Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 18 Aug 2014 10:42:37 +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/2014/Aug/18/t1408355062kpn8tum0z8jzw72.htm/, Retrieved Thu, 16 May 2024 07:30:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235697, Retrieved Thu, 16 May 2024 07:30:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsStefaan Segers
Estimated Impact130
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B - Sta...] [2014-08-18 09:42:37] [92f35a2db74bf110e350beffc19b3da6] [Current]
Feedback Forum

Post a new message
Dataseries X:
630
720
740
720
720
690
790
760
840
840
640
840
590
770
750
590
730
740
770
660
830
900
630
770
640
700
760
500
740
740
680
580
780
990
630
780
630
780
730
490
710
700
740
520
730
1110
510
750
690
740
690
640
660
580
760
510
810
1050
510
740
690
800
670
670
640
540
740
600
860
1080
480
680
650
860
650
630
600
500
760
590
800
1120
520
710
600
880
700
590
680
530
730
600
880
1120
540
740
580
850
670
530
680
540
760
620
910
1230
530
720




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235697&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235697&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235697&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.190642906397669
beta0.306737087509381
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.190642906397669 \tabularnewline
beta & 0.306737087509381 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235697&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]0.190642906397669[/C][/ROW]
[ROW][C]beta[/C][C]0.306737087509381[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235697&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235697&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
alpha0.190642906397669
beta0.306737087509381
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3740810-70
4720882.561589061771-162.561589061771
5720927.970813102369-207.970813102369
6690952.56152949266-262.56152949266
7790951.391036883488-161.391036883488
8760960.070277037569-200.070277037569
9840949.676034850988-109.676034850988
10840950.101260822536-110.101260822536
11640944.007001539669-304.007001539669
12840883.168494890236-43.1684948902362
13590869.532624386984-279.532624386984
14770794.489310147251-24.4893101472505
15750766.636127083027-16.6361270830268
16590739.307262702457-149.307262702457
17730677.95450932494652.045490675054
18740658.03170722493181.9682927750692
19770648.606755422255121.393244577745
20660653.7966341106526.20336588934845
21830637.389135315399192.610864684601
22900667.782257525234232.217742474766
23630719.305604979582-89.3056049795822
24770704.31046082399265.6895391760083
25640722.705385023513-82.7053850235126
26700707.973486113961-7.97348611396058
27760707.02242607337952.9775739266207
28500720.789236094582-220.789236094582
29740669.45319845201770.5468015479828
30740677.7836927051562.2163072948498
31680688.164275869355-8.16427586935504
32580684.649875705212-104.649875705212
33780656.621543433121123.378456566879
34990679.280027998735310.719972001265
35630755.823892995767-125.823892995767
36780741.78593157027738.2140684297229
37630761.255297498328-131.255297498328
38780740.74108213286639.2589178671337
39730755.029945916252-25.0299459162517
40490755.598911457573-265.598911457573
41710694.77361631043915.2263836895611
42700688.37606866365811.623931336342
43740681.97147456724358.028525432757
44520687.806935740471-167.806935740471
45730640.77558011797989.2244198820209
461110647.963027861992462.036972138008
47510753.243195575159-243.243195575159
48750709.84250916579140.1574908342087
