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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 06:29:10 -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/t1229866189z12hlml6spytas3.htm/, Retrieved Wed, 08 Oct 2025 23:56:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35568, Retrieved Wed, 08 Oct 2025 23:56:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords4
Estimated Impact436

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] [4] [2008-12-21 13:29:10] [783db4b4a0f63b73ca8b14666b7f4329] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
244752	0
244576	0
241572	0
240541	0
236089	0
236997	0
264579	0
270349	0
269645	0
267037	0
258113	0
262813	0
267413	0
267366	0
264777	0
258863	0
254844	0
254868	0
277267	0
285351	0
286602	0
283042	0
276687	0
277915	0
277128	0
277103	0
275037	0
270150	0
267140	0
264993	0
287259	0
291186	0
292300	0
288186	0
281477	0
282656	0
280190	0
280408	0
276836	0
275216	0
274352	0
271311	0
289802	0
290726	0
292300	0
278506	0
269826	0
265861	0
269034	1
264176	1
255198	1
253353	1
246057	1
235372	1
258556	1
260993	1
254663	1
250643	1
243422	1
247105	1
248541	1
245039	1
237080	1
237085	1
225554	1
226839	1
247934	1
248333	1
246969	1
245098	1
246263	1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35568&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]4 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=35568&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35568&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 time4 seconds
R Server'George Udny Yule' @ 72.249.76.132






Multiple Linear Regression - Estimated Regression Equation
WerklozenMannen[t] = + 255603.36761811 -43212.8518700788Kredietcrisis[t] + 5822.1028543306M1[t] + 3859.62500000003M2[t] -1399.18618766401M3[t] -4511.99737532804M4[t] -10271.4752296588M5[t] -13111.6197506561M6[t] + 8827.06906167981M7[t] + 11853.0912073491M8[t] + 10545.7800196851M9[t] + 4987.13549868769M10[t] -1697.67568897636M11[t] + 564.144520997377t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
WerklozenMannen[t] =  +  255603.36761811 -43212.8518700788Kredietcrisis[t] +  5822.1028543306M1[t] +  3859.62500000003M2[t] -1399.18618766401M3[t] -4511.99737532804M4[t] -10271.4752296588M5[t] -13111.6197506561M6[t] +  8827.06906167981M7[t] +  11853.0912073491M8[t] +  10545.7800196851M9[t] +  4987.13549868769M10[t] -1697.67568897636M11[t] +  564.144520997377t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35568&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]WerklozenMannen[t] =  +  255603.36761811 -43212.8518700788Kredietcrisis[t] +  5822.1028543306M1[t] +  3859.62500000003M2[t] -1399.18618766401M3[t] -4511.99737532804M4[t] -10271.4752296588M5[t] -13111.6197506561M6[t] +  8827.06906167981M7[t] +  11853.0912073491M8[t] +  10545.7800196851M9[t] +  4987.13549868769M10[t] -1697.67568897636M11[t] +  564.144520997377t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35568&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35568&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
WerklozenMannen[t] = + 255603.36761811 -43212.8518700788Kredietcrisis[t] + 5822.1028543306M1[t] + 3859.62500000003M2[t] -1399.18618766401M3[t] -4511.99737532804M4[t] -10271.4752296588M5[t] -13111.6197506561M6[t] + 8827.06906167981M7[t] + 11853.0912073491M8[t] + 10545.7800196851M9[t] + 4987.13549868769M10[t] -1697.67568897636M11[t] + 564.144520997377t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)255603.367618115252.91722848.659300
