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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationSat, 21 Nov 2009 07:22:35 -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/21/t12588134670coiglzelq0oaut.htm/, Retrieved Sun, 09 Nov 2025 02:24:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58551, Retrieved Sun, 09 Nov 2025 02:24:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordscvm
Estimated Impact502

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]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [model 1] [2009-11-17 14:36:29] [ed603017d2bee8fbd82b6d5ec04e12c3]
-    D      [Multiple Regression] [multiple regression] [2009-11-19 21:38:11] [ed603017d2bee8fbd82b6d5ec04e12c3]
-   P         [Multiple Regression] [monthly dummies] [2009-11-19 22:00:07] [ed603017d2bee8fbd82b6d5ec04e12c3]
-   P           [Multiple Regression] [model3] [2009-11-20 08:47:44] [ed603017d2bee8fbd82b6d5ec04e12c3]
-    D              [Multiple Regression] [W7: Linear Trend] [2009-11-21 14:22:35] [a5ada8bd39e806b5b90f09589c89554a] [Current]
Feedback Forum

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6,3	2
6,2	1,8
6,1	2,7
6,3	2,3
6,5	1,9
6,6	2
6,5	2,3
6,2	2,8
6,2	2,4
5,9	2,3
6,1	2,7
6,1	2,7
6,1	2,9
6,1	3
6,1	2,2
6,4	2,3
6,7	2,8
6,9	2,8
7	2,8
7	2,2
6,8	2,6
6,4	2,8
5,9	2,5
5,5	2,4
5,5	2,3
5,6	1,9
5,8	1,7
5,9	2
6,1	2,1
6,1	1,7
6	1,8
6	1,8
5,9	1,8
5,5	1,3
5,6	1,3
5,4	1,3
5,2	1,2
5,2	1,4
5,2	2,2
5,5	2,9
5,8	3,1
5,8	3,5
5,5	3,6
5,3	4,4
5,1	4,1
5,2	5,1
5,8	5,8
5,8	5,9
5,5	5,4
5	5,5
4,9	4,8
5,3	3,2
6,1	2,7
6,5	2,1
6,8	1,9
6,6	0,6
6,4	0,7
6,4	-0,2
6,6	-1
6,7	-1,7

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'Gwilym Jenkins' @ 72.249.127.135

\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
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58551&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58551&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58551&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'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
WMan>25[t] = + 6.59619621729017 -0.1480526479753Infl[t] -0.202067711946028M1[t] -0.297369689987745M2[t] -0.286749562110452M3[t] -0.042778910868714M4[t] + 0.324880164049072M5[t] + 0.460695027128835M6[t] + 0.460198313884645M7[t] + 0.313052124004902M8[t] + 0.177750145963182M9[t] -0.0205128850380429M10[t] + 0.110107242839249M11[t] -0.0106201278772925t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
WMan>25[t] =  +  6.59619621729017 -0.1480526479753Infl[t] -0.202067711946028M1[t] -0.297369689987745M2[t] -0.286749562110452M3[t] -0.042778910868714M4[t] +  0.324880164049072M5[t] +  0.460695027128835M6[t] +  0.460198313884645M7[t] +  0.313052124004902M8[t] +  0.177750145963182M9[t] -0.0205128850380429M10[t] +  0.110107242839249M11[t] -0.0106201278772925t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58551&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]WMan>25[t] =  +  6.59619621729017 -0.1480526479753Infl[t] -0.202067711946028M1[t] -0.297369689987745M2[t] -0.286749562110452M3[t] -0.042778910868714M4[t] +  0.324880164049072M5[t] +  0.460695027128835M6[t] +  0.460198313884645M7[t] +  0.313052124004902M8[t] +  0.177750145963182M9[t] -0.0205128850380429M10[t] +  0.110107242839249M11[t] -0.0106201278772925t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58551&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58551&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
WMan>25[t] = + 6.59619621729017 -0.1480526479753Infl[t] -0.202067711946028M1[t] -0.297369689987745M2[t] -0.286749562110452M3[t] -0.042778910868714M4[t] + 0.324880164049072M5[t] + 0.460695027128835M6[t] + 0.460198313884645M7[t] + 0.313052124004902M8[t] + 0.177750145963182M9[t] -0.0205128850380429M10[t] + 0.110107242839249M11[t] -0.0106201278772925t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)6.596196217290170.23613627.933800
Infl-0.14805264797530.039238-3.77320.000460.00023
M1-0.2020677119460280.271928-0.74310.4612040.230602
M2-0.2973696899877450.271368-1.09580.2788620.139431
M3-0.2867495621104520.270993-1.05810.2955150.147757
M4-0.0427789108687140.27011-0.15840.8748540.437427
M50.3248801640490720.2697641.20430.2346290.117315
M60.4606950271288350.2692961.71070.0938670.046933
M70.4601983138846450.2691971.70950.0940930.047046
M80.3130521240049020.2688021.16460.2501780.125089
M90.1777501459631820.268610.66170.5114390.25572
M10-0.02051288503804290.268449-0.07640.9394220.469711
M110.1101072428392490.2683890.41030.6835250.341763
t-0.01062012787729250.003229-3.28880.0019340.000967

