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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 computationMon, 18 Dec 2017 13:50:56 +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/18/t1513601510ew6yfktm31dluah.htm/, Retrieved Mon, 13 May 2024 21:01:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310146, Retrieved Mon, 13 May 2024 21:01:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact53
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-12-18 12:50:56] [eeb8783d96126a2719bfaf914027c923] [Current]
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Dataseries X:
55.5
63
77.2
71.1
90.1
91.5
76.1
87.8
81
77.2
73.8
68.9
68.4
65.2
78.7
77
97.6
88.1
98.7
93.4
68
87.9
75.8
66.3
68.4
71.3
77.4
87.1
88.5
85.9
92.7
88.5
80.2
81.8
70.4
82.2
72.8
69
83
92.4
92.3
100.5
106.9
99.5
85.9
92.6
77.4
84.1
75.3
73.8
100.1
90.7
96.5
111.8
97.4
100.8
93.7
82
86
84.3
73.1
75.4
97.9
97.5
106
112.8
99.5
100.8
102.9
88.8
91.3
88.3
77.4
80.5
96.7
93.8
105
117.1
111.1
105.8
95.7
97.1
91
90.9
83.5
82.3
101.7
108.3
114
118.2
103.4
106.8
95.4
101.8
95.6
94.8
94
82.4
95.8
106.7
114.1
103.9
117.4
105.9
101.7
98.7
91.3
102.3
80.5
86.7
102.6
107.3
108
124.3
117.1
103.9
104.7
95.9
94.2
102.7
70.3
90.2
107.3
104.6
102.7
124.5
117.8
104.2
99.9
91.5
95.7
91.4
86.2
91.5
115.5
113.9
131.9
121.2
105.2
107.5
113.8
100.5
104.8
103.8
93.1
106.2
117.5
109.9
123.6
131.7
111
122
110.9
108
103.6
107.3
94.4
85.2
113.2
111.7
124.3
124
133.4
112.6
115.8
112.3
103.6
111.4
95.1
93.4
117.3
121.5
123.1
139.3
125.8
108.6
121
111.6
99.7
116.7
90.3
90.4
117.3
121.6
114.6
133.3
127.4
115
112.6
108.3
107.6
109
89
102.5
124.5
124.2
130.8
138.7
127.6
130.9
136.9
125.2
131.3
124.1
103.2
118.1
136.5
117.8
145.1
158.8
136.9
132.7




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310146&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]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310146&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310146&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 time3 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.777825822284906
beta0.0419849844758403
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.777825822284906 \tabularnewline
beta & 0.0419849844758403 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310146&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]0.777825822284906[/C][/ROW]
[ROW][C]beta[/C][C]0.0419849844758403[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310146&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310146&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
alpha0.777825822284906
beta0.0419849844758403
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
377.270.56.7
471.183.4302349433016-12.3302349433016
590.181.15559319845338.94440680154668
691.595.7210147009064-4.22101470090637
776.199.9081856989835-23.8081856989835
887.888.0824452680828-0.282445268082753
98194.5464094161559-13.5464094161559
1077.290.2509345829649-13.0509345829649
1173.885.9146484324318-12.1146484324318
1268.981.911001691509-13.011001691509
1368.476.7852478915353-8.38524789153531
1465.274.9836877617769-9.78368776177693
1578.771.77487904915766.92512095084243
167781.7887669228591-4.78876692285911
1797.682.534903543349715.0650964566503
1888.199.2158687039576-11.1158687039576
1998.795.16959212964133.53040787035874
2093.4102.630860222889-9.23086022288864
216899.8646322189757-31.8646322189757
2287.978.45266844475589.44733155524423
2375.889.4827384179537-13.6827384179537
2466.382.0748054368065-15.7748054368065
2568.472.5244508052611-4.12445080526111
2671.371.9013506340353-0.601350634035313
2777.473.99897043977863.40102956022137
2887.179.32081235081997.77918764918012
2988.588.30214364802610.19785635197394
3085.991.3929810908588-5.49298109085879
3192.789.87795390887742.82204609112257
3288.594.9227291555576-6.4227291555576
3380.292.5669323955306-12.3669323955306
3481.885.183713888558-3.38371388855805
3570.484.6773727419104-14.2773727419104
3682.275.23140620589336.96859379410671
3772.882.5386744638809-9.73867446388087
386976.5325621095882-7.53256210958824
398371.996429992296611.0035700077034
4092.482.237523722687610.1624762773124
4192.392.15626906996640.14373093003357
42100.594.28686940094646.21313059905363
43106.9101.3413077577535.55869224224658
4499.5108.0682373023-8.56823730229956
4585.9103.527063288446-17.6270632884457
4692.691.36405340773951.23594659226053
4777.493.9135420123959-16.5135420123959
4884.182.1177372227181.98226277728202
4975.384.7731817679672-9.47318176796716
5073.878.2089199951097-4.40891999510971
51100.175.43978967734224.660210322658
5290.796.0867081657206-5.38670816572061
5396.593.1864438178513.31355618214901
54111.897.16168056151114.638319438489
5597.4110.423654269386-13.0236542693864
56100.8101.744116988359-0.944116988358786
5793.7102.429523692489-8.72952369248878
588296.7741599256413-14.7741599256413
598685.93464219467980.0653578053201613
6084.386.6398189352949-2.33981893529486
6173.185.3977756210594-12.2977756210594
6275.476.0085679385915-0.608567938591449
6397.975.6916538273422.20834617266
6497.593.84758277031233.65241722968773
6510697.68950803295748.31049196704255
66112.8105.4259998867817.37400011321851
6799.5112.674876953451-13.1748769534514
68100.8103.510054795195-2.71005479519522
69102.9102.3965392640540.503460735946319
7088.8103.799020613156-14.9990206131558
7191.392.6534485671741-1.35344856717414
7288.392.0775552416811-3.77755524168113
7377.489.4927655080902-12.0927655080902
7480.580.0452770070070.454722992993027
7596.780.372398957978416.3276010420216
7693.893.57906587953160.220934120468442
7710594.264766405251610.7352335947484
78117.1103.47934114327313.6206588567275
79111.1115.383084083723-4.28308408372305
80105.8113.220960750888-7.42096075088753
8195.7108.375769566294-12.6757695662939
8297.199.0292997228694-1.92929972286939
839197.9787064712283-6.97870647122835
8490.992.7726506108564-1.8726506108564
8583.591.4770616882112-7.97706168821124
8682.385.1727972557336-2.8727972557336
87101.782.744944548051718.9550554519483
88108.397.914374663499810.3856253365002
89114106.7574441721927.24255582780758
90118.2113.3922732382024.80772676179829
91103.4118.290235341071-14.8902353410714
92106.8107.38034338286-0.580343382859965
9395.4107.582102627054-12.182102627054
94101.898.36188295988333.43811704011672
9595.6101.403752105223-5.80375210522298
9694.897.0675236211935-2.26752362119349
979495.4078144351399-1.40781443513985
9882.494.3708342505033-11.9708342505033
9995.884.726732897316811.0732671026832
100106.793.368548367942213.3314516320578
101114.1104.2022033605859.89779663941475
102103.9112.688305230203-8.78830523020325
103117.4106.35287481929611.0471251807044
104105.9115.806720401201-9.90672040120147
105101.7108.638599994926-6.93859999492632
