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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 computationFri, 16 Dec 2016 09:34:06 +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/2016/Dec/16/t1481877312w177gejksge1hgp.htm/, Retrieved Thu, 02 May 2024 14:12:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300114, Retrieved Thu, 02 May 2024 14:12:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-16 08:34:06] [b2e25925e4919b0d6985405fcb461c0d] [Current]
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Dataseries X:
4020
3540
3430
4200
3360
4440
4390
4940
3940
4560
4850
5070
6210
5200
4860
5160
5530
8830
4410
4850
8960
4620
5120
4520
8870
9470
6590
3970
3770
5500
6580
5280
8640
5510
5690
7620
4010
3570
4040
3600
4000
3070
3230
4060
3480
3750
3990
3100
3950
3010
3160
2960
2750
3590
3060
2970
3590
3450
2930
2660
3540
3160
2680
2900
2920
2900
3150
3150
3120
3720
3360
2740
3250
2700
2610
2410
2590
2630
2650
2600
3060
2650
2700
2620
2630
2850
2680
2430
2550
2570
2520
2500
2550
2790
2770
2460
2800
2770
2450
2370
2540
3470
2690
4110
3840
2860
3540
3370




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=300114&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=300114&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300114&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
alpha0.267508201813554
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.267508201813554 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300114&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]0.267508201813554[/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=300114&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300114&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
alpha0.267508201813554
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
235404020-480
334303891.59606312949-461.596063129495
442003768.11533031751431.884669682492
533603883.64802169511-523.648021695112
644403743.56788102823696.432118971773
743903929.86918485957460.130815140431
849404052.95795181679887.04204818321
939404290.24897505929-350.248975059292
1045604196.55450155414363.445498445859
1148504293.77915330062556.220846699376
1250704442.57279181239627.427208187613
1362104610.414716043551599.58528395645
1452005038.31689900216161.683100997835
1548605081.56845461373-221.568454613735
1651605022.29707574141137.702924258594
1755305059.13373739429470.866262605709
1888305185.094324598613644.90567540139
1944106160.13648760525-1750.13648760525
2048505691.96062287768-841.960622877685
2189605466.729250653863493.27074934614
2246206401.20782725933-1781.20782725933
2351205924.72012433296-804.720124332958
2445205709.45089090947-1189.45089090947
2588705391.263021936753478.73697806325
2694706321.853695520763148.14630447924
2765907164.00865247799-574.008652477989
2839707010.45663002818-3040.45663002818
2937706197.10954423725-2427.10954423725
3055005547.83783445383-47.837834453826
3165805535.040821380431044.95917861957
3252805814.57597222152-534.575972221518
3386405671.572515159812968.42748484019
3455106465.65121384334-955.651213843337
3556906210.00667606717-520.006676067167
3676206070.90062522141549.0993747786
3740106485.29741339892-2475.29741339892
3835705823.13505338684-2253.13505338684
3940405220.40294681224-1180.40294681224
4036004904.63547709508-1304.63547709508
4140004555.6347865952-555.634786595205
4230704406.99792396806-1336.99792396806
4332304049.34001349891-819.340013498913
4440603830.15983981393229.840160186074
4534803891.64396776984-411.643967769842
4637503781.52583016434-31.5258301643353
4739903773.09241202639216.907587973606
4831003831.11697084493-731.116970844929
4939503635.53718465883314.46281534117
