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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 12 Dec 2017 13:45:51 +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/2017/Dec/12/t1513082805dtxqd4ddn3dqyj6.htm/, Retrieved Wed, 15 May 2024 19:55:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309065, Retrieved Wed, 15 May 2024 19:55:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [double] [2017-12-12 12:45:51] [c5fee8264c7526f17d5d55b94ea27fcf] [Current]
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Dataseries X:
46.8
52.8
58.3
54.5
64.7
58.3
57.5
56.7
56
66.2
58.2
53.9
53.1
54.4
59.2
57.8
61.5
60.1
60.1
58.4
56.8
63.8
53.9
63.1
55.7
54.9
64.6
60.2
63.9
69.9
58.5
52
66.7
72
68.4
70.8
56.5
62.6
66.5
69.2
63.7
73.6
64.1
53.8
72.2
80.2
69.1
72
66.3
72.5
88.9
88.6
73.7
86
70
71.6
90.5
85.7
84.8
81.1
70.8
65.7
86.2
76.1
79.8
85.2
75.8
69.4
85
75
77.7
68.5
68.4
65
73.2
67.9
76.5
85.5
71.7
57.9
75.5
78.2
75.7
67.1
74.6
66.2
74.9
69.5
76.1
82.3
82.1
60.5
71.2
81.4
74.5
61.4
83.8
85.4
91.6
91.9
86.3
96.8
81
70.8
98.8
94.5
84.5
92.8
81.2
75.7
86.7
87.5
87.8
103.1
96.4
77.1
106.5
95.7
95.3
86.6
89.6
81.9
98.4
92.9
83.9
121.8
103.9
87.5
118.9
109
112.2
100.1
111.3
102.7
122.6
124.8
120.3
118.3
108.7
100.7
124
103.1
115
112.7
101.7
111.5
114.4
112.5
107.2
136.7
107.8
94.6
110.7
126.6
127.9
109.2
87.1
90.8
94.5
103.3
103.2
105.4
103.9
79.8
105.6
113
87.7
110
90.3
108.9
105.1
113
100.4
110.1
114.7
88.6
117.2
127.7
107.8
102.8
100.2
108.4
114.2
94.4
92.2
115.3
102
86.3
112
112.5
109.5
105.9
115.3
126.2
112.2
112.5
106.9
90.6
75.6
78.8
101.8
93.9
100
89.2
97.7
121.1
108.8
92.9
113.6
112.6
98.8
78




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=309065&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=309065&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309065&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
alpha0.229838942926666
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.229838942926666 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309065&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]0.229838942926666[/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=309065&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309065&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
alpha0.229838942926666
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
252.846.86
358.348.1790336575610.12096634244
454.550.50522586310283.99477413689723
564.751.42338052795813.276619472042
658.354.47486471305173.82513528694825
757.555.35402976395542.14597023604458
856.755.847257294560.852742705440015
95656.0432507765667-0.0432507765667438
1066.256.033310063799910.1666899362001
1158.258.3700113317993-0.170011331799294
1253.958.330936107013-4.430936107013
1353.157.3125344360015-4.21253443600153
1454.456.3443299741888-1.94432997418877
1559.255.89744722822063.30255277177942
1657.856.65650246624591.14349753375409
1761.556.91932273064324.5806772693568
1860.157.97214075212042.12785924787963
1960.158.46120567234981.63879432765025
2058.458.8378644282911-0.437864428291107
2156.858.7372261309475-1.93722613094749
2263.858.29197612480065.5080238751994
2353.959.5579345098913-5.65793450989127
2463.158.25752082298964.84247917701045
2555.759.370511118178-3.67051111817803
2654.958.5268847227754-3.62688472277542
2764.657.69328537197586.90671462802415
2860.259.28071736117710.919282638822949
2963.959.4920043111354.40799568886504
3069.960.5051333806899.394866619311
3158.562.6644395934085-4.16443959340846
325261.7072891993775-9.70728919937751
3366.759.47617611110917.22382388889087
347261.136492157620210.8635078423798
3568.463.63334931658834.76665068341168
3670.864.72891127096436.07108872903565
3756.566.1242838868599-9.6242838868599
3862.663.9122486518779-1.31224865187787
3966.563.61064280887332.88935719112668
4069.264.27472961141944.92527038858056
4163.765.4067485511588-1.70674855115881
4273.665.01447126831898.58552873168114
4364.166.987760116475-2.88776011647498
4453.866.3240403838786-12.5240403838786
4572.263.4455281808778.75447181912295
4680.265.457646729665614.7423532703344
4769.168.84601362157070.253986378429289
487268.90438958230673.09561041769334
4966.369.6158814084221-3.31588140842207
5072.568.85376273064023.64623726935984
5188.969.691810050289619.2081899497104
5288.674.106600123865714.4933998761343
5373.777.4377478308099-3.73774783080987
548676.57866782045019.42133217954991
557078.7440568495588-8.74405684955883
5671.676.7343320663656-5.13433206636556
5790.575.554262611597614.9457373884024
5885.778.98937509420766.71062490579244
5984.880.53173802893234.26826197106774
6081.181.5127508484966-0.412750848496557
6170.881.417884629786-10.617884629786
6265.778.9774812503587-13.2774812503587
6386.275.925798995047610.2742010049524
6476.178.287210493442-2.18721049344197
6579.877.78450434567112.01549565432886
6685.278.24774373633546.95225626366464
6775.879.8456429669313-4.04564296693134
6869.478.9157966639531-9.51579666395313
698576.7286960176058.27130398239495
707578.6297637815438-3.62976378154383
7177.777.7955027109203-0.0955027109203002
7268.577.7735524687957-9.27355246879574
7368.475.6421289721928-7.24212897219275
746573.9776057046854-8.97760570468539
7573.271.91420229950811.28579770049191
7667.972.2097286838067-4.30972868380668
7776.571.21918519881985.28081480118017
7885.572.432922090514613.0670779094854
7971.775.4362454643711-3.73624546437109
8057.974.5775107563255-16.6775107563255
8175.570.74436931344354.75563068655646
8278.271.83739844339136.36260155660871
8375.773.29977205942582.4002279405742
8467.173.8514379120704-6.75143791207043
8574.672.29969455912512.30030544087487
8666.272.8283943300643-6.62839433006427
8774.971.30493118394123.59506881605881
8869.572.1312180003728-2.63121800037277
8976.171.52646163655754.57353836344252
9082.372.57763885944579.72236114055434
9182.174.8122160667427.28778393325803
9260.576.4872326222399-15.9872326222399
9371.272.8127439760216-1.61274397602158
9481.472.44207260536148.95792739463857
9574.574.500953168559-0.000953168558993411
9661.474.500734093305-13.100734093305
9783.871.489675217736412.3103247822636
9885.474.319067252775811.0809327472242
9991.676.865897122039314.7341028779607
10091.980.252367752482611.6476322475174
10186.382.92944723585053.37055276414948
10296.883.704131520241213.0958684797588
1038186.7140720883356-5.7140720883356
10470.885.4007557997458-14.6007557997458
10598.882.044933520801816.7550664791982
10694.585.89590028904688.60409971095325
10784.587.8734574714479-3.37345747144789
10892.887.09810557220225.70189442779777
10981.288.4086229601667-7.20862296016671
11075.786.7518006790451-11.0518006790451
11186.784.21166649353722.48833350646285
11287.584.78358243631162.71641756368842
