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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 computationMon, 01 Dec 2008 09:30:23 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/01/t1228149175nem4gjrl1k1bwze.htm/, Retrieved Thu, 09 May 2024 15:20:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26975, Retrieved Thu, 09 May 2024 15:20:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact252

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [blog] [2008-12-01 15:44:12] [12d343c4448a5f9e527bb31caeac580b]
-   PD  [Multiple Regression] [blog] [2008-12-01 16:17:50] [12d343c4448a5f9e527bb31caeac580b]
-   PD      [Multiple Regression] [dioxine] [2008-12-01 16:30:23] [98255691c21504803b38711776845ae0] [Current]
-    D        [Multiple Regression] [Hypothese 1 en 2 ...] [2008-12-03 15:49:48] [12d343c4448a5f9e527bb31caeac580b]
-               [Multiple Regression] [paper - omzet en ...] [2008-12-03 20:34:00] [7a664918911e34206ce9d0436dd7c1c8]
- RM D          [Multiple Regression] [] [2009-12-07 20:08:54] [1f74ef2f756548f1f3a7b6136ea56d7f]
- RM D          [Multiple Regression] [] [2009-12-07 20:21:10] [1f74ef2f756548f1f3a7b6136ea56d7f]
- RMPD          [Univariate Data Series] [Paper: 1 univaria...] [2009-12-11 14:47:17] [0f0e461427f61416e46aeda5f4901bed]
- RMPD          [Univariate Data Series] [Paper: 1 univaria...] [2009-12-11 14:49:38] [0f0e461427f61416e46aeda5f4901bed]
-  MPD          [Multiple Regression] [Paper: 2 Multiple...] [2009-12-11 14:53:22] [0f0e461427f61416e46aeda5f4901bed]
- RMPD          [(Partial) Autocorrelation Function] [paper:3 ACF (d,D=0)] [2009-12-11 14:59:19] [0f0e461427f61416e46aeda5f4901bed]
-                 [(Partial) Autocorrelation Function] [paper:4 ACF (d=1,...] [2009-12-11 15:01:14] [0f0e461427f61416e46aeda5f4901bed]
- RM              [Variance Reduction Matrix] [paper:5 VRM] [2009-12-11 15:03:16] [0f0e461427f61416e46aeda5f4901bed]
- RM              [Spectral Analysis] [paper6: Spectruma...] [2009-12-11 15:05:17] [0f0e461427f61416e46aeda5f4901bed]
- RM              [Spectral Analysis] [paper6: Spectruma...] [2009-12-11 15:05:17] [0f0e461427f61416e46aeda5f4901bed]
- RM              [Spectral Analysis] [paper:7 Spectruma...] [2009-12-11 15:07:09] [0f0e461427f61416e46aeda5f4901bed]
-                   [Spectral Analysis] [paper:8 Spectruma...] [2009-12-11 15:42:28] [0f0e461427f61416e46aeda5f4901bed]
-                 [(Partial) Autocorrelation Function] [paper:8 ACF (d=1,...] [2009-12-11 15:39:41] [0f0e461427f61416e46aeda5f4901bed]
- RM              [ARIMA Backward Selection] [paper: 9 Backward...] [2009-12-11 15:54:31] [0f0e461427f61416e46aeda5f4901bed]
- RM D          [Multiple Regression] [] [2009-12-12 21:02:49] [9b30bff5dd5a100f8196daf92e735633]
- RM D          [Multiple Regression] [] [2009-12-12 21:45:38] [9b30bff5dd5a100f8196daf92e735633]
-  MPD          [Multiple Regression] [mutiple regression ] [2009-12-14 19:31:04] [ba905ddf7cdf9ecb063c35348c4dab2e]
- RMPD          [Univariate Data Series] [Paper Datareeks] [2009-12-15 11:21:03] [83058a88a37d754675a5cd22dab372fc]
-   PD            [Univariate Data Series] [paper run sequenc...] [2010-12-14 13:20:41] [d87a19cd5db53e12ea62bda70b3bb267]
-   PD            [Univariate Data Series] [paper run sequenc...] [2010-12-14 13:20:41] [d87a19cd5db53e12ea62bda70b3bb267]
-  MPD          [Multiple Regression] [Multiple regression] [2009-12-16 16:36:16] [fa44bc1b850de3469c0e3e9a5981c418]
- RMPD          [Univariate Data Series] [] [2009-12-16 19:28:18] [09f192433169b2c787c4a71fde86e883]
-  M D          [Multiple Regression] [Multiple Regression] [2009-12-18 15:13:02] [976efdaed7598845c859b86bc2e467ce]
- RM D          [Multiple Regression] [] [2009-12-18 16:07:40] [4409a44d89cea4fe559b38f99bc8a66c]
- RMPD          [Univariate Data Series] [] [2009-12-18 16:38:33] [4409a44d89cea4fe559b38f99bc8a66c]
-  M D          [Multiple Regression] [Paper Multiple Re...] [2009-12-29 19:11:43] [f15cf5036ae52d4243ad71d4fb151dbe]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14929387.5	0
14717825.3	0
15826281.2	0
16301309.6	0
15033016.9	0
16998460.6	0
14066462.7	0
13328937.3	0
17319718.2	0
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15887037.4	0
17935679.1	0
15869489	0
15892510.9	0
17556558.1	0
16791643	0
15953688.5	0
18144913.6	0
14390881	0
13885708.7	0
17332571.5	0
17152595.8	0
16003877.1	0
16841467.1	0
14783398.1	0
14667847.5	0
17714362.2	0
16282088	0
15014866.2	0
17722582.4	1
13876509.4	1
15495489.6	1
17799521.1	1
17920079.1	1
17248022.4	1
18813782.4	1
16249688.3	1
17823358.5	0
20424438.3	0
17814218.7	0
