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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 13 Aug 2015 12:06:26 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Aug/13/t1439464009i37wty9y468e66z.htm/, Retrieved Thu, 16 May 2024 11:25:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280035, Retrieved Thu, 16 May 2024 11:25:03 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

160

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Histogram] [omzetontwikkeling...] [2014-09-24 09:10:11] [3d50c3f1d1505d45371c80c331b9aa00]
- R  D  [Histogram] [] [2015-07-23 12:50:11] [74be16979710d4c4e7c6647856088456]
- RMPD    [Harrell-Davis Quantiles] [] [2015-08-10 08:16:05] [74be16979710d4c4e7c6647856088456]
- RMP       [Mean versus Median] [] [2015-08-10 09:14:26] [74be16979710d4c4e7c6647856088456]
- RMP         [Mean Plot] [] [2015-08-10 09:32:31] [74be16979710d4c4e7c6647856088456]
- RMP           [(Partial) Autocorrelation Function] [] [2015-08-10 11:22:46] [74be16979710d4c4e7c6647856088456]
- RM              [Classical Decomposition] [] [2015-08-10 12:45:52] [74be16979710d4c4e7c6647856088456]
- RMP                 [Exponential Smoothing] [] [2015-08-13 11:06:26] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Maurice George Kendall' @ kendall.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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280035&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280035&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280035&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.00926118605787734
beta	1
gamma	0.929768627341032

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00926118605787734 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.929768627341032 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280035&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]0.00926118605787734[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.929768627341032[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280035&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280035&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
Parameter	Value
alpha	0.00926118605787734
beta	1
gamma	0.929768627341032

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1170000	1210010.41666667	-40010.4166666663
14	877500	916536.374295206	-39036.3742952057
15	1033500	1080959.829586	-47459.8295860023
16	780000	825615.73937803	-45615.7393780297
17	1092000	1120741.27178303	-28741.2717830334
18	897000	908756.903506539	-11756.9035065392
19	1189500	1136383.44775389	53116.5522461096
20	1072500	1170102.71941829	-97602.7194182884
21	1131000	1305522.23492101	-174522.234921007
22	1267500	1124175.60159033	143324.398409666
23	1248000	1063287.45898911	184712.541010889
24	1482000	1340868.27688663	141131.723113367
25	1072500	1093371.62178933	-20871.6217893264
26	897000	801496.984471657	95503.0155283434
27	994500	961178.006615929	33321.9933840714
28	721500	710799.790237324	10700.2097626764
29	1033500	1025031.51632054	8468.48367946385
30	799500	832422.238053606	-32922.2380536059
31	1131000	1122800.64331612	8199.35668388195
32	1072500	1020040.88213816	52459.1178618359
33	955500	1090158.07847214	-134658.078472143
34	1365000	1206499.69777699	158500.302223015
35	1228500	1188549.79851905	39950.2014809493
36	1404000	1427977.14454784	-23977.1445478417
37	1053000	1031523.63826415	21476.3617358488
38	975000	849435.707160128	125564.292839872
39	877500	954590.098700836	-77090.0987008356
40	721500	683802.058562206	37697.9414377945
41	955500	997929.031757363	-42429.0317573631
42	858000	767950.609955201	90049.3900447992
43	1170000	1099715.83874702	70284.1612529804
