Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 18 Jul 2016 22:47:21 +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/Jul/18/t1468878782003a6w0wmfnolu4.htm/, Retrieved Fri, 03 May 2024 10:40:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295892, Retrieved Fri, 03 May 2024 10:40:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [reeks b stap 17] [2016-07-11 20:05:23] [74be16979710d4c4e7c6647856088456]
- RMP     [Exponential Smoothing] [Reeks B stap 27] [2016-07-18 21:47:21] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
1230
1360
1360
1250
1420
1390
1280
1330
1400
1370
1290
1500
1260
1360
1320
1300
1440
1360
1330
1420
1510
1280
1310
1460
1280
1370
1390
1390
1460
1410
1230
1260
1590
1250
1400
1450
1220
1290
1400
1400
1460
1450
1270
1260
1550
1230
1380
1490
1180
1190
1400
1380
1510
1400
1290
1200
1600
1220
1380
1450
1260
1130
1390
1380
1570
1320
1210
1190
1580
1150
1330
1420
1260
1040
1450
1360
1500
1240
1260
1220
1680
1210
1350
1480
1270
1040
1450
1310
1510
1160
1290
1230
1680
1190
1310
1480
1320
1050
1380
1320
1480
1150
1250
1260
1680
1150
1310
1470




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295892&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295892&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295892&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0158751338414481
beta0.26613735251105
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0158751338414481 \tabularnewline
beta & 0.26613735251105 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295892&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]0.0158751338414481[/C][/ROW]
[ROW][C]beta[/C][C]0.26613735251105[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295892&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295892&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
alpha0.0158751338414481
beta0.26613735251105
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1312601259.39369658120.606303418802327
1413601355.412584972214.58741502779367
1513201309.0140557157910.9859442842146
1613001290.263519209789.73648079021973
1714401435.284283604774.71571639523427
1813601358.161933101531.83806689847324
1913301294.751665297735.2483347023019
2014201346.1873796524973.8126203475069
2115101421.4638296881588.5361703118485
2212801395.26474703421-115.264747034206
2313101312.84330789264-2.84330789263618
2414601525.52789459799-65.5278945979876
2512801286.28718023776-6.28718023776355
2613701386.28158968204-16.2815896820366
2713901345.9275881931244.0724118068772
2813901326.6913391592763.3086608407255
2914601468.06651410435-8.06651410435461
3014101388.300277174721.6997228252978
3112301358.56010559001-128.560105590008
3212601445.1302408164-185.130240816404
3315901529.4745544403460.5254455596616
3412501300.83570744201-50.8357074420135
3514001328.916492349671.0835076503986
3614501480.24022560728-30.2402256072778
3712201299.16406597377-79.1640659737698
3812901387.16199404292-97.1619940429241
3914001403.57435777773-3.57435777773117
4014001400.96575375028-0.965753750277599
4114601469.26009489392-9.26009489392231
4214501416.9451764282133.0548235717927
4312701237.7353827593332.2646172406712
4412601270.09058192794-10.0905819279353
4515501598.61310636417-48.6131063641662
4612301257.83084709657-27.8308470965671
4713801405.54021987383-25.5402198738277
4814901454.486252519235.5137474807962
4911801225.45600588841-45.4560058884088