49690722.818452913973-32.8184529139728
50740719.96291777772920.037082222271
51690728.355628942695-38.355628942695
52640723.373252241408-83.3732522414076
53660704.933146492148-44.9331464921478
54580691.19380739062-111.19380739062
55760658.320035257606101.679964742394
56510671.975102444141-161.975102444141
57810625.894342798592184.105657201408
581050656.557417537496393.442582462504
59510750.13653232583-240.13653232583
60740708.88575923606331.1142407639372
61690721.166497122186-31.166497122186
62800719.75132308554780.2486769144534
63670744.269383575135-74.2693835751354
64670734.986602621583-64.986602621583
65640723.673280209236-83.6732802092356
66540703.904491957031-163.904491957031
67740659.25550838362280.7444916163777
68600665.968833897175-65.9688338971752
69860640.854628644598219.145371355402
701080682.910442773647397.089557226353
71480782.110758929514-302.110758929514
72680730.346888323112-50.3468883231124
73650723.63586616676-73.6358661667596
74860708.17894264257151.82105735743
75650744.581860192025-94.5818601920251
76630728.478922324055-98.4789223240548
77600705.874260657864-105.874260657864
78500675.668494603399-175.668494603399
79760621.884342487823138.115657512177
80590635.997536927386-45.9975369273859
81800612.321047412858187.678952587142
821120644.1682720206475.8317279794
83520758.77511006535-238.77511006535
84710723.184311801304-13.1843118013043
85600729.829816679413-129.829816679413
86880706.64559285974173.35440714026
87700751.398579624119-51.3985796241192
88590750.298356186911-160.298356186911
89680719.063355812386-39.0633558123856
90530708.656630648064-178.656630648064
91730661.19008942545868.8099105745422
92600664.925103191408-64.9251031914081
93880639.367843764197240.632156235803
941120686.134415070308433.865584929692
95540795.110835052588-255.110835052588
96740757.820607845922-17.8206078459216
97580764.725979075985-184.725979075985
98850729.009758006801120.990241993199
99670758.651342467149-88.6513424671491
100530743.142159260045-213.142159260045
101680691.435717616388-11.435717616388
102540677.514448930397-137.514448930397
103760631.515697681932128.484302318068
104620643.741130119719-23.7411301197186
105910625.557547691889284.442452308111
1061230682.76039147734547.23960852266
107530822.064716238945-292.064716238945
108720784.282483788268-64.2824837882677

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 740 & 810 & -70 \tabularnewline
4 & 720 & 882.561589061771 & -162.561589061771 \tabularnewline
5 & 720 & 927.970813102369 & -207.970813102369 \tabularnewline
6 & 690 & 952.56152949266 & -262.56152949266 \tabularnewline
7 & 790 & 951.391036883488 & -161.391036883488 \tabularnewline
8 & 760 & 960.070277037569 & -200.070277037569 \tabularnewline
9 & 840 & 949.676034850988 & -109.676034850988 \tabularnewline
10 & 840 & 950.101260822536 & -110.101260822536 \tabularnewline
11 & 640 & 944.007001539669 & -304.007001539669 \tabularnewline
12 & 840 & 883.168494890236 & -43.1684948902362 \tabularnewline
13 & 590 & 869.532624386984 & -279.532624386984 \tabularnewline
14 & 770 & 794.489310147251 & -24.4893101472505 \tabularnewline
15 & 750 & 766.636127083027 & -16.6361270830268 \tabularnewline
16 & 590 & 739.307262702457 & -149.307262702457 \tabularnewline
17 & 730 & 677.954509324946 & 52.045490675054 \tabularnewline
18 & 740 & 658.031707224931 & 81.9682927750692 \tabularnewline
19 & 770 & 648.606755422255 & 121.393244577745 \tabularnewline
20 & 660 & 653.796634110652 & 6.20336588934845 \tabularnewline
21 & 830 & 637.389135315399 & 192.610864684601 \tabularnewline
22 & 900 & 667.782257525234 & 232.217742474766 \tabularnewline