44	1131000	1041244.74252856	89755.2574714432
45	975000	942631.733195843	32368.2668041567
46	1306500	1335401.09061893	-28901.0906189252
47	1209000	1209612.44246125	-612.442461245926
48	1560000	1392501.4625982	167498.537401795
49	1248000	1044188.90506434	203811.094935662
50	760500	965857.464277689	-205357.464277689
51	760500	884392.150645858	-123892.150645858
52	760500	721596.841566429	38903.1584335713
53	897000	964624.813862568	-67624.8138625675
54	897000	858912.675958727	38087.3240412726
55	1209000	1173974.63429288	35025.3657071223
56	1111500	1134771.27090552	-23271.2709055201
57	994500	982860.581867606	11639.4181323941
58	1248000	1319418.79916559	-71418.7991655932
59	1150500	1219320.51718975	-68820.5171897514
60	1657500	1555828.73342234	101671.266577663
61	1306500	1239140.62885035	67359.371149655
62	760500	780157.434691726	-19657.4346917258
63	799500	774694.929373099	24805.0706269015
64	663000	763854.616484065	-100854.616484065
65	916500	906782.567394751	9717.43260524888
66	1053000	899203.93995463	153796.06004537
67	1326000	1213628.21359764	112371.786402358
68	1306500	1123268.34613988	183231.653860125
69	1053000	1009168.41874774	43831.5812522583
70	1228500	1273553.22476467	-45053.2247646686
71	1092000	1180374.90504929	-88374.9050492938
72	1560000	1677853.13341287	-117853.133412873
73	1189500	1329593.50487064	-140093.504870637
74	955500	788679.780826516	166820.219173484
75	858000	827775.215636555	30224.7843634445
76	643500	703156.828659159	-59656.8286591592
77	955500	950626.315518424	4873.68448157643
78	1150500	1077982.81419068	72517.1858093247
79	1345500	1355004.1385437	-9504.13854370033
80	1267500	1329168.04926372	-61668.0492637199
81	936000	1082501.89430813	-146501.894308131
82	1345500	1259595.64224585	85904.3577541464
83	1053000	1125285.45497391	-72285.4549739065
84	1618500	1593469.01266974	25030.9873302612
85	1345500	1225079.46775256	120420.532247444
86	975000	970740.77340071	4259.22659929027
87	897000	882445.602932554	14554.3970674463
88	604500	674682.669971702	-70182.6699717017
89	955500	981195.718460067	-25695.7184600673
90	916500	1169994.59623822	-253494.596238222
91	1384500	1364837.9654814	19662.0345185981
92	1384500	1287886.79503191	96613.204968093
93	1053000	962673.022821001	90326.9771789989
94	1365000	1356368.12505093	8631.87494907063
95	1014000	1075234.06821068	-61234.0682106796
96	1579500	1632875.6859909	-53375.6859909049
97	1345500	1350614.59794239	-5114.59794238978
98	994500	985933.560565683	8566.43943431706
99	760500	905024.808888394	-144524.808888394
100	526500	614122.187363108	-87622.1873631083
101	1033500	957681.509486048	75818.4905139523
102	994500	934750.22171967	59749.7782803299
103	1306500	1384184.42005978	-77684.4200597818
104	1501500	1376383.77368878	125116.226311219
105	1111500	1045075.22852825	66424.7714717496
106	1248000	1362505.38253643	-114505.382536426
107	936000	1013943.4690828	-77943.4690827953
108	1618500	1576584.50334889	41915.496651113

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1170000 & 1210010.41666667 & -40010.4166666663 \tabularnewline
14 & 877500 & 916536.374295206 & -39036.3742952057 \tabularnewline
15 & 1033500 & 1080959.829586 & -47459.8295860023 \tabularnewline
16 & 780000 & 825615.73937803 & -45615.7393780297 \tabularnewline
17 & 1092000 & 1120741.27178303 & -28741.2717830334 \tabularnewline
18 & 897000 & 908756.903506539 & -11756.9035065392 \tabularnewline
19 & 1189500 & 1136383.44775389 & 53116.5522461096 \tabularnewline
20 & 1072500 & 1170102.71941829 & -97602.7194182884 \tabularnewline
21 & 1131000 & 1305522.23492101 & -174522.234921007 \tabularnewline
22 & 1267500 & 1124175.60159033 & 143324.398409666 \tabularnewline