5011901295.5684885136-105.5684885136
5114001403.20544402587-3.20544402587348
5213801402.42757327983-22.4275732798255
5315101461.3855469751648.614453024835
5414001451.04408535483-51.0440853548328
5512901268.7777606920221.222239307983
5612001258.2844143888-58.2844143888026
5716001546.9368222402453.0631777597564
5812201227.45654572528-7.45654572528065
5913801377.065227218632.93477278136902
6014501485.98993825918-35.9899382591766
6112601175.280019326484.7199806735966
6211301187.99066934902-57.9906693490236
6313901397.01175634294-7.01175634294304
6413801377.131212738082.86878726192276
6515701506.3865986749363.6134013250664
6613201398.25177617338-78.2517761733836
6712101286.60263584422-76.6026358442214
6811901195.82854782682-5.82854782682466
6915801594.63197425844-14.6319742584444
7011501213.97039410575-63.9703941057476
7113301372.12182726927-42.1218272692693
7214201441.04768174567-21.0476817456679
7312601248.454935510911.5450644891027
7410401118.33599261496-78.3359926149583
7514501375.894920539774.105079460297
7613601366.05973181513-6.0597318151265
7715001553.94986441343-53.9498644134326
7812401302.83516261595-62.8351626159547
7912601191.6183598663668.3816401336353
8012201171.9736469526748.0263530473298
8116801562.37308183501117.626918164991
8212101135.219478358474.780521641602
8313501317.6250515937532.3749484062464
8414801409.3376221487470.6623778512649
8512701251.5280684538918.4719315461059
8610401034.346124028495.65387597151357
8714501444.895523179915.10447682009112
8813101356.41730244821-46.4173024482063
8915101497.710919472112.2890805279003
9011601240.35742077757-80.3574207775746
9112901259.3760312224130.6239687775901
9212301220.320104106059.67989589394688
9316801679.66475626160.335243738395093
9411901209.04569974567-19.0456997456711
9513101348.39574970485-38.3957497048509
9614801476.531793164433.46820683557326
9713201265.8770697634854.1229302365218
9810501036.3806094846413.6193905153564
9913801446.28352590559-66.2835259055921
10013201305.4342760848314.5657239151733
10114801505.19419845738-25.1941984573848
10211501155.63533676622-5.63533676621523
10312501284.9408284803-34.9408284803021
10412601223.8365725061536.1634274938478
10516801674.121345738955.87865426105191
10611501184.25643993659-34.256439936587
10713101303.997303913516.00269608649069
10814701473.9002730779-3.90027307790342

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1260 & 1259.3936965812 & 0.606303418802327 \tabularnewline
14 & 1360 & 1355.41258497221 & 4.58741502779367 \tabularnewline
15 & 1320 & 1309.01405571579 & 10.9859442842146 \tabularnewline
16 & 1300 & 1290.26351920978 & 9.73648079021973 \tabularnewline
17 & 1440 & 1435.28428360477 & 4.71571639523427 \tabularnewline
18 & 1360 & 1358.16193310153 & 1.83806689847324 \tabularnewline
19 & 1330 & 1294.7516652977 & 35.2483347023019 \tabularnewline
20 & 1420 & 1346.18737965249 & 73.8126203475069 \tabularnewline
21 & 1510 & 1421.46382968815 & 88.5361703118485 \tabularnewline
22 & 1280 & 1395.26474703421 & -115.264747034206 \tabularnewline
23 & 1310 & 1312.84330789264 & -2.84330789263618 \tabularnewline
24 & 1460 & 1525.52789459799 & -65.5278945979876 \tabularnewline
25 & 1280 & 1286.28718023776 & -6.28718023776355 \tabularnewline
26 & 1370 & 1386.28158968204 & -16.2815896820366 \tabularnewline
27 & 1390 & 1345.92758819312 & 44.0724118068772 \tabularnewline
28 & 1390 & 1326.69133915927 & 63.3086608407255 \tabularnewline