\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) & 6.59619621729017 & 0.236136 & 27.9338 & 0 & 0 \tabularnewline
Infl & -0.1480526479753 & 0.039238 & -3.7732 & 0.00046 & 0.00023 \tabularnewline
M1 & -0.202067711946028 & 0.271928 & -0.7431 & 0.461204 & 0.230602 \tabularnewline
M2 & -0.297369689987745 & 0.271368 & -1.0958 & 0.278862 & 0.139431 \tabularnewline
M3 & -0.286749562110452 & 0.270993 & -1.0581 & 0.295515 & 0.147757 \tabularnewline
M4 & -0.042778910868714 & 0.27011 & -0.1584 & 0.874854 & 0.437427 \tabularnewline
M5 & 0.324880164049072 & 0.269764 & 1.2043 & 0.234629 & 0.117315 \tabularnewline
M6 & 0.460695027128835 & 0.269296 & 1.7107 & 0.093867 & 0.046933 \tabularnewline
M7 & 0.460198313884645 & 0.269197 & 1.7095 & 0.094093 & 0.047046 \tabularnewline
M8 & 0.313052124004902 & 0.268802 & 1.1646 & 0.250178 & 0.125089 \tabularnewline
M9 & 0.177750145963182 & 0.26861 & 0.6617 & 0.511439 & 0.25572 \tabularnewline
M10 & -0.0205128850380429 & 0.268449 & -0.0764 & 0.939422 & 0.469711 \tabularnewline
M11 & 0.110107242839249 & 0.268389 & 0.4103 & 0.683525 & 0.341763 \tabularnewline
t & -0.0106201278772925 & 0.003229 & -3.2888 & 0.001934 & 0.000967 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58551&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]6.59619621729017[/C][C]0.236136[/C][C]27.9338[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Infl[/C][C]-0.1480526479753[/C][C]0.039238[/C][C]-3.7732[/C][C]0.00046[/C][C]0.00023[/C][/ROW]
[ROW][C]M1[/C][C]-0.202067711946028[/C][C]0.271928[/C][C]-0.7431[/C][C]0.461204[/C][C]0.230602[/C][/ROW]
[ROW][C]M2[/C][C]-0.297369689987745[/C][C]0.271368[/C][C]-1.0958[/C][C]0.278862[/C][C]0.139431[/C][/ROW]
[ROW][C]M3[/C][C]-0.286749562110452[/C][C]0.270993[/C][C]-1.0581[/C][C]0.295515[/C][C]0.147757[/C][/ROW]
[ROW][C]M4[/C][C]-0.042778910868714[/C][C]0.27011[/C][C]-0.1584[/C][C]0.874854[/C][C]0.437427[/C][/ROW]
[ROW][C]M5[/C][C]0.324880164049072[/C][C]0.269764[/C][C]1.2043[/C][C]0.234629[/C][C]0.117315[/C][/ROW]
[ROW][C]M6[/C][C]0.460695027128835[/C][C]0.269296[/C][C]1.7107[/C][C]0.093867[/C][C]0.046933[/C][/ROW]
[ROW][C]M7[/C][C]0.460198313884645[/C][C]0.269197[/C][C]1.7095[/C][C]0.094093[/C][C]0.047046[/C][/ROW]
[ROW][C]M8[/C][C]0.313052124004902[/C][C]0.268802[/C][C]1.1646[/C][C]0.250178[/C][C]0.125089[/C][/ROW]
[ROW][C]M9[/C][C]0.177750145963182[/C][C]0.26861[/C][C]0.6617[/C][C]0.511439[/C][C]0.25572[/C][/ROW]
[ROW][C]M10[/C][C]-0.0205128850380429[/C][C]0.268449[/C][C]-0.0764[/C][C]0.939422[/C][C]0.469711[/C][/ROW]
[ROW][C]M11[/C][C]0.110107242839249[/C][C]0.268389[/C][C]0.4103[/C][C]0.683525[/C][C]0.341763[/C][/ROW]
[ROW][C]t[/C][C]-0.0106201278772925[/C][C]0.003229[/C][C]-3.2888[/C][C]0.001934[/C][C]0.000967[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58551&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58551&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)6.596196217290170.23613627.933800
Infl-0.14805264797530.039238-3.77320.000460.00023
M1-0.2020677119460280.271928-0.74310.4612040.230602
M2-0.2973696899877450.271368-1.09580.2788620.139431
M3-0.2867495621104520.270993-1.05810.2955150.147757
M4-0.0427789108687140.27011-0.15840.8748540.437427
M50.3248801640490720.2697641.20430.2346290.117315
M60.4606950271288350.2692961.71070.0938670.046933
M70.4601983138846450.2691971.70950.0940930.047046
M80.3130521240049020.2688021.16460.2501780.125089
M90.1777501459631820.268610.66170.5114390.25572
M10-0.02051288503804290.268449-0.07640.9394220.469711
M110.1101072428392490.2683890.41030.6835250.341763
t-0.01062012787729250.003229-3.28880.0019340.000967






