Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 30 Aug 2014 18:42:01 +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/2014/Aug/30/t1409420542jgk0u3kjh065max.htm/, Retrieved Thu, 31 Oct 2024 22:56:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235763, Retrieved Thu, 31 Oct 2024 22:56:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2014-08-30 17:42:01] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
2240
2240
2380
2380
2380
2380
2140
2400
2180
2260
2280
2480
2360
2160
2380
2280
2320
2400
1960
2520
2200
2420
2300
2280
2220
2240
2200
2340
2240
2500
1820
2520
2180
2480
2260
2400
2240
2240
2240
2140
2200
2460
1860
2480
1960
2540
2280
2320
2320
2440
2320
2180
2120
2460
2140
2480
2100
2700
2200
2260
2340
2720
2300
2360
2020
2380
2000
2540
1980
2940
2260
2300
2300
2820
2380
2360
1980
2340
2160
2700
1920
2980
2240
2180
2440
2740
2360
2380
2000
2500
2180
2740
1960
3060
2300
2240
2580
2740
2260
2400
1820
2440
2080
2680
1900
3000
2240
2300




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235763&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235763&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235763&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00281569529532849
beta0.484759870853942
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00281569529532849 \tabularnewline
beta & 0.484759870853942 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235763&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]0.00281569529532849[/C][/ROW]
[ROW][C]beta[/C][C]0.484759870853942[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235763&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235763&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
alpha0.00281569529532849
beta0.484759870853942
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
323802240140
423802240.58528839363139.414711606372
523802241.35922096451138.640779035489
623802242.32021017963137.679789820368
721402243.46641765562-103.466417655618
824002243.7924058424156.207594157599
921802245.06277030501-65.0627703050091
1022602245.6212983202514.3787016797532
1122802246.4231353232233.576864676776
1224802247.32485877774232.675141222259
1323602249.10476900981110.895230990194
1421602250.6931490243-90.6931490243014
1523802251.59012723358128.409872766416
1622802253.2793040598726.7206959401256
1723202254.7186271915765.2813728084325
1824002256.35563034131143.644369658694
1919602258.40934519655-298.40934519655
2025202258.81106180242261.188938197582
2122002261.14494286958-61.1449428695755
2224202262.48777100518157.512228994818
2323002264.6612652365135.3387347634894
2422802266.5389912492913.4610087507085
2522202268.37348966849-48.3734896684869
2622402269.96785425966-29.9678542596566
2722002271.5731393061-71.5731393061037
2823402272.9635837864367.0364162135656
2922402274.83581096381-34.8358109638111
3025002276.37364833487223.62635166513
3118202278.94447207882-458.944472078819
3225202278.96695449342241.03304550658
3321802281.28935501327-101.289355013269
3424802282.50962646453197.490373535472
3522602284.84073232962-24.8407323296187
3624002286.51191553392113.488084466082
3722402288.72749451889-48.7274945188919
3822402290.41981394556-50.4198139455561
3922402292.03854849278-52.0385484927815
4021402293.58169588397-153.581695883967
4122002294.62929951364-94.6292995136441
4224602295.71373218257164.286267817433
4318602297.75143245197-437.751432451973
4424802297.49647527351182.503524726487
4519602299.23707270692-339.237072706921
4625402299.04557067192240.95442932808
4722802300.81659851568-20.8165985156775
4823202301.8221455813418.1778544186559
4923202302.9623007541817.0376992458246