29 & 1460 & 1468.06651410435 & -8.06651410435461 \tabularnewline
30 & 1410 & 1388.3002771747 & 21.6997228252978 \tabularnewline
31 & 1230 & 1358.56010559001 & -128.560105590008 \tabularnewline
32 & 1260 & 1445.1302408164 & -185.130240816404 \tabularnewline
33 & 1590 & 1529.47455444034 & 60.5254455596616 \tabularnewline
34 & 1250 & 1300.83570744201 & -50.8357074420135 \tabularnewline
35 & 1400 & 1328.9164923496 & 71.0835076503986 \tabularnewline
36 & 1450 & 1480.24022560728 & -30.2402256072778 \tabularnewline
37 & 1220 & 1299.16406597377 & -79.1640659737698 \tabularnewline
38 & 1290 & 1387.16199404292 & -97.1619940429241 \tabularnewline
39 & 1400 & 1403.57435777773 & -3.57435777773117 \tabularnewline
40 & 1400 & 1400.96575375028 & -0.965753750277599 \tabularnewline
41 & 1460 & 1469.26009489392 & -9.26009489392231 \tabularnewline
42 & 1450 & 1416.94517642821 & 33.0548235717927 \tabularnewline
43 & 1270 & 1237.73538275933 & 32.2646172406712 \tabularnewline
44 & 1260 & 1270.09058192794 & -10.0905819279353 \tabularnewline
45 & 1550 & 1598.61310636417 & -48.6131063641662 \tabularnewline
46 & 1230 & 1257.83084709657 & -27.8308470965671 \tabularnewline
47 & 1380 & 1405.54021987383 & -25.5402198738277 \tabularnewline
48 & 1490 & 1454.4862525192 & 35.5137474807962 \tabularnewline
49 & 1180 & 1225.45600588841 & -45.4560058884088 \tabularnewline
50 & 1190 & 1295.5684885136 & -105.5684885136 \tabularnewline
51 & 1400 & 1403.20544402587 & -3.20544402587348 \tabularnewline
52 & 1380 & 1402.42757327983 & -22.4275732798255 \tabularnewline
53 & 1510 & 1461.38554697516 & 48.614453024835 \tabularnewline
54 & 1400 & 1451.04408535483 & -51.0440853548328 \tabularnewline
55 & 1290 & 1268.77776069202 & 21.222239307983 \tabularnewline
56 & 1200 & 1258.2844143888 & -58.2844143888026 \tabularnewline
57 & 1600 & 1546.93682224024 & 53.0631777597564 \tabularnewline
58 & 1220 & 1227.45654572528 & -7.45654572528065 \tabularnewline
59 & 1380 & 1377.06522721863 & 2.93477278136902 \tabularnewline
60 & 1450 & 1485.98993825918 & -35.9899382591766 \tabularnewline
61 & 1260 & 1175.2800193264 & 84.7199806735966 \tabularnewline
62 & 1130 & 1187.99066934902 & -57.9906693490236 \tabularnewline
63 & 1390 & 1397.01175634294 & -7.01175634294304 \tabularnewline
64 & 1380 & 1377.13121273808 & 2.86878726192276 \tabularnewline
65 & 1570 & 1506.38659867493 & 63.6134013250664 \tabularnewline
66 & 1320 & 1398.25177617338 & -78.2517761733836 \tabularnewline
67 & 1210 & 1286.60263584422 & -76.6026358442214 \tabularnewline
68 & 1190 & 1195.82854782682 & -5.82854782682466 \tabularnewline
69 & 1580 & 1594.63197425844 & -14.6319742584444 \tabularnewline
70 & 1150 & 1213.97039410575 & -63.9703941057476 \tabularnewline
71 & 1330 & 1372.12182726927 & -42.1218272692693 \tabularnewline
72 & 1420 & 1441.04768174567 & -21.0476817456679 \tabularnewline
73 & 1260 & 1248.4549355109 & 11.5450644891027 \tabularnewline
74 & 1040 & 1118.33599261496 & -78.3359926149583 \tabularnewline
75 & 1450 & 1375.8949205397 & 74.105079460297 \tabularnewline
76 & 1360 & 1366.05973181513 & -6.0597318151265 \tabularnewline
77 & 1500 & 1553.94986441343 & -53.9498644134326 \tabularnewline
78 & 1240 & 1302.83516261595 & -62.8351626159547 \tabularnewline
79 & 1260 & 1191.61835986636 & 68.3816401336353 \tabularnewline
80 & 1220 & 1171.97364695267 & 48.0263530473298 \tabularnewline
81 & 1680 & 1562.37308183501 & 117.626918164991 \tabularnewline