Multiple Linear Regression - Regression Statistics
Multiple R0.714346509058098
R-squared0.510290935003491
Adjusted R-squared0.371894894895783
F-TEST (value)3.68717872712506
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0.000506791225271641
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.424236906606732
Sum Squared Residuals8.27893983465347

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.714346509058098 \tabularnewline
R-squared & 0.510290935003491 \tabularnewline
Adjusted R-squared & 0.371894894895783 \tabularnewline
F-TEST (value) & 3.68717872712506 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 0.000506791225271641 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.424236906606732 \tabularnewline
Sum Squared Residuals & 8.27893983465347 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58551&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.714346509058098[/C][/ROW]
[ROW][C]R-squared[/C][C]0.510290935003491[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.371894894895783[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]3.68717872712506[/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]0.000506791225271641[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.424236906606732[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]8.27893983465347[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58551&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58551&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 R0.714346509058098
R-squared0.510290935003491
Adjusted R-squared0.371894894895783
F-TEST (value)3.68717872712506
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0.000506791225271641
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.424236906606732
Sum Squared Residuals8.27893983465347






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
16.36.087403081516260.212596918483744
26.26.01109150519230.188908494807704
36.15.877844122014530.222155877985473
46.36.170415704569090.129584295430907
56.56.58667571079971-0.086675710799707
66.66.69706518120465-0.0970651812046475
76.56.64153254569058-0.141532545690575
86.26.40973990394589-0.209739903945889
96.26.323038857217-0.123038857216996
105.96.12896096313601-0.228960963136009
116.16.18973990394589-0.0897399039458891
126.16.069012533229350.0309874667706529
136.15.826714163810970.273285836189033
146.15.705986793094430.394013206905573
156.15.824428911474670.275571088525333
166.46.042974170041580.357025829958418
176.76.325986793094430.374013206905574
186.96.45118152829690.448818471703104
1976.440064687175410.559935312824586
2076.371129958203560.628870041796442
216.86.165986793094430.634013206905573
226.45.927493104620850.472506895379152
235.96.09190889901344-0.191908899013438
245.55.98598679309443-0.485986793094426
255.55.78810421806864-0.288104218068636
265.65.74140317133975-0.141403171339746
275.85.77101370093480.0289862990651938
285.95.95994842990666-0.0599484299066617
296.16.30218211214963-0.202182112149626
306.16.48659790654222-0.386597906542216
3166.4606758006232-0.460675800623204
3266.30290948286617-0.302909482866168
335.96.15698737694716-0.256987376947156
345.56.02213054205629-0.522130542056288
355.66.14213054205629-0.542130542056288
365.46.02140317133975-0.621403171339746
375.25.82352059631396-0.623520596313956
385.25.68798796079989-0.487987960799885
395.25.56954584241965-0.369545842419645
405.55.69925951220138-0.199259512201382
415.86.02668792964682-0.226687929646815
425.86.09266160565917-0.292661605659166
435.56.06673949974015-0.566739499740154
445.35.79053106360288-0.490531063602878
455.15.68902475207646-0.589024752076456
465.25.33208894522264-0.132088945222638
475.85.348452091639930.451547908360072
485.85.212919456125860.587080543874144
495.55.074257940290190.425742059709814
5054.953530569573640.0464694304263549
514.95.05716742315636-0.157167423156355
525.35.52740218328128-0.227402183281281
536.15.958467454309420.141532545690575
546.56.172493778297080.327506221702925
556.86.190987466770650.609012533229347
566.66.22568959138150.374310408618493
576.46.064962220664960.335037779335035
586.45.989326444964220.410673555035783
596.66.227768563344460.372231436655543
606.76.210678046210630.489321953789375

