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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationMon, 23 Nov 2009 15:12:22 -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/23/t125901442892rrgxkdnuma2nx.htm/, Retrieved Fri, 03 May 2024 14:10:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58929, Retrieved Fri, 03 May 2024 14:10:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [WS7 link4] [2009-11-20 12:08:05] [616e2df490b611f6cb7080068870ecbd]
-    D        [Multiple Regression] [ws7 link4 y-1 en y-4] [2009-11-23 22:12:22] [ea241b681aafed79da4b5b99fad98471] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.4	8.2	1.7	1.4
1.2	8.0	1.4	1.2
1.0	7.5	1.2	1
1.7	6.8	1.0	1.7
2.4	6.5	1.7	1.4
2.0	6.6	2.4	1.2
2.1	7.6	2.0	1.0
2.0	8.0	2.1	1.7
1.8	8.1	2.0	2.4
2.7	7.7	1.8	2.0
2.3	7.5	2.7	2.1
1.9	7.6	2.3	2.0
2.0	7.8	1.9	1.8
2.3	7.8	2.0	2.7
2.8	7.8	2.3	2.3
2.4	7.5	2.8	1.9
2.3	7.5	2.4	2.0
2.7	7.1	2.3	2.3
2.7	7.5	2.7	2.8
2.9	7.5	2.7	2.4
3.0	7.6	2.9	2.3
2.2	7.7	3.0	2.7
2.3	7.7	2.2	2.7
2.8	7.9	2.3	2.9
2.8	8.1	2.8	3.0
2.8	8.2	2.8	2.2
2.2	8.2	2.8	2.3
2.6	8.2	2.2	2.8
2.8	7.9	2.6	2.8
2.5	7.3	2.8	2.8
2.4	6.9	2.5	2.2
2.3	6.6	2.4	2.6
1.9	6.7	2.3	2.8
1.7	6.9	1.9	2.5
2.0	7.0	1.7	2.4
2.1	7.1	2.0	2.3
1.7	7.2	2.1	1.9
1.8	7.1	1.7	1.7
1.8	6.9	1.8	2.0
1.8	7.0	1.8	2.1
1.3	6.8	1.8	1.7
1.3	6.4	1.3	1.8
1.3	6.7	1.3	1.8
1.2	6.6	1.3	1.8
1.4	6.4	1.2	1.3
2.2	6.3	1.4	1.3
2.9	6.2	2.2	1.3
3.1	6.5	2.9	1.2
3.5	6.8	3.1	1.4
3.6	6.8	3.5	2.2
4.4	6.4	3.6	2.9
4.1	6.1	4.4	3.1
5.1	5.8	4.1	3.5
5.8	6.1	5.1	3.6
5.9	7.2	5.8	4.4
5.4	7.3	5.9	4.1
5.5	6.9	5.4	5.1
4.8	6.1	5.5	5.8
3.2	5.8	4.8	5.9
2.7	6.2	3.2	5.4
2.1	7.1	2.7	5.5
1.9	7.7	2.1	4.8
0.6	7.9	1.9	3.2
0.7	7.7	0.6	2.7

Tables (Output of Computation)





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=58929&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=58929&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58929&T=0

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


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

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






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 1.19733911441188 -0.114838682663652X[t] + 1.04005420661093Y1[t] -0.181531956075848Y4[t] -0.100911659309453M1[t] + 0.0562361791256351M2[t] -0.144735621419419M3[t] + 0.0688315396933528M4[t] + 0.173874541939557M5[t] -0.0284129403688838M6[t] -0.0181390830330392M7[t] -0.141918406447336M8[t] -0.0166014834555407M9[t] + 0.0167579353408157M10[t] -0.170892863225451M11[t] -0.000202430578581416t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  1.19733911441188 -0.114838682663652X[t] +  1.04005420661093Y1[t] -0.181531956075848Y4[t] -0.100911659309453M1[t] +  0.0562361791256351M2[t] -0.144735621419419M3[t] +  0.0688315396933528M4[t] +  0.173874541939557M5[t] -0.0284129403688838M6[t] -0.0181390830330392M7[t] -0.141918406447336M8[t] -0.0166014834555407M9[t] +  0.0167579353408157M10[t] -0.170892863225451M11[t] -0.000202430578581416t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58929&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  1.19733911441188 -0.114838682663652X[t] +  1.04005420661093Y1[t] -0.181531956075848Y4[t] -0.100911659309453M1[t] +  0.0562361791256351M2[t] -0.144735621419419M3[t] +  0.0688315396933528M4[t] +  0.173874541939557M5[t] -0.0284129403688838M6[t] -0.0181390830330392M7[t] -0.141918406447336M8[t] -0.0166014834555407M9[t] +  0.0167579353408157M10[t] -0.170892863225451M11[t] -0.000202430578581416t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58929&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58929&T=1

