Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 16 Aug 2017 17:30:09 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/16/t1502897442437ejmdylptfl8r.htm/, Retrieved Sat, 11 May 2024 17:22:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307424, Retrieved Sat, 11 May 2024 17:22:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-08-16 15:30:09] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
152512
151944
151368
150176
161968
161344
152512
146640
147208
147208
147840
148976
150744
150744
149608
146640
161968
164304
160776
152512
156048
150744
153136
154280
155472
152512
153136
148976
161968
166072
162544
156048
163112
155472
162544
161968
163736
157240
164304
163736
174336
171944
162544
157808
164304
155472
161968
163112
165504
160208
163112
164880
171376
166072
159008
151368
158440
139000
148408
153704
159008
151368
151368
151368
155472
149608
141912
135472
140144
121904
133080
139576
140768
134272
134840
133080
139000
134840
126640
120712
130736
108968
123104
129544
129544
121904
114840
114272
120712
114840
103672
95976
104240
84808
102472
111872
114840
108344
100136
106008
108344
106576
88904
80704
86568
68904
87144
93640
98936
90104
81840
86568
88904
84232
66568
58872
65936
46504
67704
80704




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307424&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=307424&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307424&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.405343002238435
beta0.0645195510983809
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.405343002238435 \tabularnewline
beta & 0.0645195510983809 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307424&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]0.405343002238435[/C][/ROW]
[ROW][C]beta[/C][C]0.0645195510983809[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307424&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307424&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
alpha0.405343002238435
beta0.0645195510983809
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13150744150737.4444444446.55555555556202
14150744150406.606470833337.393529167108
15149608149058.69505535549.304944650037
16146640146076.379506792563.620493208058
17161968161558.273444642409.726555358444
18164304163922.83627866381.163721340476
19160776155102.789770515673.21022948972
20152512152116.539521227395.460478772584
21156048153440.9993089612607.00069103879
22150744155259.404491369-4515.40449136932
23153136154631.369905486-1495.36990548606
24154280155421.710804796-1141.71080479556
25155472156617.111272153-1145.1112721528
26152512156084.689281542-3572.68928154238
27153136153244.110092554-108.110092554358
28148976149952.878047417-976.878047417384
29161968164627.588859134-2659.58885913432
30166072165559.531943046512.468056954211
31162544159771.5860240082772.41397599154
32156048152227.1290828693820.87091713052
33163112156100.8076895357011.1923104648
34155472155429.85868280642.1413171938038
35162544158525.0951758124018.90482418792
36161968161985.144023852-17.14402385219
37163736163887.997357625-151.997357625398
38157240162594.16305458-5354.16305457981
39164304161324.73428052979.26571949982
40163736159082.0943015214653.9056984788
41174336175499.592316873-1163.59231687305
42171944179424.361269723-7480.36126972263
43162544172031.586010078-9487.58601007835
44157808160111.581318971-2303.58131897103
45164304163210.2181713551093.78182864544
46155472155652.053089164-180.053089164168
47161968160671.7837279171296.21627208334
48163112160206.6887343832905.3112656172
49165504162868.9206454182635.07935458244
50160208159339.166563094868.833436906396
51163112165438.327237423-2326.32723742264
52164880161792.793517273087.20648273037
53171376173826.706741726-2450.70674172559
54166072173150.66236296-7078.66236295991
55159008164414.82851104-5406.82851103964