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 6.3 & 6.08740308151626 & 0.212596918483744 \tabularnewline
2 & 6.2 & 6.0110915051923 & 0.188908494807704 \tabularnewline
3 & 6.1 & 5.87784412201453 & 0.222155877985473 \tabularnewline
4 & 6.3 & 6.17041570456909 & 0.129584295430907 \tabularnewline
5 & 6.5 & 6.58667571079971 & -0.086675710799707 \tabularnewline
6 & 6.6 & 6.69706518120465 & -0.0970651812046475 \tabularnewline
7 & 6.5 & 6.64153254569058 & -0.141532545690575 \tabularnewline
8 & 6.2 & 6.40973990394589 & -0.209739903945889 \tabularnewline
9 & 6.2 & 6.323038857217 & -0.123038857216996 \tabularnewline
10 & 5.9 & 6.12896096313601 & -0.228960963136009 \tabularnewline
11 & 6.1 & 6.18973990394589 & -0.0897399039458891 \tabularnewline
12 & 6.1 & 6.06901253322935 & 0.0309874667706529 \tabularnewline
13 & 6.1 & 5.82671416381097 & 0.273285836189033 \tabularnewline
14 & 6.1 & 5.70598679309443 & 0.394013206905573 \tabularnewline
15 & 6.1 & 5.82442891147467 & 0.275571088525333 \tabularnewline
16 & 6.4 & 6.04297417004158 & 0.357025829958418 \tabularnewline
17 & 6.7 & 6.32598679309443 & 0.374013206905574 \tabularnewline
18 & 6.9 & 6.4511815282969 & 0.448818471703104 \tabularnewline
19 & 7 & 6.44006468717541 & 0.559935312824586 \tabularnewline
20 & 7 & 6.37112995820356 & 0.628870041796442 \tabularnewline
21 & 6.8 & 6.16598679309443 & 0.634013206905573 \tabularnewline
22 & 6.4 & 5.92749310462085 & 0.472506895379152 \tabularnewline
23 & 5.9 & 6.09190889901344 & -0.191908899013438 \tabularnewline
24 & 5.5 & 5.98598679309443 & -0.485986793094426 \tabularnewline
25 & 5.5 & 5.78810421806864 & -0.288104218068636 \tabularnewline
26 & 5.6 & 5.74140317133975 & -0.141403171339746 \tabularnewline
27 & 5.8 & 5.7710137009348 & 0.0289862990651938 \tabularnewline
28 & 5.9 & 5.95994842990666 & -0.0599484299066617 \tabularnewline
29 & 6.1 & 6.30218211214963 & -0.202182112149626 \tabularnewline
30 & 6.1 & 6.48659790654222 & -0.386597906542216 \tabularnewline
31 & 6 & 6.4606758006232 & -0.460675800623204 \tabularnewline
32 & 6 & 6.30290948286617 & -0.302909482866168 \tabularnewline
33 & 5.9 & 6.15698737694716 & -0.256987376947156 \tabularnewline
34 & 5.5 & 6.02213054205629 & -0.522130542056288 \tabularnewline
35 & 5.6 & 6.14213054205629 & -0.542130542056288 \tabularnewline
36 & 5.4 & 6.02140317133975 & -0.621403171339746 \tabularnewline
37 & 5.2 & 5.82352059631396 & -0.623520596313956 \tabularnewline
38 & 5.2 & 5.68798796079989 & -0.487987960799885 \tabularnewline
39 & 5.2 & 5.56954584241965 & -0.369545842419645 \tabularnewline
40 & 5.5 & 5.69925951220138 & -0.199259512201382 \tabularnewline
41 & 5.8 & 6.02668792964682 & -0.226687929646815 \tabularnewline
42 & 5.8 & 6.09266160565917 & -0.292661605659166 \tabularnewline
43 & 5.5 & 6.06673949974015 & -0.566739499740154 \tabularnewline
44 & 5.3 & 5.79053106360288 & -0.490531063602878 \tabularnewline
45 & 5.1 & 5.68902475207646 & -0.589024752076456 \tabularnewline
46 & 5.2 & 5.33208894522264 & -0.132088945222638 \tabularnewline
47 & 5.8 & 5.34845209163993 & 0.451547908360072 \tabularnewline
48 & 5.8 & 5.21291945612586 & 0.587080543874144 \tabularnewline
49 & 5.5 & 5.07425794029019 & 0.425742059709814 \tabularnewline
50 & 5 & 4.95353056957364 & 0.0464694304263549 \tabularnewline
51 & 4.9 & 5.05716742315636 & -0.157167423156355 \tabularnewline
52 & 5.3 & 5.52740218328128 & -0.227402183281281 \tabularnewline
53 & 6.1 & 5.95846745430942 & 0.141532545690575 \tabularnewline
54 & 6.5 & 6.17249377829708 & 0.327506221702925 \tabularnewline
55 & 6.8 & 6.19098746677065 & 0.609012533229347 \tabularnewline
56 & 6.6 & 6.2256895913815 & 0.374310408618493 \tabularnewline
57 & 6.4 & 6.06496222066496 & 0.335037779335035 \tabularnewline
58 & 6.4 & 5.98932644496422 & 0.410673555035783 \tabularnewline
59 & 6.6 & 6.22776856334446 & 0.372231436655543 \tabularnewline
60 & 6.7 & 6.21067804621063 & 0.489321953789375 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58551&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]6.3[/C][C]6.08740308151626[/C][C]0.212596918483744[/C][/ROW]
[ROW][C]2[/C][C]6.2[/C][C]6.0110915051923[/C][C]0.188908494807704[/C][/ROW]
[ROW][C]3[/C][C]6.1[/C][C]5.87784412201453[/C][C]0.222155877985473[/C][/ROW]
[ROW][C]4[/C][C]6.3[/C][C]6.17041570456909[/C][C]0.129584295430907[/C][/ROW]
[ROW][C]5[/C][C]6.5[/C][C]6.58667571079971[/C][C]-0.086675710799707[/C][/ROW]
[ROW][C]6[/C][C]6.6[/C][C]6.69706518120465[/C][C]-0.0970651812046475[/C][/ROW]
[ROW][C]7[/C][C]6.5[/C][C]6.64153254569058[/C][C]-0.141532545690575[/C][/ROW]
[ROW][C]8[/C][C]6.2[/C][C]6.40973990394589[/C][C]-0.209739903945889[/C][/ROW]
[ROW][C]9[/C][C]6.2[/C][C]6.323038857217[/C][C]-0.123038857216996[/C][/ROW]
[ROW][C]10[/C][C]5.9[/C][C]6.12896096313601[/C][C]-0.228960963136009[/C][/ROW]
[ROW][C]11[/C][C]6.1[/C][C]6.18973990394589[/C][C]-0.0897399039458891[/C][/ROW]
[ROW][C]12[/C][C]6.1[/C][C]6.06901253322935[/C][C]0.0309874667706529[/C][/ROW]
[ROW][C]13[/C][C]6.1[/C][C]5.82671416381097[/C][C]0.273285836189033[/C][/ROW]
[ROW][C]14[/C][C]6.1[/C][C]5.70598679309443[/C][C]0.394013206905573[/C][/ROW]
[ROW][C]15[/C][C]6.1[/C][C]5.82442891147467[/C][C]0.275571088525333[/C][/ROW]
[ROW][C]16[/C][C]6.4[/C][C]6.04297417004158[/C][C]0.357025829958418[/C][/ROW]
[ROW][C]17[/C][C]6.7[/C][C]6.32598679309443[/C][C]0.374013206905574[/C][/ROW]
[ROW][C]18[/C][C]6.9[/C][C]6.4511815282969[/C][C]0.448818471703104[/C][/ROW]
[ROW][C]19[/C][C]7[/C][C]6.44006468717541[/C][C]0.559935312824586[/C][/ROW]
[ROW][C]20[/C][C]7[/C][C]6.37112995820356[/C][C]0.628870041796442[/C][/ROW]
[ROW][C]21[/C][C]6.8[/C][C]6.16598679309443[/C][C]0.634013206905573[/C][/ROW]
