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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 29 Nov 2014 17:54:24 +0000
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/Nov/29/t1417283735iemkwlylzep6vnu.htm/, Retrieved Sun, 19 May 2024 13:35:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261250, Retrieved Sun, 19 May 2024 13:35:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-29 17:54:24] [3b96c46cffecdf3c11148678d326f85c] [Current]
- R PD    [Exponential Smoothing] [] [2015-01-02 17:43:50] [3d50c3f1d1505d45371c80c331b9aa00]
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Dataseries X:
111,4
117
141,7
120
132,1
146,7
122,5
99,6
122,7
139
117,8
125,5
134,5
121,3
126,7
117,7
123
132,1
113,1
89,2
121,7
105,3
85,3
105,3
72,2
92,1
97,2
78,6
78,1
93
81
65,9
88,6
85,7
76,3
96,8
76,8
85,6
119,2
91,4
95,7
112,3
95,2
82,8
111,3
108,2
97
124,4
99,3
117,6
131,5
114,2
116,8
116,5
105,4
89,2
115,8
111,4
106,4
128,4
107,7
111
129,8
130,5
142,9
159,9
84,1
75
100,7
106,8
97,4
113
76,9
87,3
103,7
92,1
92,9
112,2
88,7
74,6
101,5
119,7
120,7
153,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261250&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261250&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261250&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.3752852883482
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.3752852883482 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261250&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]0.3752852883482[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261250&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261250&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
alpha0.3752852883482
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2117111.45.59999999999999
3141.7113.5015976147528.1984023852501
4120124.084043184857-4.08404318485705
5132.1122.5513618606019.54863813939852
6146.7126.13482527807820.5651747219217
7122.5133.852632803526-11.3526328035258
899.6129.592156728343-29.9921567283434
9122.7118.3365415423634.36345845763738
10139119.97408330783219.0259166921675
11117.8127.114229939741-9.31422993974137
12125.5123.6187364710641.8812635289359
13134.5124.3247469969810.1752530030202
14121.3128.143369754234-6.8433697542341
15126.7125.5751537627431.124846237257
16117.7125.997292007239-8.29729200723938
17123122.8834403837930.116559616206658
18132.1122.9271834929719.17281650702878
19113.1126.369606580777-13.2696065807766
2089.2121.389718448843-32.1897184488427
21121.7109.30939067892112.3906093210786
22105.3113.959404070792-8.65940407079229
2385.3110.709657117161-25.4096571171614
24105.3101.1737866191194.12621338088137
2572.2102.722293797549-30.5222937975489
2692.191.26772596868730.832274031312693
2797.291.58006616851325.61993383148679
2878.693.6891446569605-15.0891446569605
2978.188.0264106534454-9.92641065344542
309384.30117476910458.69882523089549
318187.5657159041717-6.56571590417173
3265.985.1016993178623-19.2016993178623
3388.677.895584052582910.7044159474171
