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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 06:33:45 -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/t1229866491b7hpo8z2w3wug3g.htm/, Retrieved Mon, 23 Jun 2025 00:48:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35574, Retrieved Mon, 23 Jun 2025 00:48:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords6
Estimated Impact418

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] [6] [2008-12-21 13:33:45] [783db4b4a0f63b73ca8b14666b7f4329] [Current]
-    D        [Multiple Regression] [8] [2008-12-21 13:38:48] [fe7291e888d31b8c4db0b24d6c0f75c6]
-   PD        [Multiple Regression] [7] [2008-12-21 13:40:29] [fe7291e888d31b8c4db0b24d6c0f75c6]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
274412	0
272433	0
268361	0
268586	0
264768	0
269974	0
304744	0
309365	0
308347	0
298427	0
289231	0
291975	0
294912	0
293488	0
290555	0
284736	0
281818	0
287854	0
316263	0
325412	0
326011	0
328282	0
317480	0
317539	0
313737	0
312276	0
309391	0
302950	0
300316	0
304035	0
333476	0
337698	0
335932	0
323931	0
313927	0
314485	0
313218	0
309664	0
302963	0
298989	0
298423	0
301631	0
329765	0
335083	0
327616	0
309119	0
295916	0
291413	0
291542	1
284678	1
276475	1
272566	1
264981	1
263290	1
296806	1
303598	1
286994	1
276427	1
266424	1
267153	1
268381	1
262522	1
255542	1
253158	1
243803	1
250741	1
280445	1
285257	1
270976	1
261076	1
255603	1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35574&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]3 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=35574&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35574&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 time3 seconds
R Server'George Udny Yule' @ 72.249.76.132






Multiple Linear Regression - Estimated Regression Equation
WerklozenVrouwen[t] = + 288026.821555118 -51650.2475393702Kredietcrisis[t] + 5687.39799868752M1[t] + 1641.22500000003M2[t] -4177.1146653543M3[t] -8416.78766404194M4[t] -13418.7939960630M5[t] -10038.8003280840M6[t] + 20100.8600065617M7[t] + 25397.1870078740M8[t] + 18118.3473425197M9[t] + 7826.67434383204M10[t] -2476.16532152230M11[t] + 522.672998687666t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
WerklozenVrouwen[t] =  +  288026.821555118 -51650.2475393702Kredietcrisis[t] +  5687.39799868752M1[t] +  1641.22500000003M2[t] -4177.1146653543M3[t] -8416.78766404194M4[t] -13418.7939960630M5[t] -10038.8003280840M6[t] +  20100.8600065617M7[t] +  25397.1870078740M8[t] +  18118.3473425197M9[t] +  7826.67434383204M10[t] -2476.16532152230M11[t] +  522.672998687666t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35574&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]WerklozenVrouwen[t] =  +  288026.821555118 -51650.2475393702Kredietcrisis[t] +  5687.39799868752M1[t] +  1641.22500000003M2[t] -4177.1146653543M3[t] -8416.78766404194M4[t] -13418.7939960630M5[t] -10038.8003280840M6[t] +  20100.8600065617M7[t] +  25397.1870078740M8[t] +  18118.3473425197M9[t] +  7826.67434383204M10[t] -2476.16532152230M11[t] +  522.672998687666t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35574&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35574&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