[ROW][C]22[/C][C]6.4[/C][C]5.92749310462085[/C][C]0.472506895379152[/C][/ROW]
[ROW][C]23[/C][C]5.9[/C][C]6.09190889901344[/C][C]-0.191908899013438[/C][/ROW]
[ROW][C]24[/C][C]5.5[/C][C]5.98598679309443[/C][C]-0.485986793094426[/C][/ROW]
[ROW][C]25[/C][C]5.5[/C][C]5.78810421806864[/C][C]-0.288104218068636[/C][/ROW]
[ROW][C]26[/C][C]5.6[/C][C]5.74140317133975[/C][C]-0.141403171339746[/C][/ROW]
[ROW][C]27[/C][C]5.8[/C][C]5.7710137009348[/C][C]0.0289862990651938[/C][/ROW]
[ROW][C]28[/C][C]5.9[/C][C]5.95994842990666[/C][C]-0.0599484299066617[/C][/ROW]
[ROW][C]29[/C][C]6.1[/C][C]6.30218211214963[/C][C]-0.202182112149626[/C][/ROW]
[ROW][C]30[/C][C]6.1[/C][C]6.48659790654222[/C][C]-0.386597906542216[/C][/ROW]
[ROW][C]31[/C][C]6[/C][C]6.4606758006232[/C][C]-0.460675800623204[/C][/ROW]
[ROW][C]32[/C][C]6[/C][C]6.30290948286617[/C][C]-0.302909482866168[/C][/ROW]
[ROW][C]33[/C][C]5.9[/C][C]6.15698737694716[/C][C]-0.256987376947156[/C][/ROW]
[ROW][C]34[/C][C]5.5[/C][C]6.02213054205629[/C][C]-0.522130542056288[/C][/ROW]
[ROW][C]35[/C][C]5.6[/C][C]6.14213054205629[/C][C]-0.542130542056288[/C][/ROW]
[ROW][C]36[/C][C]5.4[/C][C]6.02140317133975[/C][C]-0.621403171339746[/C][/ROW]
[ROW][C]37[/C][C]5.2[/C][C]5.82352059631396[/C][C]-0.623520596313956[/C][/ROW]
[ROW][C]38[/C][C]5.2[/C][C]5.68798796079989[/C][C]-0.487987960799885[/C][/ROW]
[ROW][C]39[/C][C]5.2[/C][C]5.56954584241965[/C][C]-0.369545842419645[/C][/ROW]
[ROW][C]40[/C][C]5.5[/C][C]5.69925951220138[/C][C]-0.199259512201382[/C][/ROW]
[ROW][C]41[/C][C]5.8[/C][C]6.02668792964682[/C][C]-0.226687929646815[/C][/ROW]
[ROW][C]42[/C][C]5.8[/C][C]6.09266160565917[/C][C]-0.292661605659166[/C][/ROW]
[ROW][C]43[/C][C]5.5[/C][C]6.06673949974015[/C][C]-0.566739499740154[/C][/ROW]
[ROW][C]44[/C][C]5.3[/C][C]5.79053106360288[/C][C]-0.490531063602878[/C][/ROW]
[ROW][C]45[/C][C]5.1[/C][C]5.68902475207646[/C][C]-0.589024752076456[/C][/ROW]
[ROW][C]46[/C][C]5.2[/C][C]5.33208894522264[/C][C]-0.132088945222638[/C][/ROW]
[ROW][C]47[/C][C]5.8[/C][C]5.34845209163993[/C][C]0.451547908360072[/C][/ROW]
[ROW][C]48[/C][C]5.8[/C][C]5.21291945612586[/C][C]0.587080543874144[/C][/ROW]
[ROW][C]49[/C][C]5.5[/C][C]5.07425794029019[/C][C]0.425742059709814[/C][/ROW]
[ROW][C]50[/C][C]5[/C][C]4.95353056957364[/C][C]0.0464694304263549[/C][/ROW]
[ROW][C]51[/C][C]4.9[/C][C]5.05716742315636[/C][C]-0.157167423156355[/C][/ROW]
[ROW][C]52[/C][C]5.3[/C][C]5.52740218328128[/C][C]-0.227402183281281[/C][/ROW]
[ROW][C]53[/C][C]6.1[/C][C]5.95846745430942[/C][C]0.141532545690575[/C][/ROW]
[ROW][C]54[/C][C]6.5[/C][C]6.17249377829708[/C][C]0.327506221702925[/C][/ROW]
[ROW][C]55[/C][C]6.8[/C][C]6.19098746677065[/C][C]0.609012533229347[/C][/ROW]
[ROW][C]56[/C][C]6.6[/C][C]6.2256895913815[/C][C]0.374310408618493[/C][/ROW]
[ROW][C]57[/C][C]6.4[/C][C]6.06496222066496[/C][C]0.335037779335035[/C][/ROW]
[ROW][C]58[/C][C]6.4[/C][C]5.98932644496422[/C][C]0.410673555035783[/C][/ROW]
[ROW][C]59[/C][C]6.6[/C][C]6.22776856334446[/C][C]0.372231436655543[/C][/ROW]
[ROW][C]60[/C][C]6.7[/C][C]6.21067804621063[/C][C]0.489321953789375[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58551&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58551&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
16.36.087403081516260.212596918483744
26.26.01109150519230.188908494807704
36.15.877844122014530.222155877985473
46.36.170415704569090.129584295430907
56.56.58667571079971-0.086675710799707
66.66.69706518120465-0.0970651812046475
76.56.64153254569058-0.141532545690575
86.26.40973990394589-0.209739903945889
96.26.323038857217-0.123038857216996
105.96.12896096313601-0.228960963136009
116.16.18973990394589-0.0897399039458891
126.16.069012533229350.0309874667706529
136.15.826714163810970.273285836189033
146.15.705986793094430.394013206905573
156.15.824428911474670.275571088525333
166.46.042974170041580.357025829958418
176.76.325986793094430.374013206905574
186.96.45118152829690.448818471703104
1976.440064687175410.559935312824586
2076.371129958203560.628870041796442
216.86.165986793094430.634013206905573
226.45.927493104620850.472506895379152
235.96.09190889901344-0.191908899013438
245.55.98598679309443-0.485986793094426
255.55.78810421806864-0.288104218068636
265.65.74140317133975-0.141403171339746
275.85.77101370093480.0289862990651938
285.95.95994842990666-0.0599484299066617
296.16.30218211214963-0.202182112149626
306.16.48659790654222-0.386597906542216
3166.4606758006232-0.460675800623204
3266.30290948286617-0.302909482866168
335.96.15698737694716-0.256987376947156
345.56.02213054205629-0.522130542056288
355.66.14213054205629-0.542130542056288
365.46.02140317133975-0.621403171339746
375.25.82352059631396-0.623520596313956
385.25.68798796079989-0.487987960799885
395.25.56954584241965-0.369545842419645
405.55.69925951220138-0.199259512201382
415.86.02668792964682-0.226687929646815
425.86.09266160565917-0.292661605659166
435.56.06673949974015-0.566739499740154
445.35.79053106360288-0.490531063602878
455.15.68902475207646-0.589024752076456
465.25.33208894522264-0.132088945222638
475.85.348452091639930.451547908360072
485.85.212919456125860.587080543874144
495.55.074257940290190.425742059709814
5054.953530569573640.0464694304263549
514.95.05716742315636-0.157167423156355
525.35.52740218328128-0.227402183281281
536.15.958467454309420.141532545690575
546.56.172493778297080.327506221702925
556.86.190987466770650.609012533229347
566.66.22568959138150.374310408618493
576.46.064962220664960.335037779335035
586.45.989326444964220.410673555035783
596.66.227768563344460.372231436655543
606.76.210678046210630.489321953789375