11387.885.40792097769722.39207902230284
114103.185.957713891580317.1422861084197
11596.489.89767881008596.50232118991406
11677.191.3921654389455-14.2921654389455
117106.588.107269242325218.3927307576748
11895.792.3346350372043.36536496279605
11995.393.10812696281542.19187303718456
12086.693.6119047447114-7.01190474471139
12189.692.0002959702844-2.40029597028445
12281.991.4486144817631-9.54861448176312
12398.489.25397102286049.14602897713958
12492.991.35608465494281.54391534505716
12583.991.7109365258191-7.81093652581905
126121.889.915679131457531.8843208685425
127103.997.2439377358186.65606226418204
12887.598.7737600506716-11.2737600506716
129118.996.182610957816422.7173890421836
130109101.4039516413267.5960483586743
131112.2103.1498193665039.05018063349677
132100.1105.229903316602-5.12990331660151
133111.3104.0508517609987.24914823900218
134102.7105.716988329369-3.01698832936877
135122.6105.02356692092517.5764330790754
136124.8109.06331572024115.7366842797594
137120.3112.6802186002717.61978139972885
138118.3114.4315411025173.8684588974829
139108.7115.32066360627-6.62066360626982
140100.7113.798977281532-13.0989772815317
141124110.78832218972413.2116778102759
142103.1113.824880251926-10.7248802519256
143115111.3598851118083.64011488819207
144112.7112.1965252698420.503474730158388
145101.7112.312243369612-10.6122433696115
146111.5109.8731365714591.62686342854052
147114.4110.2470531421614.15294685783871
148112.5111.2015620579981.29843794200244
149107.2111.499993662043-4.29999366204328
150136.7110.51168766416826.1883123358321
151107.8116.530781688469-8.73078168846892
15294.6114.524108054268-19.9241080542677
153110.7109.9447721203180.75522787968184
154126.6110.11835289785316.481647102147
155127.9113.90647724550113.9935227544992
156109.2117.122733723215-7.92273372321516
15787.1115.301780979182-28.2017809791819
15890.8108.819913450277-18.0199134502774
15994.5104.678235591236-10.1782355912356
160103.3102.3388806820870.961119317912548
161103.2102.5597833301430.640216669857139
162105.4102.7069300527872.69306994721315
163103.9103.3259024026820.574097597318101
16479.8103.457852387586-23.6578523875862
165105.698.02035660290837.57964339709167
16611399.76245382905713.237546170943
16787.7102.804957447929-15.1049574479294
16811099.333249995145110.6667500048549
16990.3101.784884540724-11.4848845407239
170108.999.14521081824919.75478918175087
171105.1101.3872412522553.71275874774476
172113102.24057779817910.7594222018214
173100.4104.713512023547-4.31351202354693
174110.1103.7220989797536.37790102024655
175114.7105.1879890083389.51201099166218
17688.6107.374219559768-18.7742195597683
177117.2103.05917278187814.140827218122
178127.7106.309285561821.3907144382002
179107.8111.225704756722-3.42570475672191
180102.8110.438344396658-7.6383443966581
181100.2108.68275539482-8.48275539482037
182108.4106.7330878617691.66691213823061
183114.2107.1162091855727.08379081442806
18494.4108.744340178274-14.3443401782737
18592.2105.447452194719-13.2474521947188
186115.3102.40267178581312.8973282141869
187102105.36698006914-3.36698006914006
18886.3104.593116929194-18.2931169291937
189112100.38864627135411.6113537286461
190112.5103.0573875382949.44261246170645
191109.5105.2276676049584.27233239504167
192105.9106.209615966466-0.309615966466055
193115.3106.138454160029.16154583997972
194126.2108.24413417145517.9558658285446
195112.2112.371091392821-0.171091392821154
196112.5112.3317679279510.16823207204871
197106.9112.370434209557-5.47043420955733
19890.6111.113115393483-20.5131153934828
19975.6106.398402635312-30.798402635312
20078.899.319730329782-20.519730329782
201101.894.60349720164477.19650279835534
20293.996.2575337975874-2.35753379758744
20310095.71568072163614.28431927836394
20489.296.7003841357356-7.50038413573557
20597.794.97650377443422.72349622556582
206121.195.60246926798325.497530732017
207108.8101.462794778677.33720522133002
20892.9103.149170270776-10.2491702707765
209113.6100.79351180986612.8064881901342
210112.6103.7369415180898.86305848191091
21198.8105.774017510669-6.97401751066872
21278104.171116698065-26.1711166980646

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 52.8 & 46.8 & 6 \tabularnewline
3 & 58.3 & 48.17903365756 & 10.12096634244 \tabularnewline
4 & 54.5 & 50.5052258631028 & 3.99477413689723 \tabularnewline
5 & 64.7 & 51.423380527958 & 13.276619472042 \tabularnewline
6 & 58.3 & 54.4748647130517 & 3.82513528694825 \tabularnewline
7 & 57.5 & 55.3540297639554 & 2.14597023604458 \tabularnewline
8 & 56.7 & 55.84725729456 & 0.852742705440015 \tabularnewline
9 & 56 & 56.0432507765667 & -0.0432507765667438 \tabularnewline
10 & 66.2 & 56.0333100637999 & 10.1666899362001 \tabularnewline
11 & 58.2 & 58.3700113317993 & -0.170011331799294 \tabularnewline
12 & 53.9 & 58.330936107013 & -4.430936107013 \tabularnewline
13 & 53.1 & 57.3125344360015 & -4.21253443600153 \tabularnewline
14 & 54.4 & 56.3443299741888 & -1.94432997418877 \tabularnewline
15 & 59.2 & 55.8974472282206 & 3.30255277177942 \tabularnewline
16 & 57.8 & 56.6565024662459 & 1.14349753375409 \tabularnewline
17 & 61.5 & 56.9193227306432 & 4.5806772693568 \tabularnewline
18 & 60.1 & 57.9721407521204 & 2.12785924787963 \tabularnewline
19 & 60.1 & 58.4612056723498 & 1.63879432765025 \tabularnewline
20 & 58.4 & 58.8378644282911 & -0.437864428291107 \tabularnewline
21 & 56.8 & 58.7372261309475 & -1.93722613094749 \tabularnewline
22 & 63.8 & 58.2919761248006 & 5.5080238751994 \tabularnewline
23 & 53.9 & 59.5579345098913 & -5.65793450989127 \tabularnewline
24 & 63.1 & 58.2575208229896 & 4.84247917701045 \tabularnewline
25 & 55.7 & 59.370511118178 & -3.67051111817803 \tabularnewline
26 & 54.9 & 58.5268847227754 & -3.62688472277542 \tabularnewline
27 & 64.6 & 57.6932853719758 & 6.90671462802415 \tabularnewline
28 & 60.2 & 59.2807173611771 & 0.919282638822949 \tabularnewline
29 & 63.9 & 59.492004311135 & 4.40799568886504 \tabularnewline
30 & 69.9 & 60.505133380689 & 9.394866619311 \tabularnewline
31 & 58.5 & 62.6644395934085 & -4.16443959340846 \tabularnewline
32 & 52 & 61.7072891993775 & -9.70728919937751 \tabularnewline
33 & 66.7 & 59.4761761111091 & 7.22382388889087 \tabularnewline
34 & 72 & 61.1364921576202 & 10.8635078423798 \tabularnewline
35 & 68.4 & 63.6333493165883 & 4.76665068341168 \tabularnewline
36 & 70.8 & 64.7289112709643 & 6.07108872903565 \tabularnewline
37 & 56.5 & 66.1242838868599 & -9.6242838868599 \tabularnewline
38 & 62.6 & 63.9122486518779 & -1.31224865187787 \tabularnewline
39 & 66.5 & 63.6106428088733 & 2.88935719112668 \tabularnewline
40 & 69.2 & 64.2747296114194 & 4.92527038858056 \tabularnewline
41 & 63.7 & 65.4067485511588 & -1.70674855115881 \tabularnewline
