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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 computationThu, 19 Nov 2009 15:17:43 -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/19/t1258669116c1w0h1kf6vxdgi5.htm/, Retrieved Tue, 23 Apr 2024 19:29:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57970, Retrieved Tue, 23 Apr 2024 19:29:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact200

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 14:14:11] [b98453cac15ba1066b407e146608df68]
-   PD      [Multiple Regression] [Model 5 - WZM & W...] [2009-11-19 22:17:43] [acc980be4047884b6edd254cd7beb9fa] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.5	20.3	8	8.2
6.8	15.8	7.5	8
6.5	15.8	6.8	7.5
6.6	15.8	6.5	6.8
7.6	23.2	6.6	6.5
8	23.2	7.6	6.6
8.1	23.2	8	7.6
7.7	20.9	8.1	8
7.5	20.9	7.7	8.1
7.6	20.9	7.5	7.7
7.8	19.8	7.6	7.5
7.8	19.8	7.8	7.6
7.8	19.8	7.8	7.8
7.5	20.6	7.8	7.8
7.5	20.6	7.5	7.8
7.1	20.6	7.5	7.5
7.5	21.1	7.1	7.5
7.5	21.1	7.5	7.1
7.6	21.1	7.5	7.5
7.7	22.4	7.6	7.5
7.7	22.4	7.7	7.6
7.9	22.4	7.7	7.7
8.1	20.5	7.9	7.7
8.2	20.5	8.1	7.9
8.2	20.5	8.2	8.1
8.2	18.4	8.2	8.2
7.9	18.4	8.2	8.2
7.3	18.4	7.9	8.2
6.9	17.6	7.3	7.9
6.6	17.6	6.9	7.3
6.7	17.6	6.6	6.9
6.9	18.5	6.7	6.6
7	18.5	6.9	6.7
7.1	18.5	7	6.9
7.2	17.3	7.1	7
7.1	17.3	7.2	7.1
6.9	17.3	7.1	7.2
7	16.2	6.9	7.1
6.8	16.2	7	6.9
6.4	16.2	6.8	7
6.7	18.5	6.4	6.8
6.6	18.5	6.7	6.4
6.4	18.5	6.6	6.7
6.3	16.3	6.4	6.6
6.2	16.3	6.3	6.4
6.5	16.3	6.2	6.3
6.8	16.8	6.5	6.2
6.8	16.8	6.8	6.5
6.4	16.8	6.8	6.8
6.1	14.8	6.4	6.8
5.8	14.8	6.1	6.4
6.1	14.8	5.8	6.1
7.2	21.4	6.1	5.8
7.3	21.4	7.2	6.1
6.9	21.4	7.3	7.2
6.1	16.1	6.9	7.3
5.8	16.1	6.1	6.9
6.2	16.1	5.8	6.1
7.1	19.6	6.2	5.8
7.7	19.6	7.1	6.2
7.9	19.6	7.7	7.1
7.7	18.9	7.9	7.7
7.4	18.9	7.7	7.9
7.5	18.9	7.4	7.7
8	21.9	7.5	7.4
8.1	21.9	8	7.5
8	21.9	8.1	8

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57970&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57970&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57970&T=0

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


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 1.00534172096945 + 0.104125740041533X[t] + 0.953792248854353`y(t-1)`[t] -0.353608708255487`y(t-2)`[t] -0.120038817733203M1[t] -0.0200034714829910M2[t] -0.083701842016721M3[t] -0.093534271571743M4[t] + 0.120752434670518M5[t] -0.3598303808755M6[t] -0.287254502541916M7[t] -0.287172802964734M8[t] -0.217506131383949M9[t] + 0.0272760961556319M10[t] + 0.126370704489030M11[t] -0.000124744305243137t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  1.00534172096945 +  0.104125740041533X[t] +  0.953792248854353`y(t-1)`[t] -0.353608708255487`y(t-2)`[t] -0.120038817733203M1[t] -0.0200034714829910M2[t] -0.083701842016721M3[t] -0.093534271571743M4[t] +  0.120752434670518M5[t] -0.3598303808755M6[t] -0.287254502541916M7[t] -0.287172802964734M8[t] -0.217506131383949M9[t] +  0.0272760961556319M10[t] +  0.126370704489030M11[t] -0.000124744305243137t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57970&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  1.00534172096945 +  0.104125740041533X[t] +  0.953792248854353`y(t-1)`[t] -0.353608708255487`y(t-2)`[t] -0.120038817733203M1[t] -0.0200034714829910M2[t] -0.083701842016721M3[t] -0.093534271571743M4[t] +  