23 & 1248000 & 1063287.45898911 & 184712.541010889 \tabularnewline
24 & 1482000 & 1340868.27688663 & 141131.723113367 \tabularnewline
25 & 1072500 & 1093371.62178933 & -20871.6217893264 \tabularnewline
26 & 897000 & 801496.984471657 & 95503.0155283434 \tabularnewline
27 & 994500 & 961178.006615929 & 33321.9933840714 \tabularnewline
28 & 721500 & 710799.790237324 & 10700.2097626764 \tabularnewline
29 & 1033500 & 1025031.51632054 & 8468.48367946385 \tabularnewline
30 & 799500 & 832422.238053606 & -32922.2380536059 \tabularnewline
31 & 1131000 & 1122800.64331612 & 8199.35668388195 \tabularnewline
32 & 1072500 & 1020040.88213816 & 52459.1178618359 \tabularnewline
33 & 955500 & 1090158.07847214 & -134658.078472143 \tabularnewline
34 & 1365000 & 1206499.69777699 & 158500.302223015 \tabularnewline
35 & 1228500 & 1188549.79851905 & 39950.2014809493 \tabularnewline
36 & 1404000 & 1427977.14454784 & -23977.1445478417 \tabularnewline
37 & 1053000 & 1031523.63826415 & 21476.3617358488 \tabularnewline
38 & 975000 & 849435.707160128 & 125564.292839872 \tabularnewline
39 & 877500 & 954590.098700836 & -77090.0987008356 \tabularnewline
40 & 721500 & 683802.058562206 & 37697.9414377945 \tabularnewline
41 & 955500 & 997929.031757363 & -42429.0317573631 \tabularnewline
42 & 858000 & 767950.609955201 & 90049.3900447992 \tabularnewline
43 & 1170000 & 1099715.83874702 & 70284.1612529804 \tabularnewline
44 & 1131000 & 1041244.74252856 & 89755.2574714432 \tabularnewline
45 & 975000 & 942631.733195843 & 32368.2668041567 \tabularnewline
46 & 1306500 & 1335401.09061893 & -28901.0906189252 \tabularnewline
47 & 1209000 & 1209612.44246125 & -612.442461245926 \tabularnewline
48 & 1560000 & 1392501.4625982 & 167498.537401795 \tabularnewline
49 & 1248000 & 1044188.90506434 & 203811.094935662 \tabularnewline
50 & 760500 & 965857.464277689 & -205357.464277689 \tabularnewline
51 & 760500 & 884392.150645858 & -123892.150645858 \tabularnewline
52 & 760500 & 721596.841566429 & 38903.1584335713 \tabularnewline
53 & 897000 & 964624.813862568 & -67624.8138625675 \tabularnewline
54 & 897000 & 858912.675958727 & 38087.3240412726 \tabularnewline
55 & 1209000 & 1173974.63429288 & 35025.3657071223 \tabularnewline
56 & 1111500 & 1134771.27090552 & -23271.2709055201 \tabularnewline
57 & 994500 & 982860.581867606 & 11639.4181323941 \tabularnewline
58 & 1248000 & 1319418.79916559 & -71418.7991655932 \tabularnewline
59 & 1150500 & 1219320.51718975 & -68820.5171897514 \tabularnewline
60 & 1657500 & 1555828.73342234 & 101671.266577663 \tabularnewline
61 & 1306500 & 1239140.62885035 & 67359.371149655 \tabularnewline
62 & 760500 & 780157.434691726 & -19657.4346917258 \tabularnewline
63 & 799500 & 774694.929373099 & 24805.0706269015 \tabularnewline
64 & 663000 & 763854.616484065 & -100854.616484065 \tabularnewline
65 & 916500 & 906782.567394751 & 9717.43260524888 \tabularnewline
66 & 1053000 & 899203.93995463 & 153796.06004537 \tabularnewline
67 & 1326000 & 1213628.21359764 & 112371.786402358 \tabularnewline
68 & 1306500 & 1123268.34613988 & 183231.653860125 \tabularnewline
69 & 1053000 & 1009168.41874774 & 43831.5812522583 \tabularnewline
70 & 1228500 & 1273553.22476467 & -45053.2247646686 \tabularnewline
71 & 1092000 & 1180374.90504929 & -88374.9050492938 \tabularnewline
72 & 1560000 & 1677853.13341287 & -117853.133412873 \tabularnewline
73 & 1189500 & 1329593.50487064 & -140093.504870637 \tabularnewline
74 & 955500 & 788679.780826516 & 166820.219173484 \tabularnewline
75 & 858000 & 827775.215636555 & 30224.7843634445 \tabularnewline
76 & 643500 & 703156.828659159 & -59656.8286591592 \tabularnewline
