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Author's title

Author*Unverified author*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 05:59:36 -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/2009/Nov/20/t12587220059x3pke4lac6x6s5.htm/, Retrieved Fri, 29 Mar 2024 09:56:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58104, Retrieved Fri, 29 Mar 2024 09:56:37 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105
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]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:06:21] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-11-20 12:59:36] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
89.1		72.7
82.6		79.7
102.7		115.8
91.8		87.8
94.1		99.2
103.1		111.4
93.2		102.3
91		94.4
94.3		118.5
99.4		112.1
115.7		136.5
116.8		139.8
99.8		104.5
96		123.3
115.9		156.6
109.1		136.2
117.3		147.5
109.8		143.8
112.8		135.8
110.7		121.6
100		128
113.3		129.7
122.4		136.2
112.5		130.5
104.2		99.2
92.5		110.4
117.2		151.6
109.3		129.6
106.1		123.6
118.8		142.7
105.3		119
106		118.1
102		120
112.9		124.3
116.5		123.3
114.8		122.4
100.5		90.5
85.4		91
114.6		137
109.9		127.7
100.7		105.1
115.5		135.6
100.7		112.4
99		102.5
102.3		112.6
108.8		110.8
105.9		103.4
113.2		117.6
95.7		87.5
80.9		87
113.9		130
98.1		102.9
102.8		111.1
104.7		128.9
95.9		106.3
94.6		99
101.6		109.9
103.9		104
110.3		112.9
114.1		113.6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135
R Framework error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=58104&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=58104&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58104&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135
R Framework error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Multiple Linear Regression - Estimated Regression Equation
TotaleIndustrieleProductie[t] = + 60.5723257968456 + 0.409406491194934Investeringsgoederen[t] -1.73997398875970M1[t] -15.2224134744869M2[t] -6.2587520538734M3[t] -6.80666085283433M4[t] -6.50781928966874M5[t] -6.61544127689258M6[t] -8.39735230028105M7[t] -6.49855556195852M8[t] -11.1638483388052M9[t] -2.95344127395409M10[t] + 0.902654510456986M11[t] + 0.0728314508847354t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
TotaleIndustrieleProductie[t] =  +  60.5723257968456 +  0.409406491194934Investeringsgoederen[t] -1.73997398875970M1[t] -15.2224134744869M2[t] -6.2587520538734M3[t] -6.80666085283433M4[t] -6.50781928966874M5[t] -6.61544127689258M6[t] -8.39735230028105M7[t] -6.49855556195852M8[t] -11.1638483388052M9[t] -2.95344127395409M10[t] +  0.902654510456986M11[t] +  0.0728314508847354t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58104&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]TotaleIndustrieleProductie[t] =  +  60.5723257968456 +  0.409406491194934Investeringsgoederen[t] -1.73997398875970M1[t] -15.2224134744869M2[t] -6.2587520538734M3[t] -6.80666085283433M4[t] -6.50781928966874M5[t] -6.61544127689258M6[t] -8.39735230028105M7[t] -6.49855556195852M8[t] -11.1638483388052M9[t] -2.95344127395409M10[t] +  0.902654510456986M11[t] +  0.0728314508847354t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58104&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58104&T=1

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Estimated Regression Equation
TotaleIndustrieleProductie[t] = + 60.5723257968456 + 0.409406491194934Investeringsgoederen[t] -1.73997398875970M1[t] -15.2224134744869M2[t] -6.2587520538734M3[t] -6.80666085283433M4[t] -6.50781928966874M5[t] -6.61544127689258M6[t] -8.39735230028105M7[t] -6.49855556195852M8[t] -11.1638483388052M9[t] -2.95344127395409M10[t] + 0.902654510456986M11[t] + 0.0728314508847354t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)60.57232579684564.25940814.220800
Investeringsgoederen0.4094064911949340.03048613.429400
M1-1.739973988759702.199106-0.79120.4328770.216439
M2-15.22241347448692.093141-7.272500
M3-6.25875205387341.945574-3.21690.0023740.001187
M4-6.806660852834331.927506-3.53130.0009530.000476
M5-6.507819289668741.922936-3.38430.0014680.000734
M6-6.615441276892581.91523-3.45410.0011970.000598
M7-8.397352300281051.928115-4.35527.4e-053.7e-05
M8-6.498555561958521.980525-3.28120.0019760.000988
M9-11.16384833880521.913423-5.83451e-060
M10-2.953441273954091.918586-1.53940.1305620.065281
M110.9026545104569861.9004590.4750.6370580.318529
t0.07283145088473540.0232353.13450.0029960.001498