WerklozenVrouwen[t] = + 288026.821555118 -51650.2475393702Kredietcrisis[t] + 5687.39799868752M1[t] + 1641.22500000003M2[t] -4177.1146653543M3[t] -8416.78766404194M4[t] -13418.7939960630M5[t] -10038.8003280840M6[t] + 20100.8600065617M7[t] + 25397.1870078740M8[t] + 18118.3473425197M9[t] + 7826.67434383204M10[t] -2476.16532152230M11[t] + 522.672998687666t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)288026.8215551186698.42245642.999200
Kredietcrisis-51650.24753937025546.938164-9.311500
M15687.397998687527637.7708710.74460.4595480.229774
M21641.225000000037617.962030.21540.8301920.415096
M3-4177.11466535437600.249127-0.54960.5847390.29237
M4-8416.787664041947584.646844-1.10970.2717820.135891
M5-13418.79399606307571.168232-1.77240.081680.04084
M6-10038.80032808407559.824648-1.32790.18950.09475
M720100.86000656177550.6257162.66210.0100720.005036
M825397.18700787407543.5792823.36670.0013680.000684
M918118.34734251977538.6913812.40340.019520.00976
M107826.674343832047535.9662131.03860.3033880.151694
M11-2476.165321522307535.406125-0.32860.7436590.37183
t522.672998687666127.7491234.09140.0001366.8e-05

\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) & 288026.821555118 & 6698.422456 & 42.9992 & 0 & 0 \tabularnewline
Kredietcrisis & -51650.2475393702 & 5546.938164 & -9.3115 & 0 & 0 \tabularnewline
M1 & 5687.39799868752 & 7637.770871 & 0.7446 & 0.459548 & 0.229774 \tabularnewline
M2 & 1641.22500000003 & 7617.96203 & 0.2154 & 0.830192 & 0.415096 \tabularnewline
M3 & -4177.1146653543 & 7600.249127 & -0.5496 & 0.584739 & 0.29237 \tabularnewline
M4 & -8416.78766404194 & 7584.646844 & -1.1097 & 0.271782 & 0.135891 \tabularnewline
M5 & -13418.7939960630 & 7571.168232 & -1.7724 & 0.08168 & 0.04084 \tabularnewline
M6 & -10038.8003280840 & 7559.824648 & -1.3279 & 0.1895 & 0.09475 \tabularnewline
M7 & 20100.8600065617 & 7550.625716 & 2.6621 & 0.010072 & 0.005036 \tabularnewline
M8 & 25397.1870078740 & 7543.579282 & 3.3667 & 0.001368 & 0.000684 \tabularnewline
M9 & 18118.3473425197 & 7538.691381 & 2.4034 & 0.01952 & 0.00976 \tabularnewline
M10 & 7826.67434383204 & 7535.966213 & 1.0386 & 0.303388 & 0.151694 \tabularnewline
M11 & -2476.16532152230 & 7535.406125 & -0.3286 & 0.743659 & 0.37183 \tabularnewline
t & 522.672998687666 & 127.749123 & 4.0914 & 0.000136 & 6.8e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35574&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]288026.821555118[/C][C]6698.422456[/C][C]42.9992[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Kredietcrisis[/C][C]-51650.2475393702[/C][C]5546.938164[/C][C]-9.3115[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]5687.39799868752[/C][C]7637.770871[/C][C]0.7446[/C][C]0.459548[/C][C]0.229774[/C][/ROW]
[ROW][C]M2[/C][C]1641.22500000003[/C][C]7617.96203[/C][C]0.2154[/C][C]0.830192[/C][C]0.415096[/C][/ROW]
[ROW][C]M3[/C][C]-4177.1146653543[/C][C]7600.249127[/C][C]-0.5496[/C][C]0.584739[/C][C]0.29237[/C][/ROW]
[ROW][C]M4[/C][C]-8416.78766404194[/C][C]7584.646844[/C][C]-1.1097[/C][C]0.271782[/C][C]0.135891[/C][/ROW]
[ROW][C]M5[/C][C]-13418.7939960630[/C][C]7571.168232[/C][C]-1.7724[/C][C]0.08168[/C][C]0.04084[/C][/ROW]
[ROW][C]M6[/C][C]-10038.8003280840[/C][C]7559.824648[/C][C]-1.3279[/C][C]0.1895[/C][C]0.09475[/C][/ROW]
[ROW][C]M7[/C][C]20100.8600065617[/C][C]7550.625716[/C][C]2.6621[/C][C]0.010072[/C][C]0.005036[/C][/ROW]
