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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 computationSun, 21 Dec 2008 06:24:07 -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/Dec/21/t1229865913fz8lj5l7k0088uk.htm/, Retrieved Mon, 10 Nov 2025 03:02:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35562, Retrieved Mon, 10 Nov 2025 03:02:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords2
Estimated Impact528

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] [Q1 T6] [2008-11-18 17:59:48] [fe7291e888d31b8c4db0b24d6c0f75c6]
-    D      [Multiple Regression] [2] [2008-12-21 13:24:07] [783db4b4a0f63b73ca8b14666b7f4329] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
519164	0
517009	0
509933	0
509127	0
500857	0
506971	0
569323	0
579714	0
577992	0
565464	0
547344	0
554788	0
562325	0
560854	0
555332	0
543599	0
536662	0
542722	0
593530	0
610763	0
612613	0
611324	0
594167	0
595454	0
590865	0
589379	0
584428	0
573100	0
567456	0
569028	0
620735	0
628884	0
628232	0
612117	0
595404	0
597141	0
593408	0
590072	0
579799	0
574205	0
572775	0
572942	0
619567	0
625809	0
619916	0
587625	0
565742	0
557274	0
560576	1
548854	1
531673	1
525919	1
511038	1
498662	1
555362	1
564591	1
541657	1
527070	1
509846	1
514258	1
516922	1
507561	1
492622	1
490243	1
469357	1
477580	1
528379	1
533590	1
517945	1
506174	1
501866	1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35562&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35562&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35562&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 time5 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Multiple Linear Regression - Estimated Regression Equation
WerklozenTotaal[t] = + 543630.189173228 -94863.0994094488Kredietcrisis[t] + 11509.5008530183M1[t] + 5500.84999999999M2[t] -5576.30085301837M3[t] -12928.7850393701M4[t] -23690.2692257218M5[t] -23150.4200787402M6[t] + 28927.9290682415M7[t] + 37250.2782152231M8[t] + 28664.1273622047M9[t] + 12813.8098425197M10[t] -4173.8410104987M11[t] + 1086.81751968504t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
WerklozenTotaal[t] =  +  543630.189173228 -94863.0994094488Kredietcrisis[t] +  11509.5008530183M1[t] +  5500.84999999999M2[t] -5576.30085301837M3[t] -12928.7850393701M4[t] -23690.2692257218M5[t] -23150.4200787402M6[t] +  28927.9290682415M7[t] +  37250.2782152231M8[t] +  28664.1273622047M9[t] +  12813.8098425197M10[t] -4173.8410104987M11[t] +  1086.81751968504t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35562&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]WerklozenTotaal[t] =  +  543630.189173228 -94863.0994094488Kredietcrisis[t] +  11509.5008530183M1[t] +  5500.84999999999M2[t] -5576.30085301837M3[t] -12928.7850393701M4[t] -23690.2692257218M5[t] -23150.4200787402M6[t] +  28927.9290682415M7[t] +  37250.2782152231M8[t] +  28664.1273622047M9[t] +  12813.8098425197M10[t] -4173.8410104987M11[t] +  1086.81751968504t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35562&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35562&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