\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) & 60.5723257968456 & 4.259408 & 14.2208 & 0 & 0 \tabularnewline
Investeringsgoederen & 0.409406491194934 & 0.030486 & 13.4294 & 0 & 0 \tabularnewline
M1 & -1.73997398875970 & 2.199106 & -0.7912 & 0.432877 & 0.216439 \tabularnewline
M2 & -15.2224134744869 & 2.093141 & -7.2725 & 0 & 0 \tabularnewline
M3 & -6.2587520538734 & 1.945574 & -3.2169 & 0.002374 & 0.001187 \tabularnewline
M4 & -6.80666085283433 & 1.927506 & -3.5313 & 0.000953 & 0.000476 \tabularnewline
M5 & -6.50781928966874 & 1.922936 & -3.3843 & 0.001468 & 0.000734 \tabularnewline
M6 & -6.61544127689258 & 1.91523 & -3.4541 & 0.001197 & 0.000598 \tabularnewline
M7 & -8.39735230028105 & 1.928115 & -4.3552 & 7.4e-05 & 3.7e-05 \tabularnewline
M8 & -6.49855556195852 & 1.980525 & -3.2812 & 0.001976 & 0.000988 \tabularnewline
M9 & -11.1638483388052 & 1.913423 & -5.8345 & 1e-06 & 0 \tabularnewline
M10 & -2.95344127395409 & 1.918586 & -1.5394 & 0.130562 & 0.065281 \tabularnewline
M11 & 0.902654510456986 & 1.900459 & 0.475 & 0.637058 & 0.318529 \tabularnewline
t & 0.0728314508847354 & 0.023235 & 3.1345 & 0.002996 & 0.001498 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58104&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]60.5723257968456[/C][C]4.259408[/C][C]14.2208[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Investeringsgoederen[/C][C]0.409406491194934[/C][C]0.030486[/C][C]13.4294[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-1.73997398875970[/C][C]2.199106[/C][C]-0.7912[/C][C]0.432877[/C][C]0.216439[/C][/ROW]
[ROW][C]M2[/C][C]-15.2224134744869[/C][C]2.093141[/C][C]-7.2725[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M3[/C][C]-6.2587520538734[/C][C]1.945574[/C][C]-3.2169[/C][C]0.002374[/C][C]0.001187[/C][/ROW]
[ROW][C]M4[/C][C]-6.80666085283433[/C][C]1.927506[/C][C]-3.5313[/C][C]0.000953[/C][C]0.000476[/C][/ROW]
[ROW][C]M5[/C][C]-6.50781928966874[/C][C]1.922936[/C][C]-3.3843[/C][C]0.001468[/C][C]0.000734[/C][/ROW]
[ROW][C]M6[/C][C]-6.61544127689258[/C][C]1.91523[/C][C]-3.4541[/C][C]0.001197[/C][C]0.000598[/C][/ROW]
[ROW][C]M7[/C][C]-8.39735230028105[/C][C]1.928115[/C][C]-4.3552[/C][C]7.4e-05[/C][C]3.7e-05[/C][/ROW]
[ROW][C]M8[/C][C]-6.49855556195852[/C][C]1.980525[/C][C]-3.2812[/C][C]0.001976[/C][C]0.000988[/C][/ROW]
[ROW][C]M9[/C][C]-11.1638483388052[/C][C]1.913423[/C][C]-5.8345[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]M10[/C][C]-2.95344127395409[/C][C]1.918586[/C][C]-1.5394[/C][C]0.130562[/C][C]0.065281[/C][/ROW]
[ROW][C]M11[/C][C]0.902654510456986[/C][C]1.900459[/C][C]0.475[/C][C]0.637058[/C][C]0.318529[/C][/ROW]
[ROW][C]t[/C][C]0.0728314508847354[/C][C]0.023235[/C][C]3.1345[/C][C]0.002996[/C][C]0.001498[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58104&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58104&T=2

As an alternative you can also use a 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)60.57232579684564.25940814.220800
Investeringsgoederen0.4094064911949340.03048613.429400
M1-1.739973988759702.199106-0.79120.4328770.216439
M2-15.22241347448692.093141-7.272500
M3-6.25875205387341.945574-3.21690.0023740.001187
M4-6.806660852834331.927506-3.53130.0009530.000476
M5-6.507819289668741.922936-3.38430.0014680.000734
M6-6.615441276892581.91523-3.45410.0011970.000598
M7-8.397352300281051.928115-4.35527.4e-053.7e-05
M8-6.498555561958521.980525-3.28120.0019760.000988
M9-11.16384833880521.913423-5.83451e-060
M10-2.953441273954091.918586-1.53940.1305620.065281
M110.9026545104569861.9004590.4750.6370580.318529
t0.07283145088473540.0232353.13450.0029960.001498







Multiple Linear Regression - Regression Statistics
Multiple R0.96132580989825
R-squared0.924147312776527
Adjusted R-squared0.902710683778589
F-TEST (value)43.1106641284607
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.00233118796081
Sum Squared Residuals414.643657861300

