Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 06 Aug 2017 19:17:26 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/06/t15020399343rqy32v8hprjy4a.htm/, Retrieved Sun, 12 May 2024 02:08:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=306973, Retrieved Sun, 12 May 2024 02:08:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-08-06 17:17:26] [eec775fda337aa2da775a098928b5865] [Current]
Feedback Forum

Post a new message
Dataseries X:
1053000
1014000
1072500
858000
1111500
1092000
1170000
1209000
1345500
1170000
1111500
1384500
1170000
877500
1033500
780000
1092000
897000
1189500
1072500
1131000
1267500
1248000
1482000
1072500
897000
994500
721500
1033500
799500
1131000
1072500
955500
1365000
1228500
1404000
1053000
975000
877500
721500
955500
858000
1170000
1131000
975000
1306500
1209000
1560000
1248000
760500
760500
760500
897000
897000
1209000
1111500
994500
1248000
1150500
1657500
1306500
760500
799500
663000
916500
1053000
1326000
1306500
1053000
1228500
1092000
1560000
1189500
955500
858000
643500
955500
1150500
1345500
1267500
936000
1345500
1053000
1618500
1345500
975000
897000
604500
955500
916500
1384500
1384500
1053000
1365000
1014000
1579500
1345500
994500
760500
526500
1033500
994500
1306500
1501500
1111500
1248000
936000
1618500




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306973&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=306973&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306973&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 time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0090380623970312
beta1
gamma0.930857409777017

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0090380623970312 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.930857409777017 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306973&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]0.0090380623970312[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.930857409777017[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306973&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306973&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
alpha0.0090380623970312
beta1
gamma0.930857409777017







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1311700001214472.13130478-44472.1313047833
14877500910180.642483087-32680.6424830868
1510335001080475.25434376-46975.2543437628
16780000814232.762945173-34232.7629451727
1710920001122512.15896693-30512.1589669348
18897000907913.634762926-10913.6347629261
1911895001136985.018164852514.9818352035
2010725001169085.49254873-96585.4925487316
2111310001299561.711194-168561.711194002
2212675001124463.36893048143036.631069525
2312480001065846.14599691182153.854003091
2414820001333025.58156198148974.418438024
2510725001091816.84660224-19316.8466022364
26897000819071.09594533777928.9040546634
27994500967729.15119140426770.8488085964
28721500732206.625209623-10706.6252096231
2910335001026415.874420127084.12557987939
30799500844557.912586455-45057.9125864547
3111310001117151.1583944813848.8416055217
3210725001019436.1195617353063.8804382727
339555001084620.9860821-129120.986082103
3413650001195286.31618951169713.683810493
3512285001178050.1421940350449.8578059669
3614040001405819.8657435-1819.86574350204
3710530001027260.4158594225739.5841405847
38975000853976.751177384121023.248822616
39877500953802.805009826-76302.8050098262
40721500694414.47920259327085.5207974074
41955500995246.339255254-39746.3392552544
42858000774365.04441792683634.9555820735
4311700001094317.3950011675682.6049988437
4411310001038678.8557127192321.1442872947