10698.7103.552566389065-4.85256638906517
10791.399.9306333028095-8.63063330280953
108102.393.08817157716569.21182842283442
10980.5100.424868042399-19.9248680423987
11086.784.44760310414592.2523968958541
111102.685.793944039375316.8060559606246
112107.399.00933225868648.2906677413136
113108105.8719800127282.12801998727225
114124.3108.01065596955116.2893440304494
115117.1121.696336635548-4.59633663554774
116103.9118.986492974709-15.0864929747089
117104.7107.624455155848-2.92445515584787
11895.9105.626860457241-9.72686045724066
11994.298.0205291302607-3.82052913026068
120102.794.88352778518557.81647221481452
12170.3101.05334915305-30.7533491530503
12290.276.218255220754313.9817447792457
123107.386.635874421531720.6641255784683
124104.6102.9260504161421.67394958385846
125102.7104.499843332462-1.79984333246182
126124.5103.31285292435821.187147075642
127117.8120.697646001836-2.89764600183587
128104.2119.254036659079-15.0540366590794
12999.9107.863253005783-7.96325300578316
13091.5101.727807984445-10.2278079844447
13195.793.49692404748022.20307595251975
13291.495.0070484930722-3.60704849307223
13386.291.8801127132552-5.68011271325524
13491.586.95519858202994.54480141797008
135115.590.131906295682425.3680937043176
136113.9110.333954419453.56604558055005
137131.9113.69426290246918.2057370975306
138121.2129.036246326443-7.83624632644323
139105.2123.866194243695-18.6661942436946
140107.5109.662747016787-2.16274701678716
141113.8108.2254783593855.57452164061544
142100.5112.988504239165-12.4885042391655
143104.8103.2938050147531.50619498524705
144103.8104.533732039474-0.733732039473978
14593.1104.007424493397-10.9074244933975
146106.295.21155243165410.988447568346
147117.5103.80570484897113.6942951510289
148109.9114.951750053492-5.05175005349183
149123.6111.35166220508912.2483377949109
150131.7121.60802344248210.0919765575179
151111130.516684956898-19.5166849568975
152122115.7576085024516.24239149754872
153110.9121.238464683291-10.3384646832909
154108113.484679477466-5.48467947746634
155103.6109.327180535034-5.72718053503424
156107.3104.7940254443052.50597455569529
15794.4106.746668605801-12.3466686058005
15885.296.7433371678007-11.5433371678007
159113.286.987886845675926.2121131543241
160111.7107.4556098283644.2443901716363
161124.3110.97487968968513.3251203103155
162124121.992534459652.00746554034968
163133.4124.2725829141679.12741708583307
164112.6132.388787640258-19.7887876402582
165115.8117.366979109552-1.56697910955178
166112.3116.467390938029-4.16739093802941
167103.6113.409040790735-9.80904079073538
168111.4105.6421358128475.75786418715279
16995.1110.171606099789-15.0716060997885
17093.498.0071830161635-4.6071830161635
171117.393.831801623162723.4681983768373
172121.5112.2605779215949.23942207840572
173123.1119.9235764492813.1764235507186
174139.3122.9743506416716.3256493583304
175125.8136.786079024197-10.9860790241972
176108.6128.995267381132-20.3952673811318
177121113.2196977169587.78030228304168
178111.6119.613895066297-8.01389506629721
17999.7113.461248063218-13.7612480632176
180116.7102.38876034152814.3112396584719
18190.3113.61914069168-23.31914069168
18290.494.8181062072024-4.41810620720241
183117.390.574502295824926.7254977041751
184121.6111.42797241984810.1720275801518
185114.6119.737913989278-5.13791398927762
186133.3115.97159878511617.3284012148835
187127.4130.246057364735-2.84605736473463
188115128.735357400709-13.7353574007088
189112.6118.306123045772-5.7061230457725
190108.3113.935889616027-5.63588961602672
191107.6109.43623428574-1.83623428574035
192109107.8320830747481.16791692525247
19389108.602778918667-19.6027789186669
194102.592.57732313775769.9226768622424
195124.599.84157418660424.658425813396
196124.2119.3729416172594.827058382741
197130.8123.6365966392267.1634033607739
198138.7129.9514564147698.74854358523052
199127.6137.784980421087-10.1849804210866
200130.9130.5589095911540.341090408846156
201136.9131.5314274511555.36857254884509
202125.2136.589772241689-11.3897722416886
203131.3128.2410878655083.05891213449181
204124.1131.230858204261-7.13085820426099
205103.2126.061889577824-22.8618895778238
206118.1107.91031769392210.1896823060782
207136.5115.79987639519220.7001236048081
208117.8132.540731783809-14.7407317838089
209145.1121.23338653464323.8666134653571
210158.8140.73524346717318.0647565328269
211136.9156.314207106123-19.4142071061234
212132.7142.107055174258-9.40705517425769

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 77.2 & 70.5 & 6.7 \tabularnewline
4 & 71.1 & 83.4302349433016 & -12.3302349433016 \tabularnewline
5 & 90.1 & 81.1555931984533 & 8.94440680154668 \tabularnewline
6 & 91.5 & 95.7210147009064 & -4.22101470090637 \tabularnewline
7 & 76.1 & 99.9081856989835 & -23.8081856989835 \tabularnewline
8 & 87.8 & 88.0824452680828 & -0.282445268082753 \tabularnewline
9 & 81 & 94.5464094161559 & -13.5464094161559 \tabularnewline
10 & 77.2 & 90.2509345829649 & -13.0509345829649 \tabularnewline
11 & 73.8 & 85.9146484324318 & -12.1146484324318 \tabularnewline
12 & 68.9 & 81.911001691509 & -13.011001691509 \tabularnewline
13 & 68.4 & 76.7852478915353 & -8.38524789153531 \tabularnewline
14 & 65.2 & 74.9836877617769 & -9.78368776177693 \tabularnewline
15 & 78.7 & 71.7748790491576 & 6.92512095084243 \tabularnewline
16 & 77 & 81.7887669228591 & -4.78876692285911 \tabularnewline
17 & 97.6 & 82.5349035433497 & 15.0650964566503 \tabularnewline
18 & 88.1 & 99.2158687039576 & -11.1158687039576 \tabularnewline
19 & 98.7 & 95.1695921296413 & 3.53040787035874 \tabularnewline
20 & 93.4 & 102.630860222889 & -9.23086022288864 \tabularnewline
21 & 68 & 99.8646322189757 & -31.8646322189757 \tabularnewline
22 & 87.9 & 78.4526684447558 & 9.44733155524423 \tabularnewline
23 & 75.8 & 89.4827384179537 & -13.6827384179537 \tabularnewline
24 & 66.3 & 82.0748054368065 & -15.7748054368065 \tabularnewline
25 & 68.4 & 72.5244508052611 & -4.12445080526111 \tabularnewline
26 & 71.3 & 71.9013506340353 & -0.601350634035313 \tabularnewline
27 & 77.4 & 73.9989704397786 & 3.40102956022137 \tabularnewline
28 & 87.1 & 79.3208123508199 & 7.77918764918012 \tabularnewline
29 & 88.5 & 88.3021436480261 & 0.19785635197394 \tabularnewline
30 & 85.9 & 91.3929810908588 & -5.49298109085879 \tabularnewline
31 & 92.7 & 89.8779539088774 & 2.82204609112257 \tabularnewline
32 & 88.5 & 94.9227291555576 & -6.4227291555576 \tabularnewline
33 & 80.2 & 92.5669323955306 & -12.3669323955306 \tabularnewline
34 & 81.8 & 85.183713888558 & -3.38371388855805 \tabularnewline
35 & 70.4 & 84.6773727419104 & -14.2773727419104 \tabularnewline
36 & 82.2 & 75.2314062058933 & 6.96859379410671 \tabularnewline
37 & 72.8 & 82.5386744638809 & -9.73867446388087 \tabularnewline
38 & 69 & 76.5325621095882 & -7.53256210958824 \tabularnewline
