Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 12 Dec 2012 07:54:46 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/12/t1355317069sq4iwvcgtmkggtf.htm/, Retrieved Mon, 29 Apr 2024 14:41:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=198855, Retrieved Mon, 29 Apr 2024 14:41:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMPD  [Exponential Smoothing] [Paper Triple Expo...] [2012-12-10 21:28:15] [86dcce9422b96d4554cb918e531c1d5d]
- R P       [Exponential Smoothing] [PAPER SINGLE SMOO...] [2012-12-12 12:54:46] [c63d55528b56cf8bb48e0b5d1a959d8e] [Current]
-   P         [Exponential Smoothing] [PAPER Double SMOO...] [2012-12-12 12:58:32] [86dcce9422b96d4554cb918e531c1d5d]
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Dataseries X:
68.897
38.683
44.720
39.525
45.315
50.380
40.600
36.279
42.438
38.064
31.879
11.379
70.249
39.253
47.060
41.697
38.708
49.267
39.018
32.228
40.870
39.383
34.571
12.066
70.938
34.077
45.409
40.809
37.013
44.953
37.848
32.745
43.412
34.931
33.008
8.620
68.906
39.556
50.669
36.432
40.891
48.428
36.222
33.425
39.401
37.967
34.801
12.657
69.116
41.519
51.321
38.529
41.547
52.073
38.401
40.898
40.439
41.888
37.898
8.771
68.184
50.530
47.221
41.756
45.633
48.138
39.486
39.341
41.117
41.629
29.722
7.054
56.676
34.870
35.117
30.169
30.936
35.699
33.228
27.733
33.666
35.429
27.438
8.170
63.410
38.040
45.389
37.353
37.024
50.957
37.994
36.454
46.080
43.373
37.395
10.963
76.058
50.179
57.452
47.568
50.050
50.856
41.992
39.284
44.521
43.832
41.153
17.100




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198855&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198855&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198855&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.174781716156648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.174781716156648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198855&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]0.174781716156648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198855&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198855&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
alpha0.174781716156648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
238.68368.897-30.214
344.7263.616145228043-18.896145228043
439.52560.3134445363404-20.7884445363404
545.31556.6800045240515-11.3650045240515
650.3854.6936095292097-4.31360952920972
740.653.9396694528648-13.3396694528648
836.27951.6081391329307-15.3291391329306
942.43848.928885888073-6.490885888073
1038.06447.7943977131786-9.73039771317863
1131.87946.0937021019825-14.2147021019825
1211.37943.6092320739425-32.2302320739425
1370.24937.975976799931832.2730232000682
1439.25343.616711180403-4.36371118040303
1547.0642.85401425148024.20598574851977
1641.69743.5891436587369-1.89214365873693
1738.70843.258431542848-4.55043154284797
1849.26742.46309930853576.80390069146434
1939.01843.6522967479492-4.63429674794921
2032.22842.8423064091635-10.6143064091635
2140.8740.9871197191574-0.117119719157365
2239.38340.9666493336473-1.58364933364725
2334.57140.6898563853221-6.11885638532205
2412.06639.6203921653794-27.5543921653794
2570.93834.804388215061136.1336117849389
2634.07741.1198828937708-7.04288289377081
2745.40939.88891573490725.52008426509276
2840.80940.8537255360895-0.0447255360894729
2937.01340.8459083301357-3.83290833013573
3044.95340.17598603432354.77701396567651
3137.84841.0109207333487-3.16292073334871
3232.74540.4581000195066-7.71310001950658
3343.41239.10999116120934.30200883879066
3434.93139.8619036489742-4.93090364897424
3533.00839.0000718470034-5.99207184700344
368.6237.9527672462502-29.3327672462502
3768.90632.825935847327136.0800641526729
3839.55639.13207137897320.423928621026761
3950.66939.206166350884211.4628336491158
4036.43241.2096600880949-4.77766008809485
4140.89140.37461245868450.516387541315488