45975000942334.51126692632665.4887330744
4613065001327938.18428072-21438.1842807175
4712090001205801.117501053198.88249895046
4815600001386713.70360976173286.296390236
4912480001043790.98315708204209.016842917
50760500966113.719987579-205613.719987579
51760500883598.430635269-123098.430635269
52760500720828.42193064139671.5780693588
53897000962951.768217033-65951.7682170327
54897000856965.53348330640034.4665166942
5512090001172888.5957258636111.4042741356
5611115001133313.90846792-21813.908467917
57994500980043.37874436614456.6212556338
5812480001318275.65087119-70275.6508711914
5911505001217417.46068273-66917.460682729
6016575001555496.40055555102003.599444453
6113065001236844.108933869655.8910661982
62760500776295.760803715-15795.7608037147
63799500770853.77368928928646.2263107114
64663000760166.249535345-97166.2495353454
65916500903108.60125396313391.3987460373
661053000895495.243423594157504.756576406
6713260001211081.30971898114918.690281017
6813065001120195.8652255186304.134774499
6910530001004629.3021516548370.6978483482
7012285001272569.70396651-44069.7039665123
7110920001177926.62056788-85926.6205678794
7215600001687074.38284238-127074.382842382
7311895001332044.93257404-142544.93257404
74955500779351.090451315176148.909548685
75858000820024.1292974137975.8707025897
76643500691768.693896245-48268.6938962451
77955500948518.4342110196981.56578898069
7811505001081883.1829908568616.8170091491
7913455001371359.85928027-25859.8592802738
8012675001345722.16861455-78222.1686145512
819360001090222.8776807-154222.8776807
8213455001274975.5117426770524.4882573306
8310530001136325.66762453-83325.6676245304
8416185001621350.67330164-2850.67330163717
8513455001239757.80871387105742.191286135
86975000975001.377105477-1.37710547691677
87897000882721.91891360514278.0810863947
88604500667107.190245297-62607.190245297
89955500982591.010140434-27091.010140434
909165001175746.17728477-259246.177284767
9113845001373921.747339310578.2526607008
9213845001293448.9576570391051.0423429748
931053000960868.91679257292131.0832074285
9413650001360310.545415464689.45458453754
9510140001073589.66965452-59589.6696545174
9615795001638815.2871945-59315.2871945021
9713455001351472.41086834-5972.41086833575
98994500982395.50361288612104.4963871137
99760500900879.20661298-140379.20661298
100526500609508.606924203-83008.606924203
1011033500953673.77248531179826.2275146893
102994500930394.05555520364105.9444447965
10313065001378214.0015197-71714.0015196961
10415015001369872.02484603131627.975153971
10511115001039548.1690021871951.8309978235
10612480001354847.24364692-106847.243646924
1079360001008794.27834314-72794.2783431424
10816185001565665.6515523752834.3484476341

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1170000 & 1214472.13130478 & -44472.1313047833 \tabularnewline
14 & 877500 & 910180.642483087 & -32680.6424830868 \tabularnewline
15 & 1033500 & 1080475.25434376 & -46975.2543437628 \tabularnewline
16 & 780000 & 814232.762945173 & -34232.7629451727 \tabularnewline
17 & 1092000 & 1122512.15896693 & -30512.1589669348 \tabularnewline
18 & 897000 & 907913.634762926 & -10913.6347629261 \tabularnewline
19 & 1189500 & 1136985.0181648 & 52514.9818352035 \tabularnewline
20 & 1072500 & 1169085.49254873 & -96585.4925487316 \tabularnewline
21 & 1131000 & 1299561.711194 & -168561.711194002 \tabularnewline
22 & 1267500 & 1124463.36893048 & 143036.631069525 \tabularnewline
23 & 1248000 & 1065846.14599691 & 182153.854003091 \tabularnewline
24 & 1482000 & 1333025.58156198 & 148974.418438024 \tabularnewline