19699959.6	0
19776328.1	0
15679833.1	0
17119266.5	0
20092613	0
20863688.3	0
20925203.1	0
21032593	0
20664684.3	0
19711511.4	0
22553293.4	0
19498332.9	0
20722827.8	0
21321275	0
17960847.7	0
17789654.9	0
20003708.5	0
21169851.7	0
20422839.4	0
19810562.3	0

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=26975&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=26975&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26975&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
x[t] = + 15686151.7530378 -1008053.78878749y[t] -1347903.07244676M1[t] -1580740.21089092M2[t] + 577128.048422425M3[t] -994847.812264233M4[t] -1142002.11295089M5[t] + 472941.124119949M6[t] -3219371.69656671M7[t] -2984974.73725337M8[t] -93667.3379400267M9[t] + 240726.881373318M10[t] -694913.239313342M11[t] + 94507.660686658t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
x[t] =  +  15686151.7530378 -1008053.78878749y[t] -1347903.07244676M1[t] -1580740.21089092M2[t] +  577128.048422425M3[t] -994847.812264233M4[t] -1142002.11295089M5[t] +  472941.124119949M6[t] -3219371.69656671M7[t] -2984974.73725337M8[t] -93667.3379400267M9[t] +  240726.881373318M10[t] -694913.239313342M11[t] +  94507.660686658t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26975&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]x[t] =  +  15686151.7530378 -1008053.78878749y[t] -1347903.07244676M1[t] -1580740.21089092M2[t] +  577128.048422425M3[t] -994847.812264233M4[t] -1142002.11295089M5[t] +  472941.124119949M6[t] -3219371.69656671M7[t] -2984974.73725337M8[t] -93667.3379400267M9[t] +  240726.881373318M10[t] -694913.239313342M11[t] +  94507.660686658t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26975&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26975&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
x[t] = + 15686151.7530378 -1008053.78878749y[t] -1347903.07244676M1[t] -1580740.21089092M2[t] + 577128.048422425M3[t] -994847.812264233M4[t] -1142002.11295089M5[t] + 472941.124119949M6[t] -3219371.69656671M7[t] -2984974.73725337M8[t] -93667.3379400267M9[t] + 240726.881373318M10[t] -694913.239313342M11[t] + 94507.660686658t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)15686151.7530378520436.86679930.140400
y-1008053.78878749389173.999703-2.59020.0128040.006402
M1-1347903.07244676627702.975277-2.14740.0370680.018534
M2-1580740.21089092631245.257239-2.50420.0158830.007941
M3577128.048422425630433.8519610.91540.3647320.182366
M4-994847.812264233629710.487874-1.57980.1209940.060497
M5-1142002.11295089629075.468688-1.81540.075990.037995
M6472941.124119949623893.3829230.7580.4522890.226144
M7-3219371.69656671623398.675531-5.16425e-063e-06
M8-2984974.73725337622993.622745-4.79131.8e-059e-06
M9-93667.3379400267622678.399524-0.15040.8810860.440543
M10240726.881373318622453.1423450.38670.7007330.350366
M11-694913.239313342622317.948901-1.11670.2699420.134971
t94507.6606866587489.65711612.618400

\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) & 15686151.7530378 & 520436.866799 & 30.1404 & 0 & 0 \tabularnewline
y & -1008053.78878749 & 389173.999703 & -2.5902 & 0.012804 & 0.006402 \tabularnewline
M1 & -1347903.07244676 & 627702.975277 & -2.1474 & 0.037068 & 0.018534 \tabularnewline
M2 & -1580740.21089092 & 631245.257239 & -2.5042 & 0.015883 & 0.007941 \tabularnewline
M3 & 577128.048422425 & 630433.851961 & 0.9154 & 0.364732 & 0.182366 \tabularnewline
M4 & -994847.812264233 & 629710.487874 & -1.5798 & 0.120994 & 0.060497 \tabularnewline
M5 & -1142002.11295089 & 629075.468688 & -1.8154 & 0.07599 & 0.037995 \tabularnewline
M6 & 472941.124119949 & 623893.382923 & 0.758 & 0.452289 & 0.226144 \tabularnewline
M7 & -3219371.69656671 & 623398.675531 & -5.1642 & 5e-06 & 3e-06 \tabularnewline
M8 & -2984974.73725337 & 622993.622745 & -4.7913 & 1.8e-05 & 9e-06 \tabularnewline
M9 & -93667.3379400267 & 622678.399524 & -0.1504 & 0.881086 & 0.440543 \tabularnewline
M10 & 240726.881373318 & 622453.142345 & 0.3867 & 0.700733 & 0.350366 \tabularnewline
M11 & -694913.239313342 & 622317.948901 & -1.1167 & 0.269942 & 0.134971 \tabularnewline
t & 94507.660686658 & 7489.657116 & 12.6184 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26975&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]15686151.7530378[/C][C]520436.866799[/C][C]30.1404[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]y[/C][C]-1008053.78878749[/C][C]389173.999703[/C][C]-2.5902[/C][C]0.012804[/C][C]0.006402[/C][/ROW]
[ROW][C]M1[/C][C]-1347903.07244676[/C][C]627702.975277[/C][C]-2.1474[/C][C]0.037068[/C][C]0.018534[/C][/ROW]