4248.42840.46486755935757.96313244064245
4336.22241.8566775133157-5.63467751331571
4433.42540.8718389075491-7.44683890754911
4539.40139.5702676233456-0.169267623345576
4637.96739.5406827376475-1.57368273764748
4734.80139.2656317680754-4.46463176807536
4812.65738.4852957656437-25.8282957656437
4969.11633.97098190632335.145018093677
5041.51940.11368848309231.4053115169077
5151.32140.359311241752110.9616887582479
5238.52942.2752140148937-3.74621401489373
5341.54741.6204443002805-0.0734443002805207
5452.07341.607607579435610.4653924205644
5538.40143.4367668269546-5.03576682695459
5640.89842.5566068587747-1.65860685877475
5740.43942.2667127055689-1.82771270556891
5841.88841.9472619422483-0.0592619422482699
5937.89841.9369040382793-4.03890403827933
608.77141.2309774590769-32.4599774590769
6168.18435.557566892373332.6264331076267
6250.5341.26007086299449.26992913700563
6347.22142.88028498621074.34071501378926
6441.75643.6389626056677-1.88296260566775
6545.63343.30985516999032.32314483000965
6648.13843.71589841025994.42210158974012
6739.48644.4888009151337-5.0028009151337
6839.34143.6144027855966-4.27340278559658
6941.11742.8674901129014-1.75049011290141
7041.62942.5615364468533-0.932536446853256
7129.72242.3985461262936-12.6765461262936
727.05440.1829176394011-33.1289176394011
7356.67634.392588559974322.2834114400257
7434.8738.2873214532867-3.4173214532867
7535.11737.6900361450223-2.57303614502231
7630.16937.2403164718622-7.07131647186222
7730.93636.0043796434234-5.06837964342337
7835.69935.11851955121240.58048044878759
7933.22835.2199769202469-1.99197692024688
8027.73334.8718157755817-7.1388157755817
8133.66633.62408130299940.041918697000618
8235.42933.63140792480021.7975920751998
8327.43833.9455941526532-6.50759415265322
848.1732.8081856786015-24.6381856786015
8563.4128.501881302709434.9081186972906
8638.0434.60318219642183.43681780357817
8745.38935.203875110248910.1851248897511
8837.35336.98404871774940.368951282250571
8937.02437.0485346560394-0.0245346560393784
9050.95737.044246446751513.9127535532485
9137.99439.4759413892528-1.48194138925278
9236.45439.2169251299956-2.76292512999562
9346.0838.73401633416277.34598366583734
9443.37340.01795996613643.35504003386359
9537.39540.6043596210293-3.20935962102934
9610.96340.043422238702-29.080422238702
9776.05834.960696133261741.0973038667383
9850.17942.14375343250158.03524656749853
9957.45243.548167617310713.9038323826893
10047.56845.97830330231151.58969669768849
10150.0546.25615321930213.79384678069794
10250.85646.91924827046783.93675172953218
10341.99247.6073204938381-5.61532049383811
10439.28446.6258651411555-7.34186514115549
10544.52145.3426413519937-0.821641351993655
10643.83245.1990334664269-1.36703346642693
10741.15344.9601010111213-3.80710101112126
10817.144.2946893628158-27.1946893628158

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 38.683 & 68.897 & -30.214 \tabularnewline
3 & 44.72 & 63.616145228043 & -18.896145228043 \tabularnewline
4 & 39.525 & 60.3134445363404 & -20.7884445363404 \tabularnewline
5 & 45.315 & 56.6800045240515 & -11.3650045240515 \tabularnewline
6 & 50.38 & 54.6936095292097 & -4.31360952920972 \tabularnewline
7 & 40.6 & 53.9396694528648 & -13.3396694528648 \tabularnewline
8 & 36.279 & 51.6081391329307 & -15.3291391329306 \tabularnewline
9 & 42.438 & 48.928885888073 & -6.490885888073 \tabularnewline
10 & 38.064 & 47.7943977131786 & -9.73039771317863 \tabularnewline
11 & 31.879 & 46.0937021019825 & -14.2147021019825 \tabularnewline
12 & 11.379 & 43.6092320739425 & -32.2302320739425 \tabularnewline
13 & 70.249 & 37.9759767999318 & 32.2730232000682 \tabularnewline
14 & 39.253 & 43.616711180403 & -4.36371118040303 \tabularnewline
15 & 47.06 & 42.8540142514802 & 4.20598574851977 \tabularnewline
16 & 41.697 & 43.5891436587369 & -1.89214365873693 \tabularnewline