42 & 73.6 & 65.0144712683189 & 8.58552873168114 \tabularnewline
43 & 64.1 & 66.987760116475 & -2.88776011647498 \tabularnewline
44 & 53.8 & 66.3240403838786 & -12.5240403838786 \tabularnewline
45 & 72.2 & 63.445528180877 & 8.75447181912295 \tabularnewline
46 & 80.2 & 65.4576467296656 & 14.7423532703344 \tabularnewline
47 & 69.1 & 68.8460136215707 & 0.253986378429289 \tabularnewline
48 & 72 & 68.9043895823067 & 3.09561041769334 \tabularnewline
49 & 66.3 & 69.6158814084221 & -3.31588140842207 \tabularnewline
50 & 72.5 & 68.8537627306402 & 3.64623726935984 \tabularnewline
51 & 88.9 & 69.6918100502896 & 19.2081899497104 \tabularnewline
52 & 88.6 & 74.1066001238657 & 14.4933998761343 \tabularnewline
53 & 73.7 & 77.4377478308099 & -3.73774783080987 \tabularnewline
54 & 86 & 76.5786678204501 & 9.42133217954991 \tabularnewline
55 & 70 & 78.7440568495588 & -8.74405684955883 \tabularnewline
56 & 71.6 & 76.7343320663656 & -5.13433206636556 \tabularnewline
57 & 90.5 & 75.5542626115976 & 14.9457373884024 \tabularnewline
58 & 85.7 & 78.9893750942076 & 6.71062490579244 \tabularnewline
59 & 84.8 & 80.5317380289323 & 4.26826197106774 \tabularnewline
60 & 81.1 & 81.5127508484966 & -0.412750848496557 \tabularnewline
61 & 70.8 & 81.417884629786 & -10.617884629786 \tabularnewline
62 & 65.7 & 78.9774812503587 & -13.2774812503587 \tabularnewline
63 & 86.2 & 75.9257989950476 & 10.2742010049524 \tabularnewline
64 & 76.1 & 78.287210493442 & -2.18721049344197 \tabularnewline
65 & 79.8 & 77.7845043456711 & 2.01549565432886 \tabularnewline
66 & 85.2 & 78.2477437363354 & 6.95225626366464 \tabularnewline
67 & 75.8 & 79.8456429669313 & -4.04564296693134 \tabularnewline
68 & 69.4 & 78.9157966639531 & -9.51579666395313 \tabularnewline
69 & 85 & 76.728696017605 & 8.27130398239495 \tabularnewline
70 & 75 & 78.6297637815438 & -3.62976378154383 \tabularnewline
71 & 77.7 & 77.7955027109203 & -0.0955027109203002 \tabularnewline
72 & 68.5 & 77.7735524687957 & -9.27355246879574 \tabularnewline
73 & 68.4 & 75.6421289721928 & -7.24212897219275 \tabularnewline
74 & 65 & 73.9776057046854 & -8.97760570468539 \tabularnewline
75 & 73.2 & 71.9142022995081 & 1.28579770049191 \tabularnewline
76 & 67.9 & 72.2097286838067 & -4.30972868380668 \tabularnewline
77 & 76.5 & 71.2191851988198 & 5.28081480118017 \tabularnewline
78 & 85.5 & 72.4329220905146 & 13.0670779094854 \tabularnewline
79 & 71.7 & 75.4362454643711 & -3.73624546437109 \tabularnewline
80 & 57.9 & 74.5775107563255 & -16.6775107563255 \tabularnewline
81 & 75.5 & 70.7443693134435 & 4.75563068655646 \tabularnewline
82 & 78.2 & 71.8373984433913 & 6.36260155660871 \tabularnewline
83 & 75.7 & 73.2997720594258 & 2.4002279405742 \tabularnewline
84 & 67.1 & 73.8514379120704 & -6.75143791207043 \tabularnewline
85 & 74.6 & 72.2996945591251 & 2.30030544087487 \tabularnewline
86 & 66.2 & 72.8283943300643 & -6.62839433006427 \tabularnewline
87 & 74.9 & 71.3049311839412 & 3.59506881605881 \tabularnewline
88 & 69.5 & 72.1312180003728 & -2.63121800037277 \tabularnewline
89 & 76.1 & 71.5264616365575 & 4.57353836344252 \tabularnewline
90 & 82.3 & 72.5776388594457 & 9.72236114055434 \tabularnewline
91 & 82.1 & 74.812216066742 & 7.28778393325803 \tabularnewline
92 & 60.5 & 76.4872326222399 & -15.9872326222399 \tabularnewline
93 & 71.2 & 72.8127439760216 & -1.61274397602158 \tabularnewline
94 & 81.4 & 72.4420726053614 & 8.95792739463857 \tabularnewline
95 & 74.5 & 74.500953168559 & -0.000953168558993411 \tabularnewline
96 & 61.4 & 74.500734093305 & -13.100734093305 \tabularnewline
97 & 83.8 & 71.4896752177364 & 12.3103247822636 \tabularnewline
98 & 85.4 & 74.3190672527758 & 11.0809327472242 \tabularnewline
99 & 91.6 & 76.8658971220393 & 14.7341028779607 \tabularnewline
100 & 91.9 & 80.2523677524826 & 11.6476322475174 \tabularnewline
101 & 86.3 & 82.9294472358505 & 3.37055276414948 \tabularnewline
102 & 96.8 & 83.7041315202412 & 13.0958684797588 \tabularnewline
103 & 81 & 86.7140720883356 & -5.7140720883356 \tabularnewline
104 & 70.8 & 85.4007557997458 & -14.6007557997458 \tabularnewline
105 & 98.8 & 82.0449335208018 & 16.7550664791982 \tabularnewline
106 & 94.5 & 85.8959002890468 & 8.60409971095325 \tabularnewline
107 & 84.5 & 87.8734574714479 & -3.37345747144789 \tabularnewline
108 & 92.8 & 87.0981055722022 & 5.70189442779777 \tabularnewline
109 & 81.2 & 88.4086229601667 & -7.20862296016671 \tabularnewline
110 & 75.7 & 86.7518006790451 & -11.0518006790451 \tabularnewline
111 & 86.7 & 84.2116664935372 & 2.48833350646285 \tabularnewline
112 & 87.5 & 84.7835824363116 & 2.71641756368842 \tabularnewline
113 & 87.8 & 85.4079209776972 & 2.39207902230284 \tabularnewline
114 & 103.1 & 85.9577138915803 & 17.1422861084197 \tabularnewline
115 & 96.4 & 89.8976788100859 & 6.50232118991406 \tabularnewline
116 & 77.1 & 91.3921654389455 & -14.2921654389455 \tabularnewline
117 & 106.5 & 88.1072692423252 & 18.3927307576748 \tabularnewline
118 & 95.7 & 92.334635037204 & 3.36536496279605 \tabularnewline
119 & 95.3 & 93.1081269628154 & 2.19187303718456 \tabularnewline
120 & 86.6 & 93.6119047447114 & -7.01190474471139 \tabularnewline
121 & 89.6 & 92.0002959702844 & -2.40029597028445 \tabularnewline
122 & 81.9 & 91.4486144817631 & -9.54861448176312 \tabularnewline
123 & 98.4 & 89.2539710228604 & 9.14602897713958 \tabularnewline
124 & 92.9 & 91.3560846549428 & 1.54391534505716 \tabularnewline
125 & 83.9 & 91.7109365258191 & -7.81093652581905 \tabularnewline
126 & 121.8 & 89.9156791314575 & 31.8843208685425 \tabularnewline
127 & 103.9 & 97.243937735818 & 6.65606226418204 \tabularnewline
128 & 87.5 & 98.7737600506716 & -11.2737600506716 \tabularnewline
129 & 118.9 & 96.1826109578164 & 22.7173890421836 \tabularnewline
130 & 109 & 101.403951641326 & 7.5960483586743 \tabularnewline
131 & 112.2 & 103.149819366503 & 9.05018063349677 \tabularnewline
132 & 100.1 & 105.229903316602 & -5.12990331660151 \tabularnewline
133 & 111.3 & 104.050851760998 & 7.24914823900218 \tabularnewline
134 & 102.7 & 105.716988329369 & -3.01698832936877 \tabularnewline
135 & 122.6 & 105.023566920925 & 17.5764330790754 \tabularnewline
136 & 124.8 & 109.063315720241 & 15.7366842797594 \tabularnewline
137 & 120.3 & 112.680218600271 & 7.61978139972885 \tabularnewline
138 & 118.3 & 114.431541102517 & 3.8684588974829 \tabularnewline
139 & 108.7 & 115.32066360627 & -6.62066360626982 \tabularnewline
140 & 100.7 & 113.798977281532 & -13.0989772815317 \tabularnewline
141 & 124 & 110.788322189724 & 13.2116778102759 \tabularnewline
142 & 103.1 & 113.824880251926 & -10.7248802519256 \tabularnewline
143 & 115 & 111.359885111808 & 3.64011488819207 \tabularnewline
144 & 112.7 & 112.196525269842 & 0.503474730158388 \tabularnewline