[ROW][C]M8[/C][C]25397.1870078740[/C][C]7543.579282[/C][C]3.3667[/C][C]0.001368[/C][C]0.000684[/C][/ROW]
[ROW][C]M9[/C][C]18118.3473425197[/C][C]7538.691381[/C][C]2.4034[/C][C]0.01952[/C][C]0.00976[/C][/ROW]
[ROW][C]M10[/C][C]7826.67434383204[/C][C]7535.966213[/C][C]1.0386[/C][C]0.303388[/C][C]0.151694[/C][/ROW]
[ROW][C]M11[/C][C]-2476.16532152230[/C][C]7535.406125[/C][C]-0.3286[/C][C]0.743659[/C][C]0.37183[/C][/ROW]
[ROW][C]t[/C][C]522.672998687666[/C][C]127.749123[/C][C]4.0914[/C][C]0.000136[/C][C]6.8e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35574&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35574&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)288026.8215551186698.42245642.999200
Kredietcrisis-51650.24753937025546.938164-9.311500
M15687.397998687527637.7708710.74460.4595480.229774
M21641.225000000037617.962030.21540.8301920.415096
M3-4177.11466535437600.249127-0.54960.5847390.29237
M4-8416.787664041947584.646844-1.10970.2717820.135891
M5-13418.79399606307571.168232-1.77240.081680.04084
M6-10038.80032808407559.824648-1.32790.18950.09475
M720100.86000656177550.6257162.66210.0100720.005036
M825397.18700787407543.5792823.36670.0013680.000684
M918118.34734251977538.6913812.40340.019520.00976
M107826.674343832047535.9662131.03860.3033880.151694
M11-2476.165321522307535.406125-0.32860.7436590.37183
t522.672998687666127.7491234.09140.0001366.8e-05






Multiple Linear Regression - Regression Statistics
Multiple R0.881973132950892
R-squared0.777876607247212
Adjusted R-squared0.727216886093068
F-TEST (value)15.3549326669275
F-TEST (DF numerator)13
F-TEST (DF denominator)57
p-value3.97459842815806e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation12424.7501620641
Sum Squared Residuals8799341745.6136

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.881973132950892 \tabularnewline
R-squared & 0.777876607247212 \tabularnewline
Adjusted R-squared & 0.727216886093068 \tabularnewline
F-TEST (value) & 15.3549326669275 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 57 \tabularnewline
p-value & 3.97459842815806e-14 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 12424.7501620641 \tabularnewline
Sum Squared Residuals & 8799341745.6136 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35574&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.881973132950892[/C][/ROW]
[ROW][C]R-squared[/C][C]0.777876607247212[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.727216886093068[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]15.3549326669275[/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]3.97459842815806e-14[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]12424.7501620641[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]8799341745.6136[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35574&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35574&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 R0.881973132950892
R-squared0.777876607247212
Adjusted R-squared0.727216886093068
F-TEST (value)15.3549326669275
F-TEST (DF numerator)13
F-TEST (DF denominator)57
p-value3.97459842815806e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation12424.7501620641
Sum Squared Residuals8799341745.6136






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1274412294236.892552494-19824.8925524944