23 & 630 & 719.305604979582 & -89.3056049795822 \tabularnewline
24 & 770 & 704.310460823992 & 65.6895391760083 \tabularnewline
25 & 640 & 722.705385023513 & -82.7053850235126 \tabularnewline
26 & 700 & 707.973486113961 & -7.97348611396058 \tabularnewline
27 & 760 & 707.022426073379 & 52.9775739266207 \tabularnewline
28 & 500 & 720.789236094582 & -220.789236094582 \tabularnewline
29 & 740 & 669.453198452017 & 70.5468015479828 \tabularnewline
30 & 740 & 677.78369270515 & 62.2163072948498 \tabularnewline
31 & 680 & 688.164275869355 & -8.16427586935504 \tabularnewline
32 & 580 & 684.649875705212 & -104.649875705212 \tabularnewline
33 & 780 & 656.621543433121 & 123.378456566879 \tabularnewline
34 & 990 & 679.280027998735 & 310.719972001265 \tabularnewline
35 & 630 & 755.823892995767 & -125.823892995767 \tabularnewline
36 & 780 & 741.785931570277 & 38.2140684297229 \tabularnewline
37 & 630 & 761.255297498328 & -131.255297498328 \tabularnewline
38 & 780 & 740.741082132866 & 39.2589178671337 \tabularnewline
39 & 730 & 755.029945916252 & -25.0299459162517 \tabularnewline
40 & 490 & 755.598911457573 & -265.598911457573 \tabularnewline
41 & 710 & 694.773616310439 & 15.2263836895611 \tabularnewline
42 & 700 & 688.376068663658 & 11.623931336342 \tabularnewline
43 & 740 & 681.971474567243 & 58.028525432757 \tabularnewline
44 & 520 & 687.806935740471 & -167.806935740471 \tabularnewline
45 & 730 & 640.775580117979 & 89.2244198820209 \tabularnewline
46 & 1110 & 647.963027861992 & 462.036972138008 \tabularnewline
47 & 510 & 753.243195575159 & -243.243195575159 \tabularnewline
48 & 750 & 709.842509165791 & 40.1574908342087 \tabularnewline
49 & 690 & 722.818452913973 & -32.8184529139728 \tabularnewline
50 & 740 & 719.962917777729 & 20.037082222271 \tabularnewline
51 & 690 & 728.355628942695 & -38.355628942695 \tabularnewline
52 & 640 & 723.373252241408 & -83.3732522414076 \tabularnewline
53 & 660 & 704.933146492148 & -44.9331464921478 \tabularnewline
54 & 580 & 691.19380739062 & -111.19380739062 \tabularnewline
55 & 760 & 658.320035257606 & 101.679964742394 \tabularnewline
56 & 510 & 671.975102444141 & -161.975102444141 \tabularnewline
57 & 810 & 625.894342798592 & 184.105657201408 \tabularnewline
58 & 1050 & 656.557417537496 & 393.442582462504 \tabularnewline
59 & 510 & 750.13653232583 & -240.13653232583 \tabularnewline
60 & 740 & 708.885759236063 & 31.1142407639372 \tabularnewline
61 & 690 & 721.166497122186 & -31.166497122186 \tabularnewline
62 & 800 & 719.751323085547 & 80.2486769144534 \tabularnewline
63 & 670 & 744.269383575135 & -74.2693835751354 \tabularnewline
64 & 670 & 734.986602621583 & -64.986602621583 \tabularnewline
65 & 640 & 723.673280209236 & -83.6732802092356 \tabularnewline
66 & 540 & 703.904491957031 & -163.904491957031 \tabularnewline
67 & 740 & 659.255508383622 & 80.7444916163777 \tabularnewline
68 & 600 & 665.968833897175 & -65.9688338971752 \tabularnewline
69 & 860 & 640.854628644598 & 219.145371355402 \tabularnewline
70 & 1080 & 682.910442773647 & 397.089557226353 \tabularnewline
71 & 480 & 782.110758929514 & -302.110758929514 \tabularnewline
72 & 680 & 730.346888323112 & -50.3468883231124 \tabularnewline
73 & 650 & 723.63586616676 & -73.6358661667596 \tabularnewline
74 & 860 & 708.17894264257 & 151.82105735743 \tabularnewline
75 & 650 & 744.581860192025 & -94.5818601920251 \tabularnewline
76 & 630 & 728.478922324055 & -98.4789223240548 \tabularnewline
77 & 600 & 705.874260657864 & -105.874260657864 \tabularnewline
78 & 500 & 675.668494603399 & -175.668494603399 \tabularnewline
79 & 760 & 621.884342487823 & 138.115657512177 \tabularnewline
