Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Nov 2014 14:59:53 +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/30/t1417359618f3mxsjmdjdpcaue.htm/, Retrieved Sun, 19 May 2024 20:46:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261489, Retrieved Sun, 19 May 2024 20:46:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-30 14:59:53] [5fd46a639be569026986aaac39788635] [Current]
Feedback Forum

Post a new message
Dataseries X:
3004
3080
3017
3114
3057
3032
3127
3050
2910
2671
2638
2672
2654
2568
2467
2419
2363
2291
2560
2527
2370
2310
2231
2367
2346
2286
2249
2226
2108
2131
2387
2358
2284
2312
2293
2576
2665
2749
2926
2886
2893
2944
3060
3045
2894
2955
2954
3243
3120
3074
3034
2981
2876
2835
2978
2881
2768
2722
2630
2753
2771
2652
2584
2501
2449
2445
2620
2579
2460
2434
2392
1037
1212
1232
1174
1158
1140
1118
1212
1207
1186
608
627
626
649
619
612
643
623
649
699
693
659
669
668
693




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=261489&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=261489&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261489&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
alpha0.931416874811562
beta0.0633662155024615
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.931416874811562 \tabularnewline
beta & 0.0633662155024615 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261489&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]0.931416874811562[/C][/ROW]
[ROW][C]beta[/C][C]0.0633662155024615[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261489&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261489&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
alpha0.931416874811562
beta0.0633662155024615
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
330173156-139
431143094.3292240259319.6707759740666
530573181.60806266047-124.608062660471
630323127.14874329492-95.1487432949157
731273094.5126177945932.4873822054051
830503182.67635049242-132.676350492417
929103109.17318915907-199.173189159066
1026712961.97847636307-290.978476363066
1126382712.10111473932-74.1011147393169
1226722659.8535128494912.1464871505059
1326542688.65527284554-34.6552728455363
1425682671.81971704756-103.819717047556
1524672584.4357534572-117.435753457201
1624192477.43848305769-58.4384830576905
1723632421.94320542724-58.9432054272356
1822912362.49897151866-71.4989715186553
1925602287.14018998523272.859810014772
2025272548.62727343631-21.627273436307
2123702534.54766843082-164.547668430817
2223102377.63793274788-67.6379327478808
2322312306.99954490998-75.9995449099847
2423672224.08748971995142.912510280054
2523462353.50856498352-7.50856498351823
2622862342.38175419278-56.3817541927783
2722492282.4059586808-33.4059586807966
2822262241.85857503284-15.8585750328357
2921082216.7191417776-108.719141777603
3021312098.671166502932.3288334971003
3123872113.90571502641273.094284973587
3223582369.51139159852-11.5113915985207
3322842359.3511318402-75.3511318401956
3423122285.2822096278326.7177903721708
3522932307.8588976285-14.8588976285018
3625762290.8333793035285.166620696504
3726652570.0873289217894.9126710782184
3827492677.7373196105771.2626803894314
3929262767.56525910571158.434740894286
4028862947.9376025934-61.9376025933975
4128932919.39584686289-26.3958468628934
4229442922.4003897321921.5996102678059