5024402304.122500968135.877499031997
5123202305.8027819489314.1972180510738
5221802307.15982663042-127.15982663042
5321202307.94528790997-187.945287909965
5424602308.30306254617151.696937453825
5521402309.82422282276-169.824222822764
5624802310.20827827071169.791721729286
5721002311.78034358434-211.780343584343
5827002311.98895159521388.01104840479
5922002314.41599968908-114.415999689084
6022602315.27219578041-55.2721957804065
6123402316.2194797874723.7805202125269
6227202317.42181104527402.578188954733
6323002320.24021461506-20.2402146150562
6423602321.8404637957838.1595362042162
6520202323.6572342082-303.657234208198
6623802324.0970800310355.9029199689726
6720002325.62564160124-325.625641601236
6825402325.63547680629214.364523193713
6919802327.45835365151-347.458353651511
7029402327.22505001971612.774949980289
7122602330.53186942625-70.5318694262501
7223002331.8184335422-31.8184335422047
7323002333.17057276925-33.1705727692474
7428202334.47362907241485.526370927593
7523802337.8998903848642.1001096151431
7623602340.1350624184219.8649375815849
7719802342.33474135287-362.334741352874
7823402342.96369868517-2.96369868517013
7921602344.6004901123-184.600490112295
8027002345.47387980957354.526120190426
8119202348.34919126256-428.349191262559
8229802348.43549511495631.564504885047
8322402352.36823815949-112.36823815949
8421802354.05291781602-174.052917816018
8524402355.3263411015484.6736588984577
8627402357.44383372461382.556166275392
8723602360.92223743919-0.922237439187029
8823802363.3196240214116.6803759785948
8920002365.78934184654-365.789341846539
9025002366.68286241339133.317137586605
9121802369.16368411846-189.163684118463
9227402370.47830175208369.521698247919
9319602373.87038068953-413.870380689535
9430602374.49175961768685.508240382318
9523002379.1443286927-79.1443286926979
9622402381.53584217604-141.535842176037
9725802383.5584927897196.441507210299
9827402386.80091473828353.199085261723
9922602390.96681243951-130.966812439507
10024002393.590685171836.40931482817314
10118202396.61011552449-576.610115524492
10224402397.200904854842.7990951452002
10320802399.59417981496-319.594179814959
10426802400.5308401063279.469159893702
10519002403.5357377666-503.535737766603
10630002403.64863812041596.35136187959
10722402407.67246690088-167.672466900878
10823002409.31617518014-109.316175180138

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2380 & 2240 & 140 \tabularnewline
4 & 2380 & 2240.58528839363 & 139.414711606372 \tabularnewline
5 & 2380 & 2241.35922096451 & 138.640779035489 \tabularnewline
6 & 2380 & 2242.32021017963 & 137.679789820368 \tabularnewline
7 & 2140 & 2243.46641765562 & -103.466417655618 \tabularnewline
8 & 2400 & 2243.7924058424 & 156.207594157599 \tabularnewline
9 & 2180 & 2245.06277030501 & -65.0627703050091 \tabularnewline
10 & 2260 & 2245.62129832025 & 14.3787016797532 \tabularnewline
11 & 2280 & 2246.42313532322 & 33.576864676776 \tabularnewline
12 & 2480 & 2247.32485877774 & 232.675141222259 \tabularnewline
13 & 2360 & 2249.10476900981 & 110.895230990194 \tabularnewline
14 & 2160 & 2250.6931490243 & -90.6931490243014 \tabularnewline
15 & 2380 & 2251.59012723358 & 128.409872766416 \tabularnewline
16 & 2280 & 2253.27930405987 & 26.7206959401256 \tabularnewline
17 & 2320 & 2254.71862719157 & 65.2813728084325 \tabularnewline
18 & 2400 & 2256.35563034131 & 143.644369658694 \tabularnewline
19 & 1960 & 2258.40934519655 & -298.40934519655 \tabularnewline
20 & 2520 & 2258.81106180242 & 261.188938197582 \tabularnewline
21 & 2200 & 2261.14494286958 & -61.1449428695755 \tabularnewline
22 & 2420 & 2262.48777100518 & 157.512228994818 \tabularnewline
