Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 24 Nov 2016 19:12:09 +0000
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/Nov/24/t1480014745qfl0bzbbly6m9bq.htm/, Retrieved Tue, 07 May 2024 08:38:31 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 07 May 2024 08:38:31 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
2884
2505
3128
2765
2398
3015
2769
2840
2895
2761
2712
3051
2980
2790
3164
2629
2919
2653
2788
3031
2794
2448
2856
2703
2918
2766
2907
2516
2754
3000
3117
3265
2748
2970
3081
2679
3034
2958
3029
2697
2844
2604
3289
3217
2834
3141
2674
2883
3237
2905
3211
3058
2784
3125
3370
3021
3152
3210
2930
3229
2961
2927
3342
2999
2593
3168
3547
3037
2911
2869
2827
2988




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0690311509383372
beta0
gamma0.537070088814664

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0690311509383372 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.537070088814664 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.0690311509383372[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.537070088814664[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.0690311509383372
beta0
gamma0.537070088814664







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1329802965.7403846153814.2596153846157
1427902768.9764905290721.0235094709292
1531643141.6795158363622.3204841636402
1626292626.472072799432.5279272005746
1729192924.68999344198-5.68999344198437
1826532667.7989548976-14.7989548976011
1927882796.94578092675-8.94578092675056
2030312852.45499162508178.545008374917
2127942907.40690729925-113.406907299247
2224482770.74671288244-322.746712882437
2328562684.42721741568171.57278258432
2427033029.64783231892-326.647832318917
2529182958.522115265-40.5221152650006
2627662761.358492019034.64150798097262
2729073133.57913044788-226.579130447877
2825162591.29367068685-75.2936706868472
2927542880.03055333425-126.030553334255
3030002610.27782749397389.722172506027
3131172770.27577330421346.72422669579
3232652944.08184913428320.91815086572
3327482862.88729608973-114.887296089734
3429702621.45594326889348.544056731108
3530812828.63395663558252.366043364417
3626792930.32374667501-251.323746675009
3730343007.45931533126.5406846689962
3829582837.50672375019120.493276249807
3930293102.1154591686-73.1154591686031
4026972646.0658257553950.9341742446072
4128442918.14814767215-74.1481476721483
4226042909.8509776193-305.850977619299
4332893000.33392793495288.666072065053
4432173157.2292601624859.7707398375196
4528342840.10662863338-6.10662863337757
4631412837.8981318599303.1018681401
4726742993.85064260559-319.850642605589
4828832804.1970165032878.8029834967233
4932373043.05258481844193.947415181559
5029052931.63214763264-26.632147632643
5132113089.28114489189121.718855108106
5230582708.70540970356349.294590296439
5327842938.84329363888-154.843293638884
5431252809.12526727242315.874732727577
5533703239.78252180317130.217478196825
5630213271.29332400813-250.293324008127
5731522899.82822402095252.171775979046
5832103070.05184667039139.948153329613
5929302903.2682026314926.7317973685094
6032292936.86458931491292.135410685086
6129613248.01844088874-287.01844088874
6229272993.10758334546-66.1075833454561
6333423222.20638296489119.793617035112
6429992955.284594988843.7154050111963
6525932912.26131139639-319.261311396394
6631683006.5502255485161.449774451497
6735473333.71955150026213.280448499741
6830373180.71058879954-143.710588799536
6929113067.83331787456-156.833317874561
7028693153.71153931789-284.711539317888
7128272901.00547688984-74.0054768898435
7229883060.34847188896-72.3484718889576