145 & 101.7 & 112.312243369612 & -10.6122433696115 \tabularnewline
146 & 111.5 & 109.873136571459 & 1.62686342854052 \tabularnewline
147 & 114.4 & 110.247053142161 & 4.15294685783871 \tabularnewline
148 & 112.5 & 111.201562057998 & 1.29843794200244 \tabularnewline
149 & 107.2 & 111.499993662043 & -4.29999366204328 \tabularnewline
150 & 136.7 & 110.511687664168 & 26.1883123358321 \tabularnewline
151 & 107.8 & 116.530781688469 & -8.73078168846892 \tabularnewline
152 & 94.6 & 114.524108054268 & -19.9241080542677 \tabularnewline
153 & 110.7 & 109.944772120318 & 0.75522787968184 \tabularnewline
154 & 126.6 & 110.118352897853 & 16.481647102147 \tabularnewline
155 & 127.9 & 113.906477245501 & 13.9935227544992 \tabularnewline
156 & 109.2 & 117.122733723215 & -7.92273372321516 \tabularnewline
157 & 87.1 & 115.301780979182 & -28.2017809791819 \tabularnewline
158 & 90.8 & 108.819913450277 & -18.0199134502774 \tabularnewline
159 & 94.5 & 104.678235591236 & -10.1782355912356 \tabularnewline
160 & 103.3 & 102.338880682087 & 0.961119317912548 \tabularnewline
161 & 103.2 & 102.559783330143 & 0.640216669857139 \tabularnewline
162 & 105.4 & 102.706930052787 & 2.69306994721315 \tabularnewline
163 & 103.9 & 103.325902402682 & 0.574097597318101 \tabularnewline
164 & 79.8 & 103.457852387586 & -23.6578523875862 \tabularnewline
165 & 105.6 & 98.0203566029083 & 7.57964339709167 \tabularnewline
166 & 113 & 99.762453829057 & 13.237546170943 \tabularnewline
167 & 87.7 & 102.804957447929 & -15.1049574479294 \tabularnewline
168 & 110 & 99.3332499951451 & 10.6667500048549 \tabularnewline
169 & 90.3 & 101.784884540724 & -11.4848845407239 \tabularnewline
170 & 108.9 & 99.1452108182491 & 9.75478918175087 \tabularnewline
171 & 105.1 & 101.387241252255 & 3.71275874774476 \tabularnewline
172 & 113 & 102.240577798179 & 10.7594222018214 \tabularnewline
173 & 100.4 & 104.713512023547 & -4.31351202354693 \tabularnewline
174 & 110.1 & 103.722098979753 & 6.37790102024655 \tabularnewline
175 & 114.7 & 105.187989008338 & 9.51201099166218 \tabularnewline
176 & 88.6 & 107.374219559768 & -18.7742195597683 \tabularnewline
177 & 117.2 & 103.059172781878 & 14.140827218122 \tabularnewline
178 & 127.7 & 106.3092855618 & 21.3907144382002 \tabularnewline
179 & 107.8 & 111.225704756722 & -3.42570475672191 \tabularnewline
180 & 102.8 & 110.438344396658 & -7.6383443966581 \tabularnewline
181 & 100.2 & 108.68275539482 & -8.48275539482037 \tabularnewline
182 & 108.4 & 106.733087861769 & 1.66691213823061 \tabularnewline
183 & 114.2 & 107.116209185572 & 7.08379081442806 \tabularnewline
184 & 94.4 & 108.744340178274 & -14.3443401782737 \tabularnewline
185 & 92.2 & 105.447452194719 & -13.2474521947188 \tabularnewline
186 & 115.3 & 102.402671785813 & 12.8973282141869 \tabularnewline
187 & 102 & 105.36698006914 & -3.36698006914006 \tabularnewline
188 & 86.3 & 104.593116929194 & -18.2931169291937 \tabularnewline
189 & 112 & 100.388646271354 & 11.6113537286461 \tabularnewline
190 & 112.5 & 103.057387538294 & 9.44261246170645 \tabularnewline
191 & 109.5 & 105.227667604958 & 4.27233239504167 \tabularnewline
192 & 105.9 & 106.209615966466 & -0.309615966466055 \tabularnewline
193 & 115.3 & 106.13845416002 & 9.16154583997972 \tabularnewline
194 & 126.2 & 108.244134171455 & 17.9558658285446 \tabularnewline
195 & 112.2 & 112.371091392821 & -0.171091392821154 \tabularnewline
196 & 112.5 & 112.331767927951 & 0.16823207204871 \tabularnewline
197 & 106.9 & 112.370434209557 & -5.47043420955733 \tabularnewline
198 & 90.6 & 111.113115393483 & -20.5131153934828 \tabularnewline
199 & 75.6 & 106.398402635312 & -30.798402635312 \tabularnewline
200 & 78.8 & 99.319730329782 & -20.519730329782 \tabularnewline
201 & 101.8 & 94.6034972016447 & 7.19650279835534 \tabularnewline
202 & 93.9 & 96.2575337975874 & -2.35753379758744 \tabularnewline
203 & 100 & 95.7156807216361 & 4.28431927836394 \tabularnewline
204 & 89.2 & 96.7003841357356 & -7.50038413573557 \tabularnewline
205 & 97.7 & 94.9765037744342 & 2.72349622556582 \tabularnewline
206 & 121.1 & 95.602469267983 & 25.497530732017 \tabularnewline
207 & 108.8 & 101.46279477867 & 7.33720522133002 \tabularnewline
208 & 92.9 & 103.149170270776 & -10.2491702707765 \tabularnewline
209 & 113.6 & 100.793511809866 & 12.8064881901342 \tabularnewline
210 & 112.6 & 103.736941518089 & 8.86305848191091 \tabularnewline
211 & 98.8 & 105.774017510669 & -6.97401751066872 \tabularnewline
212 & 78 & 104.171116698065 & -26.1711166980646 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309065&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]52.8[/C][C]46.8[/C][C]6[/C][/ROW]
[ROW][C]3[/C][C]58.3[/C][C]48.17903365756[/C][C]10.12096634244[/C][/ROW]
[ROW][C]4[/C][C]54.5[/C][C]50.5052258631028[/C][C]3.99477413689723[/C][/ROW]
[ROW][C]5[/C][C]64.7[/C][C]51.423380527958[/C][C]13.276619472042[/C][/ROW]
[ROW][C]6[/C][C]58.3[/C][C]54.4748647130517[/C][C]3.82513528694825[/C][/ROW]
[ROW][C]7[/C][C]57.5[/C][C]55.3540297639554[/C][C]2.14597023604458[/C][/ROW]
[ROW][C]8[/C][C]56.7[/C][C]55.84725729456[/C][C]0.852742705440015[/C][/ROW]
[ROW][C]9[/C][C]56[/C][C]56.0432507765667[/C][C]-0.0432507765667438[/C][/ROW]
[ROW][C]10[/C][C]66.2[/C][C]56.0333100637999[/C][C]10.1666899362001[/C][/ROW]
[ROW][C]11[/C][C]58.2[/C][C]58.3700113317993[/C][C]-0.170011331799294[/C][/ROW]
[ROW][C]12[/C][C]53.9[/C][C]58.330936107013[/C][C]-4.430936107013[/C][/ROW]
[ROW][C]13[/C][C]53.1[/C][C]57.3125344360015[/C][C]-4.21253443600153[/C][/ROW]
[ROW][C]14[/C][C]54.4[/C][C]56.3443299741888[/C][C]-1.94432997418877[/C][/ROW]
[ROW][C]15[/C][C]59.2[/C][C]55.8974472282206[/C][C]3.30255277177942[/C][/ROW]
[ROW][C]16[/C][C]57.8[/C][C]56.6565024662459[/C][C]1.14349753375409[/C][/ROW]
[ROW][C]17[/C][C]61.5[/C][C]56.9193227306432[/C][C]4.5806772693568[/C][/ROW]
[ROW][C]18[/C][C]60.1[/C][C]57.9721407521204[/C][C]2.12785924787963[/C][/ROW]
[ROW][C]19[/C][C]60.1[/C][C]58.4612056723498[/C][C]1.63879432765025[/C][/ROW]
[ROW][C]20[/C][C]58.4[/C][C]58.8378644282911[/C][C]-0.437864428291107[/C][/ROW]
[ROW][C]21[/C][C]56.8[/C][C]58.7372261309475[/C][C]-1.93722613094749[/C][/ROW]
[ROW][C]22[/C][C]63.8[/C][C]58.2919761248006[/C][C]5.5080238751994[/C][/ROW]
[ROW][C]23[/C][C]53.9[/C][C]59.5579345098913[/C][C]-5.65793450989127[/C][/ROW]
[ROW][C]24[/C][C]63.1[/C][C]58.2575208229896[/C][C]4.84247917701045[/C][/ROW]
[ROW][C]25[/C][C]55.7[/C][C]59.370511118178[/C][C]-3.67051111817803[/C][/ROW]
[ROW][C]26[/C][C]54.9[/C][C]58.5268847227754[/C][C]-3.62688472277542[/C][/ROW]
[ROW][C]27[/C][C]64.6[/C][C]57.6932853719758[/C][C]6.90671462802415[/C][/ROW]
[ROW][C]28[/C][C]60.2[/C][C]59.2807173611771[/C][C]0.919282638822949[/C][/ROW]
[ROW][C]29[/C][C]63.9[/C][C]59.492004311135[/C][C]4.40799568886504[/C][/ROW]