4330602971.3835281132988.6164718867149
4430453088.01747858956-43.0174785895601
4528943079.50643911772-185.50643911772
4629552927.3301200691227.6698799308824
4729542975.34290823401-21.3429082340122
4832432976.44469224166266.555307758337
4931203261.43192371945-141.431923719455
5030743158.06559969664-84.0655996966407
5130343103.16965575411-69.1696557541109
5229813058.06562721538-77.0656272153838
5328763001.05871636684-125.058716366841
5428352891.96922164555-56.9692216455524
5529782842.93708719722135.062912802781
5628812980.73838534218-99.7383853421775
5727682893.95519651798-125.955196517984
5827222775.31930601474-53.3193060147378
5926302721.19078487864-91.1907848786373
6027532626.40601608246126.593983917535
6127712741.9412788299729.058721170034
6226522768.34560821995-116.345608219948
6325842652.45113158326-68.4511315832633
6425012577.1263681027-76.1263681027035
6524492490.15975397524-41.1597539752406
6624452433.3323707047211.6676292952839
6726202426.39793137399193.602068626008
6825792600.34676319929-21.346763199293
6924602572.82873214113-112.828732141132
7024342453.44365880811-19.4436588081057
7123922419.89144684351-27.8914468435064
7210372376.82465924701-1339.82465924701
7312121032.72420203494179.275797965065
7412321114.12046777173117.879532228266
7511741145.2885082639328.7114917360745
7611581095.0984937954662.9015062045403
7711401080.4661054454259.5338945545768
7811181066.210778809251.7892211907961
7912121047.79855131577164.201448684232
8012071143.7801984547863.2198015452163
8111861149.4370910010636.5629089989372
826081132.42326013965-524.423260139651
83627561.94579393597365.0542060640273
84626544.35710989388281.6428901061176
85649547.037999061933101.962000938067
86619574.66228518763944.3377148123608
87612551.23116681363660.7688331863644
88643546.69086792321596.3091320767849
89623580.9376030339342.0623969660701
90649567.14055157194481.8594484280555
91699595.242519722462103.757480277538
92693649.86448835167843.135511648322
93659650.5680059456548.43199405434643
94669619.44574098222349.5542590177768
95668629.55015786248838.4498421375117
96693631.5810570931761.4189429068301

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3017 & 3156 & -139 \tabularnewline
4 & 3114 & 3094.32922402593 & 19.6707759740666 \tabularnewline
5 & 3057 & 3181.60806266047 & -124.608062660471 \tabularnewline
6 & 3032 & 3127.14874329492 & -95.1487432949157 \tabularnewline
7 & 3127 & 3094.51261779459 & 32.4873822054051 \tabularnewline
8 & 3050 & 3182.67635049242 & -132.676350492417 \tabularnewline
9 & 2910 & 3109.17318915907 & -199.173189159066 \tabularnewline
10 & 2671 & 2961.97847636307 & -290.978476363066 \tabularnewline
11 & 2638 & 2712.10111473932 & -74.1011147393169 \tabularnewline
12 & 2672 & 2659.85351284949 & 12.1464871505059 \tabularnewline
13 & 2654 & 2688.65527284554 & -34.6552728455363 \tabularnewline
14 & 2568 & 2671.81971704756 & -103.819717047556 \tabularnewline
15 & 2467 & 2584.4357534572 & -117.435753457201 \tabularnewline
16 & 2419 & 2477.43848305769 & -58.4384830576905 \tabularnewline
17 & 2363 & 2421.94320542724 & -58.9432054272356 \tabularnewline
18 & 2291 & 2362.49897151866 & -71.4989715186553 \tabularnewline
19 & 2560 & 2287.14018998523 & 272.859810014772 \tabularnewline
20 & 2527 & 2548.62727343631 & -21.627273436307 \tabularnewline
