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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationSat, 15 Nov 2008 05:00:57 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/15/t1226750566cfoossg34jsa7e3.htm/, Retrieved Mon, 29 Apr 2024 14:28:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24938, Retrieved Mon, 29 Apr 2024 14:28:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact337

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
F    D    [Multiple Regression] [The Seatbelt Law ...] [2008-11-15 12:00:57] [4127a50d3937d4bda99dae34ed7ecdc5] [Current]
-   PD      [Multiple Regression] [] [2008-11-15 18:50:27] [93834488277b53a4510bfd06084ae13b]
F   P         [Multiple Regression] [Q3 - Consumptiepr...] [2008-11-15 21:54:28] [93834488277b53a4510bfd06084ae13b]
F    D        [Multiple Regression] [q3 ] [2008-11-19 14:12:05] [44a98561a4b3e6ab8cd5a857b48b0914]
F   P           [Multiple Regression] [q3 dummie+trend] [2008-11-19 14:18:31] [44a98561a4b3e6ab8cd5a857b48b0914]
-   PD        [Multiple Regression] [Paper - Multiple ...] [2008-12-21 14:42:00] [85841a4a203c2f9589565c024425a91b]
-    D        [Multiple Regression] [Paper - Multiple ...] [2008-12-21 14:45:31] [85841a4a203c2f9589565c024425a91b]
-   PD          [Multiple Regression] [Paper - Multiple ...] [2008-12-21 15:09:11] [85841a4a203c2f9589565c024425a91b]
- RMPD            [ARIMA Forecasting] [Paper - Arima for...] [2008-12-21 19:50:13] [85841a4a203c2f9589565c024425a91b]
-   PD              [ARIMA Forecasting] [arima forecast gas] [2008-12-22 17:09:25] [44a98561a4b3e6ab8cd5a857b48b0914]
- RMPD            [ARIMA Forecasting] [Paper - Arima for...] [2008-12-21 20:01:58] [85841a4a203c2f9589565c024425a91b]
- R PD            [Multiple Regression] [Paper - Multiple ...] [2008-12-22 11:36:38] [85841a4a203c2f9589565c024425a91b]
- R  D            [Multiple Regression] [Paper - Multiple ...] [2008-12-22 11:38:40] [85841a4a203c2f9589565c024425a91b]
- R PD            [Multiple Regression] [Paper - Multiple ...] [2008-12-22 11:39:51] [85841a4a203c2f9589565c024425a91b]
-   PD              [Multiple Regression] [Paper - Multiple ...] [2008-12-22 12:06:36] [85841a4a203c2f9589565c024425a91b]
-    D              [Multiple Regression] [Paper - Multiple ...] [2008-12-22 12:08:28] [85841a4a203c2f9589565c024425a91b]
-   PD              [Multiple Regression] [Paper - Multiple ...] [2008-12-22 12:11:46] [85841a4a203c2f9589565c024425a91b]
-   PD          [Multiple Regression] [Paper - Multiple ...] [2008-12-21 15:49:26] [85841a4a203c2f9589565c024425a91b]
-   PD          [Multiple Regression] [Paper - Multiple ...] [2008-12-21 15:50:56] [85841a4a203c2f9589565c024425a91b]
F           [Multiple Regression] [seat belt q1] [2008-11-19 13:47:01] [44a98561a4b3e6ab8cd5a857b48b0914]
F R P       [Multiple Regression] [Seatbelt Law Q1] [2008-11-23 12:04:48] [3548296885df7a66ea8efc200c4aca50]
- RMP       [Univariate Explorative Data Analysis] [Seatbelt Law Q2] [2008-11-23 12:17:49] [3548296885df7a66ea8efc200c4aca50]
-           [Multiple Regression] [] [2008-11-29 13:28:42] [a4ee3bef49b119f4bd2e925060c84f5e]
-   P       [Multiple Regression] [] [2008-11-30 12:59:15] [4c8dfb519edec2da3492d7e6be9a5685]
-   P       [Multiple Regression] [] [2008-11-30 13:01:50] [4c8dfb519edec2da3492d7e6be9a5685]
Feedback Forum
2008-11-28 15:44:19 [Mehmet Yilmaz] [reply] 
De berekening en conclusie is correct.
2008-11-30 13:24:06 [Kristof Van Esbroeck] [reply] 
Student werkt correct met de Regression software om berekeningen te maken en een correcte conclusie te trekken.

In de oplossing gebruikt men de resultaten uit de berekeningen gemaakt met monthly dummies en met trend. Dit is de juiste werkwijze, toch kan een uitbreidende verklaring mbt andere berekeningswijzen nuttig zijn.

Wanneer we dezelfde, correcte, gegevens gebruiken echter met andere seizonale effecten en ander types of equation bekomen we andere resultaten:

-Zonder dummies en trend
http://www.freestatistics.org/blog/index.php?v=date/2008/Nov/30/t1228049996xq73c8osxw59pla.htm

Uit de vergelijking uit de vergelijking x[t] = + 1717.75147928994 -396.055827116028y[t] + e[t] kan worden opgemaakt dat vanaf de dummie variabele 1 wordt, het aantal slachtoffers met 396 daalt. Maw het dragen van de gordel heeft een duidelijk effect op het aantal slachtoffers. Zonder gordelplicht noteren we 1717 slachtoffers.

Na het bekijken van de ordinary least squares kunnen dezelfde conclusies getrokken worden. De parameters geven respectievelijk de resultaten weer igv het niet dragen van de gordel en vervolgens het effect bij het wel dragen van de gordel. Dus wanneer eerst D=0 en vervolgens D=1.

De p waarde is relatief klein en bijgevolg kan de nulhypothese verworpen worden.

Wanneer we het density plot bekijken concluderen we een zeer schuine verdeling, de autocorrelatiefunctie geeft dan weer de seizonaliteit weer.


-Met dummies en zonder trend
http://www.freestatistics.org/blog/index.php?v=date/2008/Nov/30/t12280501481p7kwpfnevb3xlh.htm

De variabelen M1 tot M11 die we in de Ordinary Least Squares tabel waarnemen verwijzen, zoals de student correct aangeeft, naar de verschillende maanden. December is de referentiemaand. Deze is de minst veilige maand aangezien we elke andere maand een negatieve parameter kunnen vaststellen.

Er is nog steeds een lichte scheefheid waarneembaar maar de seizonaliteit is verdwenen. De autocorrelatiefunctie is dus duidelijk gevoelig aan de wijziging van de invoergegevens.


Student trok, zoals aangegeven, de juiste conclusie door te werken met dummies en met trend. Ook de conclusie is correct. Per maand noteren we 226 minder slachtoffers na invoering van de gordelverplichting.
2008-11-30 13:32:15 [Kristof Van Esbroeck] [reply] 
Mbt tot Q2 toetst student correct de gegevens aan de 4 assumpties:

-geen autocorrelatie zijn
-vaste verdeling
-constant gemiddelde
-eenzelfde spreiding

Vervolgens wordt een correct besluit getrokken, nl dat de het model niet aan de voorwaarden voldoet.

Er kan als aanvulling ook naar r squared waarde gekeken worden. Deze lezen we af in de Regression Statistics tabel en is gelijk aan 0.741876348185605.
Bijgevolg kan er geconcludeerd worden dat 74,18% van de voorspellingen de werkelijkheid zullen benaderen.

Grafisch kan de Actuals and Interpolation - grafiek ook inzicht brengen. De punten geven de voorspellingen weer, de heeft betrekking op de werkelijke waarnemingen.
2008-12-01 10:49:52 [Hidde Van Kerckhoven] [reply] 
De student heeft de opgave correct uitgevoerd, zo werkte hij met een berekening zonder dummies en trend... En werkte hij met een berekening met dummies en trend... Als we naar de R squared zien, zien we dat deze hoger is wanneer we dummies en een trend invoeren... Zo zien we dat het aantal slachtoffers gemiddeld daald met 226 per maand, dit met een foutenmarge van 41 slachtoffers, wanneer de gordelwet is ingevoerd

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 6 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24938&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24938&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24938&T=0

As an alternative you can also use a QR Code:  
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 time6 seconds
R Server'George Udny Yule' @ 72.249.76.132