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


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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 1.19733911441188 -0.114838682663652X[t] + 1.04005420661093Y1[t] -0.181531956075848Y4[t] -0.100911659309453M1[t] + 0.0562361791256351M2[t] -0.144735621419419M3[t] + 0.0688315396933528M4[t] + 0.173874541939557M5[t] -0.0284129403688838M6[t] -0.0181390830330392M7[t] -0.141918406447336M8[t] -0.0166014834555407M9[t] + 0.0167579353408157M10[t] -0.170892863225451M11[t] -0.000202430578581416t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)1.197339114411881.0642041.12510.266140.13307
X-0.1148386826636520.134597-0.85320.3977850.198893
Y11.040054206610930.07699413.508200
Y4-0.1815319560758480.087126-2.08360.0425490.021275
M1-0.1009116593094530.305046-0.33080.742230.371115
M20.05623617912563510.3071710.18310.8555080.427754
M3-0.1447356214194190.305566-0.47370.6378870.318943
M40.06883153969335280.3015870.22820.8204360.410218
M50.1738745419395570.3170480.54840.5859480.292974
M6-0.02841294036888380.321296-0.08840.9299010.46495
M7-0.01813908303303920.316879-0.05720.9545890.477295
M8-0.1419184064473360.316506-0.44840.6558890.327944
M9-0.01660148345554070.314083-0.05290.9580650.479033
M100.01675793534081570.3145810.05330.9577370.478869
M11-0.1708928632254510.31541-0.54180.5904550.295227
t-0.0002024305785814160.005288-0.03830.9696220.484811

\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) & 1.19733911441188 & 1.064204 & 1.1251 & 0.26614 & 0.13307 \tabularnewline
X & -0.114838682663652 & 0.134597 & -0.8532 & 0.397785 & 0.198893 \tabularnewline
Y1 & 1.04005420661093 & 0.076994 & 13.5082 & 0 & 0 \tabularnewline
Y4 & -0.181531956075848 & 0.087126 & -2.0836 & 0.042549 & 0.021275 \tabularnewline
M1 & -0.100911659309453 & 0.305046 & -0.3308 & 0.74223 & 0.371115 \tabularnewline
M2 & 0.0562361791256351 & 0.307171 & 0.1831 & 0.855508 & 0.427754 \tabularnewline
M3 & -0.144735621419419 & 0.305566 & -0.4737 & 0.637887 & 0.318943 \tabularnewline
M4 & 0.0688315396933528 & 0.301587 & 0.2282 & 0.820436 & 0.410218 \tabularnewline
M5 & 0.173874541939557 & 0.317048 & 0.5484 & 0.585948 & 0.292974 \tabularnewline
M6 & -0.0284129403688838 & 0.321296 & -0.0884 & 0.929901 & 0.46495 \tabularnewline
M7 & -0.0181390830330392 & 0.316879 & -0.0572 & 0.954589 & 0.477295 \tabularnewline
M8 & -0.141918406447336 & 0.316506 & -0.4484 & 0.655889 & 0.327944 \tabularnewline
M9 & -0.0166014834555407 & 0.314083 & -0.0529 & 0.958065 & 0.479033 \tabularnewline
M10 & 0.0167579353408157 & 0.314581 & 0.0533 & 0.957737 & 0.478869 \tabularnewline
M11 & -0.170892863225451 & 0.31541 & -0.5418 & 0.590455 & 0.295227 \tabularnewline
t & -0.000202430578581416 & 0.005288 & -0.0383 & 0.969622 & 0.484811 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58929&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]1.19733911441188[/C][C]1.064204[/C][C]1.1251[/C][C]0.26614[/C][C]0.13307[/C][/ROW]
[ROW][C]X[/C][C]-0.114838682663652[/C][C]0.134597[/C][C]-0.8532[/C][C]0.397785[/C][C]0.198893[/C][/ROW]
[ROW][C]Y1[/C][C]1.04005420661093[/C][C]0.076994[/C][C]13.5082[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y4[/C][C]-0.181531956075848[/C][C]0.087126[/C][C]-2.0836[/C][C]0.042549[/C][C]0.021275[/C][/ROW]
[ROW][C]M1[/C][C]-0.100911659309453[/C][C]0.305046[/C][C]-0.3308[/C][C]0.74223[/C][C]0.371115[/C][/ROW]
[ROW][C]M2[/C][C]0.0562361791256351[/C][C]0.307171[/C][C]0.1831[/C][C]0.855508[/C][C]0.427754[/C][/ROW]
[ROW][C]M3[/C][C]-0.144735621419419[/C][C]0.305566[/C][C]-0.4737[/C][C]0.637887[/C][C]0.318943[/C][/ROW]
[ROW][C]M4[/C][C]0.0688315396933528[/C][C]0.301587[/C][C]0.2282[/C][C]0.820436[/C][C]0.410218[/C][/ROW]
[ROW][C]M5[/C][C]0.173874541939557[/C][C]0.317048[/C][C]0.5484[/C][C]0.585948[/C][C]0.292974[/C][/ROW]
[ROW][C]M6[/C][C]-0.0284129403688838[/C][C]0.321296[/C][C]-0.0884[/C][C]0.929901[/C][C]0.46495[/C][/ROW]
[ROW][C]M7[/C][C]-0.0181390830330392[/C][C]0.316879[/C][C]-0.0572[/C][C]0.954589[/C][C]0.477295[/C][/ROW]
[ROW][C]M8[/C][C]-0.141918406447336[/C][C]0.316506[/C][C]-0.4484[/C][C]0.655889[/C][C]0.327944[/C][/ROW]
[ROW][C]M9[/C][C]-0.0166014834555407[/C][C]0.314083[/C][C]-0.0529[/C][C]0.958065[/C][C]0.479033[/C][/ROW]
[ROW][C]M10[/C][C]0.0167579353408157[/C][C]0.314581[/C][C]0.0533[/C][C]0.957737[/C][C]0.478869[/C][/ROW]
[ROW][C]M11[/C][C]-0.170892863225451[/C][C]0.31541[/C][C]-0.5418[/C][C]0.590455[/C][C]0.295227[/C][/ROW]
[ROW][C]t[/C][C]-0.000202430578581416[/C][C]0.005288[/C][C]-0.0383[/C][C]0.969622[/C][C]0.484811[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58929&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58929&T=2