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.02282373858911840.04564747717823680.977176261410882
180.01708702242546270.03417404485092540.982912977574537
190.02637431782676070.05274863565352130.97362568217324
200.0509101102645360.1018202205290720.949089889735464
210.06809211845205170.1361842369041030.931907881547948
220.08809842621431420.1761968524286280.911901573785686
230.1284962830921880.2569925661843750.871503716907812
240.2745346803927680.5490693607855350.725465319607232
250.4453232167243250.890646433448650.554676783275675
260.456598198565320.913196397130640.54340180143468
270.493879952947830.987759905895660.50612004705217
280.5584831913780760.8830336172438490.441516808621924
290.5543322919225160.8913354161549670.445667708077484
300.5035710433742520.9928579132514960.496428956625748
310.4499633120954540.8999266241909080.550036687904546
320.4437584645269930.8875169290539860.556241535473007
330.551453535211460.897092929577080.44854646478854
340.4810078510651490.9620157021302970.518992148934851
350.3949981336226090.7899962672452180.605001866377391
360.3336887483819360.6673774967638710.666311251618064
370.2960740914950320.5921481829900630.703925908504968
380.2146232834525520.4292465669051050.785376716547448
390.228983597637090.457967195274180.77101640236291
400.5084497669397610.9831004661204780.491550233060239
410.7872277275421070.4255445449157870.212772272457893
420.986091182244820.02781763551035860.0139088177551793
430.9807423588543640.03851528229127120.0192576411456356