Multiple Linear Regression - Estimated Regression Equation
Slachtoffer/maand[t] = + 2324.06337310277 -226.385033602657Dumivariabele[t] -451.374973256309M1[t] -635.461053323771M2[t] -583.133697991392M3[t] -694.556342659014M4[t] -555.478987326639M5[t] -609.464131994259M6[t] -532.074276661885M7[t] -515.434421329508M8[t] -460.85706599713M9[t] -319.717210664754M10[t] -118.389855332377M11[t] -1.76485533237686t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Slachtoffer/maand[t] =  +  2324.06337310277 -226.385033602657Dumivariabele[t] -451.374973256309M1[t] -635.461053323771M2[t] -583.133697991392M3[t] -694.556342659014M4[t] -555.478987326639M5[t] -609.464131994259M6[t] -532.074276661885M7[t] -515.434421329508M8[t] -460.85706599713M9[t] -319.717210664754M10[t] -118.389855332377M11[t] -1.76485533237686t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24938&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Slachtoffer/maand[t] =  +  2324.06337310277 -226.385033602657Dumivariabele[t] -451.374973256309M1[t] -635.461053323771M2[t] -583.133697991392M3[t] -694.556342659014M4[t] -555.478987326639M5[t] -609.464131994259M6[t] -532.074276661885M7[t] -515.434421329508M8[t] -460.85706599713M9[t] -319.717210664754M10[t] -118.389855332377M11[t] -1.76485533237686t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24938&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24938&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Estimated Regression Equation
Slachtoffer/maand[t] = + 2324.06337310277 -226.385033602657Dumivariabele[t] -451.374973256309M1[t] -635.461053323771M2[t] -583.133697991392M3[t] -694.556342659014M4[t] -555.478987326639M5[t] -609.464131994259M6[t] -532.074276661885M7[t] -515.434421329508M8[t] -460.85706599713M9[t] -319.717210664754M10[t] -118.389855332377M11[t] -1.76485533237686t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)2324.0633731027744.02993952.783700
Dumivariabele-226.38503360265741.037226-5.516600
M1-451.37497325630953.942919-8.367600
M2-635.46105332377153.941479-11.780600
M3-583.13369799139253.931287-10.812500
M4-694.55634265901453.922166-12.880700
M5-555.47898732663953.914117-10.30300
M6-609.46413199425953.907141-11.305800
M7-532.07427666188553.901237-9.871300
M8-515.43442132950853.896405-9.563400
M9-460.8570659971353.892648-8.551400
M10-319.71721066475453.889963-5.932800
M11-118.38985533237753.888353-2.19690.0293160.014658
t-1.764855332376860.240551-7.336700

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 2324.06337310277 & 44.029939 & 52.7837 & 0 & 0 \tabularnewline
Dumivariabele & -226.385033602657 & 41.037226 & -5.5166 & 0 & 0 \tabularnewline
M1 & -451.374973256309 & 53.942919 & -8.3676 & 0 & 0 \tabularnewline
M2 & -635.461053323771 & 53.941479 & -11.7806 & 0 & 0 \tabularnewline
M3 & -583.133697991392 & 53.931287 & -10.8125 & 0 & 0 \tabularnewline
M4 & -694.556342659014 & 53.922166 & -12.8807 & 0 & 0 \tabularnewline
M5 & -555.478987326639 & 53.914117 & -10.303 & 0 & 0 \tabularnewline
M6 & -609.464131994259 & 53.907141 & -11.3058 & 0 & 0 \tabularnewline
M7 & -532.074276661885 & 53.901237 & -9.8713 & 0 & 0 \tabularnewline
M8 & -515.434421329508 & 53.896405 & -9.5634 & 0 & 0 \tabularnewline
M9 & -460.85706599713 & 53.892648 & -8.5514 & 0 & 0 \tabularnewline
M10 & -319.717210664754 & 53.889963 & -5.9328 & 0 & 0 \tabularnewline
M11 & -118.389855332377 & 53.888353 & -2.1969 & 0.029316 & 0.014658 \tabularnewline
t & -1.76485533237686 & 0.240551 & -7.3367 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24938&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]2324.06337310277[/C][C]44.029939[/C][C]52.7837[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Dumivariabele[/C][C]-226.385033602657[/C][C]41.037226[/C][C]-5.5166[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-451.374973256309[/C][C]53.942919[/C][C]-8.3676[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M2[/C][C]-635.461053323771[/C][C]53.941479[/C][C]-11.7806[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M3[/C][C]-583.133697991392[/C][C]53.931287[/C][C]-10.8125[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M4[/C][C]-694.556342659014[/C][C]53.922166[/C][C]-12.8807[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M5[/C][C]-555.478987326639[/C][C]53.914117[/C][C]-10.303[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M6[/C][C]-609.464131994259[/C][C]53.907141[/C][C]-11.3058[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M7[/C][C]-532.074276661885[/C][C]53.901237[/C][C]-9.8713[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M8[/C][C]-515.434421329508[/C][C]53.896405[/C][C]-9.5634[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M9[/C][C]-460.85706599713[/C][C]53.892648[/C][C]-8.5514[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M10[/C][C]-319.717210664754[/C][C]53.889963[/C][C]-5.9328[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M11[/C][C]-118.389855332377[/C][C]53.888353[/C][C]-2.1969[/C][C]0.029316[/C][C]0.014658[/C][/ROW]
[ROW][C]t[/C][C]-1.76485533237686[/C][C]0.240551[/C][C]-7.3367[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24938&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24938&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)2324.0633731027744.02993952.783700
Dumivariabele-226.38503360265741.037226-5.516600
M1-451.37497325630953.942919-8.367600
M2-635.46105332377153.941479-11.780600
M3-583.13369799139253.931287-10.812500
M4-694.55634265901453.922166-12.880700
M5-555.47898732663953.914117-10.30300
M6-609.46413199425953.907141-11.305800
M7-532.07427666188553.901237-9.871300
M8-515.43442132950853.896405-9.563400
M9-460.8570659971353.892648-8.551400
M10-319.71721066475453.889963-5.932800
M11-118.38985533237753.888353-2.19690.0293160.014658
t-1.764855332376860.240551-7.336700






Multiple Linear Regression - Regression Statistics
Multiple R0.861322441473346
R-squared0.741876348185605
Adjusted R-squared0.723024620805902
F-TEST (value)39.3532291891914
F-TEST (DF numerator)13
F-TEST (DF denominator)178
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation152.417759557721
Sum Squared Residuals4135148.87028996

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.861322441473346 \tabularnewline
R-squared & 0.741876348185605 \tabularnewline
Adjusted R-squared & 0.723024620805902 \tabularnewline
F-TEST (value) & 39.3532291891914 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 178 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 152.417759557721 \tabularnewline
Sum Squared Residuals & 4135148.87028996 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24938&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.861322441473346[/C][/ROW]
[ROW][C]R-squared[/C][C]0.741876348185605[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.723024620805902[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]39.3532291891914[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]178[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]152.417759557721[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]4135148.87028996[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24938&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24938&T=3

As an alternative you can also use a QR Code:  
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The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Regression Statistics
Multiple R0.861322441473346
R-squared0.741876348185605
Adjusted R-squared0.723024620805902
F-TEST (value)39.3532291891914
F-TEST (DF numerator)13
F-TEST (DF denominator)178
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation152.417759557721
Sum Squared Residuals4135148.87028996






