Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 11 Aug 2014 16:25:27 +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/11/t1407770807fpxf757dg6loyd2.htm/, Retrieved Fri, 17 May 2024 04:48:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235470, Retrieved Fri, 17 May 2024 04:48:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSiemon Vermetten
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [forecast aantal b...] [2014-08-11 15:25:27] [7e257b479a74cf54c1843b0823401607] [Current]
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Dataseries X:
240
150
290
210
240
240
310
310
190
230
260
320
270
250
240
250
230
230
240
300
190
270
300
330
230
260
300
330
190
260
240
270
170
230
270
320
190
300
310
360
170
280
270
260
280
300
320
370
210
310
290
450
190
290
280
310
340
220
390
410
250
310
280
450
210
390
300
310
370
250
440
360
290
300
340
600
220
410
360
250
410
290
470
350
330
250
270
580
260
450
320
240
420
380
400
370
300
310
280
560
280
480
320
170
420
310
470
420




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235470&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235470&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235470&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00717809126973187
beta1
gamma0.860544926517446

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00717809126973187 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.860544926517446 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235470&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]0.00717809126973187[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.860544926517446[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235470&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235470&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
alpha0.00717809126973187
beta1
gamma0.860544926517446







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13270268.4054487179491.59455128205116
14250251.710683044565-1.71068304456517
15240242.063245991823-2.06324599182304
16250250.315134708693-0.315134708692511
17230226.9106427955343.0893572044659
18230224.8027643240345.19723567596614
19240312.330655961953-72.3306559619533
20300305.866182600985-5.86618260098464
21190183.1700226352146.82997736478575
22270223.11402306534846.8859769346521
23300252.01543427133547.9845657286648
24330313.35250217362616.647497826374
25230268.446460362113-38.4464603621133
26260248.68275756108211.3172424389181
27300238.96350021046961.036499789531
28330249.7506729993380.2493270006696
29190231.000285910755-41.0002859107554
30260231.2274693930828.7725306069197
31240253.707111496036-13.7071114960364
32270305.889221522328-35.8892215223285
33170195.049904901233-25.049904901233
34230269.983950897015-39.9839508970153
35270299.573164292992-29.5731642929925
36320333.396179240736-13.3961792407363
37190240.804364996551-50.8043649965515
38300262.98014874068237.0198512593176
39310295.62010268236214.3798973176385
40360321.84846706225238.151532937748
41170198.26321941419-28.26321941419
42280257.34400337017122.6559966298286
43270242.59311558487927.4068844151211
44260275.520399764733-15.520399764733
45280173.636001308428106.363998691572
46300237.24542562196562.7545743780347
47320277.69545966575542.3045403342447
48370327.60017280644842.3998271935523
49210205.5936821613684.40631783863176