Kredietcrisis-43212.85187007884349.920781-9.934200
M15822.10285433065989.5562650.9720.3351360.167568
M23859.625000000035974.022130.64610.5208280.260414
M3-1399.186187664015960.131633-0.23480.8152380.407619
M4-4511.997375328045947.896289-0.75860.4512250.225613
M5-10271.47522965885937.326333-1.730.0890450.044523
M6-13111.61975065615928.43067-2.21170.0310150.015508
M78827.069061679815921.2168481.49080.141540.07077
M811853.09120734915915.6910192.00370.0498670.024933
M910545.78001968515911.8579171.78380.0797740.039887
M104987.135498687695909.7208340.84390.402260.20113
M11-1697.675688976365909.281612-0.28730.7749320.387466
t564.144520997377100.1811365.63121e-060

\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) & 255603.36761811 & 5252.917228 & 48.6593 & 0 & 0 \tabularnewline
Kredietcrisis & -43212.8518700788 & 4349.920781 & -9.9342 & 0 & 0 \tabularnewline
M1 & 5822.1028543306 & 5989.556265 & 0.972 & 0.335136 & 0.167568 \tabularnewline
M2 & 3859.62500000003 & 5974.02213 & 0.6461 & 0.520828 & 0.260414 \tabularnewline
M3 & -1399.18618766401 & 5960.131633 & -0.2348 & 0.815238 & 0.407619 \tabularnewline
M4 & -4511.99737532804 & 5947.896289 & -0.7586 & 0.451225 & 0.225613 \tabularnewline
M5 & -10271.4752296588 & 5937.326333 & -1.73 & 0.089045 & 0.044523 \tabularnewline
M6 & -13111.6197506561 & 5928.43067 & -2.2117 & 0.031015 & 0.015508 \tabularnewline
M7 & 8827.06906167981 & 5921.216848 & 1.4908 & 0.14154 & 0.07077 \tabularnewline
M8 & 11853.0912073491 & 5915.691019 & 2.0037 & 0.049867 & 0.024933 \tabularnewline
M9 & 10545.7800196851 & 5911.857917 & 1.7838 & 0.079774 & 0.039887 \tabularnewline
M10 & 4987.13549868769 & 5909.720834 & 0.8439 & 0.40226 & 0.20113 \tabularnewline
M11 & -1697.67568897636 & 5909.281612 & -0.2873 & 0.774932 & 0.387466 \tabularnewline
t & 564.144520997377 & 100.181136 & 5.6312 & 1e-06 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35568&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]255603.36761811[/C][C]5252.917228[/C][C]48.6593[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Kredietcrisis[/C][C]-43212.8518700788[/C][C]4349.920781[/C][C]-9.9342[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]5822.1028543306[/C][C]5989.556265[/C][C]0.972[/C][C]0.335136[/C][C]0.167568[/C][/ROW]
[ROW][C]M2[/C][C]3859.62500000003[/C][C]5974.02213[/C][C]0.6461[/C][C]0.520828[/C][C]0.260414[/C][/ROW]
[ROW][C]M3[/C][C]-1399.18618766401[/C][C]5960.131633[/C][C]-0.2348[/C][C]0.815238[/C][C]0.407619[/C][/ROW]
[ROW][C]M4[/C][C]-4511.99737532804[/C][C]5947.896289[/C][C]-0.7586[/C][C]0.451225[/C][C]0.225613[/C][/ROW]
[ROW][C]M5[/C][C]-10271.4752296588[/C][C]5937.326333[/C][C]-1.73[/C][C]0.089045[/C][C]0.044523[/C][/ROW]
[ROW][C]M6[/C][C]-13111.6197506561[/C][C]5928.43067[/C][C]-2.2117[/C][C]0.031015[/C][C]0.015508[/C][/ROW]
[ROW][C]M7[/C][C]8827.06906167981[/C][C]5921.216848[/C][C]1.4908[/C][C]0.14154[/C][C]0.07077[/C][/ROW]
[ROW][C]M8[/C][C]11853.0912073491[/C][C]5915.691019[/C][C]2.0037[/C][C]0.049867[/C][C]0.024933[/C][/ROW]
[ROW][C]M9[/C][C]10545.7800196851[/C][C]5911.857917[/C][C]1.7838[/C][C]0.079774[/C][C]0.039887[/C][/ROW]
