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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 06:01:05 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/20/t1258722218zhchoas2wta1qae.htm/, Retrieved Thu, 28 Mar 2024 12:00:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58107, Retrieved Thu, 28 Mar 2024 12:00:14 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact212
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] [Workshop7] [2009-11-19 18:30:59] [34b80aeb109c116fd63bf2eb7493a276]
-    D      [Multiple Regression] [workshop7] [2009-11-20 12:37:03] [34b80aeb109c116fd63bf2eb7493a276]
-   P           [Multiple Regression] [workshop7] [2009-11-20 13:01:05] [307139c5e328127f586f26d5bcc435d8] [Current]
-    D            [Multiple Regression] [Model 2 Seizonali...] [2009-12-05 14:50:04] [34b80aeb109c116fd63bf2eb7493a276]
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Dataseries X:
105.4	102.7
105.4	102.5
105.6	102.2
105.7	102.9
105.8	103.1
105.8	103
105.8	102.8
105.9	102.5
106.1	101.9
106.4	101.9
106.4	101.8
106.3	102
106.2	102.6
106.2	102.5
106.3	102.5
106.4	101.6
106.5	101.4
106.6	100.8
106.6	101.1
106.6	101.3
106.8	101.2
107	101.3
107.2	101.1
107.3	101.3
107.5	101.2
107.6	101.6
107.6	101.7
107.7	101.5
107.7	100.9
107.7	101.5
107.7	101.4
107.6	101.6
107.7	101.7
107.9	101.4
107.9	101.8
107.9	101.7
107.8	101.4
107.6	101.2
107.4	101
107	101.7
107	102.4
107.2	102
107.5	102.1
107.8	102
107.8	101.8
107.7	102.7
107.6	102.3
107.6	101.9
107.5	102
107.5	102.3
107.6	102.8
107.6	102.4
107.9	102.3
107.6	102.7
107.5	102.7
107.5	102.9
107.6	103
107.7	102.2
107.8	102.3
107.9	102.8
107.9	102.8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58107&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58107&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58107&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
Werkl[t] = + 136.683354670492 -0.287260689331883Inflatie[t] -0.299250611551335M1[t] -0.517019144853451M2[t] -0.471273931066814M3[t] -0.497019144853448M4[t] -0.397019144853448M5[t] -0.402764358640089M6[t] -0.357019144853451M7[t] -0.285528717280176M8[t] -0.20574521378664M9[t] -0.0714904275732713M10[t] -0.0429808551465507M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Werkl[t] =  +  136.683354670492 -0.287260689331883Inflatie[t] -0.299250611551335M1[t] -0.517019144853451M2[t] -0.471273931066814M3[t] -0.497019144853448M4[t] -0.397019144853448M5[t] -0.402764358640089M6[t] -0.357019144853451M7[t] -0.285528717280176M8[t] -0.20574521378664M9[t] -0.0714904275732713M10[t] -0.0429808551465507M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58107&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Werkl[t] =  +  136.683354670492 -0.287260689331883Inflatie[t] -0.299250611551335M1[t] -0.517019144853451M2[t] -0.471273931066814M3[t] -0.497019144853448M4[t] -0.397019144853448M5[t] -0.402764358640089M6[t] -0.357019144853451M7[t] -0.285528717280176M8[t] -0.20574521378664M9[t] -0.0714904275732713M10[t] -0.0429808551465507M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58107&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58107&T=1

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Estimated Regression Equation
Werkl[t] = + 136.683354670492 -0.287260689331883Inflatie[t] -0.299250611551335M1[t] -0.517019144853451M2[t] -0.471273931066814M3[t] -0.497019144853448M4[t] -0.397019144853448M5[t] -0.402764358640089M6[t] -0.357019144853451M7[t] -0.285528717280176M8[t] -0.20574521378664M9[t] -0.0714904275732713M10[t] -0.0429808551465507M11[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)136.68335467049217.1906787.95100
Inflatie-0.2872606893318830.168598-1.70380.0948820.047441
M1-0.2992506115513350.487923-0.61330.5425630.271282
M2-0.5170191448534510.508847-1.01610.3146950.157347
M3-0.4712739310668140.508947-0.9260.359090.179545
M4-0.4970191448534480.508847-0.97680.3335870.166794
M5-0.3970191448534480.508847-0.78020.4390840.219542
M6-0.4027643586400890.508769-0.79160.4324620.216231
M7-0.3570191448534510.508847-0.70160.4863020.243151
M8-0.2855287172801760.50907-0.56090.5774860.288743
M9-0.205745213786640.508679-0.40450.6876640.343832
M10-0.07149042757327130.508713-0.14050.8888280.444414
M11-0.04298085514655070.508847-0.08450.9330360.466518