50310305.741434189064.25856581093984
51290321.109685788742-31.1096857887416
52450369.30102485532580.6989751446751
53190191.563748143683-1.56374814368294
54290296.81676716819-6.81676716819015
55280288.178611180481-8.17861118048103
56310286.18461589252823.8153841074721
57340291.00888961617448.9911103838258
58220318.828371982764-98.8283719827641
59390341.36721625752148.6327837424789
60410392.16470796425817.8352920357422
61250238.11107504778211.8889249522178
62310338.829631518059-28.829631518059
63280324.148693798831-44.1486937988313
64450468.084386553948-18.0843865539476
65210218.958554203769-8.95855420376887
66390319.22054835138270.7794516486181
67300310.082928415733-10.0829284157333
68310335.503294637626-25.5032946376263
69370361.2222613989368.77773860106407
70250261.911594682818-11.9115946828178
71440411.1350240789128.8649759210896
72360435.410955581327-75.4109555813266
73290274.87099951314315.1290004868566
74300340.11083711155-40.1108371115498
75340311.46647932247628.5335206775239
76600477.919789385625122.080210614375
77220238.330394828747-18.3303948287468
78410407.3169399610662.68306003893417
79360328.78173124160331.218268758397
80250341.797791410705-91.797791410705
81410396.32753058117313.6724694188266
82290279.40885965529810.5911403447022
83470463.8266959408026.17330405919796
84350398.881546559854-48.881546559854
85330316.10868581308313.8913141869167
86250334.357849928221-84.3578499282205
87270363.939159154866-93.9391591548659
88580608.453257321152-28.453257321152
89260245.75709203258214.242907967418
90450431.10056608022418.899433919776
91320375.347622074635-55.3476220746346
92240280.306255866191-40.3062558661913
93420423.350536717493-3.35053671749347
94380301.58942196231678.4105780376843
95400481.118766536119-81.1187665361194
96370366.2824930347663.71750696523401
97300335.668429426374-35.6684294263735
98310267.415298917642.5847010824
99280288.42743343856-8.42743343855989
100560588.823785832203-28.8237858322032
101280261.91992606210618.0800739378936
102480450.61360724934529.3863927506555
103320330.921195373562-10.9211953735619
104170248.788036725704-78.7880367257041
105420422.592095469481-2.59209546948125
106310370.15816246665-60.1581624666499
107470410.86911397019459.1308860298059
108420369.00068539389350.9993146061065

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 270 & 268.405448717949 & 1.59455128205116 \tabularnewline
14 & 250 & 251.710683044565 & -1.71068304456517 \tabularnewline
15 & 240 & 242.063245991823 & -2.06324599182304 \tabularnewline
16 & 250 & 250.315134708693 & -0.315134708692511 \tabularnewline
17 & 230 & 226.910642795534 & 3.0893572044659 \tabularnewline
18 & 230 & 224.802764324034 & 5.19723567596614 \tabularnewline
19 & 240 & 312.330655961953 & -72.3306559619533 \tabularnewline
20 & 300 & 305.866182600985 & -5.86618260098464 \tabularnewline
21 & 190 & 183.170022635214 & 6.82997736478575 \tabularnewline
22 & 270 & 223.114023065348 & 46.8859769346521 \tabularnewline
23 & 300 & 252.015434271335 & 47.9845657286648 \tabularnewline
24 & 330 & 313.352502173626 & 16.647497826374 \tabularnewline
25 & 230 & 268.446460362113 & -38.4464603621133 \tabularnewline
26 & 260 & 248.682757561082 & 11.3172424389181 \tabularnewline
27 & 300 & 238.963500210469 & 61.036499789531 \tabularnewline
28 & 330 & 249.75067299933 & 80.2493270006696 \tabularnewline
29 & 190 & 231.000285910755 & -41.0002859107554 \tabularnewline