82 & 1210 & 1135.2194783584 & 74.780521641602 \tabularnewline
83 & 1350 & 1317.62505159375 & 32.3749484062464 \tabularnewline
84 & 1480 & 1409.33762214874 & 70.6623778512649 \tabularnewline
85 & 1270 & 1251.52806845389 & 18.4719315461059 \tabularnewline
86 & 1040 & 1034.34612402849 & 5.65387597151357 \tabularnewline
87 & 1450 & 1444.89552317991 & 5.10447682009112 \tabularnewline
88 & 1310 & 1356.41730244821 & -46.4173024482063 \tabularnewline
89 & 1510 & 1497.7109194721 & 12.2890805279003 \tabularnewline
90 & 1160 & 1240.35742077757 & -80.3574207775746 \tabularnewline
91 & 1290 & 1259.37603122241 & 30.6239687775901 \tabularnewline
92 & 1230 & 1220.32010410605 & 9.67989589394688 \tabularnewline
93 & 1680 & 1679.6647562616 & 0.335243738395093 \tabularnewline
94 & 1190 & 1209.04569974567 & -19.0456997456711 \tabularnewline
95 & 1310 & 1348.39574970485 & -38.3957497048509 \tabularnewline
96 & 1480 & 1476.53179316443 & 3.46820683557326 \tabularnewline
97 & 1320 & 1265.87706976348 & 54.1229302365218 \tabularnewline
98 & 1050 & 1036.38060948464 & 13.6193905153564 \tabularnewline
99 & 1380 & 1446.28352590559 & -66.2835259055921 \tabularnewline
100 & 1320 & 1305.43427608483 & 14.5657239151733 \tabularnewline
101 & 1480 & 1505.19419845738 & -25.1941984573848 \tabularnewline
102 & 1150 & 1155.63533676622 & -5.63533676621523 \tabularnewline
103 & 1250 & 1284.9408284803 & -34.9408284803021 \tabularnewline
104 & 1260 & 1223.83657250615 & 36.1634274938478 \tabularnewline
105 & 1680 & 1674.12134573895 & 5.87865426105191 \tabularnewline
106 & 1150 & 1184.25643993659 & -34.256439936587 \tabularnewline
107 & 1310 & 1303.99730391351 & 6.00269608649069 \tabularnewline
108 & 1470 & 1473.9002730779 & -3.90027307790342 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295892&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]1260[/C][C]1259.3936965812[/C][C]0.606303418802327[/C][/ROW]
[ROW][C]14[/C][C]1360[/C][C]1355.41258497221[/C][C]4.58741502779367[/C][/ROW]
[ROW][C]15[/C][C]1320[/C][C]1309.01405571579[/C][C]10.9859442842146[/C][/ROW]
[ROW][C]16[/C][C]1300[/C][C]1290.26351920978[/C][C]9.73648079021973[/C][/ROW]
[ROW][C]17[/C][C]1440[/C][C]1435.28428360477[/C][C]4.71571639523427[/C][/ROW]
[ROW][C]18[/C][C]1360[/C][C]1358.16193310153[/C][C]1.83806689847324[/C][/ROW]
[ROW][C]19[/C][C]1330[/C][C]1294.7516652977[/C][C]35.2483347023019[/C][/ROW]
[ROW][C]20[/C][C]1420[/C][C]1346.18737965249[/C][C]73.8126203475069[/C][/ROW]
[ROW][C]21[/C][C]1510[/C][C]1421.46382968815[/C][C]88.5361703118485[/C][/ROW]
[ROW][C]22[/C][C]1280[/C][C]1395.26474703421[/C][C]-115.264747034206[/C][/ROW]
[ROW][C]23[/C][C]1310[/C][C]1312.84330789264[/C][C]-2.84330789263618[/C][/ROW]
[ROW][C]24[/C][C]1460[/C][C]1525.52789459799[/C][C]-65.5278945979876[/C][/ROW]
[ROW][C]25[/C][C]1280[/C][C]1286.28718023776[/C][C]-6.28718023776355[/C][/ROW]
[ROW][C]26[/C][C]1370[/C][C]1386.28158968204[/C][C]-16.2815896820366[/C][/ROW]
[ROW][C]27[/C][C]1390[/C][C]1345.92758819312[/C][C]44.0724118068772[/C][/ROW]
[ROW][C]28[/C][C]1390[/C][C]1326.69133915927[/C][C]63.3086608407255[/C][/ROW]
[ROW][C]29[/C][C]1460[/C][C]1468.06651410435[/C][C]-8.06651410435461[/C][/ROW]
[ROW][C]30[/C][C]1410[/C][C]1388.3002771747[/C][C]21.6997228252978[/C][/ROW]
[ROW][C]31[/C][C]1230[/C][C]1358.56010559001[/C][C]-128.560105590008[/C][/ROW]
[ROW][C]32[/C][C]1260[/C][C]1445.1302408164[/C][C]-185.130240816404[/C][/ROW]
