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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Thu, 27 Nov 2008 05:29:05 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/27/t1227789188t9qvqrku6pyuhdf.htm/, Retrieved Mon, 20 May 2024 11:07:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25774, Retrieved Mon, 20 May 2024 11:07:56 +0000

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Estimated Impact

150

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

F       [Multiple Regression] [Case: the Seatbel...] [2008-11-27 12:29:05] [1828943283e41f5e3270e2e73d6433b4] [Current]

Feedback Forum

2008-11-29 13:15:56 [Sofie Sergoynne] [reply] 
Antwoord is correct. Weer had ik hierbij extra vermeld dat deze t-stat kritische waardes zijn. T-waarde is hoger dan 2, EN dan heb je dus 5% kans om je te vergissen. Volgende tabel. oke.
2008-11-30 16:03:43 [Stephanie Vanderlinden] [reply] 
De tabellen worden goed verklaard. De uitleg bij de grafieken ontbreekt. Hij had hier kunnen vermelden dat de QQ-plot redelijk dicht tegen de rechte ligt, waaruit je kan afleiden dat de gegevens redelijk normaal verdeeld zijn. Bij de autocorrelationgrafiek zijn er maar 2 verticale lijnen die buiten het 95% betrouwbaarheidsinterval (= blauwe stippellijnen) komen, de residuals zijn dus niet significant verschillend.
2008-12-01 12:54:45 [Alexander Hendrickx] [reply] 
De grafieken en tabellen zijn goed opgemaakt  de interpretaties zijn ook ok. Er zijn echter wel geen verklaringen bij de grafieken. Zeker de niet-significantie die we kunnen afleiden van de autocorrelatie grafiek is zeker de vermelding waard.

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Dataseries X:

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Histogram

Boxplots

4,8	19,2
5,5	26,6
5,4	26,6
5,9	31,4
5,8	31,2
5,1	26,4
4,1	20,7
4,4	20,7
3,6	15
3,5	13,3
3,1	8,7
2,9	10,2
2,2	4,3
1,4	-0,1
1,2	-4,6
1,3	-3,9
1,3	-3,5
1,3	-3,4
1,8	-2,5
1,8	-1,1
1,8	0,3
1,7	-0,9
2,1	3,6
2	2,7
1,7	-0,2
1,9	-1
2,3	5,8
2,4	6,4
2,5	9,6
2,8	13,2
2,6	10,6
2,2	10,9
2,8	12,9
2,8	15,9
2,8	12,2
2,3	9,1
2,2	9
3	17,4
2,9	14,7
2,7	17
2,7	13,7
2,3	9,5
2,4	14,8
2,8	13,6
2,3	12,6
2	8,9
1,9	10,2
2,3	12,7
2,7	16
1,8	10,4
2	9,9
2,1	9,5
2	8,6
2,4	10
1,7	3,5
1	-4,2
1,2	-4,4
1,4	-1,5
1,7	-0,1
1,8	0,8

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 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=25774&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=25774&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25774&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Belgische_infaltie[t] = + 1.47130483639316 + 0.118306870310270inflatie_energiedragers[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Belgische_infaltie[t] =  +  1.47130483639316 +  0.118306870310270inflatie_energiedragers[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25774&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Belgische_infaltie[t] =  +  1.47130483639316 +  0.118306870310270inflatie_energiedragers[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25774&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25774&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
Belgische_infaltie[t] = + 1.47130483639316 + 0.118306870310270inflatie_energiedragers[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	1.47130483639316	0.089396	16.4582	0	0
inflatie_energiedragers	0.118306870310270	0.006903	17.1385	0	0

\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) & 1.47130483639316 & 0.089396 & 16.4582 & 0 & 0 \tabularnewline
inflatie_energiedragers & 0.118306870310270 & 0.006903 & 17.1385 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25774&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]1.47130483639316[/C][C]0.089396[/C][C]16.4582[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]inflatie_energiedragers[/C][C]0.118306870310270[/C][C]0.006903[/C][C]17.1385[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25774&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25774&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
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	1.47130483639316	0.089396	16.4582	0	0
inflatie_energiedragers	0.118306870310270	0.006903	17.1385	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.913837761374175
R-squared	0.835099454113364
Adjusted R-squared	0.83225634125325
F-TEST (value)	293.727155832905
F-TEST (DF numerator)	1
F-TEST (DF denominator)	58
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.481063202894401
Sum Squared Residuals	13.4224647003832

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.913837761374175 \tabularnewline
R-squared & 0.835099454113364 \tabularnewline
Adjusted R-squared & 0.83225634125325 \tabularnewline
F-TEST (value) & 293.727155832905 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 58 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.481063202894401 \tabularnewline
Sum Squared Residuals & 13.4224647003832 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25774&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.913837761374175[/C][/ROW]
[ROW][C]R-squared[/C][C]0.835099454113364[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.83225634125325[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]293.727155832905[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]58[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.481063202894401[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]13.4224647003832[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25774&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25774&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 R	0.913837761374175
R-squared	0.835099454113364
Adjusted R-squared	0.83225634125325
F-TEST (value)	293.727155832905
F-TEST (DF numerator)	1
F-TEST (DF denominator)	58
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.481063202894401
Sum Squared Residuals	13.4224647003832