30 & 260 & 231.22746939308 & 28.7725306069197 \tabularnewline
31 & 240 & 253.707111496036 & -13.7071114960364 \tabularnewline
32 & 270 & 305.889221522328 & -35.8892215223285 \tabularnewline
33 & 170 & 195.049904901233 & -25.049904901233 \tabularnewline
34 & 230 & 269.983950897015 & -39.9839508970153 \tabularnewline
35 & 270 & 299.573164292992 & -29.5731642929925 \tabularnewline
36 & 320 & 333.396179240736 & -13.3961792407363 \tabularnewline
37 & 190 & 240.804364996551 & -50.8043649965515 \tabularnewline
38 & 300 & 262.980148740682 & 37.0198512593176 \tabularnewline
39 & 310 & 295.620102682362 & 14.3798973176385 \tabularnewline
40 & 360 & 321.848467062252 & 38.151532937748 \tabularnewline
41 & 170 & 198.26321941419 & -28.26321941419 \tabularnewline
42 & 280 & 257.344003370171 & 22.6559966298286 \tabularnewline
43 & 270 & 242.593115584879 & 27.4068844151211 \tabularnewline
44 & 260 & 275.520399764733 & -15.520399764733 \tabularnewline
45 & 280 & 173.636001308428 & 106.363998691572 \tabularnewline
46 & 300 & 237.245425621965 & 62.7545743780347 \tabularnewline
47 & 320 & 277.695459665755 & 42.3045403342447 \tabularnewline
48 & 370 & 327.600172806448 & 42.3998271935523 \tabularnewline
49 & 210 & 205.593682161368 & 4.40631783863176 \tabularnewline
50 & 310 & 305.74143418906 & 4.25856581093984 \tabularnewline
51 & 290 & 321.109685788742 & -31.1096857887416 \tabularnewline
52 & 450 & 369.301024855325 & 80.6989751446751 \tabularnewline
53 & 190 & 191.563748143683 & -1.56374814368294 \tabularnewline
54 & 290 & 296.81676716819 & -6.81676716819015 \tabularnewline
55 & 280 & 288.178611180481 & -8.17861118048103 \tabularnewline
56 & 310 & 286.184615892528 & 23.8153841074721 \tabularnewline
57 & 340 & 291.008889616174 & 48.9911103838258 \tabularnewline
58 & 220 & 318.828371982764 & -98.8283719827641 \tabularnewline
59 & 390 & 341.367216257521 & 48.6327837424789 \tabularnewline
60 & 410 & 392.164707964258 & 17.8352920357422 \tabularnewline
61 & 250 & 238.111075047782 & 11.8889249522178 \tabularnewline
62 & 310 & 338.829631518059 & -28.829631518059 \tabularnewline
63 & 280 & 324.148693798831 & -44.1486937988313 \tabularnewline
64 & 450 & 468.084386553948 & -18.0843865539476 \tabularnewline
65 & 210 & 218.958554203769 & -8.95855420376887 \tabularnewline
66 & 390 & 319.220548351382 & 70.7794516486181 \tabularnewline
67 & 300 & 310.082928415733 & -10.0829284157333 \tabularnewline
68 & 310 & 335.503294637626 & -25.5032946376263 \tabularnewline
69 & 370 & 361.222261398936 & 8.77773860106407 \tabularnewline
70 & 250 & 261.911594682818 & -11.9115946828178 \tabularnewline
71 & 440 & 411.13502407891 & 28.8649759210896 \tabularnewline
72 & 360 & 435.410955581327 & -75.4109555813266 \tabularnewline
73 & 290 & 274.870999513143 & 15.1290004868566 \tabularnewline
74 & 300 & 340.11083711155 & -40.1108371115498 \tabularnewline
75 & 340 & 311.466479322476 & 28.5335206775239 \tabularnewline
76 & 600 & 477.919789385625 & 122.080210614375 \tabularnewline
77 & 220 & 238.330394828747 & -18.3303948287468 \tabularnewline
78 & 410 & 407.316939961066 & 2.68306003893417 \tabularnewline
79 & 360 & 328.781731241603 & 31.218268758397 \tabularnewline
80 & 250 & 341.797791410705 & -91.797791410705 \tabularnewline
81 & 410 & 396.327530581173 & 13.6724694188266 \tabularnewline
82 & 290 & 279.408859655298 & 10.5911403447022 \tabularnewline