23 & 2300 & 2264.66126523651 & 35.3387347634894 \tabularnewline
24 & 2280 & 2266.53899124929 & 13.4610087507085 \tabularnewline
25 & 2220 & 2268.37348966849 & -48.3734896684869 \tabularnewline
26 & 2240 & 2269.96785425966 & -29.9678542596566 \tabularnewline
27 & 2200 & 2271.5731393061 & -71.5731393061037 \tabularnewline
28 & 2340 & 2272.96358378643 & 67.0364162135656 \tabularnewline
29 & 2240 & 2274.83581096381 & -34.8358109638111 \tabularnewline
30 & 2500 & 2276.37364833487 & 223.62635166513 \tabularnewline
31 & 1820 & 2278.94447207882 & -458.944472078819 \tabularnewline
32 & 2520 & 2278.96695449342 & 241.03304550658 \tabularnewline
33 & 2180 & 2281.28935501327 & -101.289355013269 \tabularnewline
34 & 2480 & 2282.50962646453 & 197.490373535472 \tabularnewline
35 & 2260 & 2284.84073232962 & -24.8407323296187 \tabularnewline
36 & 2400 & 2286.51191553392 & 113.488084466082 \tabularnewline
37 & 2240 & 2288.72749451889 & -48.7274945188919 \tabularnewline
38 & 2240 & 2290.41981394556 & -50.4198139455561 \tabularnewline
39 & 2240 & 2292.03854849278 & -52.0385484927815 \tabularnewline
40 & 2140 & 2293.58169588397 & -153.581695883967 \tabularnewline
41 & 2200 & 2294.62929951364 & -94.6292995136441 \tabularnewline
42 & 2460 & 2295.71373218257 & 164.286267817433 \tabularnewline
43 & 1860 & 2297.75143245197 & -437.751432451973 \tabularnewline
44 & 2480 & 2297.49647527351 & 182.503524726487 \tabularnewline
45 & 1960 & 2299.23707270692 & -339.237072706921 \tabularnewline
46 & 2540 & 2299.04557067192 & 240.95442932808 \tabularnewline
47 & 2280 & 2300.81659851568 & -20.8165985156775 \tabularnewline
48 & 2320 & 2301.82214558134 & 18.1778544186559 \tabularnewline
49 & 2320 & 2302.96230075418 & 17.0376992458246 \tabularnewline
50 & 2440 & 2304.122500968 & 135.877499031997 \tabularnewline
51 & 2320 & 2305.80278194893 & 14.1972180510738 \tabularnewline
52 & 2180 & 2307.15982663042 & -127.15982663042 \tabularnewline
53 & 2120 & 2307.94528790997 & -187.945287909965 \tabularnewline
54 & 2460 & 2308.30306254617 & 151.696937453825 \tabularnewline
55 & 2140 & 2309.82422282276 & -169.824222822764 \tabularnewline
56 & 2480 & 2310.20827827071 & 169.791721729286 \tabularnewline
57 & 2100 & 2311.78034358434 & -211.780343584343 \tabularnewline
58 & 2700 & 2311.98895159521 & 388.01104840479 \tabularnewline
59 & 2200 & 2314.41599968908 & -114.415999689084 \tabularnewline
60 & 2260 & 2315.27219578041 & -55.2721957804065 \tabularnewline
61 & 2340 & 2316.21947978747 & 23.7805202125269 \tabularnewline
62 & 2720 & 2317.42181104527 & 402.578188954733 \tabularnewline
63 & 2300 & 2320.24021461506 & -20.2402146150562 \tabularnewline
64 & 2360 & 2321.84046379578 & 38.1595362042162 \tabularnewline
65 & 2020 & 2323.6572342082 & -303.657234208198 \tabularnewline
66 & 2380 & 2324.09708003103 & 55.9029199689726 \tabularnewline
67 & 2000 & 2325.62564160124 & -325.625641601236 \tabularnewline
68 & 2540 & 2325.63547680629 & 214.364523193713 \tabularnewline
69 & 1980 & 2327.45835365151 & -347.458353651511 \tabularnewline
70 & 2940 & 2327.22505001971 & 612.774949980289 \tabularnewline
71 & 2260 & 2330.53186942625 & -70.5318694262501 \tabularnewline
72 & 2300 & 2331.8184335422 & -31.8184335422047 \tabularnewline
73 & 2300 & 2333.17057276925 & -33.1705727692474 \tabularnewline
74 & 2820 & 2334.47362907241 & 485.526370927593 \tabularnewline
75 & 2380 & 2337.89989038486 & 42.1001096151431 \tabularnewline
76 & 2360 & 2340.13506241842 & 19.8649375815849 \tabularnewline
77 & 1980 & 2342.33474135287 & -362.334741352874 \tabularnewline
78 & 2340 & 2342.96369868517 & -2.96369868517013 \tabularnewline
79 & 2160 & 2344.6004901123 & -184.600490112295 \tabularnewline