21 & 2370 & 2534.54766843082 & -164.547668430817 \tabularnewline
22 & 2310 & 2377.63793274788 & -67.6379327478808 \tabularnewline
23 & 2231 & 2306.99954490998 & -75.9995449099847 \tabularnewline
24 & 2367 & 2224.08748971995 & 142.912510280054 \tabularnewline
25 & 2346 & 2353.50856498352 & -7.50856498351823 \tabularnewline
26 & 2286 & 2342.38175419278 & -56.3817541927783 \tabularnewline
27 & 2249 & 2282.4059586808 & -33.4059586807966 \tabularnewline
28 & 2226 & 2241.85857503284 & -15.8585750328357 \tabularnewline
29 & 2108 & 2216.7191417776 & -108.719141777603 \tabularnewline
30 & 2131 & 2098.6711665029 & 32.3288334971003 \tabularnewline
31 & 2387 & 2113.90571502641 & 273.094284973587 \tabularnewline
32 & 2358 & 2369.51139159852 & -11.5113915985207 \tabularnewline
33 & 2284 & 2359.3511318402 & -75.3511318401956 \tabularnewline
34 & 2312 & 2285.28220962783 & 26.7177903721708 \tabularnewline
35 & 2293 & 2307.8588976285 & -14.8588976285018 \tabularnewline
36 & 2576 & 2290.8333793035 & 285.166620696504 \tabularnewline
37 & 2665 & 2570.08732892178 & 94.9126710782184 \tabularnewline
38 & 2749 & 2677.73731961057 & 71.2626803894314 \tabularnewline
39 & 2926 & 2767.56525910571 & 158.434740894286 \tabularnewline
40 & 2886 & 2947.9376025934 & -61.9376025933975 \tabularnewline
41 & 2893 & 2919.39584686289 & -26.3958468628934 \tabularnewline
42 & 2944 & 2922.40038973219 & 21.5996102678059 \tabularnewline
43 & 3060 & 2971.38352811329 & 88.6164718867149 \tabularnewline
44 & 3045 & 3088.01747858956 & -43.0174785895601 \tabularnewline
45 & 2894 & 3079.50643911772 & -185.50643911772 \tabularnewline
46 & 2955 & 2927.33012006912 & 27.6698799308824 \tabularnewline
47 & 2954 & 2975.34290823401 & -21.3429082340122 \tabularnewline
48 & 3243 & 2976.44469224166 & 266.555307758337 \tabularnewline
49 & 3120 & 3261.43192371945 & -141.431923719455 \tabularnewline
50 & 3074 & 3158.06559969664 & -84.0655996966407 \tabularnewline
51 & 3034 & 3103.16965575411 & -69.1696557541109 \tabularnewline
52 & 2981 & 3058.06562721538 & -77.0656272153838 \tabularnewline
53 & 2876 & 3001.05871636684 & -125.058716366841 \tabularnewline
54 & 2835 & 2891.96922164555 & -56.9692216455524 \tabularnewline
55 & 2978 & 2842.93708719722 & 135.062912802781 \tabularnewline
56 & 2881 & 2980.73838534218 & -99.7383853421775 \tabularnewline
57 & 2768 & 2893.95519651798 & -125.955196517984 \tabularnewline
58 & 2722 & 2775.31930601474 & -53.3193060147378 \tabularnewline
59 & 2630 & 2721.19078487864 & -91.1907848786373 \tabularnewline
60 & 2753 & 2626.40601608246 & 126.593983917535 \tabularnewline
61 & 2771 & 2741.94127882997 & 29.058721170034 \tabularnewline
62 & 2652 & 2768.34560821995 & -116.345608219948 \tabularnewline
63 & 2584 & 2652.45113158326 & -68.4511315832633 \tabularnewline
64 & 2501 & 2577.1263681027 & -76.1263681027035 \tabularnewline
65 & 2449 & 2490.15975397524 & -41.1597539752406 \tabularnewline
66 & 2445 & 2433.33237070472 & 11.6676292952839 \tabularnewline
67 & 2620 & 2426.39793137399 & 193.602068626008 \tabularnewline
68 & 2579 & 2600.34676319929 & -21.346763199293 \tabularnewline
69 & 2460 & 2572.82873214113 & -112.828732141132 \tabularnewline
70 & 2434 & 2453.44365880811 & -19.4436588081057 \tabularnewline
71 & 2392 & 2419.89144684351 & -27.8914468435064 \tabularnewline