17 & 38.708 & 43.258431542848 & -4.55043154284797 \tabularnewline
18 & 49.267 & 42.4630993085357 & 6.80390069146434 \tabularnewline
19 & 39.018 & 43.6522967479492 & -4.63429674794921 \tabularnewline
20 & 32.228 & 42.8423064091635 & -10.6143064091635 \tabularnewline
21 & 40.87 & 40.9871197191574 & -0.117119719157365 \tabularnewline
22 & 39.383 & 40.9666493336473 & -1.58364933364725 \tabularnewline
23 & 34.571 & 40.6898563853221 & -6.11885638532205 \tabularnewline
24 & 12.066 & 39.6203921653794 & -27.5543921653794 \tabularnewline
25 & 70.938 & 34.8043882150611 & 36.1336117849389 \tabularnewline
26 & 34.077 & 41.1198828937708 & -7.04288289377081 \tabularnewline
27 & 45.409 & 39.8889157349072 & 5.52008426509276 \tabularnewline
28 & 40.809 & 40.8537255360895 & -0.0447255360894729 \tabularnewline
29 & 37.013 & 40.8459083301357 & -3.83290833013573 \tabularnewline
30 & 44.953 & 40.1759860343235 & 4.77701396567651 \tabularnewline
31 & 37.848 & 41.0109207333487 & -3.16292073334871 \tabularnewline
32 & 32.745 & 40.4581000195066 & -7.71310001950658 \tabularnewline
33 & 43.412 & 39.1099911612093 & 4.30200883879066 \tabularnewline
34 & 34.931 & 39.8619036489742 & -4.93090364897424 \tabularnewline
35 & 33.008 & 39.0000718470034 & -5.99207184700344 \tabularnewline
36 & 8.62 & 37.9527672462502 & -29.3327672462502 \tabularnewline
37 & 68.906 & 32.8259358473271 & 36.0800641526729 \tabularnewline
38 & 39.556 & 39.1320713789732 & 0.423928621026761 \tabularnewline
39 & 50.669 & 39.2061663508842 & 11.4628336491158 \tabularnewline
40 & 36.432 & 41.2096600880949 & -4.77766008809485 \tabularnewline
41 & 40.891 & 40.3746124586845 & 0.516387541315488 \tabularnewline
42 & 48.428 & 40.4648675593575 & 7.96313244064245 \tabularnewline
43 & 36.222 & 41.8566775133157 & -5.63467751331571 \tabularnewline
44 & 33.425 & 40.8718389075491 & -7.44683890754911 \tabularnewline
45 & 39.401 & 39.5702676233456 & -0.169267623345576 \tabularnewline
46 & 37.967 & 39.5406827376475 & -1.57368273764748 \tabularnewline
47 & 34.801 & 39.2656317680754 & -4.46463176807536 \tabularnewline
48 & 12.657 & 38.4852957656437 & -25.8282957656437 \tabularnewline
49 & 69.116 & 33.970981906323 & 35.145018093677 \tabularnewline
50 & 41.519 & 40.1136884830923 & 1.4053115169077 \tabularnewline
51 & 51.321 & 40.3593112417521 & 10.9616887582479 \tabularnewline
52 & 38.529 & 42.2752140148937 & -3.74621401489373 \tabularnewline
53 & 41.547 & 41.6204443002805 & -0.0734443002805207 \tabularnewline
54 & 52.073 & 41.6076075794356 & 10.4653924205644 \tabularnewline
55 & 38.401 & 43.4367668269546 & -5.03576682695459 \tabularnewline
56 & 40.898 & 42.5566068587747 & -1.65860685877475 \tabularnewline
57 & 40.439 & 42.2667127055689 & -1.82771270556891 \tabularnewline
58 & 41.888 & 41.9472619422483 & -0.0592619422482699 \tabularnewline
59 & 37.898 & 41.9369040382793 & -4.03890403827933 \tabularnewline
60 & 8.771 & 41.2309774590769 & -32.4599774590769 \tabularnewline
61 & 68.184 & 35.5575668923733 & 32.6264331076267 \tabularnewline
62 & 50.53 & 41.2600708629944 & 9.26992913700563 \tabularnewline
63 & 47.221 & 42.8802849862107 & 4.34071501378926 \tabularnewline
64 & 41.756 & 43.6389626056677 & -1.88296260566775 \tabularnewline
65 & 45.633 & 43.3098551699903 & 2.32314483000965 \tabularnewline
66 & 48.138 & 43.7158984102599 & 4.42210158974012 \tabularnewline
67 & 39.486 & 44.4888009151337 & -5.0028009151337 \tabularnewline
68 & 39.341 & 43.6144027855966 & -4.27340278559658 \tabularnewline
69 & 41.117 & 42.8674901129014 & -1.75049011290141 \tabularnewline
70 & 41.629 & 42.5615364468533 & -0.932536446853256 \tabularnewline
71 & 29.722 & 42.3985461262936 & -12.6765461262936 \tabularnewline
72 & 7.054 & 40.1829176394011 & -33.1289176394011 \tabularnewline
73 & 56.676 & 34.3925885599743 & 22.2834114400257 \tabularnewline
74 & 34.87 & 38.2873214532867 & -3.4173214532867 \tabularnewline