5030103719.65856692797-709.658566927974
5131603529.81907978749-369.819079787489
5229603430.88944275719-470.889442757195
5327503304.92265467223-554.922654672231
5435903156.47629317526433.523706824741
5530603272.44744043149-212.447440431491
5629703215.61600766177-245.616007661771
5735903149.91171111555440.088288884454
5834503267.63893791423182.361062085769
5929303316.4220177136-386.422017713605
6026603213.05095861387-553.050958613873
6135403065.10529116381474.894708836186
6231603192.14352077535-32.143520775353
6326803183.54486533278-503.544865332782
6429003048.84248387516-148.842483875161
6529203009.02589866025-89.0258986602539
6629002985.21074059481-85.2107405948136
6731502962.41616860309187.583831396906
6831503012.59638202938137.403617970623
6931203049.3529767953870.6470232046249
7037203068.25163493632651.748365063675
7133603242.59966810943117.400331890568
7227403274.00521978579-534.005219785792
7332503131.15444368184118.845556318156
7427003162.94660474605-462.946604746045
7526103039.10459097474-429.104590974741
7624102924.31559345315-514.315593453148
7725902786.73195388383-196.731953883826
7826302734.1045426611-104.104542661096
7926502706.2557236532-56.2557236532039
8026002691.20685617702-91.2068561770152
8130602666.80827408803393.191725911965
8226502771.99028565471-121.990285654712
8327002739.3568837005-39.3568837004982
8426202728.82859451279-108.828594512793
8526302699.71605288878-69.7160528887794
8628502681.06643694296168.933563057037
8726802726.25755062231-46.2575506223079
8824302713.88327643503-283.883276435035
8925502637.94217163096-87.9421716309589
9025702614.41691943438-44.4169194343822
9125202602.53502918639-82.5350291863933
9225002580.45623194211-80.456231942112
9325502558.93353001058-8.93353001058358
9427902556.5437374616233.456262538395
9527702618.99520245536151.004797544636
9624602659.39022431175-199.39022431175
9728002606.05170394691193.948296053088
9827702657.93446386888112.065536131123
9924502687.91291392459-237.912913924585
10023702624.2692581324-254.269258132396
10125402556.25014611293-16.2501461129327
10234702551.90309874705918.096901252945
10326902797.50154989183-107.501549891826
10441102768.744003588091341.25599641191
10538403127.54098335989712.459016640112
10628603318.12961376714-458.129613767137
10735403195.57618459075344.423815409248
10833703287.7123801126482.2876198873564

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 3540 & 4020 & -480 \tabularnewline
3 & 3430 & 3891.59606312949 & -461.596063129495 \tabularnewline
4 & 4200 & 3768.11533031751 & 431.884669682492 \tabularnewline
5 & 3360 & 3883.64802169511 & -523.648021695112 \tabularnewline
6 & 4440 & 3743.56788102823 & 696.432118971773 \tabularnewline
7 & 4390 & 3929.86918485957 & 460.130815140431 \tabularnewline
8 & 4940 & 4052.95795181679 & 887.04204818321 \tabularnewline
9 & 3940 & 4290.24897505929 & -350.248975059292 \tabularnewline
10 & 4560 & 4196.55450155414 & 363.445498445859 \tabularnewline
11 & 4850 & 4293.77915330062 & 556.220846699376 \tabularnewline
12 & 5070 & 4442.57279181239 & 627.427208187613 \tabularnewline
13 & 6210 & 4610.41471604355 & 1599.58528395645 \tabularnewline
14 & 5200 & 5038.31689900216 & 161.683100997835 \tabularnewline
15 & 4860 & 5081.56845461373 & -221.568454613735 \tabularnewline
16 & 5160 & 5022.29707574141 & 137.702924258594 \tabularnewline
17 & 5530 & 5059.13373739429 & 470.866262605709 \tabularnewline
18 & 8830 & 5185.09432459861 & 3644.90567540139 \tabularnewline
19 & 4410 & 6160.13648760525 & -1750.13648760525 \tabularnewline
20 & 4850 & 5691.96062287768 & -841.960622877685 \tabularnewline
21 & 8960 & 5466.72925065386 & 3493.27074934614 \tabularnewline
22 & 4620 & 6401.20782725933 & -1781.20782725933 \tabularnewline