72 & 1037 & 2376.82465924701 & -1339.82465924701 \tabularnewline
73 & 1212 & 1032.72420203494 & 179.275797965065 \tabularnewline
74 & 1232 & 1114.12046777173 & 117.879532228266 \tabularnewline
75 & 1174 & 1145.28850826393 & 28.7114917360745 \tabularnewline
76 & 1158 & 1095.09849379546 & 62.9015062045403 \tabularnewline
77 & 1140 & 1080.46610544542 & 59.5338945545768 \tabularnewline
78 & 1118 & 1066.2107788092 & 51.7892211907961 \tabularnewline
79 & 1212 & 1047.79855131577 & 164.201448684232 \tabularnewline
80 & 1207 & 1143.78019845478 & 63.2198015452163 \tabularnewline
81 & 1186 & 1149.43709100106 & 36.5629089989372 \tabularnewline
82 & 608 & 1132.42326013965 & -524.423260139651 \tabularnewline
83 & 627 & 561.945793935973 & 65.0542060640273 \tabularnewline
84 & 626 & 544.357109893882 & 81.6428901061176 \tabularnewline
85 & 649 & 547.037999061933 & 101.962000938067 \tabularnewline
86 & 619 & 574.662285187639 & 44.3377148123608 \tabularnewline
87 & 612 & 551.231166813636 & 60.7688331863644 \tabularnewline
88 & 643 & 546.690867923215 & 96.3091320767849 \tabularnewline
89 & 623 & 580.93760303393 & 42.0623969660701 \tabularnewline
90 & 649 & 567.140551571944 & 81.8594484280555 \tabularnewline
91 & 699 & 595.242519722462 & 103.757480277538 \tabularnewline
92 & 693 & 649.864488351678 & 43.135511648322 \tabularnewline
93 & 659 & 650.568005945654 & 8.43199405434643 \tabularnewline
94 & 669 & 619.445740982223 & 49.5542590177768 \tabularnewline
95 & 668 & 629.550157862488 & 38.4498421375117 \tabularnewline
96 & 693 & 631.58105709317 & 61.4189429068301 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261489&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]3017[/C][C]3156[/C][C]-139[/C][/ROW]
[ROW][C]4[/C][C]3114[/C][C]3094.32922402593[/C][C]19.6707759740666[/C][/ROW]
[ROW][C]5[/C][C]3057[/C][C]3181.60806266047[/C][C]-124.608062660471[/C][/ROW]
[ROW][C]6[/C][C]3032[/C][C]3127.14874329492[/C][C]-95.1487432949157[/C][/ROW]
[ROW][C]7[/C][C]3127[/C][C]3094.51261779459[/C][C]32.4873822054051[/C][/ROW]
[ROW][C]8[/C][C]3050[/C][C]3182.67635049242[/C][C]-132.676350492417[/C][/ROW]
[ROW][C]9[/C][C]2910[/C][C]3109.17318915907[/C][C]-199.173189159066[/C][/ROW]
[ROW][C]10[/C][C]2671[/C][C]2961.97847636307[/C][C]-290.978476363066[/C][/ROW]
[ROW][C]11[/C][C]2638[/C][C]2712.10111473932[/C][C]-74.1011147393169[/C][/ROW]
[ROW][C]12[/C][C]2672[/C][C]2659.85351284949[/C][C]12.1464871505059[/C][/ROW]
[ROW][C]13[/C][C]2654[/C][C]2688.65527284554[/C][C]-34.6552728455363[/C][/ROW]
[ROW][C]14[/C][C]2568[/C][C]2671.81971704756[/C][C]-103.819717047556[/C][/ROW]
[ROW][C]15[/C][C]2467[/C][C]2584.4357534572[/C][C]-117.435753457201[/C][/ROW]
[ROW][C]16[/C][C]2419[/C][C]2477.43848305769[/C][C]-58.4384830576905[/C][/ROW]
[ROW][C]17[/C][C]2363[/C][C]2421.94320542724[/C][C]-58.9432054272356[/C][/ROW]
[ROW][C]18[/C][C]2291[/C][C]2362.49897151866[/C][C]-71.4989715186553[/C][/ROW]
[ROW][C]19[/C][C]2560[/C][C]2287.14018998523[/C][C]272.859810014772[/C][/ROW]
[ROW][C]20[/C][C]2527[/C][C]2548.62727343631[/C][C]-21.627273436307[/C][/ROW]
[ROW][C]21[/C][C]2370[/C][C]2534.54766843082[/C][C]-164.547668430817[/C][/ROW]
[ROW][C]22[/C][C]2310[/C][C]2377.63793274788[/C][C]-67.6379327478808[/C][/ROW]
[ROW][C]23[/C][C]2231[/C][C]2306.99954490998[/C][C]-75.9995449099847[/C][/ROW]
[ROW][C]24[/C][C]2367[/C][C]2224.08748971995[/C][C]142.912510280054[/C][/ROW]