WerklozenTotaal[t] = + 543630.189173228 -94863.0994094488Kredietcrisis[t] + 11509.5008530183M1[t] + 5500.84999999999M2[t] -5576.30085301837M3[t] -12928.7850393701M4[t] -23690.2692257218M5[t] -23150.4200787402M6[t] + 28927.9290682415M7[t] + 37250.2782152231M8[t] + 28664.1273622047M9[t] + 12813.8098425197M10[t] -4173.8410104987M11[t] + 1086.81751968504t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)543630.18917322811793.84297746.094400
Kredietcrisis-94863.09940944889766.43652-9.713200
M111509.500853018313447.7439940.85590.3956540.197827
M25500.8499999999913412.8667730.41010.6832570.341629
M3-5576.3008530183713381.679846-0.41670.6784550.339227
M4-12928.785039370113354.20907-0.96810.3370630.168532
M5-23690.269225721813330.477417-1.77720.0808790.04044
M6-23150.420078740213310.504887-1.73930.0873870.043694
M728927.929068241513294.3084232.1760.0337180.016859
M837250.278215223113281.9018392.80460.0068780.003439
M928664.127362204713273.2957622.15950.035030.017515
M1012813.809842519713268.4975870.96570.3382580.169129
M11-4173.841010498713267.511446-0.31460.7542210.37711
t1086.81751968504224.9265574.83191.1e-055e-06

\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) & 543630.189173228 & 11793.842977 & 46.0944 & 0 & 0 \tabularnewline
Kredietcrisis & -94863.0994094488 & 9766.43652 & -9.7132 & 0 & 0 \tabularnewline
M1 & 11509.5008530183 & 13447.743994 & 0.8559 & 0.395654 & 0.197827 \tabularnewline
M2 & 5500.84999999999 & 13412.866773 & 0.4101 & 0.683257 & 0.341629 \tabularnewline
M3 & -5576.30085301837 & 13381.679846 & -0.4167 & 0.678455 & 0.339227 \tabularnewline
M4 & -12928.7850393701 & 13354.20907 & -0.9681 & 0.337063 & 0.168532 \tabularnewline
M5 & -23690.2692257218 & 13330.477417 & -1.7772 & 0.080879 & 0.04044 \tabularnewline
M6 & -23150.4200787402 & 13310.504887 & -1.7393 & 0.087387 & 0.043694 \tabularnewline
M7 & 28927.9290682415 & 13294.308423 & 2.176 & 0.033718 & 0.016859 \tabularnewline
M8 & 37250.2782152231 & 13281.901839 & 2.8046 & 0.006878 & 0.003439 \tabularnewline
M9 & 28664.1273622047 & 13273.295762 & 2.1595 & 0.03503 & 0.017515 \tabularnewline
M10 & 12813.8098425197 & 13268.497587 & 0.9657 & 0.338258 & 0.169129 \tabularnewline
M11 & -4173.8410104987 & 13267.511446 & -0.3146 & 0.754221 & 0.37711 \tabularnewline
t & 1086.81751968504 & 224.926557 & 4.8319 & 1.1e-05 & 5e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35562&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]543630.189173228[/C][C]11793.842977[/C][C]46.0944[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Kredietcrisis[/C][C]-94863.0994094488[/C][C]9766.43652[/C][C]-9.7132[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]11509.5008530183[/C][C]13447.743994[/C][C]0.8559[/C][C]0.395654[/C][C]0.197827[/C][/ROW]
[ROW][C]M2[/C][C]5500.84999999999[/C][C]13412.866773[/C][C]0.4101[/C][C]0.683257[/C][C]0.341629[/C][/ROW]
[ROW][C]M3[/C][C]-5576.30085301837[/C][C]13381.679846[/C][C]-0.4167[/C][C]0.678455[/C][C]0.339227[/C][/ROW]
[ROW][C]M4[/C][C]-12928.7850393701[/C][C]13354.20907[/C][C]-0.9681[/C][C]0.337063[/C][C]0.168532[/C][/ROW]
[ROW][C]M5[/C][C]-23690.2692257218[/C][C]13330.477417[/C][C]-1.7772[/C][C]0.080879[/C][C]0.04044[/C][/ROW]
[ROW][C]M6[/C][C]-23150.4200787402[/C][C]13310.504887[/C][C]-1.7393[/C][C]0.087387[/C][C]0.043694[/C][/ROW]
[ROW][C]M7[/C][C]28927.9290682415[/C][C]13294.308423[/C][C]2.176[/C][C]0.033718[/C][C]0.016859[/C][/ROW]
[ROW][C]M8[/C][C]37250.2782152231[/C][C]13281.901839[/C][C]2.8046[/C][C]0.006878[/C][C]0.003439[/C][/ROW]