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


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)1.197339114411881.0642041.12510.266140.13307
X-0.1148386826636520.134597-0.85320.3977850.198893
Y11.040054206610930.07699413.508200
Y4-0.1815319560758480.087126-2.08360.0425490.021275
M1-0.1009116593094530.305046-0.33080.742230.371115
M20.05623617912563510.3071710.18310.8555080.427754
M3-0.1447356214194190.305566-0.47370.6378870.318943
M40.06883153969335280.3015870.22820.8204360.410218
M50.1738745419395570.3170480.54840.5859480.292974
M6-0.02841294036888380.321296-0.08840.9299010.46495
M7-0.01813908303303920.316879-0.05720.9545890.477295
M8-0.1419184064473360.316506-0.44840.6558890.327944
M9-0.01660148345554070.314083-0.05290.9580650.479033
M100.01675793534081570.3145810.05330.9577370.478869
M11-0.1708928632254510.31541-0.54180.5904550.295227
t-0.0002024305785814160.005288-0.03830.9696220.484811






Multiple Linear Regression - Regression Statistics
Multiple R0.930999559820629
R-squared0.866760180386205
Adjusted R-squared0.825122736756894
F-TEST (value)20.8168442833037
F-TEST (DF numerator)15
F-TEST (DF denominator)48
p-value4.44089209850063e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.495420919128886
Sum Squared Residuals11.7812105813045

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.930999559820629 \tabularnewline
R-squared & 0.866760180386205 \tabularnewline
Adjusted R-squared & 0.825122736756894 \tabularnewline
F-TEST (value) & 20.8168442833037 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 4.44089209850063e-16 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.495420919128886 \tabularnewline
Sum Squared Residuals & 11.7812105813045 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58929&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.930999559820629[/C][/ROW]
[ROW][C]R-squared[/C][C]0.866760180386205[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.825122736756894[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]20.8168442833037[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]48[/C][/ROW]
[ROW][C]p-value[/C][C]4.44089209850063e-16[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.495420919128886[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]11.7812105813045[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58929&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58929&T=3

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


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

Multiple Linear Regression - Regression Statistics
Multiple R0.930999559820629
R-squared0.866760180386205
Adjusted R-squared0.825122736756894
F-TEST (value)20.8168442833037
F-TEST (DF numerator)15
F-TEST (DF denominator)48
p-value4.44089209850063e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.495420919128886
Sum Squared Residuals11.7812105813045






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
11.41.6684952394143-0.268495239414302
21.21.57269851303543-0.372698513035428
311.25723917313660-0.257239173136603
41.71.215907770960070.484092229039932
52.42.137697478877190.262302521122805
622.68806803356663-0.688068033566632
72.12.20358548623104-0.103585486231038
822.0106013105807-0.0106013105806990
91.81.89315414481336-0.0931541448133602
102.71.836848547204750.863151452795252
112.32.58985864493489-0.289858644934887
121.92.3511967222786-0.451196722278602
1321.847399604428630.152600395571366
142.31.944971672477970.355028327522029
152.82.128426485767950.671573514232046
162.42.96888270683705-0.568882706837047
172.32.63954840025271-0.339548400252711
182.72.32452895294730.375471047052698
192.72.613920611245550.0860793887544462
202.92.562551639683020.337448360316985
2132.902346300759630.0976536992403654
222.22.9554120589418-0.755412058941799
232.31.935515464508200.364484535491797
242.82.150937190068270.649062809931734
252.82.528729271345380.271270728654616
262.82.81941637579620-0.0194163757962040
272.22.60008894906498-0.400088949064983
282.62.098655177594690.501344822405311
292.82.653969036705780.146030963294218
302.52.72839317473914-0.228393174739137
312.42.58130298622409-0.18130298622409
322.32.31515463393887-0.0151546339388751
331.92.28847344620946-0.38847344620946
341.71.93710060207289-0.237100602072885
3521.547905858947070.45209414105293
362.12.037281880918440.0627181190815605
371.72.10130212585547-0.401302125855473
381.81.89001611054914-0.0900161105491406
391.81.761355449796570.0386445502034257
401.81.94508311645681-0.145083116456815
411.32.14550420708751-0.845504207087507
421.31.45076946835289-0.150769468352894
431.31.42638929031106-0.126389290311061
441.21.31389140458455-0.113891404584549
451.41.44873419090732-0.0487341909073234
462.21.701385888713650.49861411128635
472.92.357059893123910.542940106876085
483.13.23948986120693-0.139489861206927
493.53.275628616626820.224371383373185
503.63.70337014226702-0.103370142267017
514.43.525064435616840.874935564383159
524.14.56861774502371-0.468617745023706
535.14.323280877076800.776719122923195
545.85.108240370394040.691759629605964
555.95.574801625988260.325198374011744
565.45.59780101121286-0.197801011212862
575.55.067291917310220.432708082689779
584.85.16925290306692-0.369252903066918
593.24.26966013848593-1.06966013848593
602.72.82109434552776-0.121094345527764
612.12.078445142329390.0215548576706082
621.91.669527185874240.23047281412576
630.61.52782550661704-0.927825506617044
640.70.5028534831276750.197146516872325