75 & 35.117 & 37.6900361450223 & -2.57303614502231 \tabularnewline
76 & 30.169 & 37.2403164718622 & -7.07131647186222 \tabularnewline
77 & 30.936 & 36.0043796434234 & -5.06837964342337 \tabularnewline
78 & 35.699 & 35.1185195512124 & 0.58048044878759 \tabularnewline
79 & 33.228 & 35.2199769202469 & -1.99197692024688 \tabularnewline
80 & 27.733 & 34.8718157755817 & -7.1388157755817 \tabularnewline
81 & 33.666 & 33.6240813029994 & 0.041918697000618 \tabularnewline
82 & 35.429 & 33.6314079248002 & 1.7975920751998 \tabularnewline
83 & 27.438 & 33.9455941526532 & -6.50759415265322 \tabularnewline
84 & 8.17 & 32.8081856786015 & -24.6381856786015 \tabularnewline
85 & 63.41 & 28.5018813027094 & 34.9081186972906 \tabularnewline
86 & 38.04 & 34.6031821964218 & 3.43681780357817 \tabularnewline
87 & 45.389 & 35.2038751102489 & 10.1851248897511 \tabularnewline
88 & 37.353 & 36.9840487177494 & 0.368951282250571 \tabularnewline
89 & 37.024 & 37.0485346560394 & -0.0245346560393784 \tabularnewline
90 & 50.957 & 37.0442464467515 & 13.9127535532485 \tabularnewline
91 & 37.994 & 39.4759413892528 & -1.48194138925278 \tabularnewline
92 & 36.454 & 39.2169251299956 & -2.76292512999562 \tabularnewline
93 & 46.08 & 38.7340163341627 & 7.34598366583734 \tabularnewline
94 & 43.373 & 40.0179599661364 & 3.35504003386359 \tabularnewline
95 & 37.395 & 40.6043596210293 & -3.20935962102934 \tabularnewline
96 & 10.963 & 40.043422238702 & -29.080422238702 \tabularnewline
97 & 76.058 & 34.9606961332617 & 41.0973038667383 \tabularnewline
98 & 50.179 & 42.1437534325015 & 8.03524656749853 \tabularnewline
99 & 57.452 & 43.5481676173107 & 13.9038323826893 \tabularnewline
100 & 47.568 & 45.9783033023115 & 1.58969669768849 \tabularnewline
101 & 50.05 & 46.2561532193021 & 3.79384678069794 \tabularnewline
102 & 50.856 & 46.9192482704678 & 3.93675172953218 \tabularnewline
103 & 41.992 & 47.6073204938381 & -5.61532049383811 \tabularnewline
104 & 39.284 & 46.6258651411555 & -7.34186514115549 \tabularnewline
105 & 44.521 & 45.3426413519937 & -0.821641351993655 \tabularnewline
106 & 43.832 & 45.1990334664269 & -1.36703346642693 \tabularnewline
107 & 41.153 & 44.9601010111213 & -3.80710101112126 \tabularnewline
108 & 17.1 & 44.2946893628158 & -27.1946893628158 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198855&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]38.683[/C][C]68.897[/C][C]-30.214[/C][/ROW]
[ROW][C]3[/C][C]44.72[/C][C]63.616145228043[/C][C]-18.896145228043[/C][/ROW]
[ROW][C]4[/C][C]39.525[/C][C]60.3134445363404[/C][C]-20.7884445363404[/C][/ROW]
[ROW][C]5[/C][C]45.315[/C][C]56.6800045240515[/C][C]-11.3650045240515[/C][/ROW]
[ROW][C]6[/C][C]50.38[/C][C]54.6936095292097[/C][C]-4.31360952920972[/C][/ROW]
[ROW][C]7[/C][C]40.6[/C][C]53.9396694528648[/C][C]-13.3396694528648[/C][/ROW]
[ROW][C]8[/C][C]36.279[/C][C]51.6081391329307[/C][C]-15.3291391329306[/C][/ROW]
[ROW][C]9[/C][C]42.438[/C][C]48.928885888073[/C][C]-6.490885888073[/C][/ROW]
[ROW][C]10[/C][C]38.064[/C][C]47.7943977131786[/C][C]-9.73039771317863[/C][/ROW]
[ROW][C]11[/C][C]31.879[/C][C]46.0937021019825[/C][C]-14.2147021019825[/C][/ROW]
[ROW][C]12[/C][C]11.379[/C][C]43.6092320739425[/C][C]-32.2302320739425[/C][/ROW]
[ROW][C]13[/C][C]70.249[/C][C]37.9759767999318[/C][C]32.2730232000682[/C][/ROW]
[ROW][C]14[/C][C]39.253[/C][C]43.616711180403[/C][C]-4.36371118040303[/C][/ROW]
[ROW][C]15[/C][C]47.06[/C][C]42.8540142514802[/C][C]4.20598574851977[/C][/ROW]
[ROW][C]16[/C][C]41.697[/C][C]43.5891436587369[/C][C]-1.89214365873693[/C][/ROW]
[ROW][C]17[/C][C]38.708[/C][C]43.258431542848[/C][C]-4.55043154284797[/C][/ROW]
[ROW][C]18[/C][C]49.267[/C][C]42.4630993085357[/C][C]6.80390069146434[/C][/ROW]
[ROW][C]19[/C][C]39.018[/C][C]43.6522967479492[/C][C]-4.63429674794921[/C][/ROW]
[ROW][C]20[/C][C]32.228[/C][C]42.8423064091635[/C][C]-10.6143064091635[/C][/ROW]