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
116871870.92354451406-183.923544514060
215081685.07260911425-177.072609114252
315071735.63510911425-228.635109114254
413851622.44760911424-237.447609114242
516321759.76010911425-127.760109114251
615111704.01010911425-193.010109114250
715591779.63510911425-220.635109114248
816301794.51010911426-164.510109114256
915791847.32260911425-268.322609114246
1016531986.69760911425-333.697609114249
1121522186.26010911425-34.2601091142503
1221482302.88510911425-154.885109114249
1317521849.74528052556-97.7452805255622
1417651663.89434512573101.105654874272
1517171714.456845125732.54315487427317
1615581601.26934512573-43.2693451257275
1715751738.58184512573-163.581845125727
1815201682.83184512573-162.831845125727
1918051758.4568451257346.5431548742728
2018001773.3318451257326.6681548742733
2117191826.14434512573-107.144345125727
2220081965.5193451257342.4806548742729
2322422165.0818451257376.918154874273
2424782281.70684512573196.293154874273
2520301828.56701653704201.43298346296
2616551642.7160811372012.2839188627955
2716931693.27858113720-0.278581137204542
2816231580.0910811372142.9089188627948
2918051717.4035811372087.5964188627952
3017461661.6535811372084.3464188627952
3117951737.2785811372157.721418862795
3219261752.15358113720173.846418862796
3316191804.96608113721-185.966081137205
3419921944.3410811372047.6589188627952
3522332143.9035811372089.0964188627953
3621922260.52858113721-68.5285811372049
3720801807.38875254852272.611247451482
3817681621.53781714868146.462182851318
3918351672.10031714868162.899682851318
4015691558.9128171486810.0871828513171
4119761696.22531714868279.774682851318
4218531640.47531714868212.524682851317
4319651716.10031714868248.899682851317
4416891730.97531714868-41.9753171486821
4517781783.78781714868-5.78781714868267
4619761923.1628171486852.8371828513174
4723972122.72531714868274.274682851318
4826542239.35031714868414.649682851317
4920971786.21048856000310.789511440004
5019631600.35955316016362.64044683984
5116771650.9220531601626.0779468398400
5219411537.73455316016403.265446839839
5320031675.04705316016327.95294683984
5418131619.29705316016193.702946839840
5520121694.92205316016317.07794683984
5619121709.79705316016202.20294683984
5720841762.60955316016321.39044683984
5820801901.98455316016178.015446839840
5921182101.5470531601616.4529468398398
6021502218.17205316016-68.1720531601603
6116081765.03222457147-157.032224571473
6215031579.18128917164-76.1812891716376
6315481629.74378917164-81.7437891716377
6413821516.55628917164-134.556289171638
6517311653.8687891716477.1312108283621
6617981598.11878917164199.881210828362
6717791673.74378917164105.256210828362
6818871688.61878917164198.381210828362
6920041741.43128917164262.568710828362
7020771880.80628917164196.193710828362
7120922080.3687891716411.6312108283621
7220512196.99378917164-145.993789171638
7315771743.85396058295-166.853960582951
7413561558.00302518312-202.003025183115
7516521608.5655251831243.4344748168846
7613821495.37802518312-113.378025183116
7715191632.69052518312-113.690525183116
7814211576.94052518312-155.940525183116
7914421652.56552518312-210.565525183116
8015431667.44052518312-124.440525183115
8116561720.25302518312-64.2530251831158
8215611859.62802518312-298.628025183116
8319052059.19052518312-154.190525183116
8421992175.8155251831223.1844748168843
8514731722.67569659443-249.675696594429
8616551536.82476119459118.175238805407
8714071587.38726119459-180.387261194593
8813951474.19976119459-79.1997611945937
8915301611.51226119459-81.5122611945933
9013091555.76226119459-246.762261194593
9115261631.38726119459-105.387261194593
9213271646.26226119459-319.262261194593
9316271699.07476119459-72.0747611945935
9417481838.44976119459-90.4497611945934
9519582038.01226119459-80.0122611945933
9622742154.63726119459119.362738805407
9716481701.49743260591-53.4974326059064
9814011515.64649720607-114.646497206071
9914111566.20899720607-155.208997206071
10014031453.02149720607-50.0214972060714
10113941590.33399720607-196.333997206071
10215201534.58399720607-14.5839972060711
10315281610.20899720607-82.2089972060712
10416431625.0839972060717.9160027939294
10515151677.89649720607-162.896497206071
10616851817.27149720607-132.271497206071
10720002016.83399720607-16.8339972060710
10822152133.4589972060781.5410027939288
10919561680.31916861738275.680831382616
11014621494.46823321755-32.4682332175485
11115631545.0307332175517.9692667824515
11214591431.8432332175527.1567667824508
11314461569.15573321755-123.155733217549
11416221513.40573321755108.594266782451
11516571589.0307332175567.9692667824511
11616381603.9057332175534.0942667824517
11716431656.71823321755-13.7182332175489
11816831796.09323321755-113.093233217549
11920501995.6557332175554.3442667824512
12022622112.28073321755149.719266782451
12118131659.14090462886153.859095371138
12214451473.28996922903-28.2899692290262
12317621523.85246922903238.147530770974
12414611410.6649692290350.3350307709731
12515561547.977469229038.02253077097358
12614311492.22746922903-61.2274692290265
12714271567.85246922903-140.852469229027
12815541582.72746922903-28.7274692290261
12916451635.539969229039.46003077097336
13016531774.91496922903-121.914969229026
13120161974.4774692290341.5225307709736
13222072091.10246922903115.897530770973
13316651637.9626406403427.0373593596605
13413611452.11170524050-91.111705240504
13515061502.674205240503.32579475949605
13613601389.48670524050-29.4867052405046
13714531526.79920524050-73.7992052405041
13815221471.0492052405050.9507947594957
13914601546.67420524050-86.6742052405044
14015521561.54920524050-9.54920524050376
14115481614.36170524050-66.3617052405043
14218271753.7367052405073.2632947594957
14317371953.29920524050-216.299205240504
14419412069.92420524050-128.924205240504
14514741616.78437665182-142.784376651817
14614581430.9334412519827.0665587480184
14715421481.4959412519860.5040587480183
14814041368.3084412519835.6915587480177
14915221505.6209412519816.3790587480182
15013851449.87094125198-64.870941251982
15116411525.49594125198115.504058748018
15215101540.37094125198-30.3709412519815
15316811593.1834412519887.816558748018
15419381732.55844125198205.441558748018
15518681932.12094125198-64.1209412519819
15617262048.74594125198-322.745941251982
15714561595.60611266329-139.606112663295
15814451409.7551772634635.2448227365406
15914561460.31767726346-4.31767726345942
16013651347.1301772634617.8698227365400
16114871484.442677263462.55732273654045
16215581428.69267726346129.307322736540
16314881504.31767726346-16.3176772634598
16416841519.19267726346164.807322736541
16515941572.0051772634621.9948227365402
16618501711.38017726346138.619822736540
16719981910.9426772634687.0573227365404
16820792027.5676772634651.4323227365403
16914941574.42784867477-80.4278486747727
17010571162.19187967228-105.191879672279
17112181212.754379672285.24562032772056
17211681099.5668796722868.4331203277199
17312361236.87937967228-0.879379672279542
17410761181.12937967228-105.129379672280
17511741256.75437967228-82.7543796722797
17611391271.62937967228-132.629379672279
17714271324.44187967228102.558120327720
17814871463.8168796722823.1831203277203
17914831663.37937967228-180.379379672280
18015131780.00437967228-267.00437967228
18113571326.8645510835930.1354489164073
18211651141.0136156837623.986384316243
18312821191.5761156837690.4238843162428
18411101078.3886156837631.6113843162422
18512971215.7011156837681.2988843162427
18611851159.9511156837625.0488843162426
18712221235.57611568376-13.5761156837575
18812841250.4511156837633.548884316243
18914441303.26361568376140.736384316242
19015751442.63861568376132.361384316243
19117371642.2011156837694.7988843162427
19217631758.826115683764.17388431624253