[ROW][C]M2[/C][C]-1580740.21089092[/C][C]631245.257239[/C][C]-2.5042[/C][C]0.015883[/C][C]0.007941[/C][/ROW]
[ROW][C]M3[/C][C]577128.048422425[/C][C]630433.851961[/C][C]0.9154[/C][C]0.364732[/C][C]0.182366[/C][/ROW]
[ROW][C]M4[/C][C]-994847.812264233[/C][C]629710.487874[/C][C]-1.5798[/C][C]0.120994[/C][C]0.060497[/C][/ROW]
[ROW][C]M5[/C][C]-1142002.11295089[/C][C]629075.468688[/C][C]-1.8154[/C][C]0.07599[/C][C]0.037995[/C][/ROW]
[ROW][C]M6[/C][C]472941.124119949[/C][C]623893.382923[/C][C]0.758[/C][C]0.452289[/C][C]0.226144[/C][/ROW]
[ROW][C]M7[/C][C]-3219371.69656671[/C][C]623398.675531[/C][C]-5.1642[/C][C]5e-06[/C][C]3e-06[/C][/ROW]
[ROW][C]M8[/C][C]-2984974.73725337[/C][C]622993.622745[/C][C]-4.7913[/C][C]1.8e-05[/C][C]9e-06[/C][/ROW]
[ROW][C]M9[/C][C]-93667.3379400267[/C][C]622678.399524[/C][C]-0.1504[/C][C]0.881086[/C][C]0.440543[/C][/ROW]
[ROW][C]M10[/C][C]240726.881373318[/C][C]622453.142345[/C][C]0.3867[/C][C]0.700733[/C][C]0.350366[/C][/ROW]
[ROW][C]M11[/C][C]-694913.239313342[/C][C]622317.948901[/C][C]-1.1167[/C][C]0.269942[/C][C]0.134971[/C][/ROW]
[ROW][C]t[/C][C]94507.660686658[/C][C]7489.657116[/C][C]12.6184[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26975&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26975&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)15686151.7530378520436.86679930.140400
y-1008053.78878749389173.999703-2.59020.0128040.006402
M1-1347903.07244676627702.975277-2.14740.0370680.018534
M2-1580740.21089092631245.257239-2.50420.0158830.007941
M3577128.048422425630433.8519610.91540.3647320.182366
M4-994847.812264233629710.487874-1.57980.1209940.060497
M5-1142002.11295089629075.468688-1.81540.075990.037995
M6472941.124119949623893.3829230.7580.4522890.226144
M7-3219371.69656671623398.675531-5.16425e-063e-06
M8-2984974.73725337622993.622745-4.79131.8e-059e-06
M9-93667.3379400267622678.399524-0.15040.8810860.440543
M10240726.881373318622453.1423450.38670.7007330.350366
M11-694913.239313342622317.948901-1.11670.2699420.134971
t94507.6606866587489.65711612.618400






Multiple Linear Regression - Regression Statistics
Multiple R0.923521868842376
R-squared0.852892642230114
Adjusted R-squared0.81131882372993
F-TEST (value)20.5151384452770
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value6.88338275267597e-15
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation983899.810144435
Sum Squared Residuals44530706474503.8

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.923521868842376 \tabularnewline
R-squared & 0.852892642230114 \tabularnewline
Adjusted R-squared & 0.81131882372993 \tabularnewline
F-TEST (value) & 20.5151384452770 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 6.88338275267597e-15 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 983899.810144435 \tabularnewline
Sum Squared Residuals & 44530706474503.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26975&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.923521868842376[/C][/ROW]
[ROW][C]R-squared[/C][C]0.852892642230114[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.81131882372993[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]20.5151384452770[/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]6.88338275267597e-15[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]983899.810144435[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]44530706474503.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26975&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26975&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 R0.923521868842376
R-squared0.852892642230114
Adjusted R-squared0.81131882372993
F-TEST (value)20.5151384452770
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value6.88338275267597e-15
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation983899.810144435
Sum Squared Residuals44530706474503.8






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
114929387.514432756.3412777496631.1587223
214717825.314294426.8635202423398.436479794
315826281.216546802.7835202-720521.583520209
416301309.615069334.58352021231975.01647979
515033016.915016687.943520216328.9564797894
616998460.616726138.8412777272321.758722294
714066462.713128333.6812777938129.018722295
813328937.313457238.3012777-128301.001277705
917319718.216443053.3612777876664.838722289
1017586426.816871955.2412777714471.558722298
1115887037.416030822.7812777-143785.381277706
1217935679.116820243.68127771115435.41872230
131586948915566848.2695176302640.730482396
1415892510.915428518.7917601463992.108239894
1517556558.117680894.7117601-124336.611760103
161679164316203426.5117601588216.488239895