[ROW][C]33[/C][C]1590[/C][C]1529.47455444034[/C][C]60.5254455596616[/C][/ROW]
[ROW][C]34[/C][C]1250[/C][C]1300.83570744201[/C][C]-50.8357074420135[/C][/ROW]
[ROW][C]35[/C][C]1400[/C][C]1328.9164923496[/C][C]71.0835076503986[/C][/ROW]
[ROW][C]36[/C][C]1450[/C][C]1480.24022560728[/C][C]-30.2402256072778[/C][/ROW]
[ROW][C]37[/C][C]1220[/C][C]1299.16406597377[/C][C]-79.1640659737698[/C][/ROW]
[ROW][C]38[/C][C]1290[/C][C]1387.16199404292[/C][C]-97.1619940429241[/C][/ROW]
[ROW][C]39[/C][C]1400[/C][C]1403.57435777773[/C][C]-3.57435777773117[/C][/ROW]
[ROW][C]40[/C][C]1400[/C][C]1400.96575375028[/C][C]-0.965753750277599[/C][/ROW]
[ROW][C]41[/C][C]1460[/C][C]1469.26009489392[/C][C]-9.26009489392231[/C][/ROW]
[ROW][C]42[/C][C]1450[/C][C]1416.94517642821[/C][C]33.0548235717927[/C][/ROW]
[ROW][C]43[/C][C]1270[/C][C]1237.73538275933[/C][C]32.2646172406712[/C][/ROW]
[ROW][C]44[/C][C]1260[/C][C]1270.09058192794[/C][C]-10.0905819279353[/C][/ROW]
[ROW][C]45[/C][C]1550[/C][C]1598.61310636417[/C][C]-48.6131063641662[/C][/ROW]
[ROW][C]46[/C][C]1230[/C][C]1257.83084709657[/C][C]-27.8308470965671[/C][/ROW]
[ROW][C]47[/C][C]1380[/C][C]1405.54021987383[/C][C]-25.5402198738277[/C][/ROW]
[ROW][C]48[/C][C]1490[/C][C]1454.4862525192[/C][C]35.5137474807962[/C][/ROW]
[ROW][C]49[/C][C]1180[/C][C]1225.45600588841[/C][C]-45.4560058884088[/C][/ROW]
[ROW][C]50[/C][C]1190[/C][C]1295.5684885136[/C][C]-105.5684885136[/C][/ROW]
[ROW][C]51[/C][C]1400[/C][C]1403.20544402587[/C][C]-3.20544402587348[/C][/ROW]
[ROW][C]52[/C][C]1380[/C][C]1402.42757327983[/C][C]-22.4275732798255[/C][/ROW]
[ROW][C]53[/C][C]1510[/C][C]1461.38554697516[/C][C]48.614453024835[/C][/ROW]
[ROW][C]54[/C][C]1400[/C][C]1451.04408535483[/C][C]-51.0440853548328[/C][/ROW]
[ROW][C]55[/C][C]1290[/C][C]1268.77776069202[/C][C]21.222239307983[/C][/ROW]
[ROW][C]56[/C][C]1200[/C][C]1258.2844143888[/C][C]-58.2844143888026[/C][/ROW]
[ROW][C]57[/C][C]1600[/C][C]1546.93682224024[/C][C]53.0631777597564[/C][/ROW]
[ROW][C]58[/C][C]1220[/C][C]1227.45654572528[/C][C]-7.45654572528065[/C][/ROW]
[ROW][C]59[/C][C]1380[/C][C]1377.06522721863[/C][C]2.93477278136902[/C][/ROW]
[ROW][C]60[/C][C]1450[/C][C]1485.98993825918[/C][C]-35.9899382591766[/C][/ROW]
[ROW][C]61[/C][C]1260[/C][C]1175.2800193264[/C][C]84.7199806735966[/C][/ROW]
[ROW][C]62[/C][C]1130[/C][C]1187.99066934902[/C][C]-57.9906693490236[/C][/ROW]
[ROW][C]63[/C][C]1390[/C][C]1397.01175634294[/C][C]-7.01175634294304[/C][/ROW]
[ROW][C]64[/C][C]1380[/C][C]1377.13121273808[/C][C]2.86878726192276[/C][/ROW]
[ROW][C]65[/C][C]1570[/C][C]1506.38659867493[/C][C]63.6134013250664[/C][/ROW]
[ROW][C]66[/C][C]1320[/C][C]1398.25177617338[/C][C]-78.2517761733836[/C][/ROW]
[ROW][C]67[/C][C]1210[/C][C]1286.60263584422[/C][C]-76.6026358442214[/C][/ROW]
[ROW][C]68[/C][C]1190[/C][C]1195.82854782682[/C][C]-5.82854782682466[/C][/ROW]
[ROW][C]69[/C][C]1580[/C][C]1594.63197425844[/C][C]-14.6319742584444[/C][/ROW]
[ROW][C]70[/C][C]1150[/C][C]1213.97039410575[/C][C]-63.9703941057476[/C][/ROW]
[ROW][C]71[/C][C]1330[/C][C]1372.12182726927[/C][C]-42.1218272692693[/C][/ROW]
[ROW][C]72[/C][C]1420[/C][C]1441.04768174567[/C][C]-21.0476817456679[/C][/ROW]
[ROW][C]73[/C][C]1260[/C][C]1248.4549355109[/C][C]11.5450644891027[/C][/ROW]
[ROW][C]74[/C][C]1040[/C][C]1118.33599261496[/C][C]-78.3359926149583[/C][/ROW]
[ROW][C]75[/C][C]1450[/C][C]1375.8949205397[/C][C]74.105079460297[/C][/ROW]