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.96132580989825 \tabularnewline
R-squared & 0.924147312776527 \tabularnewline
Adjusted R-squared & 0.902710683778589 \tabularnewline
F-TEST (value) & 43.1106641284607 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.00233118796081 \tabularnewline
Sum Squared Residuals & 414.643657861300 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58104&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.96132580989825[/C][/ROW]
[ROW][C]R-squared[/C][C]0.924147312776527[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.902710683778589[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]43.1106641284607[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.00233118796081[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]414.643657861300[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58104&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58104&T=3

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Regression Statistics
Multiple R0.96132580989825
R-squared0.924147312776527
Adjusted R-squared0.902710683778589
F-TEST (value)43.1106641284607
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.00233118796081
Sum Squared Residuals414.643657861300







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
189.188.66903516884270.430964831157306
282.678.12527257236454.4747274276355
3102.7101.9413397760000.758660224000175
491.890.00288067446541.79711932553455
594.195.041787688138-0.941787688138045
6103.1100.0017563443773.09824365562285
793.294.5670777019995-1.36707770199949
89193.3043946107668-2.30439461076679
994.398.5786297226028-4.27862972260281
1099.4104.241666694691-4.84166669469101
11115.7118.160112315143-2.46011231514323
12116.8118.681330676514-1.88133067651427
1399.8102.562138999458-2.76213899945812
149696.8493729990804-0.849372999080426
15115.9119.51910202737-3.61910202736996
16109.1110.692132258917-1.59213225891710
17117.3115.6900986234701.60990137652981
18109.8114.140504069710-4.34050406970983
19112.8109.1561725676473.64382743235337
20110.7105.3142285818865.38577141811418
21100103.341968799572-3.3419687995715
22113.3112.3211983503390.97880164966131
23122.4118.9112677784023.48873222159844
24112.5115.747827719018-3.2478277190182
25104.2101.2662620067422.93373799325821
2692.592.44200667328260.057993326717399
27117.2118.346046982012-1.14604698201212
28109.3108.8640268276470.435973172352637
29106.1106.779260894528-0.679260894528087
30118.8114.5641343400124.23586565998778
31105.3103.1521209261892.14787907381145
32106104.7552832733201.24471672667962
33102100.9406942806291.05930571937115
34112.9110.9843807085031.91561929149714
35116.5114.5039014526041.99609854739626
36114.8113.3056125509561.49438744904394
37100.598.57840294396271.92159705603731
3885.485.37349815471770.0265018452823059
39114.6113.2426896211831.35731037881709
40109.9108.9601319049940.939868095006193
41100.7100.0792182180390.620781781961381
42115.5112.5313256631452.96867433685499
43100.7101.324015494919-0.624015494918803
449999.2425194212962-0.242519421296228
45102.398.78506365640323.51493634359684
46108.8106.3313704879882.46862951201191
47105.9107.230689688441-1.33068968844137
48113.2112.2144388038370.985561196162808
4995.798.2241608809947-2.52416088099471
5080.984.6098496005548-3.70984960055478
51113.9111.2508215934352.64917840656482
5298.199.6808283339763-1.58082833397627
53102.8103.409634575825-0.609634575825055
54104.7110.662279582756-5.96227958275578
5595.999.7006133092465-3.80061330924653
5694.698.6835741127308-4.08357411273079
57101.698.55364354079373.04635645920633
58103.9104.421383758479-0.521383758479346
59110.3111.99402876541-1.69402876541008
60114.1111.4507902496742.64920975032571