2272433290713.392552493-18280.3925524934
3268361285417.725885827-17056.7258858267
4268586281700.725885827-13114.7258858267
5264768277221.392552493-12453.3925524934
6269974281124.05921916-11150.0592191601
7304744311786.392552493-7042.3925524934
8309365317605.392552493-8240.3925524934
9308347310849.225885827-2502.22588582670
10298427301080.225885827-2653.22588582672
11289231291300.05921916-2069.05921916005
12291975294298.89753937-2323.89753937001
13294912300508.968536745-5596.96853674519
14293488296985.468536745-3497.46853674538
15290555291689.801870079-1134.80187007871
16284736287972.801870079-3236.80187007872
17281818283493.468536745-1675.46853674538
18287854287396.135203412457.864796587952
19316263318058.468536745-1795.46853674538
20325412323877.4685367451534.53146325462
21326011317121.3018700798889.69812992127
22328282307352.30187007920929.6981299213
23317480297572.13520341219907.8647965879
24317539300570.97352362216968.026476378
25313737306781.0445209976955.95547900281
26312276303257.5445209979018.4554790026
27309391297961.87785433111429.1221456693
28302950294244.8778543318705.12214566928
29300316289765.54452099710550.4554790026
30304035293668.21118766410366.7888123360
31333476324330.5445209979145.45547900262
32337698330149.5445209977548.45547900262
33335932323393.37785433112538.6221456693
34323931313624.37785433110306.6221456693
35313927303844.21118766410082.7888123360
36314485306843.0495078747641.95049212599
37313218313053.120505249164.879494750809
38309664309529.620505249134.379494750606
39302963304233.953838583-1270.95383858271
40298989300516.953838583-1527.95383858272
41298423296037.6205052492385.37949475062
42301631299940.2871719161690.71282808396
43329765330602.620505249-837.620505249368
44335083336421.620505249-1338.62050524938
45327616329665.453838583-2049.45383858272
46309119319896.453838583-10777.4538385827
47295916310116.287171916-14200.2871719160
48291413313115.125492126-21702.125492126
49291542267674.94895013123867.0510498690
50284678264151.44895013120526.5510498687
51276475258855.78228346517619.2177165354
52272566255138.78228346517427.2177165354
53264981250659.44895013114321.5510498688
54263290254562.1156167988727.8843832021
55296806285224.44895013111581.5510498688
56303598291043.44895013112554.5510498688
57286994284287.2822834652706.71771653542
58276427274518.2822834651908.71771653543
59266424264738.1156167981685.88438320210
60267153267736.953937008-583.953937007859
61268381273947.024934383-5566.02493438304
62262522270423.524934383-7901.52493438325
63255542265127.858267717-9585.85826771656
64253158261410.858267717-8252.85826771657
65243803256931.524934383-13128.5249343832
66250741260834.19160105-10093.1916010499
67280445291496.524934383-11051.5249343832
68285257297315.524934383-12058.5249343832
69270976290559.358267717-19583.3582677166
70261076280790.358267717-19714.3582677166
71255603271010.19160105-15407.1916010499

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 274412 & 294236.892552494 & -19824.8925524944 \tabularnewline
2 & 272433 & 290713.392552493 & -18280.3925524934 \tabularnewline
3 & 268361 & 285417.725885827 & -17056.7258858267 \tabularnewline
4 & 268586 & 281700.725885827 & -13114.7258858267 \tabularnewline
5 & 264768 & 277221.392552493 & -12453.3925524934 \tabularnewline
6 & 269974 & 281124.05921916 & -11150.0592191601 \tabularnewline