[ROW][C]76[/C][C]1360[/C][C]1366.05973181513[/C][C]-6.0597318151265[/C][/ROW]
[ROW][C]77[/C][C]1500[/C][C]1553.94986441343[/C][C]-53.9498644134326[/C][/ROW]
[ROW][C]78[/C][C]1240[/C][C]1302.83516261595[/C][C]-62.8351626159547[/C][/ROW]
[ROW][C]79[/C][C]1260[/C][C]1191.61835986636[/C][C]68.3816401336353[/C][/ROW]
[ROW][C]80[/C][C]1220[/C][C]1171.97364695267[/C][C]48.0263530473298[/C][/ROW]
[ROW][C]81[/C][C]1680[/C][C]1562.37308183501[/C][C]117.626918164991[/C][/ROW]
[ROW][C]82[/C][C]1210[/C][C]1135.2194783584[/C][C]74.780521641602[/C][/ROW]
[ROW][C]83[/C][C]1350[/C][C]1317.62505159375[/C][C]32.3749484062464[/C][/ROW]
[ROW][C]84[/C][C]1480[/C][C]1409.33762214874[/C][C]70.6623778512649[/C][/ROW]
[ROW][C]85[/C][C]1270[/C][C]1251.52806845389[/C][C]18.4719315461059[/C][/ROW]
[ROW][C]86[/C][C]1040[/C][C]1034.34612402849[/C][C]5.65387597151357[/C][/ROW]
[ROW][C]87[/C][C]1450[/C][C]1444.89552317991[/C][C]5.10447682009112[/C][/ROW]
[ROW][C]88[/C][C]1310[/C][C]1356.41730244821[/C][C]-46.4173024482063[/C][/ROW]
[ROW][C]89[/C][C]1510[/C][C]1497.7109194721[/C][C]12.2890805279003[/C][/ROW]
[ROW][C]90[/C][C]1160[/C][C]1240.35742077757[/C][C]-80.3574207775746[/C][/ROW]
[ROW][C]91[/C][C]1290[/C][C]1259.37603122241[/C][C]30.6239687775901[/C][/ROW]
[ROW][C]92[/C][C]1230[/C][C]1220.32010410605[/C][C]9.67989589394688[/C][/ROW]
[ROW][C]93[/C][C]1680[/C][C]1679.6647562616[/C][C]0.335243738395093[/C][/ROW]
[ROW][C]94[/C][C]1190[/C][C]1209.04569974567[/C][C]-19.0456997456711[/C][/ROW]
[ROW][C]95[/C][C]1310[/C][C]1348.39574970485[/C][C]-38.3957497048509[/C][/ROW]
[ROW][C]96[/C][C]1480[/C][C]1476.53179316443[/C][C]3.46820683557326[/C][/ROW]
[ROW][C]97[/C][C]1320[/C][C]1265.87706976348[/C][C]54.1229302365218[/C][/ROW]
[ROW][C]98[/C][C]1050[/C][C]1036.38060948464[/C][C]13.6193905153564[/C][/ROW]
[ROW][C]99[/C][C]1380[/C][C]1446.28352590559[/C][C]-66.2835259055921[/C][/ROW]
[ROW][C]100[/C][C]1320[/C][C]1305.43427608483[/C][C]14.5657239151733[/C][/ROW]
[ROW][C]101[/C][C]1480[/C][C]1505.19419845738[/C][C]-25.1941984573848[/C][/ROW]
[ROW][C]102[/C][C]1150[/C][C]1155.63533676622[/C][C]-5.63533676621523[/C][/ROW]
[ROW][C]103[/C][C]1250[/C][C]1284.9408284803[/C][C]-34.9408284803021[/C][/ROW]
[ROW][C]104[/C][C]1260[/C][C]1223.83657250615[/C][C]36.1634274938478[/C][/ROW]
[ROW][C]105[/C][C]1680[/C][C]1674.12134573895[/C][C]5.87865426105191[/C][/ROW]
[ROW][C]106[/C][C]1150[/C][C]1184.25643993659[/C][C]-34.256439936587[/C][/ROW]
[ROW][C]107[/C][C]1310[/C][C]1303.99730391351[/C][C]6.00269608649069[/C][/ROW]
[ROW][C]108[/C][C]1470[/C][C]1473.9002730779[/C][C]-3.90027307790342[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295892&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295892&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
1312601259.39369658120.606303418802327
1413601355.412584972214.58741502779367
1513201309.0140557157910.9859442842146
1613001290.263519209789.73648079021973
1714401435.284283604774.71571639523427
1813601358.161933101531.83806689847324
1913301294.751665297735.2483347023019
2014201346.1873796524973.8126203475069
2115101421.4638296881588.5361703118485
2212801395.26474703421-115.264747034206
2313101312.84330789264-2.84330789263618
2414601525.52789459799-65.5278945979876
2512801286.28718023776-6.28718023776355
2613701386.28158968204-16.2815896820366
2713901345.9275881931244.0724118068772
2813901326.6913391592763.3086608407255
2914601468.06651410435-8.06651410435461
