.92977702535-45.9297770253481
5413731349.3882565942623.6117434057446
5513971349.6666433467347.3333566532708
5613521374.22471223711-22.2247122371093
5713551328.9626788345826.0373211654241
5813361332.269663590333.73033640966923
5913471313.3136449355833.6863550644177
6013231324.71081319325-1.71081319325435
6112891300.69064239431-11.6906423943101
6212651266.55280759259-1.55280759259495
6312441242.534499708441.46550029155787

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2343 & 2328 & 15 \tabularnewline
4 & 2362 & 2317.17685273024 & 44.8231472697571 \tabularnewline
5 & 2352 & 2336.70532579509 & 15.2946742049071 \tabularnewline
6 & 2341 & 2326.88565278785 & 14.114347212153 \tabularnewline
7 & 2324 & 2316.05206351052 & 7.94793648948144 \tabularnewline
8 & 2362 & 2299.14577112838 & 62.8542288716171 \tabularnewline
9 & 2421 & 2337.88683392727 & 83.1131660727328 \tabularnewline
10 & 2451 & 2397.86675328321 & 53.1332467167917 \tabularnewline
11 & 2436 & 2428.49320393311 & 7.50679606688891 \tabularnewline
12 & 2444 & 2413.5817104251 & 30.4182895749018 \tabularnewline
13 & 2421 & 2421.94034759581 & -0.940347595807907 \tabularnewline
14 & 2427 & 2398.92926072649 & 28.0707392735053 \tabularnewline
15 & 2390 & 2405.26021985186 & -15.2602198518589 \tabularnewline
16 & 2369 & 2368.0802990822 & 0.919700917801947 \tabularnewline
17 & 2408 & 2347.09114252342 & 60.9088574765806 \tabularnewline
18 & 2356 & 2386.80926903947 & -30.8092690394678 \tabularnewline
19 & 2297 & 2334.44602214971 & -37.4460221497061 \tabularnewline
20 & 2262 & 2275.00452673278 & -13.0045267327782 \tabularnewline
21 & 2266 & 2239.85120099556 & 26.1487990044361 \tabularnewline
22 & 2347 & 2244.15950009533 & 102.840499904668 \tabularnewline
23 & 2330 & 2326.37200830785 & 3.62799169215486 \tabularnewline
24 & 2331 & 2309.41478299025 & 21.585217009751 \tabularnewline
25 & 2267 & 2310.66927662765 & -43.6692766276533 \tabularnewline
26 & 2163 & 2246.1544079077 & -83.1544079076971 \tabularnewline
27 & 2095 & 2141.17400230302 & -46.1740023030156 \tabularnewline
28 & 2006 & 2072.62960241145 & -66.6296024114463 \tabularnewline
29 & 2061 & 1982.84402727135 & 78.1559727286522 \tabularnewline
30 & 1954 & 2038.76550041547 & -84.7655004154724 \tabularnewline
31 & 1841 & 1930.76609973688 & -89.7660997368791 \tabularnewline
32 & 1837 & 1816.7077410821 & 20.2922589179036 \tabularnewline
33 & 1777 & 1812.94699050826 & -35.9469905082585 \tabularnewline
34 & 1757 & 1752.52316894723 & 4.47683105276883 \tabularnewline
35 & 1715 & 1732.5759516002 & -17.5759516001992 \tabularnewline
36 & 1691 & 1690.36872793172 & 0.631272068275166 \tabularnewline
37 & 1683 & 1666.37617074431 & 16.6238292556884 \tabularnewline
38 & 1658 & 1658.57216871704 & -0.572168717042359 \tabularnewline
39 & 1660 & 1633.56542274372 & 26.4345772562756 \tabularnewline
40 & 1669 & 1635.8770912211 & 33.1229087789025 \tabularnewline
41 & 1689 & 1645.26761634451 & 43.7323836554931 \tabularnewline
42 & 1644 & 1665.78322910781 & -21.7832291078078 \tabularnewline
43 & 1573 & 1620.52640087173 & -47.5264008717261 \tabularnewline