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1687 & 1870.92354451406 & -183.923544514060 \tabularnewline
2 & 1508 & 1685.07260911425 & -177.072609114252 \tabularnewline
3 & 1507 & 1735.63510911425 & -228.635109114254 \tabularnewline
4 & 1385 & 1622.44760911424 & -237.447609114242 \tabularnewline
5 & 1632 & 1759.76010911425 & -127.760109114251 \tabularnewline
6 & 1511 & 1704.01010911425 & -193.010109114250 \tabularnewline
7 & 1559 & 1779.63510911425 & -220.635109114248 \tabularnewline
8 & 1630 & 1794.51010911426 & -164.510109114256 \tabularnewline
9 & 1579 & 1847.32260911425 & -268.322609114246 \tabularnewline
10 & 1653 & 1986.69760911425 & -333.697609114249 \tabularnewline
11 & 2152 & 2186.26010911425 & -34.2601091142503 \tabularnewline
12 & 2148 & 2302.88510911425 & -154.885109114249 \tabularnewline
13 & 1752 & 1849.74528052556 & -97.7452805255622 \tabularnewline
14 & 1765 & 1663.89434512573 & 101.105654874272 \tabularnewline
15 & 1717 & 1714.45684512573 & 2.54315487427317 \tabularnewline
16 & 1558 & 1601.26934512573 & -43.2693451257275 \tabularnewline
17 & 1575 & 1738.58184512573 & -163.581845125727 \tabularnewline
18 & 1520 & 1682.83184512573 & -162.831845125727 \tabularnewline
19 & 1805 & 1758.45684512573 & 46.5431548742728 \tabularnewline
20 & 1800 & 1773.33184512573 & 26.6681548742733 \tabularnewline
21 & 1719 & 1826.14434512573 & -107.144345125727 \tabularnewline
22 & 2008 & 1965.51934512573 & 42.4806548742729 \tabularnewline
23 & 2242 & 2165.08184512573 & 76.918154874273 \tabularnewline
24 & 2478 & 2281.70684512573 & 196.293154874273 \tabularnewline
25 & 2030 & 1828.56701653704 & 201.43298346296 \tabularnewline
26 & 1655 & 1642.71608113720 & 12.2839188627955 \tabularnewline
27 & 1693 & 1693.27858113720 & -0.278581137204542 \tabularnewline
28 & 1623 & 1580.09108113721 & 42.9089188627948 \tabularnewline
29 & 1805 & 1717.40358113720 & 87.5964188627952 \tabularnewline
30 & 1746 & 1661.65358113720 & 84.3464188627952 \tabularnewline
31 & 1795 & 1737.27858113721 & 57.721418862795 \tabularnewline
32 & 1926 & 1752.15358113720 & 173.846418862796 \tabularnewline
33 & 1619 & 1804.96608113721 & -185.966081137205 \tabularnewline
34 & 1992 & 1944.34108113720 & 47.6589188627952 \tabularnewline
35 & 2233 & 2143.90358113720 & 89.0964188627953 \tabularnewline
36 & 2192 & 2260.52858113721 & -68.5285811372049 \tabularnewline
37 & 2080 & 1807.38875254852 & 272.611247451482 \tabularnewline
38 & 1768 & 1621.53781714868 & 146.462182851318 \tabularnewline
39 & 1835 & 1672.10031714868 & 162.899682851318 \tabularnewline
40 & 1569 & 1558.91281714868 & 10.0871828513171 \tabularnewline
41 & 1976 & 1696.22531714868 & 279.774682851318 \tabularnewline
42 & 1853 & 1640.47531714868 & 212.524682851317 \tabularnewline
43 & 1965 & 1716.10031714868 & 248.899682851317 \tabularnewline
44 & 1689 & 1730.97531714868 & -41.9753171486821 \tabularnewline
45 & 1778 & 1783.78781714868 & -5.78781714868267 \tabularnewline
46 & 1976 & 1923.16281714868 & 52.8371828513174 \tabularnewline
47 & 2397 & 2122.72531714868 & 274.274682851318 \tabularnewline
48 & 2654 & 2239.35031714868 & 414.649682851317 \tabularnewline
49 & 2097 & 1786.21048856000 & 310.789511440004 \tabularnewline
50 & 1963 & 1600.35955316016 & 362.64044683984 \tabularnewline
51 & 1677 & 1650.92205316016 & 26.0779468398400 \tabularnewline
52 & 1941 & 1537.73455316016 & 403.265446839839 \tabularnewline
53 & 2003 & 1675.04705316016 & 327.95294683984 \tabularnewline
54 & 1813 & 1619.29705316016 & 193.702946839840 \tabularnewline
55 & 2012 & 1694.92205316016 & 317.07794683984 \tabularnewline
56 & 1912 & 1709.79705316016 & 202.20294683984 \tabularnewline
57 & 2084 & 1762.60955316016 & 321.39044683984 \tabularnewline
58 & 2080 & 1901.98455316016 & 178.015446839840 \tabularnewline
59 & 2118 & 2101.54705316016 & 16.4529468398398 \tabularnewline
60 & 2150 & 2218.17205316016 & -68.1720531601603 \tabularnewline
61 & 1608 & 1765.03222457147 & -157.032224571473 \tabularnewline
62 & 1503 & 1579.18128917164 & -76.1812891716376 \tabularnewline
63 & 1548 & 1629.74378917164 & -81.7437891716377 \tabularnewline
64 & 1382 & 1516.55628917164 & -134.556289171638 \tabularnewline
65 & 1731 & 1653.86878917164 & 77.1312108283621 \tabularnewline
66 & 1798 & 1598.11878917164 & 199.881210828362 \tabularnewline
67 & 1779 & 1673.74378917164 & 105.256210828362 \tabularnewline
68 & 1887 & 1688.61878917164 & 198.381210828362 \tabularnewline
69 & 2004 & 1741.43128917164 & 262.568710828362 \tabularnewline
70 & 2077 & 1880.80628917164 & 196.193710828362 \tabularnewline
71 & 2092 & 2080.36878917164 & 11.6312108283621 \tabularnewline
72 & 2051 & 2196.99378917164 & -145.993789171638 \tabularnewline
73 & 1577 & 1743.85396058295 & -166.853960582951 \tabularnewline
74 & 1356 & 1558.00302518312 & -202.003025183115 \tabularnewline
75 & 1652 & 1608.56552518312 & 43.4344748168846 \tabularnewline
76 & 1382 & 1495.37802518312 & -113.378025183116 \tabularnewline
77 & 1519 & 1632.69052518312 & -113.690525183116 \tabularnewline
78 & 1421 & 1576.94052518312 & -155.940525183116 \tabularnewline
79 & 1442 & 1652.56552518312 & -210.565525183116 \tabularnewline
80 & 1543 & 1667.44052518312 & -124.440525183115 \tabularnewline
81 & 1656 & 1720.25302518312 & -64.2530251831158 \tabularnewline
82 & 1561 & 1859.62802518312 & -298.628025183116 \tabularnewline
83 & 1905 & 2059.19052518312 & -154.190525183116 \tabularnewline
84 & 2199 & 2175.81552518312 & 23.1844748168843 \tabularnewline
85 & 1473 & 1722.67569659443 & -249.675696594429 \tabularnewline
86 & 1655 & 1536.82476119459 & 118.175238805407 \tabularnewline
87 & 1407 & 1587.38726119459 & -180.387261194593 \tabularnewline
88 & 1395 & 1474.19976119459 & -79.1997611945937 \tabularnewline
89 & 1530 & 1611.51226119459 & -81.5122611945933 \tabularnewline
90 & 1309 & 1555.76226119459 & -246.762261194593 \tabularnewline
91 & 1526 & 1631.38726119459 & -105.387261194593 \tabularnewline
92 & 1327 & 1646.26226119459 & -319.262261194593 \tabularnewline
93 & 1627 & 1699.07476119459 & -72.0747611945935 \tabularnewline
94 & 1748 & 1838.44976119459 & -90.4497611945934 \tabularnewline
95 & 1958 & 2038.01226119459 & -80.0122611945933 \tabularnewline
96 & 2274 & 2154.63726119459 & 119.362738805407 \tabularnewline
97 & 1648 & 1701.49743260591 & -53.4974326059064 \tabularnewline
98 & 1401 & 1515.64649720607 & -114.646497206071 \tabularnewline
99 & 1411 & 1566.20899720607 & -155.208997206071 \tabularnewline
100 & 1403 & 1453.02149720607 & -50.0214972060714 \tabularnewline
101 & 1394 & 1590.33399720607 & -196.333997206071 \tabularnewline
102 & 1520 & 1534.58399720607 & -14.5839972060711 \tabularnewline
103 & 1528 & 1610.20899720607 & -82.2089972060712 \tabularnewline
104 & 1643 & 1625.08399720607 & 17.9160027939294 \tabularnewline
105 & 1515 & 1677.89649720607 & -162.896497206071 \tabularnewline
106 & 1685 & 1817.27149720607 & -132.271497206071 \tabularnewline
107 & 2000 & 2016.83399720607 & -16.8339972060710 \tabularnewline