3014101388.300277174721.6997228252978
3112301358.56010559001-128.560105590008
3212601445.1302408164-185.130240816404
3315901529.4745544403460.5254455596616
3412501300.83570744201-50.8357074420135
3514001328.916492349671.0835076503986
3614501480.24022560728-30.2402256072778
3712201299.16406597377-79.1640659737698
3812901387.16199404292-97.1619940429241
3914001403.57435777773-3.57435777773117
4014001400.96575375028-0.965753750277599
4114601469.26009489392-9.26009489392231
4214501416.9451764282133.0548235717927
4312701237.7353827593332.2646172406712
4412601270.09058192794-10.0905819279353
4515501598.61310636417-48.6131063641662
4612301257.83084709657-27.8308470965671
4713801405.54021987383-25.5402198738277
4814901454.486252519235.5137474807962
4911801225.45600588841-45.4560058884088
5011901295.5684885136-105.5684885136
5114001403.20544402587-3.20544402587348
5213801402.42757327983-22.4275732798255
5315101461.3855469751648.614453024835
5414001451.04408535483-51.0440853548328
5512901268.7777606920221.222239307983
5612001258.2844143888-58.2844143888026
5716001546.9368222402453.0631777597564
5812201227.45654572528-7.45654572528065
5913801377.065227218632.93477278136902
6014501485.98993825918-35.9899382591766
6112601175.280019326484.7199806735966
6211301187.99066934902-57.9906693490236
6313901397.01175634294-7.01175634294304
6413801377.131212738082.86878726192276
6515701506.3865986749363.6134013250664
6613201398.25177617338-78.2517761733836
6712101286.60263584422-76.6026358442214
6811901195.82854782682-5.82854782682466
6915801594.63197425844-14.6319742584444
7011501213.97039410575-63.9703941057476
7113301372.12182726927-42.1218272692693
7214201441.04768174567-21.0476817456679
7312601248.454935510911.5450644891027
7410401118.33599261496-78.3359926149583
7514501375.894920539774.105079460297
7613601366.05973181513-6.0597318151265
7715001553.94986441343-53.9498644134326
7812401302.83516261595-62.8351626159547
7912601191.6183598663668.3816401336353
8012201171.9736469526748.0263530473298
8116801562.37308183501117.626918164991
8212101135.219478358474.780521641602
8313501317.6250515937532.3749484062464
8414801409.3376221487470.6623778512649
8512701251.5280684538918.4719315461059
8610401034.346124028495.65387597151357
8714501444.895523179915.10447682009112
8813101356.41730244821-46.4173024482063
8915101497.710919472112.2890805279003
9011601240.35742077757-80.3574207775746
9112901259.3760312224130.6239687775901
9212301220.320104106059.67989589394688
9316801679.66475626160.335243738395093
9411901209.04569974567-19.0456997456711
9513101348.39574970485-38.3957497048509
9614801476.531793164433.46820683557326
9713201265.8770697634854.1229302365218
9810501036.3806094846413.6193905153564
9913801446.28352590559-66.2835259055921
10013201305.4342760848314.5657239151733
10114801505.19419845738-25.1941984573848
10211501155.63533676622-5.63533676621523
10312501284.9408284803-34.9408284803021
10412601223.8365725061536.1634274938478
10516801674.121345738955.87865426105191
10611501184.25643993659-34.256439936587
10713101303.997303913516.00269608649069
10814701473.9002730779-3.90027307790342







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091312.810749189911210.870369806371414.75112857346
1101042.19747422817940.2365042530361144.1584442033
1111372.795127295821270.804008356991474.78624623464
1121312.389333350941210.356697508351414.42196919353