[ROW][C]M10[/C][C]4987.13549868769[/C][C]5909.720834[/C][C]0.8439[/C][C]0.40226[/C][C]0.20113[/C][/ROW]
[ROW][C]M11[/C][C]-1697.67568897636[/C][C]5909.281612[/C][C]-0.2873[/C][C]0.774932[/C][C]0.387466[/C][/ROW]
[ROW][C]t[/C][C]564.144520997377[/C][C]100.181136[/C][C]5.6312[/C][C]1e-06[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35568&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35568&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)255603.367618115252.91722848.659300
Kredietcrisis-43212.85187007884349.920781-9.934200
M15822.10285433065989.5562650.9720.3351360.167568
M23859.625000000035974.022130.64610.5208280.260414
M3-1399.186187664015960.131633-0.23480.8152380.407619
M4-4511.997375328045947.896289-0.75860.4512250.225613
M5-10271.47522965885937.326333-1.730.0890450.044523
M6-13111.61975065615928.43067-2.21170.0310150.015508
M78827.069061679815921.2168481.49080.141540.07077
M811853.09120734915915.6910192.00370.0498670.024933
M910545.78001968515911.8579171.78380.0797740.039887
M104987.135498687695909.7208340.84390.402260.20113
M11-1697.675688976365909.281612-0.28730.7749320.387466
t564.144520997377100.1811365.63121e-060






Multiple Linear Regression - Regression Statistics
Multiple R0.864667974646391
R-squared0.747650706379092
Adjusted R-squared0.690097358711166
F-TEST (value)12.9905685190185
F-TEST (DF numerator)13
F-TEST (DF denominator)57
p-value1.22379884004431e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation9743.51567119177
Sum Squared Residuals5411357565.18130

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.864667974646391 \tabularnewline
R-squared & 0.747650706379092 \tabularnewline
Adjusted R-squared & 0.690097358711166 \tabularnewline
F-TEST (value) & 12.9905685190185 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 57 \tabularnewline
p-value & 1.22379884004431e-12 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 9743.51567119177 \tabularnewline
Sum Squared Residuals & 5411357565.18130 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35568&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.864667974646391[/C][/ROW]
[ROW][C]R-squared[/C][C]0.747650706379092[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.690097358711166[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]12.9905685190185[/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]1.22379884004431e-12[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]9743.51567119177[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]5411357565.18130[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35568&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35568&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 R0.864667974646391
R-squared0.747650706379092
Adjusted R-squared0.690097358711166
F-TEST (value)12.9905685190185
F-TEST (DF numerator)13
F-TEST (DF denominator)57
p-value1.22379884004431e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation9743.51567119177
Sum Squared Residuals5411357565.18130






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1244752261989.614993439-17237.614993439
2244576260591.281660105-16015.2816601050
3241572255896.614993438-14324.6149934383
4240541253347.948326772-12806.9483267716