77 & 955500 & 950626.315518424 & 4873.68448157643 \tabularnewline
78 & 1150500 & 1077982.81419068 & 72517.1858093247 \tabularnewline
79 & 1345500 & 1355004.1385437 & -9504.13854370033 \tabularnewline
80 & 1267500 & 1329168.04926372 & -61668.0492637199 \tabularnewline
81 & 936000 & 1082501.89430813 & -146501.894308131 \tabularnewline
82 & 1345500 & 1259595.64224585 & 85904.3577541464 \tabularnewline
83 & 1053000 & 1125285.45497391 & -72285.4549739065 \tabularnewline
84 & 1618500 & 1593469.01266974 & 25030.9873302612 \tabularnewline
85 & 1345500 & 1225079.46775256 & 120420.532247444 \tabularnewline
86 & 975000 & 970740.77340071 & 4259.22659929027 \tabularnewline
87 & 897000 & 882445.602932554 & 14554.3970674463 \tabularnewline
88 & 604500 & 674682.669971702 & -70182.6699717017 \tabularnewline
89 & 955500 & 981195.718460067 & -25695.7184600673 \tabularnewline
90 & 916500 & 1169994.59623822 & -253494.596238222 \tabularnewline
91 & 1384500 & 1364837.9654814 & 19662.0345185981 \tabularnewline
92 & 1384500 & 1287886.79503191 & 96613.204968093 \tabularnewline
93 & 1053000 & 962673.022821001 & 90326.9771789989 \tabularnewline
94 & 1365000 & 1356368.12505093 & 8631.87494907063 \tabularnewline
95 & 1014000 & 1075234.06821068 & -61234.0682106796 \tabularnewline
96 & 1579500 & 1632875.6859909 & -53375.6859909049 \tabularnewline
97 & 1345500 & 1350614.59794239 & -5114.59794238978 \tabularnewline
98 & 994500 & 985933.560565683 & 8566.43943431706 \tabularnewline
99 & 760500 & 905024.808888394 & -144524.808888394 \tabularnewline
100 & 526500 & 614122.187363108 & -87622.1873631083 \tabularnewline
101 & 1033500 & 957681.509486048 & 75818.4905139523 \tabularnewline
102 & 994500 & 934750.22171967 & 59749.7782803299 \tabularnewline
103 & 1306500 & 1384184.42005978 & -77684.4200597818 \tabularnewline
104 & 1501500 & 1376383.77368878 & 125116.226311219 \tabularnewline
105 & 1111500 & 1045075.22852825 & 66424.7714717496 \tabularnewline
106 & 1248000 & 1362505.38253643 & -114505.382536426 \tabularnewline
107 & 936000 & 1013943.4690828 & -77943.4690827953 \tabularnewline
108 & 1618500 & 1576584.50334889 & 41915.496651113 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280035&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]1170000[/C][C]1210010.41666667[/C][C]-40010.4166666663[/C][/ROW]
[ROW][C]14[/C][C]877500[/C][C]916536.374295206[/C][C]-39036.3742952057[/C][/ROW]
[ROW][C]15[/C][C]1033500[/C][C]1080959.829586[/C][C]-47459.8295860023[/C][/ROW]
[ROW][C]16[/C][C]780000[/C][C]825615.73937803[/C][C]-45615.7393780297[/C][/ROW]
[ROW][C]17[/C][C]1092000[/C][C]1120741.27178303[/C][C]-28741.2717830334[/C][/ROW]
[ROW][C]18[/C][C]897000[/C][C]908756.903506539[/C][C]-11756.9035065392[/C][/ROW]
[ROW][C]19[/C][C]1189500[/C][C]1136383.44775389[/C][C]53116.5522461096[/C][/ROW]
[ROW][C]20[/C][C]1072500[/C][C]1170102.71941829[/C][C]-97602.7194182884[/C][/ROW]
[ROW][C]21[/C][C]1131000[/C][C]1305522.23492101[/C][C]-174522.234921007[/C][/ROW]
[ROW][C]22[/C][C]1267500[/C][C]1124175.60159033[/C][C]143324.398409666[/C][/ROW]
[ROW][C]23[/C][C]1248000[/C][C]1063287.45898911[/C][C]184712.541010889[/C][/ROW]
[ROW][C]24[/C][C]1482000[/C][C]1340868.27688663[/C][C]141131.723113367[/C][/ROW]
[ROW][C]25[/C][C]1072500[/C][C]1093371.62178933[/C][C]-20871.6217893264[/C][/ROW]
[ROW][C]26[/C][C]897000[/C][C]801496.984471657[/C][C]95503.0155283434[/C][/ROW]
[ROW][C]27[/C][C]994500[/C][C]961178.006615929[/C][C]33321.9933840714[/C][/ROW]
[ROW][C]28[/C][C]721500[/C][C]710799.790237324[/C][C]10700.2097626764[/C][/ROW]
[ROW][C]29[/C][C]1033500[/C][C]1025031.51632054[/C][C]8468.48367946385[/C][/ROW]
[ROW][C]30[/C][C]799500[/C][C]832422.238053606[/C][C]-32922.2380536059[/C][/ROW]