39 & 83 & 71.9964299922966 & 11.0035700077034 \tabularnewline
40 & 92.4 & 82.2375237226876 & 10.1624762773124 \tabularnewline
41 & 92.3 & 92.1562690699664 & 0.14373093003357 \tabularnewline
42 & 100.5 & 94.2868694009464 & 6.21313059905363 \tabularnewline
43 & 106.9 & 101.341307757753 & 5.55869224224658 \tabularnewline
44 & 99.5 & 108.0682373023 & -8.56823730229956 \tabularnewline
45 & 85.9 & 103.527063288446 & -17.6270632884457 \tabularnewline
46 & 92.6 & 91.3640534077395 & 1.23594659226053 \tabularnewline
47 & 77.4 & 93.9135420123959 & -16.5135420123959 \tabularnewline
48 & 84.1 & 82.117737222718 & 1.98226277728202 \tabularnewline
49 & 75.3 & 84.7731817679672 & -9.47318176796716 \tabularnewline
50 & 73.8 & 78.2089199951097 & -4.40891999510971 \tabularnewline
51 & 100.1 & 75.439789677342 & 24.660210322658 \tabularnewline
52 & 90.7 & 96.0867081657206 & -5.38670816572061 \tabularnewline
53 & 96.5 & 93.186443817851 & 3.31355618214901 \tabularnewline
54 & 111.8 & 97.161680561511 & 14.638319438489 \tabularnewline
55 & 97.4 & 110.423654269386 & -13.0236542693864 \tabularnewline
56 & 100.8 & 101.744116988359 & -0.944116988358786 \tabularnewline
57 & 93.7 & 102.429523692489 & -8.72952369248878 \tabularnewline
58 & 82 & 96.7741599256413 & -14.7741599256413 \tabularnewline
59 & 86 & 85.9346421946798 & 0.0653578053201613 \tabularnewline
60 & 84.3 & 86.6398189352949 & -2.33981893529486 \tabularnewline
61 & 73.1 & 85.3977756210594 & -12.2977756210594 \tabularnewline
62 & 75.4 & 76.0085679385915 & -0.608567938591449 \tabularnewline
63 & 97.9 & 75.69165382734 & 22.20834617266 \tabularnewline
64 & 97.5 & 93.8475827703123 & 3.65241722968773 \tabularnewline
65 & 106 & 97.6895080329574 & 8.31049196704255 \tabularnewline
66 & 112.8 & 105.425999886781 & 7.37400011321851 \tabularnewline
67 & 99.5 & 112.674876953451 & -13.1748769534514 \tabularnewline
68 & 100.8 & 103.510054795195 & -2.71005479519522 \tabularnewline
69 & 102.9 & 102.396539264054 & 0.503460735946319 \tabularnewline
70 & 88.8 & 103.799020613156 & -14.9990206131558 \tabularnewline
71 & 91.3 & 92.6534485671741 & -1.35344856717414 \tabularnewline
72 & 88.3 & 92.0775552416811 & -3.77755524168113 \tabularnewline
73 & 77.4 & 89.4927655080902 & -12.0927655080902 \tabularnewline
74 & 80.5 & 80.045277007007 & 0.454722992993027 \tabularnewline
75 & 96.7 & 80.3723989579784 & 16.3276010420216 \tabularnewline
76 & 93.8 & 93.5790658795316 & 0.220934120468442 \tabularnewline
77 & 105 & 94.2647664052516 & 10.7352335947484 \tabularnewline
78 & 117.1 & 103.479341143273 & 13.6206588567275 \tabularnewline
79 & 111.1 & 115.383084083723 & -4.28308408372305 \tabularnewline
80 & 105.8 & 113.220960750888 & -7.42096075088753 \tabularnewline
81 & 95.7 & 108.375769566294 & -12.6757695662939 \tabularnewline
82 & 97.1 & 99.0292997228694 & -1.92929972286939 \tabularnewline
83 & 91 & 97.9787064712283 & -6.97870647122835 \tabularnewline
84 & 90.9 & 92.7726506108564 & -1.8726506108564 \tabularnewline
85 & 83.5 & 91.4770616882112 & -7.97706168821124 \tabularnewline
86 & 82.3 & 85.1727972557336 & -2.8727972557336 \tabularnewline
87 & 101.7 & 82.7449445480517 & 18.9550554519483 \tabularnewline
88 & 108.3 & 97.9143746634998 & 10.3856253365002 \tabularnewline
89 & 114 & 106.757444172192 & 7.24255582780758 \tabularnewline
90 & 118.2 & 113.392273238202 & 4.80772676179829 \tabularnewline
91 & 103.4 & 118.290235341071 & -14.8902353410714 \tabularnewline
92 & 106.8 & 107.38034338286 & -0.580343382859965 \tabularnewline
93 & 95.4 & 107.582102627054 & -12.182102627054 \tabularnewline
94 & 101.8 & 98.3618829598833 & 3.43811704011672 \tabularnewline
95 & 95.6 & 101.403752105223 & -5.80375210522298 \tabularnewline
96 & 94.8 & 97.0675236211935 & -2.26752362119349 \tabularnewline
97 & 94 & 95.4078144351399 & -1.40781443513985 \tabularnewline
98 & 82.4 & 94.3708342505033 & -11.9708342505033 \tabularnewline
99 & 95.8 & 84.7267328973168 & 11.0732671026832 \tabularnewline
100 & 106.7 & 93.3685483679422 & 13.3314516320578 \tabularnewline
101 & 114.1 & 104.202203360585 & 9.89779663941475 \tabularnewline
102 & 103.9 & 112.688305230203 & -8.78830523020325 \tabularnewline
103 & 117.4 & 106.352874819296 & 11.0471251807044 \tabularnewline
104 & 105.9 & 115.806720401201 & -9.90672040120147 \tabularnewline
105 & 101.7 & 108.638599994926 & -6.93859999492632 \tabularnewline
106 & 98.7 & 103.552566389065 & -4.85256638906517 \tabularnewline
107 & 91.3 & 99.9306333028095 & -8.63063330280953 \tabularnewline
108 & 102.3 & 93.0881715771656 & 9.21182842283442 \tabularnewline
109 & 80.5 & 100.424868042399 & -19.9248680423987 \tabularnewline
110 & 86.7 & 84.4476031041459 & 2.2523968958541 \tabularnewline
111 & 102.6 & 85.7939440393753 & 16.8060559606246 \tabularnewline
112 & 107.3 & 99.0093322586864 & 8.2906677413136 \tabularnewline
113 & 108 & 105.871980012728 & 2.12801998727225 \tabularnewline
114 & 124.3 & 108.010655969551 & 16.2893440304494 \tabularnewline
115 & 117.1 & 121.696336635548 & -4.59633663554774 \tabularnewline
116 & 103.9 & 118.986492974709 & -15.0864929747089 \tabularnewline
117 & 104.7 & 107.624455155848 & -2.92445515584787 \tabularnewline
118 & 95.9 & 105.626860457241 & -9.72686045724066 \tabularnewline
119 & 94.2 & 98.0205291302607 & -3.82052913026068 \tabularnewline
120 & 102.7 & 94.8835277851855 & 7.81647221481452 \tabularnewline
121 & 70.3 & 101.05334915305 & -30.7533491530503 \tabularnewline
122 & 90.2 & 76.2182552207543 & 13.9817447792457 \tabularnewline
123 & 107.3 & 86.6358744215317 & 20.6641255784683 \tabularnewline
124 & 104.6 & 102.926050416142 & 1.67394958385846 \tabularnewline
125 & 102.7 & 104.499843332462 & -1.79984333246182 \tabularnewline
126 & 124.5 & 103.312852924358 & 21.187147075642 \tabularnewline
127 & 117.8 & 120.697646001836 & -2.89764600183587 \tabularnewline
128 & 104.2 & 119.254036659079 & -15.0540366590794 \tabularnewline
129 & 99.9 & 107.863253005783 & -7.96325300578316 \tabularnewline
130 & 91.5 & 101.727807984445 & -10.2278079844447 \tabularnewline
131 & 95.7 & 93.4969240474802 & 2.20307595251975 \tabularnewline
132 & 91.4 & 95.0070484930722 & -3.60704849307223 \tabularnewline
133 & 86.2 & 91.8801127132552 & -5.68011271325524 \tabularnewline
134 & 91.5 & 86.9551985820299 & 4.54480141797008 \tabularnewline
135 & 115.5 & 90.1319062956824 & 25.3680937043176 \tabularnewline
136 & 113.9 & 110.33395441945 & 3.56604558055005 \tabularnewline
137 & 131.9 & 113.694262902469 & 18.2057370975306 \tabularnewline
138 & 121.2 & 129.036246326443 & -7.83624632644323 \tabularnewline
139 & 105.2 & 123.866194243695 & -18.6661942436946 \tabularnewline
140 & 107.5 & 109.662747016787 & -2.16274701678716 \tabularnewline
141 & 113.8 & 108.225478359385 & 5.57452164061544 \tabularnewline