5236089248152.614993438-12063.6149934383
6236997245876.614993438-8879.6149934383
7264579268379.448326772-3800.44832677160
8270349271969.614993438-1620.61499343829
9269645271226.448326772-1581.4483267716
10267037266231.948326772805.05167322839
11258113260111.281660105-1998.28166010495
12262813262373.101870079439.898129921308
13267413268759.349245407-1346.34924540667
14267366267361.0159120734.98408792652617
15264777262666.3492454072110.65075459319
16258863260117.68257874-1254.68257874014
17254844254922.349245407-78.3492454068005
18254868252646.3492454072221.65075459320
19277267275149.182578742117.81742125986
20285351278739.3492454076611.6507545932
21286602277996.182578748605.81742125986
22283042273001.6825787410040.3174212599
23276687266881.0159120739805.98408792653
24277915269142.8361220478772.16387795279
25277128275529.0834973751598.91650262481
26277103274130.7501640422972.249835958
27275037269436.0834973755600.91650262466
28270150266887.4168307093262.58316929133
29267140261692.0834973755447.91650262467
30264993259416.0834973755576.91650262467
31287259281918.9168307095340.08316929133
32291186285509.0834973755676.91650262467
33292300284765.9168307097534.08316929133
34288186279771.4168307098414.58316929133
35281477273650.7501640427826.249835958
36282656275912.5703740166743.42962598426
37280190282298.817749344-2108.81774934372
38280408280900.484416010-492.484416010527
39276836276205.817749344630.182250656141
40275216273657.1510826771558.84891732281
41274352268461.8177493445890.18225065614
42271311266185.8177493445125.18225065614
43289802288688.6510826771113.34891732281
44290726292278.817749344-1552.81774934386
45292300291535.651082677764.348917322807
46278506286541.151082677-8035.1510826772
47269826280420.484416010-10594.4844160105
48265861282682.304625984-16821.3046259843
49269034245855.70013123323178.2998687665
50264176244457.366797919718.6332020997
51255198239762.70013123415435.2998687664
52253353237214.03346456716138.9665354331
53246057232018.70013123414038.2998687664
54235372229742.7001312345629.29986876641
55258556252245.5334645676310.46653543306
56260993255835.7001312345157.2998687664
57254663255092.533464567-429.533464566933
58250643250098.033464567544.96653543307
59243422243977.36679790-555.36679790026
60247105246239.187007874865.812992126
61248541252625.434383202-4084.43438320198
62245039251227.101049869-6188.10104986879
63237080246532.434383202-9452.43438320213
64237085243983.767716535-6898.76771653546
65225554238788.434383202-13234.4343832021
66226839236512.434383202-9673.43438320211
67247934259015.267716535-11081.2677165355
68248333262605.434383202-14272.4343832021
69246969261862.267716535-14893.2677165355
70245098256867.767716535-11769.7677165355
71246263250747.101049869-4484.10104986878

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 244752 & 261989.614993439 & -17237.614993439 \tabularnewline
2 & 244576 & 260591.281660105 & -16015.2816601050 \tabularnewline
3 & 241572 & 255896.614993438 & -14324.6149934383 \tabularnewline
4 & 240541 & 253347.948326772 & -12806.9483267716 \tabularnewline
5 & 236089 & 248152.614993438 & -12063.6149934383 \tabularnewline
6 & 236997 & 245876.614993438 & -8879.6149934383 \tabularnewline
7 & 264579 & 268379.448326772 & -3800.44832677160 \tabularnewline