56151368158215.396990907-6847.39699090729
57158440161168.111380325-2728.11138032508
58139000150878.937188472-11878.9371884724
59148408151304.188701251-2896.18870125074
60153704149256.656984044447.34301596024
61159008151583.6391344457424.36086555506
62151368148270.5219778973097.47802210273
63151368152756.953895322-1388.95389532193
64151368152119.018720988-751.018720987864
65155472158612.041107021-3140.04110702072
66149608154194.571561969-4586.57156196929
67141912146818.269392351-4906.26939235066
68135472139333.395193567-3861.39519356703
69140144145392.42139997-5248.42139997016
70121904128020.536915584-6116.53691558389
71133080135654.37509452-2574.3750945199
72139576137643.7708331051932.22916689454
73140768140195.397083006572.60291699355
74134272130826.5890965793445.41090342103
75134840132089.8968385412750.10316145897
76133080132921.030784708158.969215292309
77139000137798.0387279821201.9612720182
78134840133829.711628281010.28837172023
79126640128227.650689216-1587.65068921616
80120712122491.791223601-1779.79122360068
81130736128406.709552492329.29044751046
82108968113625.276408732-4657.27640873165
83123104124030.260154406-926.260154406264
84129544129483.96713476760.0328652331518
85129544130535.613370186-991.613370186416
86121904122267.601306789-363.601306789365
87114840121500.372289481-6660.37228948105
88114272116656.981314517-2384.98131451674
89120712120737.289831776-25.2898317757936
90114840115739.680303791-899.68030379081
91103672107350.748586837-3678.74858683674
9295976100130.536270386-4154.53627038586
93104240106941.773609727-2701.77360972724
948480885250.2589653372-442.258965337227
9510247298976.5148888853495.48511111503
96111872106318.7607524725553.23924752751
97114840108625.0416445226214.95835547803
98108344103493.4556681084850.54433189209
99100136101073.529266547-937.529266547266
100106008101220.1148518574787.88514814258
101108344109926.56141348-1582.56141348011
102106576104052.4934786322523.50652136834
1038890495762.7923887897-6858.79238878969
1048070487251.733048977-6547.733048977
1058656894175.3040624965-7607.30406249648
1066890471929.2148074459-3025.21480744593
1078714486972.7554835152171.244516484847
1089364094126.9249754302-486.924975430244
1099893694156.12117159314779.87882840693
1109010487371.70412342252732.29587657747
1118184080336.0711882351503.92881176498
1128656884625.62194215041942.37805784964
1138890488064.6937023756839.306297624382
1148423285351.6151524053-1119.61515240525
1156656869648.2737924427-3080.27379244268
1165887262594.9253373089-3722.92533730889
1176593669848.4481921012-3912.44819210118
1184650451736.4613662909-5232.46136629088
1196770467640.028895783563.9711042165291
1208070474210.44718873736493.55281126269

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 150744 & 150737.444444444 & 6.55555555556202 \tabularnewline
14 & 150744 & 150406.606470833 & 337.393529167108 \tabularnewline
15 & 149608 & 149058.69505535 & 549.304944650037 \tabularnewline
16 & 146640 & 146076.379506792 & 563.620493208058 \tabularnewline
17 & 161968 & 161558.273444642 & 409.726555358444 \tabularnewline
18 & 164304 & 163922.83627866 & 381.163721340476 \tabularnewline
19 & 160776 & 155102.78977051 & 5673.21022948972 \tabularnewline
20 & 152512 & 152116.539521227 & 395.460478772584 \tabularnewline
21 & 156048 & 153440.999308961 & 2607.00069103879 \tabularnewline
22 & 150744 & 155259.404491369 & -4515.40449136932 \tabularnewline
23 & 153136 & 154631.369905486 & -1495.36990548606 \tabularnewline
24 & 154280 & 155421.710804796 & -1141.71080479556 \tabularnewline
25 & 155472 & 156617.111272153 & -1145.1112721528 \tabularnewline
26 & 152512 & 156084.689281542 & -3572.68928154238 \tabularnewline
27 & 153136 & 153244.110092554 & -108.110092554358 \tabularnewline
28 & 148976 & 149952.878047417 & -976.878047417384 \tabularnewline
29 & 161968 & 164627.588859134 & -2659.58885913432 \tabularnewline