1715953688.516150779.8717601-197091.371760105
1818144913.617860230.7695176284682.830482399
191439088114262425.6095176128455.390482398
2013885708.714591330.2295176-705621.529517602
2117332571.517577145.2895176-244573.789517601
2217152595.818006047.1695176-853451.369517603
2316003877.117164914.7095176-1161037.60951760
2416841467.117954335.6095176-1112868.5095176
2514783398.116700940.1977575-1917542.0977575
2614667847.516562610.72-1894763.22
2717714362.218814986.64-1100624.44000000
281628208817337518.44-1055430.44
2915014866.217284871.8-2270005.6
3017722582.417986268.90897-263686.508970015
3113876509.414388463.7489700-511954.348970013
3215495489.614717368.36897778121.231029987
3317799521.117703183.4289796337.6710299895
3417920079.118132085.3089700-212006.208970013
3517248022.417290952.84897-42930.4489700140
3618813782.418080373.74897733408.651029986
3716249688.316826978.3372099-577290.037209909
3817823358.517696702.6482399126655.851760104
3920424438.319949078.5682399475359.731760106
4017814218.718471610.3682399-657391.668239896
4119699959.618418963.72823991280995.87176011
4219776328.120128414.6259974-352086.525997391
4315679833.116530609.4659974-850776.365997393
4417119266.516859514.0859974259752.414002609
452009261319845329.1459974247283.854002610
4620863688.320274231.0259974589457.274002608
4720925203.119433098.56599741492104.53400261
482103259320222519.4659974810073.53400261
4920664684.318969124.05423731695560.24576271
5019711511.418830794.5764798880716.823520207
5122553293.421083170.49647981470122.90352021
5219498332.919605702.2964798-107369.396479791
5320722827.819553055.65647981169772.14352021
542132127521262506.554237358768.445762712
5517960847.717664701.3942373296146.305762712
5617789654.917993606.0142373-203951.114237289
5720003708.520979421.0742373-975712.574237287
5821169851.721408322.9542373-238471.25423729
5920422839.420567190.4942373-144351.094237289
6019810562.321356611.3942373-1546049.09423729

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 14929387.5 & 14432756.3412777 & 496631.1587223 \tabularnewline
2 & 14717825.3 & 14294426.8635202 & 423398.436479794 \tabularnewline
3 & 15826281.2 & 16546802.7835202 & -720521.583520209 \tabularnewline
4 & 16301309.6 & 15069334.5835202 & 1231975.01647979 \tabularnewline
5 & 15033016.9 & 15016687.9435202 & 16328.9564797894 \tabularnewline
6 & 16998460.6 & 16726138.8412777 & 272321.758722294 \tabularnewline
7 & 14066462.7 & 13128333.6812777 & 938129.018722295 \tabularnewline
8 & 13328937.3 & 13457238.3012777 & -128301.001277705 \tabularnewline
9 & 17319718.2 & 16443053.3612777 & 876664.838722289 \tabularnewline
10 & 17586426.8 & 16871955.2412777 & 714471.558722298 \tabularnewline
11 & 15887037.4 & 16030822.7812777 & -143785.381277706 \tabularnewline
12 & 17935679.1 & 16820243.6812777 & 1115435.41872230 \tabularnewline
13 & 15869489 & 15566848.2695176 & 302640.730482396 \tabularnewline
14 & 15892510.9 & 15428518.7917601 & 463992.108239894 \tabularnewline
15 & 17556558.1 & 17680894.7117601 & -124336.611760103 \tabularnewline
16 & 16791643 & 16203426.5117601 & 588216.488239895 \tabularnewline
17 & 15953688.5 & 16150779.8717601 & -197091.371760105 \tabularnewline
18 & 18144913.6 & 17860230.7695176 & 284682.830482399 \tabularnewline
19 & 14390881 & 14262425.6095176 & 128455.390482398 \tabularnewline
20 & 13885708.7 & 14591330.2295176 & -705621.529517602 \tabularnewline
21 & 17332571.5 & 17577145.2895176 & -244573.789517601 \tabularnewline
22 & 17152595.8 & 18006047.1695176 & -853451.369517603 \tabularnewline
23 & 16003877.1 & 17164914.7095176 & -1161037.60951760 \tabularnewline
24 & 16841467.1 & 17954335.6095176 & -1112868.5095176 \tabularnewline
25 & 14783398.1 & 16700940.1977575 & -1917542.0977575 \tabularnewline
26 & 14667847.5 & 16562610.72 & -1894763.22 \tabularnewline
27 & 17714362.2 & 18814986.64 & -1100624.44000000 \tabularnewline
28 & 16282088 & 17337518.44 & -1055430.44 \tabularnewline
29 & 15014866.2 & 17284871.8 & -2270005.6 \tabularnewline
30 & 17722582.4 & 17986268.90897 & -263686.508970015 \tabularnewline
31 & 13876509.4 & 14388463.7489700 & -511954.348970013 \tabularnewline
32 & 15495489.6 & 14717368.36897 & 778121.231029987 \tabularnewline
33 & 17799521.1 & 17703183.42897 & 96337.6710299895 \tabularnewline
34 & 17920079.1 & 18132085.3089700 & -212006.208970013 \tabularnewline
35 & 17248022.4 & 17290952.84897 & -42930.4489700140 \tabularnewline
36 & 18813782.4 & 18080373.74897 & 733408.651029986 \tabularnewline
37 & 16249688.3 & 16826978.3372099 & -577290.037209909 \tabularnewline
38 & 17823358.5 & 17696702.6482399 & 126655.851760104 \tabularnewline