8 & 270349 & 271969.614993438 & -1620.61499343829 \tabularnewline
9 & 269645 & 271226.448326772 & -1581.4483267716 \tabularnewline
10 & 267037 & 266231.948326772 & 805.05167322839 \tabularnewline
11 & 258113 & 260111.281660105 & -1998.28166010495 \tabularnewline
12 & 262813 & 262373.101870079 & 439.898129921308 \tabularnewline
13 & 267413 & 268759.349245407 & -1346.34924540667 \tabularnewline
14 & 267366 & 267361.015912073 & 4.98408792652617 \tabularnewline
15 & 264777 & 262666.349245407 & 2110.65075459319 \tabularnewline
16 & 258863 & 260117.68257874 & -1254.68257874014 \tabularnewline
17 & 254844 & 254922.349245407 & -78.3492454068005 \tabularnewline
18 & 254868 & 252646.349245407 & 2221.65075459320 \tabularnewline
19 & 277267 & 275149.18257874 & 2117.81742125986 \tabularnewline
20 & 285351 & 278739.349245407 & 6611.6507545932 \tabularnewline
21 & 286602 & 277996.18257874 & 8605.81742125986 \tabularnewline
22 & 283042 & 273001.68257874 & 10040.3174212599 \tabularnewline
23 & 276687 & 266881.015912073 & 9805.98408792653 \tabularnewline
24 & 277915 & 269142.836122047 & 8772.16387795279 \tabularnewline
25 & 277128 & 275529.083497375 & 1598.91650262481 \tabularnewline
26 & 277103 & 274130.750164042 & 2972.249835958 \tabularnewline
27 & 275037 & 269436.083497375 & 5600.91650262466 \tabularnewline
28 & 270150 & 266887.416830709 & 3262.58316929133 \tabularnewline
29 & 267140 & 261692.083497375 & 5447.91650262467 \tabularnewline
30 & 264993 & 259416.083497375 & 5576.91650262467 \tabularnewline
31 & 287259 & 281918.916830709 & 5340.08316929133 \tabularnewline
32 & 291186 & 285509.083497375 & 5676.91650262467 \tabularnewline
33 & 292300 & 284765.916830709 & 7534.08316929133 \tabularnewline
34 & 288186 & 279771.416830709 & 8414.58316929133 \tabularnewline
35 & 281477 & 273650.750164042 & 7826.249835958 \tabularnewline
36 & 282656 & 275912.570374016 & 6743.42962598426 \tabularnewline
37 & 280190 & 282298.817749344 & -2108.81774934372 \tabularnewline
38 & 280408 & 280900.484416010 & -492.484416010527 \tabularnewline
39 & 276836 & 276205.817749344 & 630.182250656141 \tabularnewline
40 & 275216 & 273657.151082677 & 1558.84891732281 \tabularnewline
41 & 274352 & 268461.817749344 & 5890.18225065614 \tabularnewline
42 & 271311 & 266185.817749344 & 5125.18225065614 \tabularnewline
43 & 289802 & 288688.651082677 & 1113.34891732281 \tabularnewline
44 & 290726 & 292278.817749344 & -1552.81774934386 \tabularnewline
45 & 292300 & 291535.651082677 & 764.348917322807 \tabularnewline
46 & 278506 & 286541.151082677 & -8035.1510826772 \tabularnewline
47 & 269826 & 280420.484416010 & -10594.4844160105 \tabularnewline
48 & 265861 & 282682.304625984 & -16821.3046259843 \tabularnewline
49 & 269034 & 245855.700131233 & 23178.2998687665 \tabularnewline
50 & 264176 & 244457.3667979 & 19718.6332020997 \tabularnewline
51 & 255198 & 239762.700131234 & 15435.2998687664 \tabularnewline
52 & 253353 & 237214.033464567 & 16138.9665354331 \tabularnewline
53 & 246057 & 232018.700131234 & 14038.2998687664 \tabularnewline
54 & 235372 & 229742.700131234 & 5629.29986876641 \tabularnewline
55 & 258556 & 252245.533464567 & 6310.46653543306 \tabularnewline
56 & 260993 & 255835.700131234 & 5157.2998687664 \tabularnewline
57 & 254663 & 255092.533464567 & -429.533464566933 \tabularnewline