0.120752434670518M5[t] -0.3598303808755M6[t] -0.287254502541916M7[t] -0.287172802964734M8[t] -0.217506131383949M9[t] +  0.0272760961556319M10[t] +  0.126370704489030M11[t] -0.000124744305243137t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57970&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57970&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] = + 1.00534172096945 + 0.104125740041533X[t] + 0.953792248854353`y(t-1)`[t] -0.353608708255487`y(t-2)`[t] -0.120038817733203M1[t] -0.0200034714829910M2[t] -0.083701842016721M3[t] -0.093534271571743M4[t] + 0.120752434670518M5[t] -0.3598303808755M6[t] -0.287254502541916M7[t] -0.287172802964734M8[t] -0.217506131383949M9[t] + 0.0272760961556319M10[t] + 0.126370704489030M11[t] -0.000124744305243137t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)1.005341720969450.3806072.64140.0109330.005466
X0.1041257400415330.0246444.22519.9e-054.9e-05
`y(t-1)`0.9537922488543530.1544346.176100
`y(t-2)`-0.3536087082554870.12094-2.92380.0051460.002573
M1-0.1200388177332030.125125-0.95940.3419070.170953
M2-0.02000347148299100.129414-0.15460.8777710.438886
M3-0.0837018420167210.132667-0.63090.5309110.265456
M4-0.0935342715717430.134679-0.69450.4905220.245261
M50.1207524346705180.1691830.71370.4786420.239321
M6-0.35983038087550.127765-2.81640.006890.003445
M7-0.2872545025419160.143099-2.00740.0500220.025011
M8-0.2871728029647340.137875-2.08280.0422980.021149
M9-0.2175061313839490.149302-1.45680.1512960.075648
M100.02727609615563190.1462930.18640.8528330.426416
M110.1263707044890300.1299640.97230.3354660.167733
t-0.0001247443052431370.001499-0.08320.9340090.467004

\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) & 1.00534172096945 & 0.380607 & 2.6414 & 0.010933 & 0.005466 \tabularnewline
X & 0.104125740041533 & 0.024644 & 4.2251 & 9.9e-05 & 4.9e-05 \tabularnewline
`y(t-1)` & 0.953792248854353 & 0.154434 & 6.1761 & 0 & 0 \tabularnewline
`y(t-2)` & -0.353608708255487 & 0.12094 & -2.9238 & 0.005146 & 0.002573 \tabularnewline
M1 & -0.120038817733203 & 0.125125 & -0.9594 & 0.341907 & 0.170953 \tabularnewline
M2 & -0.0200034714829910 & 0.129414 & -0.1546 & 0.877771 & 0.438886 \tabularnewline
M3 & -0.083701842016721 & 0.132667 & -0.6309 & 0.530911 & 0.265456 \tabularnewline
M4 & -0.093534271571743 & 0.134679 & -0.6945 & 0.490522 & 0.245261 \tabularnewline
M5 & 0.120752434670518 & 0.169183 & 0.7137 & 0.478642 & 0.239321 \tabularnewline
M6 & -0.3598303808755 & 0.127765 & -2.8164 & 0.00689 & 0.003445 \tabularnewline
M7 & -0.287254502541916 & 0.143099 & -2.0074 & 0.050022 & 0.025011 \tabularnewline
M8 & -0.287172802964734 & 0.137875 & -2.0828 & 0.042298 & 0.021149 \tabularnewline
M9 & -0.217506131383949 & 0.149302 & -1.4568 & 0.151296 & 0.075648 \tabularnewline
M10 & 0.0272760961556319 & 0.146293 & 0.1864 & 0.852833 & 0.426416 \tabularnewline
M11 & 0.126370704489030 & 0.129964 & 0.9723 & 0.335466 & 0.167733 \tabularnewline
t & -0.000124744305243137 & 0.001499 & -0.0832 & 0.934009 & 0.467004 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57970&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]1.00534172096945[/C][C]0.380607[/C][C]2.6414[/C][C]0.010933[/C][C]0.005466[/C][/ROW]