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	4.8	3.74279674635038	1.05720325364962
2	5.5	4.61826758664635	0.881732413353647
3	5.4	4.61826758664635	0.781732413353647
4	5.9	5.18614056413565	0.71385943586435
5	5.8	5.16247919007360	0.637520809926404
6	5.1	4.5946062125843	0.505393787415701
7	4.1	3.92025705181576	0.179742948184241
8	4.4	3.92025705181576	0.479742948184241
9	3.6	3.24590789104722	0.354092108952781
10	3.5	3.04478621151976	0.45521378848024
11	3.1	2.50057460809252	0.599425391907483
12	2.9	2.67803491355792	0.221965086442078
13	2.2	1.98002437872733	0.219975621272672
14	1.4	1.45947414936214	-0.0594741493621392
15	1.2	0.927093232965923	0.272906767034077
16	1.3	1.00990804218311	0.290091957816888
17	1.3	1.05723079030722	0.24276920969278
18	1.3	1.06906147733825	0.230938522661753
19	1.8	1.17553766061749	0.62446233938251
20	1.8	1.34116727905187	0.458832720948131
21	1.8	1.50679689748625	0.293203102513753
22	1.7	1.36482865311392	0.335171346886077
23	2.1	1.89720956951014	0.202790430489861
24	2	1.79073338623090	0.209266613769105
25	1.7	1.44764346233111	0.252356537668888
26	1.9	1.35299796608290	0.547002033917104
27	2.3	2.15748468419273	0.142515315807267
28	2.4	2.22846880637890	0.171531193621105
29	2.5	2.60705079137176	-0.107050791371760
30	2.8	3.03295552448873	-0.232955524488733
31	2.6	2.72535766168203	-0.12535766168203
32	2.2	2.76084972277511	-0.560849722775111
33	2.8	2.99746346339565	-0.197463463395652
34	2.8	3.35238407432646	-0.552384074326462
35	2.8	2.91464865417846	-0.114648654178462
36	2.3	2.54789735621662	-0.247897356216625
37	2.2	2.5360666691856	-0.336066669185598
38	3	3.52984437979187	-0.529844379791867
39	2.9	3.21041582995414	-0.310415829954138
40	2.7	3.48252163166776	-0.78252163166776
41	2.7	3.09210895964387	-0.392108959643867
42	2.3	2.59522010434073	-0.295220104340733
43	2.4	3.22224651698517	-0.822246516985165
44	2.8	3.08027827261284	-0.280278272612841
45	2.3	2.96197140230257	-0.66197140230257
46	2	2.52423598215457	-0.524235982154571
47	1.9	2.67803491355792	-0.778034913557922
48	2.3	2.9738020893336	-0.673802089333598
49	2.7	3.36421476135749	-0.664214761357489
50	1.8	2.70169628761998	-0.901696287619976
51	2	2.64254285246484	-0.642542852464841
52	2.1	2.59522010434073	-0.495220104340733
53	2	2.48874392106149	-0.48874392106149
54	2.4	2.65437353949587	-0.254373539495868
55	1.7	1.88537888247911	-0.185378882479112
56	1	0.974415981090031	0.0255840189099689
57	1.2	0.950754607027977	0.249245392972023
58	1.4	1.29384453092776	0.106155469072239
59	1.7	1.45947414936214	0.240525850637861
60	1.8	1.56595033264138	0.234049667358618