[ROW][C]M9[/C][C]28664.1273622047[/C][C]13273.295762[/C][C]2.1595[/C][C]0.03503[/C][C]0.017515[/C][/ROW]
[ROW][C]M10[/C][C]12813.8098425197[/C][C]13268.497587[/C][C]0.9657[/C][C]0.338258[/C][C]0.169129[/C][/ROW]
[ROW][C]M11[/C][C]-4173.8410104987[/C][C]13267.511446[/C][C]-0.3146[/C][C]0.754221[/C][C]0.37711[/C][/ROW]
[ROW][C]t[/C][C]1086.81751968504[/C][C]224.926557[/C][C]4.8319[/C][C]1.1e-05[/C][C]5e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35562&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35562&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)543630.18917322811793.84297746.094400
Kredietcrisis-94863.09940944889766.43652-9.713200
M111509.500853018313447.7439940.85590.3956540.197827
M25500.8499999999913412.8667730.41010.6832570.341629
M3-5576.3008530183713381.679846-0.41670.6784550.339227
M4-12928.785039370113354.20907-0.96810.3370630.168532
M5-23690.269225721813330.477417-1.77720.0808790.04044
M6-23150.420078740213310.504887-1.73930.0873870.043694
M728927.929068241513294.3084232.1760.0337180.016859
M837250.278215223113281.9018392.80460.0068780.003439
M928664.127362204713273.2957622.15950.035030.017515
M1012813.809842519713268.4975870.96570.3382580.169129
M11-4173.841010498713267.511446-0.31460.7542210.37711
t1086.81751968504224.9265574.83191.1e-055e-06






Multiple Linear Regression - Regression Statistics
Multiple R0.876024537241298
R-squared0.76741898984883
Adjusted R-squared0.714374198059966
F-TEST (value)14.4673767955094
F-TEST (DF numerator)13
F-TEST (DF denominator)57
p-value1.37223565843669e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation21876.1288048348
Sum Squared Residuals27278205654.6863

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.876024537241298 \tabularnewline
R-squared & 0.76741898984883 \tabularnewline
Adjusted R-squared & 0.714374198059966 \tabularnewline
F-TEST (value) & 14.4673767955094 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 57 \tabularnewline
p-value & 1.37223565843669e-13 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 21876.1288048348 \tabularnewline
Sum Squared Residuals & 27278205654.6863 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35562&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.876024537241298[/C][/ROW]
[ROW][C]R-squared[/C][C]0.76741898984883[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.714374198059966[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]14.4673767955094[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]57[/C][/ROW]
[ROW][C]p-value[/C][C]1.37223565843669e-13[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]21876.1288048348[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]27278205654.6863[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35562&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35562&T=3

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 - Regression Statistics
Multiple R0.876024537241298
R-squared0.76741898984883
Adjusted R-squared0.714374198059966
F-TEST (value)14.4673767955094
F-TEST (DF numerator)13
F-TEST (DF denominator)57
p-value1.37223565843669e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation21876.1288048348
Sum Squared Residuals27278205654.6863






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1519164556226.507545932-37062.5075459323