7 & 304744 & 311786.392552493 & -7042.3925524934 \tabularnewline
8 & 309365 & 317605.392552493 & -8240.3925524934 \tabularnewline
9 & 308347 & 310849.225885827 & -2502.22588582670 \tabularnewline
10 & 298427 & 301080.225885827 & -2653.22588582672 \tabularnewline
11 & 289231 & 291300.05921916 & -2069.05921916005 \tabularnewline
12 & 291975 & 294298.89753937 & -2323.89753937001 \tabularnewline
13 & 294912 & 300508.968536745 & -5596.96853674519 \tabularnewline
14 & 293488 & 296985.468536745 & -3497.46853674538 \tabularnewline
15 & 290555 & 291689.801870079 & -1134.80187007871 \tabularnewline
16 & 284736 & 287972.801870079 & -3236.80187007872 \tabularnewline
17 & 281818 & 283493.468536745 & -1675.46853674538 \tabularnewline
18 & 287854 & 287396.135203412 & 457.864796587952 \tabularnewline
19 & 316263 & 318058.468536745 & -1795.46853674538 \tabularnewline
20 & 325412 & 323877.468536745 & 1534.53146325462 \tabularnewline
21 & 326011 & 317121.301870079 & 8889.69812992127 \tabularnewline
22 & 328282 & 307352.301870079 & 20929.6981299213 \tabularnewline
23 & 317480 & 297572.135203412 & 19907.8647965879 \tabularnewline
24 & 317539 & 300570.973523622 & 16968.026476378 \tabularnewline
25 & 313737 & 306781.044520997 & 6955.95547900281 \tabularnewline
26 & 312276 & 303257.544520997 & 9018.4554790026 \tabularnewline
27 & 309391 & 297961.877854331 & 11429.1221456693 \tabularnewline
28 & 302950 & 294244.877854331 & 8705.12214566928 \tabularnewline
29 & 300316 & 289765.544520997 & 10550.4554790026 \tabularnewline
30 & 304035 & 293668.211187664 & 10366.7888123360 \tabularnewline
31 & 333476 & 324330.544520997 & 9145.45547900262 \tabularnewline
32 & 337698 & 330149.544520997 & 7548.45547900262 \tabularnewline
33 & 335932 & 323393.377854331 & 12538.6221456693 \tabularnewline
34 & 323931 & 313624.377854331 & 10306.6221456693 \tabularnewline
35 & 313927 & 303844.211187664 & 10082.7888123360 \tabularnewline
36 & 314485 & 306843.049507874 & 7641.95049212599 \tabularnewline
37 & 313218 & 313053.120505249 & 164.879494750809 \tabularnewline
38 & 309664 & 309529.620505249 & 134.379494750606 \tabularnewline
39 & 302963 & 304233.953838583 & -1270.95383858271 \tabularnewline
40 & 298989 & 300516.953838583 & -1527.95383858272 \tabularnewline
41 & 298423 & 296037.620505249 & 2385.37949475062 \tabularnewline
42 & 301631 & 299940.287171916 & 1690.71282808396 \tabularnewline
43 & 329765 & 330602.620505249 & -837.620505249368 \tabularnewline
44 & 335083 & 336421.620505249 & -1338.62050524938 \tabularnewline
45 & 327616 & 329665.453838583 & -2049.45383858272 \tabularnewline
46 & 309119 & 319896.453838583 & -10777.4538385827 \tabularnewline
47 & 295916 & 310116.287171916 & -14200.2871719160 \tabularnewline
48 & 291413 & 313115.125492126 & -21702.125492126 \tabularnewline
49 & 291542 & 267674.948950131 & 23867.0510498690 \tabularnewline
50 & 284678 & 264151.448950131 & 20526.5510498687 \tabularnewline
51 & 276475 & 258855.782283465 & 17619.2177165354 \tabularnewline
52 & 272566 & 255138.782283465 & 17427.2177165354 \tabularnewline
53 & 264981 & 250659.448950131 & 14321.5510498688 \tabularnewline
54 & 263290 & 254562.115616798 & 8727.8843832021 \tabularnewline
55 & 296806 & 285224.448950131 & 11581.5510498688 \tabularnewline
56 & 303598 & 291043.448950131 & 12554.5510498688 \tabularnewline