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 89.1 & 88.6690351688427 & 0.430964831157306 \tabularnewline
2 & 82.6 & 78.1252725723645 & 4.4747274276355 \tabularnewline
3 & 102.7 & 101.941339776000 & 0.758660224000175 \tabularnewline
4 & 91.8 & 90.0028806744654 & 1.79711932553455 \tabularnewline
5 & 94.1 & 95.041787688138 & -0.941787688138045 \tabularnewline
6 & 103.1 & 100.001756344377 & 3.09824365562285 \tabularnewline
7 & 93.2 & 94.5670777019995 & -1.36707770199949 \tabularnewline
8 & 91 & 93.3043946107668 & -2.30439461076679 \tabularnewline
9 & 94.3 & 98.5786297226028 & -4.27862972260281 \tabularnewline
10 & 99.4 & 104.241666694691 & -4.84166669469101 \tabularnewline
11 & 115.7 & 118.160112315143 & -2.46011231514323 \tabularnewline
12 & 116.8 & 118.681330676514 & -1.88133067651427 \tabularnewline
13 & 99.8 & 102.562138999458 & -2.76213899945812 \tabularnewline
14 & 96 & 96.8493729990804 & -0.849372999080426 \tabularnewline
15 & 115.9 & 119.51910202737 & -3.61910202736996 \tabularnewline
16 & 109.1 & 110.692132258917 & -1.59213225891710 \tabularnewline
17 & 117.3 & 115.690098623470 & 1.60990137652981 \tabularnewline
18 & 109.8 & 114.140504069710 & -4.34050406970983 \tabularnewline
19 & 112.8 & 109.156172567647 & 3.64382743235337 \tabularnewline
20 & 110.7 & 105.314228581886 & 5.38577141811418 \tabularnewline
21 & 100 & 103.341968799572 & -3.3419687995715 \tabularnewline
22 & 113.3 & 112.321198350339 & 0.97880164966131 \tabularnewline
23 & 122.4 & 118.911267778402 & 3.48873222159844 \tabularnewline
24 & 112.5 & 115.747827719018 & -3.2478277190182 \tabularnewline
25 & 104.2 & 101.266262006742 & 2.93373799325821 \tabularnewline
26 & 92.5 & 92.4420066732826 & 0.057993326717399 \tabularnewline
27 & 117.2 & 118.346046982012 & -1.14604698201212 \tabularnewline
28 & 109.3 & 108.864026827647 & 0.435973172352637 \tabularnewline
29 & 106.1 & 106.779260894528 & -0.679260894528087 \tabularnewline
30 & 118.8 & 114.564134340012 & 4.23586565998778 \tabularnewline
31 & 105.3 & 103.152120926189 & 2.14787907381145 \tabularnewline
32 & 106 & 104.755283273320 & 1.24471672667962 \tabularnewline
33 & 102 & 100.940694280629 & 1.05930571937115 \tabularnewline
34 & 112.9 & 110.984380708503 & 1.91561929149714 \tabularnewline
35 & 116.5 & 114.503901452604 & 1.99609854739626 \tabularnewline
36 & 114.8 & 113.305612550956 & 1.49438744904394 \tabularnewline
37 & 100.5 & 98.5784029439627 & 1.92159705603731 \tabularnewline
38 & 85.4 & 85.3734981547177 & 0.0265018452823059 \tabularnewline
39 & 114.6 & 113.242689621183 & 1.35731037881709 \tabularnewline
40 & 109.9 & 108.960131904994 & 0.939868095006193 \tabularnewline
41 & 100.7 & 100.079218218039 & 0.620781781961381 \tabularnewline
42 & 115.5 & 112.531325663145 & 2.96867433685499 \tabularnewline
43 & 100.7 & 101.324015494919 & -0.624015494918803 \tabularnewline
44 & 99 & 99.2425194212962 & -0.242519421296228 \tabularnewline
45 & 102.3 & 98.7850636564032 & 3.51493634359684 \tabularnewline
46 & 108.8 & 106.331370487988 & 2.46862951201191 \tabularnewline
47 & 105.9 & 107.230689688441 & -1.33068968844137 \tabularnewline
48 & 113.2 & 112.214438803837 & 0.985561196162808 \tabularnewline
49 & 95.7 & 98.2241608809947 & -2.52416088099471 \tabularnewline
50 & 80.9 & 84.6098496005548 & -3.70984960055478 \tabularnewline
51 & 113.9 & 111.250821593435 & 2.64917840656482 \tabularnewline
52 & 98.1 & 99.6808283339763 & -1.58082833397627 \tabularnewline
53 & 102.8 & 103.409634575825 & -0.609634575825055 \tabularnewline
54 & 104.7 & 110.662279582756 & -5.96227958275578 \tabularnewline
55 & 95.9 & 99.7006133092465 & -3.80061330924653 \tabularnewline
56 & 94.6 & 98.6835741127308 & -4.08357411273079 \tabularnewline
57 & 101.6 & 98.5536435407937 & 3.04635645920633 \tabularnewline
58 & 103.9 & 104.421383758479 & -0.521383758479346 \tabularnewline
59 & 110.3 & 111.99402876541 & -1.69402876541008 \tabularnewline
60 & 114.1 & 111.450790249674 & 2.64920975032571 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58104&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]89.1[/C][C]88.6690351688427[/C][C]0.430964831157306[/C][/ROW]
[ROW][C]2[/C][C]82.6[/C][C]78.1252725723645[/C][C]4.4747274276355[/C][/ROW]
[ROW][C]3[/C][C]102.7[/C][C]101.941339776000[/C][C]0.758660224000175[/C][/ROW]
[ROW][C]4[/C][C]91.8[/C][C]90.0028806744654[/C][C]1.79711932553455[/C][/ROW]
[ROW][C]5[/C][C]94.1[/C][C]95.041787688138[/C][C]-0.941787688138045[/C][/ROW]
[ROW][C]6[/C][C]103.1[/C][C]100.001756344377[/C][C]3.09824365562285[/C][/ROW]
[ROW][C]7[/C][C]93.2[/C][C]94.5670777019995[/C][C]-1.36707770199949[/C][/ROW]
[ROW][C]8[/C][C]91[/C][C]93.3043946107668[/C][C]-2.30439461076679[/C][/ROW]
[ROW][C]9[/C][C]94.3[/C][C]98.5786297226028[/C][C]-4.27862972260281[/C][/ROW]
[ROW][C]10[/C][C]99.4[/C][C]104.241666694691[/C][C]-4.84166669469101[/C][/ROW]
[ROW][C]11[/C][C]115.7[/C][C]118.160112315143[/C][C]-2.46011231514323[/C][/ROW]
[ROW][C]12[/C][C]116.8[/C][C]118.681330676514[/C][C]-1.88133067651427[/C][/ROW]
[ROW][C]13[/C][C]99.8[/C][C]102.562138999458[/C][C]-2.76213899945812[/C][/ROW]
[ROW][C]14[/C][C]96[/C][C]96.8493729990804[/C][C]-0.849372999080426[/C][/ROW]
[ROW][C]15[/C][C]115.9[/C][C]119.51910202737[/C][C]-3.61910202736996[/C][/ROW]
[ROW][C]16[/C][C]109.1[/C][C]110.692132258917[/C][C]-1.59213225891710[/C][/ROW]
[ROW][C]17[/C][C]117.3[/C][C]115.690098623470[/C][C]1.60990137652981[/C][/ROW]
[ROW][C]18[/C][C]109.8[/C][C]114.140504069710[/C][C]-4.34050406970983[/C][/ROW]
[ROW][C]19[/C][C]112.8[/C][C]109.156172567647[/C][C]3.64382743235337[/C][/ROW]
[ROW][C]20[/C][C]110.7[/C][C]105.314228581886[/C][C]5.38577141811418[/C][/ROW]
[ROW][C]21[/C][C]100[/C][C]103.341968799572[/C][C]-3.3419687995715[/C][/ROW]
[ROW][C]22[/C][C]113.3[/C][C]112.321198350339[/C][C]0.97880164966131[/C][/ROW]
[ROW][C]23[/C][C]122.4[/C][C]118.911267778402[/C][C]3.48873222159844[/C][/ROW]
[ROW][C]24[/C][C]112.5[/C][C]115.747827719018[/C][C]-3.2478277190182[/C][/ROW]
[ROW][C]25[/C][C]104.2[/C][C]101.266262006742[/C][C]2.93373799325821[/C][/ROW]
[ROW][C]26[/C][C]92.5[/C][C]92.4420066732826[/C][C]0.057993326717399[/C][/ROW]
[ROW][C]27[/C][C]117.2[/C][C]118.346046982012[/C][C]-1.14604698201212[/C][/ROW]
[ROW][C]28[/C][C]109.3[/C][C]108.864026827647[/C][C]0.435973172352637[/C][/ROW]
[ROW][C]29[/C][C]106.1[/C][C]106.779260894528[/C][C]-0.679260894528087[/C][/ROW]
[ROW][C]30[/C][C]118.8[/C][C]114.564134340012[/C][C]4.23586565998778[/C][/ROW]
[ROW][C]31[/C][C]105.3[/C][C]103.152120926189[/C][C]2.14787907381145[/C][/ROW]
[ROW][C]32[/C][C]106[/C][C]104.755283273320[/C][C]1.24471672667962[/C][/ROW]
[ROW][C]33[/C][C]102[/C][C]100.940694280629[/C][C]1.05930571937115[/C][/ROW]
[ROW][C]34[/C][C]112.9[/C][C]110.984380708503[/C][C]1.91561929149714[/C][/ROW]
[ROW][C]35[/C][C]116.5[/C][C]114.503901452604[/C][C]1.99609854739626[/C][/ROW]
[ROW][C]36[/C][C]114.8[/C][C]113.305612550956[/C][C]1.49438744904394[/C][/ROW]
[ROW][C]37[/C][C]100.5[/C][C]98.5784029439627[/C][C]1.92159705603731[/C][/ROW]
[ROW][C]38[/C][C]85.4[/C][C]85.3734981547177[/C][C]0.0265018452823059[/C][/ROW]
[ROW][C]39[/C][C]114.6[/C][C]113.242689621183[/C][C]1.35731037881709[/C][/ROW]
[ROW][C]40[/C][C]109.9[/C][C]108.960131904994[/C][C]0.939868095006193[/C][/ROW]
[ROW][C]41[/C][C]100.7[/C][C]100.079218218039[/C][C]0.620781781961381[/C][/ROW]
[ROW][C]42[/C][C]115.5[/C][C]112.531325663145[/C][C]2.96867433685499[/C][/ROW]
[ROW][C]43[/C][C]100.7[/C][C]101.324015494919[/C][C]-0.624015494918803[/C][/ROW]
[ROW][C]44[/C][C]99[/C][C]99.2425194212962[/C][C]-0.242519421296228[/C][/ROW]
[ROW][C]45[/C][C]102.3[/C][C]98.7850636564032[/C][C]3.51493634359684[/C][/ROW]
[ROW][C]46[/C][C]108.8[/C][C]106.331370487988[/C][C]2.46862951201191[/C][/ROW]
[ROW][C]47[/C][C]105.9[/C][C]107.230689688441[/C][C]-1.33068968844137[/C][/ROW]
[ROW][C]48[/C][C]113.2[/C][C]112.214438803837[/C][C]0.985561196162808[/C][/ROW]
[ROW][C]49[/C][C]95.7[/C][C]98.2241608809947[/C][C]-2.52416088099471[/C][/ROW]
[ROW][C]50[/C][C]80.9[/C][C]84.6098496005548[/C][C]-3.70984960055478[/C][/ROW]
[ROW][C]51[/C][C]113.9[/C][C]111.250821593435[/C][C]2.64917840656482[/C][/ROW]
[ROW][C]52[/C][C]98.1[/C][C]99.6808283339763[/C][C]-1.58082833397627[/C][/ROW]
[ROW][C]53[/C][C]102.8[/C][C]103.409634575825[/C][C]-0.609634575825055[/C][/ROW]
[ROW][C]54[/C][C]104.7[/C][C]110.662279582756[/C][C]-5.96227958275578[/C][/ROW]
[ROW][C]55[/C][C]95.9[/C][C]99.7006133092465[/C][C]-3.80061330924653[/C][/ROW]
[ROW][C]56[/C][C]94.6[/C][C]98.6835741127308[/C][C]-4.08357411273079[/C][/ROW]
[ROW][C]57[/C][C]101.6[/C][C]98.5536435407937[/C][C]3.04635645920633[/C][/ROW]
[ROW][C]58[/C][C]103.9[/C][C]104.421383758479[/C][C]-0.521383758479346[/C][/ROW]
[ROW][C]59[/C][C]110.3[/C][C]111.99402876541[/C][C]-1.69402876541008[/C][/ROW]
[ROW][C]60[/C][C]114.1[/C][C]111.450790249674[/C][C]2.64920975032571[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58104&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58104&T=4