2517009551304.674212598-34295.6742125984
3509933541314.340879265-31381.3408792651
4509127535048.674212598-25921.6742125984
5500857525374.007545932-24517.0075459317
6506971527000.674212598-20029.6742125984
7569323580165.840879265-10842.8408792651
8579714589575.007545932-9861.00754593171
9577992582075.674212598-4083.67421259838
10565464567312.174212598-1848.17421259840
11547344551411.340879265-4067.34087926507
12554788556671.999409449-1883.99940944881
13562325569268.317782152-6943.31778215212
14560854564346.484448819-3492.48444881888
15555332554356.151115486975.848884514445
16543599548090.484448819-4491.48444881889
17536662538415.817782152-1753.81778215221
18542722540042.4844488192679.51555118111
19593530593207.651115486322.348884514441
20610763602616.8177821528146.18221784779
21612613595117.48444881917495.5155511811
22611324580353.98444881930970.0155511811
23594167564453.15111548629713.8488845144
24595454569713.80964566925740.1903543307
25590865582310.1280183738554.8719816274
26589379577388.29468503911990.7053149606
27584428567397.96135170617030.0386482940
28573100561132.29468503911967.7053149606
29567456551457.62801837315998.3719816273
30569028553084.29468503915943.7053149606
31620735606249.46135170614485.5386482940
32628884615658.62801837313225.3719816273
33628232608159.29468503920072.7053149606
34612117593395.79468503918721.2053149606
35595404577494.96135170617909.0386482940
36597141582755.6198818914385.3801181102
37593408595351.938254593-1943.93825459307
38590072590430.10492126-358.104921259847
39579799580439.771587927-640.771587926524
40574205574174.1049212630.8950787401495
41572775564499.4382545938275.5617454068
42572942566126.104921266815.89507874013
43619567619291.271587927275.728412073468
44625809628700.438254593-2891.4382545932
45619916621201.10492126-1285.10492125986
46587625606437.60492126-18812.6049212599
47565742590536.771587927-24794.7715879265
48557274595797.43011811-38523.4301181102
49560576513530.64908136547045.3509186353
50548854508608.81574803140245.1842519685
51531673498618.48241469833054.5175853018
52525919492352.81574803133566.1842519685
53511038482678.14908136528359.8509186352
54498662484304.81574803114357.1842519685
55555362537469.98241469817892.0175853018
56564591546879.14908136517711.8509186352
57541657539379.8157480312277.1842519685
58527070524616.3157480312453.6842519685
59509846508715.4824146981130.51758530184
60514258513976.140944882281.859055118100
61516922526572.459317585-9650.4593175852
62507561521650.625984252-14089.6259842520
63492622511660.292650919-19038.2926509187
64490243505394.625984252-15151.6259842520
65469357495719.959317585-26362.9593175853
66477580497346.625984252-19766.625984252
67528379550511.792650919-22132.7926509187
68533590559920.959317585-26330.9593175853
69517945552421.625984252-34476.625984252
70506174537658.125984252-31484.125984252
71501866521757.292650919-19891.2926509187

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 519164 & 556226.507545932 & -37062.5075459323 \tabularnewline
2 & 517009 & 551304.674212598 & -34295.6742125984 \tabularnewline
3 & 509933 & 541314.340879265 & -31381.3408792651 \tabularnewline
4 & 509127 & 535048.674212598 & -25921.6742125984 \tabularnewline
5 & 500857 & 525374.007545932 & -24517.0075459317 \tabularnewline
6 & 506971 & 527000.674212598 & -20029.6742125984 \tabularnewline