[ROW][C]31[/C][C]1131000[/C][C]1122800.64331612[/C][C]8199.35668388195[/C][/ROW]
[ROW][C]32[/C][C]1072500[/C][C]1020040.88213816[/C][C]52459.1178618359[/C][/ROW]
[ROW][C]33[/C][C]955500[/C][C]1090158.07847214[/C][C]-134658.078472143[/C][/ROW]
[ROW][C]34[/C][C]1365000[/C][C]1206499.69777699[/C][C]158500.302223015[/C][/ROW]
[ROW][C]35[/C][C]1228500[/C][C]1188549.79851905[/C][C]39950.2014809493[/C][/ROW]
[ROW][C]36[/C][C]1404000[/C][C]1427977.14454784[/C][C]-23977.1445478417[/C][/ROW]
[ROW][C]37[/C][C]1053000[/C][C]1031523.63826415[/C][C]21476.3617358488[/C][/ROW]
[ROW][C]38[/C][C]975000[/C][C]849435.707160128[/C][C]125564.292839872[/C][/ROW]
[ROW][C]39[/C][C]877500[/C][C]954590.098700836[/C][C]-77090.0987008356[/C][/ROW]
[ROW][C]40[/C][C]721500[/C][C]683802.058562206[/C][C]37697.9414377945[/C][/ROW]
[ROW][C]41[/C][C]955500[/C][C]997929.031757363[/C][C]-42429.0317573631[/C][/ROW]
[ROW][C]42[/C][C]858000[/C][C]767950.609955201[/C][C]90049.3900447992[/C][/ROW]
[ROW][C]43[/C][C]1170000[/C][C]1099715.83874702[/C][C]70284.1612529804[/C][/ROW]
[ROW][C]44[/C][C]1131000[/C][C]1041244.74252856[/C][C]89755.2574714432[/C][/ROW]
[ROW][C]45[/C][C]975000[/C][C]942631.733195843[/C][C]32368.2668041567[/C][/ROW]
[ROW][C]46[/C][C]1306500[/C][C]1335401.09061893[/C][C]-28901.0906189252[/C][/ROW]
[ROW][C]47[/C][C]1209000[/C][C]1209612.44246125[/C][C]-612.442461245926[/C][/ROW]
[ROW][C]48[/C][C]1560000[/C][C]1392501.4625982[/C][C]167498.537401795[/C][/ROW]
[ROW][C]49[/C][C]1248000[/C][C]1044188.90506434[/C][C]203811.094935662[/C][/ROW]
[ROW][C]50[/C][C]760500[/C][C]965857.464277689[/C][C]-205357.464277689[/C][/ROW]
[ROW][C]51[/C][C]760500[/C][C]884392.150645858[/C][C]-123892.150645858[/C][/ROW]
[ROW][C]52[/C][C]760500[/C][C]721596.841566429[/C][C]38903.1584335713[/C][/ROW]
[ROW][C]53[/C][C]897000[/C][C]964624.813862568[/C][C]-67624.8138625675[/C][/ROW]
[ROW][C]54[/C][C]897000[/C][C]858912.675958727[/C][C]38087.3240412726[/C][/ROW]
[ROW][C]55[/C][C]1209000[/C][C]1173974.63429288[/C][C]35025.3657071223[/C][/ROW]
[ROW][C]56[/C][C]1111500[/C][C]1134771.27090552[/C][C]-23271.2709055201[/C][/ROW]
[ROW][C]57[/C][C]994500[/C][C]982860.581867606[/C][C]11639.4181323941[/C][/ROW]
[ROW][C]58[/C][C]1248000[/C][C]1319418.79916559[/C][C]-71418.7991655932[/C][/ROW]
[ROW][C]59[/C][C]1150500[/C][C]1219320.51718975[/C][C]-68820.5171897514[/C][/ROW]
[ROW][C]60[/C][C]1657500[/C][C]1555828.73342234[/C][C]101671.266577663[/C][/ROW]
[ROW][C]61[/C][C]1306500[/C][C]1239140.62885035[/C][C]67359.371149655[/C][/ROW]
[ROW][C]62[/C][C]760500[/C][C]780157.434691726[/C][C]-19657.4346917258[/C][/ROW]
[ROW][C]63[/C][C]799500[/C][C]774694.929373099[/C][C]24805.0706269015[/C][/ROW]
[ROW][C]64[/C][C]663000[/C][C]763854.616484065[/C][C]-100854.616484065[/C][/ROW]
[ROW][C]65[/C][C]916500[/C][C]906782.567394751[/C][C]9717.43260524888[/C][/ROW]
[ROW][C]66[/C][C]1053000[/C][C]899203.93995463[/C][C]153796.06004537[/C][/ROW]
[ROW][C]67[/C][C]1326000[/C][C]1213628.21359764[/C][C]112371.786402358[/C][/ROW]
[ROW][C]68[/C][C]1306500[/C][C]1123268.34613988[/C][C]183231.653860125[/C][/ROW]
[ROW][C]69[/C][C]1053000[/C][C]1009168.41874774[/C][C]43831.5812522583[/C][/ROW]
[ROW][C]70[/C][C]1228500[/C][C]1273553.22476467[/C][C]-45053.2247646686[/C][/ROW]
[ROW][C]71[/C][C]1092000[/C][C]1180374.90504929[/C][C]-88374.9050492938[/C][/ROW]
[ROW][C]72[/C][C]1560000[/C][C]1677853.13341287[/C][C]-117853.133412873[/C][/ROW]
[ROW][C]73[/C][C]1189500[/C][C]1329593.50487064[/C][C]-140093.504870637[/C][/ROW]
[ROW][C]74[/C][C]955500[/C][C]788679.780826516[/C][C]166820.219173484[/C][/ROW]
[ROW][C]75[/C][C]858000[/C][C]827775.215636555[/C][C]30224.7843634445[/C][/ROW]