3485.781.91279387800843.78720612199162
3576.383.3340766195341-7.03407661953408
3696.880.694291147108916.1057088528911
3776.886.7385267380183-9.9385267380183
3885.683.00874386538482.59125613461519
39119.283.981204171047935.2187958289521
4091.497.1983001189926-5.79830011899256
4195.795.0222833869070.677716613092954
42112.395.2766204614717.02337953853
4395.2101.665244360248-6.46524436024806
4482.899.2389332662708-16.4389332662708
45111.393.069643455301618.2303565446984
46108.299.91122806786928.2887719321308
4797103.021882232471-6.02188223247137
48124.4100.76195842245923.6380415775405
4999.3109.632967671874-10.3329676718735
50117.6105.75515691964211.8448430803582
51131.5110.20035227049321.2996477295068
52114.2118.193796710376-3.99379671037626
53116.8116.6949835603190.105016439681393
54116.5116.734394685166-0.234394685165739
55105.4116.646429808156-11.246429808156
5689.2112.425810154714-23.2258101547144
57115.8103.70950529368212.0904947063181
58111.4108.2468900858153.15310991418515
59106.4109.430205849153-3.03020584915339
60128.4108.29301417329920.1069858267005
61107.7115.838870147086-8.13887014708594
62111112.784471917108-1.78447191710825
63129.8112.11478585914717.685214140853
64130.5118.75178654749711.7482134525033
65142.9123.16071822059619.7392817794044
66159.9130.56858027496629.3314197250343
6784.1141.576230584137-57.4762305841373
6875120.006246816202-45.0062468162017
69100.7103.116064502313-2.4160645023132
70106.8102.2093510388954.59064896110526
7197.4103.932154057968-6.53215405796848
72113101.48073273878911.5192672612111
7376.9105.803744274472-28.9037442744725
7487.394.9565942700845-7.65659427008447
75103.792.083187081670611.6168129183294
7692.196.442806067413-4.34280606741297
7792.994.8130148401636-1.91301484016357
78112.294.095088514258418.1049114857416
7988.7100.889595441704-12.1895954417036
8074.696.315019601516-21.715019601516
81101.588.165692208874213.3343077911258
82119.793.169861753190526.5301382468095
83120.7103.12623233506217.573767664938
84153.5109.72140880056343.7785911994375

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 117 & 111.4 & 5.59999999999999 \tabularnewline
3 & 141.7 & 113.50159761475 & 28.1984023852501 \tabularnewline
4 & 120 & 124.084043184857 & -4.08404318485705 \tabularnewline
5 & 132.1 & 122.551361860601 & 9.54863813939852 \tabularnewline
6 & 146.7 & 126.134825278078 & 20.5651747219217 \tabularnewline
7 & 122.5 & 133.852632803526 & -11.3526328035258 \tabularnewline
8 & 99.6 & 129.592156728343 & -29.9921567283434 \tabularnewline
9 & 122.7 & 118.336541542363 & 4.36345845763738 \tabularnewline
10 & 139 & 119.974083307832 & 19.0259166921675 \tabularnewline
11 & 117.8 & 127.114229939741 & -9.31422993974137 \tabularnewline
12 & 125.5 & 123.618736471064 & 1.8812635289359 \tabularnewline
13 & 134.5 & 124.32474699698 & 10.1752530030202 \tabularnewline
14 & 121.3 & 128.143369754234 & -6.8433697542341 \tabularnewline
15 & 126.7 & 125.575153762743 & 1.124846237257 \tabularnewline
16 & 117.7 & 125.997292007239 & -8.29729200723938 \tabularnewline