108 & 2215 & 2133.45899720607 & 81.5410027939288 \tabularnewline
109 & 1956 & 1680.31916861738 & 275.680831382616 \tabularnewline
110 & 1462 & 1494.46823321755 & -32.4682332175485 \tabularnewline
111 & 1563 & 1545.03073321755 & 17.9692667824515 \tabularnewline
112 & 1459 & 1431.84323321755 & 27.1567667824508 \tabularnewline
113 & 1446 & 1569.15573321755 & -123.155733217549 \tabularnewline
114 & 1622 & 1513.40573321755 & 108.594266782451 \tabularnewline
115 & 1657 & 1589.03073321755 & 67.9692667824511 \tabularnewline
116 & 1638 & 1603.90573321755 & 34.0942667824517 \tabularnewline
117 & 1643 & 1656.71823321755 & -13.7182332175489 \tabularnewline
118 & 1683 & 1796.09323321755 & -113.093233217549 \tabularnewline
119 & 2050 & 1995.65573321755 & 54.3442667824512 \tabularnewline
120 & 2262 & 2112.28073321755 & 149.719266782451 \tabularnewline
121 & 1813 & 1659.14090462886 & 153.859095371138 \tabularnewline
122 & 1445 & 1473.28996922903 & -28.2899692290262 \tabularnewline
123 & 1762 & 1523.85246922903 & 238.147530770974 \tabularnewline
124 & 1461 & 1410.66496922903 & 50.3350307709731 \tabularnewline
125 & 1556 & 1547.97746922903 & 8.02253077097358 \tabularnewline
126 & 1431 & 1492.22746922903 & -61.2274692290265 \tabularnewline
127 & 1427 & 1567.85246922903 & -140.852469229027 \tabularnewline
128 & 1554 & 1582.72746922903 & -28.7274692290261 \tabularnewline
129 & 1645 & 1635.53996922903 & 9.46003077097336 \tabularnewline
130 & 1653 & 1774.91496922903 & -121.914969229026 \tabularnewline
131 & 2016 & 1974.47746922903 & 41.5225307709736 \tabularnewline
132 & 2207 & 2091.10246922903 & 115.897530770973 \tabularnewline
133 & 1665 & 1637.96264064034 & 27.0373593596605 \tabularnewline
134 & 1361 & 1452.11170524050 & -91.111705240504 \tabularnewline
135 & 1506 & 1502.67420524050 & 3.32579475949605 \tabularnewline
136 & 1360 & 1389.48670524050 & -29.4867052405046 \tabularnewline
137 & 1453 & 1526.79920524050 & -73.7992052405041 \tabularnewline
138 & 1522 & 1471.04920524050 & 50.9507947594957 \tabularnewline
139 & 1460 & 1546.67420524050 & -86.6742052405044 \tabularnewline
140 & 1552 & 1561.54920524050 & -9.54920524050376 \tabularnewline
141 & 1548 & 1614.36170524050 & -66.3617052405043 \tabularnewline
142 & 1827 & 1753.73670524050 & 73.2632947594957 \tabularnewline
143 & 1737 & 1953.29920524050 & -216.299205240504 \tabularnewline
144 & 1941 & 2069.92420524050 & -128.924205240504 \tabularnewline
145 & 1474 & 1616.78437665182 & -142.784376651817 \tabularnewline
146 & 1458 & 1430.93344125198 & 27.0665587480184 \tabularnewline
147 & 1542 & 1481.49594125198 & 60.5040587480183 \tabularnewline
148 & 1404 & 1368.30844125198 & 35.6915587480177 \tabularnewline
149 & 1522 & 1505.62094125198 & 16.3790587480182 \tabularnewline
150 & 1385 & 1449.87094125198 & -64.870941251982 \tabularnewline
151 & 1641 & 1525.49594125198 & 115.504058748018 \tabularnewline
152 & 1510 & 1540.37094125198 & -30.3709412519815 \tabularnewline
153 & 1681 & 1593.18344125198 & 87.816558748018 \tabularnewline
154 & 1938 & 1732.55844125198 & 205.441558748018 \tabularnewline
155 & 1868 & 1932.12094125198 & -64.1209412519819 \tabularnewline
156 & 1726 & 2048.74594125198 & -322.745941251982 \tabularnewline
157 & 1456 & 1595.60611266329 & -139.606112663295 \tabularnewline
158 & 1445 & 1409.75517726346 & 35.2448227365406 \tabularnewline
159 & 1456 & 1460.31767726346 & -4.31767726345942 \tabularnewline
160 & 1365 & 1347.13017726346 & 17.8698227365400 \tabularnewline
161 & 1487 & 1484.44267726346 & 2.55732273654045 \tabularnewline
162 & 1558 & 1428.69267726346 & 129.307322736540 \tabularnewline
163 & 1488 & 1504.31767726346 & -16.3176772634598 \tabularnewline
164 & 1684 & 1519.19267726346 & 164.807322736541 \tabularnewline
165 & 1594 & 1572.00517726346 & 21.9948227365402 \tabularnewline
166 & 1850 & 1711.38017726346 & 138.619822736540 \tabularnewline
167 & 1998 & 1910.94267726346 & 87.0573227365404 \tabularnewline
168 & 2079 & 2027.56767726346 & 51.4323227365403 \tabularnewline
169 & 1494 & 1574.42784867477 & -80.4278486747727 \tabularnewline
170 & 1057 & 1162.19187967228 & -105.191879672279 \tabularnewline
171 & 1218 & 1212.75437967228 & 5.24562032772056 \tabularnewline
172 & 1168 & 1099.56687967228 & 68.4331203277199 \tabularnewline
173 & 1236 & 1236.87937967228 & -0.879379672279542 \tabularnewline
174 & 1076 & 1181.12937967228 & -105.129379672280 \tabularnewline
175 & 1174 & 1256.75437967228 & -82.7543796722797 \tabularnewline
176 & 1139 & 1271.62937967228 & -132.629379672279 \tabularnewline
177 & 1427 & 1324.44187967228 & 102.558120327720 \tabularnewline
178 & 1487 & 1463.81687967228 & 23.1831203277203 \tabularnewline
179 & 1483 & 1663.37937967228 & -180.379379672280 \tabularnewline
180 & 1513 & 1780.00437967228 & -267.00437967228 \tabularnewline
181 & 1357 & 1326.86455108359 & 30.1354489164073 \tabularnewline
182 & 1165 & 1141.01361568376 & 23.986384316243 \tabularnewline
183 & 1282 & 1191.57611568376 & 90.4238843162428 \tabularnewline
184 & 1110 & 1078.38861568376 & 31.6113843162422 \tabularnewline
185 & 1297 & 1215.70111568376 & 81.2988843162427 \tabularnewline
186 & 1185 & 1159.95111568376 & 25.0488843162426 \tabularnewline
187 & 1222 & 1235.57611568376 & -13.5761156837575 \tabularnewline
188 & 1284 & 1250.45111568376 & 33.548884316243 \tabularnewline
189 & 1444 & 1303.26361568376 & 140.736384316242 \tabularnewline
190 & 1575 & 1442.63861568376 & 132.361384316243 \tabularnewline
191 & 1737 & 1642.20111568376 & 94.7988843162427 \tabularnewline
192 & 1763 & 1758.82611568376 & 4.17388431624253 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24938&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]1687[/C][C]1870.92354451406[/C][C]-183.923544514060[/C][/ROW]
[ROW][C]2[/C][C]1508[/C][C]1685.07260911425[/C][C]-177.072609114252[/C][/ROW]
[ROW][C]3[/C][C]1507[/C][C]1735.63510911425[/C][C]-228.635109114254[/C][/ROW]
[ROW][C]4[/C][C]1385[/C][C]1622.44760911424[/C][C]-237.447609114242[/C][/ROW]
[ROW][C]5[/C][C]1632[/C][C]1759.76010911425[/C][C]-127.760109114251[/C][/ROW]
[ROW][C]6[/C][C]1511[/C][C]1704.01010911425[/C][C]-193.010109114250[/C][/ROW]
[ROW][C]7[/C][C]1559[/C][C]1779.63510911425[/C][C]-220.635109114248[/C][/ROW]
[ROW][C]8[/C][C]1630[/C][C]1794.51010911426[/C][C]-164.510109114256[/C][/ROW]
[ROW][C]9[/C][C]1579[/C][C]1847.32260911425[/C][C]-268.322609114246[/C][/ROW]
[ROW][C]10[/C][C]1653[/C][C]1986.69760911425[/C][C]-333.697609114249[/C][/ROW]
[ROW][C]11[/C][C]2152[/C][C]2186.26010911425[/C][C]-34.2601091142503[/C][/ROW]
[ROW][C]12[/C][C]2148[/C][C]2302.88510911425[/C][C]-154.885109114249[/C][/ROW]
[ROW][C]13[/C][C]1752[/C][C]1849.74528052556[/C][C]-97.7452805255622[/C][/ROW]
[ROW][C]14[/C][C]1765[/C][C]1663.89434512573[/C][C]101.105654874272[/C][/ROW]
[ROW][C]15[/C][C]1717[/C][C]1714.45684512573[/C][C]2.54315487427317[/C][/ROW]
[ROW][C]16[/C][C]1558[/C][C]1601.26934512573[/C][C]-43.2693451257275[/C][/ROW]
[ROW][C]17[/C][C]1575[/C][C]1738.58184512573[/C][C]-163.581845125727[/C][/ROW]