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
189.188.66903516884270.430964831157306
282.678.12527257236454.4747274276355
3102.7101.9413397760000.758660224000175
491.890.00288067446541.79711932553455
594.195.041787688138-0.941787688138045
6103.1100.0017563443773.09824365562285
793.294.5670777019995-1.36707770199949
89193.3043946107668-2.30439461076679
994.398.5786297226028-4.27862972260281
1099.4104.241666694691-4.84166669469101
11115.7118.160112315143-2.46011231514323
12116.8118.681330676514-1.88133067651427
1399.8102.562138999458-2.76213899945812
149696.8493729990804-0.849372999080426
15115.9119.51910202737-3.61910202736996
16109.1110.692132258917-1.59213225891710
17117.3115.6900986234701.60990137652981
18109.8114.140504069710-4.34050406970983
19112.8109.1561725676473.64382743235337
20110.7105.3142285818865.38577141811418
21100103.341968799572-3.3419687995715
22113.3112.3211983503390.97880164966131
23122.4118.9112677784023.48873222159844
24112.5115.747827719018-3.2478277190182
25104.2101.2662620067422.93373799325821
2692.592.44200667328260.057993326717399
27117.2118.346046982012-1.14604698201212
28109.3108.8640268276470.435973172352637
29106.1106.779260894528-0.679260894528087
30118.8114.5641343400124.23586565998778
31105.3103.1521209261892.14787907381145
32106104.7552832733201.24471672667962
33102100.9406942806291.05930571937115
34112.9110.9843807085031.91561929149714
35116.5114.5039014526041.99609854739626
36114.8113.3056125509561.49438744904394
37100.598.57840294396271.92159705603731
3885.485.37349815471770.0265018452823059
39114.6113.2426896211831.35731037881709
40109.9108.9601319049940.939868095006193
41100.7100.0792182180390.620781781961381
42115.5112.5313256631452.96867433685499
43100.7101.324015494919-0.624015494918803
449999.2425194212962-0.242519421296228
45102.398.78506365640323.51493634359684
46108.8106.3313704879882.46862951201191
47105.9107.230689688441-1.33068968844137
48113.2112.2144388038370.985561196162808
4995.798.2241608809947-2.52416088099471
5080.984.6098496005548-3.70984960055478
51113.9111.2508215934352.64917840656482
5298.199.6808283339763-1.58082833397627
53102.8103.409634575825-0.609634575825055
54104.7110.662279582756-5.96227958275578
5595.999.7006133092465-3.80061330924653
5694.698.6835741127308-4.08357411273079
57101.698.55364354079373.04635645920633
58103.9104.421383758479-0.521383758479346
59110.3111.99402876541-1.69402876541008
60114.1111.4507902496742.64920975032571