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.0228237385891184 & 0.0456474771782368 & 0.977176261410882 \tabularnewline
18 & 0.0170870224254627 & 0.0341740448509254 & 0.982912977574537 \tabularnewline
19 & 0.0263743178267607 & 0.0527486356535213 & 0.97362568217324 \tabularnewline
20 & 0.050910110264536 & 0.101820220529072 & 0.949089889735464 \tabularnewline
21 & 0.0680921184520517 & 0.136184236904103 & 0.931907881547948 \tabularnewline
22 & 0.0880984262143142 & 0.176196852428628 & 0.911901573785686 \tabularnewline
23 & 0.128496283092188 & 0.256992566184375 & 0.871503716907812 \tabularnewline
24 & 0.274534680392768 & 0.549069360785535 & 0.725465319607232 \tabularnewline
25 & 0.445323216724325 & 0.89064643344865 & 0.554676783275675 \tabularnewline
26 & 0.45659819856532 & 0.91319639713064 & 0.54340180143468 \tabularnewline
27 & 0.49387995294783 & 0.98775990589566 & 0.50612004705217 \tabularnewline
28 & 0.558483191378076 & 0.883033617243849 & 0.441516808621924 \tabularnewline
29 & 0.554332291922516 & 0.891335416154967 & 0.445667708077484 \tabularnewline
30 & 0.503571043374252 & 0.992857913251496 & 0.496428956625748 \tabularnewline
31 & 0.449963312095454 & 0.899926624190908 & 0.550036687904546 \tabularnewline
32 & 0.443758464526993 & 0.887516929053986 & 0.556241535473007 \tabularnewline
33 & 0.55145353521146 & 0.89709292957708 & 0.44854646478854 \tabularnewline
34 & 0.481007851065149 & 0.962015702130297 & 0.518992148934851 \tabularnewline
35 & 0.394998133622609 & 0.789996267245218 & 0.605001866377391 \tabularnewline
36 & 0.333688748381936 & 0.667377496763871 & 0.666311251618064 \tabularnewline
37 & 0.296074091495032 & 0.592148182990063 & 0.703925908504968 \tabularnewline
38 & 0.214623283452552 & 0.429246566905105 & 0.785376716547448 \tabularnewline
39 & 0.22898359763709 & 0.45796719527418 & 0.77101640236291 \tabularnewline
40 & 0.508449766939761 & 0.983100466120478 & 0.491550233060239 \tabularnewline
41 & 0.787227727542107 & 0.425544544915787 & 0.212772272457893 \tabularnewline
42 & 0.98609118224482 & 0.0278176355103586 & 0.0139088177551793 \tabularnewline
43 & 0.980742358854364 & 0.0385152822912712 & 0.0192576411456356 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58551&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]0.0228237385891184[/C][C]0.0456474771782368[/C][C]0.977176261410882[/C][/ROW]
[ROW][C]18[/C][C]0.0170870224254627[/C][C]0.0341740448509254[/C][C]0.982912977574537[/C][/ROW]
[ROW][C]19[/C][C]0.0263743178267607[/C][C]0.0527486356535213[/C][C]0.97362568217324[/C][/ROW]
[ROW][C]20[/C][C]0.050910110264536[/C][C]0.101820220529072[/C][C]0.949089889735464[/C][/ROW]
[ROW][C]21[/C][C]0.0680921184520517[/C][C]0.136184236904103[/C][C]0.931907881547948[/C][/ROW]
[ROW][C]22[/C][C]0.0880984262143142[/C][C]0.176196852428628[/C][C]0.911901573785686[/C][/ROW]
[ROW][C]23[/C][C]0.128496283092188[/C][C]0.256992566184375[/C][C]0.871503716907812[/C][/ROW]
[ROW][C]24[/C][C]0.274534680392768[/C][C]0.549069360785535[/C][C]0.725465319607232[/C][/ROW]
[ROW][C]25[/C][C]0.445323216724325[/C][C]0.89064643344865[/C][C]0.554676783275675[/C][/ROW]
[ROW][C]26[/C][C]0.45659819856532[/C][C]0.91319639713064[/C][C]0.54340180143468[/C][/ROW]
[ROW][C]27[/C][C]0.49387995294783[/C][C]0.98775990589566[/C][C]0.50612004705217[/C][/ROW]
[ROW][C]28[/C][C]0.558483191378076[/C][C]0.883033617243849[/C][C]0.441516808621924[/C][/ROW]
[ROW][C]29[/C][C]0.554332291922516[/C][C]0.891335416154967[/C][C]0.445667708077484[/C][/ROW]
[ROW][C]30[/C][C]0.503571043374252[/C][C]0.992857913251496[/C][C]0.496428956625748[/C][/ROW]
[ROW][C]31[/C][C]0.449963312095454[/C][C]0.899926624190908[/C][C]0.550036687904546[/C][/ROW]
[ROW][C]32[/C][C]0.443758464526993[/C][C]0.887516929053986[/C][C]0.556241535473007[/C][/ROW]
[ROW][C]33[/C][C]0.55145353521146[/C][C]0.89709292957708[/C][C]0.44854646478854[/C][/ROW]
[ROW][C]34[/C][C]0.481007851065149[/C][C]0.962015702130297[/C][C]0.518992148934851[/C][/ROW]
[ROW][C]35[/C][C]0.394998133622609[/C][C]0.789996267245218[/C][C]0.605001866377391[/C][/ROW]
[ROW][C]36[/C][C]0.333688748381936[/C][C]0.667377496763871[/C][C]0.666311251618064[/C][/ROW]
[ROW][C]37[/C][C]0.296074091495032[/C][C]0.592148182990063[/C][C]0.703925908504968[/C][/ROW]
[ROW][C]38[/C][C]0.214623283452552[/C][C]0.429246566905105[/C][C]0.785376716547448[/C][/ROW]
[ROW][C]39[/C][C]0.22898359763709[/C][C]0.45796719527418[/C][C]0.77101640236291[/C][/ROW]
[ROW][C]40[/C][C]0.508449766939761[/C][C]0.983100466120478[/C][C]0.491550233060239[/C][/ROW]
[ROW][C]41[/C][C]0.787227727542107[/C][C]0.425544544915787[/C][C]0.212772272457893[/C][/ROW]
[ROW][C]42[/C][C]0.98609118224482[/C][C]0.0278176355103586[/C][C]0.0139088177551793[/C][/ROW]
[ROW][C]43[/C][C]0.980742358854364[/C][C]0.0385152822912712[/C][C]0.0192576411456356[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58551&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58551&T=5