[ROW][C]18[/C][C]1520[/C][C]1682.83184512573[/C][C]-162.831845125727[/C][/ROW]
[ROW][C]19[/C][C]1805[/C][C]1758.45684512573[/C][C]46.5431548742728[/C][/ROW]
[ROW][C]20[/C][C]1800[/C][C]1773.33184512573[/C][C]26.6681548742733[/C][/ROW]
[ROW][C]21[/C][C]1719[/C][C]1826.14434512573[/C][C]-107.144345125727[/C][/ROW]
[ROW][C]22[/C][C]2008[/C][C]1965.51934512573[/C][C]42.4806548742729[/C][/ROW]
[ROW][C]23[/C][C]2242[/C][C]2165.08184512573[/C][C]76.918154874273[/C][/ROW]
[ROW][C]24[/C][C]2478[/C][C]2281.70684512573[/C][C]196.293154874273[/C][/ROW]
[ROW][C]25[/C][C]2030[/C][C]1828.56701653704[/C][C]201.43298346296[/C][/ROW]
[ROW][C]26[/C][C]1655[/C][C]1642.71608113720[/C][C]12.2839188627955[/C][/ROW]
[ROW][C]27[/C][C]1693[/C][C]1693.27858113720[/C][C]-0.278581137204542[/C][/ROW]
[ROW][C]28[/C][C]1623[/C][C]1580.09108113721[/C][C]42.9089188627948[/C][/ROW]
[ROW][C]29[/C][C]1805[/C][C]1717.40358113720[/C][C]87.5964188627952[/C][/ROW]
[ROW][C]30[/C][C]1746[/C][C]1661.65358113720[/C][C]84.3464188627952[/C][/ROW]
[ROW][C]31[/C][C]1795[/C][C]1737.27858113721[/C][C]57.721418862795[/C][/ROW]
[ROW][C]32[/C][C]1926[/C][C]1752.15358113720[/C][C]173.846418862796[/C][/ROW]
[ROW][C]33[/C][C]1619[/C][C]1804.96608113721[/C][C]-185.966081137205[/C][/ROW]
[ROW][C]34[/C][C]1992[/C][C]1944.34108113720[/C][C]47.6589188627952[/C][/ROW]
[ROW][C]35[/C][C]2233[/C][C]2143.90358113720[/C][C]89.0964188627953[/C][/ROW]
[ROW][C]36[/C][C]2192[/C][C]2260.52858113721[/C][C]-68.5285811372049[/C][/ROW]
[ROW][C]37[/C][C]2080[/C][C]1807.38875254852[/C][C]272.611247451482[/C][/ROW]
[ROW][C]38[/C][C]1768[/C][C]1621.53781714868[/C][C]146.462182851318[/C][/ROW]
[ROW][C]39[/C][C]1835[/C][C]1672.10031714868[/C][C]162.899682851318[/C][/ROW]
[ROW][C]40[/C][C]1569[/C][C]1558.91281714868[/C][C]10.0871828513171[/C][/ROW]
[ROW][C]41[/C][C]1976[/C][C]1696.22531714868[/C][C]279.774682851318[/C][/ROW]
[ROW][C]42[/C][C]1853[/C][C]1640.47531714868[/C][C]212.524682851317[/C][/ROW]
[ROW][C]43[/C][C]1965[/C][C]1716.10031714868[/C][C]248.899682851317[/C][/ROW]
[ROW][C]44[/C][C]1689[/C][C]1730.97531714868[/C][C]-41.9753171486821[/C][/ROW]
[ROW][C]45[/C][C]1778[/C][C]1783.78781714868[/C][C]-5.78781714868267[/C][/ROW]
[ROW][C]46[/C][C]1976[/C][C]1923.16281714868[/C][C]52.8371828513174[/C][/ROW]
[ROW][C]47[/C][C]2397[/C][C]2122.72531714868[/C][C]274.274682851318[/C][/ROW]
[ROW][C]48[/C][C]2654[/C][C]2239.35031714868[/C][C]414.649682851317[/C][/ROW]
[ROW][C]49[/C][C]2097[/C][C]1786.21048856000[/C][C]310.789511440004[/C][/ROW]
[ROW][C]50[/C][C]1963[/C][C]1600.35955316016[/C][C]362.64044683984[/C][/ROW]
[ROW][C]51[/C][C]1677[/C][C]1650.92205316016[/C][C]26.0779468398400[/C][/ROW]
[ROW][C]52[/C][C]1941[/C][C]1537.73455316016[/C][C]403.265446839839[/C][/ROW]
[ROW][C]53[/C][C]2003[/C][C]1675.04705316016[/C][C]327.95294683984[/C][/ROW]
[ROW][C]54[/C][C]1813[/C][C]1619.29705316016[/C][C]193.702946839840[/C][/ROW]
[ROW][C]55[/C][C]2012[/C][C]1694.92205316016[/C][C]317.07794683984[/C][/ROW]
[ROW][C]56[/C][C]1912[/C][C]1709.79705316016[/C][C]202.20294683984[/C][/ROW]
[ROW][C]57[/C][C]2084[/C][C]1762.60955316016[/C][C]321.39044683984[/C][/ROW]
[ROW][C]58[/C][C]2080[/C][C]1901.98455316016[/C][C]178.015446839840[/C][/ROW]
[ROW][C]59[/C][C]2118[/C][C]2101.54705316016[/C][C]16.4529468398398[/C][/ROW]
[ROW][C]60[/C][C]2150[/C][C]2218.17205316016[/C][C]-68.1720531601603[/C][/ROW]
[ROW][C]61[/C][C]1608[/C][C]1765.03222457147[/C][C]-157.032224571473[/C][/ROW]
[ROW][C]62[/C][C]1503[/C][C]1579.18128917164[/C][C]-76.1812891716376[/C][/ROW]
[ROW][C]63[/C][C]1548[/C][C]1629.74378917164[/C][C]-81.7437891716377[/C][/ROW]
[ROW][C]64[/C][C]1382[/C][C]1516.55628917164[/C][C]-134.556289171638[/C][/ROW]
[ROW][C]65[/C][C]1731[/C][C]1653.86878917164[/C][C]77.1312108283621[/C][/ROW]
[ROW][C]66[/C][C]1798[/C][C]1598.11878917164[/C][C]199.881210828362[/C][/ROW]
[ROW][C]67[/C][C]1779[/C][C]1673.74378917164[/C][C]105.256210828362[/C][/ROW]
[ROW][C]68[/C][C]1887[/C][C]1688.61878917164[/C][C]198.381210828362[/C][/ROW]
[ROW][C]69[/C][C]2004[/C][C]1741.43128917164[/C][C]262.568710828362[/C][/ROW]
[ROW][C]70[/C][C]2077[/C][C]1880.80628917164[/C][C]196.193710828362[/C][/ROW]
[ROW][C]71[/C][C]2092[/C][C]2080.36878917164[/C][C]11.6312108283621[/C][/ROW]
[ROW][C]72[/C][C]2051[/C][C]2196.99378917164[/C][C]-145.993789171638[/C][/ROW]
[ROW][C]73[/C][C]1577[/C][C]1743.85396058295[/C][C]-166.853960582951[/C][/ROW]
[ROW][C]74[/C][C]1356[/C][C]1558.00302518312[/C][C]-202.003025183115[/C][/ROW]
[ROW][C]75[/C][C]1652[/C][C]1608.56552518312[/C][C]43.4344748168846[/C][/ROW]
[ROW][C]76[/C][C]1382[/C][C]1495.37802518312[/C][C]-113.378025183116[/C][/ROW]
[ROW][C]77[/C][C]1519[/C][C]1632.69052518312[/C][C]-113.690525183116[/C][/ROW]
[ROW][C]78[/C][C]1421[/C][C]1576.94052518312[/C][C]-155.940525183116[/C][/ROW]
[ROW][C]79[/C][C]1442[/C][C]1652.56552518312[/C][C]-210.565525183116[/C][/ROW]
[ROW][C]80[/C][C]1543[/C][C]1667.44052518312[/C][C]-124.440525183115[/C][/ROW]
[ROW][C]81[/C][C]1656[/C][C]1720.25302518312[/C][C]-64.2530251831158[/C][/ROW]
[ROW][C]82[/C][C]1561[/C][C]1859.62802518312[/C][C]-298.628025183116[/C][/ROW]
[ROW][C]83[/C][C]1905[/C][C]2059.19052518312[/C][C]-154.190525183116[/C][/ROW]
[ROW][C]84[/C][C]2199[/C][C]2175.81552518312[/C][C]23.1844748168843[/C][/ROW]
[ROW][C]85[/C][C]1473[/C][C]1722.67569659443[/C][C]-249.675696594429[/C][/ROW]
[ROW][C]86[/C][C]1655[/C][C]1536.82476119459[/C][C]118.175238805407[/C][/ROW]
[ROW][C]87[/C][C]1407[/C][C]1587.38726119459[/C][C]-180.387261194593[/C][/ROW]
[ROW][C]88[/C][C]1395[/C][C]1474.19976119459[/C][C]-79.1997611945937[/C][/ROW]
[ROW][C]89[/C][C]1530[/C][C]1611.51226119459[/C][C]-81.5122611945933[/C][/ROW]
[ROW][C]90[/C][C]1309[/C][C]1555.76226119459[/C][C]-246.762261194593[/C][/ROW]
[ROW][C]91[/C][C]1526[/C][C]1631.38726119459[/C][C]-105.387261194593[/C][/ROW]
[ROW][C]92[/C][C]1327[/C][C]1646.26226119459[/C][C]-319.262261194593[/C][/ROW]
[ROW][C]93[/C][C]1627[/C][C]1699.07476119459[/C][C]-72.0747611945935[/C][/ROW]
[ROW][C]94[/C][C]1748[/C][C]1838.44976119459[/C][C]-90.4497611945934[/C][/ROW]
[ROW][C]95[/C][C]1958[/C][C]2038.01226119459[/C][C]-80.0122611945933[/C][/ROW]
[ROW][C]96[/C][C]2274[/C][C]2154.63726119459[/C][C]119.362738805407[/C][/ROW]
[ROW][C]97[/C][C]1648[/C][C]1701.49743260591[/C][C]-53.4974326059064[/C][/ROW]
[ROW][C]98[/C][C]1401[/C][C]1515.64649720607[/C][C]-114.646497206071[/C][/ROW]
[ROW][C]99[/C][C]1411[/C][C]1566.20899720607[/C][C]-155.208997206071[/C][/ROW]
[ROW][C]100[/C][C]1403[/C][C]1453.02149720607[/C][C]-50.0214972060714[/C][/ROW]
[ROW][C]101[/C][C]1394[/C][C]1590.33399720607[/C][C]-196.333997206071[/C][/ROW]
[ROW][C]102[/C][C]1520[/C][C]1534.58399720607[/C][C]-14.5839972060711[/C][/ROW]
[ROW][C]103[/C][C]1528[/C][C]1610.20899720607[/C][C]-82.2089972060712[/C][/ROW]
[ROW][C]104[/C][C]1643[/C][C]1625.08399720607[/C][C]17.9160027939294[/C][/ROW]
[ROW][C]105[/C][C]1515[/C][C]1677.89649720607[/C][C]-162.896497206071[/C][/ROW]
[ROW][C]106[/C][C]1685[/C][C]1817.27149720607[/C][C]-132.271497206071[/C][/ROW]