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.4123067903617900.8246135807235790.58769320963821
180.3385704216179470.6771408432358930.661429578382053
190.7756422593533880.4487154812932230.224357740646612
200.9120711585118120.1758576829763760.0879288414881879
210.9345968579121470.1308062841757060.0654031420878532
220.9203535548830960.1592928902338090.0796464451169044
230.8769554468356630.2460891063286750.123044553164337
240.967550624181530.06489875163694190.0324493758184709
250.945810662667430.108378674665140.05418933733257
260.9400039458351650.1199921083296710.0599960541648355
270.9532825003586920.09343499928261590.0467174996413080
280.929153954413130.1416920911737410.0708460455868707
290.930040556121480.1399188877570420.0699594438785208
300.9339292963494730.1321414073010540.0660707036505271
310.9084260249872120.1831479500255760.0915739750127881
320.8653167009574720.2693665980850560.134683299042528
330.9028571816181350.194285636763730.097142818381865
340.8778167248019240.2443665503961520.122183275198076
350.8170511944111650.365897611177670.182948805588835
360.8217967609676260.3564064780647480.178203239032374
370.7699964029828640.4600071940342730.230003597017136
380.7309057896355860.5381884207288270.269094210364414
390.722283002671720.555433994656560.27771699732828
400.6799394300717330.6401211398565330.320060569928267
410.5577152479159760.8845695041680490.442284752084024
420.8306217843383440.3387564313233120.169378215661656
430.7308660588537450.5382678822925110.269133941146255