\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) & 136.683354670492 & 17.190678 & 7.951 & 0 & 0 \tabularnewline
Inflatie & -0.287260689331883 & 0.168598 & -1.7038 & 0.094882 & 0.047441 \tabularnewline
M1 & -0.299250611551335 & 0.487923 & -0.6133 & 0.542563 & 0.271282 \tabularnewline
M2 & -0.517019144853451 & 0.508847 & -1.0161 & 0.314695 & 0.157347 \tabularnewline
M3 & -0.471273931066814 & 0.508947 & -0.926 & 0.35909 & 0.179545 \tabularnewline
M4 & -0.497019144853448 & 0.508847 & -0.9768 & 0.333587 & 0.166794 \tabularnewline
M5 & -0.397019144853448 & 0.508847 & -0.7802 & 0.439084 & 0.219542 \tabularnewline
M6 & -0.402764358640089 & 0.508769 & -0.7916 & 0.432462 & 0.216231 \tabularnewline
M7 & -0.357019144853451 & 0.508847 & -0.7016 & 0.486302 & 0.243151 \tabularnewline
M8 & -0.285528717280176 & 0.50907 & -0.5609 & 0.577486 & 0.288743 \tabularnewline
M9 & -0.20574521378664 & 0.508679 & -0.4045 & 0.687664 & 0.343832 \tabularnewline
M10 & -0.0714904275732713 & 0.508713 & -0.1405 & 0.888828 & 0.444414 \tabularnewline
M11 & -0.0429808551465507 & 0.508847 & -0.0845 & 0.933036 & 0.466518 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58107&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]136.683354670492[/C][C]17.190678[/C][C]7.951[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Inflatie[/C][C]-0.287260689331883[/C][C]0.168598[/C][C]-1.7038[/C][C]0.094882[/C][C]0.047441[/C][/ROW]
[ROW][C]M1[/C][C]-0.299250611551335[/C][C]0.487923[/C][C]-0.6133[/C][C]0.542563[/C][C]0.271282[/C][/ROW]
[ROW][C]M2[/C][C]-0.517019144853451[/C][C]0.508847[/C][C]-1.0161[/C][C]0.314695[/C][C]0.157347[/C][/ROW]
[ROW][C]M3[/C][C]-0.471273931066814[/C][C]0.508947[/C][C]-0.926[/C][C]0.35909[/C][C]0.179545[/C][/ROW]
[ROW][C]M4[/C][C]-0.497019144853448[/C][C]0.508847[/C][C]-0.9768[/C][C]0.333587[/C][C]0.166794[/C][/ROW]
[ROW][C]M5[/C][C]-0.397019144853448[/C][C]0.508847[/C][C]-0.7802[/C][C]0.439084[/C][C]0.219542[/C][/ROW]
[ROW][C]M6[/C][C]-0.402764358640089[/C][C]0.508769[/C][C]-0.7916[/C][C]0.432462[/C][C]0.216231[/C][/ROW]
[ROW][C]M7[/C][C]-0.357019144853451[/C][C]0.508847[/C][C]-0.7016[/C][C]0.486302[/C][C]0.243151[/C][/ROW]
[ROW][C]M8[/C][C]-0.285528717280176[/C][C]0.50907[/C][C]-0.5609[/C][C]0.577486[/C][C]0.288743[/C][/ROW]
[ROW][C]M9[/C][C]-0.20574521378664[/C][C]0.508679[/C][C]-0.4045[/C][C]0.687664[/C][C]0.343832[/C][/ROW]
[ROW][C]M10[/C][C]-0.0714904275732713[/C][C]0.508713[/C][C]-0.1405[/C][C]0.888828[/C][C]0.444414[/C][/ROW]
[ROW][C]M11[/C][C]-0.0429808551465507[/C][C]0.508847[/C][C]-0.0845[/C][C]0.933036[/C][C]0.466518[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58107&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58107&T=2

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)136.68335467049217.1906787.95100
Inflatie-0.2872606893318830.168598-1.70380.0948820.047441
M1-0.2992506115513350.487923-0.61330.5425630.271282
M2-0.5170191448534510.508847-1.01610.3146950.157347
M3-0.4712739310668140.508947-0.9260.359090.179545
M4-0.4970191448534480.508847-0.97680.3335870.166794
M5-0.3970191448534480.508847-0.78020.4390840.219542
M6-0.4027643586400890.508769-0.79160.4324620.216231
M7-0.3570191448534510.508847-0.70160.4863020.243151
M8-0.2855287172801760.50907-0.56090.5774860.288743
M9-0.205745213786640.508679-0.40450.6876640.343832
M10-0.07149042757327130.508713-0.14050.8888280.444414
M11-0.04298085514655070.508847-0.08450.9330360.466518







Multiple Linear Regression - Regression Statistics
Multiple R0.33680424337175
R-squared0.113437098353217
Adjusted R-squared-0.108203627058479
F-TEST (value)0.511806204128365
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.896743475231964
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.804274736354603
Sum Squared Residuals31.0491768738368

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.33680424337175 \tabularnewline
R-squared & 0.113437098353217 \tabularnewline
Adjusted R-squared & -0.108203627058479 \tabularnewline
F-TEST (value) & 0.511806204128365 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 0.896743475231964 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.804274736354603 \tabularnewline
Sum Squared Residuals & 31.0491768738368 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58107&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.33680424337175[/C][/ROW]
[ROW][C]R-squared[/C][C]0.113437098353217[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]-0.108203627058479[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]0.511806204128365[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]48[/C][/ROW]
[ROW][C]p-value[/C][C]0.896743475231964[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.804274736354603[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]31.0491768738368[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58107&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58107&T=3