[ROW][C]30[/C][C]69.9[/C][C]60.505133380689[/C][C]9.394866619311[/C][/ROW]
[ROW][C]31[/C][C]58.5[/C][C]62.6644395934085[/C][C]-4.16443959340846[/C][/ROW]
[ROW][C]32[/C][C]52[/C][C]61.7072891993775[/C][C]-9.70728919937751[/C][/ROW]
[ROW][C]33[/C][C]66.7[/C][C]59.4761761111091[/C][C]7.22382388889087[/C][/ROW]
[ROW][C]34[/C][C]72[/C][C]61.1364921576202[/C][C]10.8635078423798[/C][/ROW]
[ROW][C]35[/C][C]68.4[/C][C]63.6333493165883[/C][C]4.76665068341168[/C][/ROW]
[ROW][C]36[/C][C]70.8[/C][C]64.7289112709643[/C][C]6.07108872903565[/C][/ROW]
[ROW][C]37[/C][C]56.5[/C][C]66.1242838868599[/C][C]-9.6242838868599[/C][/ROW]
[ROW][C]38[/C][C]62.6[/C][C]63.9122486518779[/C][C]-1.31224865187787[/C][/ROW]
[ROW][C]39[/C][C]66.5[/C][C]63.6106428088733[/C][C]2.88935719112668[/C][/ROW]
[ROW][C]40[/C][C]69.2[/C][C]64.2747296114194[/C][C]4.92527038858056[/C][/ROW]
[ROW][C]41[/C][C]63.7[/C][C]65.4067485511588[/C][C]-1.70674855115881[/C][/ROW]
[ROW][C]42[/C][C]73.6[/C][C]65.0144712683189[/C][C]8.58552873168114[/C][/ROW]
[ROW][C]43[/C][C]64.1[/C][C]66.987760116475[/C][C]-2.88776011647498[/C][/ROW]
[ROW][C]44[/C][C]53.8[/C][C]66.3240403838786[/C][C]-12.5240403838786[/C][/ROW]
[ROW][C]45[/C][C]72.2[/C][C]63.445528180877[/C][C]8.75447181912295[/C][/ROW]
[ROW][C]46[/C][C]80.2[/C][C]65.4576467296656[/C][C]14.7423532703344[/C][/ROW]
[ROW][C]47[/C][C]69.1[/C][C]68.8460136215707[/C][C]0.253986378429289[/C][/ROW]
[ROW][C]48[/C][C]72[/C][C]68.9043895823067[/C][C]3.09561041769334[/C][/ROW]
[ROW][C]49[/C][C]66.3[/C][C]69.6158814084221[/C][C]-3.31588140842207[/C][/ROW]
[ROW][C]50[/C][C]72.5[/C][C]68.8537627306402[/C][C]3.64623726935984[/C][/ROW]
[ROW][C]51[/C][C]88.9[/C][C]69.6918100502896[/C][C]19.2081899497104[/C][/ROW]
[ROW][C]52[/C][C]88.6[/C][C]74.1066001238657[/C][C]14.4933998761343[/C][/ROW]
[ROW][C]53[/C][C]73.7[/C][C]77.4377478308099[/C][C]-3.73774783080987[/C][/ROW]
[ROW][C]54[/C][C]86[/C][C]76.5786678204501[/C][C]9.42133217954991[/C][/ROW]
[ROW][C]55[/C][C]70[/C][C]78.7440568495588[/C][C]-8.74405684955883[/C][/ROW]
[ROW][C]56[/C][C]71.6[/C][C]76.7343320663656[/C][C]-5.13433206636556[/C][/ROW]
[ROW][C]57[/C][C]90.5[/C][C]75.5542626115976[/C][C]14.9457373884024[/C][/ROW]
[ROW][C]58[/C][C]85.7[/C][C]78.9893750942076[/C][C]6.71062490579244[/C][/ROW]
[ROW][C]59[/C][C]84.8[/C][C]80.5317380289323[/C][C]4.26826197106774[/C][/ROW]
[ROW][C]60[/C][C]81.1[/C][C]81.5127508484966[/C][C]-0.412750848496557[/C][/ROW]
[ROW][C]61[/C][C]70.8[/C][C]81.417884629786[/C][C]-10.617884629786[/C][/ROW]
[ROW][C]62[/C][C]65.7[/C][C]78.9774812503587[/C][C]-13.2774812503587[/C][/ROW]
[ROW][C]63[/C][C]86.2[/C][C]75.9257989950476[/C][C]10.2742010049524[/C][/ROW]
[ROW][C]64[/C][C]76.1[/C][C]78.287210493442[/C][C]-2.18721049344197[/C][/ROW]
[ROW][C]65[/C][C]79.8[/C][C]77.7845043456711[/C][C]2.01549565432886[/C][/ROW]
[ROW][C]66[/C][C]85.2[/C][C]78.2477437363354[/C][C]6.95225626366464[/C][/ROW]
[ROW][C]67[/C][C]75.8[/C][C]79.8456429669313[/C][C]-4.04564296693134[/C][/ROW]
[ROW][C]68[/C][C]69.4[/C][C]78.9157966639531[/C][C]-9.51579666395313[/C][/ROW]
[ROW][C]69[/C][C]85[/C][C]76.728696017605[/C][C]8.27130398239495[/C][/ROW]
[ROW][C]70[/C][C]75[/C][C]78.6297637815438[/C][C]-3.62976378154383[/C][/ROW]
[ROW][C]71[/C][C]77.7[/C][C]77.7955027109203[/C][C]-0.0955027109203002[/C][/ROW]
[ROW][C]72[/C][C]68.5[/C][C]77.7735524687957[/C][C]-9.27355246879574[/C][/ROW]
[ROW][C]73[/C][C]68.4[/C][C]75.6421289721928[/C][C]-7.24212897219275[/C][/ROW]
[ROW][C]74[/C][C]65[/C][C]73.9776057046854[/C][C]-8.97760570468539[/C][/ROW]
[ROW][C]75[/C][C]73.2[/C][C]71.9142022995081[/C][C]1.28579770049191[/C][/ROW]
[ROW][C]76[/C][C]67.9[/C][C]72.2097286838067[/C][C]-4.30972868380668[/C][/ROW]
[ROW][C]77[/C][C]76.5[/C][C]71.2191851988198[/C][C]5.28081480118017[/C][/ROW]
[ROW][C]78[/C][C]85.5[/C][C]72.4329220905146[/C][C]13.0670779094854[/C][/ROW]
[ROW][C]79[/C][C]71.7[/C][C]75.4362454643711[/C][C]-3.73624546437109[/C][/ROW]
[ROW][C]80[/C][C]57.9[/C][C]74.5775107563255[/C][C]-16.6775107563255[/C][/ROW]
[ROW][C]81[/C][C]75.5[/C][C]70.7443693134435[/C][C]4.75563068655646[/C][/ROW]
[ROW][C]82[/C][C]78.2[/C][C]71.8373984433913[/C][C]6.36260155660871[/C][/ROW]
[ROW][C]83[/C][C]75.7[/C][C]73.2997720594258[/C][C]2.4002279405742[/C][/ROW]
[ROW][C]84[/C][C]67.1[/C][C]73.8514379120704[/C][C]-6.75143791207043[/C][/ROW]
[ROW][C]85[/C][C]74.6[/C][C]72.2996945591251[/C][C]2.30030544087487[/C][/ROW]
[ROW][C]86[/C][C]66.2[/C][C]72.8283943300643[/C][C]-6.62839433006427[/C][/ROW]
[ROW][C]87[/C][C]74.9[/C][C]71.3049311839412[/C][C]3.59506881605881[/C][/ROW]
[ROW][C]88[/C][C]69.5[/C][C]72.1312180003728[/C][C]-2.63121800037277[/C][/ROW]
[ROW][C]89[/C][C]76.1[/C][C]71.5264616365575[/C][C]4.57353836344252[/C][/ROW]
[ROW][C]90[/C][C]82.3[/C][C]72.5776388594457[/C][C]9.72236114055434[/C][/ROW]
[ROW][C]91[/C][C]82.1[/C][C]74.812216066742[/C][C]7.28778393325803[/C][/ROW]
[ROW][C]92[/C][C]60.5[/C][C]76.4872326222399[/C][C]-15.9872326222399[/C][/ROW]
[ROW][C]93[/C][C]71.2[/C][C]72.8127439760216[/C][C]-1.61274397602158[/C][/ROW]
[ROW][C]94[/C][C]81.4[/C][C]72.4420726053614[/C][C]8.95792739463857[/C][/ROW]
[ROW][C]95[/C][C]74.5[/C][C]74.500953168559[/C][C]-0.000953168558993411[/C][/ROW]
[ROW][C]96[/C][C]61.4[/C][C]74.500734093305[/C][C]-13.100734093305[/C][/ROW]
[ROW][C]97[/C][C]83.8[/C][C]71.4896752177364[/C][C]12.3103247822636[/C][/ROW]
[ROW][C]98[/C][C]85.4[/C][C]74.3190672527758[/C][C]11.0809327472242[/C][/ROW]
[ROW][C]99[/C][C]91.6[/C][C]76.8658971220393[/C][C]14.7341028779607[/C][/ROW]
[ROW][C]100[/C][C]91.9[/C][C]80.2523677524826[/C][C]11.6476322475174[/C][/ROW]
[ROW][C]101[/C][C]86.3[/C][C]82.9294472358505[/C][C]3.37055276414948[/C][/ROW]
[ROW][C]102[/C][C]96.8[/C][C]83.7041315202412[/C][C]13.0958684797588[/C][/ROW]
[ROW][C]103[/C][C]81[/C][C]86.7140720883356[/C][C]-5.7140720883356[/C][/ROW]
[ROW][C]104[/C][C]70.8[/C][C]85.4007557997458[/C][C]-14.6007557997458[/C][/ROW]
[ROW][C]105[/C][C]98.8[/C][C]82.0449335208018[/C][C]16.7550664791982[/C][/ROW]
[ROW][C]106[/C][C]94.5[/C][C]85.8959002890468[/C][C]8.60409971095325[/C][/ROW]
[ROW][C]107[/C][C]84.5[/C][C]87.8734574714479[/C][C]-3.37345747144789[/C][/ROW]
[ROW][C]108[/C][C]92.8[/C][C]87.0981055722022[/C][C]5.70189442779777[/C][/ROW]
[ROW][C]109[/C][C]81.2[/C][C]88.4086229601667[/C][C]-7.20862296016671[/C][/ROW]
[ROW][C]110[/C][C]75.7[/C][C]86.7518006790451[/C][C]-11.0518006790451[/C][/ROW]
[ROW][C]111[/C][C]86.7[/C][C]84.2116664935372[/C][C]2.48833350646285[/C][/ROW]
[ROW][C]112[/C][C]87.5[/C][C]84.7835824363116[/C][C]2.71641756368842[/C][/ROW]
[ROW][C]113[/C][C]87.8[/C][C]85.4079209776972[/C][C]2.39207902230284[/C][/ROW]
[ROW][C]114[/C][C]103.1[/C][C]85.9577138915803[/C][C]17.1422861084197[/C][/ROW]