80 & 590 & 635.997536927386 & -45.9975369273859 \tabularnewline
81 & 800 & 612.321047412858 & 187.678952587142 \tabularnewline
82 & 1120 & 644.1682720206 & 475.8317279794 \tabularnewline
83 & 520 & 758.77511006535 & -238.77511006535 \tabularnewline
84 & 710 & 723.184311801304 & -13.1843118013043 \tabularnewline
85 & 600 & 729.829816679413 & -129.829816679413 \tabularnewline
86 & 880 & 706.64559285974 & 173.35440714026 \tabularnewline
87 & 700 & 751.398579624119 & -51.3985796241192 \tabularnewline
88 & 590 & 750.298356186911 & -160.298356186911 \tabularnewline
89 & 680 & 719.063355812386 & -39.0633558123856 \tabularnewline
90 & 530 & 708.656630648064 & -178.656630648064 \tabularnewline
91 & 730 & 661.190089425458 & 68.8099105745422 \tabularnewline
92 & 600 & 664.925103191408 & -64.9251031914081 \tabularnewline
93 & 880 & 639.367843764197 & 240.632156235803 \tabularnewline
94 & 1120 & 686.134415070308 & 433.865584929692 \tabularnewline
95 & 540 & 795.110835052588 & -255.110835052588 \tabularnewline
96 & 740 & 757.820607845922 & -17.8206078459216 \tabularnewline
97 & 580 & 764.725979075985 & -184.725979075985 \tabularnewline
98 & 850 & 729.009758006801 & 120.990241993199 \tabularnewline
99 & 670 & 758.651342467149 & -88.6513424671491 \tabularnewline
100 & 530 & 743.142159260045 & -213.142159260045 \tabularnewline
101 & 680 & 691.435717616388 & -11.435717616388 \tabularnewline
102 & 540 & 677.514448930397 & -137.514448930397 \tabularnewline
103 & 760 & 631.515697681932 & 128.484302318068 \tabularnewline
104 & 620 & 643.741130119719 & -23.7411301197186 \tabularnewline
105 & 910 & 625.557547691889 & 284.442452308111 \tabularnewline
106 & 1230 & 682.76039147734 & 547.23960852266 \tabularnewline
107 & 530 & 822.064716238945 & -292.064716238945 \tabularnewline
108 & 720 & 784.282483788268 & -64.2824837882677 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235697&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]740[/C][C]810[/C][C]-70[/C][/ROW]
[ROW][C]4[/C][C]720[/C][C]882.561589061771[/C][C]-162.561589061771[/C][/ROW]
[ROW][C]5[/C][C]720[/C][C]927.970813102369[/C][C]-207.970813102369[/C][/ROW]
[ROW][C]6[/C][C]690[/C][C]952.56152949266[/C][C]-262.56152949266[/C][/ROW]
[ROW][C]7[/C][C]790[/C][C]951.391036883488[/C][C]-161.391036883488[/C][/ROW]
[ROW][C]8[/C][C]760[/C][C]960.070277037569[/C][C]-200.070277037569[/C][/ROW]
[ROW][C]9[/C][C]840[/C][C]949.676034850988[/C][C]-109.676034850988[/C][/ROW]
[ROW][C]10[/C][C]840[/C][C]950.101260822536[/C][C]-110.101260822536[/C][/ROW]
[ROW][C]11[/C][C]640[/C][C]944.007001539669[/C][C]-304.007001539669[/C][/ROW]
[ROW][C]12[/C][C]840[/C][C]883.168494890236[/C][C]-43.1684948902362[/C][/ROW]
[ROW][C]13[/C][C]590[/C][C]869.532624386984[/C][C]-279.532624386984[/C][/ROW]
[ROW][C]14[/C][C]770[/C][C]794.489310147251[/C][C]-24.4893101472505[/C][/ROW]
[ROW][C]15[/C][C]750[/C][C]766.636127083027[/C][C]-16.6361270830268[/C][/ROW]
[ROW][C]16[/C][C]590[/C][C]739.307262702457[/C][C]-149.307262702457[/C][/ROW]
[ROW][C]17[/C][C]730[/C][C]677.954509324946[/C][C]52.045490675054[/C][/ROW]
[ROW][C]18[/C][C]740[/C][C]658.031707224931[/C][C]81.9682927750692[/C][/ROW]
[ROW][C]19[/C][C]770[/C][C]648.606755422255[/C][C]121.393244577745[/C][/ROW]
[ROW][C]20[/C][C]660[/C][C]653.796634110652[/C][C]6.20336588934845[/C][/ROW]
[ROW][C]21[/C][C]830[/C][C]637.389135315399[/C][C]192.610864684601[/C][/ROW]
[ROW][C]22[/C][C]900[/C][C]667.782257525234[/C][C]232.217742474766[/C][/ROW]
[ROW][C]23[/C][C]630[/C][C]719.305604979582[/C][C]-89.3056049795822[/C][/ROW]
[ROW][C]24[/C][C]770[/C][C]704.310460823992[/C][C]65.6895391760083[/C][/ROW]