23 & 5120 & 5924.72012433296 & -804.720124332958 \tabularnewline
24 & 4520 & 5709.45089090947 & -1189.45089090947 \tabularnewline
25 & 8870 & 5391.26302193675 & 3478.73697806325 \tabularnewline
26 & 9470 & 6321.85369552076 & 3148.14630447924 \tabularnewline
27 & 6590 & 7164.00865247799 & -574.008652477989 \tabularnewline
28 & 3970 & 7010.45663002818 & -3040.45663002818 \tabularnewline
29 & 3770 & 6197.10954423725 & -2427.10954423725 \tabularnewline
30 & 5500 & 5547.83783445383 & -47.837834453826 \tabularnewline
31 & 6580 & 5535.04082138043 & 1044.95917861957 \tabularnewline
32 & 5280 & 5814.57597222152 & -534.575972221518 \tabularnewline
33 & 8640 & 5671.57251515981 & 2968.42748484019 \tabularnewline
34 & 5510 & 6465.65121384334 & -955.651213843337 \tabularnewline
35 & 5690 & 6210.00667606717 & -520.006676067167 \tabularnewline
36 & 7620 & 6070.9006252214 & 1549.0993747786 \tabularnewline
37 & 4010 & 6485.29741339892 & -2475.29741339892 \tabularnewline
38 & 3570 & 5823.13505338684 & -2253.13505338684 \tabularnewline
39 & 4040 & 5220.40294681224 & -1180.40294681224 \tabularnewline
40 & 3600 & 4904.63547709508 & -1304.63547709508 \tabularnewline
41 & 4000 & 4555.6347865952 & -555.634786595205 \tabularnewline
42 & 3070 & 4406.99792396806 & -1336.99792396806 \tabularnewline
43 & 3230 & 4049.34001349891 & -819.340013498913 \tabularnewline
44 & 4060 & 3830.15983981393 & 229.840160186074 \tabularnewline
45 & 3480 & 3891.64396776984 & -411.643967769842 \tabularnewline
46 & 3750 & 3781.52583016434 & -31.5258301643353 \tabularnewline
47 & 3990 & 3773.09241202639 & 216.907587973606 \tabularnewline
48 & 3100 & 3831.11697084493 & -731.116970844929 \tabularnewline
49 & 3950 & 3635.53718465883 & 314.46281534117 \tabularnewline
50 & 3010 & 3719.65856692797 & -709.658566927974 \tabularnewline
51 & 3160 & 3529.81907978749 & -369.819079787489 \tabularnewline
52 & 2960 & 3430.88944275719 & -470.889442757195 \tabularnewline
53 & 2750 & 3304.92265467223 & -554.922654672231 \tabularnewline
54 & 3590 & 3156.47629317526 & 433.523706824741 \tabularnewline
55 & 3060 & 3272.44744043149 & -212.447440431491 \tabularnewline
56 & 2970 & 3215.61600766177 & -245.616007661771 \tabularnewline
57 & 3590 & 3149.91171111555 & 440.088288884454 \tabularnewline
58 & 3450 & 3267.63893791423 & 182.361062085769 \tabularnewline
59 & 2930 & 3316.4220177136 & -386.422017713605 \tabularnewline
60 & 2660 & 3213.05095861387 & -553.050958613873 \tabularnewline
61 & 3540 & 3065.10529116381 & 474.894708836186 \tabularnewline
62 & 3160 & 3192.14352077535 & -32.143520775353 \tabularnewline
63 & 2680 & 3183.54486533278 & -503.544865332782 \tabularnewline
64 & 2900 & 3048.84248387516 & -148.842483875161 \tabularnewline
65 & 2920 & 3009.02589866025 & -89.0258986602539 \tabularnewline
66 & 2900 & 2985.21074059481 & -85.2107405948136 \tabularnewline
67 & 3150 & 2962.41616860309 & 187.583831396906 \tabularnewline
68 & 3150 & 3012.59638202938 & 137.403617970623 \tabularnewline
69 & 3120 & 3049.35297679538 & 70.6470232046249 \tabularnewline
70 & 3720 & 3068.25163493632 & 651.748365063675 \tabularnewline
71 & 3360 & 3242.59966810943 & 117.400331890568 \tabularnewline
72 & 2740 & 3274.00521978579 & -534.005219785792 \tabularnewline
73 & 3250 & 3131.15444368184 & 118.845556318156 \tabularnewline
74 & 2700 & 3162.94660474605 & -462.946604746045 \tabularnewline
75 & 2610 & 3039.10459097474 & -429.104590974741 \tabularnewline
76 & 2410 & 2924.31559345315 & -514.315593453148 \tabularnewline
77 & 2590 & 2786.73195388383 & -196.731953883826 \tabularnewline
78 & 2630 & 2734.1045426611 & -104.104542661096 \tabularnewline
79 & 2650 & 2706.2557236532 & -56.2557236532039 \tabularnewline