80 & 2700 & 2345.47387980957 & 354.526120190426 \tabularnewline
81 & 1920 & 2348.34919126256 & -428.349191262559 \tabularnewline
82 & 2980 & 2348.43549511495 & 631.564504885047 \tabularnewline
83 & 2240 & 2352.36823815949 & -112.36823815949 \tabularnewline
84 & 2180 & 2354.05291781602 & -174.052917816018 \tabularnewline
85 & 2440 & 2355.32634110154 & 84.6736588984577 \tabularnewline
86 & 2740 & 2357.44383372461 & 382.556166275392 \tabularnewline
87 & 2360 & 2360.92223743919 & -0.922237439187029 \tabularnewline
88 & 2380 & 2363.31962402141 & 16.6803759785948 \tabularnewline
89 & 2000 & 2365.78934184654 & -365.789341846539 \tabularnewline
90 & 2500 & 2366.68286241339 & 133.317137586605 \tabularnewline
91 & 2180 & 2369.16368411846 & -189.163684118463 \tabularnewline
92 & 2740 & 2370.47830175208 & 369.521698247919 \tabularnewline
93 & 1960 & 2373.87038068953 & -413.870380689535 \tabularnewline
94 & 3060 & 2374.49175961768 & 685.508240382318 \tabularnewline
95 & 2300 & 2379.1443286927 & -79.1443286926979 \tabularnewline
96 & 2240 & 2381.53584217604 & -141.535842176037 \tabularnewline
97 & 2580 & 2383.5584927897 & 196.441507210299 \tabularnewline
98 & 2740 & 2386.80091473828 & 353.199085261723 \tabularnewline
99 & 2260 & 2390.96681243951 & -130.966812439507 \tabularnewline
100 & 2400 & 2393.59068517183 & 6.40931482817314 \tabularnewline
101 & 1820 & 2396.61011552449 & -576.610115524492 \tabularnewline
102 & 2440 & 2397.2009048548 & 42.7990951452002 \tabularnewline
103 & 2080 & 2399.59417981496 & -319.594179814959 \tabularnewline
104 & 2680 & 2400.5308401063 & 279.469159893702 \tabularnewline
105 & 1900 & 2403.5357377666 & -503.535737766603 \tabularnewline
106 & 3000 & 2403.64863812041 & 596.35136187959 \tabularnewline
107 & 2240 & 2407.67246690088 & -167.672466900878 \tabularnewline
108 & 2300 & 2409.31617518014 & -109.316175180138 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235763&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]2380[/C][C]2240[/C][C]140[/C][/ROW]
[ROW][C]4[/C][C]2380[/C][C]2240.58528839363[/C][C]139.414711606372[/C][/ROW]
[ROW][C]5[/C][C]2380[/C][C]2241.35922096451[/C][C]138.640779035489[/C][/ROW]
[ROW][C]6[/C][C]2380[/C][C]2242.32021017963[/C][C]137.679789820368[/C][/ROW]
[ROW][C]7[/C][C]2140[/C][C]2243.46641765562[/C][C]-103.466417655618[/C][/ROW]
[ROW][C]8[/C][C]2400[/C][C]2243.7924058424[/C][C]156.207594157599[/C][/ROW]
[ROW][C]9[/C][C]2180[/C][C]2245.06277030501[/C][C]-65.0627703050091[/C][/ROW]
[ROW][C]10[/C][C]2260[/C][C]2245.62129832025[/C][C]14.3787016797532[/C][/ROW]
[ROW][C]11[/C][C]2280[/C][C]2246.42313532322[/C][C]33.576864676776[/C][/ROW]
[ROW][C]12[/C][C]2480[/C][C]2247.32485877774[/C][C]232.675141222259[/C][/ROW]
[ROW][C]13[/C][C]2360[/C][C]2249.10476900981[/C][C]110.895230990194[/C][/ROW]
[ROW][C]14[/C][C]2160[/C][C]2250.6931490243[/C][C]-90.6931490243014[/C][/ROW]
[ROW][C]15[/C][C]2380[/C][C]2251.59012723358[/C][C]128.409872766416[/C][/ROW]
[ROW][C]16[/C][C]2280[/C][C]2253.27930405987[/C][C]26.7206959401256[/C][/ROW]
[ROW][C]17[/C][C]2320[/C][C]2254.71862719157[/C][C]65.2813728084325[/C][/ROW]
[ROW][C]18[/C][C]2400[/C][C]2256.35563034131[/C][C]143.644369658694[/C][/ROW]
[ROW][C]19[/C][C]1960[/C][C]2258.40934519655[/C][C]-298.40934519655[/C][/ROW]
[ROW][C]20[/C][C]2520[/C][C]2258.81106180242[/C][C]261.188938197582[/C][/ROW]
[ROW][C]21[/C][C]2200[/C][C]2261.14494286958[/C][C]-61.1449428695755[/C][/ROW]
[ROW][C]22[/C][C]2420[/C][C]2262.48777100518[/C][C]157.512228994818[/C][/ROW]
[ROW][C]23[/C][C]2300[/C][C]2264.66126523651[/C][C]35.3387347634894[/C][/ROW]
[ROW][C]24[/C][C]2280[/C][C]2266.53899124929[/C][C]13.4610087507085[/C][/ROW]