39 & 20424438.3 & 19949078.5682399 & 475359.731760106 \tabularnewline
40 & 17814218.7 & 18471610.3682399 & -657391.668239896 \tabularnewline
41 & 19699959.6 & 18418963.7282399 & 1280995.87176011 \tabularnewline
42 & 19776328.1 & 20128414.6259974 & -352086.525997391 \tabularnewline
43 & 15679833.1 & 16530609.4659974 & -850776.365997393 \tabularnewline
44 & 17119266.5 & 16859514.0859974 & 259752.414002609 \tabularnewline
45 & 20092613 & 19845329.1459974 & 247283.854002610 \tabularnewline
46 & 20863688.3 & 20274231.0259974 & 589457.274002608 \tabularnewline
47 & 20925203.1 & 19433098.5659974 & 1492104.53400261 \tabularnewline
48 & 21032593 & 20222519.4659974 & 810073.53400261 \tabularnewline
49 & 20664684.3 & 18969124.0542373 & 1695560.24576271 \tabularnewline
50 & 19711511.4 & 18830794.5764798 & 880716.823520207 \tabularnewline
51 & 22553293.4 & 21083170.4964798 & 1470122.90352021 \tabularnewline
52 & 19498332.9 & 19605702.2964798 & -107369.396479791 \tabularnewline
53 & 20722827.8 & 19553055.6564798 & 1169772.14352021 \tabularnewline
54 & 21321275 & 21262506.5542373 & 58768.445762712 \tabularnewline
55 & 17960847.7 & 17664701.3942373 & 296146.305762712 \tabularnewline
56 & 17789654.9 & 17993606.0142373 & -203951.114237289 \tabularnewline
57 & 20003708.5 & 20979421.0742373 & -975712.574237287 \tabularnewline
58 & 21169851.7 & 21408322.9542373 & -238471.25423729 \tabularnewline
59 & 20422839.4 & 20567190.4942373 & -144351.094237289 \tabularnewline
60 & 19810562.3 & 21356611.3942373 & -1546049.09423729 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26975&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]14929387.5[/C][C]14432756.3412777[/C][C]496631.1587223[/C][/ROW]
[ROW][C]2[/C][C]14717825.3[/C][C]14294426.8635202[/C][C]423398.436479794[/C][/ROW]
[ROW][C]3[/C][C]15826281.2[/C][C]16546802.7835202[/C][C]-720521.583520209[/C][/ROW]
[ROW][C]4[/C][C]16301309.6[/C][C]15069334.5835202[/C][C]1231975.01647979[/C][/ROW]
[ROW][C]5[/C][C]15033016.9[/C][C]15016687.9435202[/C][C]16328.9564797894[/C][/ROW]
[ROW][C]6[/C][C]16998460.6[/C][C]16726138.8412777[/C][C]272321.758722294[/C][/ROW]
[ROW][C]7[/C][C]14066462.7[/C][C]13128333.6812777[/C][C]938129.018722295[/C][/ROW]
[ROW][C]8[/C][C]13328937.3[/C][C]13457238.3012777[/C][C]-128301.001277705[/C][/ROW]
[ROW][C]9[/C][C]17319718.2[/C][C]16443053.3612777[/C][C]876664.838722289[/C][/ROW]
[ROW][C]10[/C][C]17586426.8[/C][C]16871955.2412777[/C][C]714471.558722298[/C][/ROW]
[ROW][C]11[/C][C]15887037.4[/C][C]16030822.7812777[/C][C]-143785.381277706[/C][/ROW]
[ROW][C]12[/C][C]17935679.1[/C][C]16820243.6812777[/C][C]1115435.41872230[/C][/ROW]
[ROW][C]13[/C][C]15869489[/C][C]15566848.2695176[/C][C]302640.730482396[/C][/ROW]
[ROW][C]14[/C][C]15892510.9[/C][C]15428518.7917601[/C][C]463992.108239894[/C][/ROW]
[ROW][C]15[/C][C]17556558.1[/C][C]17680894.7117601[/C][C]-124336.611760103[/C][/ROW]
[ROW][C]16[/C][C]16791643[/C][C]16203426.5117601[/C][C]588216.488239895[/C][/ROW]
[ROW][C]17[/C][C]15953688.5[/C][C]16150779.8717601[/C][C]-197091.371760105[/C][/ROW]
[ROW][C]18[/C][C]18144913.6[/C][C]17860230.7695176[/C][C]284682.830482399[/C][/ROW]
[ROW][C]19[/C][C]14390881[/C][C]14262425.6095176[/C][C]128455.390482398[/C][/ROW]
[ROW][C]20[/C][C]13885708.7[/C][C]14591330.2295176[/C][C]-705621.529517602[/C][/ROW]
[ROW][C]21[/C][C]17332571.5[/C][C]17577145.2895176[/C][C]-244573.789517601[/C][/ROW]
[ROW][C]22[/C][C]17152595.8[/C][C]18006047.1695176[/C][C]-853451.369517603[/C][/ROW]
[ROW][C]23[/C][C]16003877.1[/C][C]17164914.7095176[/C][C]-1161037.60951760[/C][/ROW]
[ROW][C]24[/C][C]16841467.1[/C][C]17954335.6095176[/C][C]-1112868.5095176[/C][/ROW]
[ROW][C]25[/C][C]14783398.1[/C][C]16700940.1977575[/C][C]-1917542.0977575[/C][/ROW]
[ROW][C]26[/C][C]14667847.5[/C][C]16562610.72[/C][C]-1894763.22[/C][/ROW]
[ROW][C]27[/C][C]17714362.2[/C][C]18814986.64[/C][C]-1100624.44000000[/C][/ROW]
[ROW][C]28[/C][C]16282088[/C][C]17337518.44[/C][C]-1055430.44[/C][/ROW]
[ROW][C]29[/C][C]15014866.2[/C][C]17284871.8[/C][C]-2270005.6[/C][/ROW]
[ROW][C]30[/C][C]17722582.4[/C][C]17986268.90897[/C][C]-263686.508970015[/C][/ROW]
[ROW][C]31[/C][C]13876509.4[/C][C]14388463.7489700[/C][C]-511954.348970013[/C][/ROW]
[ROW][C]32[/C][C]15495489.6[/C][C]14717368.36897[/C][C]778121.231029987[/C][/ROW]
[ROW][C]33[/C][C]17799521.1[/C][C]17703183.42897[/C][C]96337.6710299895[/C][/ROW]
[ROW][C]34[/C][C]17920079.1[/C][C]18132085.3089700[/C][C]-212006.208970013[/C][/ROW]
[ROW][C]35[/C][C]17248022.4[/C][C]17290952.84897[/C][C]-42930.4489700140[/C][/ROW]
[ROW][C]36[/C][C]18813782.4[/C][C]18080373.74897[/C][C]733408.651029986[/C][/ROW]