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2980 & 2965.74038461538 & 14.2596153846157 \tabularnewline
14 & 2790 & 2768.97649052907 & 21.0235094709292 \tabularnewline
15 & 3164 & 3141.67951583636 & 22.3204841636402 \tabularnewline
16 & 2629 & 2626.47207279943 & 2.5279272005746 \tabularnewline
17 & 2919 & 2924.68999344198 & -5.68999344198437 \tabularnewline
18 & 2653 & 2667.7989548976 & -14.7989548976011 \tabularnewline
19 & 2788 & 2796.94578092675 & -8.94578092675056 \tabularnewline
20 & 3031 & 2852.45499162508 & 178.545008374917 \tabularnewline
21 & 2794 & 2907.40690729925 & -113.406907299247 \tabularnewline
22 & 2448 & 2770.74671288244 & -322.746712882437 \tabularnewline
23 & 2856 & 2684.42721741568 & 171.57278258432 \tabularnewline
24 & 2703 & 3029.64783231892 & -326.647832318917 \tabularnewline
25 & 2918 & 2958.522115265 & -40.5221152650006 \tabularnewline
26 & 2766 & 2761.35849201903 & 4.64150798097262 \tabularnewline
27 & 2907 & 3133.57913044788 & -226.579130447877 \tabularnewline
28 & 2516 & 2591.29367068685 & -75.2936706868472 \tabularnewline
29 & 2754 & 2880.03055333425 & -126.030553334255 \tabularnewline
30 & 3000 & 2610.27782749397 & 389.722172506027 \tabularnewline
31 & 3117 & 2770.27577330421 & 346.72422669579 \tabularnewline
32 & 3265 & 2944.08184913428 & 320.91815086572 \tabularnewline
33 & 2748 & 2862.88729608973 & -114.887296089734 \tabularnewline
34 & 2970 & 2621.45594326889 & 348.544056731108 \tabularnewline
35 & 3081 & 2828.63395663558 & 252.366043364417 \tabularnewline
36 & 2679 & 2930.32374667501 & -251.323746675009 \tabularnewline
37 & 3034 & 3007.459315331 & 26.5406846689962 \tabularnewline
38 & 2958 & 2837.50672375019 & 120.493276249807 \tabularnewline
39 & 3029 & 3102.1154591686 & -73.1154591686031 \tabularnewline
40 & 2697 & 2646.06582575539 & 50.9341742446072 \tabularnewline
41 & 2844 & 2918.14814767215 & -74.1481476721483 \tabularnewline
42 & 2604 & 2909.8509776193 & -305.850977619299 \tabularnewline
43 & 3289 & 3000.33392793495 & 288.666072065053 \tabularnewline
44 & 3217 & 3157.22926016248 & 59.7707398375196 \tabularnewline
45 & 2834 & 2840.10662863338 & -6.10662863337757 \tabularnewline
46 & 3141 & 2837.8981318599 & 303.1018681401 \tabularnewline
47 & 2674 & 2993.85064260559 & -319.850642605589 \tabularnewline
48 & 2883 & 2804.19701650328 & 78.8029834967233 \tabularnewline
49 & 3237 & 3043.05258481844 & 193.947415181559 \tabularnewline
50 & 2905 & 2931.63214763264 & -26.632147632643 \tabularnewline
51 & 3211 & 3089.28114489189 & 121.718855108106 \tabularnewline
52 & 3058 & 2708.70540970356 & 349.294590296439 \tabularnewline
53 & 2784 & 2938.84329363888 & -154.843293638884 \tabularnewline
54 & 3125 & 2809.12526727242 & 315.874732727577 \tabularnewline
55 & 3370 & 3239.78252180317 & 130.217478196825 \tabularnewline
56 & 3021 & 3271.29332400813 & -250.293324008127 \tabularnewline
57 & 3152 & 2899.82822402095 & 252.171775979046 \tabularnewline
58 & 3210 & 3070.05184667039 & 139.948153329613 \tabularnewline
59 & 2930 & 2903.26820263149 & 26.7317973685094 \tabularnewline
60 & 3229 & 2936.86458931491 & 292.135410685086 \tabularnewline
61 & 2961 & 3248.01844088874 & -287.01844088874 \tabularnewline
62 & 2927 & 2993.10758334546 & -66.1075833454561 \tabularnewline
63 & 3342 & 3222.20638296489 & 119.793617035112 \tabularnewline
64 & 2999 & 2955.2845949888 & 43.7154050111963 \tabularnewline
65 & 2593 & 2912.26131139639 & -319.261311396394 \tabularnewline
66 & 3168 & 3006.5502255485 & 161.449774451497 \tabularnewline
67 & 3547 & 3333.71955150026 & 213.280448499741 \tabularnewline
68 & 3037 & 3180.71058879954 & -143.710588799536 \tabularnewline