7 & 569323 & 580165.840879265 & -10842.8408792651 \tabularnewline
8 & 579714 & 589575.007545932 & -9861.00754593171 \tabularnewline
9 & 577992 & 582075.674212598 & -4083.67421259838 \tabularnewline
10 & 565464 & 567312.174212598 & -1848.17421259840 \tabularnewline
11 & 547344 & 551411.340879265 & -4067.34087926507 \tabularnewline
12 & 554788 & 556671.999409449 & -1883.99940944881 \tabularnewline
13 & 562325 & 569268.317782152 & -6943.31778215212 \tabularnewline
14 & 560854 & 564346.484448819 & -3492.48444881888 \tabularnewline
15 & 555332 & 554356.151115486 & 975.848884514445 \tabularnewline
16 & 543599 & 548090.484448819 & -4491.48444881889 \tabularnewline
17 & 536662 & 538415.817782152 & -1753.81778215221 \tabularnewline
18 & 542722 & 540042.484448819 & 2679.51555118111 \tabularnewline
19 & 593530 & 593207.651115486 & 322.348884514441 \tabularnewline
20 & 610763 & 602616.817782152 & 8146.18221784779 \tabularnewline
21 & 612613 & 595117.484448819 & 17495.5155511811 \tabularnewline
22 & 611324 & 580353.984448819 & 30970.0155511811 \tabularnewline
23 & 594167 & 564453.151115486 & 29713.8488845144 \tabularnewline
24 & 595454 & 569713.809645669 & 25740.1903543307 \tabularnewline
25 & 590865 & 582310.128018373 & 8554.8719816274 \tabularnewline
26 & 589379 & 577388.294685039 & 11990.7053149606 \tabularnewline
27 & 584428 & 567397.961351706 & 17030.0386482940 \tabularnewline
28 & 573100 & 561132.294685039 & 11967.7053149606 \tabularnewline
29 & 567456 & 551457.628018373 & 15998.3719816273 \tabularnewline
30 & 569028 & 553084.294685039 & 15943.7053149606 \tabularnewline
31 & 620735 & 606249.461351706 & 14485.5386482940 \tabularnewline
32 & 628884 & 615658.628018373 & 13225.3719816273 \tabularnewline
33 & 628232 & 608159.294685039 & 20072.7053149606 \tabularnewline
34 & 612117 & 593395.794685039 & 18721.2053149606 \tabularnewline
35 & 595404 & 577494.961351706 & 17909.0386482940 \tabularnewline
36 & 597141 & 582755.61988189 & 14385.3801181102 \tabularnewline
37 & 593408 & 595351.938254593 & -1943.93825459307 \tabularnewline
38 & 590072 & 590430.10492126 & -358.104921259847 \tabularnewline
39 & 579799 & 580439.771587927 & -640.771587926524 \tabularnewline
40 & 574205 & 574174.10492126 & 30.8950787401495 \tabularnewline
41 & 572775 & 564499.438254593 & 8275.5617454068 \tabularnewline
42 & 572942 & 566126.10492126 & 6815.89507874013 \tabularnewline
43 & 619567 & 619291.271587927 & 275.728412073468 \tabularnewline
44 & 625809 & 628700.438254593 & -2891.4382545932 \tabularnewline
45 & 619916 & 621201.10492126 & -1285.10492125986 \tabularnewline
46 & 587625 & 606437.60492126 & -18812.6049212599 \tabularnewline
47 & 565742 & 590536.771587927 & -24794.7715879265 \tabularnewline
48 & 557274 & 595797.43011811 & -38523.4301181102 \tabularnewline
49 & 560576 & 513530.649081365 & 47045.3509186353 \tabularnewline
50 & 548854 & 508608.815748031 & 40245.1842519685 \tabularnewline
51 & 531673 & 498618.482414698 & 33054.5175853018 \tabularnewline
52 & 525919 & 492352.815748031 & 33566.1842519685 \tabularnewline
53 & 511038 & 482678.149081365 & 28359.8509186352 \tabularnewline
54 & 498662 & 484304.815748031 & 14357.1842519685 \tabularnewline
55 & 555362 & 537469.982414698 & 17892.0175853018 \tabularnewline
56 & 564591 & 546879.149081365 & 17711.8509186352 \tabularnewline