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 4.8 & 3.74279674635038 & 1.05720325364962 \tabularnewline
2 & 5.5 & 4.61826758664635 & 0.881732413353647 \tabularnewline
3 & 5.4 & 4.61826758664635 & 0.781732413353647 \tabularnewline
4 & 5.9 & 5.18614056413565 & 0.71385943586435 \tabularnewline
5 & 5.8 & 5.16247919007360 & 0.637520809926404 \tabularnewline
6 & 5.1 & 4.5946062125843 & 0.505393787415701 \tabularnewline
7 & 4.1 & 3.92025705181576 & 0.179742948184241 \tabularnewline
8 & 4.4 & 3.92025705181576 & 0.479742948184241 \tabularnewline
9 & 3.6 & 3.24590789104722 & 0.354092108952781 \tabularnewline
10 & 3.5 & 3.04478621151976 & 0.45521378848024 \tabularnewline
11 & 3.1 & 2.50057460809252 & 0.599425391907483 \tabularnewline
12 & 2.9 & 2.67803491355792 & 0.221965086442078 \tabularnewline
13 & 2.2 & 1.98002437872733 & 0.219975621272672 \tabularnewline
14 & 1.4 & 1.45947414936214 & -0.0594741493621392 \tabularnewline
15 & 1.2 & 0.927093232965923 & 0.272906767034077 \tabularnewline
16 & 1.3 & 1.00990804218311 & 0.290091957816888 \tabularnewline
17 & 1.3 & 1.05723079030722 & 0.24276920969278 \tabularnewline
18 & 1.3 & 1.06906147733825 & 0.230938522661753 \tabularnewline
19 & 1.8 & 1.17553766061749 & 0.62446233938251 \tabularnewline
20 & 1.8 & 1.34116727905187 & 0.458832720948131 \tabularnewline
21 & 1.8 & 1.50679689748625 & 0.293203102513753 \tabularnewline
22 & 1.7 & 1.36482865311392 & 0.335171346886077 \tabularnewline
23 & 2.1 & 1.89720956951014 & 0.202790430489861 \tabularnewline
24 & 2 & 1.79073338623090 & 0.209266613769105 \tabularnewline
25 & 1.7 & 1.44764346233111 & 0.252356537668888 \tabularnewline
26 & 1.9 & 1.35299796608290 & 0.547002033917104 \tabularnewline
27 & 2.3 & 2.15748468419273 & 0.142515315807267 \tabularnewline
28 & 2.4 & 2.22846880637890 & 0.171531193621105 \tabularnewline
29 & 2.5 & 2.60705079137176 & -0.107050791371760 \tabularnewline
30 & 2.8 & 3.03295552448873 & -0.232955524488733 \tabularnewline
31 & 2.6 & 2.72535766168203 & -0.12535766168203 \tabularnewline
32 & 2.2 & 2.76084972277511 & -0.560849722775111 \tabularnewline
33 & 2.8 & 2.99746346339565 & -0.197463463395652 \tabularnewline
34 & 2.8 & 3.35238407432646 & -0.552384074326462 \tabularnewline
35 & 2.8 & 2.91464865417846 & -0.114648654178462 \tabularnewline
36 & 2.3 & 2.54789735621662 & -0.247897356216625 \tabularnewline
37 & 2.2 & 2.5360666691856 & -0.336066669185598 \tabularnewline
38 & 3 & 3.52984437979187 & -0.529844379791867 \tabularnewline
39 & 2.9 & 3.21041582995414 & -0.310415829954138 \tabularnewline
40 & 2.7 & 3.48252163166776 & -0.78252163166776 \tabularnewline
41 & 2.7 & 3.09210895964387 & -0.392108959643867 \tabularnewline
42 & 2.3 & 2.59522010434073 & -0.295220104340733 \tabularnewline
43 & 2.4 & 3.22224651698517 & -0.822246516985165 \tabularnewline
44 & 2.8 & 3.08027827261284 & -0.280278272612841 \tabularnewline
45 & 2.3 & 2.96197140230257 & -0.66197140230257 \tabularnewline
46 & 2 & 2.52423598215457 & -0.524235982154571 \tabularnewline
47 & 1.9 & 2.67803491355792 & -0.778034913557922 \tabularnewline
48 & 2.3 & 2.9738020893336 & -0.673802089333598 \tabularnewline
49 & 2.7 & 3.36421476135749 & -0.664214761357489 \tabularnewline
50 & 1.8 & 2.70169628761998 & -0.901696287619976 \tabularnewline
51 & 2 & 2.64254285246484 & -0.642542852464841 \tabularnewline
52 & 2.1 & 2.59522010434073 & -0.495220104340733 \tabularnewline
53 & 2 & 2.48874392106149 & -0.48874392106149 \tabularnewline
54 & 2.4 & 2.65437353949587 & -0.254373539495868 \tabularnewline
55 & 1.7 & 1.88537888247911 & -0.185378882479112 \tabularnewline
56 & 1 & 0.974415981090031 & 0.0255840189099689 \tabularnewline
57 & 1.2 & 0.950754607027977 & 0.249245392972023 \tabularnewline
58 & 1.4 & 1.29384453092776 & 0.106155469072239 \tabularnewline
59 & 1.7 & 1.45947414936214 & 0.240525850637861 \tabularnewline
60 & 1.8 & 1.56595033264138 & 0.234049667358618 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25774&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]4.8[/C][C]3.74279674635038[/C][C]1.05720325364962[/C][/ROW]
[ROW][C]2[/C][C]5.5[/C][C]4.61826758664635[/C][C]0.881732413353647[/C][/ROW]
[ROW][C]3[/C][C]5.4[/C][C]4.61826758664635[/C][C]0.781732413353647[/C][/ROW]
[ROW][C]4[/C][C]5.9[/C][C]5.18614056413565[/C][C]0.71385943586435[/C][/ROW]
[ROW][C]5[/C][C]5.8[/C][C]5.16247919007360[/C][C]0.637520809926404[/C][/ROW]
[ROW][C]6[/C][C]5.1[/C][C]4.5946062125843[/C][C]0.505393787415701[/C][/ROW]
[ROW][C]7[/C][C]4.1[/C][C]3.92025705181576[/C][C]0.179742948184241[/C][/ROW]
[ROW][C]8[/C][C]4.4[/C][C]3.92025705181576[/C][C]0.479742948184241[/C][/ROW]
[ROW][C]9[/C][C]3.6[/C][C]3.24590789104722[/C][C]0.354092108952781[/C][/ROW]
[ROW][C]10[/C][C]3.5[/C][C]3.04478621151976[/C][C]0.45521378848024[/C][/ROW]
[ROW][C]11[/C][C]3.1[/C][C]2.50057460809252[/C][C]0.599425391907483[/C][/ROW]
[ROW][C]12[/C][C]2.9[/C][C]2.67803491355792[/C][C]0.221965086442078[/C][/ROW]
[ROW][C]13[/C][C]2.2[/C][C]1.98002437872733[/C][C]0.219975621272672[/C][/ROW]
[ROW][C]14[/C][C]1.4[/C][C]1.45947414936214[/C][C]-0.0594741493621392[/C][/ROW]
[ROW][C]15[/C][C]1.2[/C][C]0.927093232965923[/C][C]0.272906767034077[/C][/ROW]
[ROW][C]16[/C][C]1.3[/C][C]1.00990804218311[/C][C]0.290091957816888[/C][/ROW]
[ROW][C]17[/C][C]1.3[/C][C]1.05723079030722[/C][C]0.24276920969278[/C][/ROW]
[ROW][C]18[/C][C]1.3[/C][C]1.06906147733825[/C][C]0.230938522661753[/C][/ROW]
[ROW][C]19[/C][C]1.8[/C][C]1.17553766061749[/C][C]0.62446233938251[/C][/ROW]
[ROW][C]20[/C][C]1.8[/C][C]1.34116727905187[/C][C]0.458832720948131[/C][/ROW]
[ROW][C]21[/C][C]1.8[/C][C]1.50679689748625[/C][C]0.293203102513753[/C][/ROW]
[ROW][C]22[/C][C]1.7[/C][C]1.36482865311392[/C][C]0.335171346886077[/C][/ROW]