80 & 2600 & 2691.20685617702 & -91.2068561770152 \tabularnewline
81 & 3060 & 2666.80827408803 & 393.191725911965 \tabularnewline
82 & 2650 & 2771.99028565471 & -121.990285654712 \tabularnewline
83 & 2700 & 2739.3568837005 & -39.3568837004982 \tabularnewline
84 & 2620 & 2728.82859451279 & -108.828594512793 \tabularnewline
85 & 2630 & 2699.71605288878 & -69.7160528887794 \tabularnewline
86 & 2850 & 2681.06643694296 & 168.933563057037 \tabularnewline
87 & 2680 & 2726.25755062231 & -46.2575506223079 \tabularnewline
88 & 2430 & 2713.88327643503 & -283.883276435035 \tabularnewline
89 & 2550 & 2637.94217163096 & -87.9421716309589 \tabularnewline
90 & 2570 & 2614.41691943438 & -44.4169194343822 \tabularnewline
91 & 2520 & 2602.53502918639 & -82.5350291863933 \tabularnewline
92 & 2500 & 2580.45623194211 & -80.456231942112 \tabularnewline
93 & 2550 & 2558.93353001058 & -8.93353001058358 \tabularnewline
94 & 2790 & 2556.5437374616 & 233.456262538395 \tabularnewline
95 & 2770 & 2618.99520245536 & 151.004797544636 \tabularnewline
96 & 2460 & 2659.39022431175 & -199.39022431175 \tabularnewline
97 & 2800 & 2606.05170394691 & 193.948296053088 \tabularnewline
98 & 2770 & 2657.93446386888 & 112.065536131123 \tabularnewline
99 & 2450 & 2687.91291392459 & -237.912913924585 \tabularnewline
100 & 2370 & 2624.2692581324 & -254.269258132396 \tabularnewline
101 & 2540 & 2556.25014611293 & -16.2501461129327 \tabularnewline
102 & 3470 & 2551.90309874705 & 918.096901252945 \tabularnewline
103 & 2690 & 2797.50154989183 & -107.501549891826 \tabularnewline
104 & 4110 & 2768.74400358809 & 1341.25599641191 \tabularnewline
105 & 3840 & 3127.54098335989 & 712.459016640112 \tabularnewline
106 & 2860 & 3318.12961376714 & -458.129613767137 \tabularnewline
107 & 3540 & 3195.57618459075 & 344.423815409248 \tabularnewline
108 & 3370 & 3287.71238011264 & 82.2876198873564 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300114&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]3540[/C][C]4020[/C][C]-480[/C][/ROW]
[ROW][C]3[/C][C]3430[/C][C]3891.59606312949[/C][C]-461.596063129495[/C][/ROW]
[ROW][C]4[/C][C]4200[/C][C]3768.11533031751[/C][C]431.884669682492[/C][/ROW]
[ROW][C]5[/C][C]3360[/C][C]3883.64802169511[/C][C]-523.648021695112[/C][/ROW]
[ROW][C]6[/C][C]4440[/C][C]3743.56788102823[/C][C]696.432118971773[/C][/ROW]
[ROW][C]7[/C][C]4390[/C][C]3929.86918485957[/C][C]460.130815140431[/C][/ROW]
[ROW][C]8[/C][C]4940[/C][C]4052.95795181679[/C][C]887.04204818321[/C][/ROW]
[ROW][C]9[/C][C]3940[/C][C]4290.24897505929[/C][C]-350.248975059292[/C][/ROW]
[ROW][C]10[/C][C]4560[/C][C]4196.55450155414[/C][C]363.445498445859[/C][/ROW]
[ROW][C]11[/C][C]4850[/C][C]4293.77915330062[/C][C]556.220846699376[/C][/ROW]
[ROW][C]12[/C][C]5070[/C][C]4442.57279181239[/C][C]627.427208187613[/C][/ROW]
[ROW][C]13[/C][C]6210[/C][C]4610.41471604355[/C][C]1599.58528395645[/C][/ROW]
[ROW][C]14[/C][C]5200[/C][C]5038.31689900216[/C][C]161.683100997835[/C][/ROW]
[ROW][C]15[/C][C]4860[/C][C]5081.56845461373[/C][C]-221.568454613735[/C][/ROW]
[ROW][C]16[/C][C]5160[/C][C]5022.29707574141[/C][C]137.702924258594[/C][/ROW]
[ROW][C]17[/C][C]5530[/C][C]5059.13373739429[/C][C]470.866262605709[/C][/ROW]
[ROW][C]18[/C][C]8830[/C][C]5185.09432459861[/C][C]3644.90567540139[/C][/ROW]
[ROW][C]19[/C][C]4410[/C][C]6160.13648760525[/C][C]-1750.13648760525[/C][/ROW]
[ROW][C]20[/C][C]4850[/C][C]5691.96062287768[/C][C]-841.960622877685[/C][/ROW]
[ROW][C]21[/C][C]8960[/C][C]5466.72925065386[/C][C]3493.27074934614[/C][/ROW]
[ROW][C]22[/C][C]4620[/C][C]6401.20782725933[/C][C]-1781.20782725933[/C][/ROW]
[ROW][C]23[/C][C]5120[/C][C]5924.72012433296[/C][C]-804.720124332958[/C][/ROW]