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1.4 & 1.6684952394143 & -0.268495239414302 \tabularnewline
2 & 1.2 & 1.57269851303543 & -0.372698513035428 \tabularnewline
3 & 1 & 1.25723917313660 & -0.257239173136603 \tabularnewline
4 & 1.7 & 1.21590777096007 & 0.484092229039932 \tabularnewline
5 & 2.4 & 2.13769747887719 & 0.262302521122805 \tabularnewline
6 & 2 & 2.68806803356663 & -0.688068033566632 \tabularnewline
7 & 2.1 & 2.20358548623104 & -0.103585486231038 \tabularnewline
8 & 2 & 2.0106013105807 & -0.0106013105806990 \tabularnewline
9 & 1.8 & 1.89315414481336 & -0.0931541448133602 \tabularnewline
10 & 2.7 & 1.83684854720475 & 0.863151452795252 \tabularnewline
11 & 2.3 & 2.58985864493489 & -0.289858644934887 \tabularnewline
12 & 1.9 & 2.3511967222786 & -0.451196722278602 \tabularnewline
13 & 2 & 1.84739960442863 & 0.152600395571366 \tabularnewline
14 & 2.3 & 1.94497167247797 & 0.355028327522029 \tabularnewline
15 & 2.8 & 2.12842648576795 & 0.671573514232046 \tabularnewline
16 & 2.4 & 2.96888270683705 & -0.568882706837047 \tabularnewline
17 & 2.3 & 2.63954840025271 & -0.339548400252711 \tabularnewline
18 & 2.7 & 2.3245289529473 & 0.375471047052698 \tabularnewline
19 & 2.7 & 2.61392061124555 & 0.0860793887544462 \tabularnewline
20 & 2.9 & 2.56255163968302 & 0.337448360316985 \tabularnewline
21 & 3 & 2.90234630075963 & 0.0976536992403654 \tabularnewline
22 & 2.2 & 2.9554120589418 & -0.755412058941799 \tabularnewline
23 & 2.3 & 1.93551546450820 & 0.364484535491797 \tabularnewline
24 & 2.8 & 2.15093719006827 & 0.649062809931734 \tabularnewline
25 & 2.8 & 2.52872927134538 & 0.271270728654616 \tabularnewline
26 & 2.8 & 2.81941637579620 & -0.0194163757962040 \tabularnewline
27 & 2.2 & 2.60008894906498 & -0.400088949064983 \tabularnewline
28 & 2.6 & 2.09865517759469 & 0.501344822405311 \tabularnewline
29 & 2.8 & 2.65396903670578 & 0.146030963294218 \tabularnewline
30 & 2.5 & 2.72839317473914 & -0.228393174739137 \tabularnewline
31 & 2.4 & 2.58130298622409 & -0.18130298622409 \tabularnewline
32 & 2.3 & 2.31515463393887 & -0.0151546339388751 \tabularnewline
33 & 1.9 & 2.28847344620946 & -0.38847344620946 \tabularnewline
34 & 1.7 & 1.93710060207289 & -0.237100602072885 \tabularnewline
35 & 2 & 1.54790585894707 & 0.45209414105293 \tabularnewline
36 & 2.1 & 2.03728188091844 & 0.0627181190815605 \tabularnewline
37 & 1.7 & 2.10130212585547 & -0.401302125855473 \tabularnewline
38 & 1.8 & 1.89001611054914 & -0.0900161105491406 \tabularnewline
39 & 1.8 & 1.76135544979657 & 0.0386445502034257 \tabularnewline
40 & 1.8 & 1.94508311645681 & -0.145083116456815 \tabularnewline
41 & 1.3 & 2.14550420708751 & -0.845504207087507 \tabularnewline
42 & 1.3 & 1.45076946835289 & -0.150769468352894 \tabularnewline
43 & 1.3 & 1.42638929031106 & -0.126389290311061 \tabularnewline
44 & 1.2 & 1.31389140458455 & -0.113891404584549 \tabularnewline
45 & 1.4 & 1.44873419090732 & -0.0487341909073234 \tabularnewline
46 & 2.2 & 1.70138588871365 & 0.49861411128635 \tabularnewline
47 & 2.9 & 2.35705989312391 & 0.542940106876085 \tabularnewline
48 & 3.1 & 3.23948986120693 & -0.139489861206927 \tabularnewline
49 & 3.5 & 3.27562861662682 & 0.224371383373185 \tabularnewline
50 & 3.6 & 3.70337014226702 & -0.103370142267017 \tabularnewline
51 & 4.4 & 3.52506443561684 & 0.874935564383159 \tabularnewline
52 & 4.1 & 4.56861774502371 & -0.468617745023706 \tabularnewline
53 & 5.1 & 4.32328087707680 & 0.776719122923195 \tabularnewline
54 & 5.8 & 5.10824037039404 & 0.691759629605964 \tabularnewline
55 & 5.9 & 5.57480162598826 & 0.325198374011744 \tabularnewline
56 & 5.4 & 5.59780101121286 & -0.197801011212862 \tabularnewline
57 & 5.5 & 5.06729191731022 & 0.432708082689779 \tabularnewline
58 & 4.8 & 5.16925290306692 & -0.369252903066918 \tabularnewline
59 & 3.2 & 4.26966013848593 & -1.06966013848593 \tabularnewline
60 & 2.7 & 2.82109434552776 & -0.121094345527764 \tabularnewline
61 & 2.1 & 2.07844514232939 & 0.0215548576706082 \tabularnewline
62 & 1.9 & 1.66952718587424 & 0.23047281412576 \tabularnewline
63 & 0.6 & 1.52782550661704 & -0.927825506617044 \tabularnewline
64 & 0.7 & 0.502853483127675 & 0.197146516872325 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58929&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]1.4[/C][C]1.6684952394143[/C][C]-0.268495239414302[/C][/ROW]
[ROW][C]2[/C][C]1.2[/C][C]1.57269851303543[/C][C]-0.372698513035428[/C][/ROW]
[ROW][C]3[/C][C]1[/C][C]1.25723917313660[/C][C]-0.257239173136603[/C][/ROW]
[ROW][C]4[/C][C]1.7[/C][C]1.21590777096007[/C][C]0.484092229039932[/C][/ROW]
[ROW][C]5[/C][C]2.4[/C][C]2.13769747887719[/C][C]0.262302521122805[/C][/ROW]
[ROW][C]6[/C][C]2[/C][C]2.68806803356663[/C][C]-0.688068033566632[/C][/ROW]