[ROW][C]23[/C][C]2.1[/C][C]1.89720956951014[/C][C]0.202790430489861[/C][/ROW]
[ROW][C]24[/C][C]2[/C][C]1.79073338623090[/C][C]0.209266613769105[/C][/ROW]
[ROW][C]25[/C][C]1.7[/C][C]1.44764346233111[/C][C]0.252356537668888[/C][/ROW]
[ROW][C]26[/C][C]1.9[/C][C]1.35299796608290[/C][C]0.547002033917104[/C][/ROW]
[ROW][C]27[/C][C]2.3[/C][C]2.15748468419273[/C][C]0.142515315807267[/C][/ROW]
[ROW][C]28[/C][C]2.4[/C][C]2.22846880637890[/C][C]0.171531193621105[/C][/ROW]
[ROW][C]29[/C][C]2.5[/C][C]2.60705079137176[/C][C]-0.107050791371760[/C][/ROW]
[ROW][C]30[/C][C]2.8[/C][C]3.03295552448873[/C][C]-0.232955524488733[/C][/ROW]
[ROW][C]31[/C][C]2.6[/C][C]2.72535766168203[/C][C]-0.12535766168203[/C][/ROW]
[ROW][C]32[/C][C]2.2[/C][C]2.76084972277511[/C][C]-0.560849722775111[/C][/ROW]
[ROW][C]33[/C][C]2.8[/C][C]2.99746346339565[/C][C]-0.197463463395652[/C][/ROW]
[ROW][C]34[/C][C]2.8[/C][C]3.35238407432646[/C][C]-0.552384074326462[/C][/ROW]
[ROW][C]35[/C][C]2.8[/C][C]2.91464865417846[/C][C]-0.114648654178462[/C][/ROW]
[ROW][C]36[/C][C]2.3[/C][C]2.54789735621662[/C][C]-0.247897356216625[/C][/ROW]
[ROW][C]37[/C][C]2.2[/C][C]2.5360666691856[/C][C]-0.336066669185598[/C][/ROW]
[ROW][C]38[/C][C]3[/C][C]3.52984437979187[/C][C]-0.529844379791867[/C][/ROW]
[ROW][C]39[/C][C]2.9[/C][C]3.21041582995414[/C][C]-0.310415829954138[/C][/ROW]
[ROW][C]40[/C][C]2.7[/C][C]3.48252163166776[/C][C]-0.78252163166776[/C][/ROW]
[ROW][C]41[/C][C]2.7[/C][C]3.09210895964387[/C][C]-0.392108959643867[/C][/ROW]
[ROW][C]42[/C][C]2.3[/C][C]2.59522010434073[/C][C]-0.295220104340733[/C][/ROW]
[ROW][C]43[/C][C]2.4[/C][C]3.22224651698517[/C][C]-0.822246516985165[/C][/ROW]
[ROW][C]44[/C][C]2.8[/C][C]3.08027827261284[/C][C]-0.280278272612841[/C][/ROW]
[ROW][C]45[/C][C]2.3[/C][C]2.96197140230257[/C][C]-0.66197140230257[/C][/ROW]
[ROW][C]46[/C][C]2[/C][C]2.52423598215457[/C][C]-0.524235982154571[/C][/ROW]
[ROW][C]47[/C][C]1.9[/C][C]2.67803491355792[/C][C]-0.778034913557922[/C][/ROW]
[ROW][C]48[/C][C]2.3[/C][C]2.9738020893336[/C][C]-0.673802089333598[/C][/ROW]
[ROW][C]49[/C][C]2.7[/C][C]3.36421476135749[/C][C]-0.664214761357489[/C][/ROW]
[ROW][C]50[/C][C]1.8[/C][C]2.70169628761998[/C][C]-0.901696287619976[/C][/ROW]
[ROW][C]51[/C][C]2[/C][C]2.64254285246484[/C][C]-0.642542852464841[/C][/ROW]
[ROW][C]52[/C][C]2.1[/C][C]2.59522010434073[/C][C]-0.495220104340733[/C][/ROW]
[ROW][C]53[/C][C]2[/C][C]2.48874392106149[/C][C]-0.48874392106149[/C][/ROW]
[ROW][C]54[/C][C]2.4[/C][C]2.65437353949587[/C][C]-0.254373539495868[/C][/ROW]
[ROW][C]55[/C][C]1.7[/C][C]1.88537888247911[/C][C]-0.185378882479112[/C][/ROW]
[ROW][C]56[/C][C]1[/C][C]0.974415981090031[/C][C]0.0255840189099689[/C][/ROW]
[ROW][C]57[/C][C]1.2[/C][C]0.950754607027977[/C][C]0.249245392972023[/C][/ROW]
[ROW][C]58[/C][C]1.4[/C][C]1.29384453092776[/C][C]0.106155469072239[/C][/ROW]
[ROW][C]59[/C][C]1.7[/C][C]1.45947414936214[/C][C]0.240525850637861[/C][/ROW]
[ROW][C]60[/C][C]1.8[/C][C]1.56595033264138[/C][C]0.234049667358618[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25774&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25774&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 Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	4.8	3.74279674635038	1.05720325364962
2	5.5	4.61826758664635	0.881732413353647
3	5.4	4.61826758664635	0.781732413353647
4	5.9	5.18614056413565	0.71385943586435
5	5.8	5.16247919007360	0.637520809926404
6	5.1	4.5946062125843	0.505393787415701
7	4.1	3.92025705181576	0.179742948184241
8	4.4	3.92025705181576	0.479742948184241
9	3.6	3.24590789104722	0.354092108952781
10	3.5	3.04478621151976	0.45521378848024
11	3.1	2.50057460809252	0.599425391907483
12	2.9	2.67803491355792	0.221965086442078
13	2.2	1.98002437872733	0.219975621272672
14	1.4	1.45947414936214	-0.0594741493621392
15	1.2	0.927093232965923	0.272906767034077
16	1.3	1.00990804218311	0.290091957816888
17	1.3	1.05723079030722	0.24276920969278
18	1.3	1.06906147733825	0.230938522661753
19	1.8	1.17553766061749	0.62446233938251
20	1.8	1.34116727905187	0.458832720948131
21	1.8	1.50679689748625	0.293203102513753
22	1.7	1.36482865311392	0.335171346886077
23	2.1	1.89720956951014	0.202790430489861
24	2	1.79073338623090	0.209266613769105
25	1.7	1.44764346233111	0.252356537668888
26	1.9	1.35299796608290	0.547002033917104
27	2.3	2.15748468419273	0.142515315807267
28	2.4	2.22846880637890	0.171531193621105
29	2.5	2.60705079137176	-0.107050791371760
30	2.8	3.03295552448873	-0.232955524488733
31	2.6	2.72535766168203	-0.12535766168203
32	2.2	2.76084972277511	-0.560849722775111
33	2.8	2.99746346339565	-0.197463463395652
34	2.8	3.35238407432646	-0.552384074326462
35	2.8	2.91464865417846	-0.114648654178462
36	2.3	2.54789735621662	-0.247897356216625
37	2.2	2.5360666691856	-0.336066669185598
38	3	3.52984437979187	-0.529844379791867
39	2.9	3.21041582995414	-0.310415829954138
40	2.7	3.48252163166776	-0.78252163166776
41	2.7	3.09210895964387	-0.392108959643867
42	2.3	2.59522010434073	-0.295220104340733
43	2.4	3.22224651698517	-0.822246516985165
44	2.8	3.08027827261284	-0.280278272612841
45	2.3	2.96197140230257	-0.66197140230257
46	2	2.52423598215457	-0.524235982154571
47	1.9	2.67803491355792	-0.778034913557922
48	2.3	2.9738020893336	-0.673802089333598
49	2.7	3.36421476135749	-0.664214761357489
50	1.8	2.70169628761998	-0.901696287619976
51	2	2.64254285246484	-0.642542852464841
52	2.1	2.59522010434073	-0.495220104340733
53	2	2.48874392106149	-0.48874392106149
54	2.4	2.65437353949587	-0.254373539495868
55	1.7	1.88537888247911	-0.185378882479112
56	1	0.974415981090031	0.0255840189099689
57	1.2	0.950754607027977	0.249245392972023
58	1.4	1.29384453092776	0.106155469072239
59	1.7	1.45947414936214	0.240525850637861
60	1.8	1.56595033264138	0.234049667358618