57 & 286994 & 284287.282283465 & 2706.71771653542 \tabularnewline
58 & 276427 & 274518.282283465 & 1908.71771653543 \tabularnewline
59 & 266424 & 264738.115616798 & 1685.88438320210 \tabularnewline
60 & 267153 & 267736.953937008 & -583.953937007859 \tabularnewline
61 & 268381 & 273947.024934383 & -5566.02493438304 \tabularnewline
62 & 262522 & 270423.524934383 & -7901.52493438325 \tabularnewline
63 & 255542 & 265127.858267717 & -9585.85826771656 \tabularnewline
64 & 253158 & 261410.858267717 & -8252.85826771657 \tabularnewline
65 & 243803 & 256931.524934383 & -13128.5249343832 \tabularnewline
66 & 250741 & 260834.19160105 & -10093.1916010499 \tabularnewline
67 & 280445 & 291496.524934383 & -11051.5249343832 \tabularnewline
68 & 285257 & 297315.524934383 & -12058.5249343832 \tabularnewline
69 & 270976 & 290559.358267717 & -19583.3582677166 \tabularnewline
70 & 261076 & 280790.358267717 & -19714.3582677166 \tabularnewline
71 & 255603 & 271010.19160105 & -15407.1916010499 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35574&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]274412[/C][C]294236.892552494[/C][C]-19824.8925524944[/C][/ROW]
[ROW][C]2[/C][C]272433[/C][C]290713.392552493[/C][C]-18280.3925524934[/C][/ROW]
[ROW][C]3[/C][C]268361[/C][C]285417.725885827[/C][C]-17056.7258858267[/C][/ROW]
[ROW][C]4[/C][C]268586[/C][C]281700.725885827[/C][C]-13114.7258858267[/C][/ROW]
[ROW][C]5[/C][C]264768[/C][C]277221.392552493[/C][C]-12453.3925524934[/C][/ROW]
[ROW][C]6[/C][C]269974[/C][C]281124.05921916[/C][C]-11150.0592191601[/C][/ROW]
[ROW][C]7[/C][C]304744[/C][C]311786.392552493[/C][C]-7042.3925524934[/C][/ROW]
[ROW][C]8[/C][C]309365[/C][C]317605.392552493[/C][C]-8240.3925524934[/C][/ROW]
[ROW][C]9[/C][C]308347[/C][C]310849.225885827[/C][C]-2502.22588582670[/C][/ROW]
[ROW][C]10[/C][C]298427[/C][C]301080.225885827[/C][C]-2653.22588582672[/C][/ROW]
[ROW][C]11[/C][C]289231[/C][C]291300.05921916[/C][C]-2069.05921916005[/C][/ROW]
[ROW][C]12[/C][C]291975[/C][C]294298.89753937[/C][C]-2323.89753937001[/C][/ROW]
[ROW][C]13[/C][C]294912[/C][C]300508.968536745[/C][C]-5596.96853674519[/C][/ROW]
[ROW][C]14[/C][C]293488[/C][C]296985.468536745[/C][C]-3497.46853674538[/C][/ROW]
[ROW][C]15[/C][C]290555[/C][C]291689.801870079[/C][C]-1134.80187007871[/C][/ROW]
[ROW][C]16[/C][C]284736[/C][C]287972.801870079[/C][C]-3236.80187007872[/C][/ROW]
[ROW][C]17[/C][C]281818[/C][C]283493.468536745[/C][C]-1675.46853674538[/C][/ROW]
[ROW][C]18[/C][C]287854[/C][C]287396.135203412[/C][C]457.864796587952[/C][/ROW]
[ROW][C]19[/C][C]316263[/C][C]318058.468536745[/C][C]-1795.46853674538[/C][/ROW]
[ROW][C]20[/C][C]325412[/C][C]323877.468536745[/C][C]1534.53146325462[/C][/ROW]
[ROW][C]21[/C][C]326011[/C][C]317121.301870079[/C][C]8889.69812992127[/C][/ROW]
[ROW][C]22[/C][C]328282[/C][C]307352.301870079[/C][C]20929.6981299213[/C][/ROW]
[ROW][C]23[/C][C]317480[/C][C]297572.135203412[/C][C]19907.8647965879[/C][/ROW]
[ROW][C]24[/C][C]317539[/C][C]300570.973523622[/C][C]16968.026476378[/C][/ROW]
[ROW][C]25[/C][C]313737[/C][C]306781.044520997[/C][C]6955.95547900281[/C][/ROW]
[ROW][C]26[/C][C]312276[/C][C]303257.544520997[/C][C]9018.4554790026[/C][/ROW]
[ROW][C]27[/C][C]309391[/C][C]297961.877854331[/C][C]11429.1221456693[/C][/ROW]
[ROW][C]28[/C][C]302950[/C][C]294244.877854331[/C][C]8705.12214566928[/C][/ROW]