[ROW][C]7[/C][C]2.1[/C][C]2.20358548623104[/C][C]-0.103585486231038[/C][/ROW]
[ROW][C]8[/C][C]2[/C][C]2.0106013105807[/C][C]-0.0106013105806990[/C][/ROW]
[ROW][C]9[/C][C]1.8[/C][C]1.89315414481336[/C][C]-0.0931541448133602[/C][/ROW]
[ROW][C]10[/C][C]2.7[/C][C]1.83684854720475[/C][C]0.863151452795252[/C][/ROW]
[ROW][C]11[/C][C]2.3[/C][C]2.58985864493489[/C][C]-0.289858644934887[/C][/ROW]
[ROW][C]12[/C][C]1.9[/C][C]2.3511967222786[/C][C]-0.451196722278602[/C][/ROW]
[ROW][C]13[/C][C]2[/C][C]1.84739960442863[/C][C]0.152600395571366[/C][/ROW]
[ROW][C]14[/C][C]2.3[/C][C]1.94497167247797[/C][C]0.355028327522029[/C][/ROW]
[ROW][C]15[/C][C]2.8[/C][C]2.12842648576795[/C][C]0.671573514232046[/C][/ROW]
[ROW][C]16[/C][C]2.4[/C][C]2.96888270683705[/C][C]-0.568882706837047[/C][/ROW]
[ROW][C]17[/C][C]2.3[/C][C]2.63954840025271[/C][C]-0.339548400252711[/C][/ROW]
[ROW][C]18[/C][C]2.7[/C][C]2.3245289529473[/C][C]0.375471047052698[/C][/ROW]
[ROW][C]19[/C][C]2.7[/C][C]2.61392061124555[/C][C]0.0860793887544462[/C][/ROW]
[ROW][C]20[/C][C]2.9[/C][C]2.56255163968302[/C][C]0.337448360316985[/C][/ROW]
[ROW][C]21[/C][C]3[/C][C]2.90234630075963[/C][C]0.0976536992403654[/C][/ROW]
[ROW][C]22[/C][C]2.2[/C][C]2.9554120589418[/C][C]-0.755412058941799[/C][/ROW]
[ROW][C]23[/C][C]2.3[/C][C]1.93551546450820[/C][C]0.364484535491797[/C][/ROW]
[ROW][C]24[/C][C]2.8[/C][C]2.15093719006827[/C][C]0.649062809931734[/C][/ROW]
[ROW][C]25[/C][C]2.8[/C][C]2.52872927134538[/C][C]0.271270728654616[/C][/ROW]
[ROW][C]26[/C][C]2.8[/C][C]2.81941637579620[/C][C]-0.0194163757962040[/C][/ROW]
[ROW][C]27[/C][C]2.2[/C][C]2.60008894906498[/C][C]-0.400088949064983[/C][/ROW]
[ROW][C]28[/C][C]2.6[/C][C]2.09865517759469[/C][C]0.501344822405311[/C][/ROW]
[ROW][C]29[/C][C]2.8[/C][C]2.65396903670578[/C][C]0.146030963294218[/C][/ROW]
[ROW][C]30[/C][C]2.5[/C][C]2.72839317473914[/C][C]-0.228393174739137[/C][/ROW]
[ROW][C]31[/C][C]2.4[/C][C]2.58130298622409[/C][C]-0.18130298622409[/C][/ROW]
[ROW][C]32[/C][C]2.3[/C][C]2.31515463393887[/C][C]-0.0151546339388751[/C][/ROW]
[ROW][C]33[/C][C]1.9[/C][C]2.28847344620946[/C][C]-0.38847344620946[/C][/ROW]
[ROW][C]34[/C][C]1.7[/C][C]1.93710060207289[/C][C]-0.237100602072885[/C][/ROW]
[ROW][C]35[/C][C]2[/C][C]1.54790585894707[/C][C]0.45209414105293[/C][/ROW]
[ROW][C]36[/C][C]2.1[/C][C]2.03728188091844[/C][C]0.0627181190815605[/C][/ROW]
[ROW][C]37[/C][C]1.7[/C][C]2.10130212585547[/C][C]-0.401302125855473[/C][/ROW]
[ROW][C]38[/C][C]1.8[/C][C]1.89001611054914[/C][C]-0.0900161105491406[/C][/ROW]
[ROW][C]39[/C][C]1.8[/C][C]1.76135544979657[/C][C]0.0386445502034257[/C][/ROW]
[ROW][C]40[/C][C]1.8[/C][C]1.94508311645681[/C][C]-0.145083116456815[/C][/ROW]
[ROW][C]41[/C][C]1.3[/C][C]2.14550420708751[/C][C]-0.845504207087507[/C][/ROW]
[ROW][C]42[/C][C]1.3[/C][C]1.45076946835289[/C][C]-0.150769468352894[/C][/ROW]
[ROW][C]43[/C][C]1.3[/C][C]1.42638929031106[/C][C]-0.126389290311061[/C][/ROW]
[ROW][C]44[/C][C]1.2[/C][C]1.31389140458455[/C][C]-0.113891404584549[/C][/ROW]
[ROW][C]45[/C][C]1.4[/C][C]1.44873419090732[/C][C]-0.0487341909073234[/C][/ROW]
[ROW][C]46[/C][C]2.2[/C][C]1.70138588871365[/C][C]0.49861411128635[/C][/ROW]
[ROW][C]47[/C][C]2.9[/C][C]2.35705989312391[/C][C]0.542940106876085[/C][/ROW]
[ROW][C]48[/C][C]3.1[/C][C]3.23948986120693[/C][C]-0.139489861206927[/C][/ROW]
[ROW][C]49[/C][C]3.5[/C][C]3.27562861662682[/C][C]0.224371383373185[/C][/ROW]
[ROW][C]50[/C][C]3.6[/C][C]3.70337014226702[/C][C]-0.103370142267017[/C][/ROW]
[ROW][C]51[/C][C]4.4[/C][C]3.52506443561684[/C][C]0.874935564383159[/C][/ROW]
[ROW][C]52[/C][C]4.1[/C][C]4.56861774502371[/C][C]-0.468617745023706[/C][/ROW]
[ROW][C]53[/C][C]5.1[/C][C]4.32328087707680[/C][C]0.776719122923195[/C][/ROW]
[ROW][C]54[/C][C]5.8[/C][C]5.10824037039404[/C][C]0.691759629605964[/C][/ROW]
[ROW][C]55[/C][C]5.9[/C][C]5.57480162598826[/C][C]0.325198374011744[/C][/ROW]
[ROW][C]56[/C][C]5.4[/C][C]5.59780101121286[/C][C]-0.197801011212862[/C][/ROW]
[ROW][C]57[/C][C]5.5[/C][C]5.06729191731022[/C][C]0.432708082689779[/C][/ROW]
[ROW][C]58[/C][C]4.8[/C][C]5.16925290306692[/C][C]-0.369252903066918[/C][/ROW]
[ROW][C]59[/C][C]3.2[/C][C]4.26966013848593[/C][C]-1.06966013848593[/C][/ROW]
[ROW][C]60[/C][C]2.7[/C][C]2.82109434552776[/C][C]-0.121094345527764[/C][/ROW]
[ROW][C]61[/C][C]2.1[/C][C]2.07844514232939[/C][C]0.0215548576706082[/C][/ROW]
[ROW][C]62[/C][C]1.9[/C][C]1.66952718587424[/C][C]0.23047281412576[/C][/ROW]
[ROW][C]63[/C][C]0.6[/C][C]1.52782550661704[/C][C]-0.927825506617044[/C][/ROW]
[ROW][C]64[/C][C]0.7[/C][C]0.502853483127675[/C][C]0.197146516872325[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58929&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58929&T=4