57 & 541657 & 539379.815748031 & 2277.1842519685 \tabularnewline
58 & 527070 & 524616.315748031 & 2453.6842519685 \tabularnewline
59 & 509846 & 508715.482414698 & 1130.51758530184 \tabularnewline
60 & 514258 & 513976.140944882 & 281.859055118100 \tabularnewline
61 & 516922 & 526572.459317585 & -9650.4593175852 \tabularnewline
62 & 507561 & 521650.625984252 & -14089.6259842520 \tabularnewline
63 & 492622 & 511660.292650919 & -19038.2926509187 \tabularnewline
64 & 490243 & 505394.625984252 & -15151.6259842520 \tabularnewline
65 & 469357 & 495719.959317585 & -26362.9593175853 \tabularnewline
66 & 477580 & 497346.625984252 & -19766.625984252 \tabularnewline
67 & 528379 & 550511.792650919 & -22132.7926509187 \tabularnewline
68 & 533590 & 559920.959317585 & -26330.9593175853 \tabularnewline
69 & 517945 & 552421.625984252 & -34476.625984252 \tabularnewline
70 & 506174 & 537658.125984252 & -31484.125984252 \tabularnewline
71 & 501866 & 521757.292650919 & -19891.2926509187 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35562&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]519164[/C][C]556226.507545932[/C][C]-37062.5075459323[/C][/ROW]
[ROW][C]2[/C][C]517009[/C][C]551304.674212598[/C][C]-34295.6742125984[/C][/ROW]
[ROW][C]3[/C][C]509933[/C][C]541314.340879265[/C][C]-31381.3408792651[/C][/ROW]
[ROW][C]4[/C][C]509127[/C][C]535048.674212598[/C][C]-25921.6742125984[/C][/ROW]
[ROW][C]5[/C][C]500857[/C][C]525374.007545932[/C][C]-24517.0075459317[/C][/ROW]
[ROW][C]6[/C][C]506971[/C][C]527000.674212598[/C][C]-20029.6742125984[/C][/ROW]
[ROW][C]7[/C][C]569323[/C][C]580165.840879265[/C][C]-10842.8408792651[/C][/ROW]
[ROW][C]8[/C][C]579714[/C][C]589575.007545932[/C][C]-9861.00754593171[/C][/ROW]
[ROW][C]9[/C][C]577992[/C][C]582075.674212598[/C][C]-4083.67421259838[/C][/ROW]
[ROW][C]10[/C][C]565464[/C][C]567312.174212598[/C][C]-1848.17421259840[/C][/ROW]
[ROW][C]11[/C][C]547344[/C][C]551411.340879265[/C][C]-4067.34087926507[/C][/ROW]
[ROW][C]12[/C][C]554788[/C][C]556671.999409449[/C][C]-1883.99940944881[/C][/ROW]
[ROW][C]13[/C][C]562325[/C][C]569268.317782152[/C][C]-6943.31778215212[/C][/ROW]
[ROW][C]14[/C][C]560854[/C][C]564346.484448819[/C][C]-3492.48444881888[/C][/ROW]
[ROW][C]15[/C][C]555332[/C][C]554356.151115486[/C][C]975.848884514445[/C][/ROW]
[ROW][C]16[/C][C]543599[/C][C]548090.484448819[/C][C]-4491.48444881889[/C][/ROW]
[ROW][C]17[/C][C]536662[/C][C]538415.817782152[/C][C]-1753.81778215221[/C][/ROW]
[ROW][C]18[/C][C]542722[/C][C]540042.484448819[/C][C]2679.51555118111[/C][/ROW]
[ROW][C]19[/C][C]593530[/C][C]593207.651115486[/C][C]322.348884514441[/C][/ROW]
[ROW][C]20[/C][C]610763[/C][C]602616.817782152[/C][C]8146.18221784779[/C][/ROW]
[ROW][C]21[/C][C]612613[/C][C]595117.484448819[/C][C]17495.5155511811[/C][/ROW]
[ROW][C]22[/C][C]611324[/C][C]580353.984448819[/C][C]30970.0155511811[/C][/ROW]
[ROW][C]23[/C][C]594167[/C][C]564453.151115486[/C][C]29713.8488845144[/C][/ROW]
[ROW][C]24[/C][C]595454[/C][C]569713.809645669[/C][C]25740.1903543307[/C][/ROW]
[ROW][C]25[/C][C]590865[/C][C]582310.128018373[/C][C]8554.8719816274[/C][/ROW]
[ROW][C]26[/C][C]589379[/C][C]577388.294685039[/C][C]11990.7053149606[/C][/ROW]
[ROW][C]27[/C][C]584428[/C][C]567397.961351706[/C][C]17030.0386482940[/C][/ROW]
[ROW][C]28[/C][C]573100[/C][C]561132.294685039[/C][C]11967.7053149606[/C][/ROW]