[ROW][C]X[/C][C]0.104125740041533[/C][C]0.024644[/C][C]4.2251[/C][C]9.9e-05[/C][C]4.9e-05[/C][/ROW]
[ROW][C]`y(t-1)`[/C][C]0.953792248854353[/C][C]0.154434[/C][C]6.1761[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`y(t-2)`[/C][C]-0.353608708255487[/C][C]0.12094[/C][C]-2.9238[/C][C]0.005146[/C][C]0.002573[/C][/ROW]
[ROW][C]M1[/C][C]-0.120038817733203[/C][C]0.125125[/C][C]-0.9594[/C][C]0.341907[/C][C]0.170953[/C][/ROW]
[ROW][C]M2[/C][C]-0.0200034714829910[/C][C]0.129414[/C][C]-0.1546[/C][C]0.877771[/C][C]0.438886[/C][/ROW]
[ROW][C]M3[/C][C]-0.083701842016721[/C][C]0.132667[/C][C]-0.6309[/C][C]0.530911[/C][C]0.265456[/C][/ROW]
[ROW][C]M4[/C][C]-0.093534271571743[/C][C]0.134679[/C][C]-0.6945[/C][C]0.490522[/C][C]0.245261[/C][/ROW]
[ROW][C]M5[/C][C]0.120752434670518[/C][C]0.169183[/C][C]0.7137[/C][C]0.478642[/C][C]0.239321[/C][/ROW]
[ROW][C]M6[/C][C]-0.3598303808755[/C][C]0.127765[/C][C]-2.8164[/C][C]0.00689[/C][C]0.003445[/C][/ROW]
[ROW][C]M7[/C][C]-0.287254502541916[/C][C]0.143099[/C][C]-2.0074[/C][C]0.050022[/C][C]0.025011[/C][/ROW]
[ROW][C]M8[/C][C]-0.287172802964734[/C][C]0.137875[/C][C]-2.0828[/C][C]0.042298[/C][C]0.021149[/C][/ROW]
[ROW][C]M9[/C][C]-0.217506131383949[/C][C]0.149302[/C][C]-1.4568[/C][C]0.151296[/C][C]0.075648[/C][/ROW]
[ROW][C]M10[/C][C]0.0272760961556319[/C][C]0.146293[/C][C]0.1864[/C][C]0.852833[/C][C]0.426416[/C][/ROW]
[ROW][C]M11[/C][C]0.126370704489030[/C][C]0.129964[/C][C]0.9723[/C][C]0.335466[/C][C]0.167733[/C][/ROW]
[ROW][C]t[/C][C]-0.000124744305243137[/C][C]0.001499[/C][C]-0.0832[/C][C]0.934009[/C][C]0.467004[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57970&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57970&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)1.005341720969450.3806072.64140.0109330.005466
X0.1041257400415330.0246444.22519.9e-054.9e-05
`y(t-1)`0.9537922488543530.1544346.176100
`y(t-2)`-0.3536087082554870.12094-2.92380.0051460.002573
M1-0.1200388177332030.125125-0.95940.3419070.170953
M2-0.02000347148299100.129414-0.15460.8777710.438886
M3-0.0837018420167210.132667-0.63090.5309110.265456
M4-0.0935342715717430.134679-0.69450.4905220.245261
M50.1207524346705180.1691830.71370.4786420.239321
M6-0.35983038087550.127765-2.81640.006890.003445
M7-0.2872545025419160.143099-2.00740.0500220.025011
M8-0.2871728029647340.137875-2.08280.0422980.021149
M9-0.2175061313839490.149302-1.45680.1512960.075648
M100.02727609615563190.1462930.18640.8528330.426416
M110.1263707044890300.1299640.97230.3354660.167733
t-0.0001247443052431370.001499-0.08320.9340090.467004






Multiple Linear Regression - Regression Statistics
Multiple R0.963304547754958
R-squared0.927955651725384
Adjusted R-squared0.906766137526968
F-TEST (value)43.7931536813967
F-TEST (DF numerator)15
F-TEST (DF denominator)51
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.199820452761184
Sum Squared Residuals2.03633888042591

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.963304547754958 \tabularnewline
R-squared & 0.927955651725384 \tabularnewline
Adjusted R-squared & 0.906766137526968 \tabularnewline
F-TEST (value) & 43.7931536813967 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 51 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.199820452761184 \tabularnewline