[ROW][C]37[/C][C]16249688.3[/C][C]16826978.3372099[/C][C]-577290.037209909[/C][/ROW]
[ROW][C]38[/C][C]17823358.5[/C][C]17696702.6482399[/C][C]126655.851760104[/C][/ROW]
[ROW][C]39[/C][C]20424438.3[/C][C]19949078.5682399[/C][C]475359.731760106[/C][/ROW]
[ROW][C]40[/C][C]17814218.7[/C][C]18471610.3682399[/C][C]-657391.668239896[/C][/ROW]
[ROW][C]41[/C][C]19699959.6[/C][C]18418963.7282399[/C][C]1280995.87176011[/C][/ROW]
[ROW][C]42[/C][C]19776328.1[/C][C]20128414.6259974[/C][C]-352086.525997391[/C][/ROW]
[ROW][C]43[/C][C]15679833.1[/C][C]16530609.4659974[/C][C]-850776.365997393[/C][/ROW]
[ROW][C]44[/C][C]17119266.5[/C][C]16859514.0859974[/C][C]259752.414002609[/C][/ROW]
[ROW][C]45[/C][C]20092613[/C][C]19845329.1459974[/C][C]247283.854002610[/C][/ROW]
[ROW][C]46[/C][C]20863688.3[/C][C]20274231.0259974[/C][C]589457.274002608[/C][/ROW]
[ROW][C]47[/C][C]20925203.1[/C][C]19433098.5659974[/C][C]1492104.53400261[/C][/ROW]
[ROW][C]48[/C][C]21032593[/C][C]20222519.4659974[/C][C]810073.53400261[/C][/ROW]
[ROW][C]49[/C][C]20664684.3[/C][C]18969124.0542373[/C][C]1695560.24576271[/C][/ROW]
[ROW][C]50[/C][C]19711511.4[/C][C]18830794.5764798[/C][C]880716.823520207[/C][/ROW]
[ROW][C]51[/C][C]22553293.4[/C][C]21083170.4964798[/C][C]1470122.90352021[/C][/ROW]
[ROW][C]52[/C][C]19498332.9[/C][C]19605702.2964798[/C][C]-107369.396479791[/C][/ROW]
[ROW][C]53[/C][C]20722827.8[/C][C]19553055.6564798[/C][C]1169772.14352021[/C][/ROW]
[ROW][C]54[/C][C]21321275[/C][C]21262506.5542373[/C][C]58768.445762712[/C][/ROW]
[ROW][C]55[/C][C]17960847.7[/C][C]17664701.3942373[/C][C]296146.305762712[/C][/ROW]
[ROW][C]56[/C][C]17789654.9[/C][C]17993606.0142373[/C][C]-203951.114237289[/C][/ROW]
[ROW][C]57[/C][C]20003708.5[/C][C]20979421.0742373[/C][C]-975712.574237287[/C][/ROW]
[ROW][C]58[/C][C]21169851.7[/C][C]21408322.9542373[/C][C]-238471.25423729[/C][/ROW]
[ROW][C]59[/C][C]20422839.4[/C][C]20567190.4942373[/C][C]-144351.094237289[/C][/ROW]
[ROW][C]60[/C][C]19810562.3[/C][C]21356611.3942373[/C][C]-1546049.09423729[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26975&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26975&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
114929387.514432756.3412777496631.1587223
214717825.314294426.8635202423398.436479794
315826281.216546802.7835202-720521.583520209
416301309.615069334.58352021231975.01647979
515033016.915016687.943520216328.9564797894
616998460.616726138.8412777272321.758722294
714066462.713128333.6812777938129.018722295
813328937.313457238.3012777-128301.001277705
917319718.216443053.3612777876664.838722289
1017586426.816871955.2412777714471.558722298
1115887037.416030822.7812777-143785.381277706
1217935679.116820243.68127771115435.41872230
131586948915566848.2695176302640.730482396
1415892510.915428518.7917601463992.108239894
1517556558.117680894.7117601-124336.611760103
161679164316203426.5117601588216.488239895
1715953688.516150779.8717601-197091.371760105
1818144913.617860230.7695176284682.830482399
191439088114262425.6095176128455.390482398
2013885708.714591330.2295176-705621.529517602
2117332571.517577145.2895176-244573.789517601
2217152595.818006047.1695176-853451.369517603
2316003877.117164914.7095176-1161037.60951760
2416841467.117954335.6095176-1112868.5095176
2514783398.116700940.1977575-1917542.0977575
2614667847.516562610.72-1894763.22
2717714362.218814986.64-1100624.44000000
281628208817337518.44-1055430.44
2915014866.217284871.8-2270005.6
3017722582.417986268.90897-263686.508970015
3113876509.414388463.7489700-511954.348970013
3215495489.614717368.36897778121.231029987
3317799521.117703183.4289796337.6710299895
3417920079.118132085.3089700-212006.208970013
3517248022.417290952.84897-42930.4489700140
3618813782.418080373.74897733408.651029986
3716249688.316826978.3372099-577290.037209909
3817823358.517696702.6482399126655.851760104
3920424438.319949078.5682399475359.731760106
4017814218.718471610.3682399-657391.668239896
4119699959.618418963.72823991280995.87176011
4219776328.120128414.6259974-352086.525997391
4315679833.116530609.4659974-850776.365997393
4417119266.516859514.0859974259752.414002609
452009261319845329.1459974247283.854002610
4620863688.320274231.0259974589457.274002608
4720925203.119433098.56599741492104.53400261
482103259320222519.4659974810073.53400261
4920664684.318969124.05423731695560.24576271
5019711511.418830794.5764798880716.823520207
5122553293.421083170.49647981470122.90352021
5219498332.919605702.2964798-107369.396479791
5320722827.819553055.65647981169772.14352021
542132127521262506.554237358768.445762712