44 & 1535 & 1548.96605595487 & -13.9660559548731 \tabularnewline
45 & 1526 & 1510.80139361312 & 15.1986063868833 \tabularnewline
46 & 1536 & 1501.98058794881 & 34.0194120511894 \tabularnewline
47 & 1526 & 1512.38168300898 & 13.6183169910214 \tabularnewline
48 & 1498 & 1502.54224544506 & -4.54224544505701 \tabularnewline
49 & 1470 & 1474.4886915445 & -4.48869154449767 \tabularnewline
50 & 1485 & 1446.43576905417 & 38.5642309458267 \tabularnewline
51 & 1452 & 1461.89044835634 & -9.89044835633968 \tabularnewline
52 & 1442 & 1428.77383817 & 13.2261618300035 \tabularnewline
53 & 1373 & 1418.92977702535 & -45.9297770253481 \tabularnewline
54 & 1373 & 1349.38825659426 & 23.6117434057446 \tabularnewline
55 & 1397 & 1349.66664334673 & 47.3333566532708 \tabularnewline
56 & 1352 & 1374.22471223711 & -22.2247122371093 \tabularnewline
57 & 1355 & 1328.96267883458 & 26.0373211654241 \tabularnewline
58 & 1336 & 1332.26966359033 & 3.73033640966923 \tabularnewline
59 & 1347 & 1313.31364493558 & 33.6863550644177 \tabularnewline
60 & 1323 & 1324.71081319325 & -1.71081319325435 \tabularnewline
61 & 1289 & 1300.69064239431 & -11.6906423943101 \tabularnewline
62 & 1265 & 1266.55280759259 & -1.55280759259495 \tabularnewline
63 & 1244 & 1242.53449970844 & 1.46550029155787 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300539&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]2343[/C][C]2328[/C][C]15[/C][/ROW]
[ROW][C]4[/C][C]2362[/C][C]2317.17685273024[/C][C]44.8231472697571[/C][/ROW]
[ROW][C]5[/C][C]2352[/C][C]2336.70532579509[/C][C]15.2946742049071[/C][/ROW]
[ROW][C]6[/C][C]2341[/C][C]2326.88565278785[/C][C]14.114347212153[/C][/ROW]
[ROW][C]7[/C][C]2324[/C][C]2316.05206351052[/C][C]7.94793648948144[/C][/ROW]
[ROW][C]8[/C][C]2362[/C][C]2299.14577112838[/C][C]62.8542288716171[/C][/ROW]
[ROW][C]9[/C][C]2421[/C][C]2337.88683392727[/C][C]83.1131660727328[/C][/ROW]
[ROW][C]10[/C][C]2451[/C][C]2397.86675328321[/C][C]53.1332467167917[/C][/ROW]
[ROW][C]11[/C][C]2436[/C][C]2428.49320393311[/C][C]7.50679606688891[/C][/ROW]
[ROW][C]12[/C][C]2444[/C][C]2413.5817104251[/C][C]30.4182895749018[/C][/ROW]
[ROW][C]13[/C][C]2421[/C][C]2421.94034759581[/C][C]-0.940347595807907[/C][/ROW]
[ROW][C]14[/C][C]2427[/C][C]2398.92926072649[/C][C]28.0707392735053[/C][/ROW]
[ROW][C]15[/C][C]2390[/C][C]2405.26021985186[/C][C]-15.2602198518589[/C][/ROW]
[ROW][C]16[/C][C]2369[/C][C]2368.0802990822[/C][C]0.919700917801947[/C][/ROW]
[ROW][C]17[/C][C]2408[/C][C]2347.09114252342[/C][C]60.9088574765806[/C][/ROW]
[ROW][C]18[/C][C]2356[/C][C]2386.80926903947[/C][C]-30.8092690394678[/C][/ROW]
[ROW][C]19[/C][C]2297[/C][C]2334.44602214971[/C][C]-37.4460221497061[/C][/ROW]
[ROW][C]20[/C][C]2262[/C][C]2275.00452673278[/C][C]-13.0045267327782[/C][/ROW]
[ROW][C]21[/C][C]2266[/C][C]2239.85120099556[/C][C]26.1487990044361[/C][/ROW]
[ROW][C]22[/C][C]2347[/C][C]2244.15950009533[/C][C]102.840499904668[/C][/ROW]
[ROW][C]23[/C][C]2330[/C][C]2326.37200830785[/C][C]3.62799169215486[/C][/ROW]
[ROW][C]24[/C][C]2331[/C][C]2309.41478299025[/C][C]21.585217009751[/C][/ROW]