Sum Squared Residuals & 2.03633888042591 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57970&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.963304547754958[/C][/ROW]
[ROW][C]R-squared[/C][C]0.927955651725384[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.906766137526968[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]43.7931536813967[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]51[/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]0.199820452761184[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2.03633888042591[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57970&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57970&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 R0.963304547754958
R-squared0.927955651725384
Adjusted R-squared0.906766137526968
F-TEST (value)43.7931536813967
F-TEST (DF numerator)15
F-TEST (DF denominator)51
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.199820452761184
Sum Squared Residuals2.03633888042591






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
17.57.72967726491395-0.22967726491395
26.86.95484765389596-0.154847653895955
36.56.400174318986680.0998256810133238
46.66.351605566248950.248394433751053
57.67.537759841855390.0622401581446084
687.975483660032930.0245163399670651
78.18.075842985347530.0241570146524692
87.77.79024648010718-0.0902464801071824
97.57.442910637015430.0570893629845652
107.67.6382531537811-0.0382531537810969
117.87.78878567030010.0112143296999025
127.87.81768780045115-0.0176878004511470
137.87.62680249676160.173197503238397
147.57.8100136907398-0.310013690739799
157.57.460052901244520.0399470987554803
167.17.5561783398609-0.456178339860901
177.57.440886272276940.0591137277230566
187.57.483139095269620.0168609047303809
197.67.414146745995770.185853254004235
207.77.644846388207130.0551536117928682
217.77.77440666954256-0.0744066695425606
227.97.98370328195135-0.0837032819513493
238.18.075592689671460.0244073103285375
248.28.069133948996960.130866051003037
258.27.973627870192850.226372129807146
268.27.819513547225050.380486452774946
277.97.755690432386080.14430956761392
287.37.45959558386951-0.159595583869511
296.97.12426421693733-0.224264216937335
306.66.474204982497630.125795017502374
316.76.401961925171850.298038074828145
326.96.697093883843260.202906116156745
3376.922033390064120.0779666099358808
347.17.1913483565328-0.0913483565327949
357.27.225385686571-0.0253856865709956
367.17.15890859183661-0.0589085918366104
376.96.90800493408718-0.00800493408717858
3876.737979643041140.262020356958860
396.86.8402574947387-0.0402574947386995
406.46.60418100028201-0.204181000282014
416.76.74703700642392-0.0470370064239158
426.66.69391060453116-0.0939106045311558
436.46.56489990119741-0.164899901197414
446.36.180382649432660.119617350567341
456.26.22526709347386-0.0252670934738619
466.56.409906222648310.0900937773516862
476.86.88243750217909-0.0824375021790897
486.86.93599711556448-0.135997115564476
496.46.70975094104938-0.309750941049384
506.16.21989316336955-0.119893163369546
515.86.01137585717646-0.211375857176461
526.15.821363621136540.278636378863464
537.27.114975754480620.085024245519375