83 & 470 & 463.826695940802 & 6.17330405919796 \tabularnewline
84 & 350 & 398.881546559854 & -48.881546559854 \tabularnewline
85 & 330 & 316.108685813083 & 13.8913141869167 \tabularnewline
86 & 250 & 334.357849928221 & -84.3578499282205 \tabularnewline
87 & 270 & 363.939159154866 & -93.9391591548659 \tabularnewline
88 & 580 & 608.453257321152 & -28.453257321152 \tabularnewline
89 & 260 & 245.757092032582 & 14.242907967418 \tabularnewline
90 & 450 & 431.100566080224 & 18.899433919776 \tabularnewline
91 & 320 & 375.347622074635 & -55.3476220746346 \tabularnewline
92 & 240 & 280.306255866191 & -40.3062558661913 \tabularnewline
93 & 420 & 423.350536717493 & -3.35053671749347 \tabularnewline
94 & 380 & 301.589421962316 & 78.4105780376843 \tabularnewline
95 & 400 & 481.118766536119 & -81.1187665361194 \tabularnewline
96 & 370 & 366.282493034766 & 3.71750696523401 \tabularnewline
97 & 300 & 335.668429426374 & -35.6684294263735 \tabularnewline
98 & 310 & 267.4152989176 & 42.5847010824 \tabularnewline
99 & 280 & 288.42743343856 & -8.42743343855989 \tabularnewline
100 & 560 & 588.823785832203 & -28.8237858322032 \tabularnewline
101 & 280 & 261.919926062106 & 18.0800739378936 \tabularnewline
102 & 480 & 450.613607249345 & 29.3863927506555 \tabularnewline
103 & 320 & 330.921195373562 & -10.9211953735619 \tabularnewline
104 & 170 & 248.788036725704 & -78.7880367257041 \tabularnewline
105 & 420 & 422.592095469481 & -2.59209546948125 \tabularnewline
106 & 310 & 370.15816246665 & -60.1581624666499 \tabularnewline
107 & 470 & 410.869113970194 & 59.1308860298059 \tabularnewline
108 & 420 & 369.000685393893 & 50.9993146061065 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235470&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]270[/C][C]268.405448717949[/C][C]1.59455128205116[/C][/ROW]
[ROW][C]14[/C][C]250[/C][C]251.710683044565[/C][C]-1.71068304456517[/C][/ROW]
[ROW][C]15[/C][C]240[/C][C]242.063245991823[/C][C]-2.06324599182304[/C][/ROW]
[ROW][C]16[/C][C]250[/C][C]250.315134708693[/C][C]-0.315134708692511[/C][/ROW]
[ROW][C]17[/C][C]230[/C][C]226.910642795534[/C][C]3.0893572044659[/C][/ROW]
[ROW][C]18[/C][C]230[/C][C]224.802764324034[/C][C]5.19723567596614[/C][/ROW]
[ROW][C]19[/C][C]240[/C][C]312.330655961953[/C][C]-72.3306559619533[/C][/ROW]
[ROW][C]20[/C][C]300[/C][C]305.866182600985[/C][C]-5.86618260098464[/C][/ROW]
[ROW][C]21[/C][C]190[/C][C]183.170022635214[/C][C]6.82997736478575[/C][/ROW]
[ROW][C]22[/C][C]270[/C][C]223.114023065348[/C][C]46.8859769346521[/C][/ROW]
[ROW][C]23[/C][C]300[/C][C]252.015434271335[/C][C]47.9845657286648[/C][/ROW]
[ROW][C]24[/C][C]330[/C][C]313.352502173626[/C][C]16.647497826374[/C][/ROW]
[ROW][C]25[/C][C]230[/C][C]268.446460362113[/C][C]-38.4464603621133[/C][/ROW]
[ROW][C]26[/C][C]260[/C][C]248.682757561082[/C][C]11.3172424389181[/C][/ROW]
[ROW][C]27[/C][C]300[/C][C]238.963500210469[/C][C]61.036499789531[/C][/ROW]
[ROW][C]28[/C][C]330[/C][C]249.75067299933[/C][C]80.2493270006696[/C][/ROW]
[ROW][C]29[/C][C]190[/C][C]231.000285910755[/C][C]-41.0002859107554[/C][/ROW]
[ROW][C]30[/C][C]260[/C][C]231.22746939308[/C][C]28.7725306069197[/C][/ROW]
[ROW][C]31[/C][C]240[/C][C]253.707111496036[/C][C]-13.7071114960364[/C][/ROW]
[ROW][C]32[/C][C]270[/C][C]305.889221522328[/C][C]-35.8892215223285[/C][/ROW]
[ROW][C]33[/C][C]170[/C][C]195.049904901233[/C][C]-25.049904901233[/C][/ROW]