30 & 166072 & 165559.531943046 & 512.468056954211 \tabularnewline
31 & 162544 & 159771.586024008 & 2772.41397599154 \tabularnewline
32 & 156048 & 152227.129082869 & 3820.87091713052 \tabularnewline
33 & 163112 & 156100.807689535 & 7011.1923104648 \tabularnewline
34 & 155472 & 155429.858682806 & 42.1413171938038 \tabularnewline
35 & 162544 & 158525.095175812 & 4018.90482418792 \tabularnewline
36 & 161968 & 161985.144023852 & -17.14402385219 \tabularnewline
37 & 163736 & 163887.997357625 & -151.997357625398 \tabularnewline
38 & 157240 & 162594.16305458 & -5354.16305457981 \tabularnewline
39 & 164304 & 161324.7342805 & 2979.26571949982 \tabularnewline
40 & 163736 & 159082.094301521 & 4653.9056984788 \tabularnewline
41 & 174336 & 175499.592316873 & -1163.59231687305 \tabularnewline
42 & 171944 & 179424.361269723 & -7480.36126972263 \tabularnewline
43 & 162544 & 172031.586010078 & -9487.58601007835 \tabularnewline
44 & 157808 & 160111.581318971 & -2303.58131897103 \tabularnewline
45 & 164304 & 163210.218171355 & 1093.78182864544 \tabularnewline
46 & 155472 & 155652.053089164 & -180.053089164168 \tabularnewline
47 & 161968 & 160671.783727917 & 1296.21627208334 \tabularnewline
48 & 163112 & 160206.688734383 & 2905.3112656172 \tabularnewline
49 & 165504 & 162868.920645418 & 2635.07935458244 \tabularnewline
50 & 160208 & 159339.166563094 & 868.833436906396 \tabularnewline
51 & 163112 & 165438.327237423 & -2326.32723742264 \tabularnewline
52 & 164880 & 161792.79351727 & 3087.20648273037 \tabularnewline
53 & 171376 & 173826.706741726 & -2450.70674172559 \tabularnewline
54 & 166072 & 173150.66236296 & -7078.66236295991 \tabularnewline
55 & 159008 & 164414.82851104 & -5406.82851103964 \tabularnewline
56 & 151368 & 158215.396990907 & -6847.39699090729 \tabularnewline
57 & 158440 & 161168.111380325 & -2728.11138032508 \tabularnewline
58 & 139000 & 150878.937188472 & -11878.9371884724 \tabularnewline
59 & 148408 & 151304.188701251 & -2896.18870125074 \tabularnewline
60 & 153704 & 149256.65698404 & 4447.34301596024 \tabularnewline
61 & 159008 & 151583.639134445 & 7424.36086555506 \tabularnewline
62 & 151368 & 148270.521977897 & 3097.47802210273 \tabularnewline
63 & 151368 & 152756.953895322 & -1388.95389532193 \tabularnewline
64 & 151368 & 152119.018720988 & -751.018720987864 \tabularnewline
65 & 155472 & 158612.041107021 & -3140.04110702072 \tabularnewline
66 & 149608 & 154194.571561969 & -4586.57156196929 \tabularnewline
67 & 141912 & 146818.269392351 & -4906.26939235066 \tabularnewline
68 & 135472 & 139333.395193567 & -3861.39519356703 \tabularnewline
69 & 140144 & 145392.42139997 & -5248.42139997016 \tabularnewline
70 & 121904 & 128020.536915584 & -6116.53691558389 \tabularnewline
71 & 133080 & 135654.37509452 & -2574.3750945199 \tabularnewline
72 & 139576 & 137643.770833105 & 1932.22916689454 \tabularnewline
73 & 140768 & 140195.397083006 & 572.60291699355 \tabularnewline
74 & 134272 & 130826.589096579 & 3445.41090342103 \tabularnewline
75 & 134840 & 132089.896838541 & 2750.10316145897 \tabularnewline
76 & 133080 & 132921.030784708 & 158.969215292309 \tabularnewline
77 & 139000 & 137798.038727982 & 1201.9612720182 \tabularnewline
78 & 134840 & 133829.71162828 & 1010.28837172023 \tabularnewline
79 & 126640 & 128227.650689216 & -1587.65068921616 \tabularnewline
80 & 120712 & 122491.791223601 & -1779.79122360068 \tabularnewline
81 & 130736 & 128406.70955249 & 2329.29044751046 \tabularnewline
82 & 108968 & 113625.276408732 & -4657.27640873165 \tabularnewline
83 & 123104 & 124030.260154406 & -926.260154406264 \tabularnewline
84 & 129544 & 129483.967134767 & 60.0328652331518 \tabularnewline
85 & 129544 & 130535.613370186 & -991.613370186416 \tabularnewline
86 & 121904 & 122267.601306789 & -363.601306789365 \tabularnewline
87 & 114840 & 121500.372289481 & -6660.37228948105 \tabularnewline