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


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
11.41.6684952394143-0.268495239414302
21.21.57269851303543-0.372698513035428
311.25723917313660-0.257239173136603
41.71.215907770960070.484092229039932
52.42.137697478877190.262302521122805
622.68806803356663-0.688068033566632
72.12.20358548623104-0.103585486231038
822.0106013105807-0.0106013105806990
91.81.89315414481336-0.0931541448133602
102.71.836848547204750.863151452795252
112.32.58985864493489-0.289858644934887
121.92.3511967222786-0.451196722278602
1321.847399604428630.152600395571366
142.31.944971672477970.355028327522029
152.82.128426485767950.671573514232046
162.42.96888270683705-0.568882706837047
172.32.63954840025271-0.339548400252711
182.72.32452895294730.375471047052698
192.72.613920611245550.0860793887544462
202.92.562551639683020.337448360316985
2132.902346300759630.0976536992403654
222.22.9554120589418-0.755412058941799
232.31.935515464508200.364484535491797
242.82.150937190068270.649062809931734
252.82.528729271345380.271270728654616
262.82.81941637579620-0.0194163757962040
272.22.60008894906498-0.400088949064983
282.62.098655177594690.501344822405311
292.82.653969036705780.146030963294218
302.52.72839317473914-0.228393174739137
312.42.58130298622409-0.18130298622409
322.32.31515463393887-0.0151546339388751
331.92.28847344620946-0.38847344620946
341.71.93710060207289-0.237100602072885
3521.547905858947070.45209414105293
362.12.037281880918440.0627181190815605
371.72.10130212585547-0.401302125855473
381.81.89001611054914-0.0900161105491406
391.81.761355449796570.0386445502034257
401.81.94508311645681-0.145083116456815
411.32.14550420708751-0.845504207087507
421.31.45076946835289-0.150769468352894
431.31.42638929031106-0.126389290311061
441.21.31389140458455-0.113891404584549
451.41.44873419090732-0.0487341909073234
462.21.701385888713650.49861411128635
472.92.357059893123910.542940106876085
483.13.23948986120693-0.139489861206927
493.53.275628616626820.224371383373185
503.63.70337014226702-0.103370142267017
514.43.525064435616840.874935564383159
524.14.56861774502371-0.468617745023706
535.14.323280877076800.776719122923195
545.85.108240370394040.691759629605964
555.95.574801625988260.325198374011744
565.45.59780101121286-0.197801011212862
575.55.067291917310220.432708082689779
584.85.16925290306692-0.369252903066918
593.24.26966013848593-1.06966013848593
602.72.82109434552776-0.121094345527764
612.12.078445142329390.0215548576706082
621.91.669527185874240.23047281412576
630.61.52782550661704-0.927825506617044
640.70.5028534831276750.197146516872325