[ROW][C]25[/C][C]2346[/C][C]2353.50856498352[/C][C]-7.50856498351823[/C][/ROW]
[ROW][C]26[/C][C]2286[/C][C]2342.38175419278[/C][C]-56.3817541927783[/C][/ROW]
[ROW][C]27[/C][C]2249[/C][C]2282.4059586808[/C][C]-33.4059586807966[/C][/ROW]
[ROW][C]28[/C][C]2226[/C][C]2241.85857503284[/C][C]-15.8585750328357[/C][/ROW]
[ROW][C]29[/C][C]2108[/C][C]2216.7191417776[/C][C]-108.719141777603[/C][/ROW]
[ROW][C]30[/C][C]2131[/C][C]2098.6711665029[/C][C]32.3288334971003[/C][/ROW]
[ROW][C]31[/C][C]2387[/C][C]2113.90571502641[/C][C]273.094284973587[/C][/ROW]
[ROW][C]32[/C][C]2358[/C][C]2369.51139159852[/C][C]-11.5113915985207[/C][/ROW]
[ROW][C]33[/C][C]2284[/C][C]2359.3511318402[/C][C]-75.3511318401956[/C][/ROW]
[ROW][C]34[/C][C]2312[/C][C]2285.28220962783[/C][C]26.7177903721708[/C][/ROW]
[ROW][C]35[/C][C]2293[/C][C]2307.8588976285[/C][C]-14.8588976285018[/C][/ROW]
[ROW][C]36[/C][C]2576[/C][C]2290.8333793035[/C][C]285.166620696504[/C][/ROW]
[ROW][C]37[/C][C]2665[/C][C]2570.08732892178[/C][C]94.9126710782184[/C][/ROW]
[ROW][C]38[/C][C]2749[/C][C]2677.73731961057[/C][C]71.2626803894314[/C][/ROW]
[ROW][C]39[/C][C]2926[/C][C]2767.56525910571[/C][C]158.434740894286[/C][/ROW]
[ROW][C]40[/C][C]2886[/C][C]2947.9376025934[/C][C]-61.9376025933975[/C][/ROW]
[ROW][C]41[/C][C]2893[/C][C]2919.39584686289[/C][C]-26.3958468628934[/C][/ROW]
[ROW][C]42[/C][C]2944[/C][C]2922.40038973219[/C][C]21.5996102678059[/C][/ROW]
[ROW][C]43[/C][C]3060[/C][C]2971.38352811329[/C][C]88.6164718867149[/C][/ROW]
[ROW][C]44[/C][C]3045[/C][C]3088.01747858956[/C][C]-43.0174785895601[/C][/ROW]
[ROW][C]45[/C][C]2894[/C][C]3079.50643911772[/C][C]-185.50643911772[/C][/ROW]
[ROW][C]46[/C][C]2955[/C][C]2927.33012006912[/C][C]27.6698799308824[/C][/ROW]
[ROW][C]47[/C][C]2954[/C][C]2975.34290823401[/C][C]-21.3429082340122[/C][/ROW]
[ROW][C]48[/C][C]3243[/C][C]2976.44469224166[/C][C]266.555307758337[/C][/ROW]
[ROW][C]49[/C][C]3120[/C][C]3261.43192371945[/C][C]-141.431923719455[/C][/ROW]
[ROW][C]50[/C][C]3074[/C][C]3158.06559969664[/C][C]-84.0655996966407[/C][/ROW]
[ROW][C]51[/C][C]3034[/C][C]3103.16965575411[/C][C]-69.1696557541109[/C][/ROW]
[ROW][C]52[/C][C]2981[/C][C]3058.06562721538[/C][C]-77.0656272153838[/C][/ROW]
[ROW][C]53[/C][C]2876[/C][C]3001.05871636684[/C][C]-125.058716366841[/C][/ROW]
[ROW][C]54[/C][C]2835[/C][C]2891.96922164555[/C][C]-56.9692216455524[/C][/ROW]
[ROW][C]55[/C][C]2978[/C][C]2842.93708719722[/C][C]135.062912802781[/C][/ROW]
[ROW][C]56[/C][C]2881[/C][C]2980.73838534218[/C][C]-99.7383853421775[/C][/ROW]
[ROW][C]57[/C][C]2768[/C][C]2893.95519651798[/C][C]-125.955196517984[/C][/ROW]
[ROW][C]58[/C][C]2722[/C][C]2775.31930601474[/C][C]-53.3193060147378[/C][/ROW]
[ROW][C]59[/C][C]2630[/C][C]2721.19078487864[/C][C]-91.1907848786373[/C][/ROW]
[ROW][C]60[/C][C]2753[/C][C]2626.40601608246[/C][C]126.593983917535[/C][/ROW]
[ROW][C]61[/C][C]2771[/C][C]2741.94127882997[/C][C]29.058721170034[/C][/ROW]
[ROW][C]62[/C][C]2652[/C][C]2768.34560821995[/C][C]-116.345608219948[/C][/ROW]
[ROW][C]63[/C][C]2584[/C][C]2652.45113158326[/C][C]-68.4511315832633[/C][/ROW]
[ROW][C]64[/C][C]2501[/C][C]2577.1263681027[/C][C]-76.1263681027035[/C][/ROW]
[ROW][C]65[/C][C]2449[/C][C]2490.15975397524[/C][C]-41.1597539752406[/C][/ROW]
[ROW][C]66[/C][C]2445[/C][C]2433.33237070472[/C][C]11.6676292952839[/C][/ROW]