25 & 1072500 & 1091816.84660224 & -19316.8466022364 \tabularnewline
26 & 897000 & 819071.095945337 & 77928.9040546634 \tabularnewline
27 & 994500 & 967729.151191404 & 26770.8488085964 \tabularnewline
28 & 721500 & 732206.625209623 & -10706.6252096231 \tabularnewline
29 & 1033500 & 1026415.87442012 & 7084.12557987939 \tabularnewline
30 & 799500 & 844557.912586455 & -45057.9125864547 \tabularnewline
31 & 1131000 & 1117151.15839448 & 13848.8416055217 \tabularnewline
32 & 1072500 & 1019436.11956173 & 53063.8804382727 \tabularnewline
33 & 955500 & 1084620.9860821 & -129120.986082103 \tabularnewline
34 & 1365000 & 1195286.31618951 & 169713.683810493 \tabularnewline
35 & 1228500 & 1178050.14219403 & 50449.8578059669 \tabularnewline
36 & 1404000 & 1405819.8657435 & -1819.86574350204 \tabularnewline
37 & 1053000 & 1027260.41585942 & 25739.5841405847 \tabularnewline
38 & 975000 & 853976.751177384 & 121023.248822616 \tabularnewline
39 & 877500 & 953802.805009826 & -76302.8050098262 \tabularnewline
40 & 721500 & 694414.479202593 & 27085.5207974074 \tabularnewline
41 & 955500 & 995246.339255254 & -39746.3392552544 \tabularnewline
42 & 858000 & 774365.044417926 & 83634.9555820735 \tabularnewline
43 & 1170000 & 1094317.39500116 & 75682.6049988437 \tabularnewline
44 & 1131000 & 1038678.85571271 & 92321.1442872947 \tabularnewline
45 & 975000 & 942334.511266926 & 32665.4887330744 \tabularnewline
46 & 1306500 & 1327938.18428072 & -21438.1842807175 \tabularnewline
47 & 1209000 & 1205801.11750105 & 3198.88249895046 \tabularnewline
48 & 1560000 & 1386713.70360976 & 173286.296390236 \tabularnewline
49 & 1248000 & 1043790.98315708 & 204209.016842917 \tabularnewline
50 & 760500 & 966113.719987579 & -205613.719987579 \tabularnewline
51 & 760500 & 883598.430635269 & -123098.430635269 \tabularnewline
52 & 760500 & 720828.421930641 & 39671.5780693588 \tabularnewline
53 & 897000 & 962951.768217033 & -65951.7682170327 \tabularnewline
54 & 897000 & 856965.533483306 & 40034.4665166942 \tabularnewline
55 & 1209000 & 1172888.59572586 & 36111.4042741356 \tabularnewline
56 & 1111500 & 1133313.90846792 & -21813.908467917 \tabularnewline
57 & 994500 & 980043.378744366 & 14456.6212556338 \tabularnewline
58 & 1248000 & 1318275.65087119 & -70275.6508711914 \tabularnewline
59 & 1150500 & 1217417.46068273 & -66917.460682729 \tabularnewline
60 & 1657500 & 1555496.40055555 & 102003.599444453 \tabularnewline
61 & 1306500 & 1236844.1089338 & 69655.8910661982 \tabularnewline
62 & 760500 & 776295.760803715 & -15795.7608037147 \tabularnewline
63 & 799500 & 770853.773689289 & 28646.2263107114 \tabularnewline
64 & 663000 & 760166.249535345 & -97166.2495353454 \tabularnewline
65 & 916500 & 903108.601253963 & 13391.3987460373 \tabularnewline
66 & 1053000 & 895495.243423594 & 157504.756576406 \tabularnewline
67 & 1326000 & 1211081.30971898 & 114918.690281017 \tabularnewline
68 & 1306500 & 1120195.8652255 & 186304.134774499 \tabularnewline
69 & 1053000 & 1004629.30215165 & 48370.6978483482 \tabularnewline
70 & 1228500 & 1272569.70396651 & -44069.7039665123 \tabularnewline
71 & 1092000 & 1177926.62056788 & -85926.6205678794 \tabularnewline
72 & 1560000 & 1687074.38284238 & -127074.382842382 \tabularnewline
73 & 1189500 & 1332044.93257404 & -142544.93257404 \tabularnewline
74 & 955500 & 779351.090451315 & 176148.909548685 \tabularnewline
75 & 858000 & 820024.12929741 & 37975.8707025897 \tabularnewline
76 & 643500 & 691768.693896245 & -48268.6938962451 \tabularnewline
77 & 955500 & 948518.434211019 & 6981.56578898069 \tabularnewline
78 & 1150500 & 1081883.18299085 & 68616.8170091491 \tabularnewline