142 & 100.5 & 112.988504239165 & -12.4885042391655 \tabularnewline
143 & 104.8 & 103.293805014753 & 1.50619498524705 \tabularnewline
144 & 103.8 & 104.533732039474 & -0.733732039473978 \tabularnewline
145 & 93.1 & 104.007424493397 & -10.9074244933975 \tabularnewline
146 & 106.2 & 95.211552431654 & 10.988447568346 \tabularnewline
147 & 117.5 & 103.805704848971 & 13.6942951510289 \tabularnewline
148 & 109.9 & 114.951750053492 & -5.05175005349183 \tabularnewline
149 & 123.6 & 111.351662205089 & 12.2483377949109 \tabularnewline
150 & 131.7 & 121.608023442482 & 10.0919765575179 \tabularnewline
151 & 111 & 130.516684956898 & -19.5166849568975 \tabularnewline
152 & 122 & 115.757608502451 & 6.24239149754872 \tabularnewline
153 & 110.9 & 121.238464683291 & -10.3384646832909 \tabularnewline
154 & 108 & 113.484679477466 & -5.48467947746634 \tabularnewline
155 & 103.6 & 109.327180535034 & -5.72718053503424 \tabularnewline
156 & 107.3 & 104.794025444305 & 2.50597455569529 \tabularnewline
157 & 94.4 & 106.746668605801 & -12.3466686058005 \tabularnewline
158 & 85.2 & 96.7433371678007 & -11.5433371678007 \tabularnewline
159 & 113.2 & 86.9878868456759 & 26.2121131543241 \tabularnewline
160 & 111.7 & 107.455609828364 & 4.2443901716363 \tabularnewline
161 & 124.3 & 110.974879689685 & 13.3251203103155 \tabularnewline
162 & 124 & 121.99253445965 & 2.00746554034968 \tabularnewline
163 & 133.4 & 124.272582914167 & 9.12741708583307 \tabularnewline
164 & 112.6 & 132.388787640258 & -19.7887876402582 \tabularnewline
165 & 115.8 & 117.366979109552 & -1.56697910955178 \tabularnewline
166 & 112.3 & 116.467390938029 & -4.16739093802941 \tabularnewline
167 & 103.6 & 113.409040790735 & -9.80904079073538 \tabularnewline
168 & 111.4 & 105.642135812847 & 5.75786418715279 \tabularnewline
169 & 95.1 & 110.171606099789 & -15.0716060997885 \tabularnewline
170 & 93.4 & 98.0071830161635 & -4.6071830161635 \tabularnewline
171 & 117.3 & 93.8318016231627 & 23.4681983768373 \tabularnewline
172 & 121.5 & 112.260577921594 & 9.23942207840572 \tabularnewline
173 & 123.1 & 119.923576449281 & 3.1764235507186 \tabularnewline
174 & 139.3 & 122.97435064167 & 16.3256493583304 \tabularnewline
175 & 125.8 & 136.786079024197 & -10.9860790241972 \tabularnewline
176 & 108.6 & 128.995267381132 & -20.3952673811318 \tabularnewline
177 & 121 & 113.219697716958 & 7.78030228304168 \tabularnewline
178 & 111.6 & 119.613895066297 & -8.01389506629721 \tabularnewline
179 & 99.7 & 113.461248063218 & -13.7612480632176 \tabularnewline
180 & 116.7 & 102.388760341528 & 14.3112396584719 \tabularnewline
181 & 90.3 & 113.61914069168 & -23.31914069168 \tabularnewline
182 & 90.4 & 94.8181062072024 & -4.41810620720241 \tabularnewline
183 & 117.3 & 90.5745022958249 & 26.7254977041751 \tabularnewline
184 & 121.6 & 111.427972419848 & 10.1720275801518 \tabularnewline
185 & 114.6 & 119.737913989278 & -5.13791398927762 \tabularnewline
186 & 133.3 & 115.971598785116 & 17.3284012148835 \tabularnewline
187 & 127.4 & 130.246057364735 & -2.84605736473463 \tabularnewline
188 & 115 & 128.735357400709 & -13.7353574007088 \tabularnewline
189 & 112.6 & 118.306123045772 & -5.7061230457725 \tabularnewline
190 & 108.3 & 113.935889616027 & -5.63588961602672 \tabularnewline
191 & 107.6 & 109.43623428574 & -1.83623428574035 \tabularnewline
192 & 109 & 107.832083074748 & 1.16791692525247 \tabularnewline
193 & 89 & 108.602778918667 & -19.6027789186669 \tabularnewline
194 & 102.5 & 92.5773231377576 & 9.9226768622424 \tabularnewline
195 & 124.5 & 99.841574186604 & 24.658425813396 \tabularnewline
196 & 124.2 & 119.372941617259 & 4.827058382741 \tabularnewline
197 & 130.8 & 123.636596639226 & 7.1634033607739 \tabularnewline
198 & 138.7 & 129.951456414769 & 8.74854358523052 \tabularnewline
199 & 127.6 & 137.784980421087 & -10.1849804210866 \tabularnewline
200 & 130.9 & 130.558909591154 & 0.341090408846156 \tabularnewline
201 & 136.9 & 131.531427451155 & 5.36857254884509 \tabularnewline
202 & 125.2 & 136.589772241689 & -11.3897722416886 \tabularnewline
203 & 131.3 & 128.241087865508 & 3.05891213449181 \tabularnewline
204 & 124.1 & 131.230858204261 & -7.13085820426099 \tabularnewline
205 & 103.2 & 126.061889577824 & -22.8618895778238 \tabularnewline
206 & 118.1 & 107.910317693922 & 10.1896823060782 \tabularnewline
207 & 136.5 & 115.799876395192 & 20.7001236048081 \tabularnewline
208 & 117.8 & 132.540731783809 & -14.7407317838089 \tabularnewline
209 & 145.1 & 121.233386534643 & 23.8666134653571 \tabularnewline
210 & 158.8 & 140.735243467173 & 18.0647565328269 \tabularnewline
211 & 136.9 & 156.314207106123 & -19.4142071061234 \tabularnewline
212 & 132.7 & 142.107055174258 & -9.40705517425769 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310146&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]77.2[/C][C]70.5[/C][C]6.7[/C][/ROW]
[ROW][C]4[/C][C]71.1[/C][C]83.4302349433016[/C][C]-12.3302349433016[/C][/ROW]
[ROW][C]5[/C][C]90.1[/C][C]81.1555931984533[/C][C]8.94440680154668[/C][/ROW]
[ROW][C]6[/C][C]91.5[/C][C]95.7210147009064[/C][C]-4.22101470090637[/C][/ROW]
[ROW][C]7[/C][C]76.1[/C][C]99.9081856989835[/C][C]-23.8081856989835[/C][/ROW]
[ROW][C]8[/C][C]87.8[/C][C]88.0824452680828[/C][C]-0.282445268082753[/C][/ROW]
[ROW][C]9[/C][C]81[/C][C]94.5464094161559[/C][C]-13.5464094161559[/C][/ROW]
[ROW][C]10[/C][C]77.2[/C][C]90.2509345829649[/C][C]-13.0509345829649[/C][/ROW]
[ROW][C]11[/C][C]73.8[/C][C]85.9146484324318[/C][C]-12.1146484324318[/C][/ROW]
[ROW][C]12[/C][C]68.9[/C][C]81.911001691509[/C][C]-13.011001691509[/C][/ROW]
[ROW][C]13[/C][C]68.4[/C][C]76.7852478915353[/C][C]-8.38524789153531[/C][/ROW]
[ROW][C]14[/C][C]65.2[/C][C]74.9836877617769[/C][C]-9.78368776177693[/C][/ROW]
[ROW][C]15[/C][C]78.7[/C][C]71.7748790491576[/C][C]6.92512095084243[/C][/ROW]
[ROW][C]16[/C][C]77[/C][C]81.7887669228591[/C][C]-4.78876692285911[/C][/ROW]
[ROW][C]17[/C][C]97.6[/C][C]82.5349035433497[/C][C]15.0650964566503[/C][/ROW]
[ROW][C]18[/C][C]88.1[/C][C]99.2158687039576[/C][C]-11.1158687039576[/C][/ROW]
[ROW][C]19[/C][C]98.7[/C][C]95.1695921296413[/C][C]3.53040787035874[/C][/ROW]
[ROW][C]20[/C][C]93.4[/C][C]102.630860222889[/C][C]-9.23086022288864[/C][/ROW]
[ROW][C]21[/C][C]68[/C][C]99.8646322189757[/C][C]-31.8646322189757[/C][/ROW]
[ROW][C]22[/C][C]87.9[/C][C]78.4526684447558[/C][C]9.44733155524423[/C][/ROW]
[ROW][C]23[/C][C]75.8[/C][C]89.4827384179537[/C][C]-13.6827384179537[/C][/ROW]
[ROW][C]24[/C][C]66.3[/C][C]82.0748054368065[/C][C]-15.7748054368065[/C][/ROW]
[ROW][C]25[/C][C]68.4[/C][C]72.5244508052611[/C][C]-4.12445080526111[/C][/ROW]
[ROW][C]26[/C][C]71.3[/C][C]71.9013506340353[/C][C]-0.601350634035313[/C][/ROW]
[ROW][C]27[/C][C]77.4[/C][C]73.9989704397786[/C][C]3.40102956022137[/C][/ROW]
[ROW][C]28[/C][C]87.1[/C][C]79.3208123508199[/C][C]7.77918764918012[/C][/ROW]