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Regression Statistics
Multiple R0.33680424337175
R-squared0.113437098353217
Adjusted R-squared-0.108203627058479
F-TEST (value)0.511806204128365
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.896743475231964
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.804274736354603
Sum Squared Residuals31.0491768738368







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1105.4106.882431264556-1.48243126455624
2105.4106.722114869121-1.32211486912069
3105.6106.854038289707-1.2540382897069
4105.7106.627210593388-0.92721059338794
5105.8106.669758455522-0.869758455521573
6105.8106.692739310668-0.892739310668119
7105.8106.795936662321-0.995936662321133
8105.9106.953605296694-1.05360529669396
9106.1107.205745213787-1.10574521378664
10106.4107.34-0.939999999999997
11106.4107.39723564136-0.997235641359909
12106.3107.382764358640-1.08276435864009
13106.2106.911157333490-0.711157333489622
14106.2106.722114869121-0.522114869120693
15106.3106.767860082907-0.467860082907334
16106.4107.000649489519-0.600649489519388
17106.5107.158101627386-0.658101627385768
18106.6107.324712827198-0.724712827198264
19106.6107.284279834185-0.684279834185338
20106.6107.298318123892-0.698318123892236
21106.8107.406827696319-0.606827696318955
22107107.512356413599-0.512356413599135
23107.2107.598318123892-0.39831812389223
24107.3107.583846841172-0.283846841172409
25107.5107.3133222985540.186677701445742
26107.6106.9806494895190.619350510480603
27107.6106.9976686343730.602331365627158
28107.7107.0293755584530.670624441547422
29107.7107.3017319720520.398268027948294
30107.7107.1236303446660.576369655334063
31107.7107.1981016273860.501898372614238
32107.6107.2121399170930.387860082907328
33107.7107.2631973516530.436802648346992
34107.9107.4836303446660.416369655334062
35107.9107.397235641360.502764358640092
36107.9107.4689425654400.431057434560354
37107.8107.2558701606880.544129839312116
38107.6107.0955537652520.504446234747852
39107.4107.1987511169050.20124888309485
40107106.9719234205860.0280765794137966
41107106.8708409380540.129159061946116
42107.2106.980.220000000000005
43107.5106.9970191448530.502980855146551
44107.8107.097235641360.702764358640086
45107.8107.2344712827200.565528717280173
46107.7107.1101914485340.589808551465506
47107.6107.2536052966940.346394703306022
48107.6107.4114904275730.188509572426721
49107.5107.0835137470890.416486252911247
50107.5106.7795670069870.720432993012927
51107.6106.6816818761080.918318123892227
52107.6106.7708409380540.82915906194611
53107.9106.8995670069871.00043299301293
54107.6106.7789175174680.821082482532315
55107.5106.8246627312540.675337268745682
56107.5106.8387010209610.661298979038785
57107.6106.8897584555220.71024154447843
58107.7107.2538217932000.446178206799564
59107.8107.2536052966940.546394703306024
60107.9107.1529558071750.747044192825424
61107.9106.8537051956231.04629480437676