[ROW][C]25[/C][C]2220[/C][C]2268.37348966849[/C][C]-48.3734896684869[/C][/ROW]
[ROW][C]26[/C][C]2240[/C][C]2269.96785425966[/C][C]-29.9678542596566[/C][/ROW]
[ROW][C]27[/C][C]2200[/C][C]2271.5731393061[/C][C]-71.5731393061037[/C][/ROW]
[ROW][C]28[/C][C]2340[/C][C]2272.96358378643[/C][C]67.0364162135656[/C][/ROW]
[ROW][C]29[/C][C]2240[/C][C]2274.83581096381[/C][C]-34.8358109638111[/C][/ROW]
[ROW][C]30[/C][C]2500[/C][C]2276.37364833487[/C][C]223.62635166513[/C][/ROW]
[ROW][C]31[/C][C]1820[/C][C]2278.94447207882[/C][C]-458.944472078819[/C][/ROW]
[ROW][C]32[/C][C]2520[/C][C]2278.96695449342[/C][C]241.03304550658[/C][/ROW]
[ROW][C]33[/C][C]2180[/C][C]2281.28935501327[/C][C]-101.289355013269[/C][/ROW]
[ROW][C]34[/C][C]2480[/C][C]2282.50962646453[/C][C]197.490373535472[/C][/ROW]
[ROW][C]35[/C][C]2260[/C][C]2284.84073232962[/C][C]-24.8407323296187[/C][/ROW]
[ROW][C]36[/C][C]2400[/C][C]2286.51191553392[/C][C]113.488084466082[/C][/ROW]
[ROW][C]37[/C][C]2240[/C][C]2288.72749451889[/C][C]-48.7274945188919[/C][/ROW]
[ROW][C]38[/C][C]2240[/C][C]2290.41981394556[/C][C]-50.4198139455561[/C][/ROW]
[ROW][C]39[/C][C]2240[/C][C]2292.03854849278[/C][C]-52.0385484927815[/C][/ROW]
[ROW][C]40[/C][C]2140[/C][C]2293.58169588397[/C][C]-153.581695883967[/C][/ROW]
[ROW][C]41[/C][C]2200[/C][C]2294.62929951364[/C][C]-94.6292995136441[/C][/ROW]
[ROW][C]42[/C][C]2460[/C][C]2295.71373218257[/C][C]164.286267817433[/C][/ROW]
[ROW][C]43[/C][C]1860[/C][C]2297.75143245197[/C][C]-437.751432451973[/C][/ROW]
[ROW][C]44[/C][C]2480[/C][C]2297.49647527351[/C][C]182.503524726487[/C][/ROW]
[ROW][C]45[/C][C]1960[/C][C]2299.23707270692[/C][C]-339.237072706921[/C][/ROW]
[ROW][C]46[/C][C]2540[/C][C]2299.04557067192[/C][C]240.95442932808[/C][/ROW]
[ROW][C]47[/C][C]2280[/C][C]2300.81659851568[/C][C]-20.8165985156775[/C][/ROW]
[ROW][C]48[/C][C]2320[/C][C]2301.82214558134[/C][C]18.1778544186559[/C][/ROW]
[ROW][C]49[/C][C]2320[/C][C]2302.96230075418[/C][C]17.0376992458246[/C][/ROW]
[ROW][C]50[/C][C]2440[/C][C]2304.122500968[/C][C]135.877499031997[/C][/ROW]
[ROW][C]51[/C][C]2320[/C][C]2305.80278194893[/C][C]14.1972180510738[/C][/ROW]
[ROW][C]52[/C][C]2180[/C][C]2307.15982663042[/C][C]-127.15982663042[/C][/ROW]
[ROW][C]53[/C][C]2120[/C][C]2307.94528790997[/C][C]-187.945287909965[/C][/ROW]
[ROW][C]54[/C][C]2460[/C][C]2308.30306254617[/C][C]151.696937453825[/C][/ROW]
[ROW][C]55[/C][C]2140[/C][C]2309.82422282276[/C][C]-169.824222822764[/C][/ROW]
[ROW][C]56[/C][C]2480[/C][C]2310.20827827071[/C][C]169.791721729286[/C][/ROW]
[ROW][C]57[/C][C]2100[/C][C]2311.78034358434[/C][C]-211.780343584343[/C][/ROW]
[ROW][C]58[/C][C]2700[/C][C]2311.98895159521[/C][C]388.01104840479[/C][/ROW]
[ROW][C]59[/C][C]2200[/C][C]2314.41599968908[/C][C]-114.415999689084[/C][/ROW]
[ROW][C]60[/C][C]2260[/C][C]2315.27219578041[/C][C]-55.2721957804065[/C][/ROW]
[ROW][C]61[/C][C]2340[/C][C]2316.21947978747[/C][C]23.7805202125269[/C][/ROW]
[ROW][C]62[/C][C]2720[/C][C]2317.42181104527[/C][C]402.578188954733[/C][/ROW]
[ROW][C]63[/C][C]2300[/C][C]2320.24021461506[/C][C]-20.2402146150562[/C][/ROW]
[ROW][C]64[/C][C]2360[/C][C]2321.84046379578[/C][C]38.1595362042162[/C][/ROW]
[ROW][C]65[/C][C]2020[/C][C]2323.6572342082[/C][C]-303.657234208198[/C][/ROW]
[ROW][C]66[/C][C]2380[/C][C]2324.09708003103[/C][C]55.9029199689726[/C][/ROW]
[ROW][C]67[/C][C]2000[/C][C]2325.62564160124[/C][C]-325.625641601236[/C][/ROW]
[ROW][C]68[/C][C]2540[/C][C]2325.63547680629[/C][C]214.364523193713[/C][/ROW]
[ROW][C]69[/C][C]1980[/C][C]2327.45835365151[/C][C]-347.458353651511[/C][/ROW]
[ROW][C]70[/C][C]2940[/C][C]2327.22505001971[/C][C]612.774949980289[/C][/ROW]