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.412306790361790 & 0.824613580723579 & 0.58769320963821 \tabularnewline
18 & 0.338570421617947 & 0.677140843235893 & 0.661429578382053 \tabularnewline
19 & 0.775642259353388 & 0.448715481293223 & 0.224357740646612 \tabularnewline
20 & 0.912071158511812 & 0.175857682976376 & 0.0879288414881879 \tabularnewline
21 & 0.934596857912147 & 0.130806284175706 & 0.0654031420878532 \tabularnewline
22 & 0.920353554883096 & 0.159292890233809 & 0.0796464451169044 \tabularnewline
23 & 0.876955446835663 & 0.246089106328675 & 0.123044553164337 \tabularnewline
24 & 0.96755062418153 & 0.0648987516369419 & 0.0324493758184709 \tabularnewline
25 & 0.94581066266743 & 0.10837867466514 & 0.05418933733257 \tabularnewline
26 & 0.940003945835165 & 0.119992108329671 & 0.0599960541648355 \tabularnewline
27 & 0.953282500358692 & 0.0934349992826159 & 0.0467174996413080 \tabularnewline
28 & 0.92915395441313 & 0.141692091173741 & 0.0708460455868707 \tabularnewline
29 & 0.93004055612148 & 0.139918887757042 & 0.0699594438785208 \tabularnewline
30 & 0.933929296349473 & 0.132141407301054 & 0.0660707036505271 \tabularnewline
31 & 0.908426024987212 & 0.183147950025576 & 0.0915739750127881 \tabularnewline
32 & 0.865316700957472 & 0.269366598085056 & 0.134683299042528 \tabularnewline
33 & 0.902857181618135 & 0.19428563676373 & 0.097142818381865 \tabularnewline
34 & 0.877816724801924 & 0.244366550396152 & 0.122183275198076 \tabularnewline
35 & 0.817051194411165 & 0.36589761117767 & 0.182948805588835 \tabularnewline
36 & 0.821796760967626 & 0.356406478064748 & 0.178203239032374 \tabularnewline
37 & 0.769996402982864 & 0.460007194034273 & 0.230003597017136 \tabularnewline
38 & 0.730905789635586 & 0.538188420728827 & 0.269094210364414 \tabularnewline
39 & 0.72228300267172 & 0.55543399465656 & 0.27771699732828 \tabularnewline
40 & 0.679939430071733 & 0.640121139856533 & 0.320060569928267 \tabularnewline
41 & 0.557715247915976 & 0.884569504168049 & 0.442284752084024 \tabularnewline
42 & 0.830621784338344 & 0.338756431323312 & 0.169378215661656 \tabularnewline
43 & 0.730866058853745 & 0.538267882292511 & 0.269133941146255 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58104&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]17[/C][C]0.412306790361790[/C][C]0.824613580723579[/C][C]0.58769320963821[/C][/ROW]
[ROW][C]18[/C][C]0.338570421617947[/C][C]0.677140843235893[/C][C]0.661429578382053[/C][/ROW]
[ROW][C]19[/C][C]0.775642259353388[/C][C]0.448715481293223[/C][C]0.224357740646612[/C][/ROW]
[ROW][C]20[/C][C]0.912071158511812[/C][C]0.175857682976376[/C][C]0.0879288414881879[/C][/ROW]
[ROW][C]21[/C][C]0.934596857912147[/C][C]0.130806284175706[/C][C]0.0654031420878532[/C][/ROW]
[ROW][C]22[/C][C]0.920353554883096[/C][C]0.159292890233809[/C][C]0.0796464451169044[/C][/ROW]
[ROW][C]23[/C][C]0.876955446835663[/C][C]0.246089106328675[/C][C]0.123044553164337[/C][/ROW]
[ROW][C]24[/C][C]0.96755062418153[/C][C]0.0648987516369419[/C][C]0.0324493758184709[/C][/ROW]
[ROW][C]25[/C][C]0.94581066266743[/C][C]0.10837867466514[/C][C]0.05418933733257[/C][/ROW]
[ROW][C]26[/C][C]0.940003945835165[/C][C]0.119992108329671[/C][C]0.0599960541648355[/C][/ROW]
[ROW][C]27[/C][C]0.953282500358692[/C][C]0.0934349992826159[/C][C]0.0467174996413080[/C][/ROW]
[ROW][C]28[/C][C]0.92915395441313[/C][C]0.141692091173741[/C][C]0.0708460455868707[/C][/ROW]
[ROW][C]29[/C][C]0.93004055612148[/C][C]0.139918887757042[/C][C]0.0699594438785208[/C][/ROW]
[ROW][C]30[/C][C]0.933929296349473[/C][C]0.132141407301054[/C][C]0.0660707036505271[/C][/ROW]
[ROW][C]31[/C][C]0.908426024987212[/C][C]0.183147950025576[/C][C]0.0915739750127881[/C][/ROW]
[ROW][C]32[/C][C]0.865316700957472[/C][C]0.269366598085056[/C][C]0.134683299042528[/C][/ROW]
[ROW][C]33[/C][C]0.902857181618135[/C][C]0.19428563676373[/C][C]0.097142818381865[/C][/ROW]
[ROW][C]34[/C][C]0.877816724801924[/C][C]0.244366550396152[/C][C]0.122183275198076[/C][/ROW]
[ROW][C]35[/C][C]0.817051194411165[/C][C]0.36589761117767[/C][C]0.182948805588835[/C][/ROW]
[ROW][C]36[/C][C]0.821796760967626[/C][C]0.356406478064748[/C][C]0.178203239032374[/C][/ROW]
[ROW][C]37[/C][C]0.769996402982864[/C][C]0.460007194034273[/C][C]0.230003597017136[/C][/ROW]
[ROW][C]38[/C][C]0.730905789635586[/C][C]0.538188420728827[/C][C]0.269094210364414[/C][/ROW]
[ROW][C]39[/C][C]0.72228300267172[/C][C]0.55543399465656[/C][C]0.27771699732828[/C][/ROW]
[ROW][C]40[/C][C]0.679939430071733[/C][C]0.640121139856533[/C][C]0.320060569928267[/C][/ROW]
[ROW][C]41[/C][C]0.557715247915976[/C][C]0.884569504168049[/C][C]0.442284752084024[/C][/ROW]
[ROW][C]42[/C][C]0.830621784338344[/C][C]0.338756431323312[/C][C]0.169378215661656[/C][/ROW]
[ROW][C]43[/C][C]0.730866058853745[/C][C]0.538267882292511[/C][C]0.269133941146255[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58104&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58104&T=5