[ROW][C]29[/C][C]567456[/C][C]551457.628018373[/C][C]15998.3719816273[/C][/ROW]
[ROW][C]30[/C][C]569028[/C][C]553084.294685039[/C][C]15943.7053149606[/C][/ROW]
[ROW][C]31[/C][C]620735[/C][C]606249.461351706[/C][C]14485.5386482940[/C][/ROW]
[ROW][C]32[/C][C]628884[/C][C]615658.628018373[/C][C]13225.3719816273[/C][/ROW]
[ROW][C]33[/C][C]628232[/C][C]608159.294685039[/C][C]20072.7053149606[/C][/ROW]
[ROW][C]34[/C][C]612117[/C][C]593395.794685039[/C][C]18721.2053149606[/C][/ROW]
[ROW][C]35[/C][C]595404[/C][C]577494.961351706[/C][C]17909.0386482940[/C][/ROW]
[ROW][C]36[/C][C]597141[/C][C]582755.61988189[/C][C]14385.3801181102[/C][/ROW]
[ROW][C]37[/C][C]593408[/C][C]595351.938254593[/C][C]-1943.93825459307[/C][/ROW]
[ROW][C]38[/C][C]590072[/C][C]590430.10492126[/C][C]-358.104921259847[/C][/ROW]
[ROW][C]39[/C][C]579799[/C][C]580439.771587927[/C][C]-640.771587926524[/C][/ROW]
[ROW][C]40[/C][C]574205[/C][C]574174.10492126[/C][C]30.8950787401495[/C][/ROW]
[ROW][C]41[/C][C]572775[/C][C]564499.438254593[/C][C]8275.5617454068[/C][/ROW]
[ROW][C]42[/C][C]572942[/C][C]566126.10492126[/C][C]6815.89507874013[/C][/ROW]
[ROW][C]43[/C][C]619567[/C][C]619291.271587927[/C][C]275.728412073468[/C][/ROW]
[ROW][C]44[/C][C]625809[/C][C]628700.438254593[/C][C]-2891.4382545932[/C][/ROW]
[ROW][C]45[/C][C]619916[/C][C]621201.10492126[/C][C]-1285.10492125986[/C][/ROW]
[ROW][C]46[/C][C]587625[/C][C]606437.60492126[/C][C]-18812.6049212599[/C][/ROW]
[ROW][C]47[/C][C]565742[/C][C]590536.771587927[/C][C]-24794.7715879265[/C][/ROW]
[ROW][C]48[/C][C]557274[/C][C]595797.43011811[/C][C]-38523.4301181102[/C][/ROW]
[ROW][C]49[/C][C]560576[/C][C]513530.649081365[/C][C]47045.3509186353[/C][/ROW]
[ROW][C]50[/C][C]548854[/C][C]508608.815748031[/C][C]40245.1842519685[/C][/ROW]
[ROW][C]51[/C][C]531673[/C][C]498618.482414698[/C][C]33054.5175853018[/C][/ROW]
[ROW][C]52[/C][C]525919[/C][C]492352.815748031[/C][C]33566.1842519685[/C][/ROW]
[ROW][C]53[/C][C]511038[/C][C]482678.149081365[/C][C]28359.8509186352[/C][/ROW]
[ROW][C]54[/C][C]498662[/C][C]484304.815748031[/C][C]14357.1842519685[/C][/ROW]
[ROW][C]55[/C][C]555362[/C][C]537469.982414698[/C][C]17892.0175853018[/C][/ROW]
[ROW][C]56[/C][C]564591[/C][C]546879.149081365[/C][C]17711.8509186352[/C][/ROW]
[ROW][C]57[/C][C]541657[/C][C]539379.815748031[/C][C]2277.1842519685[/C][/ROW]
[ROW][C]58[/C][C]527070[/C][C]524616.315748031[/C][C]2453.6842519685[/C][/ROW]
[ROW][C]59[/C][C]509846[/C][C]508715.482414698[/C][C]1130.51758530184[/C][/ROW]
[ROW][C]60[/C][C]514258[/C][C]513976.140944882[/C][C]281.859055118100[/C][/ROW]
[ROW][C]61[/C][C]516922[/C][C]526572.459317585[/C][C]-9650.4593175852[/C][/ROW]
[ROW][C]62[/C][C]507561[/C][C]521650.625984252[/C][C]-14089.6259842520[/C][/ROW]
[ROW][C]63[/C][C]492622[/C][C]511660.292650919[/C][C]-19038.2926509187[/C][/ROW]
[ROW][C]64[/C][C]490243[/C][C]505394.625984252[/C][C]-15151.6259842520[/C][/ROW]
[ROW][C]65[/C][C]469357[/C][C]495719.959317585[/C][C]-26362.9593175853[/C][/ROW]
[ROW][C]66[/C][C]477580[/C][C]497346.625984252[/C][C]-19766.625984252[/C][/ROW]
[ROW][C]67[/C][C]528379[/C][C]550511.792650919[/C][C]-22132.7926509187[/C][/ROW]
[ROW][C]68[/C][C]533590[/C][C]559920.959317585[/C][C]-26330.9593175853[/C][/ROW]
[ROW][C]69[/C][C]517945[/C][C]552421.625984252[/C][C]-34476.625984252[/C][/ROW]