[ROW][C]21[/C][C]40.87[/C][C]40.9871197191574[/C][C]-0.117119719157365[/C][/ROW]
[ROW][C]22[/C][C]39.383[/C][C]40.9666493336473[/C][C]-1.58364933364725[/C][/ROW]
[ROW][C]23[/C][C]34.571[/C][C]40.6898563853221[/C][C]-6.11885638532205[/C][/ROW]
[ROW][C]24[/C][C]12.066[/C][C]39.6203921653794[/C][C]-27.5543921653794[/C][/ROW]
[ROW][C]25[/C][C]70.938[/C][C]34.8043882150611[/C][C]36.1336117849389[/C][/ROW]
[ROW][C]26[/C][C]34.077[/C][C]41.1198828937708[/C][C]-7.04288289377081[/C][/ROW]
[ROW][C]27[/C][C]45.409[/C][C]39.8889157349072[/C][C]5.52008426509276[/C][/ROW]
[ROW][C]28[/C][C]40.809[/C][C]40.8537255360895[/C][C]-0.0447255360894729[/C][/ROW]
[ROW][C]29[/C][C]37.013[/C][C]40.8459083301357[/C][C]-3.83290833013573[/C][/ROW]
[ROW][C]30[/C][C]44.953[/C][C]40.1759860343235[/C][C]4.77701396567651[/C][/ROW]
[ROW][C]31[/C][C]37.848[/C][C]41.0109207333487[/C][C]-3.16292073334871[/C][/ROW]
[ROW][C]32[/C][C]32.745[/C][C]40.4581000195066[/C][C]-7.71310001950658[/C][/ROW]
[ROW][C]33[/C][C]43.412[/C][C]39.1099911612093[/C][C]4.30200883879066[/C][/ROW]
[ROW][C]34[/C][C]34.931[/C][C]39.8619036489742[/C][C]-4.93090364897424[/C][/ROW]
[ROW][C]35[/C][C]33.008[/C][C]39.0000718470034[/C][C]-5.99207184700344[/C][/ROW]
[ROW][C]36[/C][C]8.62[/C][C]37.9527672462502[/C][C]-29.3327672462502[/C][/ROW]
[ROW][C]37[/C][C]68.906[/C][C]32.8259358473271[/C][C]36.0800641526729[/C][/ROW]
[ROW][C]38[/C][C]39.556[/C][C]39.1320713789732[/C][C]0.423928621026761[/C][/ROW]
[ROW][C]39[/C][C]50.669[/C][C]39.2061663508842[/C][C]11.4628336491158[/C][/ROW]
[ROW][C]40[/C][C]36.432[/C][C]41.2096600880949[/C][C]-4.77766008809485[/C][/ROW]
[ROW][C]41[/C][C]40.891[/C][C]40.3746124586845[/C][C]0.516387541315488[/C][/ROW]
[ROW][C]42[/C][C]48.428[/C][C]40.4648675593575[/C][C]7.96313244064245[/C][/ROW]
[ROW][C]43[/C][C]36.222[/C][C]41.8566775133157[/C][C]-5.63467751331571[/C][/ROW]
[ROW][C]44[/C][C]33.425[/C][C]40.8718389075491[/C][C]-7.44683890754911[/C][/ROW]
[ROW][C]45[/C][C]39.401[/C][C]39.5702676233456[/C][C]-0.169267623345576[/C][/ROW]
[ROW][C]46[/C][C]37.967[/C][C]39.5406827376475[/C][C]-1.57368273764748[/C][/ROW]
[ROW][C]47[/C][C]34.801[/C][C]39.2656317680754[/C][C]-4.46463176807536[/C][/ROW]
[ROW][C]48[/C][C]12.657[/C][C]38.4852957656437[/C][C]-25.8282957656437[/C][/ROW]
[ROW][C]49[/C][C]69.116[/C][C]33.970981906323[/C][C]35.145018093677[/C][/ROW]
[ROW][C]50[/C][C]41.519[/C][C]40.1136884830923[/C][C]1.4053115169077[/C][/ROW]
[ROW][C]51[/C][C]51.321[/C][C]40.3593112417521[/C][C]10.9616887582479[/C][/ROW]
[ROW][C]52[/C][C]38.529[/C][C]42.2752140148937[/C][C]-3.74621401489373[/C][/ROW]
[ROW][C]53[/C][C]41.547[/C][C]41.6204443002805[/C][C]-0.0734443002805207[/C][/ROW]
[ROW][C]54[/C][C]52.073[/C][C]41.6076075794356[/C][C]10.4653924205644[/C][/ROW]
[ROW][C]55[/C][C]38.401[/C][C]43.4367668269546[/C][C]-5.03576682695459[/C][/ROW]
[ROW][C]56[/C][C]40.898[/C][C]42.5566068587747[/C][C]-1.65860685877475[/C][/ROW]
[ROW][C]57[/C][C]40.439[/C][C]42.2667127055689[/C][C]-1.82771270556891[/C][/ROW]
[ROW][C]58[/C][C]41.888[/C][C]41.9472619422483[/C][C]-0.0592619422482699[/C][/ROW]
[ROW][C]59[/C][C]37.898[/C][C]41.9369040382793[/C][C]-4.03890403827933[/C][/ROW]
[ROW][C]60[/C][C]8.771[/C][C]41.2309774590769[/C][C]-32.4599774590769[/C][/ROW]
[ROW][C]61[/C][C]68.184[/C][C]35.5575668923733[/C][C]32.6264331076267[/C][/ROW]
[ROW][C]62[/C][C]50.53[/C][C]41.2600708629944[/C][C]9.26992913700563[/C][/ROW]
[ROW][C]63[/C][C]47.221[/C][C]42.8802849862107[/C][C]4.34071501378926[/C][/ROW]
[ROW][C]64[/C][C]41.756[/C][C]43.6389626056677[/C][C]-1.88296260566775[/C][/ROW]
[ROW][C]65[/C][C]45.633[/C][C]43.3098551699903[/C][C]2.32314483000965[/C][/ROW]
[ROW][C]66[/C][C]48.138[/C][C]43.7158984102599[/C][C]4.42210158974012[/C][/ROW]
[ROW][C]67[/C][C]39.486[/C][C]44.4888009151337[/C][C]-5.0028009151337[/C][/ROW]