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.00364598967906205	0.00729197935812411	0.996354010320938
6	0.0591244541194345	0.118248908238869	0.940875545880565
7	0.447050907210713	0.894101814421427	0.552949092789287
8	0.476723725614675	0.95344745122935	0.523276274385325
9	0.483664092480833	0.967328184961666	0.516335907519167
10	0.51051909236596	0.97896181526808	0.48948090763404
11	0.609812867746168	0.780374264507665	0.390187132253832
12	0.668736440947533	0.662527118104933	0.331263559052467
13	0.610628748375838	0.778742503248324	0.389371251624162
14	0.608565027181119	0.782869945637762	0.391434972818881
15	0.571645628382967	0.856708743234067	0.428354371617033
16	0.510924295308659	0.978151409382682	0.489075704691341
17	0.435203250077549	0.870406500155099	0.564796749922451
18	0.362635040858275	0.725270081716549	0.637364959141725
19	0.4880474364273	0.9760948728546	0.5119525635727
20	0.458694958001557	0.917389916003115	0.541305041998443
21	0.38766090864115	0.7753218172823	0.61233909135885
22	0.321212358950351	0.642424717900703	0.678787641049649
23	0.293649649925222	0.587299299850443	0.706350350074778
24	0.257816095321686	0.515632190643372	0.742183904678314
25	0.204776785924229	0.409553571848459	0.79522321407577
26	0.269345005993229	0.538690011986458	0.730654994006771
27	0.301723638267301	0.603447276534602	0.698276361732699
28	0.358118206352348	0.716236412704697	0.641881793647652
29	0.539403362984553	0.921193274030895	0.460596637015447
30	0.77792486829742	0.44415026340516	0.22207513170258
31	0.85841147759108	0.283177044817841	0.141588522408920
32	0.962331587242774	0.0753368255144527	0.0376684127572263
33	0.979140037702007	0.0417199245959863	0.0208599622979931
34	0.991996132651402	0.0160077346971960	0.00800386734859801
35	0.995910100207948	0.00817979958410382	0.00408989979205191
36	0.995560338530266	0.0088793229394672	0.0044396614697336
37	0.994953398778569	0.0100932024428623	0.00504660122143117
38	0.997254021453342	0.00549195709331564	0.00274597854665782
39	0.998677587087065	0.00264482582587034	0.00132241291293517
40	0.999048256777856	0.00190348644428709	0.000951743222143547
41	0.999203397721791	0.00159320455641789	0.000796602278208946
42	0.99886359161349	0.00227281677302189	0.00113640838651094
43	0.99881849911458	0.00236300177083834	0.00118150088541917
44	0.999599562093657	0.00080087581268584	0.00040043790634292
45	0.999299076667787	0.00140184666442695	0.000700923332213475
46	0.998595284237279	0.0028094315254428	0.0014047157627214
47	0.998683890096433	0.00263221980713315	0.00131610990356658
48	0.997292255603644	0.00541548879271251	0.00270774439635625
49	0.995996053719323	0.00800789256135335	0.00400394628067668
50	0.998374936127663	0.00325012774467374	0.00162506387233687
51	0.997649932626434	0.00470013474713214	0.00235006737356607
52	0.994483538520484	0.011032922959031	0.0055164614795155
53	0.993243224387688	0.0135135512246250	0.00675677561231248
54	0.97699366143397	0.0460126771320593	0.0230063385660296
55	0.98764143004463	0.0247171399107388	0.0123585699553694