17 & 123 & 122.883440383793 & 0.116559616206658 \tabularnewline
18 & 132.1 & 122.927183492971 & 9.17281650702878 \tabularnewline
19 & 113.1 & 126.369606580777 & -13.2696065807766 \tabularnewline
20 & 89.2 & 121.389718448843 & -32.1897184488427 \tabularnewline
21 & 121.7 & 109.309390678921 & 12.3906093210786 \tabularnewline
22 & 105.3 & 113.959404070792 & -8.65940407079229 \tabularnewline
23 & 85.3 & 110.709657117161 & -25.4096571171614 \tabularnewline
24 & 105.3 & 101.173786619119 & 4.12621338088137 \tabularnewline
25 & 72.2 & 102.722293797549 & -30.5222937975489 \tabularnewline
26 & 92.1 & 91.2677259686873 & 0.832274031312693 \tabularnewline
27 & 97.2 & 91.5800661685132 & 5.61993383148679 \tabularnewline
28 & 78.6 & 93.6891446569605 & -15.0891446569605 \tabularnewline
29 & 78.1 & 88.0264106534454 & -9.92641065344542 \tabularnewline
30 & 93 & 84.3011747691045 & 8.69882523089549 \tabularnewline
31 & 81 & 87.5657159041717 & -6.56571590417173 \tabularnewline
32 & 65.9 & 85.1016993178623 & -19.2016993178623 \tabularnewline
33 & 88.6 & 77.8955840525829 & 10.7044159474171 \tabularnewline
34 & 85.7 & 81.9127938780084 & 3.78720612199162 \tabularnewline
35 & 76.3 & 83.3340766195341 & -7.03407661953408 \tabularnewline
36 & 96.8 & 80.6942911471089 & 16.1057088528911 \tabularnewline
37 & 76.8 & 86.7385267380183 & -9.9385267380183 \tabularnewline
38 & 85.6 & 83.0087438653848 & 2.59125613461519 \tabularnewline
39 & 119.2 & 83.9812041710479 & 35.2187958289521 \tabularnewline
40 & 91.4 & 97.1983001189926 & -5.79830011899256 \tabularnewline
41 & 95.7 & 95.022283386907 & 0.677716613092954 \tabularnewline
42 & 112.3 & 95.27662046147 & 17.02337953853 \tabularnewline
43 & 95.2 & 101.665244360248 & -6.46524436024806 \tabularnewline
44 & 82.8 & 99.2389332662708 & -16.4389332662708 \tabularnewline
45 & 111.3 & 93.0696434553016 & 18.2303565446984 \tabularnewline
46 & 108.2 & 99.9112280678692 & 8.2887719321308 \tabularnewline
47 & 97 & 103.021882232471 & -6.02188223247137 \tabularnewline
48 & 124.4 & 100.761958422459 & 23.6380415775405 \tabularnewline
49 & 99.3 & 109.632967671874 & -10.3329676718735 \tabularnewline
50 & 117.6 & 105.755156919642 & 11.8448430803582 \tabularnewline
51 & 131.5 & 110.200352270493 & 21.2996477295068 \tabularnewline
52 & 114.2 & 118.193796710376 & -3.99379671037626 \tabularnewline
53 & 116.8 & 116.694983560319 & 0.105016439681393 \tabularnewline
54 & 116.5 & 116.734394685166 & -0.234394685165739 \tabularnewline
55 & 105.4 & 116.646429808156 & -11.246429808156 \tabularnewline
56 & 89.2 & 112.425810154714 & -23.2258101547144 \tabularnewline
57 & 115.8 & 103.709505293682 & 12.0904947063181 \tabularnewline
58 & 111.4 & 108.246890085815 & 3.15310991418515 \tabularnewline
59 & 106.4 & 109.430205849153 & -3.03020584915339 \tabularnewline
60 & 128.4 & 108.293014173299 & 20.1069858267005 \tabularnewline
61 & 107.7 & 115.838870147086 & -8.13887014708594 \tabularnewline
62 & 111 & 112.784471917108 & -1.78447191710825 \tabularnewline