88 & 114272 & 116656.981314517 & -2384.98131451674 \tabularnewline
89 & 120712 & 120737.289831776 & -25.2898317757936 \tabularnewline
90 & 114840 & 115739.680303791 & -899.68030379081 \tabularnewline
91 & 103672 & 107350.748586837 & -3678.74858683674 \tabularnewline
92 & 95976 & 100130.536270386 & -4154.53627038586 \tabularnewline
93 & 104240 & 106941.773609727 & -2701.77360972724 \tabularnewline
94 & 84808 & 85250.2589653372 & -442.258965337227 \tabularnewline
95 & 102472 & 98976.514888885 & 3495.48511111503 \tabularnewline
96 & 111872 & 106318.760752472 & 5553.23924752751 \tabularnewline
97 & 114840 & 108625.041644522 & 6214.95835547803 \tabularnewline
98 & 108344 & 103493.455668108 & 4850.54433189209 \tabularnewline
99 & 100136 & 101073.529266547 & -937.529266547266 \tabularnewline
100 & 106008 & 101220.114851857 & 4787.88514814258 \tabularnewline
101 & 108344 & 109926.56141348 & -1582.56141348011 \tabularnewline
102 & 106576 & 104052.493478632 & 2523.50652136834 \tabularnewline
103 & 88904 & 95762.7923887897 & -6858.79238878969 \tabularnewline
104 & 80704 & 87251.733048977 & -6547.733048977 \tabularnewline
105 & 86568 & 94175.3040624965 & -7607.30406249648 \tabularnewline
106 & 68904 & 71929.2148074459 & -3025.21480744593 \tabularnewline
107 & 87144 & 86972.7554835152 & 171.244516484847 \tabularnewline
108 & 93640 & 94126.9249754302 & -486.924975430244 \tabularnewline
109 & 98936 & 94156.1211715931 & 4779.87882840693 \tabularnewline
110 & 90104 & 87371.7041234225 & 2732.29587657747 \tabularnewline
111 & 81840 & 80336.071188235 & 1503.92881176498 \tabularnewline
112 & 86568 & 84625.6219421504 & 1942.37805784964 \tabularnewline
113 & 88904 & 88064.6937023756 & 839.306297624382 \tabularnewline
114 & 84232 & 85351.6151524053 & -1119.61515240525 \tabularnewline
115 & 66568 & 69648.2737924427 & -3080.27379244268 \tabularnewline
116 & 58872 & 62594.9253373089 & -3722.92533730889 \tabularnewline
117 & 65936 & 69848.4481921012 & -3912.44819210118 \tabularnewline
118 & 46504 & 51736.4613662909 & -5232.46136629088 \tabularnewline
119 & 67704 & 67640.0288957835 & 63.9711042165291 \tabularnewline
120 & 80704 & 74210.4471887373 & 6493.55281126269 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307424&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]150744[/C][C]150737.444444444[/C][C]6.55555555556202[/C][/ROW]
[ROW][C]14[/C][C]150744[/C][C]150406.606470833[/C][C]337.393529167108[/C][/ROW]
[ROW][C]15[/C][C]149608[/C][C]149058.69505535[/C][C]549.304944650037[/C][/ROW]
[ROW][C]16[/C][C]146640[/C][C]146076.379506792[/C][C]563.620493208058[/C][/ROW]
[ROW][C]17[/C][C]161968[/C][C]161558.273444642[/C][C]409.726555358444[/C][/ROW]
[ROW][C]18[/C][C]164304[/C][C]163922.83627866[/C][C]381.163721340476[/C][/ROW]
[ROW][C]19[/C][C]160776[/C][C]155102.78977051[/C][C]5673.21022948972[/C][/ROW]
[ROW][C]20[/C][C]152512[/C][C]152116.539521227[/C][C]395.460478772584[/C][/ROW]
[ROW][C]21[/C][C]156048[/C][C]153440.999308961[/C][C]2607.00069103879[/C][/ROW]
[ROW][C]22[/C][C]150744[/C][C]155259.404491369[/C][C]-4515.40449136932[/C][/ROW]
[ROW][C]23[/C][C]153136[/C][C]154631.369905486[/C][C]-1495.36990548606[/C][/ROW]
[ROW][C]24[/C][C]154280[/C][C]155421.710804796[/C][C]-1141.71080479556[/C][/ROW]
[ROW][C]25[/C][C]155472[/C][C]156617.111272153[/C][C]-1145.1112721528[/C][/ROW]
[ROW][C]26[/C][C]152512[/C][C]156084.689281542[/C][C]-3572.68928154238[/C][/ROW]
[ROW][C]27[/C][C]153136[/C][C]153244.110092554[/C][C]-108.110092554358[/C][/ROW]
[ROW][C]28[/C][C]148976[/C][C]149952.878047417[/C][C]-976.878047417384[/C][/ROW]
[ROW][C]29[/C][C]161968[/C][C]164627.588859134[/C][C]-2659.58885913432[/C][/ROW]
[ROW][C]30[/C][C]166072[/C][C]165559.531943046[/C][C]512.468056954211[/C][/ROW]
[ROW][C]31[/C][C]162544[/C][C]159771.586024008[/C][C]2772.41397599154[/C][/ROW]