[ROW][C]71[/C][C]2260[/C][C]2330.53186942625[/C][C]-70.5318694262501[/C][/ROW]
[ROW][C]72[/C][C]2300[/C][C]2331.8184335422[/C][C]-31.8184335422047[/C][/ROW]
[ROW][C]73[/C][C]2300[/C][C]2333.17057276925[/C][C]-33.1705727692474[/C][/ROW]
[ROW][C]74[/C][C]2820[/C][C]2334.47362907241[/C][C]485.526370927593[/C][/ROW]
[ROW][C]75[/C][C]2380[/C][C]2337.89989038486[/C][C]42.1001096151431[/C][/ROW]
[ROW][C]76[/C][C]2360[/C][C]2340.13506241842[/C][C]19.8649375815849[/C][/ROW]
[ROW][C]77[/C][C]1980[/C][C]2342.33474135287[/C][C]-362.334741352874[/C][/ROW]
[ROW][C]78[/C][C]2340[/C][C]2342.96369868517[/C][C]-2.96369868517013[/C][/ROW]
[ROW][C]79[/C][C]2160[/C][C]2344.6004901123[/C][C]-184.600490112295[/C][/ROW]
[ROW][C]80[/C][C]2700[/C][C]2345.47387980957[/C][C]354.526120190426[/C][/ROW]
[ROW][C]81[/C][C]1920[/C][C]2348.34919126256[/C][C]-428.349191262559[/C][/ROW]
[ROW][C]82[/C][C]2980[/C][C]2348.43549511495[/C][C]631.564504885047[/C][/ROW]
[ROW][C]83[/C][C]2240[/C][C]2352.36823815949[/C][C]-112.36823815949[/C][/ROW]
[ROW][C]84[/C][C]2180[/C][C]2354.05291781602[/C][C]-174.052917816018[/C][/ROW]
[ROW][C]85[/C][C]2440[/C][C]2355.32634110154[/C][C]84.6736588984577[/C][/ROW]
[ROW][C]86[/C][C]2740[/C][C]2357.44383372461[/C][C]382.556166275392[/C][/ROW]
[ROW][C]87[/C][C]2360[/C][C]2360.92223743919[/C][C]-0.922237439187029[/C][/ROW]
[ROW][C]88[/C][C]2380[/C][C]2363.31962402141[/C][C]16.6803759785948[/C][/ROW]
[ROW][C]89[/C][C]2000[/C][C]2365.78934184654[/C][C]-365.789341846539[/C][/ROW]
[ROW][C]90[/C][C]2500[/C][C]2366.68286241339[/C][C]133.317137586605[/C][/ROW]
[ROW][C]91[/C][C]2180[/C][C]2369.16368411846[/C][C]-189.163684118463[/C][/ROW]
[ROW][C]92[/C][C]2740[/C][C]2370.47830175208[/C][C]369.521698247919[/C][/ROW]
[ROW][C]93[/C][C]1960[/C][C]2373.87038068953[/C][C]-413.870380689535[/C][/ROW]
[ROW][C]94[/C][C]3060[/C][C]2374.49175961768[/C][C]685.508240382318[/C][/ROW]
[ROW][C]95[/C][C]2300[/C][C]2379.1443286927[/C][C]-79.1443286926979[/C][/ROW]
[ROW][C]96[/C][C]2240[/C][C]2381.53584217604[/C][C]-141.535842176037[/C][/ROW]
[ROW][C]97[/C][C]2580[/C][C]2383.5584927897[/C][C]196.441507210299[/C][/ROW]
[ROW][C]98[/C][C]2740[/C][C]2386.80091473828[/C][C]353.199085261723[/C][/ROW]
[ROW][C]99[/C][C]2260[/C][C]2390.96681243951[/C][C]-130.966812439507[/C][/ROW]
[ROW][C]100[/C][C]2400[/C][C]2393.59068517183[/C][C]6.40931482817314[/C][/ROW]
[ROW][C]101[/C][C]1820[/C][C]2396.61011552449[/C][C]-576.610115524492[/C][/ROW]
[ROW][C]102[/C][C]2440[/C][C]2397.2009048548[/C][C]42.7990951452002[/C][/ROW]
[ROW][C]103[/C][C]2080[/C][C]2399.59417981496[/C][C]-319.594179814959[/C][/ROW]
[ROW][C]104[/C][C]2680[/C][C]2400.5308401063[/C][C]279.469159893702[/C][/ROW]
[ROW][C]105[/C][C]1900[/C][C]2403.5357377666[/C][C]-503.535737766603[/C][/ROW]
[ROW][C]106[/C][C]3000[/C][C]2403.64863812041[/C][C]596.35136187959[/C][/ROW]
[ROW][C]107[/C][C]2240[/C][C]2407.67246690088[/C][C]-167.672466900878[/C][/ROW]
[ROW][C]108[/C][C]2300[/C][C]2409.31617518014[/C][C]-109.316175180138[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235763&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235763&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
323802240140
423802240.58528839363139.414711606372
523802241.35922096451138.640779035489
623802242.32021017963137.679789820368
721402243.46641765562-103.466417655618
824002243.7924058424156.207594157599
921802245.06277030501-65.0627703050091
1022602245.6212983202514.3787016797532
1122802246.4231353232233.576864676776
1224802247.32485877774232.675141222259
1323602249.10476900981110.895230990194
1421602250.6931490243-90.6931490243014
1523802251.59012723358128.409872766416
1622802253.2793040598726.7206959401256