[ROW][C]24[/C][C]4520[/C][C]5709.45089090947[/C][C]-1189.45089090947[/C][/ROW]
[ROW][C]25[/C][C]8870[/C][C]5391.26302193675[/C][C]3478.73697806325[/C][/ROW]
[ROW][C]26[/C][C]9470[/C][C]6321.85369552076[/C][C]3148.14630447924[/C][/ROW]
[ROW][C]27[/C][C]6590[/C][C]7164.00865247799[/C][C]-574.008652477989[/C][/ROW]
[ROW][C]28[/C][C]3970[/C][C]7010.45663002818[/C][C]-3040.45663002818[/C][/ROW]
[ROW][C]29[/C][C]3770[/C][C]6197.10954423725[/C][C]-2427.10954423725[/C][/ROW]
[ROW][C]30[/C][C]5500[/C][C]5547.83783445383[/C][C]-47.837834453826[/C][/ROW]
[ROW][C]31[/C][C]6580[/C][C]5535.04082138043[/C][C]1044.95917861957[/C][/ROW]
[ROW][C]32[/C][C]5280[/C][C]5814.57597222152[/C][C]-534.575972221518[/C][/ROW]
[ROW][C]33[/C][C]8640[/C][C]5671.57251515981[/C][C]2968.42748484019[/C][/ROW]
[ROW][C]34[/C][C]5510[/C][C]6465.65121384334[/C][C]-955.651213843337[/C][/ROW]
[ROW][C]35[/C][C]5690[/C][C]6210.00667606717[/C][C]-520.006676067167[/C][/ROW]
[ROW][C]36[/C][C]7620[/C][C]6070.9006252214[/C][C]1549.0993747786[/C][/ROW]
[ROW][C]37[/C][C]4010[/C][C]6485.29741339892[/C][C]-2475.29741339892[/C][/ROW]
[ROW][C]38[/C][C]3570[/C][C]5823.13505338684[/C][C]-2253.13505338684[/C][/ROW]
[ROW][C]39[/C][C]4040[/C][C]5220.40294681224[/C][C]-1180.40294681224[/C][/ROW]
[ROW][C]40[/C][C]3600[/C][C]4904.63547709508[/C][C]-1304.63547709508[/C][/ROW]
[ROW][C]41[/C][C]4000[/C][C]4555.6347865952[/C][C]-555.634786595205[/C][/ROW]
[ROW][C]42[/C][C]3070[/C][C]4406.99792396806[/C][C]-1336.99792396806[/C][/ROW]
[ROW][C]43[/C][C]3230[/C][C]4049.34001349891[/C][C]-819.340013498913[/C][/ROW]
[ROW][C]44[/C][C]4060[/C][C]3830.15983981393[/C][C]229.840160186074[/C][/ROW]
[ROW][C]45[/C][C]3480[/C][C]3891.64396776984[/C][C]-411.643967769842[/C][/ROW]
[ROW][C]46[/C][C]3750[/C][C]3781.52583016434[/C][C]-31.5258301643353[/C][/ROW]
[ROW][C]47[/C][C]3990[/C][C]3773.09241202639[/C][C]216.907587973606[/C][/ROW]
[ROW][C]48[/C][C]3100[/C][C]3831.11697084493[/C][C]-731.116970844929[/C][/ROW]
[ROW][C]49[/C][C]3950[/C][C]3635.53718465883[/C][C]314.46281534117[/C][/ROW]
[ROW][C]50[/C][C]3010[/C][C]3719.65856692797[/C][C]-709.658566927974[/C][/ROW]
[ROW][C]51[/C][C]3160[/C][C]3529.81907978749[/C][C]-369.819079787489[/C][/ROW]
[ROW][C]52[/C][C]2960[/C][C]3430.88944275719[/C][C]-470.889442757195[/C][/ROW]
[ROW][C]53[/C][C]2750[/C][C]3304.92265467223[/C][C]-554.922654672231[/C][/ROW]
[ROW][C]54[/C][C]3590[/C][C]3156.47629317526[/C][C]433.523706824741[/C][/ROW]
[ROW][C]55[/C][C]3060[/C][C]3272.44744043149[/C][C]-212.447440431491[/C][/ROW]
[ROW][C]56[/C][C]2970[/C][C]3215.61600766177[/C][C]-245.616007661771[/C][/ROW]
[ROW][C]57[/C][C]3590[/C][C]3149.91171111555[/C][C]440.088288884454[/C][/ROW]
[ROW][C]58[/C][C]3450[/C][C]3267.63893791423[/C][C]182.361062085769[/C][/ROW]
[ROW][C]59[/C][C]2930[/C][C]3316.4220177136[/C][C]-386.422017713605[/C][/ROW]
[ROW][C]60[/C][C]2660[/C][C]3213.05095861387[/C][C]-553.050958613873[/C][/ROW]
[ROW][C]61[/C][C]3540[/C][C]3065.10529116381[/C][C]474.894708836186[/C][/ROW]
[ROW][C]62[/C][C]3160[/C][C]3192.14352077535[/C][C]-32.143520775353[/C][/ROW]
[ROW][C]63[/C][C]2680[/C][C]3183.54486533278[/C][C]-503.544865332782[/C][/ROW]
[ROW][C]64[/C][C]2900[/C][C]3048.84248387516[/C][C]-148.842483875161[/C][/ROW]
[ROW][C]65[/C][C]2920[/C][C]3009.02589866025[/C][C]-89.0258986602539[/C][/ROW]
[ROW][C]66[/C][C]2900[/C][C]2985.21074059481[/C][C]-85.2107405948136[/C][/ROW]
[ROW][C]67[/C][C]3150[/C][C]2962.41616860309[/C][C]187.583831396906[/C][/ROW]
[ROW][C]68[/C][C]3150[/C][C]3012.59638202938[/C][C]137.403617970623[/C][/ROW]
[ROW][C]69[/C][C]3120[/C][C]3049.35297679538[/C][C]70.6470232046249[/C][/ROW]
[ROW][C]70[/C][C]3720[/C][C]3068.25163493632[/C][C]651.748365063675[/C][/ROW]