[ROW][C]32[/C][C]156048[/C][C]152227.129082869[/C][C]3820.87091713052[/C][/ROW]
[ROW][C]33[/C][C]163112[/C][C]156100.807689535[/C][C]7011.1923104648[/C][/ROW]
[ROW][C]34[/C][C]155472[/C][C]155429.858682806[/C][C]42.1413171938038[/C][/ROW]
[ROW][C]35[/C][C]162544[/C][C]158525.095175812[/C][C]4018.90482418792[/C][/ROW]
[ROW][C]36[/C][C]161968[/C][C]161985.144023852[/C][C]-17.14402385219[/C][/ROW]
[ROW][C]37[/C][C]163736[/C][C]163887.997357625[/C][C]-151.997357625398[/C][/ROW]
[ROW][C]38[/C][C]157240[/C][C]162594.16305458[/C][C]-5354.16305457981[/C][/ROW]
[ROW][C]39[/C][C]164304[/C][C]161324.7342805[/C][C]2979.26571949982[/C][/ROW]
[ROW][C]40[/C][C]163736[/C][C]159082.094301521[/C][C]4653.9056984788[/C][/ROW]
[ROW][C]41[/C][C]174336[/C][C]175499.592316873[/C][C]-1163.59231687305[/C][/ROW]
[ROW][C]42[/C][C]171944[/C][C]179424.361269723[/C][C]-7480.36126972263[/C][/ROW]
[ROW][C]43[/C][C]162544[/C][C]172031.586010078[/C][C]-9487.58601007835[/C][/ROW]
[ROW][C]44[/C][C]157808[/C][C]160111.581318971[/C][C]-2303.58131897103[/C][/ROW]
[ROW][C]45[/C][C]164304[/C][C]163210.218171355[/C][C]1093.78182864544[/C][/ROW]
[ROW][C]46[/C][C]155472[/C][C]155652.053089164[/C][C]-180.053089164168[/C][/ROW]
[ROW][C]47[/C][C]161968[/C][C]160671.783727917[/C][C]1296.21627208334[/C][/ROW]
[ROW][C]48[/C][C]163112[/C][C]160206.688734383[/C][C]2905.3112656172[/C][/ROW]
[ROW][C]49[/C][C]165504[/C][C]162868.920645418[/C][C]2635.07935458244[/C][/ROW]
[ROW][C]50[/C][C]160208[/C][C]159339.166563094[/C][C]868.833436906396[/C][/ROW]
[ROW][C]51[/C][C]163112[/C][C]165438.327237423[/C][C]-2326.32723742264[/C][/ROW]
[ROW][C]52[/C][C]164880[/C][C]161792.79351727[/C][C]3087.20648273037[/C][/ROW]
[ROW][C]53[/C][C]171376[/C][C]173826.706741726[/C][C]-2450.70674172559[/C][/ROW]
[ROW][C]54[/C][C]166072[/C][C]173150.66236296[/C][C]-7078.66236295991[/C][/ROW]
[ROW][C]55[/C][C]159008[/C][C]164414.82851104[/C][C]-5406.82851103964[/C][/ROW]
[ROW][C]56[/C][C]151368[/C][C]158215.396990907[/C][C]-6847.39699090729[/C][/ROW]
[ROW][C]57[/C][C]158440[/C][C]161168.111380325[/C][C]-2728.11138032508[/C][/ROW]
[ROW][C]58[/C][C]139000[/C][C]150878.937188472[/C][C]-11878.9371884724[/C][/ROW]
[ROW][C]59[/C][C]148408[/C][C]151304.188701251[/C][C]-2896.18870125074[/C][/ROW]
[ROW][C]60[/C][C]153704[/C][C]149256.65698404[/C][C]4447.34301596024[/C][/ROW]
[ROW][C]61[/C][C]159008[/C][C]151583.639134445[/C][C]7424.36086555506[/C][/ROW]
[ROW][C]62[/C][C]151368[/C][C]148270.521977897[/C][C]3097.47802210273[/C][/ROW]
[ROW][C]63[/C][C]151368[/C][C]152756.953895322[/C][C]-1388.95389532193[/C][/ROW]
[ROW][C]64[/C][C]151368[/C][C]152119.018720988[/C][C]-751.018720987864[/C][/ROW]
[ROW][C]65[/C][C]155472[/C][C]158612.041107021[/C][C]-3140.04110702072[/C][/ROW]
[ROW][C]66[/C][C]149608[/C][C]154194.571561969[/C][C]-4586.57156196929[/C][/ROW]
[ROW][C]67[/C][C]141912[/C][C]146818.269392351[/C][C]-4906.26939235066[/C][/ROW]
[ROW][C]68[/C][C]135472[/C][C]139333.395193567[/C][C]-3861.39519356703[/C][/ROW]
[ROW][C]69[/C][C]140144[/C][C]145392.42139997[/C][C]-5248.42139997016[/C][/ROW]
[ROW][C]70[/C][C]121904[/C][C]128020.536915584[/C][C]-6116.53691558389[/C][/ROW]
[ROW][C]71[/C][C]133080[/C][C]135654.37509452[/C][C]-2574.3750945199[/C][/ROW]
[ROW][C]72[/C][C]139576[/C][C]137643.770833105[/C][C]1932.22916689454[/C][/ROW]
[ROW][C]73[/C][C]140768[/C][C]140195.397083006[/C][C]572.60291699355[/C][/ROW]
[ROW][C]74[/C][C]134272[/C][C]130826.589096579[/C][C]3445.41090342103[/C][/ROW]
[ROW][C]75[/C][C]134840[/C][C]132089.896838541[/C][C]2750.10316145897[/C][/ROW]
[ROW][C]76[/C][C]133080[/C][C]132921.030784708[/C][C]158.969215292309[/C][/ROW]
[ROW][C]77[/C][C]139000[/C][C]137798.038727982[/C][C]1201.9612720182[/C][/ROW]
[ROW][C]78[/C][C]134840[/C][C]133829.71162828[/C][C]1010.28837172023[/C][/ROW]
[ROW][C]79[/C][C]126640[/C][C]128227.650689216[/C][C]-1587.65068921616[/C][/ROW]