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 105.4 & 106.882431264556 & -1.48243126455624 \tabularnewline
2 & 105.4 & 106.722114869121 & -1.32211486912069 \tabularnewline
3 & 105.6 & 106.854038289707 & -1.2540382897069 \tabularnewline
4 & 105.7 & 106.627210593388 & -0.92721059338794 \tabularnewline
5 & 105.8 & 106.669758455522 & -0.869758455521573 \tabularnewline
6 & 105.8 & 106.692739310668 & -0.892739310668119 \tabularnewline
7 & 105.8 & 106.795936662321 & -0.995936662321133 \tabularnewline
8 & 105.9 & 106.953605296694 & -1.05360529669396 \tabularnewline
9 & 106.1 & 107.205745213787 & -1.10574521378664 \tabularnewline
10 & 106.4 & 107.34 & -0.939999999999997 \tabularnewline
11 & 106.4 & 107.39723564136 & -0.997235641359909 \tabularnewline
12 & 106.3 & 107.382764358640 & -1.08276435864009 \tabularnewline
13 & 106.2 & 106.911157333490 & -0.711157333489622 \tabularnewline
14 & 106.2 & 106.722114869121 & -0.522114869120693 \tabularnewline
15 & 106.3 & 106.767860082907 & -0.467860082907334 \tabularnewline
16 & 106.4 & 107.000649489519 & -0.600649489519388 \tabularnewline
17 & 106.5 & 107.158101627386 & -0.658101627385768 \tabularnewline
18 & 106.6 & 107.324712827198 & -0.724712827198264 \tabularnewline
19 & 106.6 & 107.284279834185 & -0.684279834185338 \tabularnewline
20 & 106.6 & 107.298318123892 & -0.698318123892236 \tabularnewline
21 & 106.8 & 107.406827696319 & -0.606827696318955 \tabularnewline
22 & 107 & 107.512356413599 & -0.512356413599135 \tabularnewline
23 & 107.2 & 107.598318123892 & -0.39831812389223 \tabularnewline
24 & 107.3 & 107.583846841172 & -0.283846841172409 \tabularnewline
25 & 107.5 & 107.313322298554 & 0.186677701445742 \tabularnewline
26 & 107.6 & 106.980649489519 & 0.619350510480603 \tabularnewline
27 & 107.6 & 106.997668634373 & 0.602331365627158 \tabularnewline
28 & 107.7 & 107.029375558453 & 0.670624441547422 \tabularnewline
29 & 107.7 & 107.301731972052 & 0.398268027948294 \tabularnewline
30 & 107.7 & 107.123630344666 & 0.576369655334063 \tabularnewline
31 & 107.7 & 107.198101627386 & 0.501898372614238 \tabularnewline
32 & 107.6 & 107.212139917093 & 0.387860082907328 \tabularnewline
33 & 107.7 & 107.263197351653 & 0.436802648346992 \tabularnewline
34 & 107.9 & 107.483630344666 & 0.416369655334062 \tabularnewline
35 & 107.9 & 107.39723564136 & 0.502764358640092 \tabularnewline
36 & 107.9 & 107.468942565440 & 0.431057434560354 \tabularnewline
37 & 107.8 & 107.255870160688 & 0.544129839312116 \tabularnewline
38 & 107.6 & 107.095553765252 & 0.504446234747852 \tabularnewline
39 & 107.4 & 107.198751116905 & 0.20124888309485 \tabularnewline
40 & 107 & 106.971923420586 & 0.0280765794137966 \tabularnewline
41 & 107 & 106.870840938054 & 0.129159061946116 \tabularnewline
42 & 107.2 & 106.98 & 0.220000000000005 \tabularnewline
43 & 107.5 & 106.997019144853 & 0.502980855146551 \tabularnewline
44 & 107.8 & 107.09723564136 & 0.702764358640086 \tabularnewline
45 & 107.8 & 107.234471282720 & 0.565528717280173 \tabularnewline
46 & 107.7 & 107.110191448534 & 0.589808551465506 \tabularnewline
47 & 107.6 & 107.253605296694 & 0.346394703306022 \tabularnewline
48 & 107.6 & 107.411490427573 & 0.188509572426721 \tabularnewline
49 & 107.5 & 107.083513747089 & 0.416486252911247 \tabularnewline
50 & 107.5 & 106.779567006987 & 0.720432993012927 \tabularnewline
51 & 107.6 & 106.681681876108 & 0.918318123892227 \tabularnewline
52 & 107.6 & 106.770840938054 & 0.82915906194611 \tabularnewline
53 & 107.9 & 106.899567006987 & 1.00043299301293 \tabularnewline
54 & 107.6 & 106.778917517468 & 0.821082482532315 \tabularnewline
55 & 107.5 & 106.824662731254 & 0.675337268745682 \tabularnewline
56 & 107.5 & 106.838701020961 & 0.661298979038785 \tabularnewline
57 & 107.6 & 106.889758455522 & 0.71024154447843 \tabularnewline
58 & 107.7 & 107.253821793200 & 0.446178206799564 \tabularnewline
59 & 107.8 & 107.253605296694 & 0.546394703306024 \tabularnewline
60 & 107.9 & 107.152955807175 & 0.747044192825424 \tabularnewline
61 & 107.9 & 106.853705195623 & 1.04629480437676 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58107&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]105.4[/C][C]106.882431264556[/C][C]-1.48243126455624[/C][/ROW]
[ROW][C]2[/C][C]105.4[/C][C]106.722114869121[/C][C]-1.32211486912069[/C][/ROW]
[ROW][C]3[/C][C]105.6[/C][C]106.854038289707[/C][C]-1.2540382897069[/C][/ROW]
[ROW][C]4[/C][C]105.7[/C][C]106.627210593388[/C][C]-0.92721059338794[/C][/ROW]
[ROW][C]5[/C][C]105.8[/C][C]106.669758455522[/C][C]-0.869758455521573[/C][/ROW]
[ROW][C]6[/C][C]105.8[/C][C]106.692739310668[/C][C]-0.892739310668119[/C][/ROW]
[ROW][C]7[/C][C]105.8[/C][C]106.795936662321[/C][C]-0.995936662321133[/C][/ROW]
[ROW][C]8[/C][C]105.9[/C][C]106.953605296694[/C][C]-1.05360529669396[/C][/ROW]
[ROW][C]9[/C][C]106.1[/C][C]107.205745213787[/C][C]-1.10574521378664[/C][/ROW]
[ROW][C]10[/C][C]106.4[/C][C]107.34[/C][C]-0.939999999999997[/C][/ROW]
[ROW][C]11[/C][C]106.4[/C][C]107.39723564136[/C][C]-0.997235641359909[/C][/ROW]
[ROW][C]12[/C][C]106.3[/C][C]107.382764358640[/C][C]-1.08276435864009[/C][/ROW]
[ROW][C]13[/C][C]106.2[/C][C]106.911157333490[/C][C]-0.711157333489622[/C][/ROW]
[ROW][C]14[/C][C]106.2[/C][C]106.722114869121[/C][C]-0.522114869120693[/C][/ROW]
[ROW][C]15[/C][C]106.3[/C][C]106.767860082907[/C][C]-0.467860082907334[/C][/ROW]
[ROW][C]16[/C][C]106.4[/C][C]107.000649489519[/C][C]-0.600649489519388[/C][/ROW]
[ROW][C]17[/C][C]106.5[/C][C]107.158101627386[/C][C]-0.658101627385768[/C][/ROW]
[ROW][C]18[/C][C]106.6[/C][C]107.324712827198[/C][C]-0.724712827198264[/C][/ROW]
[ROW][C]19[/C][C]106.6[/C][C]107.284279834185[/C][C]-0.684279834185338[/C][/ROW]
[ROW][C]20[/C][C]106.6[/C][C]107.298318123892[/C][C]-0.698318123892236[/C][/ROW]
[ROW][C]21[/C][C]106.8[/C][C]107.406827696319[/C][C]-0.606827696318955[/C][/ROW]
[ROW][C]22[/C][C]107[/C][C]107.512356413599[/C][C]-0.512356413599135[/C][/ROW]
[ROW][C]23[/C][C]107.2[/C][C]107.598318123892[/C][C]-0.39831812389223[/C][/ROW]
[ROW][C]24[/C][C]107.3[/C][C]107.583846841172[/C][C]-0.283846841172409[/C][/ROW]
[ROW][C]25[/C][C]107.5[/C][C]107.313322298554[/C][C]0.186677701445742[/C][/ROW]
[ROW][C]26[/C][C]107.6[/C][C]106.980649489519[/C][C]0.619350510480603[/C][/ROW]
[ROW][C]27[/C][C]107.6[/C][C]106.997668634373[/C][C]0.602331365627158[/C][/ROW]
[ROW][C]28[/C][C]107.7[/C][C]107.029375558453[/C][C]0.670624441547422[/C][/ROW]
[ROW][C]29[/C][C]107.7[/C][C]107.301731972052[/C][C]0.398268027948294[/C][/ROW]
[ROW][C]30[/C][C]107.7[/C][C]107.123630344666[/C][C]0.576369655334063[/C][/ROW]
[ROW][C]31[/C][C]107.7[/C][C]107.198101627386[/C][C]0.501898372614238[/C][/ROW]
[ROW][C]32[/C][C]107.6[/C][C]107.212139917093[/C][C]0.387860082907328[/C][/ROW]
[ROW][C]33[/C][C]107.7[/C][C]107.263197351653[/C][C]0.436802648346992[/C][/ROW]
[ROW][C]34[/C][C]107.9[/C][C]107.483630344666[/C][C]0.416369655334062[/C][/ROW]
[ROW][C]35[/C][C]107.9[/C][C]107.39723564136[/C][C]0.502764358640092[/C][/ROW]
[ROW][C]36[/C][C]107.9[/C][C]107.468942565440[/C][C]0.431057434560354[/C][/ROW]
[ROW][C]37[/C][C]107.8[/C][C]107.255870160688[/C][C]0.544129839312116[/C][/ROW]
[ROW][C]38[/C][C]107.6[/C][C]107.095553765252[/C][C]0.504446234747852[/C][/ROW]
[ROW][C]39[/C][C]107.4[/C][C]107.198751116905[/C][C]0.20124888309485[/C][/ROW]
[ROW][C]40[/C][C]107[/C][C]106.971923420586[/C][C]0.0280765794137966[/C][/ROW]
[ROW][C]41[/C][C]107[/C][C]106.870840938054[/C][C]0.129159061946116[/C][/ROW]
[ROW][C]42[/C][C]107.2[/C][C]106.98[/C][C]0.220000000000005[/C][/ROW]
[ROW][C]43[/C][C]107.5[/C][C]106.997019144853[/C][C]0.502980855146551[/C][/ROW]
[ROW][C]44[/C][C]107.8[/C][C]107.09723564136[/C][C]0.702764358640086[/C][/ROW]
[ROW][C]45[/C][C]107.8[/C][C]107.234471282720[/C][C]0.565528717280173[/C][/ROW]
[ROW][C]46[/C][C]107.7[/C][C]107.110191448534[/C][C]0.589808551465506[/C][/ROW]
[ROW][C]47[/C][C]107.6[/C][C]107.253605296694[/C][C]0.346394703306022[/C][/ROW]
[ROW][C]48[/C][C]107.6[/C][C]107.411490427573[/C][C]0.188509572426721[/C][/ROW]
[ROW][C]49[/C][C]107.5[/C][C]107.083513747089[/C][C]0.416486252911247[/C][/ROW]
[ROW][C]50[/C][C]107.5[/C][C]106.779567006987[/C][C]0.720432993012927[/C][/ROW]
[ROW][C]51[/C][C]107.6[/C][C]106.681681876108[/C][C]0.918318123892227[/C][/ROW]
[ROW][C]52[/C][C]107.6[/C][C]106.770840938054[/C][C]0.82915906194611[/C][/ROW]
[ROW][C]53[/C][C]107.9[/C][C]106.899567006987[/C][C]1.00043299301293[/C][/ROW]
[ROW][C]54[/C][C]107.6[/C][C]106.778917517468[/C][C]0.821082482532315[/C][/ROW]
[ROW][C]55[/C][C]107.5[/C][C]106.824662731254[/C][C]0.675337268745682[/C][/ROW]
[ROW][C]56[/C][C]107.5[/C][C]106.838701020961[/C][C]0.661298979038785[/C][/ROW]
[ROW][C]57[/C][C]107.6[/C][C]106.889758455522[/C][C]0.71024154447843[/C][/ROW]
[ROW][C]58[/C][C]107.7[/C][C]107.253821793200[/C][C]0.446178206799564[/C][/ROW]
[ROW][C]59[/C][C]107.8[/C][C]107.253605296694[/C][C]0.546394703306024[/C][/ROW]
[ROW][C]60[/C][C]107.9[/C][C]107.152955807175[/C][C]0.747044192825424[/C][/ROW]
[ROW][C]61[/C][C]107.9[/C][C]106.853705195623[/C][C]1.04629480437676[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58107&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58107&T=4