63 & 129.8 & 112.114785859147 & 17.685214140853 \tabularnewline
64 & 130.5 & 118.751786547497 & 11.7482134525033 \tabularnewline
65 & 142.9 & 123.160718220596 & 19.7392817794044 \tabularnewline
66 & 159.9 & 130.568580274966 & 29.3314197250343 \tabularnewline
67 & 84.1 & 141.576230584137 & -57.4762305841373 \tabularnewline
68 & 75 & 120.006246816202 & -45.0062468162017 \tabularnewline
69 & 100.7 & 103.116064502313 & -2.4160645023132 \tabularnewline
70 & 106.8 & 102.209351038895 & 4.59064896110526 \tabularnewline
71 & 97.4 & 103.932154057968 & -6.53215405796848 \tabularnewline
72 & 113 & 101.480732738789 & 11.5192672612111 \tabularnewline
73 & 76.9 & 105.803744274472 & -28.9037442744725 \tabularnewline
74 & 87.3 & 94.9565942700845 & -7.65659427008447 \tabularnewline
75 & 103.7 & 92.0831870816706 & 11.6168129183294 \tabularnewline
76 & 92.1 & 96.442806067413 & -4.34280606741297 \tabularnewline
77 & 92.9 & 94.8130148401636 & -1.91301484016357 \tabularnewline
78 & 112.2 & 94.0950885142584 & 18.1049114857416 \tabularnewline
79 & 88.7 & 100.889595441704 & -12.1895954417036 \tabularnewline
80 & 74.6 & 96.315019601516 & -21.715019601516 \tabularnewline
81 & 101.5 & 88.1656922088742 & 13.3343077911258 \tabularnewline
82 & 119.7 & 93.1698617531905 & 26.5301382468095 \tabularnewline
83 & 120.7 & 103.126232335062 & 17.573767664938 \tabularnewline
84 & 153.5 & 109.721408800563 & 43.7785911994375 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261250&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]2[/C][C]117[/C][C]111.4[/C][C]5.59999999999999[/C][/ROW]
[ROW][C]3[/C][C]141.7[/C][C]113.50159761475[/C][C]28.1984023852501[/C][/ROW]
[ROW][C]4[/C][C]120[/C][C]124.084043184857[/C][C]-4.08404318485705[/C][/ROW]
[ROW][C]5[/C][C]132.1[/C][C]122.551361860601[/C][C]9.54863813939852[/C][/ROW]
[ROW][C]6[/C][C]146.7[/C][C]126.134825278078[/C][C]20.5651747219217[/C][/ROW]
[ROW][C]7[/C][C]122.5[/C][C]133.852632803526[/C][C]-11.3526328035258[/C][/ROW]
[ROW][C]8[/C][C]99.6[/C][C]129.592156728343[/C][C]-29.9921567283434[/C][/ROW]
[ROW][C]9[/C][C]122.7[/C][C]118.336541542363[/C][C]4.36345845763738[/C][/ROW]
[ROW][C]10[/C][C]139[/C][C]119.974083307832[/C][C]19.0259166921675[/C][/ROW]
[ROW][C]11[/C][C]117.8[/C][C]127.114229939741[/C][C]-9.31422993974137[/C][/ROW]
[ROW][C]12[/C][C]125.5[/C][C]123.618736471064[/C][C]1.8812635289359[/C][/ROW]
[ROW][C]13[/C][C]134.5[/C][C]124.32474699698[/C][C]10.1752530030202[/C][/ROW]
[ROW][C]14[/C][C]121.3[/C][C]128.143369754234[/C][C]-6.8433697542341[/C][/ROW]
[ROW][C]15[/C][C]126.7[/C][C]125.575153762743[/C][C]1.124846237257[/C][/ROW]
[ROW][C]16[/C][C]117.7[/C][C]125.997292007239[/C][C]-8.29729200723938[/C][/ROW]
[ROW][C]17[/C][C]123[/C][C]122.883440383793[/C][C]0.116559616206658[/C][/ROW]
[ROW][C]18[/C][C]132.1[/C][C]122.927183492971[/C][C]9.17281650702878[/C][/ROW]
[ROW][C]19[/C][C]113.1[/C][C]126.369606580777[/C][C]-13.2696065807766[/C][/ROW]
[ROW][C]20[/C][C]89.2[/C][C]121.389718448843[/C][C]-32.1897184488427[/C][/ROW]
[ROW][C]21[/C][C]121.7[/C][C]109.309390678921[/C][C]12.3906093210786[/C][/ROW]