58 & 250643 & 250098.033464567 & 544.96653543307 \tabularnewline
59 & 243422 & 243977.36679790 & -555.36679790026 \tabularnewline
60 & 247105 & 246239.187007874 & 865.812992126 \tabularnewline
61 & 248541 & 252625.434383202 & -4084.43438320198 \tabularnewline
62 & 245039 & 251227.101049869 & -6188.10104986879 \tabularnewline
63 & 237080 & 246532.434383202 & -9452.43438320213 \tabularnewline
64 & 237085 & 243983.767716535 & -6898.76771653546 \tabularnewline
65 & 225554 & 238788.434383202 & -13234.4343832021 \tabularnewline
66 & 226839 & 236512.434383202 & -9673.43438320211 \tabularnewline
67 & 247934 & 259015.267716535 & -11081.2677165355 \tabularnewline
68 & 248333 & 262605.434383202 & -14272.4343832021 \tabularnewline
69 & 246969 & 261862.267716535 & -14893.2677165355 \tabularnewline
70 & 245098 & 256867.767716535 & -11769.7677165355 \tabularnewline
71 & 246263 & 250747.101049869 & -4484.10104986878 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35568&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]244752[/C][C]261989.614993439[/C][C]-17237.614993439[/C][/ROW]
[ROW][C]2[/C][C]244576[/C][C]260591.281660105[/C][C]-16015.2816601050[/C][/ROW]
[ROW][C]3[/C][C]241572[/C][C]255896.614993438[/C][C]-14324.6149934383[/C][/ROW]
[ROW][C]4[/C][C]240541[/C][C]253347.948326772[/C][C]-12806.9483267716[/C][/ROW]
[ROW][C]5[/C][C]236089[/C][C]248152.614993438[/C][C]-12063.6149934383[/C][/ROW]
[ROW][C]6[/C][C]236997[/C][C]245876.614993438[/C][C]-8879.6149934383[/C][/ROW]
[ROW][C]7[/C][C]264579[/C][C]268379.448326772[/C][C]-3800.44832677160[/C][/ROW]
[ROW][C]8[/C][C]270349[/C][C]271969.614993438[/C][C]-1620.61499343829[/C][/ROW]
[ROW][C]9[/C][C]269645[/C][C]271226.448326772[/C][C]-1581.4483267716[/C][/ROW]
[ROW][C]10[/C][C]267037[/C][C]266231.948326772[/C][C]805.05167322839[/C][/ROW]
[ROW][C]11[/C][C]258113[/C][C]260111.281660105[/C][C]-1998.28166010495[/C][/ROW]
[ROW][C]12[/C][C]262813[/C][C]262373.101870079[/C][C]439.898129921308[/C][/ROW]
[ROW][C]13[/C][C]267413[/C][C]268759.349245407[/C][C]-1346.34924540667[/C][/ROW]
[ROW][C]14[/C][C]267366[/C][C]267361.015912073[/C][C]4.98408792652617[/C][/ROW]
[ROW][C]15[/C][C]264777[/C][C]262666.349245407[/C][C]2110.65075459319[/C][/ROW]
[ROW][C]16[/C][C]258863[/C][C]260117.68257874[/C][C]-1254.68257874014[/C][/ROW]
[ROW][C]17[/C][C]254844[/C][C]254922.349245407[/C][C]-78.3492454068005[/C][/ROW]
[ROW][C]18[/C][C]254868[/C][C]252646.349245407[/C][C]2221.65075459320[/C][/ROW]
[ROW][C]19[/C][C]277267[/C][C]275149.18257874[/C][C]2117.81742125986[/C][/ROW]
[ROW][C]20[/C][C]285351[/C][C]278739.349245407[/C][C]6611.6507545932[/C][/ROW]
[ROW][C]21[/C][C]286602[/C][C]277996.18257874[/C][C]8605.81742125986[/C][/ROW]
[ROW][C]22[/C][C]283042[/C][C]273001.68257874[/C][C]10040.3174212599[/C][/ROW]
[ROW][C]23[/C][C]276687[/C][C]266881.015912073[/C][C]9805.98408792653[/C][/ROW]
[ROW][C]24[/C][C]277915[/C][C]269142.836122047[/C][C]8772.16387795279[/C][/ROW]
[ROW][C]25[/C][C]277128[/C][C]275529.083497375[/C][C]1598.91650262481[/C][/ROW]
[ROW][C]26[/C][C]277103[/C][C]274130.750164042[/C][C]2972.249835958[/C][/ROW]
[ROW][C]27[/C][C]275037[/C][C]269436.083497375[/C][C]5600.91650262466[/C][/ROW]
[ROW][C]28[/C][C]270150[/C][C]266887.416830709[/C][C]3262.58316929133[/C][/ROW]