[ROW][C]25[/C][C]640[/C][C]722.705385023513[/C][C]-82.7053850235126[/C][/ROW]
[ROW][C]26[/C][C]700[/C][C]707.973486113961[/C][C]-7.97348611396058[/C][/ROW]
[ROW][C]27[/C][C]760[/C][C]707.022426073379[/C][C]52.9775739266207[/C][/ROW]
[ROW][C]28[/C][C]500[/C][C]720.789236094582[/C][C]-220.789236094582[/C][/ROW]
[ROW][C]29[/C][C]740[/C][C]669.453198452017[/C][C]70.5468015479828[/C][/ROW]
[ROW][C]30[/C][C]740[/C][C]677.78369270515[/C][C]62.2163072948498[/C][/ROW]
[ROW][C]31[/C][C]680[/C][C]688.164275869355[/C][C]-8.16427586935504[/C][/ROW]
[ROW][C]32[/C][C]580[/C][C]684.649875705212[/C][C]-104.649875705212[/C][/ROW]
[ROW][C]33[/C][C]780[/C][C]656.621543433121[/C][C]123.378456566879[/C][/ROW]
[ROW][C]34[/C][C]990[/C][C]679.280027998735[/C][C]310.719972001265[/C][/ROW]
[ROW][C]35[/C][C]630[/C][C]755.823892995767[/C][C]-125.823892995767[/C][/ROW]
[ROW][C]36[/C][C]780[/C][C]741.785931570277[/C][C]38.2140684297229[/C][/ROW]
[ROW][C]37[/C][C]630[/C][C]761.255297498328[/C][C]-131.255297498328[/C][/ROW]
[ROW][C]38[/C][C]780[/C][C]740.741082132866[/C][C]39.2589178671337[/C][/ROW]
[ROW][C]39[/C][C]730[/C][C]755.029945916252[/C][C]-25.0299459162517[/C][/ROW]
[ROW][C]40[/C][C]490[/C][C]755.598911457573[/C][C]-265.598911457573[/C][/ROW]
[ROW][C]41[/C][C]710[/C][C]694.773616310439[/C][C]15.2263836895611[/C][/ROW]
[ROW][C]42[/C][C]700[/C][C]688.376068663658[/C][C]11.623931336342[/C][/ROW]
[ROW][C]43[/C][C]740[/C][C]681.971474567243[/C][C]58.028525432757[/C][/ROW]
[ROW][C]44[/C][C]520[/C][C]687.806935740471[/C][C]-167.806935740471[/C][/ROW]
[ROW][C]45[/C][C]730[/C][C]640.775580117979[/C][C]89.2244198820209[/C][/ROW]
[ROW][C]46[/C][C]1110[/C][C]647.963027861992[/C][C]462.036972138008[/C][/ROW]
[ROW][C]47[/C][C]510[/C][C]753.243195575159[/C][C]-243.243195575159[/C][/ROW]
[ROW][C]48[/C][C]750[/C][C]709.842509165791[/C][C]40.1574908342087[/C][/ROW]
[ROW][C]49[/C][C]690[/C][C]722.818452913973[/C][C]-32.8184529139728[/C][/ROW]
[ROW][C]50[/C][C]740[/C][C]719.962917777729[/C][C]20.037082222271[/C][/ROW]
[ROW][C]51[/C][C]690[/C][C]728.355628942695[/C][C]-38.355628942695[/C][/ROW]
[ROW][C]52[/C][C]640[/C][C]723.373252241408[/C][C]-83.3732522414076[/C][/ROW]
[ROW][C]53[/C][C]660[/C][C]704.933146492148[/C][C]-44.9331464921478[/C][/ROW]
[ROW][C]54[/C][C]580[/C][C]691.19380739062[/C][C]-111.19380739062[/C][/ROW]
[ROW][C]55[/C][C]760[/C][C]658.320035257606[/C][C]101.679964742394[/C][/ROW]
[ROW][C]56[/C][C]510[/C][C]671.975102444141[/C][C]-161.975102444141[/C][/ROW]
[ROW][C]57[/C][C]810[/C][C]625.894342798592[/C][C]184.105657201408[/C][/ROW]
[ROW][C]58[/C][C]1050[/C][C]656.557417537496[/C][C]393.442582462504[/C][/ROW]
[ROW][C]59[/C][C]510[/C][C]750.13653232583[/C][C]-240.13653232583[/C][/ROW]
[ROW][C]60[/C][C]740[/C][C]708.885759236063[/C][C]31.1142407639372[/C][/ROW]
[ROW][C]61[/C][C]690[/C][C]721.166497122186[/C][C]-31.166497122186[/C][/ROW]
[ROW][C]62[/C][C]800[/C][C]719.751323085547[/C][C]80.2486769144534[/C][/ROW]
[ROW][C]63[/C][C]670[/C][C]744.269383575135[/C][C]-74.2693835751354[/C][/ROW]
[ROW][C]64[/C][C]670[/C][C]734.986602621583[/C][C]-64.986602621583[/C][/ROW]
[ROW][C]65[/C][C]640[/C][C]723.673280209236[/C][C]-83.6732802092356[/C][/ROW]
[ROW][C]66[/C][C]540[/C][C]703.904491957031[/C][C]-163.904491957031[/C][/ROW]
[ROW][C]67[/C][C]740[/C][C]659.255508383622[/C][C]80.7444916163777[/C][/ROW]
[ROW][C]68[/C][C]600[/C][C]665.968833897175[/C][C]-65.9688338971752[/C][/ROW]
[ROW][C]69[/C][C]860[/C][C]640.854628644598[/C][C]219.145371355402[/C][/ROW]
[ROW][C]70[/C][C]1080[/C][C]682.910442773647[/C][C]397.089557226353[/C][/ROW]