[ROW][C]71[/C][C]3360[/C][C]3242.59966810943[/C][C]117.400331890568[/C][/ROW]
[ROW][C]72[/C][C]2740[/C][C]3274.00521978579[/C][C]-534.005219785792[/C][/ROW]
[ROW][C]73[/C][C]3250[/C][C]3131.15444368184[/C][C]118.845556318156[/C][/ROW]
[ROW][C]74[/C][C]2700[/C][C]3162.94660474605[/C][C]-462.946604746045[/C][/ROW]
[ROW][C]75[/C][C]2610[/C][C]3039.10459097474[/C][C]-429.104590974741[/C][/ROW]
[ROW][C]76[/C][C]2410[/C][C]2924.31559345315[/C][C]-514.315593453148[/C][/ROW]
[ROW][C]77[/C][C]2590[/C][C]2786.73195388383[/C][C]-196.731953883826[/C][/ROW]
[ROW][C]78[/C][C]2630[/C][C]2734.1045426611[/C][C]-104.104542661096[/C][/ROW]
[ROW][C]79[/C][C]2650[/C][C]2706.2557236532[/C][C]-56.2557236532039[/C][/ROW]
[ROW][C]80[/C][C]2600[/C][C]2691.20685617702[/C][C]-91.2068561770152[/C][/ROW]
[ROW][C]81[/C][C]3060[/C][C]2666.80827408803[/C][C]393.191725911965[/C][/ROW]
[ROW][C]82[/C][C]2650[/C][C]2771.99028565471[/C][C]-121.990285654712[/C][/ROW]
[ROW][C]83[/C][C]2700[/C][C]2739.3568837005[/C][C]-39.3568837004982[/C][/ROW]
[ROW][C]84[/C][C]2620[/C][C]2728.82859451279[/C][C]-108.828594512793[/C][/ROW]
[ROW][C]85[/C][C]2630[/C][C]2699.71605288878[/C][C]-69.7160528887794[/C][/ROW]
[ROW][C]86[/C][C]2850[/C][C]2681.06643694296[/C][C]168.933563057037[/C][/ROW]
[ROW][C]87[/C][C]2680[/C][C]2726.25755062231[/C][C]-46.2575506223079[/C][/ROW]
[ROW][C]88[/C][C]2430[/C][C]2713.88327643503[/C][C]-283.883276435035[/C][/ROW]
[ROW][C]89[/C][C]2550[/C][C]2637.94217163096[/C][C]-87.9421716309589[/C][/ROW]
[ROW][C]90[/C][C]2570[/C][C]2614.41691943438[/C][C]-44.4169194343822[/C][/ROW]
[ROW][C]91[/C][C]2520[/C][C]2602.53502918639[/C][C]-82.5350291863933[/C][/ROW]
[ROW][C]92[/C][C]2500[/C][C]2580.45623194211[/C][C]-80.456231942112[/C][/ROW]
[ROW][C]93[/C][C]2550[/C][C]2558.93353001058[/C][C]-8.93353001058358[/C][/ROW]
[ROW][C]94[/C][C]2790[/C][C]2556.5437374616[/C][C]233.456262538395[/C][/ROW]
[ROW][C]95[/C][C]2770[/C][C]2618.99520245536[/C][C]151.004797544636[/C][/ROW]
[ROW][C]96[/C][C]2460[/C][C]2659.39022431175[/C][C]-199.39022431175[/C][/ROW]
[ROW][C]97[/C][C]2800[/C][C]2606.05170394691[/C][C]193.948296053088[/C][/ROW]
[ROW][C]98[/C][C]2770[/C][C]2657.93446386888[/C][C]112.065536131123[/C][/ROW]
[ROW][C]99[/C][C]2450[/C][C]2687.91291392459[/C][C]-237.912913924585[/C][/ROW]
[ROW][C]100[/C][C]2370[/C][C]2624.2692581324[/C][C]-254.269258132396[/C][/ROW]
[ROW][C]101[/C][C]2540[/C][C]2556.25014611293[/C][C]-16.2501461129327[/C][/ROW]
[ROW][C]102[/C][C]3470[/C][C]2551.90309874705[/C][C]918.096901252945[/C][/ROW]
[ROW][C]103[/C][C]2690[/C][C]2797.50154989183[/C][C]-107.501549891826[/C][/ROW]
[ROW][C]104[/C][C]4110[/C][C]2768.74400358809[/C][C]1341.25599641191[/C][/ROW]
[ROW][C]105[/C][C]3840[/C][C]3127.54098335989[/C][C]712.459016640112[/C][/ROW]
[ROW][C]106[/C][C]2860[/C][C]3318.12961376714[/C][C]-458.129613767137[/C][/ROW]
[ROW][C]107[/C][C]3540[/C][C]3195.57618459075[/C][C]344.423815409248[/C][/ROW]
[ROW][C]108[/C][C]3370[/C][C]3287.71238011264[/C][C]82.2876198873564[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300114&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300114&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
235404020-480
334303891.59606312949-461.596063129495
442003768.11533031751431.884669682492
533603883.64802169511-523.648021695112
644403743.56788102823696.432118971773
743903929.86918485957460.130815140431
849404052.95795181679887.04204818321
939404290.24897505929-350.248975059292
1045604196.55450155414363.445498445859
1148504293.77915330062556.220846699376
1250704442.57279181239627.427208187613
1362104610.414716043551599.58528395645
1452005038.31689900216161.683100997835
1548605081.56845461373-221.568454613735
1651605022.29707574141137.702924258594