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1105.4106.882431264556-1.48243126455624
2105.4106.722114869121-1.32211486912069
3105.6106.854038289707-1.2540382897069
4105.7106.627210593388-0.92721059338794
5105.8106.669758455522-0.869758455521573
6105.8106.692739310668-0.892739310668119
7105.8106.795936662321-0.995936662321133
8105.9106.953605296694-1.05360529669396
9106.1107.205745213787-1.10574521378664
10106.4107.34-0.939999999999997
11106.4107.39723564136-0.997235641359909
12106.3107.382764358640-1.08276435864009
13106.2106.911157333490-0.711157333489622
14106.2106.722114869121-0.522114869120693
15106.3106.767860082907-0.467860082907334
16106.4107.000649489519-0.600649489519388
17106.5107.158101627386-0.658101627385768
18106.6107.324712827198-0.724712827198264
19106.6107.284279834185-0.684279834185338
20106.6107.298318123892-0.698318123892236
21106.8107.406827696319-0.606827696318955
22107107.512356413599-0.512356413599135
23107.2107.598318123892-0.39831812389223
24107.3107.583846841172-0.283846841172409
25107.5107.3133222985540.186677701445742
26107.6106.9806494895190.619350510480603
27107.6106.9976686343730.602331365627158
28107.7107.0293755584530.670624441547422
29107.7107.3017319720520.398268027948294
30107.7107.1236303446660.576369655334063
31107.7107.1981016273860.501898372614238
32107.6107.2121399170930.387860082907328
33107.7107.2631973516530.436802648346992
34107.9107.4836303446660.416369655334062
35107.9107.397235641360.502764358640092
36107.9107.4689425654400.431057434560354
37107.8107.2558701606880.544129839312116
38107.6107.0955537652520.504446234747852
39107.4107.1987511169050.20124888309485
40107106.9719234205860.0280765794137966
41107106.8708409380540.129159061946116
42107.2106.980.220000000000005
43107.5106.9970191448530.502980855146551
44107.8107.097235641360.702764358640086
45107.8107.2344712827200.565528717280173
46107.7107.1101914485340.589808551465506
47107.6107.2536052966940.346394703306022
48107.6107.4114904275730.188509572426721
49107.5107.0835137470890.416486252911247
50107.5106.7795670069870.720432993012927
51107.6106.6816818761080.918318123892227
52107.6106.7708409380540.82915906194611
53107.9106.8995670069871.00043299301293
54107.6106.7789175174680.821082482532315
55107.5106.8246627312540.675337268745682
56107.5106.8387010209610.661298979038785
57107.6106.8897584555220.71024154447843
58107.7107.2538217932000.446178206799564
59107.8107.2536052966940.546394703306024
60107.9107.1529558071750.747044192825424
61107.9106.8537051956231.04629480437676