[ROW][C]25[/C][C]2267[/C][C]2310.66927662765[/C][C]-43.6692766276533[/C][/ROW]
[ROW][C]26[/C][C]2163[/C][C]2246.1544079077[/C][C]-83.1544079076971[/C][/ROW]
[ROW][C]27[/C][C]2095[/C][C]2141.17400230302[/C][C]-46.1740023030156[/C][/ROW]
[ROW][C]28[/C][C]2006[/C][C]2072.62960241145[/C][C]-66.6296024114463[/C][/ROW]
[ROW][C]29[/C][C]2061[/C][C]1982.84402727135[/C][C]78.1559727286522[/C][/ROW]
[ROW][C]30[/C][C]1954[/C][C]2038.76550041547[/C][C]-84.7655004154724[/C][/ROW]
[ROW][C]31[/C][C]1841[/C][C]1930.76609973688[/C][C]-89.7660997368791[/C][/ROW]
[ROW][C]32[/C][C]1837[/C][C]1816.7077410821[/C][C]20.2922589179036[/C][/ROW]
[ROW][C]33[/C][C]1777[/C][C]1812.94699050826[/C][C]-35.9469905082585[/C][/ROW]
[ROW][C]34[/C][C]1757[/C][C]1752.52316894723[/C][C]4.47683105276883[/C][/ROW]
[ROW][C]35[/C][C]1715[/C][C]1732.5759516002[/C][C]-17.5759516001992[/C][/ROW]
[ROW][C]36[/C][C]1691[/C][C]1690.36872793172[/C][C]0.631272068275166[/C][/ROW]
[ROW][C]37[/C][C]1683[/C][C]1666.37617074431[/C][C]16.6238292556884[/C][/ROW]
[ROW][C]38[/C][C]1658[/C][C]1658.57216871704[/C][C]-0.572168717042359[/C][/ROW]
[ROW][C]39[/C][C]1660[/C][C]1633.56542274372[/C][C]26.4345772562756[/C][/ROW]
[ROW][C]40[/C][C]1669[/C][C]1635.8770912211[/C][C]33.1229087789025[/C][/ROW]
[ROW][C]41[/C][C]1689[/C][C]1645.26761634451[/C][C]43.7323836554931[/C][/ROW]
[ROW][C]42[/C][C]1644[/C][C]1665.78322910781[/C][C]-21.7832291078078[/C][/ROW]
[ROW][C]43[/C][C]1573[/C][C]1620.52640087173[/C][C]-47.5264008717261[/C][/ROW]
[ROW][C]44[/C][C]1535[/C][C]1548.96605595487[/C][C]-13.9660559548731[/C][/ROW]
[ROW][C]45[/C][C]1526[/C][C]1510.80139361312[/C][C]15.1986063868833[/C][/ROW]
[ROW][C]46[/C][C]1536[/C][C]1501.98058794881[/C][C]34.0194120511894[/C][/ROW]
[ROW][C]47[/C][C]1526[/C][C]1512.38168300898[/C][C]13.6183169910214[/C][/ROW]
[ROW][C]48[/C][C]1498[/C][C]1502.54224544506[/C][C]-4.54224544505701[/C][/ROW]
[ROW][C]49[/C][C]1470[/C][C]1474.4886915445[/C][C]-4.48869154449767[/C][/ROW]
[ROW][C]50[/C][C]1485[/C][C]1446.43576905417[/C][C]38.5642309458267[/C][/ROW]
[ROW][C]51[/C][C]1452[/C][C]1461.89044835634[/C][C]-9.89044835633968[/C][/ROW]
[ROW][C]52[/C][C]1442[/C][C]1428.77383817[/C][C]13.2261618300035[/C][/ROW]
[ROW][C]53[/C][C]1373[/C][C]1418.92977702535[/C][C]-45.9297770253481[/C][/ROW]
[ROW][C]54[/C][C]1373[/C][C]1349.38825659426[/C][C]23.6117434057446[/C][/ROW]
[ROW][C]55[/C][C]1397[/C][C]1349.66664334673[/C][C]47.3333566532708[/C][/ROW]
[ROW][C]56[/C][C]1352[/C][C]1374.22471223711[/C][C]-22.2247122371093[/C][/ROW]
[ROW][C]57[/C][C]1355[/C][C]1328.96267883458[/C][C]26.0373211654241[/C][/ROW]
[ROW][C]58[/C][C]1336[/C][C]1332.26966359033[/C][C]3.73033640966923[/C][/ROW]
[ROW][C]59[/C][C]1347[/C][C]1313.31364493558[/C][C]33.6863550644177[/C][/ROW]
[ROW][C]60[/C][C]1323[/C][C]1324.71081319325[/C][C]-1.71081319325435[/C][/ROW]
[ROW][C]61[/C][C]1289[/C][C]1300.69064239431[/C][C]-11.6906423943101[/C][/ROW]
[ROW][C]62[/C][C]1265[/C][C]1266.55280759259[/C][C]-1.55280759259495[/C][/ROW]