1723202254.7186271915765.2813728084325
1824002256.35563034131143.644369658694
1919602258.40934519655-298.40934519655
2025202258.81106180242261.188938197582
2122002261.14494286958-61.1449428695755
2224202262.48777100518157.512228994818
2323002264.6612652365135.3387347634894
2422802266.5389912492913.4610087507085
2522202268.37348966849-48.3734896684869
2622402269.96785425966-29.9678542596566
2722002271.5731393061-71.5731393061037
2823402272.9635837864367.0364162135656
2922402274.83581096381-34.8358109638111
3025002276.37364833487223.62635166513
3118202278.94447207882-458.944472078819
3225202278.96695449342241.03304550658
3321802281.28935501327-101.289355013269
3424802282.50962646453197.490373535472
3522602284.84073232962-24.8407323296187
3624002286.51191553392113.488084466082
3722402288.72749451889-48.7274945188919
3822402290.41981394556-50.4198139455561
3922402292.03854849278-52.0385484927815
4021402293.58169588397-153.581695883967
4122002294.62929951364-94.6292995136441
4224602295.71373218257164.286267817433
4318602297.75143245197-437.751432451973
4424802297.49647527351182.503524726487
4519602299.23707270692-339.237072706921
4625402299.04557067192240.95442932808
4722802300.81659851568-20.8165985156775
4823202301.8221455813418.1778544186559
4923202302.9623007541817.0376992458246
5024402304.122500968135.877499031997
5123202305.8027819489314.1972180510738
5221802307.15982663042-127.15982663042
5321202307.94528790997-187.945287909965
5424602308.30306254617151.696937453825
5521402309.82422282276-169.824222822764
5624802310.20827827071169.791721729286
5721002311.78034358434-211.780343584343
5827002311.98895159521388.01104840479
5922002314.41599968908-114.415999689084
6022602315.27219578041-55.2721957804065
6123402316.2194797874723.7805202125269
6227202317.42181104527402.578188954733
6323002320.24021461506-20.2402146150562
6423602321.8404637957838.1595362042162
6520202323.6572342082-303.657234208198
6623802324.0970800310355.9029199689726
6720002325.62564160124-325.625641601236
6825402325.63547680629214.364523193713
6919802327.45835365151-347.458353651511
7029402327.22505001971612.774949980289
7122602330.53186942625-70.5318694262501
7223002331.8184335422-31.8184335422047
7323002333.17057276925-33.1705727692474
7428202334.47362907241485.526370927593
7523802337.8998903848642.1001096151431
7623602340.1350624184219.8649375815849
7719802342.33474135287-362.334741352874
7823402342.96369868517-2.96369868517013
7921602344.6004901123-184.600490112295
8027002345.47387980957354.526120190426
8119202348.34919126256-428.349191262559
8229802348.43549511495631.564504885047
8322402352.36823815949-112.36823815949
8421802354.05291781602-174.052917816018
8524402355.3263411015484.6736588984577
8627402357.44383372461382.556166275392
8723602360.92223743919-0.922237439187029
8823802363.3196240214116.6803759785948
8920002365.78934184654-365.789341846539
9025002366.68286241339133.317137586605
9121802369.16368411846-189.163684118463
9227402370.47830175208369.521698247919
9319602373.87038068953-413.870380689535
9430602374.49175961768685.508240382318
9523002379.1443286927-79.1443286926979
9622402381.53584217604-141.535842176037
9725802383.5584927897196.441507210299
9827402386.80091473828353.199085261723
9922602390.96681243951-130.966812439507
10024002393.590685171836.40931482817314
10118202396.61011552449-576.610115524492
10224402397.200904854842.7990951452002
10320802399.59417981496-319.594179814959
10426802400.5308401063279.469159893702
10519002403.5357377666-503.535737766603
10630002403.64863812041596.35136187959
10722402407.67246690088-167.672466900878
10823002409.31617518014-109.316175180138