1755305059.13373739429470.866262605709
1888305185.094324598613644.90567540139
1944106160.13648760525-1750.13648760525
2048505691.96062287768-841.960622877685
2189605466.729250653863493.27074934614
2246206401.20782725933-1781.20782725933
2351205924.72012433296-804.720124332958
2445205709.45089090947-1189.45089090947
2588705391.263021936753478.73697806325
2694706321.853695520763148.14630447924
2765907164.00865247799-574.008652477989
2839707010.45663002818-3040.45663002818
2937706197.10954423725-2427.10954423725
3055005547.83783445383-47.837834453826
3165805535.040821380431044.95917861957
3252805814.57597222152-534.575972221518
3386405671.572515159812968.42748484019
3455106465.65121384334-955.651213843337
3556906210.00667606717-520.006676067167
3676206070.90062522141549.0993747786
3740106485.29741339892-2475.29741339892
3835705823.13505338684-2253.13505338684
3940405220.40294681224-1180.40294681224
4036004904.63547709508-1304.63547709508
4140004555.6347865952-555.634786595205
4230704406.99792396806-1336.99792396806
4332304049.34001349891-819.340013498913
4440603830.15983981393229.840160186074
4534803891.64396776984-411.643967769842
4637503781.52583016434-31.5258301643353
4739903773.09241202639216.907587973606
4831003831.11697084493-731.116970844929
4939503635.53718465883314.46281534117
5030103719.65856692797-709.658566927974
5131603529.81907978749-369.819079787489
5229603430.88944275719-470.889442757195
5327503304.92265467223-554.922654672231
5435903156.47629317526433.523706824741
5530603272.44744043149-212.447440431491
5629703215.61600766177-245.616007661771
5735903149.91171111555440.088288884454
5834503267.63893791423182.361062085769
5929303316.4220177136-386.422017713605
6026603213.05095861387-553.050958613873
6135403065.10529116381474.894708836186
6231603192.14352077535-32.143520775353
6326803183.54486533278-503.544865332782
6429003048.84248387516-148.842483875161
6529203009.02589866025-89.0258986602539
6629002985.21074059481-85.2107405948136
6731502962.41616860309187.583831396906
6831503012.59638202938137.403617970623
6931203049.3529767953870.6470232046249
7037203068.25163493632651.748365063675
7133603242.59966810943117.400331890568
7227403274.00521978579-534.005219785792
7332503131.15444368184118.845556318156
7427003162.94660474605-462.946604746045
7526103039.10459097474-429.104590974741
7624102924.31559345315-514.315593453148
7725902786.73195388383-196.731953883826
7826302734.1045426611-104.104542661096
7926502706.2557236532-56.2557236532039
8026002691.20685617702-91.2068561770152
8130602666.80827408803393.191725911965
8226502771.99028565471-121.990285654712
8327002739.3568837005-39.3568837004982
8426202728.82859451279-108.828594512793
8526302699.71605288878-69.7160528887794
8628502681.06643694296168.933563057037
8726802726.25755062231-46.2575506223079
8824302713.88327643503-283.883276435035
8925502637.94217163096-87.9421716309589
9025702614.41691943438-44.4169194343822
9125202602.53502918639-82.5350291863933
9225002580.45623194211-80.456231942112
9325502558.93353001058-8.93353001058358
9427902556.5437374616233.456262538395
9527702618.99520245536151.004797544636
9624602659.39022431175-199.39022431175
9728002606.05170394691193.948296053088
9827702657.93446386888112.065536131123
9924502687.91291392459-237.912913924585
10023702624.2692581324-254.269258132396
10125402556.25014611293-16.2501461129327
10234702551.90309874705918.096901252945
10326902797.50154989183-107.501549891826
10441102768.744003588091341.25599641191
10538403127.54098335989712.459016640112
10628603318.12961376714-458.129613767137
10735403195.57618459075344.423815409248
10833703287.7123801126482.2876198873564