[ROW][C]115[/C][C]96.4[/C][C]89.8976788100859[/C][C]6.50232118991406[/C][/ROW]
[ROW][C]116[/C][C]77.1[/C][C]91.3921654389455[/C][C]-14.2921654389455[/C][/ROW]
[ROW][C]117[/C][C]106.5[/C][C]88.1072692423252[/C][C]18.3927307576748[/C][/ROW]
[ROW][C]118[/C][C]95.7[/C][C]92.334635037204[/C][C]3.36536496279605[/C][/ROW]
[ROW][C]119[/C][C]95.3[/C][C]93.1081269628154[/C][C]2.19187303718456[/C][/ROW]
[ROW][C]120[/C][C]86.6[/C][C]93.6119047447114[/C][C]-7.01190474471139[/C][/ROW]
[ROW][C]121[/C][C]89.6[/C][C]92.0002959702844[/C][C]-2.40029597028445[/C][/ROW]
[ROW][C]122[/C][C]81.9[/C][C]91.4486144817631[/C][C]-9.54861448176312[/C][/ROW]
[ROW][C]123[/C][C]98.4[/C][C]89.2539710228604[/C][C]9.14602897713958[/C][/ROW]
[ROW][C]124[/C][C]92.9[/C][C]91.3560846549428[/C][C]1.54391534505716[/C][/ROW]
[ROW][C]125[/C][C]83.9[/C][C]91.7109365258191[/C][C]-7.81093652581905[/C][/ROW]
[ROW][C]126[/C][C]121.8[/C][C]89.9156791314575[/C][C]31.8843208685425[/C][/ROW]
[ROW][C]127[/C][C]103.9[/C][C]97.243937735818[/C][C]6.65606226418204[/C][/ROW]
[ROW][C]128[/C][C]87.5[/C][C]98.7737600506716[/C][C]-11.2737600506716[/C][/ROW]
[ROW][C]129[/C][C]118.9[/C][C]96.1826109578164[/C][C]22.7173890421836[/C][/ROW]
[ROW][C]130[/C][C]109[/C][C]101.403951641326[/C][C]7.5960483586743[/C][/ROW]
[ROW][C]131[/C][C]112.2[/C][C]103.149819366503[/C][C]9.05018063349677[/C][/ROW]
[ROW][C]132[/C][C]100.1[/C][C]105.229903316602[/C][C]-5.12990331660151[/C][/ROW]
[ROW][C]133[/C][C]111.3[/C][C]104.050851760998[/C][C]7.24914823900218[/C][/ROW]
[ROW][C]134[/C][C]102.7[/C][C]105.716988329369[/C][C]-3.01698832936877[/C][/ROW]
[ROW][C]135[/C][C]122.6[/C][C]105.023566920925[/C][C]17.5764330790754[/C][/ROW]
[ROW][C]136[/C][C]124.8[/C][C]109.063315720241[/C][C]15.7366842797594[/C][/ROW]
[ROW][C]137[/C][C]120.3[/C][C]112.680218600271[/C][C]7.61978139972885[/C][/ROW]
[ROW][C]138[/C][C]118.3[/C][C]114.431541102517[/C][C]3.8684588974829[/C][/ROW]
[ROW][C]139[/C][C]108.7[/C][C]115.32066360627[/C][C]-6.62066360626982[/C][/ROW]
[ROW][C]140[/C][C]100.7[/C][C]113.798977281532[/C][C]-13.0989772815317[/C][/ROW]
[ROW][C]141[/C][C]124[/C][C]110.788322189724[/C][C]13.2116778102759[/C][/ROW]
[ROW][C]142[/C][C]103.1[/C][C]113.824880251926[/C][C]-10.7248802519256[/C][/ROW]
[ROW][C]143[/C][C]115[/C][C]111.359885111808[/C][C]3.64011488819207[/C][/ROW]
[ROW][C]144[/C][C]112.7[/C][C]112.196525269842[/C][C]0.503474730158388[/C][/ROW]
[ROW][C]145[/C][C]101.7[/C][C]112.312243369612[/C][C]-10.6122433696115[/C][/ROW]
[ROW][C]146[/C][C]111.5[/C][C]109.873136571459[/C][C]1.62686342854052[/C][/ROW]
[ROW][C]147[/C][C]114.4[/C][C]110.247053142161[/C][C]4.15294685783871[/C][/ROW]
[ROW][C]148[/C][C]112.5[/C][C]111.201562057998[/C][C]1.29843794200244[/C][/ROW]
[ROW][C]149[/C][C]107.2[/C][C]111.499993662043[/C][C]-4.29999366204328[/C][/ROW]
[ROW][C]150[/C][C]136.7[/C][C]110.511687664168[/C][C]26.1883123358321[/C][/ROW]
[ROW][C]151[/C][C]107.8[/C][C]116.530781688469[/C][C]-8.73078168846892[/C][/ROW]
[ROW][C]152[/C][C]94.6[/C][C]114.524108054268[/C][C]-19.9241080542677[/C][/ROW]
[ROW][C]153[/C][C]110.7[/C][C]109.944772120318[/C][C]0.75522787968184[/C][/ROW]
[ROW][C]154[/C][C]126.6[/C][C]110.118352897853[/C][C]16.481647102147[/C][/ROW]
[ROW][C]155[/C][C]127.9[/C][C]113.906477245501[/C][C]13.9935227544992[/C][/ROW]
[ROW][C]156[/C][C]109.2[/C][C]117.122733723215[/C][C]-7.92273372321516[/C][/ROW]
[ROW][C]157[/C][C]87.1[/C][C]115.301780979182[/C][C]-28.2017809791819[/C][/ROW]
[ROW][C]158[/C][C]90.8[/C][C]108.819913450277[/C][C]-18.0199134502774[/C][/ROW]
[ROW][C]159[/C][C]94.5[/C][C]104.678235591236[/C][C]-10.1782355912356[/C][/ROW]
[ROW][C]160[/C][C]103.3[/C][C]102.338880682087[/C][C]0.961119317912548[/C][/ROW]
[ROW][C]161[/C][C]103.2[/C][C]102.559783330143[/C][C]0.640216669857139[/C][/ROW]
[ROW][C]162[/C][C]105.4[/C][C]102.706930052787[/C][C]2.69306994721315[/C][/ROW]
[ROW][C]163[/C][C]103.9[/C][C]103.325902402682[/C][C]0.574097597318101[/C][/ROW]
[ROW][C]164[/C][C]79.8[/C][C]103.457852387586[/C][C]-23.6578523875862[/C][/ROW]
[ROW][C]165[/C][C]105.6[/C][C]98.0203566029083[/C][C]7.57964339709167[/C][/ROW]
[ROW][C]166[/C][C]113[/C][C]99.762453829057[/C][C]13.237546170943[/C][/ROW]
[ROW][C]167[/C][C]87.7[/C][C]102.804957447929[/C][C]-15.1049574479294[/C][/ROW]
[ROW][C]168[/C][C]110[/C][C]99.3332499951451[/C][C]10.6667500048549[/C][/ROW]
[ROW][C]169[/C][C]90.3[/C][C]101.784884540724[/C][C]-11.4848845407239[/C][/ROW]
[ROW][C]170[/C][C]108.9[/C][C]99.1452108182491[/C][C]9.75478918175087[/C][/ROW]
[ROW][C]171[/C][C]105.1[/C][C]101.387241252255[/C][C]3.71275874774476[/C][/ROW]
[ROW][C]172[/C][C]113[/C][C]102.240577798179[/C][C]10.7594222018214[/C][/ROW]
[ROW][C]173[/C][C]100.4[/C][C]104.713512023547[/C][C]-4.31351202354693[/C][/ROW]
[ROW][C]174[/C][C]110.1[/C][C]103.722098979753[/C][C]6.37790102024655[/C][/ROW]
[ROW][C]175[/C][C]114.7[/C][C]105.187989008338[/C][C]9.51201099166218[/C][/ROW]
[ROW][C]176[/C][C]88.6[/C][C]107.374219559768[/C][C]-18.7742195597683[/C][/ROW]
[ROW][C]177[/C][C]117.2[/C][C]103.059172781878[/C][C]14.140827218122[/C][/ROW]
[ROW][C]178[/C][C]127.7[/C][C]106.3092855618[/C][C]21.3907144382002[/C][/ROW]
[ROW][C]179[/C][C]107.8[/C][C]111.225704756722[/C][C]-3.42570475672191[/C][/ROW]
[ROW][C]180[/C][C]102.8[/C][C]110.438344396658[/C][C]-7.6383443966581[/C][/ROW]
[ROW][C]181[/C][C]100.2[/C][C]108.68275539482[/C][C]-8.48275539482037[/C][/ROW]
[ROW][C]182[/C][C]108.4[/C][C]106.733087861769[/C][C]1.66691213823061[/C][/ROW]
[ROW][C]183[/C][C]114.2[/C][C]107.116209185572[/C][C]7.08379081442806[/C][/ROW]
[ROW][C]184[/C][C]94.4[/C][C]108.744340178274[/C][C]-14.3443401782737[/C][/ROW]
[ROW][C]185[/C][C]92.2[/C][C]105.447452194719[/C][C]-13.2474521947188[/C][/ROW]
[ROW][C]186[/C][C]115.3[/C][C]102.402671785813[/C][C]12.8973282141869[/C][/ROW]
[ROW][C]187[/C][C]102[/C][C]105.36698006914[/C][C]-3.36698006914006[/C][/ROW]
[ROW][C]188[/C][C]86.3[/C][C]104.593116929194[/C][C]-18.2931169291937[/C][/ROW]
[ROW][C]189[/C][C]112[/C][C]100.388646271354[/C][C]11.6113537286461[/C][/ROW]
[ROW][C]190[/C][C]112.5[/C][C]103.057387538294[/C][C]9.44261246170645[/C][/ROW]
[ROW][C]191[/C][C]109.5[/C][C]105.227667604958[/C][C]4.27233239504167[/C][/ROW]
[ROW][C]192[/C][C]105.9[/C][C]106.209615966466[/C][C]-0.309615966466055[/C][/ROW]
[ROW][C]193[/C][C]115.3[/C][C]106.13845416002[/C][C]9.16154583997972[/C][/ROW]
[ROW][C]194[/C][C]126.2[/C][C]108.244134171455[/C][C]17.9558658285446[/C][/ROW]
[ROW][C]195[/C][C]112.2[/C][C]112.371091392821[/C][C]-0.171091392821154[/C][/ROW]
[ROW][C]196[/C][C]112.5[/C][C]112.331767927951[/C][C]0.16823207204871[/C][/ROW]
[ROW][C]197[/C][C]106.9[/C][C]112.370434209557[/C][C]-5.47043420955733[/C][/ROW]