[ROW][C]80[/C][C]120712[/C][C]122491.791223601[/C][C]-1779.79122360068[/C][/ROW]
[ROW][C]81[/C][C]130736[/C][C]128406.70955249[/C][C]2329.29044751046[/C][/ROW]
[ROW][C]82[/C][C]108968[/C][C]113625.276408732[/C][C]-4657.27640873165[/C][/ROW]
[ROW][C]83[/C][C]123104[/C][C]124030.260154406[/C][C]-926.260154406264[/C][/ROW]
[ROW][C]84[/C][C]129544[/C][C]129483.967134767[/C][C]60.0328652331518[/C][/ROW]
[ROW][C]85[/C][C]129544[/C][C]130535.613370186[/C][C]-991.613370186416[/C][/ROW]
[ROW][C]86[/C][C]121904[/C][C]122267.601306789[/C][C]-363.601306789365[/C][/ROW]
[ROW][C]87[/C][C]114840[/C][C]121500.372289481[/C][C]-6660.37228948105[/C][/ROW]
[ROW][C]88[/C][C]114272[/C][C]116656.981314517[/C][C]-2384.98131451674[/C][/ROW]
[ROW][C]89[/C][C]120712[/C][C]120737.289831776[/C][C]-25.2898317757936[/C][/ROW]
[ROW][C]90[/C][C]114840[/C][C]115739.680303791[/C][C]-899.68030379081[/C][/ROW]
[ROW][C]91[/C][C]103672[/C][C]107350.748586837[/C][C]-3678.74858683674[/C][/ROW]
[ROW][C]92[/C][C]95976[/C][C]100130.536270386[/C][C]-4154.53627038586[/C][/ROW]
[ROW][C]93[/C][C]104240[/C][C]106941.773609727[/C][C]-2701.77360972724[/C][/ROW]
[ROW][C]94[/C][C]84808[/C][C]85250.2589653372[/C][C]-442.258965337227[/C][/ROW]
[ROW][C]95[/C][C]102472[/C][C]98976.514888885[/C][C]3495.48511111503[/C][/ROW]
[ROW][C]96[/C][C]111872[/C][C]106318.760752472[/C][C]5553.23924752751[/C][/ROW]
[ROW][C]97[/C][C]114840[/C][C]108625.041644522[/C][C]6214.95835547803[/C][/ROW]
[ROW][C]98[/C][C]108344[/C][C]103493.455668108[/C][C]4850.54433189209[/C][/ROW]
[ROW][C]99[/C][C]100136[/C][C]101073.529266547[/C][C]-937.529266547266[/C][/ROW]
[ROW][C]100[/C][C]106008[/C][C]101220.114851857[/C][C]4787.88514814258[/C][/ROW]
[ROW][C]101[/C][C]108344[/C][C]109926.56141348[/C][C]-1582.56141348011[/C][/ROW]
[ROW][C]102[/C][C]106576[/C][C]104052.493478632[/C][C]2523.50652136834[/C][/ROW]
[ROW][C]103[/C][C]88904[/C][C]95762.7923887897[/C][C]-6858.79238878969[/C][/ROW]
[ROW][C]104[/C][C]80704[/C][C]87251.733048977[/C][C]-6547.733048977[/C][/ROW]
[ROW][C]105[/C][C]86568[/C][C]94175.3040624965[/C][C]-7607.30406249648[/C][/ROW]
[ROW][C]106[/C][C]68904[/C][C]71929.2148074459[/C][C]-3025.21480744593[/C][/ROW]
[ROW][C]107[/C][C]87144[/C][C]86972.7554835152[/C][C]171.244516484847[/C][/ROW]
[ROW][C]108[/C][C]93640[/C][C]94126.9249754302[/C][C]-486.924975430244[/C][/ROW]
[ROW][C]109[/C][C]98936[/C][C]94156.1211715931[/C][C]4779.87882840693[/C][/ROW]
[ROW][C]110[/C][C]90104[/C][C]87371.7041234225[/C][C]2732.29587657747[/C][/ROW]
[ROW][C]111[/C][C]81840[/C][C]80336.071188235[/C][C]1503.92881176498[/C][/ROW]
[ROW][C]112[/C][C]86568[/C][C]84625.6219421504[/C][C]1942.37805784964[/C][/ROW]
[ROW][C]113[/C][C]88904[/C][C]88064.6937023756[/C][C]839.306297624382[/C][/ROW]
[ROW][C]114[/C][C]84232[/C][C]85351.6151524053[/C][C]-1119.61515240525[/C][/ROW]
[ROW][C]115[/C][C]66568[/C][C]69648.2737924427[/C][C]-3080.27379244268[/C][/ROW]
[ROW][C]116[/C][C]58872[/C][C]62594.9253373089[/C][C]-3722.92533730889[/C][/ROW]
[ROW][C]117[/C][C]65936[/C][C]69848.4481921012[/C][C]-3912.44819210118[/C][/ROW]
[ROW][C]118[/C][C]46504[/C][C]51736.4613662909[/C][C]-5232.46136629088[/C][/ROW]
[ROW][C]119[/C][C]67704[/C][C]67640.0288957835[/C][C]63.9711042165291[/C][/ROW]
[ROW][C]120[/C][C]80704[/C][C]74210.4471887373[/C][C]6493.55281126269[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307424&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307424&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
13150744150737.4444444446.55555555556202
14150744150406.606470833337.393529167108
15149608149058.69505535549.304944650037
16146640146076.379506792563.620493208058
17161968161558.273444642409.726555358444
18164304163922.83627866381.163721340476
19160776155102.789770515673.21022948972
20152512152116.539521227395.460478772584
21156048153440.9993089612607.00069103879
22150744155259.404491369-4515.40449136932