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.8946316579144020.2107366841711960.105368342085598
170.858707212931760.2825855741364790.141292787068239
180.8007832883484450.3984334233031090.199216711651554
190.773998784429020.4520024311419590.226001215570979
200.8043854250939040.3912291498121920.195614574906096
210.8643026244013740.2713947511972510.135697375598626
220.9079625050000510.1840749899998980.092037494999949
230.9386689582572630.1226620834854740.0613310417427369
240.972116140891290.05576771821742130.0278838591087106
250.9913576503040180.01728469939196350.00864234969598177
260.9984279171390180.003144165721963300.00157208286098165
270.9994349051898850.001130189620230130.000565094810115066
280.999773147044760.0004537059104811520.000226852955240576
290.999608414585090.0007831708298188460.000391585414909423
300.9997810844040760.0004378311918470110.000218915595923505
310.9997760412918350.0004479174163300630.000223958708165032
320.9997114204850920.0005771590298158910.000288579514907946
330.999710716422430.0005785671551418250.000289283577570912
340.9995956435257940.0008087129484128860.000404356474206443
350.9995620704112620.0008758591774753380.000437929588737669
360.999291260518110.001417478963780820.000708739481890411
370.9985421182785840.002915763442831510.00145788172141576
380.9966421601525450.006715679694909780.00335783984745489
390.9915918615766610.01681627684667690.00840813842333847
400.9891378547549320.02172429049013610.0108621452450680
410.9985538753694510.002892249261098220.00144612463054911
420.9978108272581850.004378345483630060.00218917274181503
430.9929278978012720.01414420439745640.00707210219872821
440.9891055565545740.02178888689085220.0108944434454261
450.993298005056890.01340398988622100.00670199494311051