[ROW][C]71[/C][C]480[/C][C]782.110758929514[/C][C]-302.110758929514[/C][/ROW]
[ROW][C]72[/C][C]680[/C][C]730.346888323112[/C][C]-50.3468883231124[/C][/ROW]
[ROW][C]73[/C][C]650[/C][C]723.63586616676[/C][C]-73.6358661667596[/C][/ROW]
[ROW][C]74[/C][C]860[/C][C]708.17894264257[/C][C]151.82105735743[/C][/ROW]
[ROW][C]75[/C][C]650[/C][C]744.581860192025[/C][C]-94.5818601920251[/C][/ROW]
[ROW][C]76[/C][C]630[/C][C]728.478922324055[/C][C]-98.4789223240548[/C][/ROW]
[ROW][C]77[/C][C]600[/C][C]705.874260657864[/C][C]-105.874260657864[/C][/ROW]
[ROW][C]78[/C][C]500[/C][C]675.668494603399[/C][C]-175.668494603399[/C][/ROW]
[ROW][C]79[/C][C]760[/C][C]621.884342487823[/C][C]138.115657512177[/C][/ROW]
[ROW][C]80[/C][C]590[/C][C]635.997536927386[/C][C]-45.9975369273859[/C][/ROW]
[ROW][C]81[/C][C]800[/C][C]612.321047412858[/C][C]187.678952587142[/C][/ROW]
[ROW][C]82[/C][C]1120[/C][C]644.1682720206[/C][C]475.8317279794[/C][/ROW]
[ROW][C]83[/C][C]520[/C][C]758.77511006535[/C][C]-238.77511006535[/C][/ROW]
[ROW][C]84[/C][C]710[/C][C]723.184311801304[/C][C]-13.1843118013043[/C][/ROW]
[ROW][C]85[/C][C]600[/C][C]729.829816679413[/C][C]-129.829816679413[/C][/ROW]
[ROW][C]86[/C][C]880[/C][C]706.64559285974[/C][C]173.35440714026[/C][/ROW]
[ROW][C]87[/C][C]700[/C][C]751.398579624119[/C][C]-51.3985796241192[/C][/ROW]
[ROW][C]88[/C][C]590[/C][C]750.298356186911[/C][C]-160.298356186911[/C][/ROW]
[ROW][C]89[/C][C]680[/C][C]719.063355812386[/C][C]-39.0633558123856[/C][/ROW]
[ROW][C]90[/C][C]530[/C][C]708.656630648064[/C][C]-178.656630648064[/C][/ROW]
[ROW][C]91[/C][C]730[/C][C]661.190089425458[/C][C]68.8099105745422[/C][/ROW]
[ROW][C]92[/C][C]600[/C][C]664.925103191408[/C][C]-64.9251031914081[/C][/ROW]
[ROW][C]93[/C][C]880[/C][C]639.367843764197[/C][C]240.632156235803[/C][/ROW]
[ROW][C]94[/C][C]1120[/C][C]686.134415070308[/C][C]433.865584929692[/C][/ROW]
[ROW][C]95[/C][C]540[/C][C]795.110835052588[/C][C]-255.110835052588[/C][/ROW]
[ROW][C]96[/C][C]740[/C][C]757.820607845922[/C][C]-17.8206078459216[/C][/ROW]
[ROW][C]97[/C][C]580[/C][C]764.725979075985[/C][C]-184.725979075985[/C][/ROW]
[ROW][C]98[/C][C]850[/C][C]729.009758006801[/C][C]120.990241993199[/C][/ROW]
[ROW][C]99[/C][C]670[/C][C]758.651342467149[/C][C]-88.6513424671491[/C][/ROW]
[ROW][C]100[/C][C]530[/C][C]743.142159260045[/C][C]-213.142159260045[/C][/ROW]
[ROW][C]101[/C][C]680[/C][C]691.435717616388[/C][C]-11.435717616388[/C][/ROW]
[ROW][C]102[/C][C]540[/C][C]677.514448930397[/C][C]-137.514448930397[/C][/ROW]
[ROW][C]103[/C][C]760[/C][C]631.515697681932[/C][C]128.484302318068[/C][/ROW]
[ROW][C]104[/C][C]620[/C][C]643.741130119719[/C][C]-23.7411301197186[/C][/ROW]
[ROW][C]105[/C][C]910[/C][C]625.557547691889[/C][C]284.442452308111[/C][/ROW]
[ROW][C]106[/C][C]1230[/C][C]682.76039147734[/C][C]547.23960852266[/C][/ROW]
[ROW][C]107[/C][C]530[/C][C]822.064716238945[/C][C]-292.064716238945[/C][/ROW]
[ROW][C]108[/C][C]720[/C][C]784.282483788268[/C][C]-64.2824837882677[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235697&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235697&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
3740810-70
4720882.561589061771-162.561589061771
5720927.970813102369-207.970813102369
6690952.56152949266-262.56152949266
7790951.391036883488-161.391036883488
8760960.070277037569-200.070277037569
9840949.676034850988-109.676034850988
10840950.101260822536-110.101260822536
11640944.007001539669-304.007001539669
12840883.168494890236-43.1684948902362
13590869.532624386984-279.532624386984
14770794.489310147251-24.4893101472505
15750766.636127083027-16.6361270830268
16590739.307262702457-149.307262702457