[ROW][C]63[/C][C]1244[/C][C]1242.53449970844[/C][C]1.46550029155787[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300539&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300539&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
32343232815
423622317.1768527302444.8231472697571
523522336.7053257950915.2946742049071
623412326.8856527878514.114347212153
723242316.052063510527.94793648948144
823622299.1457711283862.8542288716171
924212337.8868339272783.1131660727328
1024512397.8667532832153.1332467167917
1124362428.493203933117.50679606688891
1224442413.581710425130.4182895749018
1324212421.94034759581-0.940347595807907
1424272398.9292607264928.0707392735053
1523902405.26021985186-15.2602198518589
1623692368.08029908220.919700917801947
1724082347.0911425234260.9088574765806
1823562386.80926903947-30.8092690394678
1922972334.44602214971-37.4460221497061
2022622275.00452673278-13.0045267327782
2122662239.8512009955626.1487990044361
2223472244.15950009533102.840499904668
2323302326.372008307853.62799169215486
2423312309.4147829902521.585217009751
2522672310.66927662765-43.6692766276533
2621632246.1544079077-83.1544079076971
2720952141.17400230302-46.1740023030156
2820062072.62960241145-66.6296024114463
2920611982.8440272713578.1559727286522
3019542038.76550041547-84.7655004154724
3118411930.76609973688-89.7660997368791
3218371816.707741082120.2922589179036
3317771812.94699050826-35.9469905082585
3417571752.523168947234.47683105276883
3517151732.5759516002-17.5759516001992
3616911690.368727931720.631272068275166
3716831666.3761707443116.6238292556884
3816581658.57216871704-0.572168717042359
3916601633.5654227437226.4345772562756
4016691635.877091221133.1229087789025
4116891645.2676163445143.7323836554931
4216441665.78322910781-21.7832291078078
4315731620.52640087173-47.5264008717261
4415351548.96605595487-13.9660559548731
4515261510.8013936131215.1986063868833
4615361501.9805879488134.0194120511894
4715261512.3816830089813.6183169910214
4814981502.54224544506-4.54224544505701
4914701474.4886915445-4.48869154449767
5014851446.4357690541738.5642309458267
5114521461.89044835634-9.89044835633968
5214421428.7738381713.2261618300035
5313731418.92977702535-45.9297770253481
5413731349.3882565942623.6117434057446
5513971349.6666433467347.3333566532708
5613521374.22471223711-22.2247122371093
5713551328.9626788345826.0373211654241
5813361332.269663590333.73033640966923
5913471313.3136449355833.6863550644177
6013231324.71081319325-1.71081319325435
6112891300.69064239431-11.6906423943101
6212651266.55280759259-1.55280759259495
6312441242.534499708441.46550029155787







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
641221.551778223621145.081310506921298.02224594033
651199.103556447251090.318587774941307.88852511955
661176.655334670871042.636915427721310.67375391403
671154.2071128945998.5483191731841309.86590661581
681131.75889111812956.7104256126511306.80735662359
691109.31066934175916.439007080711302.18233160278
701086.86244756537877.33005314131296.39484198944
711064.41422578899839.1219052966371289.70654628135
721041.96600401262801.6339005592081282.29810746603
731019.51778223624764.7352849696971274.30027950279