[ROW][C]29[/C][C]88.5[/C][C]88.3021436480261[/C][C]0.19785635197394[/C][/ROW]
[ROW][C]30[/C][C]85.9[/C][C]91.3929810908588[/C][C]-5.49298109085879[/C][/ROW]
[ROW][C]31[/C][C]92.7[/C][C]89.8779539088774[/C][C]2.82204609112257[/C][/ROW]
[ROW][C]32[/C][C]88.5[/C][C]94.9227291555576[/C][C]-6.4227291555576[/C][/ROW]
[ROW][C]33[/C][C]80.2[/C][C]92.5669323955306[/C][C]-12.3669323955306[/C][/ROW]
[ROW][C]34[/C][C]81.8[/C][C]85.183713888558[/C][C]-3.38371388855805[/C][/ROW]
[ROW][C]35[/C][C]70.4[/C][C]84.6773727419104[/C][C]-14.2773727419104[/C][/ROW]
[ROW][C]36[/C][C]82.2[/C][C]75.2314062058933[/C][C]6.96859379410671[/C][/ROW]
[ROW][C]37[/C][C]72.8[/C][C]82.5386744638809[/C][C]-9.73867446388087[/C][/ROW]
[ROW][C]38[/C][C]69[/C][C]76.5325621095882[/C][C]-7.53256210958824[/C][/ROW]
[ROW][C]39[/C][C]83[/C][C]71.9964299922966[/C][C]11.0035700077034[/C][/ROW]
[ROW][C]40[/C][C]92.4[/C][C]82.2375237226876[/C][C]10.1624762773124[/C][/ROW]
[ROW][C]41[/C][C]92.3[/C][C]92.1562690699664[/C][C]0.14373093003357[/C][/ROW]
[ROW][C]42[/C][C]100.5[/C][C]94.2868694009464[/C][C]6.21313059905363[/C][/ROW]
[ROW][C]43[/C][C]106.9[/C][C]101.341307757753[/C][C]5.55869224224658[/C][/ROW]
[ROW][C]44[/C][C]99.5[/C][C]108.0682373023[/C][C]-8.56823730229956[/C][/ROW]
[ROW][C]45[/C][C]85.9[/C][C]103.527063288446[/C][C]-17.6270632884457[/C][/ROW]
[ROW][C]46[/C][C]92.6[/C][C]91.3640534077395[/C][C]1.23594659226053[/C][/ROW]
[ROW][C]47[/C][C]77.4[/C][C]93.9135420123959[/C][C]-16.5135420123959[/C][/ROW]
[ROW][C]48[/C][C]84.1[/C][C]82.117737222718[/C][C]1.98226277728202[/C][/ROW]
[ROW][C]49[/C][C]75.3[/C][C]84.7731817679672[/C][C]-9.47318176796716[/C][/ROW]
[ROW][C]50[/C][C]73.8[/C][C]78.2089199951097[/C][C]-4.40891999510971[/C][/ROW]
[ROW][C]51[/C][C]100.1[/C][C]75.439789677342[/C][C]24.660210322658[/C][/ROW]
[ROW][C]52[/C][C]90.7[/C][C]96.0867081657206[/C][C]-5.38670816572061[/C][/ROW]
[ROW][C]53[/C][C]96.5[/C][C]93.186443817851[/C][C]3.31355618214901[/C][/ROW]
[ROW][C]54[/C][C]111.8[/C][C]97.161680561511[/C][C]14.638319438489[/C][/ROW]
[ROW][C]55[/C][C]97.4[/C][C]110.423654269386[/C][C]-13.0236542693864[/C][/ROW]
[ROW][C]56[/C][C]100.8[/C][C]101.744116988359[/C][C]-0.944116988358786[/C][/ROW]
[ROW][C]57[/C][C]93.7[/C][C]102.429523692489[/C][C]-8.72952369248878[/C][/ROW]
[ROW][C]58[/C][C]82[/C][C]96.7741599256413[/C][C]-14.7741599256413[/C][/ROW]
[ROW][C]59[/C][C]86[/C][C]85.9346421946798[/C][C]0.0653578053201613[/C][/ROW]
[ROW][C]60[/C][C]84.3[/C][C]86.6398189352949[/C][C]-2.33981893529486[/C][/ROW]
[ROW][C]61[/C][C]73.1[/C][C]85.3977756210594[/C][C]-12.2977756210594[/C][/ROW]
[ROW][C]62[/C][C]75.4[/C][C]76.0085679385915[/C][C]-0.608567938591449[/C][/ROW]
[ROW][C]63[/C][C]97.9[/C][C]75.69165382734[/C][C]22.20834617266[/C][/ROW]
[ROW][C]64[/C][C]97.5[/C][C]93.8475827703123[/C][C]3.65241722968773[/C][/ROW]
[ROW][C]65[/C][C]106[/C][C]97.6895080329574[/C][C]8.31049196704255[/C][/ROW]
[ROW][C]66[/C][C]112.8[/C][C]105.425999886781[/C][C]7.37400011321851[/C][/ROW]
[ROW][C]67[/C][C]99.5[/C][C]112.674876953451[/C][C]-13.1748769534514[/C][/ROW]
[ROW][C]68[/C][C]100.8[/C][C]103.510054795195[/C][C]-2.71005479519522[/C][/ROW]
[ROW][C]69[/C][C]102.9[/C][C]102.396539264054[/C][C]0.503460735946319[/C][/ROW]
[ROW][C]70[/C][C]88.8[/C][C]103.799020613156[/C][C]-14.9990206131558[/C][/ROW]
[ROW][C]71[/C][C]91.3[/C][C]92.6534485671741[/C][C]-1.35344856717414[/C][/ROW]
[ROW][C]72[/C][C]88.3[/C][C]92.0775552416811[/C][C]-3.77755524168113[/C][/ROW]
[ROW][C]73[/C][C]77.4[/C][C]89.4927655080902[/C][C]-12.0927655080902[/C][/ROW]
[ROW][C]74[/C][C]80.5[/C][C]80.045277007007[/C][C]0.454722992993027[/C][/ROW]
[ROW][C]75[/C][C]96.7[/C][C]80.3723989579784[/C][C]16.3276010420216[/C][/ROW]
[ROW][C]76[/C][C]93.8[/C][C]93.5790658795316[/C][C]0.220934120468442[/C][/ROW]
[ROW][C]77[/C][C]105[/C][C]94.2647664052516[/C][C]10.7352335947484[/C][/ROW]
[ROW][C]78[/C][C]117.1[/C][C]103.479341143273[/C][C]13.6206588567275[/C][/ROW]
[ROW][C]79[/C][C]111.1[/C][C]115.383084083723[/C][C]-4.28308408372305[/C][/ROW]
[ROW][C]80[/C][C]105.8[/C][C]113.220960750888[/C][C]-7.42096075088753[/C][/ROW]
[ROW][C]81[/C][C]95.7[/C][C]108.375769566294[/C][C]-12.6757695662939[/C][/ROW]
[ROW][C]82[/C][C]97.1[/C][C]99.0292997228694[/C][C]-1.92929972286939[/C][/ROW]
[ROW][C]83[/C][C]91[/C][C]97.9787064712283[/C][C]-6.97870647122835[/C][/ROW]
[ROW][C]84[/C][C]90.9[/C][C]92.7726506108564[/C][C]-1.8726506108564[/C][/ROW]
[ROW][C]85[/C][C]83.5[/C][C]91.4770616882112[/C][C]-7.97706168821124[/C][/ROW]
[ROW][C]86[/C][C]82.3[/C][C]85.1727972557336[/C][C]-2.8727972557336[/C][/ROW]
[ROW][C]87[/C][C]101.7[/C][C]82.7449445480517[/C][C]18.9550554519483[/C][/ROW]
[ROW][C]88[/C][C]108.3[/C][C]97.9143746634998[/C][C]10.3856253365002[/C][/ROW]
[ROW][C]89[/C][C]114[/C][C]106.757444172192[/C][C]7.24255582780758[/C][/ROW]
[ROW][C]90[/C][C]118.2[/C][C]113.392273238202[/C][C]4.80772676179829[/C][/ROW]
[ROW][C]91[/C][C]103.4[/C][C]118.290235341071[/C][C]-14.8902353410714[/C][/ROW]
[ROW][C]92[/C][C]106.8[/C][C]107.38034338286[/C][C]-0.580343382859965[/C][/ROW]
[ROW][C]93[/C][C]95.4[/C][C]107.582102627054[/C][C]-12.182102627054[/C][/ROW]
[ROW][C]94[/C][C]101.8[/C][C]98.3618829598833[/C][C]3.43811704011672[/C][/ROW]
[ROW][C]95[/C][C]95.6[/C][C]101.403752105223[/C][C]-5.80375210522298[/C][/ROW]
[ROW][C]96[/C][C]94.8[/C][C]97.0675236211935[/C][C]-2.26752362119349[/C][/ROW]
[ROW][C]97[/C][C]94[/C][C]95.4078144351399[/C][C]-1.40781443513985[/C][/ROW]
[ROW][C]98[/C][C]82.4[/C][C]94.3708342505033[/C][C]-11.9708342505033[/C][/ROW]
[ROW][C]99[/C][C]95.8[/C][C]84.7267328973168[/C][C]11.0732671026832[/C][/ROW]
[ROW][C]100[/C][C]106.7[/C][C]93.3685483679422[/C][C]13.3314516320578[/C][/ROW]
[ROW][C]101[/C][C]114.1[/C][C]104.202203360585[/C][C]9.89779663941475[/C][/ROW]
[ROW][C]102[/C][C]103.9[/C][C]112.688305230203[/C][C]-8.78830523020325[/C][/ROW]
[ROW][C]103[/C][C]117.4[/C][C]106.352874819296[/C][C]11.0471251807044[/C][/ROW]
[ROW][C]104[/C][C]105.9[/C][C]115.806720401201[/C][C]-9.90672040120147[/C][/ROW]
[ROW][C]105[/C][C]101.7[/C][C]108.638599994926[/C][C]-6.93859999492632[/C][/ROW]
[ROW][C]106[/C][C]98.7[/C][C]103.552566389065[/C][C]-4.85256638906517[/C][/ROW]
[ROW][C]107[/C][C]91.3[/C][C]99.9306333028095[/C][C]-8.63063330280953[/C][/ROW]
[ROW][C]108[/C][C]102.3[/C][C]93.0881715771656[/C][C]9.21182842283442[/C][/ROW]
[ROW][C]109[/C][C]80.5[/C][C]100.424868042399[/C][C]-19.9248680423987[/C][/ROW]
[ROW][C]110[/C][C]86.7[/C][C]84.4476031041459[/C][C]2.2523968958541[/C][/ROW]
[ROW][C]111[/C][C]102.6[/C][C]85.7939440393753[/C][C]16.8060559606246[/C][/ROW]
[ROW][C]112[/C][C]107.3[/C][C]99.0093322586864[/C][C]8.2906677413136[/C][/ROW]
[ROW][C]113[/C][C]108[/C][C]105.871980012728[/C][C]2.12801998727225[/C][/ROW]