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1093309.724993340231240.364024421895379.08596225856
1103309.724993340231167.600882365715451.84910431474
1113309.724993340231097.229435388965522.2205512915
1123309.724993340231029.028283760055590.4217029204
1133309.72499334023962.8082141966685656.64177248379
1143309.72499334023898.406006693855721.04397998661
1153309.72499334023835.6796941395335783.77029254092
1163309.72499334023774.5048787086035844.94510797185
1173309.72499334023714.7718306090525904.6781560714
1183309.72499334023656.383175197635963.06681148282
1193309.72499334023599.2520288854996020.19795779496
1203309.72499334023543.3004817773796076.14950490307

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 3309.72499334023 & 1240.36402442189 & 5379.08596225856 \tabularnewline
110 & 3309.72499334023 & 1167.60088236571 & 5451.84910431474 \tabularnewline
111 & 3309.72499334023 & 1097.22943538896 & 5522.2205512915 \tabularnewline
112 & 3309.72499334023 & 1029.02828376005 & 5590.4217029204 \tabularnewline
113 & 3309.72499334023 & 962.808214196668 & 5656.64177248379 \tabularnewline
114 & 3309.72499334023 & 898.40600669385 & 5721.04397998661 \tabularnewline
115 & 3309.72499334023 & 835.679694139533 & 5783.77029254092 \tabularnewline
116 & 3309.72499334023 & 774.504878708603 & 5844.94510797185 \tabularnewline
117 & 3309.72499334023 & 714.771830609052 & 5904.6781560714 \tabularnewline
118 & 3309.72499334023 & 656.38317519763 & 5963.06681148282 \tabularnewline
119 & 3309.72499334023 & 599.252028885499 & 6020.19795779496 \tabularnewline
120 & 3309.72499334023 & 543.300481777379 & 6076.14950490307 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300114&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]109[/C][C]3309.72499334023[/C][C]1240.36402442189[/C][C]5379.08596225856[/C][/ROW]
[ROW][C]110[/C][C]3309.72499334023[/C][C]1167.60088236571[/C][C]5451.84910431474[/C][/ROW]
[ROW][C]111[/C][C]3309.72499334023[/C][C]1097.22943538896[/C][C]5522.2205512915[/C][/ROW]
[ROW][C]112[/C][C]3309.72499334023[/C][C]1029.02828376005[/C][C]5590.4217029204[/C][/ROW]
[ROW][C]113[/C][C]3309.72499334023[/C][C]962.808214196668[/C][C]5656.64177248379[/C][/ROW]
[ROW][C]114[/C][C]3309.72499334023[/C][C]898.40600669385[/C][C]5721.04397998661[/C][/ROW]
[ROW][C]115[/C][C]3309.72499334023[/C][C]835.679694139533[/C][C]5783.77029254092[/C][/ROW]
[ROW][C]116[/C][C]3309.72499334023[/C][C]774.504878708603[/C][C]5844.94510797185[/C][/ROW]
[ROW][C]117[/C][C]3309.72499334023[/C][C]714.771830609052[/C][C]5904.6781560714[/C][/ROW]
[ROW][C]118[/C][C]3309.72499334023[/C][C]656.38317519763[/C][C]5963.06681148282[/C][/ROW]
[ROW][C]119[/C][C]3309.72499334023[/C][C]599.252028885499[/C][C]6020.19795779496[/C][/ROW]
[ROW][C]120[/C][C]3309.72499334023[/C][C]543.300481777379[/C][C]6076.14950490307[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300114&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300114&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
1093309.724993340231240.364024421895379.08596225856
1103309.724993340231167.600882365715451.84910431474
1113309.724993340231097.229435388965522.2205512915
1123309.724993340231029.028283760055590.4217029204
1133309.72499334023962.8082141966685656.64177248379
1143309.72499334023898.406006693855721.04397998661
1153309.72499334023835.6796941395335783.77029254092
1163309.72499334023774.5048787086035844.94510797185
1173309.72499334023714.7718306090525904.6781560714
1183309.72499334023656.383175197635963.06681148282
1193309.72499334023599.2520288854996020.19795779496
1203309.72499334023543.3004817773796076.14950490307



Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = Pearson Chi-Squared ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')