79 & 1345500 & 1371359.85928027 & -25859.8592802738 \tabularnewline
80 & 1267500 & 1345722.16861455 & -78222.1686145512 \tabularnewline
81 & 936000 & 1090222.8776807 & -154222.8776807 \tabularnewline
82 & 1345500 & 1274975.51174267 & 70524.4882573306 \tabularnewline
83 & 1053000 & 1136325.66762453 & -83325.6676245304 \tabularnewline
84 & 1618500 & 1621350.67330164 & -2850.67330163717 \tabularnewline
85 & 1345500 & 1239757.80871387 & 105742.191286135 \tabularnewline
86 & 975000 & 975001.377105477 & -1.37710547691677 \tabularnewline
87 & 897000 & 882721.918913605 & 14278.0810863947 \tabularnewline
88 & 604500 & 667107.190245297 & -62607.190245297 \tabularnewline
89 & 955500 & 982591.010140434 & -27091.010140434 \tabularnewline
90 & 916500 & 1175746.17728477 & -259246.177284767 \tabularnewline
91 & 1384500 & 1373921.7473393 & 10578.2526607008 \tabularnewline
92 & 1384500 & 1293448.95765703 & 91051.0423429748 \tabularnewline
93 & 1053000 & 960868.916792572 & 92131.0832074285 \tabularnewline
94 & 1365000 & 1360310.54541546 & 4689.45458453754 \tabularnewline
95 & 1014000 & 1073589.66965452 & -59589.6696545174 \tabularnewline
96 & 1579500 & 1638815.2871945 & -59315.2871945021 \tabularnewline
97 & 1345500 & 1351472.41086834 & -5972.41086833575 \tabularnewline
98 & 994500 & 982395.503612886 & 12104.4963871137 \tabularnewline
99 & 760500 & 900879.20661298 & -140379.20661298 \tabularnewline
100 & 526500 & 609508.606924203 & -83008.606924203 \tabularnewline
101 & 1033500 & 953673.772485311 & 79826.2275146893 \tabularnewline
102 & 994500 & 930394.055555203 & 64105.9444447965 \tabularnewline
103 & 1306500 & 1378214.0015197 & -71714.0015196961 \tabularnewline
104 & 1501500 & 1369872.02484603 & 131627.975153971 \tabularnewline
105 & 1111500 & 1039548.16900218 & 71951.8309978235 \tabularnewline
106 & 1248000 & 1354847.24364692 & -106847.243646924 \tabularnewline
107 & 936000 & 1008794.27834314 & -72794.2783431424 \tabularnewline
108 & 1618500 & 1565665.65155237 & 52834.3484476341 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306973&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]13[/C][C]1170000[/C][C]1214472.13130478[/C][C]-44472.1313047833[/C][/ROW]
[ROW][C]14[/C][C]877500[/C][C]910180.642483087[/C][C]-32680.6424830868[/C][/ROW]
[ROW][C]15[/C][C]1033500[/C][C]1080475.25434376[/C][C]-46975.2543437628[/C][/ROW]
[ROW][C]16[/C][C]780000[/C][C]814232.762945173[/C][C]-34232.7629451727[/C][/ROW]
[ROW][C]17[/C][C]1092000[/C][C]1122512.15896693[/C][C]-30512.1589669348[/C][/ROW]
[ROW][C]18[/C][C]897000[/C][C]907913.634762926[/C][C]-10913.6347629261[/C][/ROW]
[ROW][C]19[/C][C]1189500[/C][C]1136985.0181648[/C][C]52514.9818352035[/C][/ROW]
[ROW][C]20[/C][C]1072500[/C][C]1169085.49254873[/C][C]-96585.4925487316[/C][/ROW]
[ROW][C]21[/C][C]1131000[/C][C]1299561.711194[/C][C]-168561.711194002[/C][/ROW]
[ROW][C]22[/C][C]1267500[/C][C]1124463.36893048[/C][C]143036.631069525[/C][/ROW]
[ROW][C]23[/C][C]1248000[/C][C]1065846.14599691[/C][C]182153.854003091[/C][/ROW]
[ROW][C]24[/C][C]1482000[/C][C]1333025.58156198[/C][C]148974.418438024[/C][/ROW]
[ROW][C]25[/C][C]1072500[/C][C]1091816.84660224[/C][C]-19316.8466022364[/C][/ROW]
[ROW][C]26[/C][C]897000[/C][C]819071.095945337[/C][C]77928.9040546634[/C][/ROW]
[ROW][C]27[/C][C]994500[/C][C]967729.151191404[/C][C]26770.8488085964[/C][/ROW]
[ROW][C]28[/C][C]721500[/C][C]732206.625209623[/C][C]-10706.6252096231[/C][/ROW]
[ROW][C]29[/C][C]1033500[/C][C]1026415.87442012[/C][C]7084.12557987939[/C][/ROW]
[ROW][C]30[/C][C]799500[/C][C]844557.912586455[/C][C]-45057.9125864547[/C][/ROW]