[ROW][C]67[/C][C]2620[/C][C]2426.39793137399[/C][C]193.602068626008[/C][/ROW]
[ROW][C]68[/C][C]2579[/C][C]2600.34676319929[/C][C]-21.346763199293[/C][/ROW]
[ROW][C]69[/C][C]2460[/C][C]2572.82873214113[/C][C]-112.828732141132[/C][/ROW]
[ROW][C]70[/C][C]2434[/C][C]2453.44365880811[/C][C]-19.4436588081057[/C][/ROW]
[ROW][C]71[/C][C]2392[/C][C]2419.89144684351[/C][C]-27.8914468435064[/C][/ROW]
[ROW][C]72[/C][C]1037[/C][C]2376.82465924701[/C][C]-1339.82465924701[/C][/ROW]
[ROW][C]73[/C][C]1212[/C][C]1032.72420203494[/C][C]179.275797965065[/C][/ROW]
[ROW][C]74[/C][C]1232[/C][C]1114.12046777173[/C][C]117.879532228266[/C][/ROW]
[ROW][C]75[/C][C]1174[/C][C]1145.28850826393[/C][C]28.7114917360745[/C][/ROW]
[ROW][C]76[/C][C]1158[/C][C]1095.09849379546[/C][C]62.9015062045403[/C][/ROW]
[ROW][C]77[/C][C]1140[/C][C]1080.46610544542[/C][C]59.5338945545768[/C][/ROW]
[ROW][C]78[/C][C]1118[/C][C]1066.2107788092[/C][C]51.7892211907961[/C][/ROW]
[ROW][C]79[/C][C]1212[/C][C]1047.79855131577[/C][C]164.201448684232[/C][/ROW]
[ROW][C]80[/C][C]1207[/C][C]1143.78019845478[/C][C]63.2198015452163[/C][/ROW]
[ROW][C]81[/C][C]1186[/C][C]1149.43709100106[/C][C]36.5629089989372[/C][/ROW]
[ROW][C]82[/C][C]608[/C][C]1132.42326013965[/C][C]-524.423260139651[/C][/ROW]
[ROW][C]83[/C][C]627[/C][C]561.945793935973[/C][C]65.0542060640273[/C][/ROW]
[ROW][C]84[/C][C]626[/C][C]544.357109893882[/C][C]81.6428901061176[/C][/ROW]
[ROW][C]85[/C][C]649[/C][C]547.037999061933[/C][C]101.962000938067[/C][/ROW]
[ROW][C]86[/C][C]619[/C][C]574.662285187639[/C][C]44.3377148123608[/C][/ROW]
[ROW][C]87[/C][C]612[/C][C]551.231166813636[/C][C]60.7688331863644[/C][/ROW]
[ROW][C]88[/C][C]643[/C][C]546.690867923215[/C][C]96.3091320767849[/C][/ROW]
[ROW][C]89[/C][C]623[/C][C]580.93760303393[/C][C]42.0623969660701[/C][/ROW]
[ROW][C]90[/C][C]649[/C][C]567.140551571944[/C][C]81.8594484280555[/C][/ROW]
[ROW][C]91[/C][C]699[/C][C]595.242519722462[/C][C]103.757480277538[/C][/ROW]
[ROW][C]92[/C][C]693[/C][C]649.864488351678[/C][C]43.135511648322[/C][/ROW]
[ROW][C]93[/C][C]659[/C][C]650.568005945654[/C][C]8.43199405434643[/C][/ROW]
[ROW][C]94[/C][C]669[/C][C]619.445740982223[/C][C]49.5542590177768[/C][/ROW]
[ROW][C]95[/C][C]668[/C][C]629.550157862488[/C][C]38.4498421375117[/C][/ROW]
[ROW][C]96[/C][C]693[/C][C]631.58105709317[/C][C]61.4189429068301[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261489&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261489&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
330173156-139
431143094.3292240259319.6707759740666
530573181.60806266047-124.608062660471
630323127.14874329492-95.1487432949157
731273094.5126177945932.4873822054051
830503182.67635049242-132.676350492417
929103109.17318915907-199.173189159066
1026712961.97847636307-290.978476363066
1126382712.10111473932-74.1011147393169
1226722659.8535128494912.1464871505059
1326542688.65527284554-34.6552728455363
1425682671.81971704756-103.819717047556
1524672584.4357534572-117.435753457201
1624192477.43848305769-58.4384830576905
1723632421.94320542724-58.9432054272356
1822912362.49897151866-71.4989715186553
1925602287.14018998523272.859810014772
2025272548.62727343631-21.627273436307
2123702534.54766843082-164.547668430817
2223102377.63793274788-67.6379327478808
2322312306.99954490998-75.9995449099847