[ROW][C]68[/C][C]39.341[/C][C]43.6144027855966[/C][C]-4.27340278559658[/C][/ROW]
[ROW][C]69[/C][C]41.117[/C][C]42.8674901129014[/C][C]-1.75049011290141[/C][/ROW]
[ROW][C]70[/C][C]41.629[/C][C]42.5615364468533[/C][C]-0.932536446853256[/C][/ROW]
[ROW][C]71[/C][C]29.722[/C][C]42.3985461262936[/C][C]-12.6765461262936[/C][/ROW]
[ROW][C]72[/C][C]7.054[/C][C]40.1829176394011[/C][C]-33.1289176394011[/C][/ROW]
[ROW][C]73[/C][C]56.676[/C][C]34.3925885599743[/C][C]22.2834114400257[/C][/ROW]
[ROW][C]74[/C][C]34.87[/C][C]38.2873214532867[/C][C]-3.4173214532867[/C][/ROW]
[ROW][C]75[/C][C]35.117[/C][C]37.6900361450223[/C][C]-2.57303614502231[/C][/ROW]
[ROW][C]76[/C][C]30.169[/C][C]37.2403164718622[/C][C]-7.07131647186222[/C][/ROW]
[ROW][C]77[/C][C]30.936[/C][C]36.0043796434234[/C][C]-5.06837964342337[/C][/ROW]
[ROW][C]78[/C][C]35.699[/C][C]35.1185195512124[/C][C]0.58048044878759[/C][/ROW]
[ROW][C]79[/C][C]33.228[/C][C]35.2199769202469[/C][C]-1.99197692024688[/C][/ROW]
[ROW][C]80[/C][C]27.733[/C][C]34.8718157755817[/C][C]-7.1388157755817[/C][/ROW]
[ROW][C]81[/C][C]33.666[/C][C]33.6240813029994[/C][C]0.041918697000618[/C][/ROW]
[ROW][C]82[/C][C]35.429[/C][C]33.6314079248002[/C][C]1.7975920751998[/C][/ROW]
[ROW][C]83[/C][C]27.438[/C][C]33.9455941526532[/C][C]-6.50759415265322[/C][/ROW]
[ROW][C]84[/C][C]8.17[/C][C]32.8081856786015[/C][C]-24.6381856786015[/C][/ROW]
[ROW][C]85[/C][C]63.41[/C][C]28.5018813027094[/C][C]34.9081186972906[/C][/ROW]
[ROW][C]86[/C][C]38.04[/C][C]34.6031821964218[/C][C]3.43681780357817[/C][/ROW]
[ROW][C]87[/C][C]45.389[/C][C]35.2038751102489[/C][C]10.1851248897511[/C][/ROW]
[ROW][C]88[/C][C]37.353[/C][C]36.9840487177494[/C][C]0.368951282250571[/C][/ROW]
[ROW][C]89[/C][C]37.024[/C][C]37.0485346560394[/C][C]-0.0245346560393784[/C][/ROW]
[ROW][C]90[/C][C]50.957[/C][C]37.0442464467515[/C][C]13.9127535532485[/C][/ROW]
[ROW][C]91[/C][C]37.994[/C][C]39.4759413892528[/C][C]-1.48194138925278[/C][/ROW]
[ROW][C]92[/C][C]36.454[/C][C]39.2169251299956[/C][C]-2.76292512999562[/C][/ROW]
[ROW][C]93[/C][C]46.08[/C][C]38.7340163341627[/C][C]7.34598366583734[/C][/ROW]
[ROW][C]94[/C][C]43.373[/C][C]40.0179599661364[/C][C]3.35504003386359[/C][/ROW]
[ROW][C]95[/C][C]37.395[/C][C]40.6043596210293[/C][C]-3.20935962102934[/C][/ROW]
[ROW][C]96[/C][C]10.963[/C][C]40.043422238702[/C][C]-29.080422238702[/C][/ROW]
[ROW][C]97[/C][C]76.058[/C][C]34.9606961332617[/C][C]41.0973038667383[/C][/ROW]
[ROW][C]98[/C][C]50.179[/C][C]42.1437534325015[/C][C]8.03524656749853[/C][/ROW]
[ROW][C]99[/C][C]57.452[/C][C]43.5481676173107[/C][C]13.9038323826893[/C][/ROW]
[ROW][C]100[/C][C]47.568[/C][C]45.9783033023115[/C][C]1.58969669768849[/C][/ROW]
[ROW][C]101[/C][C]50.05[/C][C]46.2561532193021[/C][C]3.79384678069794[/C][/ROW]
[ROW][C]102[/C][C]50.856[/C][C]46.9192482704678[/C][C]3.93675172953218[/C][/ROW]
[ROW][C]103[/C][C]41.992[/C][C]47.6073204938381[/C][C]-5.61532049383811[/C][/ROW]
[ROW][C]104[/C][C]39.284[/C][C]46.6258651411555[/C][C]-7.34186514115549[/C][/ROW]
[ROW][C]105[/C][C]44.521[/C][C]45.3426413519937[/C][C]-0.821641351993655[/C][/ROW]
[ROW][C]106[/C][C]43.832[/C][C]45.1990334664269[/C][C]-1.36703346642693[/C][/ROW]
[ROW][C]107[/C][C]41.153[/C][C]44.9601010111213[/C][C]-3.80710101112126[/C][/ROW]
[ROW][C]108[/C][C]17.1[/C][C]44.2946893628158[/C][C]-27.1946893628158[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198855&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198855&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
238.68368.897-30.214
344.7263.616145228043-18.896145228043
439.52560.3134445363404-20.7884445363404
545.31556.6800045240515-11.3650045240515
650.3854.6936095292097-4.31360952920972
740.653.9396694528648-13.3396694528648
836.27951.6081391329307-15.3291391329306
942.43848.928885888073-6.490885888073
1038.06447.7943977131786-9.73039771317863
1131.87946.0937021019825-14.2147021019825