1131472.553193805621370.465869921571574.64051768967
1141142.512999347351040.356021609111244.66997708558
1151242.961842599071140.718461487351345.20522371079
1161252.429520086041150.081216068841354.77782410324
1171672.225183146541569.751683360041774.69868293303
1181142.633159084241040.012457241011245.25386092747
1191302.546748146381199.755127885441405.33836840732
1201462.592186982011359.60424884621565.58012511781

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1312.81074918991 & 1210.87036980637 & 1414.75112857346 \tabularnewline
110 & 1042.19747422817 & 940.236504253036 & 1144.1584442033 \tabularnewline
111 & 1372.79512729582 & 1270.80400835699 & 1474.78624623464 \tabularnewline
112 & 1312.38933335094 & 1210.35669750835 & 1414.42196919353 \tabularnewline
113 & 1472.55319380562 & 1370.46586992157 & 1574.64051768967 \tabularnewline
114 & 1142.51299934735 & 1040.35602160911 & 1244.66997708558 \tabularnewline
115 & 1242.96184259907 & 1140.71846148735 & 1345.20522371079 \tabularnewline
116 & 1252.42952008604 & 1150.08121606884 & 1354.77782410324 \tabularnewline
117 & 1672.22518314654 & 1569.75168336004 & 1774.69868293303 \tabularnewline
118 & 1142.63315908424 & 1040.01245724101 & 1245.25386092747 \tabularnewline
119 & 1302.54674814638 & 1199.75512788544 & 1405.33836840732 \tabularnewline
120 & 1462.59218698201 & 1359.6042488462 & 1565.58012511781 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295892&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]1312.81074918991[/C][C]1210.87036980637[/C][C]1414.75112857346[/C][/ROW]
[ROW][C]110[/C][C]1042.19747422817[/C][C]940.236504253036[/C][C]1144.1584442033[/C][/ROW]
[ROW][C]111[/C][C]1372.79512729582[/C][C]1270.80400835699[/C][C]1474.78624623464[/C][/ROW]
[ROW][C]112[/C][C]1312.38933335094[/C][C]1210.35669750835[/C][C]1414.42196919353[/C][/ROW]
[ROW][C]113[/C][C]1472.55319380562[/C][C]1370.46586992157[/C][C]1574.64051768967[/C][/ROW]
[ROW][C]114[/C][C]1142.51299934735[/C][C]1040.35602160911[/C][C]1244.66997708558[/C][/ROW]
[ROW][C]115[/C][C]1242.96184259907[/C][C]1140.71846148735[/C][C]1345.20522371079[/C][/ROW]
[ROW][C]116[/C][C]1252.42952008604[/C][C]1150.08121606884[/C][C]1354.77782410324[/C][/ROW]
[ROW][C]117[/C][C]1672.22518314654[/C][C]1569.75168336004[/C][C]1774.69868293303[/C][/ROW]
[ROW][C]118[/C][C]1142.63315908424[/C][C]1040.01245724101[/C][C]1245.25386092747[/C][/ROW]
[ROW][C]119[/C][C]1302.54674814638[/C][C]1199.75512788544[/C][C]1405.33836840732[/C][/ROW]
[ROW][C]120[/C][C]1462.59218698201[/C][C]1359.6042488462[/C][C]1565.58012511781[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295892&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295892&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
1091312.810749189911210.870369806371414.75112857346
1101042.19747422817940.2365042530361144.1584442033
1111372.795127295821270.804008356991474.78624623464
1121312.389333350941210.356697508351414.42196919353
1131472.553193805621370.465869921571574.64051768967
1141142.512999347351040.356021609111244.66997708558
1151242.961842599071140.718461487351345.20522371079
1161252.429520086041150.081216068841354.77782410324
1171672.225183146541569.751683360041774.69868293303
1181142.633159084241040.012457241011245.25386092747
1191302.546748146381199.755127885441405.33836840732
1201462.592186982011359.60424884621565.58012511781



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')