69 & 2911 & 3067.83331787456 & -156.833317874561 \tabularnewline
70 & 2869 & 3153.71153931789 & -284.711539317888 \tabularnewline
71 & 2827 & 2901.00547688984 & -74.0054768898435 \tabularnewline
72 & 2988 & 3060.34847188896 & -72.3484718889576 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]2980[/C][C]2965.74038461538[/C][C]14.2596153846157[/C][/ROW]
[ROW][C]14[/C][C]2790[/C][C]2768.97649052907[/C][C]21.0235094709292[/C][/ROW]
[ROW][C]15[/C][C]3164[/C][C]3141.67951583636[/C][C]22.3204841636402[/C][/ROW]
[ROW][C]16[/C][C]2629[/C][C]2626.47207279943[/C][C]2.5279272005746[/C][/ROW]
[ROW][C]17[/C][C]2919[/C][C]2924.68999344198[/C][C]-5.68999344198437[/C][/ROW]
[ROW][C]18[/C][C]2653[/C][C]2667.7989548976[/C][C]-14.7989548976011[/C][/ROW]
[ROW][C]19[/C][C]2788[/C][C]2796.94578092675[/C][C]-8.94578092675056[/C][/ROW]
[ROW][C]20[/C][C]3031[/C][C]2852.45499162508[/C][C]178.545008374917[/C][/ROW]
[ROW][C]21[/C][C]2794[/C][C]2907.40690729925[/C][C]-113.406907299247[/C][/ROW]
[ROW][C]22[/C][C]2448[/C][C]2770.74671288244[/C][C]-322.746712882437[/C][/ROW]
[ROW][C]23[/C][C]2856[/C][C]2684.42721741568[/C][C]171.57278258432[/C][/ROW]
[ROW][C]24[/C][C]2703[/C][C]3029.64783231892[/C][C]-326.647832318917[/C][/ROW]
[ROW][C]25[/C][C]2918[/C][C]2958.522115265[/C][C]-40.5221152650006[/C][/ROW]
[ROW][C]26[/C][C]2766[/C][C]2761.35849201903[/C][C]4.64150798097262[/C][/ROW]
[ROW][C]27[/C][C]2907[/C][C]3133.57913044788[/C][C]-226.579130447877[/C][/ROW]
[ROW][C]28[/C][C]2516[/C][C]2591.29367068685[/C][C]-75.2936706868472[/C][/ROW]
[ROW][C]29[/C][C]2754[/C][C]2880.03055333425[/C][C]-126.030553334255[/C][/ROW]
[ROW][C]30[/C][C]3000[/C][C]2610.27782749397[/C][C]389.722172506027[/C][/ROW]
[ROW][C]31[/C][C]3117[/C][C]2770.27577330421[/C][C]346.72422669579[/C][/ROW]
[ROW][C]32[/C][C]3265[/C][C]2944.08184913428[/C][C]320.91815086572[/C][/ROW]
[ROW][C]33[/C][C]2748[/C][C]2862.88729608973[/C][C]-114.887296089734[/C][/ROW]
[ROW][C]34[/C][C]2970[/C][C]2621.45594326889[/C][C]348.544056731108[/C][/ROW]
[ROW][C]35[/C][C]3081[/C][C]2828.63395663558[/C][C]252.366043364417[/C][/ROW]
[ROW][C]36[/C][C]2679[/C][C]2930.32374667501[/C][C]-251.323746675009[/C][/ROW]
[ROW][C]37[/C][C]3034[/C][C]3007.459315331[/C][C]26.5406846689962[/C][/ROW]
[ROW][C]38[/C][C]2958[/C][C]2837.50672375019[/C][C]120.493276249807[/C][/ROW]
[ROW][C]39[/C][C]3029[/C][C]3102.1154591686[/C][C]-73.1154591686031[/C][/ROW]
[ROW][C]40[/C][C]2697[/C][C]2646.06582575539[/C][C]50.9341742446072[/C][/ROW]
[ROW][C]41[/C][C]2844[/C][C]2918.14814767215[/C][C]-74.1481476721483[/C][/ROW]
[ROW][C]42[/C][C]2604[/C][C]2909.8509776193[/C][C]-305.850977619299[/C][/ROW]
[ROW][C]43[/C][C]3289[/C][C]3000.33392793495[/C][C]288.666072065053[/C][/ROW]
[ROW][C]44[/C][C]3217[/C][C]3157.22926016248[/C][C]59.7707398375196[/C][/ROW]
[ROW][C]45[/C][C]2834[/C][C]2840.10662863338[/C][C]-6.10662863337757[/C][/ROW]
[ROW][C]46[/C][C]3141[/C][C]2837.8981318599[/C][C]303.1018681401[/C][/ROW]
[ROW][C]47[/C][C]2674[/C][C]2993.85064260559[/C][C]-319.850642605589[/C][/ROW]
[ROW][C]48[/C][C]2883[/C][C]2804.19701650328[/C][C]78.8029834967233[/C][/ROW]
[ROW][C]49[/C][C]3237[/C][C]3043.05258481844[/C][C]193.947415181559[/C][/ROW]
[ROW][C]50[/C][C]2905[/C][C]2931.63214763264[/C][C]-26.632147632643[/C][/ROW]
[ROW][C]51[/C][C]3211[/C][C]3089.28114489189[/C][C]121.718855108106[/C][/ROW]
[ROW][C]52[/C][C]3058[/C][C]2708.70540970356[/C][C]349.294590296439[/C][/ROW]
[ROW][C]53[/C][C]2784[/C][C]2938.84329363888[/C][C]-154.843293638884[/C][/ROW]
[ROW][C]54[/C][C]3125[/C][C]2809.12526727242[/C][C]315.874732727577[/C][/ROW]