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.894631657914402 & 0.210736684171196 & 0.105368342085598 \tabularnewline
17 & 0.85870721293176 & 0.282585574136479 & 0.141292787068239 \tabularnewline
18 & 0.800783288348445 & 0.398433423303109 & 0.199216711651554 \tabularnewline
19 & 0.77399878442902 & 0.452002431141959 & 0.226001215570979 \tabularnewline
20 & 0.804385425093904 & 0.391229149812192 & 0.195614574906096 \tabularnewline
21 & 0.864302624401374 & 0.271394751197251 & 0.135697375598626 \tabularnewline
22 & 0.907962505000051 & 0.184074989999898 & 0.092037494999949 \tabularnewline
23 & 0.938668958257263 & 0.122662083485474 & 0.0613310417427369 \tabularnewline
24 & 0.97211614089129 & 0.0557677182174213 & 0.0278838591087106 \tabularnewline
25 & 0.991357650304018 & 0.0172846993919635 & 0.00864234969598177 \tabularnewline
26 & 0.998427917139018 & 0.00314416572196330 & 0.00157208286098165 \tabularnewline
27 & 0.999434905189885 & 0.00113018962023013 & 0.000565094810115066 \tabularnewline
28 & 0.99977314704476 & 0.000453705910481152 & 0.000226852955240576 \tabularnewline
29 & 0.99960841458509 & 0.000783170829818846 & 0.000391585414909423 \tabularnewline
30 & 0.999781084404076 & 0.000437831191847011 & 0.000218915595923505 \tabularnewline
31 & 0.999776041291835 & 0.000447917416330063 & 0.000223958708165032 \tabularnewline
32 & 0.999711420485092 & 0.000577159029815891 & 0.000288579514907946 \tabularnewline
33 & 0.99971071642243 & 0.000578567155141825 & 0.000289283577570912 \tabularnewline
34 & 0.999595643525794 & 0.000808712948412886 & 0.000404356474206443 \tabularnewline
35 & 0.999562070411262 & 0.000875859177475338 & 0.000437929588737669 \tabularnewline
36 & 0.99929126051811 & 0.00141747896378082 & 0.000708739481890411 \tabularnewline
37 & 0.998542118278584 & 0.00291576344283151 & 0.00145788172141576 \tabularnewline
38 & 0.996642160152545 & 0.00671567969490978 & 0.00335783984745489 \tabularnewline
39 & 0.991591861576661 & 0.0168162768466769 & 0.00840813842333847 \tabularnewline
40 & 0.989137854754932 & 0.0217242904901361 & 0.0108621452450680 \tabularnewline
41 & 0.998553875369451 & 0.00289224926109822 & 0.00144612463054911 \tabularnewline
42 & 0.997810827258185 & 0.00437834548363006 & 0.00218917274181503 \tabularnewline
43 & 0.992927897801272 & 0.0141442043974564 & 0.00707210219872821 \tabularnewline
44 & 0.989105556554574 & 0.0217888868908522 & 0.0108944434454261 \tabularnewline
45 & 0.99329800505689 & 0.0134039898862210 & 0.00670199494311051 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58107&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]16[/C][C]0.894631657914402[/C][C]0.210736684171196[/C][C]0.105368342085598[/C][/ROW]
[ROW][C]17[/C][C]0.85870721293176[/C][C]0.282585574136479[/C][C]0.141292787068239[/C][/ROW]
[ROW][C]18[/C][C]0.800783288348445[/C][C]0.398433423303109[/C][C]0.199216711651554[/C][/ROW]
[ROW][C]19[/C][C]0.77399878442902[/C][C]0.452002431141959[/C][C]0.226001215570979[/C][/ROW]
[ROW][C]20[/C][C]0.804385425093904[/C][C]0.391229149812192[/C][C]0.195614574906096[/C][/ROW]
[ROW][C]21[/C][C]0.864302624401374[/C][C]0.271394751197251[/C][C]0.135697375598626[/C][/ROW]
[ROW][C]22[/C][C]0.907962505000051[/C][C]0.184074989999898[/C][C]0.092037494999949[/C][/ROW]
[ROW][C]23[/C][C]0.938668958257263[/C][C]0.122662083485474[/C][C]0.0613310417427369[/C][/ROW]
[ROW][C]24[/C][C]0.97211614089129[/C][C]0.0557677182174213[/C][C]0.0278838591087106[/C][/ROW]
[ROW][C]25[/C][C]0.991357650304018[/C][C]0.0172846993919635[/C][C]0.00864234969598177[/C][/ROW]
[ROW][C]26[/C][C]0.998427917139018[/C][C]0.00314416572196330[/C][C]0.00157208286098165[/C][/ROW]
[ROW][C]27[/C][C]0.999434905189885[/C][C]0.00113018962023013[/C][C]0.000565094810115066[/C][/ROW]
[ROW][C]28[/C][C]0.99977314704476[/C][C]0.000453705910481152[/C][C]0.000226852955240576[/C][/ROW]
[ROW][C]29[/C][C]0.99960841458509[/C][C]0.000783170829818846[/C][C]0.000391585414909423[/C][/ROW]
[ROW][C]30[/C][C]0.999781084404076[/C][C]0.000437831191847011[/C][C]0.000218915595923505[/C][/ROW]
[ROW][C]31[/C][C]0.999776041291835[/C][C]0.000447917416330063[/C][C]0.000223958708165032[/C][/ROW]
[ROW][C]32[/C][C]0.999711420485092[/C][C]0.000577159029815891[/C][C]0.000288579514907946[/C][/ROW]
[ROW][C]33[/C][C]0.99971071642243[/C][C]0.000578567155141825[/C][C]0.000289283577570912[/C][/ROW]
[ROW][C]34[/C][C]0.999595643525794[/C][C]0.000808712948412886[/C][C]0.000404356474206443[/C][/ROW]
[ROW][C]35[/C][C]0.999562070411262[/C][C]0.000875859177475338[/C][C]0.000437929588737669[/C][/ROW]
[ROW][C]36[/C][C]0.99929126051811[/C][C]0.00141747896378082[/C][C]0.000708739481890411[/C][/ROW]
[ROW][C]37[/C][C]0.998542118278584[/C][C]0.00291576344283151[/C][C]0.00145788172141576[/C][/ROW]
[ROW][C]38[/C][C]0.996642160152545[/C][C]0.00671567969490978[/C][C]0.00335783984745489[/C][/ROW]
[ROW][C]39[/C][C]0.991591861576661[/C][C]0.0168162768466769[/C][C]0.00840813842333847[/C][/ROW]
[ROW][C]40[/C][C]0.989137854754932[/C][C]0.0217242904901361[/C][C]0.0108621452450680[/C][/ROW]
[ROW][C]41[/C][C]0.998553875369451[/C][C]0.00289224926109822[/C][C]0.00144612463054911[/C][/ROW]
[ROW][C]42[/C][C]0.997810827258185[/C][C]0.00437834548363006[/C][C]0.00218917274181503[/C][/ROW]
[ROW][C]43[/C][C]0.992927897801272[/C][C]0.0141442043974564[/C][C]0.00707210219872821[/C][/ROW]
[ROW][C]44[/C][C]0.989105556554574[/C][C]0.0217888868908522[/C][C]0.0108944434454261[/C][/ROW]
[ROW][C]45[/C][C]0.99329800505689[/C][C]0.0134039898862210[/C][C]0.00670199494311051[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58107&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58107&T=5