[ROW][C]31[/C][C]1131000[/C][C]1117151.15839448[/C][C]13848.8416055217[/C][/ROW]
[ROW][C]32[/C][C]1072500[/C][C]1019436.11956173[/C][C]53063.8804382727[/C][/ROW]
[ROW][C]33[/C][C]955500[/C][C]1084620.9860821[/C][C]-129120.986082103[/C][/ROW]
[ROW][C]34[/C][C]1365000[/C][C]1195286.31618951[/C][C]169713.683810493[/C][/ROW]
[ROW][C]35[/C][C]1228500[/C][C]1178050.14219403[/C][C]50449.8578059669[/C][/ROW]
[ROW][C]36[/C][C]1404000[/C][C]1405819.8657435[/C][C]-1819.86574350204[/C][/ROW]
[ROW][C]37[/C][C]1053000[/C][C]1027260.41585942[/C][C]25739.5841405847[/C][/ROW]
[ROW][C]38[/C][C]975000[/C][C]853976.751177384[/C][C]121023.248822616[/C][/ROW]
[ROW][C]39[/C][C]877500[/C][C]953802.805009826[/C][C]-76302.8050098262[/C][/ROW]
[ROW][C]40[/C][C]721500[/C][C]694414.479202593[/C][C]27085.5207974074[/C][/ROW]
[ROW][C]41[/C][C]955500[/C][C]995246.339255254[/C][C]-39746.3392552544[/C][/ROW]
[ROW][C]42[/C][C]858000[/C][C]774365.044417926[/C][C]83634.9555820735[/C][/ROW]
[ROW][C]43[/C][C]1170000[/C][C]1094317.39500116[/C][C]75682.6049988437[/C][/ROW]
[ROW][C]44[/C][C]1131000[/C][C]1038678.85571271[/C][C]92321.1442872947[/C][/ROW]
[ROW][C]45[/C][C]975000[/C][C]942334.511266926[/C][C]32665.4887330744[/C][/ROW]
[ROW][C]46[/C][C]1306500[/C][C]1327938.18428072[/C][C]-21438.1842807175[/C][/ROW]
[ROW][C]47[/C][C]1209000[/C][C]1205801.11750105[/C][C]3198.88249895046[/C][/ROW]
[ROW][C]48[/C][C]1560000[/C][C]1386713.70360976[/C][C]173286.296390236[/C][/ROW]
[ROW][C]49[/C][C]1248000[/C][C]1043790.98315708[/C][C]204209.016842917[/C][/ROW]
[ROW][C]50[/C][C]760500[/C][C]966113.719987579[/C][C]-205613.719987579[/C][/ROW]
[ROW][C]51[/C][C]760500[/C][C]883598.430635269[/C][C]-123098.430635269[/C][/ROW]
[ROW][C]52[/C][C]760500[/C][C]720828.421930641[/C][C]39671.5780693588[/C][/ROW]
[ROW][C]53[/C][C]897000[/C][C]962951.768217033[/C][C]-65951.7682170327[/C][/ROW]
[ROW][C]54[/C][C]897000[/C][C]856965.533483306[/C][C]40034.4665166942[/C][/ROW]
[ROW][C]55[/C][C]1209000[/C][C]1172888.59572586[/C][C]36111.4042741356[/C][/ROW]
[ROW][C]56[/C][C]1111500[/C][C]1133313.90846792[/C][C]-21813.908467917[/C][/ROW]
[ROW][C]57[/C][C]994500[/C][C]980043.378744366[/C][C]14456.6212556338[/C][/ROW]
[ROW][C]58[/C][C]1248000[/C][C]1318275.65087119[/C][C]-70275.6508711914[/C][/ROW]
[ROW][C]59[/C][C]1150500[/C][C]1217417.46068273[/C][C]-66917.460682729[/C][/ROW]
[ROW][C]60[/C][C]1657500[/C][C]1555496.40055555[/C][C]102003.599444453[/C][/ROW]
[ROW][C]61[/C][C]1306500[/C][C]1236844.1089338[/C][C]69655.8910661982[/C][/ROW]
[ROW][C]62[/C][C]760500[/C][C]776295.760803715[/C][C]-15795.7608037147[/C][/ROW]
[ROW][C]63[/C][C]799500[/C][C]770853.773689289[/C][C]28646.2263107114[/C][/ROW]
[ROW][C]64[/C][C]663000[/C][C]760166.249535345[/C][C]-97166.2495353454[/C][/ROW]
[ROW][C]65[/C][C]916500[/C][C]903108.601253963[/C][C]13391.3987460373[/C][/ROW]
[ROW][C]66[/C][C]1053000[/C][C]895495.243423594[/C][C]157504.756576406[/C][/ROW]
[ROW][C]67[/C][C]1326000[/C][C]1211081.30971898[/C][C]114918.690281017[/C][/ROW]
[ROW][C]68[/C][C]1306500[/C][C]1120195.8652255[/C][C]186304.134774499[/C][/ROW]
[ROW][C]69[/C][C]1053000[/C][C]1004629.30215165[/C][C]48370.6978483482[/C][/ROW]
[ROW][C]70[/C][C]1228500[/C][C]1272569.70396651[/C][C]-44069.7039665123[/C][/ROW]
[ROW][C]71[/C][C]1092000[/C][C]1177926.62056788[/C][C]-85926.6205678794[/C][/ROW]
[ROW][C]72[/C][C]1560000[/C][C]1687074.38284238[/C][C]-127074.382842382[/C][/ROW]
[ROW][C]73[/C][C]1189500[/C][C]1332044.93257404[/C][C]-142544.93257404[/C][/ROW]
[ROW][C]74[/C][C]955500[/C][C]779351.090451315[/C][C]176148.909548685[/C][/ROW]