74997.069560459868728.3279404422271265.81118047751
75974.621338683492692.3360964778641256.90658088912

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
64 & 1221.55177822362 & 1145.08131050692 & 1298.02224594033 \tabularnewline
65 & 1199.10355644725 & 1090.31858777494 & 1307.88852511955 \tabularnewline
66 & 1176.65533467087 & 1042.63691542772 & 1310.67375391403 \tabularnewline
67 & 1154.2071128945 & 998.548319173184 & 1309.86590661581 \tabularnewline
68 & 1131.75889111812 & 956.710425612651 & 1306.80735662359 \tabularnewline
69 & 1109.31066934175 & 916.43900708071 & 1302.18233160278 \tabularnewline
70 & 1086.86244756537 & 877.3300531413 & 1296.39484198944 \tabularnewline
71 & 1064.41422578899 & 839.121905296637 & 1289.70654628135 \tabularnewline
72 & 1041.96600401262 & 801.633900559208 & 1282.29810746603 \tabularnewline
73 & 1019.51778223624 & 764.735284969697 & 1274.30027950279 \tabularnewline
74 & 997.069560459868 & 728.327940442227 & 1265.81118047751 \tabularnewline
75 & 974.621338683492 & 692.336096477864 & 1256.90658088912 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300539&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]64[/C][C]1221.55177822362[/C][C]1145.08131050692[/C][C]1298.02224594033[/C][/ROW]
[ROW][C]65[/C][C]1199.10355644725[/C][C]1090.31858777494[/C][C]1307.88852511955[/C][/ROW]
[ROW][C]66[/C][C]1176.65533467087[/C][C]1042.63691542772[/C][C]1310.67375391403[/C][/ROW]
[ROW][C]67[/C][C]1154.2071128945[/C][C]998.548319173184[/C][C]1309.86590661581[/C][/ROW]
[ROW][C]68[/C][C]1131.75889111812[/C][C]956.710425612651[/C][C]1306.80735662359[/C][/ROW]
[ROW][C]69[/C][C]1109.31066934175[/C][C]916.43900708071[/C][C]1302.18233160278[/C][/ROW]
[ROW][C]70[/C][C]1086.86244756537[/C][C]877.3300531413[/C][C]1296.39484198944[/C][/ROW]
[ROW][C]71[/C][C]1064.41422578899[/C][C]839.121905296637[/C][C]1289.70654628135[/C][/ROW]
[ROW][C]72[/C][C]1041.96600401262[/C][C]801.633900559208[/C][C]1282.29810746603[/C][/ROW]
[ROW][C]73[/C][C]1019.51778223624[/C][C]764.735284969697[/C][C]1274.30027950279[/C][/ROW]
[ROW][C]74[/C][C]997.069560459868[/C][C]728.327940442227[/C][C]1265.81118047751[/C][/ROW]
[ROW][C]75[/C][C]974.621338683492[/C][C]692.336096477864[/C][C]1256.90658088912[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300539&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300539&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
641221.551778223621145.081310506921298.02224594033
651199.103556447251090.318587774941307.88852511955
661176.655334670871042.636915427721310.67375391403
671154.2071128945998.5483191731841309.86590661581
681131.75889111812956.7104256126511306.80735662359
691109.31066934175916.439007080711302.18233160278
701086.86244756537877.33005314131296.39484198944
711064.41422578899839.1219052966371289.70654628135
721041.96600401262801.6339005592081282.29810746603
731019.51778223624764.7352849696971274.30027950279
74997.069560459868728.3279404422271265.81118047751
75974.621338683492692.3360964778641256.90658088912



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')