[ROW][C]34[/C][C]230[/C][C]269.983950897015[/C][C]-39.9839508970153[/C][/ROW]
[ROW][C]35[/C][C]270[/C][C]299.573164292992[/C][C]-29.5731642929925[/C][/ROW]
[ROW][C]36[/C][C]320[/C][C]333.396179240736[/C][C]-13.3961792407363[/C][/ROW]
[ROW][C]37[/C][C]190[/C][C]240.804364996551[/C][C]-50.8043649965515[/C][/ROW]
[ROW][C]38[/C][C]300[/C][C]262.980148740682[/C][C]37.0198512593176[/C][/ROW]
[ROW][C]39[/C][C]310[/C][C]295.620102682362[/C][C]14.3798973176385[/C][/ROW]
[ROW][C]40[/C][C]360[/C][C]321.848467062252[/C][C]38.151532937748[/C][/ROW]
[ROW][C]41[/C][C]170[/C][C]198.26321941419[/C][C]-28.26321941419[/C][/ROW]
[ROW][C]42[/C][C]280[/C][C]257.344003370171[/C][C]22.6559966298286[/C][/ROW]
[ROW][C]43[/C][C]270[/C][C]242.593115584879[/C][C]27.4068844151211[/C][/ROW]
[ROW][C]44[/C][C]260[/C][C]275.520399764733[/C][C]-15.520399764733[/C][/ROW]
[ROW][C]45[/C][C]280[/C][C]173.636001308428[/C][C]106.363998691572[/C][/ROW]
[ROW][C]46[/C][C]300[/C][C]237.245425621965[/C][C]62.7545743780347[/C][/ROW]
[ROW][C]47[/C][C]320[/C][C]277.695459665755[/C][C]42.3045403342447[/C][/ROW]
[ROW][C]48[/C][C]370[/C][C]327.600172806448[/C][C]42.3998271935523[/C][/ROW]
[ROW][C]49[/C][C]210[/C][C]205.593682161368[/C][C]4.40631783863176[/C][/ROW]
[ROW][C]50[/C][C]310[/C][C]305.74143418906[/C][C]4.25856581093984[/C][/ROW]
[ROW][C]51[/C][C]290[/C][C]321.109685788742[/C][C]-31.1096857887416[/C][/ROW]
[ROW][C]52[/C][C]450[/C][C]369.301024855325[/C][C]80.6989751446751[/C][/ROW]
[ROW][C]53[/C][C]190[/C][C]191.563748143683[/C][C]-1.56374814368294[/C][/ROW]
[ROW][C]54[/C][C]290[/C][C]296.81676716819[/C][C]-6.81676716819015[/C][/ROW]
[ROW][C]55[/C][C]280[/C][C]288.178611180481[/C][C]-8.17861118048103[/C][/ROW]
[ROW][C]56[/C][C]310[/C][C]286.184615892528[/C][C]23.8153841074721[/C][/ROW]
[ROW][C]57[/C][C]340[/C][C]291.008889616174[/C][C]48.9911103838258[/C][/ROW]
[ROW][C]58[/C][C]220[/C][C]318.828371982764[/C][C]-98.8283719827641[/C][/ROW]
[ROW][C]59[/C][C]390[/C][C]341.367216257521[/C][C]48.6327837424789[/C][/ROW]
[ROW][C]60[/C][C]410[/C][C]392.164707964258[/C][C]17.8352920357422[/C][/ROW]
[ROW][C]61[/C][C]250[/C][C]238.111075047782[/C][C]11.8889249522178[/C][/ROW]
[ROW][C]62[/C][C]310[/C][C]338.829631518059[/C][C]-28.829631518059[/C][/ROW]
[ROW][C]63[/C][C]280[/C][C]324.148693798831[/C][C]-44.1486937988313[/C][/ROW]
[ROW][C]64[/C][C]450[/C][C]468.084386553948[/C][C]-18.0843865539476[/C][/ROW]
[ROW][C]65[/C][C]210[/C][C]218.958554203769[/C][C]-8.95855420376887[/C][/ROW]
[ROW][C]66[/C][C]390[/C][C]319.220548351382[/C][C]70.7794516486181[/C][/ROW]
[ROW][C]67[/C][C]300[/C][C]310.082928415733[/C][C]-10.0829284157333[/C][/ROW]
[ROW][C]68[/C][C]310[/C][C]335.503294637626[/C][C]-25.5032946376263[/C][/ROW]
[ROW][C]69[/C][C]370[/C][C]361.222261398936[/C][C]8.77773860106407[/C][/ROW]
[ROW][C]70[/C][C]250[/C][C]261.911594682818[/C][C]-11.9115946828178[/C][/ROW]
[ROW][C]71[/C][C]440[/C][C]411.13502407891[/C][C]28.8649759210896[/C][/ROW]
[ROW][C]72[/C][C]360[/C][C]435.410955581327[/C][C]-75.4109555813266[/C][/ROW]
[ROW][C]73[/C][C]290[/C][C]274.870999513143[/C][C]15.1290004868566[/C][/ROW]
[ROW][C]74[/C][C]300[/C][C]340.11083711155[/C][C]-40.1108371115498[/C][/ROW]
[ROW][C]75[/C][C]340[/C][C]311.466479322476[/C][C]28.5335206775239[/C][/ROW]
[ROW][C]76[/C][C]600[/C][C]477.919789385625[/C][C]122.080210614375[/C][/ROW]