[ROW][C]114[/C][C]124.3[/C][C]108.010655969551[/C][C]16.2893440304494[/C][/ROW]
[ROW][C]115[/C][C]117.1[/C][C]121.696336635548[/C][C]-4.59633663554774[/C][/ROW]
[ROW][C]116[/C][C]103.9[/C][C]118.986492974709[/C][C]-15.0864929747089[/C][/ROW]
[ROW][C]117[/C][C]104.7[/C][C]107.624455155848[/C][C]-2.92445515584787[/C][/ROW]
[ROW][C]118[/C][C]95.9[/C][C]105.626860457241[/C][C]-9.72686045724066[/C][/ROW]
[ROW][C]119[/C][C]94.2[/C][C]98.0205291302607[/C][C]-3.82052913026068[/C][/ROW]
[ROW][C]120[/C][C]102.7[/C][C]94.8835277851855[/C][C]7.81647221481452[/C][/ROW]
[ROW][C]121[/C][C]70.3[/C][C]101.05334915305[/C][C]-30.7533491530503[/C][/ROW]
[ROW][C]122[/C][C]90.2[/C][C]76.2182552207543[/C][C]13.9817447792457[/C][/ROW]
[ROW][C]123[/C][C]107.3[/C][C]86.6358744215317[/C][C]20.6641255784683[/C][/ROW]
[ROW][C]124[/C][C]104.6[/C][C]102.926050416142[/C][C]1.67394958385846[/C][/ROW]
[ROW][C]125[/C][C]102.7[/C][C]104.499843332462[/C][C]-1.79984333246182[/C][/ROW]
[ROW][C]126[/C][C]124.5[/C][C]103.312852924358[/C][C]21.187147075642[/C][/ROW]
[ROW][C]127[/C][C]117.8[/C][C]120.697646001836[/C][C]-2.89764600183587[/C][/ROW]
[ROW][C]128[/C][C]104.2[/C][C]119.254036659079[/C][C]-15.0540366590794[/C][/ROW]
[ROW][C]129[/C][C]99.9[/C][C]107.863253005783[/C][C]-7.96325300578316[/C][/ROW]
[ROW][C]130[/C][C]91.5[/C][C]101.727807984445[/C][C]-10.2278079844447[/C][/ROW]
[ROW][C]131[/C][C]95.7[/C][C]93.4969240474802[/C][C]2.20307595251975[/C][/ROW]
[ROW][C]132[/C][C]91.4[/C][C]95.0070484930722[/C][C]-3.60704849307223[/C][/ROW]
[ROW][C]133[/C][C]86.2[/C][C]91.8801127132552[/C][C]-5.68011271325524[/C][/ROW]
[ROW][C]134[/C][C]91.5[/C][C]86.9551985820299[/C][C]4.54480141797008[/C][/ROW]
[ROW][C]135[/C][C]115.5[/C][C]90.1319062956824[/C][C]25.3680937043176[/C][/ROW]
[ROW][C]136[/C][C]113.9[/C][C]110.33395441945[/C][C]3.56604558055005[/C][/ROW]
[ROW][C]137[/C][C]131.9[/C][C]113.694262902469[/C][C]18.2057370975306[/C][/ROW]
[ROW][C]138[/C][C]121.2[/C][C]129.036246326443[/C][C]-7.83624632644323[/C][/ROW]
[ROW][C]139[/C][C]105.2[/C][C]123.866194243695[/C][C]-18.6661942436946[/C][/ROW]
[ROW][C]140[/C][C]107.5[/C][C]109.662747016787[/C][C]-2.16274701678716[/C][/ROW]
[ROW][C]141[/C][C]113.8[/C][C]108.225478359385[/C][C]5.57452164061544[/C][/ROW]
[ROW][C]142[/C][C]100.5[/C][C]112.988504239165[/C][C]-12.4885042391655[/C][/ROW]
[ROW][C]143[/C][C]104.8[/C][C]103.293805014753[/C][C]1.50619498524705[/C][/ROW]
[ROW][C]144[/C][C]103.8[/C][C]104.533732039474[/C][C]-0.733732039473978[/C][/ROW]
[ROW][C]145[/C][C]93.1[/C][C]104.007424493397[/C][C]-10.9074244933975[/C][/ROW]
[ROW][C]146[/C][C]106.2[/C][C]95.211552431654[/C][C]10.988447568346[/C][/ROW]
[ROW][C]147[/C][C]117.5[/C][C]103.805704848971[/C][C]13.6942951510289[/C][/ROW]
[ROW][C]148[/C][C]109.9[/C][C]114.951750053492[/C][C]-5.05175005349183[/C][/ROW]
[ROW][C]149[/C][C]123.6[/C][C]111.351662205089[/C][C]12.2483377949109[/C][/ROW]
[ROW][C]150[/C][C]131.7[/C][C]121.608023442482[/C][C]10.0919765575179[/C][/ROW]
[ROW][C]151[/C][C]111[/C][C]130.516684956898[/C][C]-19.5166849568975[/C][/ROW]
[ROW][C]152[/C][C]122[/C][C]115.757608502451[/C][C]6.24239149754872[/C][/ROW]
[ROW][C]153[/C][C]110.9[/C][C]121.238464683291[/C][C]-10.3384646832909[/C][/ROW]
[ROW][C]154[/C][C]108[/C][C]113.484679477466[/C][C]-5.48467947746634[/C][/ROW]
[ROW][C]155[/C][C]103.6[/C][C]109.327180535034[/C][C]-5.72718053503424[/C][/ROW]
[ROW][C]156[/C][C]107.3[/C][C]104.794025444305[/C][C]2.50597455569529[/C][/ROW]
[ROW][C]157[/C][C]94.4[/C][C]106.746668605801[/C][C]-12.3466686058005[/C][/ROW]
[ROW][C]158[/C][C]85.2[/C][C]96.7433371678007[/C][C]-11.5433371678007[/C][/ROW]
[ROW][C]159[/C][C]113.2[/C][C]86.9878868456759[/C][C]26.2121131543241[/C][/ROW]
[ROW][C]160[/C][C]111.7[/C][C]107.455609828364[/C][C]4.2443901716363[/C][/ROW]
[ROW][C]161[/C][C]124.3[/C][C]110.974879689685[/C][C]13.3251203103155[/C][/ROW]
[ROW][C]162[/C][C]124[/C][C]121.99253445965[/C][C]2.00746554034968[/C][/ROW]
[ROW][C]163[/C][C]133.4[/C][C]124.272582914167[/C][C]9.12741708583307[/C][/ROW]
[ROW][C]164[/C][C]112.6[/C][C]132.388787640258[/C][C]-19.7887876402582[/C][/ROW]
[ROW][C]165[/C][C]115.8[/C][C]117.366979109552[/C][C]-1.56697910955178[/C][/ROW]
[ROW][C]166[/C][C]112.3[/C][C]116.467390938029[/C][C]-4.16739093802941[/C][/ROW]
[ROW][C]167[/C][C]103.6[/C][C]113.409040790735[/C][C]-9.80904079073538[/C][/ROW]
[ROW][C]168[/C][C]111.4[/C][C]105.642135812847[/C][C]5.75786418715279[/C][/ROW]
[ROW][C]169[/C][C]95.1[/C][C]110.171606099789[/C][C]-15.0716060997885[/C][/ROW]
[ROW][C]170[/C][C]93.4[/C][C]98.0071830161635[/C][C]-4.6071830161635[/C][/ROW]
[ROW][C]171[/C][C]117.3[/C][C]93.8318016231627[/C][C]23.4681983768373[/C][/ROW]
[ROW][C]172[/C][C]121.5[/C][C]112.260577921594[/C][C]9.23942207840572[/C][/ROW]
[ROW][C]173[/C][C]123.1[/C][C]119.923576449281[/C][C]3.1764235507186[/C][/ROW]
[ROW][C]174[/C][C]139.3[/C][C]122.97435064167[/C][C]16.3256493583304[/C][/ROW]
[ROW][C]175[/C][C]125.8[/C][C]136.786079024197[/C][C]-10.9860790241972[/C][/ROW]
[ROW][C]176[/C][C]108.6[/C][C]128.995267381132[/C][C]-20.3952673811318[/C][/ROW]
[ROW][C]177[/C][C]121[/C][C]113.219697716958[/C][C]7.78030228304168[/C][/ROW]
[ROW][C]178[/C][C]111.6[/C][C]119.613895066297[/C][C]-8.01389506629721[/C][/ROW]
[ROW][C]179[/C][C]99.7[/C][C]113.461248063218[/C][C]-13.7612480632176[/C][/ROW]
[ROW][C]180[/C][C]116.7[/C][C]102.388760341528[/C][C]14.3112396584719[/C][/ROW]
[ROW][C]181[/C][C]90.3[/C][C]113.61914069168[/C][C]-23.31914069168[/C][/ROW]
[ROW][C]182[/C][C]90.4[/C][C]94.8181062072024[/C][C]-4.41810620720241[/C][/ROW]
[ROW][C]183[/C][C]117.3[/C][C]90.5745022958249[/C][C]26.7254977041751[/C][/ROW]
[ROW][C]184[/C][C]121.6[/C][C]111.427972419848[/C][C]10.1720275801518[/C][/ROW]
[ROW][C]185[/C][C]114.6[/C][C]119.737913989278[/C][C]-5.13791398927762[/C][/ROW]
[ROW][C]186[/C][C]133.3[/C][C]115.971598785116[/C][C]17.3284012148835[/C][/ROW]
[ROW][C]187[/C][C]127.4[/C][C]130.246057364735[/C][C]-2.84605736473463[/C][/ROW]
[ROW][C]188[/C][C]115[/C][C]128.735357400709[/C][C]-13.7353574007088[/C][/ROW]
[ROW][C]189[/C][C]112.6[/C][C]118.306123045772[/C][C]-5.7061230457725[/C][/ROW]
[ROW][C]190[/C][C]108.3[/C][C]113.935889616027[/C][C]-5.63588961602672[/C][/ROW]
[ROW][C]191[/C][C]107.6[/C][C]109.43623428574[/C][C]-1.83623428574035[/C][/ROW]
[ROW][C]192[/C][C]109[/C][C]107.832083074748[/C][C]1.16791692525247[/C][/ROW]
[ROW][C]193[/C][C]89[/C][C]108.602778918667[/C][C]-19.6027789186669[/C][/ROW]
[ROW][C]194[/C][C]102.5[/C][C]92.5773231377576[/C][C]9.9226768622424[/C][/ROW]
[ROW][C]195[/C][C]124.5[/C][C]99.841574186604[/C][C]24.658425813396[/C][/ROW]
[ROW][C]196[/C][C]124.2[/C][C]119.372941617259[/C][C]4.827058382741[/C][/ROW]
[ROW][C]197[/C][C]130.8[/C][C]123.636596639226[/C][C]7.1634033607739[/C][/ROW]