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.4744075063568120.9488150127136240.525592493643188
200.3072644548747090.6145289097494190.69273554512529
210.2028595505043440.4057191010086870.797140449495656
220.5428137795337620.9143724409324750.457186220466238
230.4359702730356340.8719405460712670.564029726964366
240.3863062835614730.7726125671229450.613693716438527
250.2872804493751580.5745608987503150.712719550624842
260.2087894655369840.4175789310739680.791210534463016
270.1734110797087880.3468221594175760.826588920291212
280.1390204847349720.2780409694699430.860979515265028
290.09721661659681890.1944332331936380.902783383403181
300.08198056930734840.1639611386146970.918019430692652
310.0751429940637340.1502859881274680.924857005936266
320.06557545361947420.1311509072389480.934424546380526
330.05589406351357660.1117881270271530.944105936486423
340.03679291763038440.07358583526076880.963207082369616
350.03904081937740860.07808163875481710.960959180622591
360.03052939243508340.06105878487016670.969470607564917
370.01672601737137070.03345203474274140.98327398262863
380.008975581266379260.01795116253275850.99102441873362
390.004963616080204730.009927232160409460.995036383919795
400.005164556212857090.01032911242571420.994835443787143
410.005184564778959240.01036912955791850.99481543522104
420.005781469690007120.01156293938001420.994218530309993
430.005021522946096220.01004304589219240.994978477053904
440.003019352080302130.006038704160604260.996980647919698
450.01854288184272380.03708576368544760.981457118157276

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.474407506356812 & 0.948815012713624 & 0.525592493643188 \tabularnewline
20 & 0.307264454874709 & 0.614528909749419 & 0.69273554512529 \tabularnewline
21 & 0.202859550504344 & 0.405719101008687 & 0.797140449495656 \tabularnewline
22 & 0.542813779533762 & 0.914372440932475 & 0.457186220466238 \tabularnewline
23 & 0.435970273035634 & 0.871940546071267 & 0.564029726964366 \tabularnewline
24 & 0.386306283561473 & 0.772612567122945 & 0.613693716438527 \tabularnewline
25 & 0.287280449375158 & 0.574560898750315 & 0.712719550624842 \tabularnewline
26 & 0.208789465536984 & 0.417578931073968 & 0.791210534463016 \tabularnewline
27 & 0.173411079708788 & 0.346822159417576 & 0.826588920291212 \tabularnewline
28 & 0.139020484734972 & 0.278040969469943 & 0.860979515265028 \tabularnewline
29 & 0.0972166165968189 & 0.194433233193638 & 0.902783383403181 \tabularnewline
30 & 0.0819805693073484 & 0.163961138614697 & 0.918019430692652 \tabularnewline
31 & 0.075142994063734 & 0.150285988127468 & 0.924857005936266 \tabularnewline
32 & 0.0655754536194742 & 0.131150907238948 & 0.934424546380526 \tabularnewline
33 & 0.0558940635135766 & 0.111788127027153 & 0.944105936486423 \tabularnewline
34 & 0.0367929176303844 & 0.0735858352607688 & 0.963207082369616 \tabularnewline
35 & 0.0390408193774086 & 0.0780816387548171 & 0.960959180622591 \tabularnewline
36 & 0.0305293924350834 & 0.0610587848701667 & 0.969470607564917 \tabularnewline
37 & 0.0167260173713707 & 0.0334520347427414 & 0.98327398262863 \tabularnewline
38 & 0.00897558126637926 & 0.0179511625327585 & 0.99102441873362 \tabularnewline
39 & 0.00496361608020473 & 0.00992723216040946 & 0.995036383919795 \tabularnewline
40 & 0.00516455621285709 & 0.0103291124257142 & 0.994835443787143 \tabularnewline
41 & 0.00518456477895924 & 0.0103691295579185 & 0.99481543522104 \tabularnewline
42 & 0.00578146969000712 & 0.0115629393800142 & 0.994218530309993 \tabularnewline
43 & 0.00502152294609622 & 0.0100430458921924 & 0.994978477053904 \tabularnewline
44 & 0.00301935208030213 & 0.00603870416060426 & 0.996980647919698 \tabularnewline
45 & 0.0185428818427238 & 0.0370857636854476 & 0.981457118157276 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58929&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]19[/C][C]0.474407506356812[/C][C]0.948815012713624[/C][C]0.525592493643188[/C][/ROW]
[ROW][C]20[/C][C]0.307264454874709[/C][C]0.614528909749419[/C][C]0.69273554512529[/C][/ROW]
[ROW][C]21[/C][C]0.202859550504344[/C][C]0.405719101008687[/C][C]0.797140449495656[/C][/ROW]
[ROW][C]22[/C][C]0.542813779533762[/C][C]0.914372440932475[/C][C]0.457186220466238[/C][/ROW]
[ROW][C]23[/C][C]0.435970273035634[/C][C]0.871940546071267[/C][C]0.564029726964366[/C][/ROW]
[ROW][C]24[/C][C]0.386306283561473[/C][C]0.772612567122945[/C][C]0.613693716438527[/C][/ROW]
[ROW][C]25[/C][C]0.287280449375158[/C][C]0.574560898750315[/C][C]0.712719550624842[/C][/ROW]
[ROW][C]26[/C][C]0.208789465536984[/C][C]0.417578931073968[/C][C]0.791210534463016[/C][/ROW]
[ROW][C]27[/C][C]0.173411079708788[/C][C]0.346822159417576[/C][C]0.826588920291212[/C][/ROW]
[ROW][C]28[/C][C]0.139020484734972[/C][C]0.278040969469943[/C][C]0.860979515265028[/C][/ROW]
[ROW][C]29[/C][C]0.0972166165968189[/C][C]0.194433233193638[/C][C]0.902783383403181[/C][/ROW]
[ROW][C]30[/C][C]0.0819805693073484[/C][C]0.163961138614697[/C][C]0.918019430692652[/C][/ROW]
[ROW][C]31[/C][C]0.075142994063734[/C][C]0.150285988127468[/C][C]0.924857005936266[/C][/ROW]
[ROW][C]32[/C][C]0.0655754536194742[/C][C]0.131150907238948[/C][C]0.934424546380526[/C][/ROW]
[ROW][C]33[/C][C]0.0558940635135766[/C][C]0.111788127027153[/C][C]0.944105936486423[/C][/ROW]
[ROW][C]34[/C][C]0.0367929176303844[/C][C]0.0735858352607688[/C][C]0.963207082369616[/C][/ROW]
[ROW][C]35[/C][C]0.0390408193774086[/C][C]0.0780816387548171[/C][C]0.960959180622591[/C][/ROW]
[ROW][C]36[/C][C]0.0305293924350834[/C][C]0.0610587848701667[/C][C]0.969470607564917[/C][/ROW]
[ROW][C]37[/C][C]0.0167260173713707[/C][C]0.0334520347427414[/C][C]0.98327398262863[/C][/ROW]
[ROW][C]38[/C][C]0.00897558126637926[/C][C]0.0179511625327585[/C][C]0.99102441873362[/C][/ROW]
[ROW][C]39[/C][C]0.00496361608020473[/C][C]0.00992723216040946[/C][C]0.995036383919795[/C][/ROW]
[ROW][C]40[/C][C]0.00516455621285709[/C][C]0.0103291124257142[/C][C]0.994835443787143[/C][/ROW]
[ROW][C]41[/C][C]0.00518456477895924[/C][C]0.0103691295579185[/C][C]0.99481543522104[/C][/ROW]
[ROW][C]42[/C][C]0.00578146969000712[/C][C]0.0115629393800142[/C][C]0.994218530309993[/C][/ROW]
[ROW][C]43[/C][C]0.00502152294609622[/C][C]0.0100430458921924[/C][C]0.994978477053904[/C][/ROW]
[ROW][C]44[/C][C]0.00301935208030213[/C][C]0.00603870416060426[/C][C]0.996980647919698[/C][/ROW]
[ROW][C]45[/C][C]0.0185428818427238[/C][C]0.0370857636854476[/C][C]0.981457118157276[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58929&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58929&T=5