[ROW][C]29[/C][C]267140[/C][C]261692.083497375[/C][C]5447.91650262467[/C][/ROW]
[ROW][C]30[/C][C]264993[/C][C]259416.083497375[/C][C]5576.91650262467[/C][/ROW]
[ROW][C]31[/C][C]287259[/C][C]281918.916830709[/C][C]5340.08316929133[/C][/ROW]
[ROW][C]32[/C][C]291186[/C][C]285509.083497375[/C][C]5676.91650262467[/C][/ROW]
[ROW][C]33[/C][C]292300[/C][C]284765.916830709[/C][C]7534.08316929133[/C][/ROW]
[ROW][C]34[/C][C]288186[/C][C]279771.416830709[/C][C]8414.58316929133[/C][/ROW]
[ROW][C]35[/C][C]281477[/C][C]273650.750164042[/C][C]7826.249835958[/C][/ROW]
[ROW][C]36[/C][C]282656[/C][C]275912.570374016[/C][C]6743.42962598426[/C][/ROW]
[ROW][C]37[/C][C]280190[/C][C]282298.817749344[/C][C]-2108.81774934372[/C][/ROW]
[ROW][C]38[/C][C]280408[/C][C]280900.484416010[/C][C]-492.484416010527[/C][/ROW]
[ROW][C]39[/C][C]276836[/C][C]276205.817749344[/C][C]630.182250656141[/C][/ROW]
[ROW][C]40[/C][C]275216[/C][C]273657.151082677[/C][C]1558.84891732281[/C][/ROW]
[ROW][C]41[/C][C]274352[/C][C]268461.817749344[/C][C]5890.18225065614[/C][/ROW]
[ROW][C]42[/C][C]271311[/C][C]266185.817749344[/C][C]5125.18225065614[/C][/ROW]
[ROW][C]43[/C][C]289802[/C][C]288688.651082677[/C][C]1113.34891732281[/C][/ROW]
[ROW][C]44[/C][C]290726[/C][C]292278.817749344[/C][C]-1552.81774934386[/C][/ROW]
[ROW][C]45[/C][C]292300[/C][C]291535.651082677[/C][C]764.348917322807[/C][/ROW]
[ROW][C]46[/C][C]278506[/C][C]286541.151082677[/C][C]-8035.1510826772[/C][/ROW]
[ROW][C]47[/C][C]269826[/C][C]280420.484416010[/C][C]-10594.4844160105[/C][/ROW]
[ROW][C]48[/C][C]265861[/C][C]282682.304625984[/C][C]-16821.3046259843[/C][/ROW]
[ROW][C]49[/C][C]269034[/C][C]245855.700131233[/C][C]23178.2998687665[/C][/ROW]
[ROW][C]50[/C][C]264176[/C][C]244457.3667979[/C][C]19718.6332020997[/C][/ROW]
[ROW][C]51[/C][C]255198[/C][C]239762.700131234[/C][C]15435.2998687664[/C][/ROW]
[ROW][C]52[/C][C]253353[/C][C]237214.033464567[/C][C]16138.9665354331[/C][/ROW]
[ROW][C]53[/C][C]246057[/C][C]232018.700131234[/C][C]14038.2998687664[/C][/ROW]
[ROW][C]54[/C][C]235372[/C][C]229742.700131234[/C][C]5629.29986876641[/C][/ROW]
[ROW][C]55[/C][C]258556[/C][C]252245.533464567[/C][C]6310.46653543306[/C][/ROW]
[ROW][C]56[/C][C]260993[/C][C]255835.700131234[/C][C]5157.2998687664[/C][/ROW]
[ROW][C]57[/C][C]254663[/C][C]255092.533464567[/C][C]-429.533464566933[/C][/ROW]
[ROW][C]58[/C][C]250643[/C][C]250098.033464567[/C][C]544.96653543307[/C][/ROW]
[ROW][C]59[/C][C]243422[/C][C]243977.36679790[/C][C]-555.36679790026[/C][/ROW]
[ROW][C]60[/C][C]247105[/C][C]246239.187007874[/C][C]865.812992126[/C][/ROW]
[ROW][C]61[/C][C]248541[/C][C]252625.434383202[/C][C]-4084.43438320198[/C][/ROW]
[ROW][C]62[/C][C]245039[/C][C]251227.101049869[/C][C]-6188.10104986879[/C][/ROW]
[ROW][C]63[/C][C]237080[/C][C]246532.434383202[/C][C]-9452.43438320213[/C][/ROW]
[ROW][C]64[/C][C]237085[/C][C]243983.767716535[/C][C]-6898.76771653546[/C][/ROW]
[ROW][C]65[/C][C]225554[/C][C]238788.434383202[/C][C]-13234.4343832021[/C][/ROW]
[ROW][C]66[/C][C]226839[/C][C]236512.434383202[/C][C]-9673.43438320211[/C][/ROW]
[ROW][C]67[/C][C]247934[/C][C]259015.267716535[/C][C]-11081.2677165355[/C][/ROW]
[ROW][C]68[/C][C]248333[/C][C]262605.434383202[/C][C]-14272.4343832021[/C][/ROW]
[ROW][C]69[/C][C]246969[/C][C]261862.267716535[/C][C]-14893.2677165355[/C][/ROW]