[ROW][C]77[/C][C]220[/C][C]238.330394828747[/C][C]-18.3303948287468[/C][/ROW]
[ROW][C]78[/C][C]410[/C][C]407.316939961066[/C][C]2.68306003893417[/C][/ROW]
[ROW][C]79[/C][C]360[/C][C]328.781731241603[/C][C]31.218268758397[/C][/ROW]
[ROW][C]80[/C][C]250[/C][C]341.797791410705[/C][C]-91.797791410705[/C][/ROW]
[ROW][C]81[/C][C]410[/C][C]396.327530581173[/C][C]13.6724694188266[/C][/ROW]
[ROW][C]82[/C][C]290[/C][C]279.408859655298[/C][C]10.5911403447022[/C][/ROW]
[ROW][C]83[/C][C]470[/C][C]463.826695940802[/C][C]6.17330405919796[/C][/ROW]
[ROW][C]84[/C][C]350[/C][C]398.881546559854[/C][C]-48.881546559854[/C][/ROW]
[ROW][C]85[/C][C]330[/C][C]316.108685813083[/C][C]13.8913141869167[/C][/ROW]
[ROW][C]86[/C][C]250[/C][C]334.357849928221[/C][C]-84.3578499282205[/C][/ROW]
[ROW][C]87[/C][C]270[/C][C]363.939159154866[/C][C]-93.9391591548659[/C][/ROW]
[ROW][C]88[/C][C]580[/C][C]608.453257321152[/C][C]-28.453257321152[/C][/ROW]
[ROW][C]89[/C][C]260[/C][C]245.757092032582[/C][C]14.242907967418[/C][/ROW]
[ROW][C]90[/C][C]450[/C][C]431.100566080224[/C][C]18.899433919776[/C][/ROW]
[ROW][C]91[/C][C]320[/C][C]375.347622074635[/C][C]-55.3476220746346[/C][/ROW]
[ROW][C]92[/C][C]240[/C][C]280.306255866191[/C][C]-40.3062558661913[/C][/ROW]
[ROW][C]93[/C][C]420[/C][C]423.350536717493[/C][C]-3.35053671749347[/C][/ROW]
[ROW][C]94[/C][C]380[/C][C]301.589421962316[/C][C]78.4105780376843[/C][/ROW]
[ROW][C]95[/C][C]400[/C][C]481.118766536119[/C][C]-81.1187665361194[/C][/ROW]
[ROW][C]96[/C][C]370[/C][C]366.282493034766[/C][C]3.71750696523401[/C][/ROW]
[ROW][C]97[/C][C]300[/C][C]335.668429426374[/C][C]-35.6684294263735[/C][/ROW]
[ROW][C]98[/C][C]310[/C][C]267.4152989176[/C][C]42.5847010824[/C][/ROW]
[ROW][C]99[/C][C]280[/C][C]288.42743343856[/C][C]-8.42743343855989[/C][/ROW]
[ROW][C]100[/C][C]560[/C][C]588.823785832203[/C][C]-28.8237858322032[/C][/ROW]
[ROW][C]101[/C][C]280[/C][C]261.919926062106[/C][C]18.0800739378936[/C][/ROW]
[ROW][C]102[/C][C]480[/C][C]450.613607249345[/C][C]29.3863927506555[/C][/ROW]
[ROW][C]103[/C][C]320[/C][C]330.921195373562[/C][C]-10.9211953735619[/C][/ROW]
[ROW][C]104[/C][C]170[/C][C]248.788036725704[/C][C]-78.7880367257041[/C][/ROW]
[ROW][C]105[/C][C]420[/C][C]422.592095469481[/C][C]-2.59209546948125[/C][/ROW]
[ROW][C]106[/C][C]310[/C][C]370.15816246665[/C][C]-60.1581624666499[/C][/ROW]
[ROW][C]107[/C][C]470[/C][C]410.869113970194[/C][C]59.1308860298059[/C][/ROW]
[ROW][C]108[/C][C]420[/C][C]369.000685393893[/C][C]50.9993146061065[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235470&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235470&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
13270268.4054487179491.59455128205116
14250251.710683044565-1.71068304456517
15240242.063245991823-2.06324599182304
16250250.315134708693-0.315134708692511
17230226.9106427955343.0893572044659
18230224.8027643240345.19723567596614
19240312.330655961953-72.3306559619533
20300305.866182600985-5.86618260098464
21190183.1700226352146.82997736478575
22270223.11402306534846.8859769346521
23300252.01543427133547.9845657286648
24330313.35250217362616.647497826374
25230268.446460362113-38.4464603621133
26260248.68275756108211.3172424389181
27300238.96350021046961.036499789531
28330249.7506729993380.2493270006696
29190231.000285910755-41.0002859107554
30260231.2274693930828.7725306069197