As an alternative you can also use a QR Code:  

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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.4123067903617900.8246135807235790.58769320963821
180.3385704216179470.6771408432358930.661429578382053
190.7756422593533880.4487154812932230.224357740646612
200.9120711585118120.1758576829763760.0879288414881879
210.9345968579121470.1308062841757060.0654031420878532
220.9203535548830960.1592928902338090.0796464451169044
230.8769554468356630.2460891063286750.123044553164337
240.967550624181530.06489875163694190.0324493758184709
250.945810662667430.108378674665140.05418933733257
260.9400039458351650.1199921083296710.0599960541648355
270.9532825003586920.09343499928261590.0467174996413080
280.929153954413130.1416920911737410.0708460455868707
290.930040556121480.1399188877570420.0699594438785208
300.9339292963494730.1321414073010540.0660707036505271
310.9084260249872120.1831479500255760.0915739750127881
320.8653167009574720.2693665980850560.134683299042528
330.9028571816181350.194285636763730.097142818381865
340.8778167248019240.2443665503961520.122183275198076
350.8170511944111650.365897611177670.182948805588835
360.8217967609676260.3564064780647480.178203239032374
370.7699964029828640.4600071940342730.230003597017136
380.7309057896355860.5381884207288270.269094210364414
390.722283002671720.555433994656560.27771699732828
400.6799394300717330.6401211398565330.320060569928267
410.5577152479159760.8845695041680490.442284752084024
420.8306217843383440.3387564313233120.169378215661656
430.7308660588537450.5382678822925110.269133941146255







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level20.0740740740740741OK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 2 & 0.0740740740740741 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58104&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]2[/C][C]0.0740740740740741[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58104&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58104&T=6

As an alternative you can also use a QR Code:  

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level20.0740740740740741OK



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)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
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))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$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')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$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()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
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')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}