[ROW][C]107[/C][C]2000[/C][C]2016.83399720607[/C][C]-16.8339972060710[/C][/ROW]
[ROW][C]108[/C][C]2215[/C][C]2133.45899720607[/C][C]81.5410027939288[/C][/ROW]
[ROW][C]109[/C][C]1956[/C][C]1680.31916861738[/C][C]275.680831382616[/C][/ROW]
[ROW][C]110[/C][C]1462[/C][C]1494.46823321755[/C][C]-32.4682332175485[/C][/ROW]
[ROW][C]111[/C][C]1563[/C][C]1545.03073321755[/C][C]17.9692667824515[/C][/ROW]
[ROW][C]112[/C][C]1459[/C][C]1431.84323321755[/C][C]27.1567667824508[/C][/ROW]
[ROW][C]113[/C][C]1446[/C][C]1569.15573321755[/C][C]-123.155733217549[/C][/ROW]
[ROW][C]114[/C][C]1622[/C][C]1513.40573321755[/C][C]108.594266782451[/C][/ROW]
[ROW][C]115[/C][C]1657[/C][C]1589.03073321755[/C][C]67.9692667824511[/C][/ROW]
[ROW][C]116[/C][C]1638[/C][C]1603.90573321755[/C][C]34.0942667824517[/C][/ROW]
[ROW][C]117[/C][C]1643[/C][C]1656.71823321755[/C][C]-13.7182332175489[/C][/ROW]
[ROW][C]118[/C][C]1683[/C][C]1796.09323321755[/C][C]-113.093233217549[/C][/ROW]
[ROW][C]119[/C][C]2050[/C][C]1995.65573321755[/C][C]54.3442667824512[/C][/ROW]
[ROW][C]120[/C][C]2262[/C][C]2112.28073321755[/C][C]149.719266782451[/C][/ROW]
[ROW][C]121[/C][C]1813[/C][C]1659.14090462886[/C][C]153.859095371138[/C][/ROW]
[ROW][C]122[/C][C]1445[/C][C]1473.28996922903[/C][C]-28.2899692290262[/C][/ROW]
[ROW][C]123[/C][C]1762[/C][C]1523.85246922903[/C][C]238.147530770974[/C][/ROW]
[ROW][C]124[/C][C]1461[/C][C]1410.66496922903[/C][C]50.3350307709731[/C][/ROW]
[ROW][C]125[/C][C]1556[/C][C]1547.97746922903[/C][C]8.02253077097358[/C][/ROW]
[ROW][C]126[/C][C]1431[/C][C]1492.22746922903[/C][C]-61.2274692290265[/C][/ROW]
[ROW][C]127[/C][C]1427[/C][C]1567.85246922903[/C][C]-140.852469229027[/C][/ROW]
[ROW][C]128[/C][C]1554[/C][C]1582.72746922903[/C][C]-28.7274692290261[/C][/ROW]
[ROW][C]129[/C][C]1645[/C][C]1635.53996922903[/C][C]9.46003077097336[/C][/ROW]
[ROW][C]130[/C][C]1653[/C][C]1774.91496922903[/C][C]-121.914969229026[/C][/ROW]
[ROW][C]131[/C][C]2016[/C][C]1974.47746922903[/C][C]41.5225307709736[/C][/ROW]
[ROW][C]132[/C][C]2207[/C][C]2091.10246922903[/C][C]115.897530770973[/C][/ROW]
[ROW][C]133[/C][C]1665[/C][C]1637.96264064034[/C][C]27.0373593596605[/C][/ROW]
[ROW][C]134[/C][C]1361[/C][C]1452.11170524050[/C][C]-91.111705240504[/C][/ROW]
[ROW][C]135[/C][C]1506[/C][C]1502.67420524050[/C][C]3.32579475949605[/C][/ROW]
[ROW][C]136[/C][C]1360[/C][C]1389.48670524050[/C][C]-29.4867052405046[/C][/ROW]
[ROW][C]137[/C][C]1453[/C][C]1526.79920524050[/C][C]-73.7992052405041[/C][/ROW]
[ROW][C]138[/C][C]1522[/C][C]1471.04920524050[/C][C]50.9507947594957[/C][/ROW]
[ROW][C]139[/C][C]1460[/C][C]1546.67420524050[/C][C]-86.6742052405044[/C][/ROW]
[ROW][C]140[/C][C]1552[/C][C]1561.54920524050[/C][C]-9.54920524050376[/C][/ROW]
[ROW][C]141[/C][C]1548[/C][C]1614.36170524050[/C][C]-66.3617052405043[/C][/ROW]
[ROW][C]142[/C][C]1827[/C][C]1753.73670524050[/C][C]73.2632947594957[/C][/ROW]
[ROW][C]143[/C][C]1737[/C][C]1953.29920524050[/C][C]-216.299205240504[/C][/ROW]
[ROW][C]144[/C][C]1941[/C][C]2069.92420524050[/C][C]-128.924205240504[/C][/ROW]
[ROW][C]145[/C][C]1474[/C][C]1616.78437665182[/C][C]-142.784376651817[/C][/ROW]
[ROW][C]146[/C][C]1458[/C][C]1430.93344125198[/C][C]27.0665587480184[/C][/ROW]
[ROW][C]147[/C][C]1542[/C][C]1481.49594125198[/C][C]60.5040587480183[/C][/ROW]
[ROW][C]148[/C][C]1404[/C][C]1368.30844125198[/C][C]35.6915587480177[/C][/ROW]
[ROW][C]149[/C][C]1522[/C][C]1505.62094125198[/C][C]16.3790587480182[/C][/ROW]
[ROW][C]150[/C][C]1385[/C][C]1449.87094125198[/C][C]-64.870941251982[/C][/ROW]
[ROW][C]151[/C][C]1641[/C][C]1525.49594125198[/C][C]115.504058748018[/C][/ROW]
[ROW][C]152[/C][C]1510[/C][C]1540.37094125198[/C][C]-30.3709412519815[/C][/ROW]
[ROW][C]153[/C][C]1681[/C][C]1593.18344125198[/C][C]87.816558748018[/C][/ROW]
[ROW][C]154[/C][C]1938[/C][C]1732.55844125198[/C][C]205.441558748018[/C][/ROW]
[ROW][C]155[/C][C]1868[/C][C]1932.12094125198[/C][C]-64.1209412519819[/C][/ROW]
[ROW][C]156[/C][C]1726[/C][C]2048.74594125198[/C][C]-322.745941251982[/C][/ROW]
[ROW][C]157[/C][C]1456[/C][C]1595.60611266329[/C][C]-139.606112663295[/C][/ROW]
[ROW][C]158[/C][C]1445[/C][C]1409.75517726346[/C][C]35.2448227365406[/C][/ROW]
[ROW][C]159[/C][C]1456[/C][C]1460.31767726346[/C][C]-4.31767726345942[/C][/ROW]
[ROW][C]160[/C][C]1365[/C][C]1347.13017726346[/C][C]17.8698227365400[/C][/ROW]
[ROW][C]161[/C][C]1487[/C][C]1484.44267726346[/C][C]2.55732273654045[/C][/ROW]
[ROW][C]162[/C][C]1558[/C][C]1428.69267726346[/C][C]129.307322736540[/C][/ROW]
[ROW][C]163[/C][C]1488[/C][C]1504.31767726346[/C][C]-16.3176772634598[/C][/ROW]
[ROW][C]164[/C][C]1684[/C][C]1519.19267726346[/C][C]164.807322736541[/C][/ROW]
[ROW][C]165[/C][C]1594[/C][C]1572.00517726346[/C][C]21.9948227365402[/C][/ROW]
[ROW][C]166[/C][C]1850[/C][C]1711.38017726346[/C][C]138.619822736540[/C][/ROW]
[ROW][C]167[/C][C]1998[/C][C]1910.94267726346[/C][C]87.0573227365404[/C][/ROW]
[ROW][C]168[/C][C]2079[/C][C]2027.56767726346[/C][C]51.4323227365403[/C][/ROW]
[ROW][C]169[/C][C]1494[/C][C]1574.42784867477[/C][C]-80.4278486747727[/C][/ROW]
[ROW][C]170[/C][C]1057[/C][C]1162.19187967228[/C][C]-105.191879672279[/C][/ROW]
[ROW][C]171[/C][C]1218[/C][C]1212.75437967228[/C][C]5.24562032772056[/C][/ROW]
[ROW][C]172[/C][C]1168[/C][C]1099.56687967228[/C][C]68.4331203277199[/C][/ROW]
[ROW][C]173[/C][C]1236[/C][C]1236.87937967228[/C][C]-0.879379672279542[/C][/ROW]
[ROW][C]174[/C][C]1076[/C][C]1181.12937967228[/C][C]-105.129379672280[/C][/ROW]
[ROW][C]175[/C][C]1174[/C][C]1256.75437967228[/C][C]-82.7543796722797[/C][/ROW]
[ROW][C]176[/C][C]1139[/C][C]1271.62937967228[/C][C]-132.629379672279[/C][/ROW]
[ROW][C]177[/C][C]1427[/C][C]1324.44187967228[/C][C]102.558120327720[/C][/ROW]
[ROW][C]178[/C][C]1487[/C][C]1463.81687967228[/C][C]23.1831203277203[/C][/ROW]
[ROW][C]179[/C][C]1483[/C][C]1663.37937967228[/C][C]-180.379379672280[/C][/ROW]
[ROW][C]180[/C][C]1513[/C][C]1780.00437967228[/C][C]-267.00437967228[/C][/ROW]
[ROW][C]181[/C][C]1357[/C][C]1326.86455108359[/C][C]30.1354489164073[/C][/ROW]
[ROW][C]182[/C][C]1165[/C][C]1141.01361568376[/C][C]23.986384316243[/C][/ROW]
[ROW][C]183[/C][C]1282[/C][C]1191.57611568376[/C][C]90.4238843162428[/C][/ROW]
[ROW][C]184[/C][C]1110[/C][C]1078.38861568376[/C][C]31.6113843162422[/C][/ROW]
[ROW][C]185[/C][C]1297[/C][C]1215.70111568376[/C][C]81.2988843162427[/C][/ROW]
[ROW][C]186[/C][C]1185[/C][C]1159.95111568376[/C][C]25.0488843162426[/C][/ROW]
[ROW][C]187[/C][C]1222[/C][C]1235.57611568376[/C][C]-13.5761156837575[/C][/ROW]
[ROW][C]188[/C][C]1284[/C][C]1250.45111568376[/C][C]33.548884316243[/C][/ROW]
[ROW][C]189[/C][C]1444[/C][C]1303.26361568376[/C][C]140.736384316242[/C][/ROW]
[ROW][C]190[/C][C]1575[/C][C]1442.63861568376[/C][C]132.361384316243[/C][/ROW]
[ROW][C]191[/C][C]1737[/C][C]1642.20111568376[/C][C]94.7988843162427[/C][/ROW]
[ROW][C]192[/C][C]1763[/C][C]1758.82611568376[/C][C]4.17388431624253[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24938&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24938&T=4