[ROW][C]22[/C][C]105.3[/C][C]113.959404070792[/C][C]-8.65940407079229[/C][/ROW]
[ROW][C]23[/C][C]85.3[/C][C]110.709657117161[/C][C]-25.4096571171614[/C][/ROW]
[ROW][C]24[/C][C]105.3[/C][C]101.173786619119[/C][C]4.12621338088137[/C][/ROW]
[ROW][C]25[/C][C]72.2[/C][C]102.722293797549[/C][C]-30.5222937975489[/C][/ROW]
[ROW][C]26[/C][C]92.1[/C][C]91.2677259686873[/C][C]0.832274031312693[/C][/ROW]
[ROW][C]27[/C][C]97.2[/C][C]91.5800661685132[/C][C]5.61993383148679[/C][/ROW]
[ROW][C]28[/C][C]78.6[/C][C]93.6891446569605[/C][C]-15.0891446569605[/C][/ROW]
[ROW][C]29[/C][C]78.1[/C][C]88.0264106534454[/C][C]-9.92641065344542[/C][/ROW]
[ROW][C]30[/C][C]93[/C][C]84.3011747691045[/C][C]8.69882523089549[/C][/ROW]
[ROW][C]31[/C][C]81[/C][C]87.5657159041717[/C][C]-6.56571590417173[/C][/ROW]
[ROW][C]32[/C][C]65.9[/C][C]85.1016993178623[/C][C]-19.2016993178623[/C][/ROW]
[ROW][C]33[/C][C]88.6[/C][C]77.8955840525829[/C][C]10.7044159474171[/C][/ROW]
[ROW][C]34[/C][C]85.7[/C][C]81.9127938780084[/C][C]3.78720612199162[/C][/ROW]
[ROW][C]35[/C][C]76.3[/C][C]83.3340766195341[/C][C]-7.03407661953408[/C][/ROW]
[ROW][C]36[/C][C]96.8[/C][C]80.6942911471089[/C][C]16.1057088528911[/C][/ROW]
[ROW][C]37[/C][C]76.8[/C][C]86.7385267380183[/C][C]-9.9385267380183[/C][/ROW]
[ROW][C]38[/C][C]85.6[/C][C]83.0087438653848[/C][C]2.59125613461519[/C][/ROW]
[ROW][C]39[/C][C]119.2[/C][C]83.9812041710479[/C][C]35.2187958289521[/C][/ROW]
[ROW][C]40[/C][C]91.4[/C][C]97.1983001189926[/C][C]-5.79830011899256[/C][/ROW]
[ROW][C]41[/C][C]95.7[/C][C]95.022283386907[/C][C]0.677716613092954[/C][/ROW]
[ROW][C]42[/C][C]112.3[/C][C]95.27662046147[/C][C]17.02337953853[/C][/ROW]
[ROW][C]43[/C][C]95.2[/C][C]101.665244360248[/C][C]-6.46524436024806[/C][/ROW]
[ROW][C]44[/C][C]82.8[/C][C]99.2389332662708[/C][C]-16.4389332662708[/C][/ROW]
[ROW][C]45[/C][C]111.3[/C][C]93.0696434553016[/C][C]18.2303565446984[/C][/ROW]
[ROW][C]46[/C][C]108.2[/C][C]99.9112280678692[/C][C]8.2887719321308[/C][/ROW]
[ROW][C]47[/C][C]97[/C][C]103.021882232471[/C][C]-6.02188223247137[/C][/ROW]
[ROW][C]48[/C][C]124.4[/C][C]100.761958422459[/C][C]23.6380415775405[/C][/ROW]
[ROW][C]49[/C][C]99.3[/C][C]109.632967671874[/C][C]-10.3329676718735[/C][/ROW]
[ROW][C]50[/C][C]117.6[/C][C]105.755156919642[/C][C]11.8448430803582[/C][/ROW]
[ROW][C]51[/C][C]131.5[/C][C]110.200352270493[/C][C]21.2996477295068[/C][/ROW]
[ROW][C]52[/C][C]114.2[/C][C]118.193796710376[/C][C]-3.99379671037626[/C][/ROW]
[ROW][C]53[/C][C]116.8[/C][C]116.694983560319[/C][C]0.105016439681393[/C][/ROW]
[ROW][C]54[/C][C]116.5[/C][C]116.734394685166[/C][C]-0.234394685165739[/C][/ROW]
[ROW][C]55[/C][C]105.4[/C][C]116.646429808156[/C][C]-11.246429808156[/C][/ROW]
[ROW][C]56[/C][C]89.2[/C][C]112.425810154714[/C][C]-23.2258101547144[/C][/ROW]
[ROW][C]57[/C][C]115.8[/C][C]103.709505293682[/C][C]12.0904947063181[/C][/ROW]
[ROW][C]58[/C][C]111.4[/C][C]108.246890085815[/C][C]3.15310991418515[/C][/ROW]
[ROW][C]59[/C][C]106.4[/C][C]109.430205849153[/C][C]-3.03020584915339[/C][/ROW]