1211.37943.6092320739425-32.2302320739425
1370.24937.975976799931832.2730232000682
1439.25343.616711180403-4.36371118040303
1547.0642.85401425148024.20598574851977
1641.69743.5891436587369-1.89214365873693
1738.70843.258431542848-4.55043154284797
1849.26742.46309930853576.80390069146434
1939.01843.6522967479492-4.63429674794921
2032.22842.8423064091635-10.6143064091635
2140.8740.9871197191574-0.117119719157365
2239.38340.9666493336473-1.58364933364725
2334.57140.6898563853221-6.11885638532205
2412.06639.6203921653794-27.5543921653794
2570.93834.804388215061136.1336117849389
2634.07741.1198828937708-7.04288289377081
2745.40939.88891573490725.52008426509276
2840.80940.8537255360895-0.0447255360894729
2937.01340.8459083301357-3.83290833013573
3044.95340.17598603432354.77701396567651
3137.84841.0109207333487-3.16292073334871
3232.74540.4581000195066-7.71310001950658
3343.41239.10999116120934.30200883879066
3434.93139.8619036489742-4.93090364897424
3533.00839.0000718470034-5.99207184700344
368.6237.9527672462502-29.3327672462502
3768.90632.825935847327136.0800641526729
3839.55639.13207137897320.423928621026761
3950.66939.206166350884211.4628336491158
4036.43241.2096600880949-4.77766008809485
4140.89140.37461245868450.516387541315488
4248.42840.46486755935757.96313244064245
4336.22241.8566775133157-5.63467751331571
4433.42540.8718389075491-7.44683890754911
4539.40139.5702676233456-0.169267623345576
4637.96739.5406827376475-1.57368273764748
4734.80139.2656317680754-4.46463176807536
4812.65738.4852957656437-25.8282957656437
4969.11633.97098190632335.145018093677
5041.51940.11368848309231.4053115169077
5151.32140.359311241752110.9616887582479
5238.52942.2752140148937-3.74621401489373
5341.54741.6204443002805-0.0734443002805207
5452.07341.607607579435610.4653924205644
5538.40143.4367668269546-5.03576682695459
5640.89842.5566068587747-1.65860685877475
5740.43942.2667127055689-1.82771270556891
5841.88841.9472619422483-0.0592619422482699
5937.89841.9369040382793-4.03890403827933
608.77141.2309774590769-32.4599774590769
6168.18435.557566892373332.6264331076267
6250.5341.26007086299449.26992913700563
6347.22142.88028498621074.34071501378926
6441.75643.6389626056677-1.88296260566775
6545.63343.30985516999032.32314483000965
6648.13843.71589841025994.42210158974012
6739.48644.4888009151337-5.0028009151337
6839.34143.6144027855966-4.27340278559658
6941.11742.8674901129014-1.75049011290141
7041.62942.5615364468533-0.932536446853256
7129.72242.3985461262936-12.6765461262936
727.05440.1829176394011-33.1289176394011
7356.67634.392588559974322.2834114400257
7434.8738.2873214532867-3.4173214532867
7535.11737.6900361450223-2.57303614502231
7630.16937.2403164718622-7.07131647186222
7730.93636.0043796434234-5.06837964342337
7835.69935.11851955121240.58048044878759
7933.22835.2199769202469-1.99197692024688
8027.73334.8718157755817-7.1388157755817
8133.66633.62408130299940.041918697000618
8235.42933.63140792480021.7975920751998
8327.43833.9455941526532-6.50759415265322
848.1732.8081856786015-24.6381856786015
8563.4128.501881302709434.9081186972906
8638.0434.60318219642183.43681780357817
8745.38935.203875110248910.1851248897511
8837.35336.98404871774940.368951282250571
8937.02437.0485346560394-0.0245346560393784
9050.95737.044246446751513.9127535532485
9137.99439.4759413892528-1.48194138925278
9236.45439.2169251299956-2.76292512999562
9346.0838.73401633416277.34598366583734
9443.37340.01795996613643.35504003386359
9537.39540.6043596210293-3.20935962102934
9610.96340.043422238702-29.080422238702
9776.05834.960696133261741.0973038667383
9850.17942.14375343250158.03524656749853
9957.45243.548167617310713.9038323826893
10047.56845.97830330231151.58969669768849
10150.0546.25615321930213.79384678069794
10250.85646.91924827046783.93675172953218
10341.99247.6073204938381-5.61532049383811
10439.28446.6258651411555-7.34186514115549