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1092410.974987402971935.268294884832886.68167992111
1102412.941600665971937.230751041612888.65245029032
1112414.908213928961939.190049645032890.62637821289
1122416.874827191951941.145304616852892.60434976706
1132418.841440454951943.095630053122894.58725085678
1142420.808053717941945.040140307762896.57596712813
1152422.774666980941946.977950092442898.57138386943
1162424.741280243931948.9081745932900.57438589486
1172426.707893506921950.829929602042902.58585741181
1182428.674506769921952.742331667862904.60668187198
1192430.641120032911954.644498259482906.63774180634
1202432.60773329591956.535547947672908.67991864414

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 2410.97498740297 & 1935.26829488483 & 2886.68167992111 \tabularnewline
110 & 2412.94160066597 & 1937.23075104161 & 2888.65245029032 \tabularnewline
111 & 2414.90821392896 & 1939.19004964503 & 2890.62637821289 \tabularnewline
112 & 2416.87482719195 & 1941.14530461685 & 2892.60434976706 \tabularnewline
113 & 2418.84144045495 & 1943.09563005312 & 2894.58725085678 \tabularnewline
114 & 2420.80805371794 & 1945.04014030776 & 2896.57596712813 \tabularnewline
115 & 2422.77466698094 & 1946.97795009244 & 2898.57138386943 \tabularnewline
116 & 2424.74128024393 & 1948.908174593 & 2900.57438589486 \tabularnewline
117 & 2426.70789350692 & 1950.82992960204 & 2902.58585741181 \tabularnewline
118 & 2428.67450676992 & 1952.74233166786 & 2904.60668187198 \tabularnewline
119 & 2430.64112003291 & 1954.64449825948 & 2906.63774180634 \tabularnewline
120 & 2432.6077332959 & 1956.53554794767 & 2908.67991864414 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235763&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]2410.97498740297[/C][C]1935.26829488483[/C][C]2886.68167992111[/C][/ROW]
[ROW][C]110[/C][C]2412.94160066597[/C][C]1937.23075104161[/C][C]2888.65245029032[/C][/ROW]
[ROW][C]111[/C][C]2414.90821392896[/C][C]1939.19004964503[/C][C]2890.62637821289[/C][/ROW]
[ROW][C]112[/C][C]2416.87482719195[/C][C]1941.14530461685[/C][C]2892.60434976706[/C][/ROW]
[ROW][C]113[/C][C]2418.84144045495[/C][C]1943.09563005312[/C][C]2894.58725085678[/C][/ROW]
[ROW][C]114[/C][C]2420.80805371794[/C][C]1945.04014030776[/C][C]2896.57596712813[/C][/ROW]
[ROW][C]115[/C][C]2422.77466698094[/C][C]1946.97795009244[/C][C]2898.57138386943[/C][/ROW]
[ROW][C]116[/C][C]2424.74128024393[/C][C]1948.908174593[/C][C]2900.57438589486[/C][/ROW]
[ROW][C]117[/C][C]2426.70789350692[/C][C]1950.82992960204[/C][C]2902.58585741181[/C][/ROW]
[ROW][C]118[/C][C]2428.67450676992[/C][C]1952.74233166786[/C][C]2904.60668187198[/C][/ROW]
[ROW][C]119[/C][C]2430.64112003291[/C][C]1954.64449825948[/C][C]2906.63774180634[/C][/ROW]
[ROW][C]120[/C][C]2432.6077332959[/C][C]1956.53554794767[/C][C]2908.67991864414[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235763&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235763&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
1092410.974987402971935.268294884832886.68167992111
1102412.941600665971937.230751041612888.65245029032
1112414.908213928961939.190049645032890.62637821289
1122416.874827191951941.145304616852892.60434976706
1132418.841440454951943.095630053122894.58725085678
1142420.808053717941945.040140307762896.57596712813
1152422.774666980941946.977950092442898.57138386943
1162424.741280243931948.9081745932900.57438589486
1172426.707893506921950.829929602042902.58585741181
1182428.674506769921952.742331667862904.60668187198
1192430.641120032911954.644498259482906.63774180634
1202432.60773329591956.535547947672908.67991864414



Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')