[ROW][C]70[/C][C]506174[/C][C]537658.125984252[/C][C]-31484.125984252[/C][/ROW]
[ROW][C]71[/C][C]501866[/C][C]521757.292650919[/C][C]-19891.2926509187[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35562&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35562&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
1519164556226.507545932-37062.5075459323
2517009551304.674212598-34295.6742125984
3509933541314.340879265-31381.3408792651
4509127535048.674212598-25921.6742125984
5500857525374.007545932-24517.0075459317
6506971527000.674212598-20029.6742125984
7569323580165.840879265-10842.8408792651
8579714589575.007545932-9861.00754593171
9577992582075.674212598-4083.67421259838
10565464567312.174212598-1848.17421259840
11547344551411.340879265-4067.34087926507
12554788556671.999409449-1883.99940944881
13562325569268.317782152-6943.31778215212
14560854564346.484448819-3492.48444881888
15555332554356.151115486975.848884514445
16543599548090.484448819-4491.48444881889
17536662538415.817782152-1753.81778215221
18542722540042.4844488192679.51555118111
19593530593207.651115486322.348884514441
20610763602616.8177821528146.18221784779
21612613595117.48444881917495.5155511811
22611324580353.98444881930970.0155511811
23594167564453.15111548629713.8488845144
24595454569713.80964566925740.1903543307
25590865582310.1280183738554.8719816274
26589379577388.29468503911990.7053149606
27584428567397.96135170617030.0386482940
28573100561132.29468503911967.7053149606
29567456551457.62801837315998.3719816273
30569028553084.29468503915943.7053149606
31620735606249.46135170614485.5386482940
32628884615658.62801837313225.3719816273
33628232608159.29468503920072.7053149606
34612117593395.79468503918721.2053149606
35595404577494.96135170617909.0386482940
36597141582755.6198818914385.3801181102
37593408595351.938254593-1943.93825459307
38590072590430.10492126-358.104921259847
39579799580439.771587927-640.771587926524
40574205574174.1049212630.8950787401495
41572775564499.4382545938275.5617454068
42572942566126.104921266815.89507874013
43619567619291.271587927275.728412073468
44625809628700.438254593-2891.4382545932
45619916621201.10492126-1285.10492125986
46587625606437.60492126-18812.6049212599
47565742590536.771587927-24794.7715879265
48557274595797.43011811-38523.4301181102
49560576513530.64908136547045.3509186353
50548854508608.81574803140245.1842519685
51531673498618.48241469833054.5175853018
52525919492352.81574803133566.1842519685
53511038482678.14908136528359.8509186352
54498662484304.81574803114357.1842519685
55555362537469.98241469817892.0175853018
56564591546879.14908136517711.8509186352
57541657539379.8157480312277.1842519685
58527070524616.3157480312453.6842519685
59509846508715.4824146981130.51758530184
60514258513976.140944882281.859055118100
61516922526572.459317585-9650.4593175852
62507561521650.625984252-14089.6259842520
63492622511660.292650919-19038.2926509187
64490243505394.625984252-15151.6259842520
65469357495719.959317585-26362.9593175853
66477580497346.625984252-19766.625984252
67528379550511.792650919-22132.7926509187
68533590559920.959317585-26330.9593175853
69517945552421.625984252-34476.625984252
70506174537658.125984252-31484.125984252
71501866521757.292650919-19891.2926509187


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')