[ROW][C]29[/C][C]300316[/C][C]289765.544520997[/C][C]10550.4554790026[/C][/ROW]
[ROW][C]30[/C][C]304035[/C][C]293668.211187664[/C][C]10366.7888123360[/C][/ROW]
[ROW][C]31[/C][C]333476[/C][C]324330.544520997[/C][C]9145.45547900262[/C][/ROW]
[ROW][C]32[/C][C]337698[/C][C]330149.544520997[/C][C]7548.45547900262[/C][/ROW]
[ROW][C]33[/C][C]335932[/C][C]323393.377854331[/C][C]12538.6221456693[/C][/ROW]
[ROW][C]34[/C][C]323931[/C][C]313624.377854331[/C][C]10306.6221456693[/C][/ROW]
[ROW][C]35[/C][C]313927[/C][C]303844.211187664[/C][C]10082.7888123360[/C][/ROW]
[ROW][C]36[/C][C]314485[/C][C]306843.049507874[/C][C]7641.95049212599[/C][/ROW]
[ROW][C]37[/C][C]313218[/C][C]313053.120505249[/C][C]164.879494750809[/C][/ROW]
[ROW][C]38[/C][C]309664[/C][C]309529.620505249[/C][C]134.379494750606[/C][/ROW]
[ROW][C]39[/C][C]302963[/C][C]304233.953838583[/C][C]-1270.95383858271[/C][/ROW]
[ROW][C]40[/C][C]298989[/C][C]300516.953838583[/C][C]-1527.95383858272[/C][/ROW]
[ROW][C]41[/C][C]298423[/C][C]296037.620505249[/C][C]2385.37949475062[/C][/ROW]
[ROW][C]42[/C][C]301631[/C][C]299940.287171916[/C][C]1690.71282808396[/C][/ROW]
[ROW][C]43[/C][C]329765[/C][C]330602.620505249[/C][C]-837.620505249368[/C][/ROW]
[ROW][C]44[/C][C]335083[/C][C]336421.620505249[/C][C]-1338.62050524938[/C][/ROW]
[ROW][C]45[/C][C]327616[/C][C]329665.453838583[/C][C]-2049.45383858272[/C][/ROW]
[ROW][C]46[/C][C]309119[/C][C]319896.453838583[/C][C]-10777.4538385827[/C][/ROW]
[ROW][C]47[/C][C]295916[/C][C]310116.287171916[/C][C]-14200.2871719160[/C][/ROW]
[ROW][C]48[/C][C]291413[/C][C]313115.125492126[/C][C]-21702.125492126[/C][/ROW]
[ROW][C]49[/C][C]291542[/C][C]267674.948950131[/C][C]23867.0510498690[/C][/ROW]
[ROW][C]50[/C][C]284678[/C][C]264151.448950131[/C][C]20526.5510498687[/C][/ROW]
[ROW][C]51[/C][C]276475[/C][C]258855.782283465[/C][C]17619.2177165354[/C][/ROW]
[ROW][C]52[/C][C]272566[/C][C]255138.782283465[/C][C]17427.2177165354[/C][/ROW]
[ROW][C]53[/C][C]264981[/C][C]250659.448950131[/C][C]14321.5510498688[/C][/ROW]
[ROW][C]54[/C][C]263290[/C][C]254562.115616798[/C][C]8727.8843832021[/C][/ROW]
[ROW][C]55[/C][C]296806[/C][C]285224.448950131[/C][C]11581.5510498688[/C][/ROW]
[ROW][C]56[/C][C]303598[/C][C]291043.448950131[/C][C]12554.5510498688[/C][/ROW]
[ROW][C]57[/C][C]286994[/C][C]284287.282283465[/C][C]2706.71771653542[/C][/ROW]
[ROW][C]58[/C][C]276427[/C][C]274518.282283465[/C][C]1908.71771653543[/C][/ROW]
[ROW][C]59[/C][C]266424[/C][C]264738.115616798[/C][C]1685.88438320210[/C][/ROW]
[ROW][C]60[/C][C]267153[/C][C]267736.953937008[/C][C]-583.953937007859[/C][/ROW]
[ROW][C]61[/C][C]268381[/C][C]273947.024934383[/C][C]-5566.02493438304[/C][/ROW]
[ROW][C]62[/C][C]262522[/C][C]270423.524934383[/C][C]-7901.52493438325[/C][/ROW]
[ROW][C]63[/C][C]255542[/C][C]265127.858267717[/C][C]-9585.85826771656[/C][/ROW]
[ROW][C]64[/C][C]253158[/C][C]261410.858267717[/C][C]-8252.85826771657[/C][/ROW]
[ROW][C]65[/C][C]243803[/C][C]256931.524934383[/C][C]-13128.5249343832[/C][/ROW]
[ROW][C]66[/C][C]250741[/C][C]260834.19160105[/C][C]-10093.1916010499[/C][/ROW]
[ROW][C]67[/C][C]280445[/C][C]291496.524934383[/C][C]-11051.5249343832[/C][/ROW]
[ROW][C]68[/C][C]285257[/C][C]297315.524934383[/C][C]-12058.5249343832[/C][/ROW]
[ROW][C]69[/C][C]270976[/C][C]290559.358267717[/C][C]-19583.3582677166[/C][/ROW]