[ROW][C]75[/C][C]858000[/C][C]820024.12929741[/C][C]37975.8707025897[/C][/ROW]
[ROW][C]76[/C][C]643500[/C][C]691768.693896245[/C][C]-48268.6938962451[/C][/ROW]
[ROW][C]77[/C][C]955500[/C][C]948518.434211019[/C][C]6981.56578898069[/C][/ROW]
[ROW][C]78[/C][C]1150500[/C][C]1081883.18299085[/C][C]68616.8170091491[/C][/ROW]
[ROW][C]79[/C][C]1345500[/C][C]1371359.85928027[/C][C]-25859.8592802738[/C][/ROW]
[ROW][C]80[/C][C]1267500[/C][C]1345722.16861455[/C][C]-78222.1686145512[/C][/ROW]
[ROW][C]81[/C][C]936000[/C][C]1090222.8776807[/C][C]-154222.8776807[/C][/ROW]
[ROW][C]82[/C][C]1345500[/C][C]1274975.51174267[/C][C]70524.4882573306[/C][/ROW]
[ROW][C]83[/C][C]1053000[/C][C]1136325.66762453[/C][C]-83325.6676245304[/C][/ROW]
[ROW][C]84[/C][C]1618500[/C][C]1621350.67330164[/C][C]-2850.67330163717[/C][/ROW]
[ROW][C]85[/C][C]1345500[/C][C]1239757.80871387[/C][C]105742.191286135[/C][/ROW]
[ROW][C]86[/C][C]975000[/C][C]975001.377105477[/C][C]-1.37710547691677[/C][/ROW]
[ROW][C]87[/C][C]897000[/C][C]882721.918913605[/C][C]14278.0810863947[/C][/ROW]
[ROW][C]88[/C][C]604500[/C][C]667107.190245297[/C][C]-62607.190245297[/C][/ROW]
[ROW][C]89[/C][C]955500[/C][C]982591.010140434[/C][C]-27091.010140434[/C][/ROW]
[ROW][C]90[/C][C]916500[/C][C]1175746.17728477[/C][C]-259246.177284767[/C][/ROW]
[ROW][C]91[/C][C]1384500[/C][C]1373921.7473393[/C][C]10578.2526607008[/C][/ROW]
[ROW][C]92[/C][C]1384500[/C][C]1293448.95765703[/C][C]91051.0423429748[/C][/ROW]
[ROW][C]93[/C][C]1053000[/C][C]960868.916792572[/C][C]92131.0832074285[/C][/ROW]
[ROW][C]94[/C][C]1365000[/C][C]1360310.54541546[/C][C]4689.45458453754[/C][/ROW]
[ROW][C]95[/C][C]1014000[/C][C]1073589.66965452[/C][C]-59589.6696545174[/C][/ROW]
[ROW][C]96[/C][C]1579500[/C][C]1638815.2871945[/C][C]-59315.2871945021[/C][/ROW]
[ROW][C]97[/C][C]1345500[/C][C]1351472.41086834[/C][C]-5972.41086833575[/C][/ROW]
[ROW][C]98[/C][C]994500[/C][C]982395.503612886[/C][C]12104.4963871137[/C][/ROW]
[ROW][C]99[/C][C]760500[/C][C]900879.20661298[/C][C]-140379.20661298[/C][/ROW]
[ROW][C]100[/C][C]526500[/C][C]609508.606924203[/C][C]-83008.606924203[/C][/ROW]
[ROW][C]101[/C][C]1033500[/C][C]953673.772485311[/C][C]79826.2275146893[/C][/ROW]
[ROW][C]102[/C][C]994500[/C][C]930394.055555203[/C][C]64105.9444447965[/C][/ROW]
[ROW][C]103[/C][C]1306500[/C][C]1378214.0015197[/C][C]-71714.0015196961[/C][/ROW]
[ROW][C]104[/C][C]1501500[/C][C]1369872.02484603[/C][C]131627.975153971[/C][/ROW]
[ROW][C]105[/C][C]1111500[/C][C]1039548.16900218[/C][C]71951.8309978235[/C][/ROW]
[ROW][C]106[/C][C]1248000[/C][C]1354847.24364692[/C][C]-106847.243646924[/C][/ROW]
[ROW][C]107[/C][C]936000[/C][C]1008794.27834314[/C][C]-72794.2783431424[/C][/ROW]
[ROW][C]108[/C][C]1618500[/C][C]1565665.65155237[/C][C]52834.3484476341[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306973&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306973&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
1311700001214472.13130478-44472.1313047833
14877500910180.642483087-32680.6424830868
1510335001080475.25434376-46975.2543437628
16780000814232.762945173-34232.7629451727
1710920001122512.15896693-30512.1589669348
18897000907913.634762926-10913.6347629261
1911895001136985.018164852514.9818352035
2010725001169085.49254873-96585.4925487316
2111310001299561.711194-168561.711194002
2212675001124463.36893048143036.631069525
2312480001065846.14599691182153.854003091
2414820001333025.58156198148974.418438024
2510725001091816.84660224-19316.8466022364
26897000819071.09594533777928.9040546634
27994500967729.15119140426770.8488085964
28721500732206.625209623-10706.6252096231