[ROW][C]60[/C][C]128.4[/C][C]108.293014173299[/C][C]20.1069858267005[/C][/ROW]
[ROW][C]61[/C][C]107.7[/C][C]115.838870147086[/C][C]-8.13887014708594[/C][/ROW]
[ROW][C]62[/C][C]111[/C][C]112.784471917108[/C][C]-1.78447191710825[/C][/ROW]
[ROW][C]63[/C][C]129.8[/C][C]112.114785859147[/C][C]17.685214140853[/C][/ROW]
[ROW][C]64[/C][C]130.5[/C][C]118.751786547497[/C][C]11.7482134525033[/C][/ROW]
[ROW][C]65[/C][C]142.9[/C][C]123.160718220596[/C][C]19.7392817794044[/C][/ROW]
[ROW][C]66[/C][C]159.9[/C][C]130.568580274966[/C][C]29.3314197250343[/C][/ROW]
[ROW][C]67[/C][C]84.1[/C][C]141.576230584137[/C][C]-57.4762305841373[/C][/ROW]
[ROW][C]68[/C][C]75[/C][C]120.006246816202[/C][C]-45.0062468162017[/C][/ROW]
[ROW][C]69[/C][C]100.7[/C][C]103.116064502313[/C][C]-2.4160645023132[/C][/ROW]
[ROW][C]70[/C][C]106.8[/C][C]102.209351038895[/C][C]4.59064896110526[/C][/ROW]
[ROW][C]71[/C][C]97.4[/C][C]103.932154057968[/C][C]-6.53215405796848[/C][/ROW]
[ROW][C]72[/C][C]113[/C][C]101.480732738789[/C][C]11.5192672612111[/C][/ROW]
[ROW][C]73[/C][C]76.9[/C][C]105.803744274472[/C][C]-28.9037442744725[/C][/ROW]
[ROW][C]74[/C][C]87.3[/C][C]94.9565942700845[/C][C]-7.65659427008447[/C][/ROW]
[ROW][C]75[/C][C]103.7[/C][C]92.0831870816706[/C][C]11.6168129183294[/C][/ROW]
[ROW][C]76[/C][C]92.1[/C][C]96.442806067413[/C][C]-4.34280606741297[/C][/ROW]
[ROW][C]77[/C][C]92.9[/C][C]94.8130148401636[/C][C]-1.91301484016357[/C][/ROW]
[ROW][C]78[/C][C]112.2[/C][C]94.0950885142584[/C][C]18.1049114857416[/C][/ROW]
[ROW][C]79[/C][C]88.7[/C][C]100.889595441704[/C][C]-12.1895954417036[/C][/ROW]
[ROW][C]80[/C][C]74.6[/C][C]96.315019601516[/C][C]-21.715019601516[/C][/ROW]
[ROW][C]81[/C][C]101.5[/C][C]88.1656922088742[/C][C]13.3343077911258[/C][/ROW]
[ROW][C]82[/C][C]119.7[/C][C]93.1698617531905[/C][C]26.5301382468095[/C][/ROW]
[ROW][C]83[/C][C]120.7[/C][C]103.126232335062[/C][C]17.573767664938[/C][/ROW]
[ROW][C]84[/C][C]153.5[/C][C]109.721408800563[/C][C]43.7785911994375[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261250&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261250&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
2117111.45.59999999999999
3141.7113.5015976147528.1984023852501
4120124.084043184857-4.08404318485705
5132.1122.5513618606019.54863813939852
6146.7126.13482527807820.5651747219217
7122.5133.852632803526-11.3526328035258
899.6129.592156728343-29.9921567283434
9122.7118.3365415423634.36345845763738
10139119.97408330783219.0259166921675
11117.8127.114229939741-9.31422993974137
12125.5123.6187364710641.8812635289359
13134.5124.3247469969810.1752530030202
14121.3128.143369754234-6.8433697542341
15126.7125.5751537627431.124846237257
16117.7125.997292007239-8.29729200723938
17123122.8834403837930.116559616206658
18132.1122.9271834929719.17281650702878
19113.1126.369606580777-13.2696065807766
2089.2121.389718448843-32.1897184488427
21121.7109.30939067892112.3906093210786
22105.3113.959404070792-8.65940407079229
2385.3110.709657117161-25.4096571171614