[ROW][C]70[/C][C]261076[/C][C]280790.358267717[/C][C]-19714.3582677166[/C][/ROW]
[ROW][C]71[/C][C]255603[/C][C]271010.19160105[/C][C]-15407.1916010499[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35574&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35574&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
1274412294236.892552494-19824.8925524944
2272433290713.392552493-18280.3925524934
3268361285417.725885827-17056.7258858267
4268586281700.725885827-13114.7258858267
5264768277221.392552493-12453.3925524934
6269974281124.05921916-11150.0592191601
7304744311786.392552493-7042.3925524934
8309365317605.392552493-8240.3925524934
9308347310849.225885827-2502.22588582670
10298427301080.225885827-2653.22588582672
11289231291300.05921916-2069.05921916005
12291975294298.89753937-2323.89753937001
13294912300508.968536745-5596.96853674519
14293488296985.468536745-3497.46853674538
15290555291689.801870079-1134.80187007871
16284736287972.801870079-3236.80187007872
17281818283493.468536745-1675.46853674538
18287854287396.135203412457.864796587952
19316263318058.468536745-1795.46853674538
20325412323877.4685367451534.53146325462
21326011317121.3018700798889.69812992127
22328282307352.30187007920929.6981299213
23317480297572.13520341219907.8647965879
24317539300570.97352362216968.026476378
25313737306781.0445209976955.95547900281
26312276303257.5445209979018.4554790026
27309391297961.87785433111429.1221456693
28302950294244.8778543318705.12214566928
29300316289765.54452099710550.4554790026
30304035293668.21118766410366.7888123360
31333476324330.5445209979145.45547900262
32337698330149.5445209977548.45547900262
33335932323393.37785433112538.6221456693
34323931313624.37785433110306.6221456693
35313927303844.21118766410082.7888123360
36314485306843.0495078747641.95049212599
37313218313053.120505249164.879494750809
38309664309529.620505249134.379494750606
39302963304233.953838583-1270.95383858271
40298989300516.953838583-1527.95383858272
41298423296037.6205052492385.37949475062
42301631299940.2871719161690.71282808396
43329765330602.620505249-837.620505249368
44335083336421.620505249-1338.62050524938
45327616329665.453838583-2049.45383858272
46309119319896.453838583-10777.4538385827
47295916310116.287171916-14200.2871719160
48291413313115.125492126-21702.125492126
49291542267674.94895013123867.0510498690
50284678264151.44895013120526.5510498687
51276475258855.78228346517619.2177165354
52272566255138.78228346517427.2177165354
53264981250659.44895013114321.5510498688
54263290254562.1156167988727.8843832021
55296806285224.44895013111581.5510498688
56303598291043.44895013112554.5510498688
57286994284287.2822834652706.71771653542
58276427274518.2822834651908.71771653543
59266424264738.1156167981685.88438320210
60267153267736.953937008-583.953937007859
61268381273947.024934383-5566.02493438304
62262522270423.524934383-7901.52493438325
63255542265127.858267717-9585.85826771656
64253158261410.858267717-8252.85826771657
65243803256931.524934383-13128.5249343832
66250741260834.19160105-10093.1916010499
67280445291496.524934383-11051.5249343832
68285257297315.524934383-12058.5249343832
69270976290559.358267717-19583.3582677166
70261076280790.358267717-19714.3582677166
71255603271010.19160105-15407.1916010499


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')