[ROW][C]198[/C][C]138.7[/C][C]129.951456414769[/C][C]8.74854358523052[/C][/ROW]
[ROW][C]199[/C][C]127.6[/C][C]137.784980421087[/C][C]-10.1849804210866[/C][/ROW]
[ROW][C]200[/C][C]130.9[/C][C]130.558909591154[/C][C]0.341090408846156[/C][/ROW]
[ROW][C]201[/C][C]136.9[/C][C]131.531427451155[/C][C]5.36857254884509[/C][/ROW]
[ROW][C]202[/C][C]125.2[/C][C]136.589772241689[/C][C]-11.3897722416886[/C][/ROW]
[ROW][C]203[/C][C]131.3[/C][C]128.241087865508[/C][C]3.05891213449181[/C][/ROW]
[ROW][C]204[/C][C]124.1[/C][C]131.230858204261[/C][C]-7.13085820426099[/C][/ROW]
[ROW][C]205[/C][C]103.2[/C][C]126.061889577824[/C][C]-22.8618895778238[/C][/ROW]
[ROW][C]206[/C][C]118.1[/C][C]107.910317693922[/C][C]10.1896823060782[/C][/ROW]
[ROW][C]207[/C][C]136.5[/C][C]115.799876395192[/C][C]20.7001236048081[/C][/ROW]
[ROW][C]208[/C][C]117.8[/C][C]132.540731783809[/C][C]-14.7407317838089[/C][/ROW]
[ROW][C]209[/C][C]145.1[/C][C]121.233386534643[/C][C]23.8666134653571[/C][/ROW]
[ROW][C]210[/C][C]158.8[/C][C]140.735243467173[/C][C]18.0647565328269[/C][/ROW]
[ROW][C]211[/C][C]136.9[/C][C]156.314207106123[/C][C]-19.4142071061234[/C][/ROW]
[ROW][C]212[/C][C]132.7[/C][C]142.107055174258[/C][C]-9.40705517425769[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310146&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310146&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
377.270.56.7
471.183.4302349433016-12.3302349433016
590.181.15559319845338.94440680154668
691.595.7210147009064-4.22101470090637
776.199.9081856989835-23.8081856989835
887.888.0824452680828-0.282445268082753
98194.5464094161559-13.5464094161559
1077.290.2509345829649-13.0509345829649
1173.885.9146484324318-12.1146484324318
1268.981.911001691509-13.011001691509
1368.476.7852478915353-8.38524789153531
1465.274.9836877617769-9.78368776177693
1578.771.77487904915766.92512095084243
167781.7887669228591-4.78876692285911
1797.682.534903543349715.0650964566503
1888.199.2158687039576-11.1158687039576
1998.795.16959212964133.53040787035874
2093.4102.630860222889-9.23086022288864
216899.8646322189757-31.8646322189757
2287.978.45266844475589.44733155524423
2375.889.4827384179537-13.6827384179537
2466.382.0748054368065-15.7748054368065
2568.472.5244508052611-4.12445080526111
2671.371.9013506340353-0.601350634035313
2777.473.99897043977863.40102956022137
2887.179.32081235081997.77918764918012
2988.588.30214364802610.19785635197394
3085.991.3929810908588-5.49298109085879
3192.789.87795390887742.82204609112257
3288.594.9227291555576-6.4227291555576
3380.292.5669323955306-12.3669323955306
3481.885.183713888558-3.38371388855805
3570.484.6773727419104-14.2773727419104
3682.275.23140620589336.96859379410671
3772.882.5386744638809-9.73867446388087
386976.5325621095882-7.53256210958824
398371.996429992296611.0035700077034
4092.482.237523722687610.1624762773124
4192.392.15626906996640.14373093003357
42100.594.28686940094646.21313059905363
43106.9101.3413077577535.55869224224658
4499.5108.0682373023-8.56823730229956
4585.9103.527063288446-17.6270632884457
4692.691.36405340773951.23594659226053
4777.493.9135420123959-16.5135420123959
4884.182.1177372227181.98226277728202
4975.384.7731817679672-9.47318176796716
5073.878.2089199951097-4.40891999510971
51100.175.43978967734224.660210322658
5290.796.0867081657206-5.38670816572061
5396.593.1864438178513.31355618214901
54111.897.16168056151114.638319438489
5597.4110.423654269386-13.0236542693864
56100.8101.744116988359-0.944116988358786
5793.7102.429523692489-8.72952369248878
588296.7741599256413-14.7741599256413
598685.93464219467980.0653578053201613
6084.386.6398189352949-2.33981893529486
6173.185.3977756210594-12.2977756210594
6275.476.0085679385915-0.608567938591449
6397.975.6916538273422.20834617266
6497.593.84758277031233.65241722968773
6510697.68950803295748.31049196704255
66112.8105.4259998867817.37400011321851
6799.5112.674876953451-13.1748769534514
68100.8103.510054795195-2.71005479519522
69102.9102.3965392640540.503460735946319
7088.8103.799020613156-14.9990206131558
7191.392.6534485671741-1.35344856717414
7288.392.0775552416811-3.77755524168113
7377.489.4927655080902-12.0927655080902
7480.580.0452770070070.454722992993027
7596.780.372398957978416.3276010420216
7693.893.57906587953160.220934120468442
7710594.264766405251610.7352335947484
78117.1103.47934114327313.6206588567275
79111.1115.383084083723-4.28308408372305
80105.8113.220960750888-7.42096075088753
8195.7108.375769566294-12.6757695662939
8297.199.0292997228694-1.92929972286939
839197.9787064712283-6.97870647122835
8490.992.7726506108564-1.8726506108564
8583.591.4770616882112-7.97706168821124
8682.385.1727972557336-2.8727972557336
87101.782.744944548051718.9550554519483
88108.397.914374663499810.3856253365002
89114106.7574441721927.24255582780758
90118.2113.3922732382024.80772676179829
91103.4118.290235341071-14.8902353410714
92106.8107.38034338286-0.580343382859965
9395.4107.582102627054-12.182102627054
94101.898.36188295988333.43811704011672
9595.6101.403752105223-5.80375210522298
9694.897.0675236211935-2.26752362119349
979495.4078144351399-1.40781443513985
9882.494.3708342505033-11.9708342505033
9995.884.726732897316811.0732671026832
100106.793.368548367942213.3314516320578
101114.1104.2022033605859.89779663941475
102103.9112.688305230203-8.78830523020325
103117.4106.35287481929611.0471251807044
104105.9115.806720401201-9.90672040120147
105101.7108.638599994926-6.93859999492632
10698.7103.552566389065-4.85256638906517
10791.399.9306333028095-8.63063330280953
108102.393.08817157716569.21182842283442
10980.5100.424868042399-19.9248680423987
11086.784.44760310414592.2523968958541
111102.685.793944039375316.8060559606246
112107.399.00933225868648.2906677413136
113108105.8719800127282.12801998727225
114124.3108.01065596955116.2893440304494
115117.1121.696336635548-4.59633663554774
116103.9118.986492974709-15.0864929747089
117104.7107.624455155848-2.92445515584787
11895.9105.626860457241-9.72686045724066
11994.298.0205291302607-3.82052913026068
120102.794.88352778518557.81647221481452
12170.3101.05334915305-30.7533491530503
12290.276.218255220754313.9817447792457
123107.386.635874421531720.6641255784683
124104.6102.9260504161421.67394958385846
125102.7104.499843332462-1.79984333246182
126124.5103.31285292435821.187147075642
127117.8120.697646001836-2.89764600183587
128104.2119.254036659079-15.0540366590794
12999.9107.863253005783-7.96325300578316
13091.5101.727807984445-10.2278079844447
13195.793.49692404748022.20307595251975
13291.495.0070484930722-3.60704849307223
13386.291.8801127132552-5.68011271325524
13491.586.95519858202994.54480141797008
135115.590.131906295682425.3680937043176
136113.9110.333954419453.56604558055005
137131.9113.69426290246918.2057370975306
138121.2129.036246326443-7.83624632644323