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
5 & 0.00364598967906205 & 0.00729197935812411 & 0.996354010320938 \tabularnewline
6 & 0.0591244541194345 & 0.118248908238869 & 0.940875545880565 \tabularnewline
7 & 0.447050907210713 & 0.894101814421427 & 0.552949092789287 \tabularnewline
8 & 0.476723725614675 & 0.95344745122935 & 0.523276274385325 \tabularnewline
9 & 0.483664092480833 & 0.967328184961666 & 0.516335907519167 \tabularnewline
10 & 0.51051909236596 & 0.97896181526808 & 0.48948090763404 \tabularnewline
11 & 0.609812867746168 & 0.780374264507665 & 0.390187132253832 \tabularnewline
12 & 0.668736440947533 & 0.662527118104933 & 0.331263559052467 \tabularnewline
13 & 0.610628748375838 & 0.778742503248324 & 0.389371251624162 \tabularnewline
14 & 0.608565027181119 & 0.782869945637762 & 0.391434972818881 \tabularnewline
15 & 0.571645628382967 & 0.856708743234067 & 0.428354371617033 \tabularnewline
16 & 0.510924295308659 & 0.978151409382682 & 0.489075704691341 \tabularnewline
17 & 0.435203250077549 & 0.870406500155099 & 0.564796749922451 \tabularnewline
18 & 0.362635040858275 & 0.725270081716549 & 0.637364959141725 \tabularnewline
19 & 0.4880474364273 & 0.9760948728546 & 0.5119525635727 \tabularnewline
20 & 0.458694958001557 & 0.917389916003115 & 0.541305041998443 \tabularnewline
21 & 0.38766090864115 & 0.7753218172823 & 0.61233909135885 \tabularnewline
22 & 0.321212358950351 & 0.642424717900703 & 0.678787641049649 \tabularnewline
23 & 0.293649649925222 & 0.587299299850443 & 0.706350350074778 \tabularnewline
24 & 0.257816095321686 & 0.515632190643372 & 0.742183904678314 \tabularnewline
25 & 0.204776785924229 & 0.409553571848459 & 0.79522321407577 \tabularnewline
26 & 0.269345005993229 & 0.538690011986458 & 0.730654994006771 \tabularnewline
27 & 0.301723638267301 & 0.603447276534602 & 0.698276361732699 \tabularnewline
28 & 0.358118206352348 & 0.716236412704697 & 0.641881793647652 \tabularnewline
29 & 0.539403362984553 & 0.921193274030895 & 0.460596637015447 \tabularnewline
30 & 0.77792486829742 & 0.44415026340516 & 0.22207513170258 \tabularnewline
31 & 0.85841147759108 & 0.283177044817841 & 0.141588522408920 \tabularnewline
32 & 0.962331587242774 & 0.0753368255144527 & 0.0376684127572263 \tabularnewline
33 & 0.979140037702007 & 0.0417199245959863 & 0.0208599622979931 \tabularnewline
34 & 0.991996132651402 & 0.0160077346971960 & 0.00800386734859801 \tabularnewline
35 & 0.995910100207948 & 0.00817979958410382 & 0.00408989979205191 \tabularnewline
36 & 0.995560338530266 & 0.0088793229394672 & 0.0044396614697336 \tabularnewline
37 & 0.994953398778569 & 0.0100932024428623 & 0.00504660122143117 \tabularnewline
38 & 0.997254021453342 & 0.00549195709331564 & 0.00274597854665782 \tabularnewline
39 & 0.998677587087065 & 0.00264482582587034 & 0.00132241291293517 \tabularnewline
40 & 0.999048256777856 & 0.00190348644428709 & 0.000951743222143547 \tabularnewline
41 & 0.999203397721791 & 0.00159320455641789 & 0.000796602278208946 \tabularnewline
42 & 0.99886359161349 & 0.00227281677302189 & 0.00113640838651094 \tabularnewline
43 & 0.99881849911458 & 0.00236300177083834 & 0.00118150088541917 \tabularnewline
44 & 0.999599562093657 & 0.00080087581268584 & 0.00040043790634292 \tabularnewline
45 & 0.999299076667787 & 0.00140184666442695 & 0.000700923332213475 \tabularnewline
46 & 0.998595284237279 & 0.0028094315254428 & 0.0014047157627214 \tabularnewline
47 & 0.998683890096433 & 0.00263221980713315 & 0.00131610990356658 \tabularnewline
48 & 0.997292255603644 & 0.00541548879271251 & 0.00270774439635625 \tabularnewline
49 & 0.995996053719323 & 0.00800789256135335 & 0.00400394628067668 \tabularnewline
50 & 0.998374936127663 & 0.00325012774467374 & 0.00162506387233687 \tabularnewline
51 & 0.997649932626434 & 0.00470013474713214 & 0.00235006737356607 \tabularnewline
52 & 0.994483538520484 & 0.011032922959031 & 0.0055164614795155 \tabularnewline
53 & 0.993243224387688 & 0.0135135512246250 & 0.00675677561231248 \tabularnewline
54 & 0.97699366143397 & 0.0460126771320593 & 0.0230063385660296 \tabularnewline
55 & 0.98764143004463 & 0.0247171399107388 & 0.0123585699553694 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25774&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]5[/C][C]0.00364598967906205[/C][C]0.00729197935812411[/C][C]0.996354010320938[/C][/ROW]
[ROW][C]6[/C][C]0.0591244541194345[/C][C]0.118248908238869[/C][C]0.940875545880565[/C][/ROW]