[ROW][C]70[/C][C]245098[/C][C]256867.767716535[/C][C]-11769.7677165355[/C][/ROW]
[ROW][C]71[/C][C]246263[/C][C]250747.101049869[/C][C]-4484.10104986878[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35568&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35568&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
1244752261989.614993439-17237.614993439
2244576260591.281660105-16015.2816601050
3241572255896.614993438-14324.6149934383
4240541253347.948326772-12806.9483267716
5236089248152.614993438-12063.6149934383
6236997245876.614993438-8879.6149934383
7264579268379.448326772-3800.44832677160
8270349271969.614993438-1620.61499343829
9269645271226.448326772-1581.4483267716
10267037266231.948326772805.05167322839
11258113260111.281660105-1998.28166010495
12262813262373.101870079439.898129921308
13267413268759.349245407-1346.34924540667
14267366267361.0159120734.98408792652617
15264777262666.3492454072110.65075459319
16258863260117.68257874-1254.68257874014
17254844254922.349245407-78.3492454068005
18254868252646.3492454072221.65075459320
19277267275149.182578742117.81742125986
20285351278739.3492454076611.6507545932
21286602277996.182578748605.81742125986
22283042273001.6825787410040.3174212599
23276687266881.0159120739805.98408792653
24277915269142.8361220478772.16387795279
25277128275529.0834973751598.91650262481
26277103274130.7501640422972.249835958
27275037269436.0834973755600.91650262466
28270150266887.4168307093262.58316929133
29267140261692.0834973755447.91650262467
30264993259416.0834973755576.91650262467
31287259281918.9168307095340.08316929133
32291186285509.0834973755676.91650262467
33292300284765.9168307097534.08316929133
34288186279771.4168307098414.58316929133
35281477273650.7501640427826.249835958
36282656275912.5703740166743.42962598426
37280190282298.817749344-2108.81774934372
38280408280900.484416010-492.484416010527
39276836276205.817749344630.182250656141
40275216273657.1510826771558.84891732281
41274352268461.8177493445890.18225065614
42271311266185.8177493445125.18225065614
43289802288688.6510826771113.34891732281
44290726292278.817749344-1552.81774934386
45292300291535.651082677764.348917322807
46278506286541.151082677-8035.1510826772
47269826280420.484416010-10594.4844160105
48265861282682.304625984-16821.3046259843
49269034245855.70013123323178.2998687665
50264176244457.366797919718.6332020997
51255198239762.70013123415435.2998687664
52253353237214.03346456716138.9665354331
53246057232018.70013123414038.2998687664
54235372229742.7001312345629.29986876641
55258556252245.5334645676310.46653543306
56260993255835.7001312345157.2998687664
57254663255092.533464567-429.533464566933
58250643250098.033464567544.96653543307
59243422243977.36679790-555.36679790026
60247105246239.187007874865.812992126
61248541252625.434383202-4084.43438320198
62245039251227.101049869-6188.10104986879
63237080246532.434383202-9452.43438320213
64237085243983.767716535-6898.76771653546
65225554238788.434383202-13234.4343832021
66226839236512.434383202-9673.43438320211
67247934259015.267716535-11081.2677165355
68248333262605.434383202-14272.4343832021
69246969261862.267716535-14893.2677165355
70245098256867.767716535-11769.7677165355
71246263250747.101049869-4484.10104986878


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')