[ROW][C]198[/C][C]90.6[/C][C]111.113115393483[/C][C]-20.5131153934828[/C][/ROW]
[ROW][C]199[/C][C]75.6[/C][C]106.398402635312[/C][C]-30.798402635312[/C][/ROW]
[ROW][C]200[/C][C]78.8[/C][C]99.319730329782[/C][C]-20.519730329782[/C][/ROW]
[ROW][C]201[/C][C]101.8[/C][C]94.6034972016447[/C][C]7.19650279835534[/C][/ROW]
[ROW][C]202[/C][C]93.9[/C][C]96.2575337975874[/C][C]-2.35753379758744[/C][/ROW]
[ROW][C]203[/C][C]100[/C][C]95.7156807216361[/C][C]4.28431927836394[/C][/ROW]
[ROW][C]204[/C][C]89.2[/C][C]96.7003841357356[/C][C]-7.50038413573557[/C][/ROW]
[ROW][C]205[/C][C]97.7[/C][C]94.9765037744342[/C][C]2.72349622556582[/C][/ROW]
[ROW][C]206[/C][C]121.1[/C][C]95.602469267983[/C][C]25.497530732017[/C][/ROW]
[ROW][C]207[/C][C]108.8[/C][C]101.46279477867[/C][C]7.33720522133002[/C][/ROW]
[ROW][C]208[/C][C]92.9[/C][C]103.149170270776[/C][C]-10.2491702707765[/C][/ROW]
[ROW][C]209[/C][C]113.6[/C][C]100.793511809866[/C][C]12.8064881901342[/C][/ROW]
[ROW][C]210[/C][C]112.6[/C][C]103.736941518089[/C][C]8.86305848191091[/C][/ROW]
[ROW][C]211[/C][C]98.8[/C][C]105.774017510669[/C][C]-6.97401751066872[/C][/ROW]
[ROW][C]212[/C][C]78[/C][C]104.171116698065[/C][C]-26.1711166980646[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309065&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309065&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
252.846.86
358.348.1790336575610.12096634244
454.550.50522586310283.99477413689723
564.751.42338052795813.276619472042
658.354.47486471305173.82513528694825
757.555.35402976395542.14597023604458
856.755.847257294560.852742705440015
95656.0432507765667-0.0432507765667438
1066.256.033310063799910.1666899362001
1158.258.3700113317993-0.170011331799294
1253.958.330936107013-4.430936107013
1353.157.3125344360015-4.21253443600153
1454.456.3443299741888-1.94432997418877
1559.255.89744722822063.30255277177942
1657.856.65650246624591.14349753375409
1761.556.91932273064324.5806772693568
1860.157.97214075212042.12785924787963
1960.158.46120567234981.63879432765025
2058.458.8378644282911-0.437864428291107
2156.858.7372261309475-1.93722613094749
2263.858.29197612480065.5080238751994
2353.959.5579345098913-5.65793450989127
2463.158.25752082298964.84247917701045
2555.759.370511118178-3.67051111817803
2654.958.5268847227754-3.62688472277542
2764.657.69328537197586.90671462802415
2860.259.28071736117710.919282638822949
2963.959.4920043111354.40799568886504
3069.960.5051333806899.394866619311
3158.562.6644395934085-4.16443959340846
325261.7072891993775-9.70728919937751
3366.759.47617611110917.22382388889087
347261.136492157620210.8635078423798
3568.463.63334931658834.76665068341168
3670.864.72891127096436.07108872903565
3756.566.1242838868599-9.6242838868599
3862.663.9122486518779-1.31224865187787
3966.563.61064280887332.88935719112668
4069.264.27472961141944.92527038858056
4163.765.4067485511588-1.70674855115881
4273.665.01447126831898.58552873168114
4364.166.987760116475-2.88776011647498
4453.866.3240403838786-12.5240403838786
4572.263.4455281808778.75447181912295
4680.265.457646729665614.7423532703344
4769.168.84601362157070.253986378429289
487268.90438958230673.09561041769334
4966.369.6158814084221-3.31588140842207
5072.568.85376273064023.64623726935984
5188.969.691810050289619.2081899497104
5288.674.106600123865714.4933998761343
5373.777.4377478308099-3.73774783080987
548676.57866782045019.42133217954991
557078.7440568495588-8.74405684955883
5671.676.7343320663656-5.13433206636556
5790.575.554262611597614.9457373884024
5885.778.98937509420766.71062490579244
5984.880.53173802893234.26826197106774
6081.181.5127508484966-0.412750848496557
6170.881.417884629786-10.617884629786
6265.778.9774812503587-13.2774812503587
6386.275.925798995047610.2742010049524
6476.178.287210493442-2.18721049344197
6579.877.78450434567112.01549565432886
6685.278.24774373633546.95225626366464
6775.879.8456429669313-4.04564296693134
6869.478.9157966639531-9.51579666395313
698576.7286960176058.27130398239495
707578.6297637815438-3.62976378154383
7177.777.7955027109203-0.0955027109203002
7268.577.7735524687957-9.27355246879574
7368.475.6421289721928-7.24212897219275
746573.9776057046854-8.97760570468539
7573.271.91420229950811.28579770049191
7667.972.2097286838067-4.30972868380668
7776.571.21918519881985.28081480118017
7885.572.432922090514613.0670779094854
7971.775.4362454643711-3.73624546437109
8057.974.5775107563255-16.6775107563255
8175.570.74436931344354.75563068655646
8278.271.83739844339136.36260155660871
8375.773.29977205942582.4002279405742
8467.173.8514379120704-6.75143791207043
8574.672.29969455912512.30030544087487
8666.272.8283943300643-6.62839433006427
8774.971.30493118394123.59506881605881
8869.572.1312180003728-2.63121800037277
8976.171.52646163655754.57353836344252
9082.372.57763885944579.72236114055434
9182.174.8122160667427.28778393325803
9260.576.4872326222399-15.9872326222399
9371.272.8127439760216-1.61274397602158
9481.472.44207260536148.95792739463857
9574.574.500953168559-0.000953168558993411
9661.474.500734093305-13.100734093305
9783.871.489675217736412.3103247822636
9885.474.319067252775811.0809327472242
9991.676.865897122039314.7341028779607
10091.980.252367752482611.6476322475174
10186.382.92944723585053.37055276414948
10296.883.704131520241213.0958684797588
1038186.7140720883356-5.7140720883356
10470.885.4007557997458-14.6007557997458
10598.882.044933520801816.7550664791982
10694.585.89590028904688.60409971095325
10784.587.8734574714479-3.37345747144789
10892.887.09810557220225.70189442779777
10981.288.4086229601667-7.20862296016671
11075.786.7518006790451-11.0518006790451
11186.784.21166649353722.48833350646285
11287.584.78358243631162.71641756368842
11387.885.40792097769722.39207902230284
114103.185.957713891580317.1422861084197
11596.489.89767881008596.50232118991406
11677.191.3921654389455-14.2921654389455
117106.588.107269242325218.3927307576748
11895.792.3346350372043.36536496279605
11995.393.10812696281542.19187303718456
12086.693.6119047447114-7.01190474471139
12189.692.0002959702844-2.40029597028445
12281.991.4486144817631-9.54861448176312
12398.489.25397102286049.14602897713958
12492.991.35608465494281.54391534505716
12583.991.7109365258191-7.81093652581905
126121.889.915679131457531.8843208685425
127103.997.2439377358186.65606226418204
12887.598.7737600506716-11.2737600506716
129118.996.182610957816422.7173890421836
130109101.4039516413267.5960483586743
131112.2103.1498193665039.05018063349677
132100.1105.229903316602-5.12990331660151
133111.3104.0508517609987.24914823900218
134102.7105.716988329369-3.01698832936877
135122.6105.02356692092517.5764330790754
136124.8109.06331572024115.7366842797594
137120.3112.6802186002717.61978139972885
138118.3114.4315411025173.8684588974829