24105.3101.1737866191194.12621338088137
2572.2102.722293797549-30.5222937975489
2692.191.26772596868730.832274031312693
2797.291.58006616851325.61993383148679
2878.693.6891446569605-15.0891446569605
2978.188.0264106534454-9.92641065344542
309384.30117476910458.69882523089549
318187.5657159041717-6.56571590417173
3265.985.1016993178623-19.2016993178623
3388.677.895584052582910.7044159474171
3485.781.91279387800843.78720612199162
3576.383.3340766195341-7.03407661953408
3696.880.694291147108916.1057088528911
3776.886.7385267380183-9.9385267380183
3885.683.00874386538482.59125613461519
39119.283.981204171047935.2187958289521
4091.497.1983001189926-5.79830011899256
4195.795.0222833869070.677716613092954
42112.395.2766204614717.02337953853
4395.2101.665244360248-6.46524436024806
4482.899.2389332662708-16.4389332662708
45111.393.069643455301618.2303565446984
46108.299.91122806786928.2887719321308
4797103.021882232471-6.02188223247137
48124.4100.76195842245923.6380415775405
4999.3109.632967671874-10.3329676718735
50117.6105.75515691964211.8448430803582
51131.5110.20035227049321.2996477295068
52114.2118.193796710376-3.99379671037626
53116.8116.6949835603190.105016439681393
54116.5116.734394685166-0.234394685165739
55105.4116.646429808156-11.246429808156
5689.2112.425810154714-23.2258101547144
57115.8103.70950529368212.0904947063181
58111.4108.2468900858153.15310991418515
59106.4109.430205849153-3.03020584915339
60128.4108.29301417329920.1069858267005
61107.7115.838870147086-8.13887014708594
62111112.784471917108-1.78447191710825
63129.8112.11478585914717.685214140853
64130.5118.75178654749711.7482134525033
65142.9123.16071822059619.7392817794044
66159.9130.56858027496629.3314197250343
6784.1141.576230584137-57.4762305841373
6875120.006246816202-45.0062468162017
69100.7103.116064502313-2.4160645023132
70106.8102.2093510388954.59064896110526
7197.4103.932154057968-6.53215405796848
72113101.48073273878911.5192672612111
7376.9105.803744274472-28.9037442744725
7487.394.9565942700845-7.65659427008447
75103.792.083187081670611.6168129183294
7692.196.442806067413-4.34280606741297
7792.994.8130148401636-1.91301484016357
78112.294.095088514258418.1049114857416
7988.7100.889595441704-12.1895954417036
8074.696.315019601516-21.715019601516
81101.588.165692208874213.3343077911258
82119.793.169861753190526.5301382468095
83120.7103.12623233506217.573767664938
84153.5109.72140880056343.7785911994375







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85126.15087002232192.0655674519304160.236172592712
86126.15087002232189.744335407677162.557404636966
87126.15087002232187.5624822096711164.739257834972
88126.15087002232185.4975603746224166.80417967002
89126.15087002232183.5325700017446168.769170042898
90126.15087002232181.6542700625931170.64746998205
91126.15087002232179.8521084912794172.449631553363
92126.15087002232178.1175146258837174.184225418759
93126.15087002232176.4434144248691175.858325619774
94126.15087002232174.8238882943366177.477851750306
95126.15087002232173.2539233747399179.047816669903