[ROW][C]76[/C][C]643500[/C][C]703156.828659159[/C][C]-59656.8286591592[/C][/ROW]
[ROW][C]77[/C][C]955500[/C][C]950626.315518424[/C][C]4873.68448157643[/C][/ROW]
[ROW][C]78[/C][C]1150500[/C][C]1077982.81419068[/C][C]72517.1858093247[/C][/ROW]
[ROW][C]79[/C][C]1345500[/C][C]1355004.1385437[/C][C]-9504.13854370033[/C][/ROW]
[ROW][C]80[/C][C]1267500[/C][C]1329168.04926372[/C][C]-61668.0492637199[/C][/ROW]
[ROW][C]81[/C][C]936000[/C][C]1082501.89430813[/C][C]-146501.894308131[/C][/ROW]
[ROW][C]82[/C][C]1345500[/C][C]1259595.64224585[/C][C]85904.3577541464[/C][/ROW]
[ROW][C]83[/C][C]1053000[/C][C]1125285.45497391[/C][C]-72285.4549739065[/C][/ROW]
[ROW][C]84[/C][C]1618500[/C][C]1593469.01266974[/C][C]25030.9873302612[/C][/ROW]
[ROW][C]85[/C][C]1345500[/C][C]1225079.46775256[/C][C]120420.532247444[/C][/ROW]
[ROW][C]86[/C][C]975000[/C][C]970740.77340071[/C][C]4259.22659929027[/C][/ROW]
[ROW][C]87[/C][C]897000[/C][C]882445.602932554[/C][C]14554.3970674463[/C][/ROW]
[ROW][C]88[/C][C]604500[/C][C]674682.669971702[/C][C]-70182.6699717017[/C][/ROW]
[ROW][C]89[/C][C]955500[/C][C]981195.718460067[/C][C]-25695.7184600673[/C][/ROW]
[ROW][C]90[/C][C]916500[/C][C]1169994.59623822[/C][C]-253494.596238222[/C][/ROW]
[ROW][C]91[/C][C]1384500[/C][C]1364837.9654814[/C][C]19662.0345185981[/C][/ROW]
[ROW][C]92[/C][C]1384500[/C][C]1287886.79503191[/C][C]96613.204968093[/C][/ROW]
[ROW][C]93[/C][C]1053000[/C][C]962673.022821001[/C][C]90326.9771789989[/C][/ROW]
[ROW][C]94[/C][C]1365000[/C][C]1356368.12505093[/C][C]8631.87494907063[/C][/ROW]
[ROW][C]95[/C][C]1014000[/C][C]1075234.06821068[/C][C]-61234.0682106796[/C][/ROW]
[ROW][C]96[/C][C]1579500[/C][C]1632875.6859909[/C][C]-53375.6859909049[/C][/ROW]
[ROW][C]97[/C][C]1345500[/C][C]1350614.59794239[/C][C]-5114.59794238978[/C][/ROW]
[ROW][C]98[/C][C]994500[/C][C]985933.560565683[/C][C]8566.43943431706[/C][/ROW]
[ROW][C]99[/C][C]760500[/C][C]905024.808888394[/C][C]-144524.808888394[/C][/ROW]
[ROW][C]100[/C][C]526500[/C][C]614122.187363108[/C][C]-87622.1873631083[/C][/ROW]
[ROW][C]101[/C][C]1033500[/C][C]957681.509486048[/C][C]75818.4905139523[/C][/ROW]
[ROW][C]102[/C][C]994500[/C][C]934750.22171967[/C][C]59749.7782803299[/C][/ROW]
[ROW][C]103[/C][C]1306500[/C][C]1384184.42005978[/C][C]-77684.4200597818[/C][/ROW]
[ROW][C]104[/C][C]1501500[/C][C]1376383.77368878[/C][C]125116.226311219[/C][/ROW]
[ROW][C]105[/C][C]1111500[/C][C]1045075.22852825[/C][C]66424.7714717496[/C][/ROW]
[ROW][C]106[/C][C]1248000[/C][C]1362505.38253643[/C][C]-114505.382536426[/C][/ROW]
[ROW][C]107[/C][C]936000[/C][C]1013943.4690828[/C][C]-77943.4690827953[/C][/ROW]
[ROW][C]108[/C][C]1618500[/C][C]1576584.50334889[/C][C]41915.496651113[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280035&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280035&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
t	Observed	Fitted	Residuals
13	1170000	1210010.41666667	-40010.4166666663
14	877500	916536.374295206	-39036.3742952057
15	1033500	1080959.829586	-47459.8295860023
16	780000	825615.73937803	-45615.7393780297
17	1092000	1120741.27178303	-28741.2717830334
18	897000	908756.903506539	-11756.9035065392
19	1189500	1136383.44775389	53116.5522461096
20	1072500	1170102.71941829	-97602.7194182884
21	1131000	1305522.23492101	-174522.234921007
22	1267500	1124175.60159033	143324.398409666
23	1248000	1063287.45898911	184712.541010889
24	1482000	1340868.27688663	141131.723113367
25	1072500	1093371.62178933	-20871.6217893264
26	897000	801496.984471657	95503.0155283434
27	994500	961178.006615929	33321.9933840714
28	721500	710799.790237324	10700.2097626764
29	1033500	1025031.51632054	8468.48367946385