139108.7115.32066360627-6.62066360626982
140100.7113.798977281532-13.0989772815317
141124110.78832218972413.2116778102759
142103.1113.824880251926-10.7248802519256
143115111.3598851118083.64011488819207
144112.7112.1965252698420.503474730158388
145101.7112.312243369612-10.6122433696115
146111.5109.8731365714591.62686342854052
147114.4110.2470531421614.15294685783871
148112.5111.2015620579981.29843794200244
149107.2111.499993662043-4.29999366204328
150136.7110.51168766416826.1883123358321
151107.8116.530781688469-8.73078168846892
15294.6114.524108054268-19.9241080542677
153110.7109.9447721203180.75522787968184
154126.6110.11835289785316.481647102147
155127.9113.90647724550113.9935227544992
156109.2117.122733723215-7.92273372321516
15787.1115.301780979182-28.2017809791819
15890.8108.819913450277-18.0199134502774
15994.5104.678235591236-10.1782355912356
160103.3102.3388806820870.961119317912548
161103.2102.5597833301430.640216669857139
162105.4102.7069300527872.69306994721315
163103.9103.3259024026820.574097597318101
16479.8103.457852387586-23.6578523875862
165105.698.02035660290837.57964339709167
16611399.76245382905713.237546170943
16787.7102.804957447929-15.1049574479294
16811099.333249995145110.6667500048549
16990.3101.784884540724-11.4848845407239
170108.999.14521081824919.75478918175087
171105.1101.3872412522553.71275874774476
172113102.24057779817910.7594222018214
173100.4104.713512023547-4.31351202354693
174110.1103.7220989797536.37790102024655
175114.7105.1879890083389.51201099166218
17688.6107.374219559768-18.7742195597683
177117.2103.05917278187814.140827218122
178127.7106.309285561821.3907144382002
179107.8111.225704756722-3.42570475672191
180102.8110.438344396658-7.6383443966581
181100.2108.68275539482-8.48275539482037
182108.4106.7330878617691.66691213823061
183114.2107.1162091855727.08379081442806
18494.4108.744340178274-14.3443401782737
18592.2105.447452194719-13.2474521947188
186115.3102.40267178581312.8973282141869
187102105.36698006914-3.36698006914006
18886.3104.593116929194-18.2931169291937
189112100.38864627135411.6113537286461
190112.5103.0573875382949.44261246170645
191109.5105.2276676049584.27233239504167
192105.9106.209615966466-0.309615966466055
193115.3106.138454160029.16154583997972
194126.2108.24413417145517.9558658285446
195112.2112.371091392821-0.171091392821154
196112.5112.3317679279510.16823207204871
197106.9112.370434209557-5.47043420955733
19890.6111.113115393483-20.5131153934828
19975.6106.398402635312-30.798402635312
20078.899.319730329782-20.519730329782
201101.894.60349720164477.19650279835534
20293.996.2575337975874-2.35753379758744
20310095.71568072163614.28431927836394
20489.296.7003841357356-7.50038413573557
20597.794.97650377443422.72349622556582
206121.195.60246926798325.497530732017
207108.8101.462794778677.33720522133002
20892.9103.149170270776-10.2491702707765
209113.6100.79351180986612.8064881901342
210112.6103.7369415180898.86305848191091
21198.8105.774017510669-6.97401751066872
21278104.171116698065-26.1711166980646







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
21398.15597490097178.0782972701007118.233652531841
21498.15597490097177.5548106275846118.757139174357
21598.15597490097177.0443004105628119.267649391379
21698.15597490097176.5458469476511119.766102854291
21798.15597490097176.0586343250384120.253315476904
21898.15597490097175.581934702135120.730015099807
21998.15597490097175.1150955499444121.196854251998
22098.15597490097174.6575291728283121.654420629114
22198.15597490097174.2087040333258122.103245768616
22298.15597490097173.768137514719122.543812287223
22398.15597490097173.3353898404175122.976559961524
22498.15597490097172.9100589318865123.401890870055

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
213 & 98.155974900971 & 78.0782972701007 & 118.233652531841 \tabularnewline
214 & 98.155974900971 & 77.5548106275846 & 118.757139174357 \tabularnewline
215 & 98.155974900971 & 77.0443004105628 & 119.267649391379 \tabularnewline
216 & 98.155974900971 & 76.5458469476511 & 119.766102854291 \tabularnewline
217 & 98.155974900971 & 76.0586343250384 & 120.253315476904 \tabularnewline
218 & 98.155974900971 & 75.581934702135 & 120.730015099807 \tabularnewline
219 & 98.155974900971 & 75.1150955499444 & 121.196854251998 \tabularnewline
220 & 98.155974900971 & 74.6575291728283 & 121.654420629114 \tabularnewline
221 & 98.155974900971 & 74.2087040333258 & 122.103245768616 \tabularnewline
222 & 98.155974900971 & 73.768137514719 & 122.543812287223 \tabularnewline
223 & 98.155974900971 & 73.3353898404175 & 122.976559961524 \tabularnewline
224 & 98.155974900971 & 72.9100589318865 & 123.401890870055 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309065&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]213[/C][C]98.155974900971[/C][C]78.0782972701007[/C][C]118.233652531841[/C][/ROW]
[ROW][C]214[/C][C]98.155974900971[/C][C]77.5548106275846[/C][C]118.757139174357[/C][/ROW]
[ROW][C]215[/C][C]98.155974900971[/C][C]77.0443004105628[/C][C]119.267649391379[/C][/ROW]
[ROW][C]216[/C][C]98.155974900971[/C][C]76.5458469476511[/C][C]119.766102854291[/C][/ROW]
[ROW][C]217[/C][C]98.155974900971[/C][C]76.0586343250384[/C][C]120.253315476904[/C][/ROW]
[ROW][C]218[/C][C]98.155974900971[/C][C]75.581934702135[/C][C]120.730015099807[/C][/ROW]
[ROW][C]219[/C][C]98.155974900971[/C][C]75.1150955499444[/C][C]121.196854251998[/C][/ROW]
[ROW][C]220[/C][C]98.155974900971[/C][C]74.6575291728283[/C][C]121.654420629114[/C][/ROW]
[ROW][C]221[/C][C]98.155974900971[/C][C]74.2087040333258[/C][C]122.103245768616[/C][/ROW]
[ROW][C]222[/C][C]98.155974900971[/C][C]73.768137514719[/C][C]122.543812287223[/C][/ROW]
[ROW][C]223[/C][C]98.155974900971[/C][C]73.3353898404175[/C][C]122.976559961524[/C][/ROW]
[ROW][C]224[/C][C]98.155974900971[/C][C]72.9100589318865[/C][C]123.401890870055[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309065&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309065&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
21398.15597490097178.0782972701007118.233652531841
21498.15597490097177.5548106275846118.757139174357
21598.15597490097177.0443004105628119.267649391379
21698.15597490097176.5458469476511119.766102854291
21798.15597490097176.0586343250384120.253315476904
21898.15597490097175.581934702135120.730015099807
21998.15597490097175.1150955499444121.196854251998
22098.15597490097174.6575291728283121.654420629114
22198.15597490097174.2087040333258122.103245768616
22298.15597490097173.768137514719122.543812287223
22398.15597490097173.3353898404175122.976559961524
22498.15597490097172.9100589318865123.401890870055



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