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
116871870.92354451406-183.923544514060
215081685.07260911425-177.072609114252
315071735.63510911425-228.635109114254
413851622.44760911424-237.447609114242
516321759.76010911425-127.760109114251
615111704.01010911425-193.010109114250
715591779.63510911425-220.635109114248
816301794.51010911426-164.510109114256
915791847.32260911425-268.322609114246
1016531986.69760911425-333.697609114249
1121522186.26010911425-34.2601091142503
1221482302.88510911425-154.885109114249
1317521849.74528052556-97.7452805255622
1417651663.89434512573101.105654874272
1517171714.456845125732.54315487427317
1615581601.26934512573-43.2693451257275
1715751738.58184512573-163.581845125727
1815201682.83184512573-162.831845125727
1918051758.4568451257346.5431548742728
2018001773.3318451257326.6681548742733
2117191826.14434512573-107.144345125727
2220081965.5193451257342.4806548742729
2322422165.0818451257376.918154874273
2424782281.70684512573196.293154874273
2520301828.56701653704201.43298346296
2616551642.7160811372012.2839188627955
2716931693.27858113720-0.278581137204542
2816231580.0910811372142.9089188627948
2918051717.4035811372087.5964188627952
3017461661.6535811372084.3464188627952
3117951737.2785811372157.721418862795
3219261752.15358113720173.846418862796
3316191804.96608113721-185.966081137205
3419921944.3410811372047.6589188627952
3522332143.9035811372089.0964188627953
3621922260.52858113721-68.5285811372049
3720801807.38875254852272.611247451482
3817681621.53781714868146.462182851318
3918351672.10031714868162.899682851318
4015691558.9128171486810.0871828513171
4119761696.22531714868279.774682851318
4218531640.47531714868212.524682851317
4319651716.10031714868248.899682851317
4416891730.97531714868-41.9753171486821
4517781783.78781714868-5.78781714868267
4619761923.1628171486852.8371828513174
4723972122.72531714868274.274682851318
4826542239.35031714868414.649682851317
4920971786.21048856000310.789511440004
5019631600.35955316016362.64044683984
5116771650.9220531601626.0779468398400
5219411537.73455316016403.265446839839
5320031675.04705316016327.95294683984
5418131619.29705316016193.702946839840
5520121694.92205316016317.07794683984
5619121709.79705316016202.20294683984
5720841762.60955316016321.39044683984
5820801901.98455316016178.015446839840
5921182101.5470531601616.4529468398398
6021502218.17205316016-68.1720531601603
6116081765.03222457147-157.032224571473
6215031579.18128917164-76.1812891716376
6315481629.74378917164-81.7437891716377
6413821516.55628917164-134.556289171638
6517311653.8687891716477.1312108283621
6617981598.11878917164199.881210828362
6717791673.74378917164105.256210828362
6818871688.61878917164198.381210828362
6920041741.43128917164262.568710828362
7020771880.80628917164196.193710828362
7120922080.3687891716411.6312108283621
7220512196.99378917164-145.993789171638
7315771743.85396058295-166.853960582951
7413561558.00302518312-202.003025183115
7516521608.5655251831243.4344748168846
7613821495.37802518312-113.378025183116
7715191632.69052518312-113.690525183116
7814211576.94052518312-155.940525183116
7914421652.56552518312-210.565525183116
8015431667.44052518312-124.440525183115
8116561720.25302518312-64.2530251831158
8215611859.62802518312-298.628025183116
8319052059.19052518312-154.190525183116
8421992175.8155251831223.1844748168843
8514731722.67569659443-249.675696594429
8616551536.82476119459118.175238805407
8714071587.38726119459-180.387261194593
8813951474.19976119459-79.1997611945937
8915301611.51226119459-81.5122611945933
9013091555.76226119459-246.762261194593
9115261631.38726119459-105.387261194593
9213271646.26226119459-319.262261194593
9316271699.07476119459-72.0747611945935
9417481838.44976119459-90.4497611945934
9519582038.01226119459-80.0122611945933
9622742154.63726119459119.362738805407
9716481701.49743260591-53.4974326059064
9814011515.64649720607-114.646497206071
9914111566.20899720607-155.208997206071
10014031453.02149720607-50.0214972060714
10113941590.33399720607-196.333997206071
10215201534.58399720607-14.5839972060711
10315281610.20899720607-82.2089972060712
10416431625.0839972060717.9160027939294
10515151677.89649720607-162.896497206071
10616851817.27149720607-132.271497206071
10720002016.83399720607-16.8339972060710
10822152133.4589972060781.5410027939288
10919561680.31916861738275.680831382616
11014621494.46823321755-32.4682332175485
11115631545.0307332175517.9692667824515
11214591431.8432332175527.1567667824508
11314461569.15573321755-123.155733217549
11416221513.40573321755108.594266782451
11516571589.0307332175567.9692667824511
11616381603.9057332175534.0942667824517
11716431656.71823321755-13.7182332175489
11816831796.09323321755-113.093233217549
11920501995.6557332175554.3442667824512
12022622112.28073321755149.719266782451
12118131659.14090462886153.859095371138
12214451473.28996922903-28.2899692290262
12317621523.85246922903238.147530770974
12414611410.6649692290350.3350307709731
12515561547.977469229038.02253077097358
12614311492.22746922903-61.2274692290265
12714271567.85246922903-140.852469229027
12815541582.72746922903-28.7274692290261
12916451635.539969229039.46003077097336
13016531774.91496922903-121.914969229026
13120161974.4774692290341.5225307709736
13222072091.10246922903115.897530770973
13316651637.9626406403427.0373593596605
13413611452.11170524050-91.111705240504
13515061502.674205240503.32579475949605
13613601389.48670524050-29.4867052405046
13714531526.79920524050-73.7992052405041
13815221471.0492052405050.9507947594957
13914601546.67420524050-86.6742052405044
14015521561.54920524050-9.54920524050376
14115481614.36170524050-66.3617052405043
14218271753.7367052405073.2632947594957
14317371953.29920524050-216.299205240504
14419412069.92420524050-128.924205240504
14514741616.78437665182-142.784376651817
14614581430.9334412519827.0665587480184
14715421481.4959412519860.5040587480183
14814041368.3084412519835.6915587480177
14915221505.6209412519816.3790587480182
15013851449.87094125198-64.870941251982
15116411525.49594125198115.504058748018
15215101540.37094125198-30.3709412519815
15316811593.1834412519887.816558748018
15419381732.55844125198205.441558748018
15518681932.12094125198-64.1209412519819
15617262048.74594125198-322.745941251982
15714561595.60611266329-139.606112663295
15814451409.7551772634635.2448227365406
15914561460.31767726346-4.31767726345942
16013651347.1301772634617.8698227365400
16114871484.442677263462.55732273654045
16215581428.69267726346129.307322736540
16314881504.31767726346-16.3176772634598
16416841519.19267726346164.807322736541
16515941572.0051772634621.9948227365402
16618501711.38017726346138.619822736540
16719981910.9426772634687.0573227365404
16820792027.5676772634651.4323227365403
16914941574.42784867477-80.4278486747727
17010571162.19187967228-105.191879672279
17112181212.754379672285.24562032772056
17211681099.5668796722868.4331203277199
17312361236.87937967228-0.879379672279542
17410761181.12937967228-105.129379672280
17511741256.75437967228-82.7543796722797
17611391271.62937967228-132.629379672279
17714271324.44187967228102.558120327720
17814871463.8168796722823.1831203277203
17914831663.37937967228-180.379379672280
18015131780.00437967228-267.00437967228
18113571326.8645510835930.1354489164073
18211651141.0136156837623.986384316243
18312821191.5761156837690.4238843162428
18411101078.3886156837631.6113843162422
18512971215.7011156837681.2988843162427
18611851159.9511156837625.0488843162426
18712221235.57611568376-13.5761156837575
18812841250.4511156837633.548884316243
18914441303.26361568376140.736384316242
19015751442.63861568376132.361384316243
19117371642.2011156837694.7988843162427
19217631758.826115683764.17388431624253


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 3
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Figure 4
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Figure 5
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Figure 6
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Figure 7
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Figure 8
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Figure 9
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
R code (references can be found in the software module):
library(lattice)
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')