23153136154631.369905486-1495.36990548606
24154280155421.710804796-1141.71080479556
25155472156617.111272153-1145.1112721528
26152512156084.689281542-3572.68928154238
27153136153244.110092554-108.110092554358
28148976149952.878047417-976.878047417384
29161968164627.588859134-2659.58885913432
30166072165559.531943046512.468056954211
31162544159771.5860240082772.41397599154
32156048152227.1290828693820.87091713052
33163112156100.8076895357011.1923104648
34155472155429.85868280642.1413171938038
35162544158525.0951758124018.90482418792
36161968161985.144023852-17.14402385219
37163736163887.997357625-151.997357625398
38157240162594.16305458-5354.16305457981
39164304161324.73428052979.26571949982
40163736159082.0943015214653.9056984788
41174336175499.592316873-1163.59231687305
42171944179424.361269723-7480.36126972263
43162544172031.586010078-9487.58601007835
44157808160111.581318971-2303.58131897103
45164304163210.2181713551093.78182864544
46155472155652.053089164-180.053089164168
47161968160671.7837279171296.21627208334
48163112160206.6887343832905.3112656172
49165504162868.9206454182635.07935458244
50160208159339.166563094868.833436906396
51163112165438.327237423-2326.32723742264
52164880161792.793517273087.20648273037
53171376173826.706741726-2450.70674172559
54166072173150.66236296-7078.66236295991
55159008164414.82851104-5406.82851103964
56151368158215.396990907-6847.39699090729
57158440161168.111380325-2728.11138032508
58139000150878.937188472-11878.9371884724
59148408151304.188701251-2896.18870125074
60153704149256.656984044447.34301596024
61159008151583.6391344457424.36086555506
62151368148270.5219778973097.47802210273
63151368152756.953895322-1388.95389532193
64151368152119.018720988-751.018720987864
65155472158612.041107021-3140.04110702072
66149608154194.571561969-4586.57156196929
67141912146818.269392351-4906.26939235066
68135472139333.395193567-3861.39519356703
69140144145392.42139997-5248.42139997016
70121904128020.536915584-6116.53691558389
71133080135654.37509452-2574.3750945199
72139576137643.7708331051932.22916689454
73140768140195.397083006572.60291699355
74134272130826.5890965793445.41090342103
75134840132089.8968385412750.10316145897
76133080132921.030784708158.969215292309
77139000137798.0387279821201.9612720182
78134840133829.711628281010.28837172023
79126640128227.650689216-1587.65068921616
80120712122491.791223601-1779.79122360068
81130736128406.709552492329.29044751046
82108968113625.276408732-4657.27640873165
83123104124030.260154406-926.260154406264
84129544129483.96713476760.0328652331518
85129544130535.613370186-991.613370186416
86121904122267.601306789-363.601306789365
87114840121500.372289481-6660.37228948105
88114272116656.981314517-2384.98131451674
89120712120737.289831776-25.2898317757936
90114840115739.680303791-899.68030379081
91103672107350.748586837-3678.74858683674
9295976100130.536270386-4154.53627038586
93104240106941.773609727-2701.77360972724
948480885250.2589653372-442.258965337227
9510247298976.5148888853495.48511111503
96111872106318.7607524725553.23924752751
97114840108625.0416445226214.95835547803
98108344103493.4556681084850.54433189209
99100136101073.529266547-937.529266547266
100106008101220.1148518574787.88514814258
101108344109926.56141348-1582.56141348011
102106576104052.4934786322523.50652136834
1038890495762.7923887897-6858.79238878969
1048070487251.733048977-6547.733048977
1058656894175.3040624965-7607.30406249648
1066890471929.2148074459-3025.21480744593
1078714486972.7554835152171.244516484847
1089364094126.9249754302-486.924975430244
1099893694156.12117159314779.87882840693
1109010487371.70412342252732.29587657747
1118184080336.0711882351503.92881176498
1128656884625.62194215041942.37805784964
1138890488064.6937023756839.306297624382
1148423285351.6151524053-1119.61515240525
1156656869648.2737924427-3080.27379244268