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


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.02282373858911840.04564747717823680.977176261410882
180.01708702242546270.03417404485092540.982912977574537
190.02637431782676070.05274863565352130.97362568217324
200.0509101102645360.1018202205290720.949089889735464
210.06809211845205170.1361842369041030.931907881547948
220.08809842621431420.1761968524286280.911901573785686
230.1284962830921880.2569925661843750.871503716907812
240.2745346803927680.5490693607855350.725465319607232
250.4453232167243250.890646433448650.554676783275675
260.456598198565320.913196397130640.54340180143468
270.493879952947830.987759905895660.50612004705217
280.5584831913780760.8830336172438490.441516808621924
290.5543322919225160.8913354161549670.445667708077484
300.5035710433742520.9928579132514960.496428956625748
310.4499633120954540.8999266241909080.550036687904546
320.4437584645269930.8875169290539860.556241535473007
330.551453535211460.897092929577080.44854646478854
340.4810078510651490.9620157021302970.518992148934851
350.3949981336226090.7899962672452180.605001866377391
360.3336887483819360.6673774967638710.666311251618064
370.2960740914950320.5921481829900630.703925908504968
380.2146232834525520.4292465669051050.785376716547448
390.228983597637090.457967195274180.77101640236291
400.5084497669397610.9831004661204780.491550233060239
410.7872277275421070.4255445449157870.212772272457893
420.986091182244820.02781763551035860.0139088177551793
430.9807423588543640.03851528229127120.0192576411456356






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level40.148148148148148NOK
10% type I error level50.185185185185185NOK

\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 & 4 & 0.148148148148148 & NOK \tabularnewline
10% type I error level & 5 & 0.185185185185185 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58551&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]4[/C][C]0.148148148148148[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]5[/C][C]0.185185185185185[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58551&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58551&T=6

As an alternative you can also use a QR Code:  
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 level40.148148148148148NOK
10% type I error level50.185185185185185NOK


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 10
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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)
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')
}