2910335001026415.874420127084.12557987939
30799500844557.912586455-45057.9125864547
3111310001117151.1583944813848.8416055217
3210725001019436.1195617353063.8804382727
339555001084620.9860821-129120.986082103
3413650001195286.31618951169713.683810493
3512285001178050.1421940350449.8578059669
3614040001405819.8657435-1819.86574350204
3710530001027260.4158594225739.5841405847
38975000853976.751177384121023.248822616
39877500953802.805009826-76302.8050098262
40721500694414.47920259327085.5207974074
41955500995246.339255254-39746.3392552544
42858000774365.04441792683634.9555820735
4311700001094317.3950011675682.6049988437
4411310001038678.8557127192321.1442872947
45975000942334.51126692632665.4887330744
4613065001327938.18428072-21438.1842807175
4712090001205801.117501053198.88249895046
4815600001386713.70360976173286.296390236
4912480001043790.98315708204209.016842917
50760500966113.719987579-205613.719987579
51760500883598.430635269-123098.430635269
52760500720828.42193064139671.5780693588
53897000962951.768217033-65951.7682170327
54897000856965.53348330640034.4665166942
5512090001172888.5957258636111.4042741356
5611115001133313.90846792-21813.908467917
57994500980043.37874436614456.6212556338
5812480001318275.65087119-70275.6508711914
5911505001217417.46068273-66917.460682729
6016575001555496.40055555102003.599444453
6113065001236844.108933869655.8910661982
62760500776295.760803715-15795.7608037147
63799500770853.77368928928646.2263107114
64663000760166.249535345-97166.2495353454
65916500903108.60125396313391.3987460373
661053000895495.243423594157504.756576406
6713260001211081.30971898114918.690281017
6813065001120195.8652255186304.134774499
6910530001004629.3021516548370.6978483482
7012285001272569.70396651-44069.7039665123
7110920001177926.62056788-85926.6205678794
7215600001687074.38284238-127074.382842382
7311895001332044.93257404-142544.93257404
74955500779351.090451315176148.909548685
75858000820024.1292974137975.8707025897
76643500691768.693896245-48268.6938962451
77955500948518.4342110196981.56578898069
7811505001081883.1829908568616.8170091491
7913455001371359.85928027-25859.8592802738
8012675001345722.16861455-78222.1686145512
819360001090222.8776807-154222.8776807
8213455001274975.5117426770524.4882573306
8310530001136325.66762453-83325.6676245304
8416185001621350.67330164-2850.67330163717
8513455001239757.80871387105742.191286135
86975000975001.377105477-1.37710547691677
87897000882721.91891360514278.0810863947
88604500667107.190245297-62607.190245297
89955500982591.010140434-27091.010140434
909165001175746.17728477-259246.177284767
9113845001373921.747339310578.2526607008
9213845001293448.9576570391051.0423429748
931053000960868.91679257292131.0832074285
9413650001360310.545415464689.45458453754
9510140001073589.66965452-59589.6696545174
9615795001638815.2871945-59315.2871945021
9713455001351472.41086834-5972.41086833575
98994500982395.50361288612104.4963871137
99760500900879.20661298-140379.20661298
100526500609508.606924203-83008.606924203
1011033500953673.77248531179826.2275146893
102994500930394.05555520364105.9444447965
10313065001378214.0015197-71714.0015196961
10415015001369872.02484603131627.975153971
10511115001039548.1690021871951.8309978235
10612480001354847.24364692-106847.243646924
1079360001008794.27834314-72794.2783431424
10816185001565665.6515523752834.3484476341







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091329499.333183751162330.333968951496668.33239855
110980262.799050681813076.6524332771147448.94566808
111759795.85291534592584.679102772927007.026727908
112525748.939787905358524.571350871692973.308224939