10544.52145.3426413519937-0.821641351993655
10643.83245.1990334664269-1.36703346642693
10741.15344.9601010111213-3.80710101112126
10817.144.2946893628158-27.1946893628158







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10939.541554885635911.400752852366867.682356918905
11039.541554885635910.974154611216968.1089551600549
11139.541554885635910.553833729910168.5292760413616
11239.541554885635910.139520990591468.9435887806804
11339.54155488563599.7309658856080869.3521438856637
11439.54155488563599.32793484612769.7551749251448
11539.54155488563598.930209680711570.1529000905603
11639.54155488563598.5375861942202470.5455235770515
11739.54155488563598.1498729622104470.9332368090613
11839.54155488563597.7668902399665471.3162195313052
11939.54155488563597.3884689885095671.6946407827622
12039.54155488563597.0144500026122972.0686597686595

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 39.5415548856359 & 11.4007528523668 & 67.682356918905 \tabularnewline
110 & 39.5415548856359 & 10.9741546112169 & 68.1089551600549 \tabularnewline
111 & 39.5415548856359 & 10.5538337299101 & 68.5292760413616 \tabularnewline
112 & 39.5415548856359 & 10.1395209905914 & 68.9435887806804 \tabularnewline
113 & 39.5415548856359 & 9.73096588560808 & 69.3521438856637 \tabularnewline
114 & 39.5415548856359 & 9.327934846127 & 69.7551749251448 \tabularnewline
115 & 39.5415548856359 & 8.9302096807115 & 70.1529000905603 \tabularnewline
116 & 39.5415548856359 & 8.53758619422024 & 70.5455235770515 \tabularnewline
117 & 39.5415548856359 & 8.14987296221044 & 70.9332368090613 \tabularnewline
118 & 39.5415548856359 & 7.76689023996654 & 71.3162195313052 \tabularnewline
119 & 39.5415548856359 & 7.38846898850956 & 71.6946407827622 \tabularnewline
120 & 39.5415548856359 & 7.01445000261229 & 72.0686597686595 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198855&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]39.5415548856359[/C][C]11.4007528523668[/C][C]67.682356918905[/C][/ROW]
[ROW][C]110[/C][C]39.5415548856359[/C][C]10.9741546112169[/C][C]68.1089551600549[/C][/ROW]
[ROW][C]111[/C][C]39.5415548856359[/C][C]10.5538337299101[/C][C]68.5292760413616[/C][/ROW]
[ROW][C]112[/C][C]39.5415548856359[/C][C]10.1395209905914[/C][C]68.9435887806804[/C][/ROW]
[ROW][C]113[/C][C]39.5415548856359[/C][C]9.73096588560808[/C][C]69.3521438856637[/C][/ROW]
[ROW][C]114[/C][C]39.5415548856359[/C][C]9.327934846127[/C][C]69.7551749251448[/C][/ROW]
[ROW][C]115[/C][C]39.5415548856359[/C][C]8.9302096807115[/C][C]70.1529000905603[/C][/ROW]
[ROW][C]116[/C][C]39.5415548856359[/C][C]8.53758619422024[/C][C]70.5455235770515[/C][/ROW]
[ROW][C]117[/C][C]39.5415548856359[/C][C]8.14987296221044[/C][C]70.9332368090613[/C][/ROW]
[ROW][C]118[/C][C]39.5415548856359[/C][C]7.76689023996654[/C][C]71.3162195313052[/C][/ROW]
[ROW][C]119[/C][C]39.5415548856359[/C][C]7.38846898850956[/C][C]71.6946407827622[/C][/ROW]
[ROW][C]120[/C][C]39.5415548856359[/C][C]7.01445000261229[/C][C]72.0686597686595[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198855&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198855&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
10939.541554885635911.400752852366867.682356918905
11039.541554885635910.974154611216968.1089551600549
11139.541554885635910.553833729910168.5292760413616
11239.541554885635910.139520990591468.9435887806804
11339.54155488563599.7309658856080869.3521438856637
11439.54155488563599.32793484612769.7551749251448
11539.54155488563598.930209680711570.1529000905603
11639.54155488563598.5375861942202470.5455235770515
11739.54155488563598.1498729622104470.9332368090613
11839.54155488563597.7668902399665471.3162195313052
11939.54155488563597.3884689885095671.6946407827622
12039.54155488563597.0144500026122972.0686597686595



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