[ROW][C]55[/C][C]3370[/C][C]3239.78252180317[/C][C]130.217478196825[/C][/ROW]
[ROW][C]56[/C][C]3021[/C][C]3271.29332400813[/C][C]-250.293324008127[/C][/ROW]
[ROW][C]57[/C][C]3152[/C][C]2899.82822402095[/C][C]252.171775979046[/C][/ROW]
[ROW][C]58[/C][C]3210[/C][C]3070.05184667039[/C][C]139.948153329613[/C][/ROW]
[ROW][C]59[/C][C]2930[/C][C]2903.26820263149[/C][C]26.7317973685094[/C][/ROW]
[ROW][C]60[/C][C]3229[/C][C]2936.86458931491[/C][C]292.135410685086[/C][/ROW]
[ROW][C]61[/C][C]2961[/C][C]3248.01844088874[/C][C]-287.01844088874[/C][/ROW]
[ROW][C]62[/C][C]2927[/C][C]2993.10758334546[/C][C]-66.1075833454561[/C][/ROW]
[ROW][C]63[/C][C]3342[/C][C]3222.20638296489[/C][C]119.793617035112[/C][/ROW]
[ROW][C]64[/C][C]2999[/C][C]2955.2845949888[/C][C]43.7154050111963[/C][/ROW]
[ROW][C]65[/C][C]2593[/C][C]2912.26131139639[/C][C]-319.261311396394[/C][/ROW]
[ROW][C]66[/C][C]3168[/C][C]3006.5502255485[/C][C]161.449774451497[/C][/ROW]
[ROW][C]67[/C][C]3547[/C][C]3333.71955150026[/C][C]213.280448499741[/C][/ROW]
[ROW][C]68[/C][C]3037[/C][C]3180.71058879954[/C][C]-143.710588799536[/C][/ROW]
[ROW][C]69[/C][C]2911[/C][C]3067.83331787456[/C][C]-156.833317874561[/C][/ROW]
[ROW][C]70[/C][C]2869[/C][C]3153.71153931789[/C][C]-284.711539317888[/C][/ROW]
[ROW][C]71[/C][C]2827[/C][C]2901.00547688984[/C][C]-74.0054768898435[/C][/ROW]
[ROW][C]72[/C][C]2988[/C][C]3060.34847188896[/C][C]-72.3484718889576[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
1329802965.7403846153814.2596153846157
1427902768.9764905290721.0235094709292
1531643141.6795158363622.3204841636402
1626292626.472072799432.5279272005746
1729192924.68999344198-5.68999344198437
1826532667.7989548976-14.7989548976011
1927882796.94578092675-8.94578092675056
2030312852.45499162508178.545008374917
2127942907.40690729925-113.406907299247
2224482770.74671288244-322.746712882437
2328562684.42721741568171.57278258432
2427033029.64783231892-326.647832318917
2529182958.522115265-40.5221152650006
2627662761.358492019034.64150798097262
2729073133.57913044788-226.579130447877
2825162591.29367068685-75.2936706868472
2927542880.03055333425-126.030553334255
3030002610.27782749397389.722172506027
3131172770.27577330421346.72422669579
3232652944.08184913428320.91815086572
3327482862.88729608973-114.887296089734
3429702621.45594326889348.544056731108
3530812828.63395663558252.366043364417
3626792930.32374667501-251.323746675009
3730343007.45931533126.5406846689962
3829582837.50672375019120.493276249807
3930293102.1154591686-73.1154591686031
4026972646.0658257553950.9341742446072
4128442918.14814767215-74.1481476721483
4226042909.8509776193-305.850977619299
4332893000.33392793495288.666072065053
4432173157.2292601624859.7707398375196
4528342840.10662863338-6.10662863337757
4631412837.8981318599303.1018681401
4726742993.85064260559-319.850642605589
4828832804.1970165032878.8029834967233
4932373043.05258481844193.947415181559
5029052931.63214763264-26.632147632643
5132113089.28114489189121.718855108106
5230582708.70540970356349.294590296439
5327842938.84329363888-154.843293638884
5431252809.12526727242315.874732727577
5533703239.78252180317130.217478196825
5630213271.29332400813-250.293324008127
5731522899.82822402095252.171775979046
5832103070.05184667039139.948153329613
5929302903.2682026314926.7317973685094
6032292936.86458931491292.135410685086
6129613248.01844088874-287.01844088874
6229272993.10758334546-66.1075833454561
6333423222.20638296489119.793617035112
6429992955.284594988843.7154050111963
6525932912.26131139639-319.261311396394
6631683006.5502255485161.449774451497
6735473333.71955150026213.280448499741
6830373180.71058879954-143.710588799536