2423672224.08748971995142.912510280054
2523462353.50856498352-7.50856498351823
2622862342.38175419278-56.3817541927783
2722492282.4059586808-33.4059586807966
2822262241.85857503284-15.8585750328357
2921082216.7191417776-108.719141777603
3021312098.671166502932.3288334971003
3123872113.90571502641273.094284973587
3223582369.51139159852-11.5113915985207
3322842359.3511318402-75.3511318401956
3423122285.2822096278326.7177903721708
3522932307.8588976285-14.8588976285018
3625762290.8333793035285.166620696504
3726652570.0873289217894.9126710782184
3827492677.7373196105771.2626803894314
3929262767.56525910571158.434740894286
4028862947.9376025934-61.9376025933975
4128932919.39584686289-26.3958468628934
4229442922.4003897321921.5996102678059
4330602971.3835281132988.6164718867149
4430453088.01747858956-43.0174785895601
4528943079.50643911772-185.50643911772
4629552927.3301200691227.6698799308824
4729542975.34290823401-21.3429082340122
4832432976.44469224166266.555307758337
4931203261.43192371945-141.431923719455
5030743158.06559969664-84.0655996966407
5130343103.16965575411-69.1696557541109
5229813058.06562721538-77.0656272153838
5328763001.05871636684-125.058716366841
5428352891.96922164555-56.9692216455524
5529782842.93708719722135.062912802781
5628812980.73838534218-99.7383853421775
5727682893.95519651798-125.955196517984
5827222775.31930601474-53.3193060147378
5926302721.19078487864-91.1907848786373
6027532626.40601608246126.593983917535
6127712741.9412788299729.058721170034
6226522768.34560821995-116.345608219948
6325842652.45113158326-68.4511315832633
6425012577.1263681027-76.1263681027035
6524492490.15975397524-41.1597539752406
6624452433.3323707047211.6676292952839
6726202426.39793137399193.602068626008
6825792600.34676319929-21.346763199293
6924602572.82873214113-112.828732141132
7024342453.44365880811-19.4436588081057
7123922419.89144684351-27.8914468435064
7210372376.82465924701-1339.82465924701
7312121032.72420203494179.275797965065
7412321114.12046777173117.879532228266
7511741145.2885082639328.7114917360745
7611581095.0984937954662.9015062045403
7711401080.4661054454259.5338945545768
7811181066.210778809251.7892211907961
7912121047.79855131577164.201448684232
8012071143.7801984547863.2198015452163
8111861149.4370910010636.5629089989372
826081132.42326013965-524.423260139651
83627561.94579393597365.0542060640273
84626544.35710989388281.6428901061176
85649547.037999061933101.962000938067
86619574.66228518763944.3377148123608
87612551.23116681363660.7688331863644
88643546.69086792321596.3091320767849
89623580.9376030339342.0623969660701
90649567.14055157194481.8594484280555
91699595.242519722462103.757480277538
92693649.86448835167843.135511648322
93659650.5680059456548.43199405434643
94669619.44574098222349.5542590177768
95668629.55015786248838.4498421375117
96693631.5810570931761.4189429068301







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97658.630732648961300.7478054908871016.51365980704
98628.473768348243124.7650324296551132.18250426683
99598.316804047525-30.00242114356271226.63602923861
100568.159839746807-174.9149705800341311.23465007365
101538.002875446089-314.487696649751390.49344754193
102507.84591114537-451.0166253705491466.70844766129
103477.688946844652-585.8354059021921541.2132995915