1131016172.76343821848507.3570823591183838.16979406
114978638.10180264810632.3747721441146643.82883314
1151296766.683054781127221.830842641466311.53526691
1161475152.349398371303420.925066811646883.77372994
1171092548.89051584921845.1507555871263252.6302761
1181238967.362252421065698.644327651412236.08017719
119928998.931101167757323.866698681100673.99550365
1201594283.479541271518502.743908511670064.21517404

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1329499.33318375 & 1162330.33396895 & 1496668.33239855 \tabularnewline
110 & 980262.799050681 & 813076.652433277 & 1147448.94566808 \tabularnewline
111 & 759795.85291534 & 592584.679102772 & 927007.026727908 \tabularnewline
112 & 525748.939787905 & 358524.571350871 & 692973.308224939 \tabularnewline
113 & 1016172.76343821 & 848507.357082359 & 1183838.16979406 \tabularnewline
114 & 978638.10180264 & 810632.374772144 & 1146643.82883314 \tabularnewline
115 & 1296766.68305478 & 1127221.83084264 & 1466311.53526691 \tabularnewline
116 & 1475152.34939837 & 1303420.92506681 & 1646883.77372994 \tabularnewline
117 & 1092548.89051584 & 921845.150755587 & 1263252.6302761 \tabularnewline
118 & 1238967.36225242 & 1065698.64432765 & 1412236.08017719 \tabularnewline
119 & 928998.931101167 & 757323.86669868 & 1100673.99550365 \tabularnewline
120 & 1594283.47954127 & 1518502.74390851 & 1670064.21517404 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306973&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]109[/C][C]1329499.33318375[/C][C]1162330.33396895[/C][C]1496668.33239855[/C][/ROW]
[ROW][C]110[/C][C]980262.799050681[/C][C]813076.652433277[/C][C]1147448.94566808[/C][/ROW]
[ROW][C]111[/C][C]759795.85291534[/C][C]592584.679102772[/C][C]927007.026727908[/C][/ROW]
[ROW][C]112[/C][C]525748.939787905[/C][C]358524.571350871[/C][C]692973.308224939[/C][/ROW]
[ROW][C]113[/C][C]1016172.76343821[/C][C]848507.357082359[/C][C]1183838.16979406[/C][/ROW]
[ROW][C]114[/C][C]978638.10180264[/C][C]810632.374772144[/C][C]1146643.82883314[/C][/ROW]
[ROW][C]115[/C][C]1296766.68305478[/C][C]1127221.83084264[/C][C]1466311.53526691[/C][/ROW]
[ROW][C]116[/C][C]1475152.34939837[/C][C]1303420.92506681[/C][C]1646883.77372994[/C][/ROW]
[ROW][C]117[/C][C]1092548.89051584[/C][C]921845.150755587[/C][C]1263252.6302761[/C][/ROW]
[ROW][C]118[/C][C]1238967.36225242[/C][C]1065698.64432765[/C][C]1412236.08017719[/C][/ROW]
[ROW][C]119[/C][C]928998.931101167[/C][C]757323.86669868[/C][C]1100673.99550365[/C][/ROW]
[ROW][C]120[/C][C]1594283.47954127[/C][C]1518502.74390851[/C][C]1670064.21517404[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306973&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306973&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
1091329499.333183751162330.333968951496668.33239855
110980262.799050681813076.6524332771147448.94566808
111759795.85291534592584.679102772927007.026727908
112525748.939787905358524.571350871692973.308224939
1131016172.76343821848507.3570823591183838.16979406
114978638.10180264810632.3747721441146643.82883314
1151296766.683054781127221.830842641466311.53526691
1161475152.349398371303420.925066811646883.77372994
1171092548.89051584921845.1507555871263252.6302761
1181238967.362252421065698.644327651412236.08017719
119928998.931101167757323.866698681100673.99550365
1201594283.479541271518502.743908511670064.21517404



Parameters (Session):
par1 = 121260additive12 ; par2 = 112Triple ; par3 = 0multiplicative ; par4 = 012 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; 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')