17730677.95450932494652.045490675054
18740658.03170722493181.9682927750692
19770648.606755422255121.393244577745
20660653.7966341106526.20336588934845
21830637.389135315399192.610864684601
22900667.782257525234232.217742474766
23630719.305604979582-89.3056049795822
24770704.31046082399265.6895391760083
25640722.705385023513-82.7053850235126
26700707.973486113961-7.97348611396058
27760707.02242607337952.9775739266207
28500720.789236094582-220.789236094582
29740669.45319845201770.5468015479828
30740677.7836927051562.2163072948498
31680688.164275869355-8.16427586935504
32580684.649875705212-104.649875705212
33780656.621543433121123.378456566879
34990679.280027998735310.719972001265
35630755.823892995767-125.823892995767
36780741.78593157027738.2140684297229
37630761.255297498328-131.255297498328
38780740.74108213286639.2589178671337
39730755.029945916252-25.0299459162517
40490755.598911457573-265.598911457573
41710694.77361631043915.2263836895611
42700688.37606866365811.623931336342
43740681.97147456724358.028525432757
44520687.806935740471-167.806935740471
45730640.77558011797989.2244198820209
461110647.963027861992462.036972138008
47510753.243195575159-243.243195575159
48750709.84250916579140.1574908342087
49690722.818452913973-32.8184529139728
50740719.96291777772920.037082222271
51690728.355628942695-38.355628942695
52640723.373252241408-83.3732522414076
53660704.933146492148-44.9331464921478
54580691.19380739062-111.19380739062
55760658.320035257606101.679964742394
56510671.975102444141-161.975102444141
57810625.894342798592184.105657201408
581050656.557417537496393.442582462504
59510750.13653232583-240.13653232583
60740708.88575923606331.1142407639372
61690721.166497122186-31.166497122186
62800719.75132308554780.2486769144534
63670744.269383575135-74.2693835751354
64670734.986602621583-64.986602621583
65640723.673280209236-83.6732802092356
66540703.904491957031-163.904491957031
67740659.25550838362280.7444916163777
68600665.968833897175-65.9688338971752
69860640.854628644598219.145371355402
701080682.910442773647397.089557226353
71480782.110758929514-302.110758929514
72680730.346888323112-50.3468883231124
73650723.63586616676-73.6358661667596
74860708.17894264257151.82105735743
75650744.581860192025-94.5818601920251
76630728.478922324055-98.4789223240548
77600705.874260657864-105.874260657864
78500675.668494603399-175.668494603399
79760621.884342487823138.115657512177
80590635.997536927386-45.9975369273859
81800612.321047412858187.678952587142
821120644.1682720206475.8317279794
83520758.77511006535-238.77511006535
84710723.184311801304-13.1843118013043
85600729.829816679413-129.829816679413
86880706.64559285974173.35440714026
87700751.398579624119-51.3985796241192
88590750.298356186911-160.298356186911
89680719.063355812386-39.0633558123856
90530708.656630648064-178.656630648064
91730661.19008942545868.8099105745422
92600664.925103191408-64.9251031914081
93880639.367843764197240.632156235803
941120686.134415070308433.865584929692
95540795.110835052588-255.110835052588
96740757.820607845922-17.8206078459216
97580764.725979075985-184.725979075985
98850729.009758006801120.990241993199
99670758.651342467149-88.6513424671491
100530743.142159260045-213.142159260045
101680691.435717616388-11.435717616388
102540677.514448930397-137.514448930397
103760631.515697681932128.484302318068
104620643.741130119719-23.7411301197186
105910625.557547691889284.442452308111
1061230682.76039147734547.23960852266
107530822.064716238945-292.064716238945
108720784.282483788268-64.2824837882677







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109786.166255291453439.3154188285891133.01709175432