104447.531982543934-719.7865430722741614.85050816014
105417.375018243216-853.4338375239761688.18387401041
106387.218053942498-987.1706035023741761.60671138737
107357.06108964178-1121.279856005111835.40203528867
108326.904125341062-1255.97008550591909.77833618802

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 658.630732648961 & 300.747805490887 & 1016.51365980704 \tabularnewline
98 & 628.473768348243 & 124.765032429655 & 1132.18250426683 \tabularnewline
99 & 598.316804047525 & -30.0024211435627 & 1226.63602923861 \tabularnewline
100 & 568.159839746807 & -174.914970580034 & 1311.23465007365 \tabularnewline
101 & 538.002875446089 & -314.48769664975 & 1390.49344754193 \tabularnewline
102 & 507.84591114537 & -451.016625370549 & 1466.70844766129 \tabularnewline
103 & 477.688946844652 & -585.835405902192 & 1541.2132995915 \tabularnewline
104 & 447.531982543934 & -719.786543072274 & 1614.85050816014 \tabularnewline
105 & 417.375018243216 & -853.433837523976 & 1688.18387401041 \tabularnewline
106 & 387.218053942498 & -987.170603502374 & 1761.60671138737 \tabularnewline
107 & 357.06108964178 & -1121.27985600511 & 1835.40203528867 \tabularnewline
108 & 326.904125341062 & -1255.9700855059 & 1909.77833618802 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261489&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]97[/C][C]658.630732648961[/C][C]300.747805490887[/C][C]1016.51365980704[/C][/ROW]
[ROW][C]98[/C][C]628.473768348243[/C][C]124.765032429655[/C][C]1132.18250426683[/C][/ROW]
[ROW][C]99[/C][C]598.316804047525[/C][C]-30.0024211435627[/C][C]1226.63602923861[/C][/ROW]
[ROW][C]100[/C][C]568.159839746807[/C][C]-174.914970580034[/C][C]1311.23465007365[/C][/ROW]
[ROW][C]101[/C][C]538.002875446089[/C][C]-314.48769664975[/C][C]1390.49344754193[/C][/ROW]
[ROW][C]102[/C][C]507.84591114537[/C][C]-451.016625370549[/C][C]1466.70844766129[/C][/ROW]
[ROW][C]103[/C][C]477.688946844652[/C][C]-585.835405902192[/C][C]1541.2132995915[/C][/ROW]
[ROW][C]104[/C][C]447.531982543934[/C][C]-719.786543072274[/C][C]1614.85050816014[/C][/ROW]
[ROW][C]105[/C][C]417.375018243216[/C][C]-853.433837523976[/C][C]1688.18387401041[/C][/ROW]
[ROW][C]106[/C][C]387.218053942498[/C][C]-987.170603502374[/C][C]1761.60671138737[/C][/ROW]
[ROW][C]107[/C][C]357.06108964178[/C][C]-1121.27985600511[/C][C]1835.40203528867[/C][/ROW]
[ROW][C]108[/C][C]326.904125341062[/C][C]-1255.9700855059[/C][C]1909.77833618802[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261489&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261489&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
97658.630732648961300.7478054908871016.51365980704
98628.473768348243124.7650324296551132.18250426683
99598.316804047525-30.00242114356271226.63602923861
100568.159839746807-174.9149705800341311.23465007365
101538.002875446089-314.487696649751390.49344754193
102507.84591114537-451.0166253705491466.70844766129
103477.688946844652-585.8354059021921541.2132995915
104447.531982543934-719.7865430722741614.85050816014
105417.375018243216-853.4338375239761688.18387401041
106387.218053942498-987.1706035023741761.60671138737
107357.06108964178-1121.279856005111835.40203528867
108326.904125341062-1255.97008550591909.77833618802



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
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')