As an alternative you can also use a QR Code:  

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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.8946316579144020.2107366841711960.105368342085598
170.858707212931760.2825855741364790.141292787068239
180.8007832883484450.3984334233031090.199216711651554
190.773998784429020.4520024311419590.226001215570979
200.8043854250939040.3912291498121920.195614574906096
210.8643026244013740.2713947511972510.135697375598626
220.9079625050000510.1840749899998980.092037494999949
230.9386689582572630.1226620834854740.0613310417427369
240.972116140891290.05576771821742130.0278838591087106
250.9913576503040180.01728469939196350.00864234969598177
260.9984279171390180.003144165721963300.00157208286098165
270.9994349051898850.001130189620230130.000565094810115066
280.999773147044760.0004537059104811520.000226852955240576
290.999608414585090.0007831708298188460.000391585414909423
300.9997810844040760.0004378311918470110.000218915595923505
310.9997760412918350.0004479174163300630.000223958708165032
320.9997114204850920.0005771590298158910.000288579514907946
330.999710716422430.0005785671551418250.000289283577570912
340.9995956435257940.0008087129484128860.000404356474206443
350.9995620704112620.0008758591774753380.000437929588737669
360.999291260518110.001417478963780820.000708739481890411
370.9985421182785840.002915763442831510.00145788172141576
380.9966421601525450.006715679694909780.00335783984745489
390.9915918615766610.01681627684667690.00840813842333847
400.9891378547549320.02172429049013610.0108621452450680
410.9985538753694510.002892249261098220.00144612463054911
420.9978108272581850.004378345483630060.00218917274181503
430.9929278978012720.01414420439745640.00707210219872821
440.9891055565545740.02178888689085220.0108944434454261
450.993298005056890.01340398988622100.00670199494311051







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level150.5NOK
5% type I error level210.7NOK
10% type I error level220.733333333333333NOK

\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 & 15 & 0.5 & NOK \tabularnewline
5% type I error level & 21 & 0.7 & NOK \tabularnewline
10% type I error level & 22 & 0.733333333333333 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58107&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]15[/C][C]0.5[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]21[/C][C]0.7[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]22[/C][C]0.733333333333333[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58107&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58107&T=6

As an alternative you can also use a QR Code:  

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level150.5NOK
5% type I error level210.7NOK
10% type I error level220.733333333333333NOK



Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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')
}