139105.2123.866194243695-18.6661942436946
140107.5109.662747016787-2.16274701678716
141113.8108.2254783593855.57452164061544
142100.5112.988504239165-12.4885042391655
143104.8103.2938050147531.50619498524705
144103.8104.533732039474-0.733732039473978
14593.1104.007424493397-10.9074244933975
146106.295.21155243165410.988447568346
147117.5103.80570484897113.6942951510289
148109.9114.951750053492-5.05175005349183
149123.6111.35166220508912.2483377949109
150131.7121.60802344248210.0919765575179
151111130.516684956898-19.5166849568975
152122115.7576085024516.24239149754872
153110.9121.238464683291-10.3384646832909
154108113.484679477466-5.48467947746634
155103.6109.327180535034-5.72718053503424
156107.3104.7940254443052.50597455569529
15794.4106.746668605801-12.3466686058005
15885.296.7433371678007-11.5433371678007
159113.286.987886845675926.2121131543241
160111.7107.4556098283644.2443901716363
161124.3110.97487968968513.3251203103155
162124121.992534459652.00746554034968
163133.4124.2725829141679.12741708583307
164112.6132.388787640258-19.7887876402582
165115.8117.366979109552-1.56697910955178
166112.3116.467390938029-4.16739093802941
167103.6113.409040790735-9.80904079073538
168111.4105.6421358128475.75786418715279
16995.1110.171606099789-15.0716060997885
17093.498.0071830161635-4.6071830161635
171117.393.831801623162723.4681983768373
172121.5112.2605779215949.23942207840572
173123.1119.9235764492813.1764235507186
174139.3122.9743506416716.3256493583304
175125.8136.786079024197-10.9860790241972
176108.6128.995267381132-20.3952673811318
177121113.2196977169587.78030228304168
178111.6119.613895066297-8.01389506629721
17999.7113.461248063218-13.7612480632176
180116.7102.38876034152814.3112396584719
18190.3113.61914069168-23.31914069168
18290.494.8181062072024-4.41810620720241
183117.390.574502295824926.7254977041751
184121.6111.42797241984810.1720275801518
185114.6119.737913989278-5.13791398927762
186133.3115.97159878511617.3284012148835
187127.4130.246057364735-2.84605736473463
188115128.735357400709-13.7353574007088
189112.6118.306123045772-5.7061230457725
190108.3113.935889616027-5.63588961602672
191107.6109.43623428574-1.83623428574035
192109107.8320830747481.16791692525247
19389108.602778918667-19.6027789186669
194102.592.57732313775769.9226768622424
195124.599.84157418660424.658425813396
196124.2119.3729416172594.827058382741
197130.8123.6365966392267.1634033607739
198138.7129.9514564147698.74854358523052
199127.6137.784980421087-10.1849804210866
200130.9130.5589095911540.341090408846156
201136.9131.5314274511555.36857254884509
202125.2136.589772241689-11.3897722416886
203131.3128.2410878655083.05891213449181
204124.1131.230858204261-7.13085820426099
205103.2126.061889577824-22.8618895778238
206118.1107.91031769392210.1896823060782
207136.5115.79987639519220.7001236048081
208117.8132.540731783809-14.7407317838089
209145.1121.23338653464323.8666134653571
210158.8140.73524346717318.0647565328269
211136.9156.314207106123-19.4142071061234
212132.7142.107055174258-9.40705517425769







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
213135.376518173973112.682598892583158.070437455362
214135.963031599884106.751431276306165.174631923462
215136.549545025795101.629161488845171.469928562746
216137.13605845170796.9557242664077177.316392637006
217137.72257187761892.5618112078683182.883332547368
218138.30908530352988.3527359810028188.265434626056
219138.89559872944184.2697316011632193.521465857718
220139.48211215535280.2736805421229198.690543768581
221140.06862558126476.3372017342853203.800049428242
222140.65513900717572.4403906158431208.869887398507
223141.24165243308668.5683463580958213.914958508077
224141.82816585899864.7096502931813218.946681424814

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
213 & 135.376518173973 & 112.682598892583 & 158.070437455362 \tabularnewline
214 & 135.963031599884 & 106.751431276306 & 165.174631923462 \tabularnewline
215 & 136.549545025795 & 101.629161488845 & 171.469928562746 \tabularnewline
216 & 137.136058451707 & 96.9557242664077 & 177.316392637006 \tabularnewline
217 & 137.722571877618 & 92.5618112078683 & 182.883332547368 \tabularnewline
218 & 138.309085303529 & 88.3527359810028 & 188.265434626056 \tabularnewline
219 & 138.895598729441 & 84.2697316011632 & 193.521465857718 \tabularnewline
220 & 139.482112155352 & 80.2736805421229 & 198.690543768581 \tabularnewline
221 & 140.068625581264 & 76.3372017342853 & 203.800049428242 \tabularnewline
222 & 140.655139007175 & 72.4403906158431 & 208.869887398507 \tabularnewline
223 & 141.241652433086 & 68.5683463580958 & 213.914958508077 \tabularnewline
224 & 141.828165858998 & 64.7096502931813 & 218.946681424814 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310146&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]135.376518173973[/C][C]112.682598892583[/C][C]158.070437455362[/C][/ROW]
[ROW][C]214[/C][C]135.963031599884[/C][C]106.751431276306[/C][C]165.174631923462[/C][/ROW]
[ROW][C]215[/C][C]136.549545025795[/C][C]101.629161488845[/C][C]171.469928562746[/C][/ROW]
[ROW][C]216[/C][C]137.136058451707[/C][C]96.9557242664077[/C][C]177.316392637006[/C][/ROW]
[ROW][C]217[/C][C]137.722571877618[/C][C]92.5618112078683[/C][C]182.883332547368[/C][/ROW]
[ROW][C]218[/C][C]138.309085303529[/C][C]88.3527359810028[/C][C]188.265434626056[/C][/ROW]
[ROW][C]219[/C][C]138.895598729441[/C][C]84.2697316011632[/C][C]193.521465857718[/C][/ROW]
[ROW][C]220[/C][C]139.482112155352[/C][C]80.2736805421229[/C][C]198.690543768581[/C][/ROW]
[ROW][C]221[/C][C]140.068625581264[/C][C]76.3372017342853[/C][C]203.800049428242[/C][/ROW]
[ROW][C]222[/C][C]140.655139007175[/C][C]72.4403906158431[/C][C]208.869887398507[/C][/ROW]
[ROW][C]223[/C][C]141.241652433086[/C][C]68.5683463580958[/C][C]213.914958508077[/C][/ROW]
[ROW][C]224[/C][C]141.828165858998[/C][C]64.7096502931813[/C][C]218.946681424814[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310146&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310146&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
213135.376518173973112.682598892583158.070437455362
214135.963031599884106.751431276306165.174631923462
215136.549545025795101.629161488845171.469928562746
216137.13605845170796.9557242664077177.316392637006
217137.72257187761892.5618112078683182.883332547368
218138.30908530352988.3527359810028188.265434626056
219138.89559872944184.2697316011632193.521465857718
220139.48211215535280.2736805421229198.690543768581
221140.06862558126476.3372017342853203.800049428242
222140.65513900717572.4403906158431208.869887398507
223141.24165243308668.5683463580958213.914958508077
224141.82816585899864.7096502931813218.946681424814



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