547.37.5773570558925-0.277357055892507
556.97.35621783572525-0.456217835725247
566.16.38743059840977-0.287430598409771
575.85.83538220990402-0.0353822099040236
586.26.076788985086440.123211014913555
597.17.027798451278350.0722015487216452
607.77.61827254315080.0817274568491964
617.97.752136492995030.147863507004969
627.77.7577523017285-0.0577523017285054
637.47.43244899546756-0.0324489954675638
647.57.207075888602090.292924111397909
6587.935076908025790.0649230919742107
668.17.895904601776160.204095398223843
6787.886930606562190.113069393437811

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 7.5 & 7.72967726491395 & -0.22967726491395 \tabularnewline
2 & 6.8 & 6.95484765389596 & -0.154847653895955 \tabularnewline
3 & 6.5 & 6.40017431898668 & 0.0998256810133238 \tabularnewline
4 & 6.6 & 6.35160556624895 & 0.248394433751053 \tabularnewline
5 & 7.6 & 7.53775984185539 & 0.0622401581446084 \tabularnewline
6 & 8 & 7.97548366003293 & 0.0245163399670651 \tabularnewline
7 & 8.1 & 8.07584298534753 & 0.0241570146524692 \tabularnewline
8 & 7.7 & 7.79024648010718 & -0.0902464801071824 \tabularnewline
9 & 7.5 & 7.44291063701543 & 0.0570893629845652 \tabularnewline
10 & 7.6 & 7.6382531537811 & -0.0382531537810969 \tabularnewline
11 & 7.8 & 7.7887856703001 & 0.0112143296999025 \tabularnewline
12 & 7.8 & 7.81768780045115 & -0.0176878004511470 \tabularnewline
13 & 7.8 & 7.6268024967616 & 0.173197503238397 \tabularnewline
14 & 7.5 & 7.8100136907398 & -0.310013690739799 \tabularnewline
15 & 7.5 & 7.46005290124452 & 0.0399470987554803 \tabularnewline
16 & 7.1 & 7.5561783398609 & -0.456178339860901 \tabularnewline
17 & 7.5 & 7.44088627227694 & 0.0591137277230566 \tabularnewline
18 & 7.5 & 7.48313909526962 & 0.0168609047303809 \tabularnewline
19 & 7.6 & 7.41414674599577 & 0.185853254004235 \tabularnewline
20 & 7.7 & 7.64484638820713 & 0.0551536117928682 \tabularnewline
21 & 7.7 & 7.77440666954256 & -0.0744066695425606 \tabularnewline
22 & 7.9 & 7.98370328195135 & -0.0837032819513493 \tabularnewline
23 & 8.1 & 8.07559268967146 & 0.0244073103285375 \tabularnewline
24 & 8.2 & 8.06913394899696 & 0.130866051003037 \tabularnewline
25 & 8.2 & 7.97362787019285 & 0.226372129807146 \tabularnewline
26 & 8.2 & 7.81951354722505 & 0.380486452774946 \tabularnewline
27 & 7.9 & 7.75569043238608 & 0.14430956761392 \tabularnewline
28 & 7.3 & 7.45959558386951 & -0.159595583869511 \tabularnewline
29 & 6.9 & 7.12426421693733 & -0.224264216937335 \tabularnewline
30 & 6.6 & 6.47420498249763 & 0.125795017502374 \tabularnewline
31 & 6.7 & 6.40196192517185 & 0.298038074828145 \tabularnewline
32 & 6.9 & 6.69709388384326 & 0.202906116156745 \tabularnewline
33 & 7 & 6.92203339006412 & 0.0779666099358808 \tabularnewline
34 & 7.1 & 7.1913483565328 & -0.0913483565327949 \tabularnewline
35 & 7.2 & 7.225385686571 & -0.0253856865709956 \tabularnewline
36 & 7.1 & 7.15890859183661 & -0.0589085918366104 \tabularnewline
37 & 6.9 & 6.90800493408718 & -0.00800493408717858 \tabularnewline
38 & 7 & 6.73797964304114 & 0.262020356958860 \tabularnewline
39 & 6.8 & 6.8402574947387 & -0.0402574947386995 \tabularnewline
40 & 6.4 & 6.60418100028201 & -0.204181000282014 \tabularnewline
41 & 6.7 & 6.74703700642392 & -0.0470370064239158 \tabularnewline