1165887262594.9253373089-3722.92533730889
1176593669848.4481921012-3912.44819210118
1184650451736.4613662909-5232.46136629088
1196770467640.028895783563.9711042165291
1208070474210.44718873736493.55281126269







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12180234.746652100272930.974762187538.5185421004
12270203.897331678462249.193051970678158.6016113861
12361167.501504606152539.059603674269795.943405538
12464906.051772538455582.097484785774230.006060291
12566648.926322993556608.576065004476689.2765809827
12662155.8859764651379.035312873972932.7366400461
12745494.865679069333962.098201790757027.6331563478
12839142.896698157426835.409097481751450.3842988332
12947725.113465814434624.653258205260825.5736734236
13030448.708827766616537.522074849444359.8955806837
13151794.274550863437055.061543737966533.4875579889
13262331.981314280446747.858669926477916.1039586343

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 80234.7466521002 & 72930.9747621 & 87538.5185421004 \tabularnewline
122 & 70203.8973316784 & 62249.1930519706 & 78158.6016113861 \tabularnewline
123 & 61167.5015046061 & 52539.0596036742 & 69795.943405538 \tabularnewline
124 & 64906.0517725384 & 55582.0974847857 & 74230.006060291 \tabularnewline
125 & 66648.9263229935 & 56608.5760650044 & 76689.2765809827 \tabularnewline
126 & 62155.88597646 & 51379.0353128739 & 72932.7366400461 \tabularnewline
127 & 45494.8656790693 & 33962.0982017907 & 57027.6331563478 \tabularnewline
128 & 39142.8966981574 & 26835.4090974817 & 51450.3842988332 \tabularnewline
129 & 47725.1134658144 & 34624.6532582052 & 60825.5736734236 \tabularnewline
130 & 30448.7088277666 & 16537.5220748494 & 44359.8955806837 \tabularnewline
131 & 51794.2745508634 & 37055.0615437379 & 66533.4875579889 \tabularnewline
132 & 62331.9813142804 & 46747.8586699264 & 77916.1039586343 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307424&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]121[/C][C]80234.7466521002[/C][C]72930.9747621[/C][C]87538.5185421004[/C][/ROW]
[ROW][C]122[/C][C]70203.8973316784[/C][C]62249.1930519706[/C][C]78158.6016113861[/C][/ROW]
[ROW][C]123[/C][C]61167.5015046061[/C][C]52539.0596036742[/C][C]69795.943405538[/C][/ROW]
[ROW][C]124[/C][C]64906.0517725384[/C][C]55582.0974847857[/C][C]74230.006060291[/C][/ROW]
[ROW][C]125[/C][C]66648.9263229935[/C][C]56608.5760650044[/C][C]76689.2765809827[/C][/ROW]
[ROW][C]126[/C][C]62155.88597646[/C][C]51379.0353128739[/C][C]72932.7366400461[/C][/ROW]
[ROW][C]127[/C][C]45494.8656790693[/C][C]33962.0982017907[/C][C]57027.6331563478[/C][/ROW]
[ROW][C]128[/C][C]39142.8966981574[/C][C]26835.4090974817[/C][C]51450.3842988332[/C][/ROW]
[ROW][C]129[/C][C]47725.1134658144[/C][C]34624.6532582052[/C][C]60825.5736734236[/C][/ROW]
[ROW][C]130[/C][C]30448.7088277666[/C][C]16537.5220748494[/C][C]44359.8955806837[/C][/ROW]
[ROW][C]131[/C][C]51794.2745508634[/C][C]37055.0615437379[/C][C]66533.4875579889[/C][/ROW]
[ROW][C]132[/C][C]62331.9813142804[/C][C]46747.8586699264[/C][C]77916.1039586343[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307424&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307424&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
12180234.746652100272930.974762187538.5185421004
12270203.897331678462249.193051970678158.6016113861
12361167.501504606152539.059603674269795.943405538
12464906.051772538455582.097484785774230.006060291
12566648.926322993556608.576065004476689.2765809827
12662155.8859764651379.035312873972932.7366400461
12745494.865679069333962.098201790757027.6331563478
12839142.896698157426835.409097481751450.3842988332
12947725.113465814434624.653258205260825.5736734236
13030448.708827766616537.522074849444359.8955806837
13151794.274550863437055.061543737966533.4875579889
13262331.981314280446747.858669926477916.1039586343



Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')