31240253.707111496036-13.7071114960364
32270305.889221522328-35.8892215223285
33170195.049904901233-25.049904901233
34230269.983950897015-39.9839508970153
35270299.573164292992-29.5731642929925
36320333.396179240736-13.3961792407363
37190240.804364996551-50.8043649965515
38300262.98014874068237.0198512593176
39310295.62010268236214.3798973176385
40360321.84846706225238.151532937748
41170198.26321941419-28.26321941419
42280257.34400337017122.6559966298286
43270242.59311558487927.4068844151211
44260275.520399764733-15.520399764733
45280173.636001308428106.363998691572
46300237.24542562196562.7545743780347
47320277.69545966575542.3045403342447
48370327.60017280644842.3998271935523
49210205.5936821613684.40631783863176
50310305.741434189064.25856581093984
51290321.109685788742-31.1096857887416
52450369.30102485532580.6989751446751
53190191.563748143683-1.56374814368294
54290296.81676716819-6.81676716819015
55280288.178611180481-8.17861118048103
56310286.18461589252823.8153841074721
57340291.00888961617448.9911103838258
58220318.828371982764-98.8283719827641
59390341.36721625752148.6327837424789
60410392.16470796425817.8352920357422
61250238.11107504778211.8889249522178
62310338.829631518059-28.829631518059
63280324.148693798831-44.1486937988313
64450468.084386553948-18.0843865539476
65210218.958554203769-8.95855420376887
66390319.22054835138270.7794516486181
67300310.082928415733-10.0829284157333
68310335.503294637626-25.5032946376263
69370361.2222613989368.77773860106407
70250261.911594682818-11.9115946828178
71440411.1350240789128.8649759210896
72360435.410955581327-75.4109555813266
73290274.87099951314315.1290004868566
74300340.11083711155-40.1108371115498
75340311.46647932247628.5335206775239
76600477.919789385625122.080210614375
77220238.330394828747-18.3303948287468
78410407.3169399610662.68306003893417
79360328.78173124160331.218268758397
80250341.797791410705-91.797791410705
81410396.32753058117313.6724694188266
82290279.40885965529810.5911403447022
83470463.8266959408026.17330405919796
84350398.881546559854-48.881546559854
85330316.10868581308313.8913141869167
86250334.357849928221-84.3578499282205
87270363.939159154866-93.9391591548659
88580608.453257321152-28.453257321152
89260245.75709203258214.242907967418
90450431.10056608022418.899433919776
91320375.347622074635-55.3476220746346
92240280.306255866191-40.3062558661913
93420423.350536717493-3.35053671749347
94380301.58942196231678.4105780376843
95400481.118766536119-81.1187665361194
96370366.2824930347663.71750696523401
97300335.668429426374-35.6684294263735
98310267.415298917642.5847010824
99280288.42743343856-8.42743343855989
100560588.823785832203-28.8237858322032
101280261.91992606210618.0800739378936
102480450.61360724934529.3863927506555
103320330.921195373562-10.9211953735619
104170248.788036725704-78.7880367257041
105420422.592095469481-2.59209546948125
106310370.15816246665-60.1581624666499
107470410.86911397019459.1308860298059
108420369.00068539389350.9993146061065







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109304.895064970078219.342072996789390.448056943368
110303.830084426517218.268276672594389.391892180441
111280.722896526214195.14125658616366.304536466267
112563.583729293418477.966843476546649.200615110291
113276.996794549249191.324866078837362.668723019662
114475.127545391046389.376417569437560.878673212655