5517960847.717664701.3942373296146.305762712
5617789654.917993606.0142373-203951.114237289
5720003708.520979421.0742373-975712.574237287
5821169851.721408322.9542373-238471.25423729
5920422839.420567190.4942373-144351.094237289
6019810562.321356611.3942373-1546049.09423729






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.06337716862663330.1267543372532670.936622831373367
180.02069692095463190.04139384190926380.979303079045368
190.01836412903014380.03672825806028770.981635870969856
200.007642450358698040.01528490071739610.992357549641302
210.009382891494566280.01876578298913260.990617108505434
220.01759295379675430.03518590759350860.982407046203246
230.009643891177879570.01928778235575910.99035610882212
240.02968193534342500.059363870686850.970318064656575
250.04215378217530240.08430756435060470.957846217824698
260.05139783934896560.1027956786979310.948602160651034
270.04814339808467550.0962867961693510.951856601915325
280.03238033447370130.06476066894740260.967619665526299
290.1817533281362110.3635066562724230.818246671863789
300.1214820710313190.2429641420626370.878517928968682
310.08148089592539550.1629617918507910.918519104074604
320.1474877848961530.2949755697923060.852512215103847
330.1106843700964150.221368740192830.889315629903585
340.06917084079169190.1383416815833840.930829159208308
350.04980271689963530.09960543379927060.950197283100365
360.1321829406422380.2643658812844760.867817059357762
370.08338711032964760.1667742206592950.916612889670352
380.202541638751830.405083277503660.79745836124817
390.3931252292642880.7862504585285770.606874770735712
400.3524272377421280.7048544754842560.647572762257872
410.4373917328134410.8747834656268830.562608267186559
420.3905127090026840.7810254180053690.609487290997316
430.7229444274145680.5541111451708640.277055572585432

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.0633771686266333 & 0.126754337253267 & 0.936622831373367 \tabularnewline
18 & 0.0206969209546319 & 0.0413938419092638 & 0.979303079045368 \tabularnewline
19 & 0.0183641290301438 & 0.0367282580602877 & 0.981635870969856 \tabularnewline
20 & 0.00764245035869804 & 0.0152849007173961 & 0.992357549641302 \tabularnewline
21 & 0.00938289149456628 & 0.0187657829891326 & 0.990617108505434 \tabularnewline
22 & 0.0175929537967543 & 0.0351859075935086 & 0.982407046203246 \tabularnewline
23 & 0.00964389117787957 & 0.0192877823557591 & 0.99035610882212 \tabularnewline
24 & 0.0296819353434250 & 0.05936387068685 & 0.970318064656575 \tabularnewline
25 & 0.0421537821753024 & 0.0843075643506047 & 0.957846217824698 \tabularnewline
26 & 0.0513978393489656 & 0.102795678697931 & 0.948602160651034 \tabularnewline
27 & 0.0481433980846755 & 0.096286796169351 & 0.951856601915325 \tabularnewline
28 & 0.0323803344737013 & 0.0647606689474026 & 0.967619665526299 \tabularnewline
29 & 0.181753328136211 & 0.363506656272423 & 0.818246671863789 \tabularnewline
30 & 0.121482071031319 & 0.242964142062637 & 0.878517928968682 \tabularnewline
31 & 0.0814808959253955 & 0.162961791850791 & 0.918519104074604 \tabularnewline
32 & 0.147487784896153 & 0.294975569792306 & 0.852512215103847 \tabularnewline
33 & 0.110684370096415 & 0.22136874019283 & 0.889315629903585 \tabularnewline
34 & 0.0691708407916919 & 0.138341681583384 & 0.930829159208308 \tabularnewline
35 & 0.0498027168996353 & 0.0996054337992706 & 0.950197283100365 \tabularnewline
36 & 0.132182940642238 & 0.264365881284476 & 0.867817059357762 \tabularnewline
37 & 0.0833871103296476 & 0.166774220659295 & 0.916612889670352 \tabularnewline
38 & 0.20254163875183 & 0.40508327750366 & 0.79745836124817 \tabularnewline
39 & 0.393125229264288 & 0.786250458528577 & 0.606874770735712 \tabularnewline
40 & 0.352427237742128 & 0.704854475484256 & 0.647572762257872 \tabularnewline
41 & 0.437391732813441 & 0.874783465626883 & 0.562608267186559 \tabularnewline
42 & 0.390512709002684 & 0.781025418005369 & 0.609487290997316 \tabularnewline
43 & 0.722944427414568 & 0.554111145170864 & 0.277055572585432 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26975&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]0.0633771686266333[/C][C]0.126754337253267[/C][C]0.936622831373367[/C][/ROW]
[ROW][C]18[/C][C]0.0206969209546319[/C][C]0.0413938419092638[/C][C]0.979303079045368[/C][/ROW]
[ROW][C]19[/C][C]0.0183641290301438[/C][C]0.0367282580602877[/C][C]0.981635870969856[/C][/ROW]
[ROW][C]20[/C][C]0.00764245035869804[/C][C]0.0152849007173961[/C][C]0.992357549641302[/C][/ROW]
[ROW][C]21[/C][C]0.00938289149456628[/C][C]0.0187657829891326[/C][C]0.990617108505434[/C][/ROW]