110800.305026334494442.8532606556061157.75679201338
111814.443797377536441.4094692035131187.47812555156
112828.582568420577434.5307582854281222.63437855573
113842.721339463619422.0537596591881263.38891926805
114856.86011050666404.0571162946481309.66310471867
115870.998881549702380.7870534944631361.21070960494
116885.137652592744352.5822491086241417.69305607686
117899.276423635785319.8144261761421478.73842109543
118913.415194678827282.8493589308471543.98103042681
119927.553965721868242.025520939341613.0824105044
120941.69273676491197.6450747377651685.74039879205

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 786.166255291453 & 439.315418828589 & 1133.01709175432 \tabularnewline
110 & 800.305026334494 & 442.853260655606 & 1157.75679201338 \tabularnewline
111 & 814.443797377536 & 441.409469203513 & 1187.47812555156 \tabularnewline
112 & 828.582568420577 & 434.530758285428 & 1222.63437855573 \tabularnewline
113 & 842.721339463619 & 422.053759659188 & 1263.38891926805 \tabularnewline
114 & 856.86011050666 & 404.057116294648 & 1309.66310471867 \tabularnewline
115 & 870.998881549702 & 380.787053494463 & 1361.21070960494 \tabularnewline
116 & 885.137652592744 & 352.582249108624 & 1417.69305607686 \tabularnewline
117 & 899.276423635785 & 319.814426176142 & 1478.73842109543 \tabularnewline
118 & 913.415194678827 & 282.849358930847 & 1543.98103042681 \tabularnewline
119 & 927.553965721868 & 242.02552093934 & 1613.0824105044 \tabularnewline
120 & 941.69273676491 & 197.645074737765 & 1685.74039879205 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235697&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]786.166255291453[/C][C]439.315418828589[/C][C]1133.01709175432[/C][/ROW]
[ROW][C]110[/C][C]800.305026334494[/C][C]442.853260655606[/C][C]1157.75679201338[/C][/ROW]
[ROW][C]111[/C][C]814.443797377536[/C][C]441.409469203513[/C][C]1187.47812555156[/C][/ROW]
[ROW][C]112[/C][C]828.582568420577[/C][C]434.530758285428[/C][C]1222.63437855573[/C][/ROW]
[ROW][C]113[/C][C]842.721339463619[/C][C]422.053759659188[/C][C]1263.38891926805[/C][/ROW]
[ROW][C]114[/C][C]856.86011050666[/C][C]404.057116294648[/C][C]1309.66310471867[/C][/ROW]
[ROW][C]115[/C][C]870.998881549702[/C][C]380.787053494463[/C][C]1361.21070960494[/C][/ROW]
[ROW][C]116[/C][C]885.137652592744[/C][C]352.582249108624[/C][C]1417.69305607686[/C][/ROW]
[ROW][C]117[/C][C]899.276423635785[/C][C]319.814426176142[/C][C]1478.73842109543[/C][/ROW]
[ROW][C]118[/C][C]913.415194678827[/C][C]282.849358930847[/C][C]1543.98103042681[/C][/ROW]
[ROW][C]119[/C][C]927.553965721868[/C][C]242.02552093934[/C][C]1613.0824105044[/C][/ROW]
[ROW][C]120[/C][C]941.69273676491[/C][C]197.645074737765[/C][C]1685.74039879205[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235697&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235697&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
109786.166255291453439.3154188285891133.01709175432
110800.305026334494442.8532606556061157.75679201338
111814.443797377536441.4094692035131187.47812555156
112828.582568420577434.5307582854281222.63437855573
113842.721339463619422.0537596591881263.38891926805
114856.86011050666404.0571162946481309.66310471867
115870.998881549702380.7870534944631361.21070960494
116885.137652592744352.5822491086241417.69305607686
117899.276423635785319.8144261761421478.73842109543
118913.415194678827282.8493589308471543.98103042681
119927.553965721868242.025520939341613.0824105044
120941.69273676491197.6450747377651685.74039879205



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')