115320.48284413722234.624034590595406.341653683845
116180.21938088800894.2201288833228266.218632892693
117420.02844790798333.851776565023506.205119250936
118318.789227786807232.394022785649405.184432787965
119462.639253369904375.980359475771549.298147264038
120413.765102384571326.793438779069500.736765990073

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 304.895064970078 & 219.342072996789 & 390.448056943368 \tabularnewline
110 & 303.830084426517 & 218.268276672594 & 389.391892180441 \tabularnewline
111 & 280.722896526214 & 195.14125658616 & 366.304536466267 \tabularnewline
112 & 563.583729293418 & 477.966843476546 & 649.200615110291 \tabularnewline
113 & 276.996794549249 & 191.324866078837 & 362.668723019662 \tabularnewline
114 & 475.127545391046 & 389.376417569437 & 560.878673212655 \tabularnewline
115 & 320.48284413722 & 234.624034590595 & 406.341653683845 \tabularnewline
116 & 180.219380888008 & 94.2201288833228 & 266.218632892693 \tabularnewline
117 & 420.02844790798 & 333.851776565023 & 506.205119250936 \tabularnewline
118 & 318.789227786807 & 232.394022785649 & 405.184432787965 \tabularnewline
119 & 462.639253369904 & 375.980359475771 & 549.298147264038 \tabularnewline
120 & 413.765102384571 & 326.793438779069 & 500.736765990073 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235470&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]304.895064970078[/C][C]219.342072996789[/C][C]390.448056943368[/C][/ROW]
[ROW][C]110[/C][C]303.830084426517[/C][C]218.268276672594[/C][C]389.391892180441[/C][/ROW]
[ROW][C]111[/C][C]280.722896526214[/C][C]195.14125658616[/C][C]366.304536466267[/C][/ROW]
[ROW][C]112[/C][C]563.583729293418[/C][C]477.966843476546[/C][C]649.200615110291[/C][/ROW]
[ROW][C]113[/C][C]276.996794549249[/C][C]191.324866078837[/C][C]362.668723019662[/C][/ROW]
[ROW][C]114[/C][C]475.127545391046[/C][C]389.376417569437[/C][C]560.878673212655[/C][/ROW]
[ROW][C]115[/C][C]320.48284413722[/C][C]234.624034590595[/C][C]406.341653683845[/C][/ROW]
[ROW][C]116[/C][C]180.219380888008[/C][C]94.2201288833228[/C][C]266.218632892693[/C][/ROW]
[ROW][C]117[/C][C]420.02844790798[/C][C]333.851776565023[/C][C]506.205119250936[/C][/ROW]
[ROW][C]118[/C][C]318.789227786807[/C][C]232.394022785649[/C][C]405.184432787965[/C][/ROW]
[ROW][C]119[/C][C]462.639253369904[/C][C]375.980359475771[/C][C]549.298147264038[/C][/ROW]
[ROW][C]120[/C][C]413.765102384571[/C][C]326.793438779069[/C][C]500.736765990073[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235470&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235470&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
109304.895064970078219.342072996789390.448056943368
110303.830084426517218.268276672594389.391892180441
111280.722896526214195.14125658616366.304536466267
112563.583729293418477.966843476546649.200615110291
113276.996794549249191.324866078837362.668723019662
114475.127545391046389.376417569437560.878673212655
115320.48284413722234.624034590595406.341653683845
116180.21938088800894.2201288833228266.218632892693
117420.02844790798333.851776565023506.205119250936
118318.789227786807232.394022785649405.184432787965
119462.639253369904375.980359475771549.298147264038
120413.765102384571326.793438779069500.736765990073



Parameters (Session):
par1 = 0.01 ; par2 = 0.9 ; par3 = 0.1 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')