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


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.4744075063568120.9488150127136240.525592493643188
200.3072644548747090.6145289097494190.69273554512529
210.2028595505043440.4057191010086870.797140449495656
220.5428137795337620.9143724409324750.457186220466238
230.4359702730356340.8719405460712670.564029726964366
240.3863062835614730.7726125671229450.613693716438527
250.2872804493751580.5745608987503150.712719550624842
260.2087894655369840.4175789310739680.791210534463016
270.1734110797087880.3468221594175760.826588920291212
280.1390204847349720.2780409694699430.860979515265028
290.09721661659681890.1944332331936380.902783383403181
300.08198056930734840.1639611386146970.918019430692652
310.0751429940637340.1502859881274680.924857005936266
320.06557545361947420.1311509072389480.934424546380526
330.05589406351357660.1117881270271530.944105936486423
340.03679291763038440.07358583526076880.963207082369616
350.03904081937740860.07808163875481710.960959180622591
360.03052939243508340.06105878487016670.969470607564917
370.01672601737137070.03345203474274140.98327398262863
380.008975581266379260.01795116253275850.99102441873362
390.004963616080204730.009927232160409460.995036383919795
400.005164556212857090.01032911242571420.994835443787143
410.005184564778959240.01036912955791850.99481543522104
420.005781469690007120.01156293938001420.994218530309993
430.005021522946096220.01004304589219240.994978477053904
440.003019352080302130.006038704160604260.996980647919698
450.01854288184272380.03708576368544760.981457118157276






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level20.0740740740740741NOK
5% type I error level90.333333333333333NOK
10% type I error level120.444444444444444NOK

\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 & 2 & 0.0740740740740741 & NOK \tabularnewline
5% type I error level & 9 & 0.333333333333333 & NOK \tabularnewline
10% type I error level & 12 & 0.444444444444444 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58929&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]2[/C][C]0.0740740740740741[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]9[/C][C]0.333333333333333[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]12[/C][C]0.444444444444444[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58929&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58929&T=6

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


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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level20.0740740740740741NOK
5% type I error level90.333333333333333NOK
10% type I error level120.444444444444444NOK


Figures (Output of Computation)

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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}