[ROW][C]7[/C][C]0.447050907210713[/C][C]0.894101814421427[/C][C]0.552949092789287[/C][/ROW]
[ROW][C]8[/C][C]0.476723725614675[/C][C]0.95344745122935[/C][C]0.523276274385325[/C][/ROW]
[ROW][C]9[/C][C]0.483664092480833[/C][C]0.967328184961666[/C][C]0.516335907519167[/C][/ROW]
[ROW][C]10[/C][C]0.51051909236596[/C][C]0.97896181526808[/C][C]0.48948090763404[/C][/ROW]
[ROW][C]11[/C][C]0.609812867746168[/C][C]0.780374264507665[/C][C]0.390187132253832[/C][/ROW]
[ROW][C]12[/C][C]0.668736440947533[/C][C]0.662527118104933[/C][C]0.331263559052467[/C][/ROW]
[ROW][C]13[/C][C]0.610628748375838[/C][C]0.778742503248324[/C][C]0.389371251624162[/C][/ROW]
[ROW][C]14[/C][C]0.608565027181119[/C][C]0.782869945637762[/C][C]0.391434972818881[/C][/ROW]
[ROW][C]15[/C][C]0.571645628382967[/C][C]0.856708743234067[/C][C]0.428354371617033[/C][/ROW]
[ROW][C]16[/C][C]0.510924295308659[/C][C]0.978151409382682[/C][C]0.489075704691341[/C][/ROW]
[ROW][C]17[/C][C]0.435203250077549[/C][C]0.870406500155099[/C][C]0.564796749922451[/C][/ROW]
[ROW][C]18[/C][C]0.362635040858275[/C][C]0.725270081716549[/C][C]0.637364959141725[/C][/ROW]
[ROW][C]19[/C][C]0.4880474364273[/C][C]0.9760948728546[/C][C]0.5119525635727[/C][/ROW]
[ROW][C]20[/C][C]0.458694958001557[/C][C]0.917389916003115[/C][C]0.541305041998443[/C][/ROW]
[ROW][C]21[/C][C]0.38766090864115[/C][C]0.7753218172823[/C][C]0.61233909135885[/C][/ROW]
[ROW][C]22[/C][C]0.321212358950351[/C][C]0.642424717900703[/C][C]0.678787641049649[/C][/ROW]
[ROW][C]23[/C][C]0.293649649925222[/C][C]0.587299299850443[/C][C]0.706350350074778[/C][/ROW]
[ROW][C]24[/C][C]0.257816095321686[/C][C]0.515632190643372[/C][C]0.742183904678314[/C][/ROW]
[ROW][C]25[/C][C]0.204776785924229[/C][C]0.409553571848459[/C][C]0.79522321407577[/C][/ROW]
[ROW][C]26[/C][C]0.269345005993229[/C][C]0.538690011986458[/C][C]0.730654994006771[/C][/ROW]
[ROW][C]27[/C][C]0.301723638267301[/C][C]0.603447276534602[/C][C]0.698276361732699[/C][/ROW]
[ROW][C]28[/C][C]0.358118206352348[/C][C]0.716236412704697[/C][C]0.641881793647652[/C][/ROW]
[ROW][C]29[/C][C]0.539403362984553[/C][C]0.921193274030895[/C][C]0.460596637015447[/C][/ROW]
[ROW][C]30[/C][C]0.77792486829742[/C][C]0.44415026340516[/C][C]0.22207513170258[/C][/ROW]
[ROW][C]31[/C][C]0.85841147759108[/C][C]0.283177044817841[/C][C]0.141588522408920[/C][/ROW]
[ROW][C]32[/C][C]0.962331587242774[/C][C]0.0753368255144527[/C][C]0.0376684127572263[/C][/ROW]
[ROW][C]33[/C][C]0.979140037702007[/C][C]0.0417199245959863[/C][C]0.0208599622979931[/C][/ROW]
[ROW][C]34[/C][C]0.991996132651402[/C][C]0.0160077346971960[/C][C]0.00800386734859801[/C][/ROW]
[ROW][C]35[/C][C]0.995910100207948[/C][C]0.00817979958410382[/C][C]0.00408989979205191[/C][/ROW]
[ROW][C]36[/C][C]0.995560338530266[/C][C]0.0088793229394672[/C][C]0.0044396614697336[/C][/ROW]
[ROW][C]37[/C][C]0.994953398778569[/C][C]0.0100932024428623[/C][C]0.00504660122143117[/C][/ROW]
[ROW][C]38[/C][C]0.997254021453342[/C][C]0.00549195709331564[/C][C]0.00274597854665782[/C][/ROW]
[ROW][C]39[/C][C]0.998677587087065[/C][C]0.00264482582587034[/C][C]0.00132241291293517[/C][/ROW]
[ROW][C]40[/C][C]0.999048256777856[/C][C]0.00190348644428709[/C][C]0.000951743222143547[/C][/ROW]
[ROW][C]41[/C][C]0.999203397721791[/C][C]0.00159320455641789[/C][C]0.000796602278208946[/C][/ROW]
[ROW][C]42[/C][C]0.99886359161349[/C][C]0.00227281677302189[/C][C]0.00113640838651094[/C][/ROW]
[ROW][C]43[/C][C]0.99881849911458[/C][C]0.00236300177083834[/C][C]0.00118150088541917[/C][/ROW]
[ROW][C]44[/C][C]0.999599562093657[/C][C]0.00080087581268584[/C][C]0.00040043790634292[/C][/ROW]
[ROW][C]45[/C][C]0.999299076667787[/C][C]0.00140184666442695[/C][C]0.000700923332213475[/C][/ROW]
[ROW][C]46[/C][C]0.998595284237279[/C][C]0.0028094315254428[/C][C]0.0014047157627214[/C][/ROW]
[ROW][C]47[/C][C]0.998683890096433[/C][C]0.00263221980713315[/C][C]0.00131610990356658[/C][/ROW]
[ROW][C]48[/C][C]0.997292255603644[/C][C]0.00541548879271251[/C][C]0.00270774439635625[/C][/ROW]
[ROW][C]49[/C][C]0.995996053719323[/C][C]0.00800789256135335[/C][C]0.00400394628067668[/C][/ROW]
[ROW][C]50[/C][C]0.998374936127663[/C][C]0.00325012774467374[/C][C]0.00162506387233687[/C][/ROW]
[ROW][C]51[/C][C]0.997649932626434[/C][C]0.00470013474713214[/C][C]0.00235006737356607[/C][/ROW]
[ROW][C]52[/C][C]0.994483538520484[/C][C]0.011032922959031[/C][C]0.0055164614795155[/C][/ROW]
[ROW][C]53[/C][C]0.993243224387688[/C][C]0.0135135512246250[/C][C]0.00675677561231248[/C][/ROW]