30	799500	832422.238053606	-32922.2380536059
31	1131000	1122800.64331612	8199.35668388195
32	1072500	1020040.88213816	52459.1178618359
33	955500	1090158.07847214	-134658.078472143
34	1365000	1206499.69777699	158500.302223015
35	1228500	1188549.79851905	39950.2014809493
36	1404000	1427977.14454784	-23977.1445478417
37	1053000	1031523.63826415	21476.3617358488
38	975000	849435.707160128	125564.292839872
39	877500	954590.098700836	-77090.0987008356
40	721500	683802.058562206	37697.9414377945
41	955500	997929.031757363	-42429.0317573631
42	858000	767950.609955201	90049.3900447992
43	1170000	1099715.83874702	70284.1612529804
44	1131000	1041244.74252856	89755.2574714432
45	975000	942631.733195843	32368.2668041567
46	1306500	1335401.09061893	-28901.0906189252
47	1209000	1209612.44246125	-612.442461245926
48	1560000	1392501.4625982	167498.537401795
49	1248000	1044188.90506434	203811.094935662
50	760500	965857.464277689	-205357.464277689
51	760500	884392.150645858	-123892.150645858
52	760500	721596.841566429	38903.1584335713
53	897000	964624.813862568	-67624.8138625675
54	897000	858912.675958727	38087.3240412726
55	1209000	1173974.63429288	35025.3657071223
56	1111500	1134771.27090552	-23271.2709055201
57	994500	982860.581867606	11639.4181323941
58	1248000	1319418.79916559	-71418.7991655932
59	1150500	1219320.51718975	-68820.5171897514
60	1657500	1555828.73342234	101671.266577663
61	1306500	1239140.62885035	67359.371149655
62	760500	780157.434691726	-19657.4346917258
63	799500	774694.929373099	24805.0706269015
64	663000	763854.616484065	-100854.616484065
65	916500	906782.567394751	9717.43260524888
66	1053000	899203.93995463	153796.06004537
67	1326000	1213628.21359764	112371.786402358
68	1306500	1123268.34613988	183231.653860125
69	1053000	1009168.41874774	43831.5812522583
70	1228500	1273553.22476467	-45053.2247646686
71	1092000	1180374.90504929	-88374.9050492938
72	1560000	1677853.13341287	-117853.133412873
73	1189500	1329593.50487064	-140093.504870637
74	955500	788679.780826516	166820.219173484
75	858000	827775.215636555	30224.7843634445
76	643500	703156.828659159	-59656.8286591592
77	955500	950626.315518424	4873.68448157643
78	1150500	1077982.81419068	72517.1858093247
79	1345500	1355004.1385437	-9504.13854370033
80	1267500	1329168.04926372	-61668.0492637199
81	936000	1082501.89430813	-146501.894308131
82	1345500	1259595.64224585	85904.3577541464
83	1053000	1125285.45497391	-72285.4549739065
84	1618500	1593469.01266974	25030.9873302612
85	1345500	1225079.46775256	120420.532247444
86	975000	970740.77340071	4259.22659929027
87	897000	882445.602932554	14554.3970674463
88	604500	674682.669971702	-70182.6699717017
89	955500	981195.718460067	-25695.7184600673
90	916500	1169994.59623822	-253494.596238222
91	1384500	1364837.9654814	19662.0345185981
92	1384500	1287886.79503191	96613.204968093
93	1053000	962673.022821001	90326.9771789989
94	1365000	1356368.12505093	8631.87494907063
95	1014000	1075234.06821068	-61234.0682106796
96	1579500	1632875.6859909	-53375.6859909049
97	1345500	1350614.59794239	-5114.59794238978
98	994500	985933.560565683	8566.43943431706
99	760500	905024.808888394	-144524.808888394
100	526500	614122.187363108	-87622.1873631083
101	1033500	957681.509486048	75818.4905139523
102	994500	934750.22171967	59749.7782803299
103	1306500	1384184.42005978	-77684.4200597818
104	1501500	1376383.77368878	125116.226311219
105	1111500	1045075.22852825	66424.7714717496
106	1248000	1362505.38253643	-114505.382536426
107	936000	1013943.4690828	-77943.4690827953
108	1618500	1576584.50334889	41915.496651113

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	1338459.86972684	1159717.67149434	1517202.06795935