6929113067.83331787456-156.833317874561
7028693153.71153931789-284.711539317888
7128272901.00547688984-74.0054768898435
7229883060.34847188896-72.3484718889576







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
733056.767248954082665.807817124073447.7266807841
742932.124044357942540.234200182883324.01388853299
753258.736094349682865.918041559013651.55414714035
762945.506049746692551.761976484693339.2501230087
772717.978308475512323.310387484123112.64622946689
783074.659588919052679.069977717783470.24920012031
793416.598956071333020.089797134153813.10811500851
803070.373078333882672.946499263263467.79965740449
812960.855008975932562.513122674133359.19689527773
822993.621076717182594.365981554733392.87617187964
832865.921067300612465.754847282123266.0872873191
843031.201240626292630.125965553663432.27651569892

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 3056.76724895408 & 2665.80781712407 & 3447.7266807841 \tabularnewline
74 & 2932.12404435794 & 2540.23420018288 & 3324.01388853299 \tabularnewline
75 & 3258.73609434968 & 2865.91804155901 & 3651.55414714035 \tabularnewline
76 & 2945.50604974669 & 2551.76197648469 & 3339.2501230087 \tabularnewline
77 & 2717.97830847551 & 2323.31038748412 & 3112.64622946689 \tabularnewline
78 & 3074.65958891905 & 2679.06997771778 & 3470.24920012031 \tabularnewline
79 & 3416.59895607133 & 3020.08979713415 & 3813.10811500851 \tabularnewline
80 & 3070.37307833388 & 2672.94649926326 & 3467.79965740449 \tabularnewline
81 & 2960.85500897593 & 2562.51312267413 & 3359.19689527773 \tabularnewline
82 & 2993.62107671718 & 2594.36598155473 & 3392.87617187964 \tabularnewline
83 & 2865.92106730061 & 2465.75484728212 & 3266.0872873191 \tabularnewline
84 & 3031.20124062629 & 2630.12596555366 & 3432.27651569892 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]73[/C][C]3056.76724895408[/C][C]2665.80781712407[/C][C]3447.7266807841[/C][/ROW]
[ROW][C]74[/C][C]2932.12404435794[/C][C]2540.23420018288[/C][C]3324.01388853299[/C][/ROW]
[ROW][C]75[/C][C]3258.73609434968[/C][C]2865.91804155901[/C][C]3651.55414714035[/C][/ROW]
[ROW][C]76[/C][C]2945.50604974669[/C][C]2551.76197648469[/C][C]3339.2501230087[/C][/ROW]
[ROW][C]77[/C][C]2717.97830847551[/C][C]2323.31038748412[/C][C]3112.64622946689[/C][/ROW]
[ROW][C]78[/C][C]3074.65958891905[/C][C]2679.06997771778[/C][C]3470.24920012031[/C][/ROW]
[ROW][C]79[/C][C]3416.59895607133[/C][C]3020.08979713415[/C][C]3813.10811500851[/C][/ROW]
[ROW][C]80[/C][C]3070.37307833388[/C][C]2672.94649926326[/C][C]3467.79965740449[/C][/ROW]
[ROW][C]81[/C][C]2960.85500897593[/C][C]2562.51312267413[/C][C]3359.19689527773[/C][/ROW]
[ROW][C]82[/C][C]2993.62107671718[/C][C]2594.36598155473[/C][C]3392.87617187964[/C][/ROW]
[ROW][C]83[/C][C]2865.92106730061[/C][C]2465.75484728212[/C][C]3266.0872873191[/C][/ROW]
[ROW][C]84[/C][C]3031.20124062629[/C][C]2630.12596555366[/C][C]3432.27651569892[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
733056.767248954082665.807817124073447.7266807841
742932.124044357942540.234200182883324.01388853299
753258.736094349682865.918041559013651.55414714035
762945.506049746692551.761976484693339.2501230087
772717.978308475512323.310387484123112.64622946689
783074.659588919052679.069977717783470.24920012031
793416.598956071333020.089797134153813.10811500851
803070.373078333882672.946499263263467.79965740449
812960.855008975932562.513122674133359.19689527773
822993.621076717182594.365981554733392.87617187964
832865.921067300612465.754847282123266.0872873191
843031.201240626292630.125965553663432.27651569892



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