[ROW][C]54[/C][C]0.97699366143397[/C][C]0.0460126771320593[/C][C]0.0230063385660296[/C][/ROW]
[ROW][C]55[/C][C]0.98764143004463[/C][C]0.0247171399107388[/C][C]0.0123585699553694[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25774&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25774&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-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.00364598967906205	0.00729197935812411	0.996354010320938
6	0.0591244541194345	0.118248908238869	0.940875545880565
7	0.447050907210713	0.894101814421427	0.552949092789287
8	0.476723725614675	0.95344745122935	0.523276274385325
9	0.483664092480833	0.967328184961666	0.516335907519167
10	0.51051909236596	0.97896181526808	0.48948090763404
11	0.609812867746168	0.780374264507665	0.390187132253832
12	0.668736440947533	0.662527118104933	0.331263559052467
13	0.610628748375838	0.778742503248324	0.389371251624162
14	0.608565027181119	0.782869945637762	0.391434972818881
15	0.571645628382967	0.856708743234067	0.428354371617033
16	0.510924295308659	0.978151409382682	0.489075704691341
17	0.435203250077549	0.870406500155099	0.564796749922451
18	0.362635040858275	0.725270081716549	0.637364959141725
19	0.4880474364273	0.9760948728546	0.5119525635727
20	0.458694958001557	0.917389916003115	0.541305041998443
21	0.38766090864115	0.7753218172823	0.61233909135885
22	0.321212358950351	0.642424717900703	0.678787641049649
23	0.293649649925222	0.587299299850443	0.706350350074778
24	0.257816095321686	0.515632190643372	0.742183904678314
25	0.204776785924229	0.409553571848459	0.79522321407577
26	0.269345005993229	0.538690011986458	0.730654994006771
27	0.301723638267301	0.603447276534602	0.698276361732699
28	0.358118206352348	0.716236412704697	0.641881793647652
29	0.539403362984553	0.921193274030895	0.460596637015447
30	0.77792486829742	0.44415026340516	0.22207513170258
31	0.85841147759108	0.283177044817841	0.141588522408920
32	0.962331587242774	0.0753368255144527	0.0376684127572263
33	0.979140037702007	0.0417199245959863	0.0208599622979931
34	0.991996132651402	0.0160077346971960	0.00800386734859801
35	0.995910100207948	0.00817979958410382	0.00408989979205191
36	0.995560338530266	0.0088793229394672	0.0044396614697336
37	0.994953398778569	0.0100932024428623	0.00504660122143117
38	0.997254021453342	0.00549195709331564	0.00274597854665782
39	0.998677587087065	0.00264482582587034	0.00132241291293517
40	0.999048256777856	0.00190348644428709	0.000951743222143547
41	0.999203397721791	0.00159320455641789	0.000796602278208946
42	0.99886359161349	0.00227281677302189	0.00113640838651094
43	0.99881849911458	0.00236300177083834	0.00118150088541917
44	0.999599562093657	0.00080087581268584	0.00040043790634292
45	0.999299076667787	0.00140184666442695	0.000700923332213475
46	0.998595284237279	0.0028094315254428	0.0014047157627214
47	0.998683890096433	0.00263221980713315	0.00131610990356658
48	0.997292255603644	0.00541548879271251	0.00270774439635625
49	0.995996053719323	0.00800789256135335	0.00400394628067668
50	0.998374936127663	0.00325012774467374	0.00162506387233687
51	0.997649932626434	0.00470013474713214	0.00235006737356607
52	0.994483538520484	0.011032922959031	0.0055164614795155
53	0.993243224387688	0.0135135512246250	0.00675677561231248
54	0.97699366143397	0.0460126771320593	0.0230063385660296
55	0.98764143004463	0.0247171399107388	0.0123585699553694

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	17	0.333333333333333	NOK
5% type I error level	24	0.470588235294118	NOK
10% type I error level	25	0.490196078431373	NOK

\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 & 17 & 0.333333333333333 & NOK \tabularnewline
5% type I error level & 24 & 0.470588235294118 & NOK \tabularnewline
10% type I error level & 25 & 0.490196078431373 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25774&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]17[/C][C]0.333333333333333[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]24[/C][C]0.470588235294118[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]25[/C][C]0.490196078431373[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25774&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25774&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 tests	OK/NOK
1% type I error level	17	0.333333333333333	NOK
5% type I error level	24	0.470588235294118	NOK
10% type I error level	25	0.490196078431373	NOK

Figure 1

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code