[ROW][C]22[/C][C]0.0175929537967543[/C][C]0.0351859075935086[/C][C]0.982407046203246[/C][/ROW]
[ROW][C]23[/C][C]0.00964389117787957[/C][C]0.0192877823557591[/C][C]0.99035610882212[/C][/ROW]
[ROW][C]24[/C][C]0.0296819353434250[/C][C]0.05936387068685[/C][C]0.970318064656575[/C][/ROW]
[ROW][C]25[/C][C]0.0421537821753024[/C][C]0.0843075643506047[/C][C]0.957846217824698[/C][/ROW]
[ROW][C]26[/C][C]0.0513978393489656[/C][C]0.102795678697931[/C][C]0.948602160651034[/C][/ROW]
[ROW][C]27[/C][C]0.0481433980846755[/C][C]0.096286796169351[/C][C]0.951856601915325[/C][/ROW]
[ROW][C]28[/C][C]0.0323803344737013[/C][C]0.0647606689474026[/C][C]0.967619665526299[/C][/ROW]
[ROW][C]29[/C][C]0.181753328136211[/C][C]0.363506656272423[/C][C]0.818246671863789[/C][/ROW]
[ROW][C]30[/C][C]0.121482071031319[/C][C]0.242964142062637[/C][C]0.878517928968682[/C][/ROW]
[ROW][C]31[/C][C]0.0814808959253955[/C][C]0.162961791850791[/C][C]0.918519104074604[/C][/ROW]
[ROW][C]32[/C][C]0.147487784896153[/C][C]0.294975569792306[/C][C]0.852512215103847[/C][/ROW]
[ROW][C]33[/C][C]0.110684370096415[/C][C]0.22136874019283[/C][C]0.889315629903585[/C][/ROW]
[ROW][C]34[/C][C]0.0691708407916919[/C][C]0.138341681583384[/C][C]0.930829159208308[/C][/ROW]
[ROW][C]35[/C][C]0.0498027168996353[/C][C]0.0996054337992706[/C][C]0.950197283100365[/C][/ROW]
[ROW][C]36[/C][C]0.132182940642238[/C][C]0.264365881284476[/C][C]0.867817059357762[/C][/ROW]
[ROW][C]37[/C][C]0.0833871103296476[/C][C]0.166774220659295[/C][C]0.916612889670352[/C][/ROW]
[ROW][C]38[/C][C]0.20254163875183[/C][C]0.40508327750366[/C][C]0.79745836124817[/C][/ROW]
[ROW][C]39[/C][C]0.393125229264288[/C][C]0.786250458528577[/C][C]0.606874770735712[/C][/ROW]
[ROW][C]40[/C][C]0.352427237742128[/C][C]0.704854475484256[/C][C]0.647572762257872[/C][/ROW]
[ROW][C]41[/C][C]0.437391732813441[/C][C]0.874783465626883[/C][C]0.562608267186559[/C][/ROW]
[ROW][C]42[/C][C]0.390512709002684[/C][C]0.781025418005369[/C][C]0.609487290997316[/C][/ROW]
[ROW][C]43[/C][C]0.722944427414568[/C][C]0.554111145170864[/C][C]0.277055572585432[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26975&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26975&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
170.06337716862663330.1267543372532670.936622831373367
180.02069692095463190.04139384190926380.979303079045368
190.01836412903014380.03672825806028770.981635870969856
200.007642450358698040.01528490071739610.992357549641302
210.009382891494566280.01876578298913260.990617108505434
220.01759295379675430.03518590759350860.982407046203246
230.009643891177879570.01928778235575910.99035610882212
240.02968193534342500.059363870686850.970318064656575
250.04215378217530240.08430756435060470.957846217824698
260.05139783934896560.1027956786979310.948602160651034
270.04814339808467550.0962867961693510.951856601915325
280.03238033447370130.06476066894740260.967619665526299
290.1817533281362110.3635066562724230.818246671863789
300.1214820710313190.2429641420626370.878517928968682
310.08148089592539550.1629617918507910.918519104074604
320.1474877848961530.2949755697923060.852512215103847
330.1106843700964150.221368740192830.889315629903585
340.06917084079169190.1383416815833840.930829159208308
350.04980271689963530.09960543379927060.950197283100365
360.1321829406422380.2643658812844760.867817059357762
370.08338711032964760.1667742206592950.916612889670352
380.202541638751830.405083277503660.79745836124817
390.3931252292642880.7862504585285770.606874770735712
400.3524272377421280.7048544754842560.647572762257872
410.4373917328134410.8747834656268830.562608267186559
420.3905127090026840.7810254180053690.609487290997316
430.7229444274145680.5541111451708640.277055572585432






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level60.222222222222222NOK
10% type I error level110.407407407407407NOK

\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 & 6 & 0.222222222222222 & NOK \tabularnewline
10% type I error level & 11 & 0.407407407407407 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26975&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]6[/C][C]0.222222222222222[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]11[/C][C]0.407407407407407[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26975&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26975&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 level60.222222222222222NOK
10% type I error level110.407407407407407NOK


Figures (Output of Computation)

Figure 1
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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')
}