110	985273.826170004	806500.969284891	1164046.68305512
111	762030.427305509	583188.60766846	940872.246942558
112	524986.941524331	346022.587055059	703951.295993604
113	1020828.2677594	841672.620395598	1199983.91512319
114	982606.673513198	803175.922661387	1162037.42436501
115	1304549.25457313	1124744.73365597	1484353.7754903
116	1484659.24833609	1304367.70493956	1664950.79173262
117	1097348.93792753	916442.886480005	1278254.98937505
118	1246104.5676011	1064442.73149542	1427766.40370678
119	931948.742257552	749376.589873624	1114520.89464148
120	1606108.84193336	1422459.21818828	1789758.46567845

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1338459.86972684 & 1159717.67149434 & 1517202.06795935 \tabularnewline
110 & 985273.826170004 & 806500.969284891 & 1164046.68305512 \tabularnewline
111 & 762030.427305509 & 583188.60766846 & 940872.246942558 \tabularnewline
112 & 524986.941524331 & 346022.587055059 & 703951.295993604 \tabularnewline
113 & 1020828.2677594 & 841672.620395598 & 1199983.91512319 \tabularnewline
114 & 982606.673513198 & 803175.922661387 & 1162037.42436501 \tabularnewline
115 & 1304549.25457313 & 1124744.73365597 & 1484353.7754903 \tabularnewline
116 & 1484659.24833609 & 1304367.70493956 & 1664950.79173262 \tabularnewline
117 & 1097348.93792753 & 916442.886480005 & 1278254.98937505 \tabularnewline
118 & 1246104.5676011 & 1064442.73149542 & 1427766.40370678 \tabularnewline
119 & 931948.742257552 & 749376.589873624 & 1114520.89464148 \tabularnewline
120 & 1606108.84193336 & 1422459.21818828 & 1789758.46567845 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280035&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]1338459.86972684[/C][C]1159717.67149434[/C][C]1517202.06795935[/C][/ROW]
[ROW][C]110[/C][C]985273.826170004[/C][C]806500.969284891[/C][C]1164046.68305512[/C][/ROW]
[ROW][C]111[/C][C]762030.427305509[/C][C]583188.60766846[/C][C]940872.246942558[/C][/ROW]
[ROW][C]112[/C][C]524986.941524331[/C][C]346022.587055059[/C][C]703951.295993604[/C][/ROW]
[ROW][C]113[/C][C]1020828.2677594[/C][C]841672.620395598[/C][C]1199983.91512319[/C][/ROW]
[ROW][C]114[/C][C]982606.673513198[/C][C]803175.922661387[/C][C]1162037.42436501[/C][/ROW]
[ROW][C]115[/C][C]1304549.25457313[/C][C]1124744.73365597[/C][C]1484353.7754903[/C][/ROW]
[ROW][C]116[/C][C]1484659.24833609[/C][C]1304367.70493956[/C][C]1664950.79173262[/C][/ROW]
[ROW][C]117[/C][C]1097348.93792753[/C][C]916442.886480005[/C][C]1278254.98937505[/C][/ROW]
[ROW][C]118[/C][C]1246104.5676011[/C][C]1064442.73149542[/C][C]1427766.40370678[/C][/ROW]
[ROW][C]119[/C][C]931948.742257552[/C][C]749376.589873624[/C][C]1114520.89464148[/C][/ROW]
[ROW][C]120[/C][C]1606108.84193336[/C][C]1422459.21818828[/C][C]1789758.46567845[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280035&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280035&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
t	Forecast	95% Lower Bound	95% Upper Bound
109	1338459.86972684	1159717.67149434	1517202.06795935
110	985273.826170004	806500.969284891	1164046.68305512
111	762030.427305509	583188.60766846	940872.246942558
112	524986.941524331	346022.587055059	703951.295993604
113	1020828.2677594	841672.620395598	1199983.91512319
114	982606.673513198	803175.922661387	1162037.42436501
115	1304549.25457313	1124744.73365597	1484353.7754903
116	1484659.24833609	1304367.70493956	1664950.79173262
117	1097348.93792753	916442.886480005	1278254.98937505
118	1246104.5676011	1064442.73149542	1427766.40370678
119	931948.742257552	749376.589873624	1114520.89464148
120	1606108.84193336	1422459.21818828	1789758.46567845

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code