96126.15087002232171.7292302457648180.572509798878

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 126.150870022321 & 92.0655674519304 & 160.236172592712 \tabularnewline
86 & 126.150870022321 & 89.744335407677 & 162.557404636966 \tabularnewline
87 & 126.150870022321 & 87.5624822096711 & 164.739257834972 \tabularnewline
88 & 126.150870022321 & 85.4975603746224 & 166.80417967002 \tabularnewline
89 & 126.150870022321 & 83.5325700017446 & 168.769170042898 \tabularnewline
90 & 126.150870022321 & 81.6542700625931 & 170.64746998205 \tabularnewline
91 & 126.150870022321 & 79.8521084912794 & 172.449631553363 \tabularnewline
92 & 126.150870022321 & 78.1175146258837 & 174.184225418759 \tabularnewline
93 & 126.150870022321 & 76.4434144248691 & 175.858325619774 \tabularnewline
94 & 126.150870022321 & 74.8238882943366 & 177.477851750306 \tabularnewline
95 & 126.150870022321 & 73.2539233747399 & 179.047816669903 \tabularnewline
96 & 126.150870022321 & 71.7292302457648 & 180.572509798878 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261250&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]85[/C][C]126.150870022321[/C][C]92.0655674519304[/C][C]160.236172592712[/C][/ROW]
[ROW][C]86[/C][C]126.150870022321[/C][C]89.744335407677[/C][C]162.557404636966[/C][/ROW]
[ROW][C]87[/C][C]126.150870022321[/C][C]87.5624822096711[/C][C]164.739257834972[/C][/ROW]
[ROW][C]88[/C][C]126.150870022321[/C][C]85.4975603746224[/C][C]166.80417967002[/C][/ROW]
[ROW][C]89[/C][C]126.150870022321[/C][C]83.5325700017446[/C][C]168.769170042898[/C][/ROW]
[ROW][C]90[/C][C]126.150870022321[/C][C]81.6542700625931[/C][C]170.64746998205[/C][/ROW]
[ROW][C]91[/C][C]126.150870022321[/C][C]79.8521084912794[/C][C]172.449631553363[/C][/ROW]
[ROW][C]92[/C][C]126.150870022321[/C][C]78.1175146258837[/C][C]174.184225418759[/C][/ROW]
[ROW][C]93[/C][C]126.150870022321[/C][C]76.4434144248691[/C][C]175.858325619774[/C][/ROW]
[ROW][C]94[/C][C]126.150870022321[/C][C]74.8238882943366[/C][C]177.477851750306[/C][/ROW]
[ROW][C]95[/C][C]126.150870022321[/C][C]73.2539233747399[/C][C]179.047816669903[/C][/ROW]
[ROW][C]96[/C][C]126.150870022321[/C][C]71.7292302457648[/C][C]180.572509798878[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261250&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261250&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
85126.15087002232192.0655674519304160.236172592712
86126.15087002232189.744335407677162.557404636966
87126.15087002232187.5624822096711164.739257834972
88126.15087002232185.4975603746224166.80417967002
89126.15087002232183.5325700017446168.769170042898
90126.15087002232181.6542700625931170.64746998205
91126.15087002232179.8521084912794172.449631553363
92126.15087002232178.1175146258837174.184225418759
93126.15087002232176.4434144248691175.858325619774
94126.15087002232174.8238882943366177.477851750306
95126.15087002232173.2539233747399179.047816669903
96126.15087002232171.7292302457648180.572509798878



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')