42 & 6.6 & 6.69391060453116 & -0.0939106045311558 \tabularnewline
43 & 6.4 & 6.56489990119741 & -0.164899901197414 \tabularnewline
44 & 6.3 & 6.18038264943266 & 0.119617350567341 \tabularnewline
45 & 6.2 & 6.22526709347386 & -0.0252670934738619 \tabularnewline
46 & 6.5 & 6.40990622264831 & 0.0900937773516862 \tabularnewline
47 & 6.8 & 6.88243750217909 & -0.0824375021790897 \tabularnewline
48 & 6.8 & 6.93599711556448 & -0.135997115564476 \tabularnewline
49 & 6.4 & 6.70975094104938 & -0.309750941049384 \tabularnewline
50 & 6.1 & 6.21989316336955 & -0.119893163369546 \tabularnewline
51 & 5.8 & 6.01137585717646 & -0.211375857176461 \tabularnewline
52 & 6.1 & 5.82136362113654 & 0.278636378863464 \tabularnewline
53 & 7.2 & 7.11497575448062 & 0.085024245519375 \tabularnewline
54 & 7.3 & 7.5773570558925 & -0.277357055892507 \tabularnewline
55 & 6.9 & 7.35621783572525 & -0.456217835725247 \tabularnewline
56 & 6.1 & 6.38743059840977 & -0.287430598409771 \tabularnewline
57 & 5.8 & 5.83538220990402 & -0.0353822099040236 \tabularnewline
58 & 6.2 & 6.07678898508644 & 0.123211014913555 \tabularnewline
59 & 7.1 & 7.02779845127835 & 0.0722015487216452 \tabularnewline
60 & 7.7 & 7.6182725431508 & 0.0817274568491964 \tabularnewline
61 & 7.9 & 7.75213649299503 & 0.147863507004969 \tabularnewline
62 & 7.7 & 7.7577523017285 & -0.0577523017285054 \tabularnewline
63 & 7.4 & 7.43244899546756 & -0.0324489954675638 \tabularnewline
64 & 7.5 & 7.20707588860209 & 0.292924111397909 \tabularnewline
65 & 8 & 7.93507690802579 & 0.0649230919742107 \tabularnewline
66 & 8.1 & 7.89590460177616 & 0.204095398223843 \tabularnewline
67 & 8 & 7.88693060656219 & 0.113069393437811 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57970&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]7.5[/C][C]7.72967726491395[/C][C]-0.22967726491395[/C][/ROW]
[ROW][C]2[/C][C]6.8[/C][C]6.95484765389596[/C][C]-0.154847653895955[/C][/ROW]
[ROW][C]3[/C][C]6.5[/C][C]6.40017431898668[/C][C]0.0998256810133238[/C][/ROW]
[ROW][C]4[/C][C]6.6[/C][C]6.35160556624895[/C][C]0.248394433751053[/C][/ROW]
[ROW][C]5[/C][C]7.6[/C][C]7.53775984185539[/C][C]0.0622401581446084[/C][/ROW]
[ROW][C]6[/C][C]8[/C][C]7.97548366003293[/C][C]0.0245163399670651[/C][/ROW]
[ROW][C]7[/C][C]8.1[/C][C]8.07584298534753[/C][C]0.0241570146524692[/C][/ROW]
[ROW][C]8[/C][C]7.7[/C][C]7.79024648010718[/C][C]-0.0902464801071824[/C][/ROW]
[ROW][C]9[/C][C]7.5[/C][C]7.44291063701543[/C][C]0.0570893629845652[/C][/ROW]
[ROW][C]10[/C][C]7.6[/C][C]7.6382531537811[/C][C]-0.0382531537810969[/C][/ROW]
[ROW][C]11[/C][C]7.8[/C][C]7.7887856703001[/C][C]0.0112143296999025[/C][/ROW]
[ROW][C]12[/C][C]7.8[/C][C]7.81768780045115[/C][C]-0.0176878004511470[/C][/ROW]
[ROW][C]13[/C][C]7.8[/C][C]7.6268024967616[/C][C]0.173197503238397[/C][/ROW]
[ROW][C]14[/C][C]7.5[/C][C]7.8100136907398[/C][C]-0.310013690739799[/C][/ROW]
[ROW][C]15[/C][C]7.5[/C][C]7.46005290124452[/C][C]0.0399470987554803[/C][/ROW]
[ROW][C]16[/C][C]7.1[/C][C]7.5561783398609[/C][C]-0.456178339860901[/C][/ROW]
[ROW][C]17[/C][C]7.5[/C][C]7.44088627227694[/C][C]0.0591137277230566[/C][/ROW]
[ROW][C]18[/C][C]7.5[/C][C]7.48313909526962[/C][C]0.0168609047303809[/C][/ROW]
[ROW][C]19[/C][C]7.6[/C][C]7.41414674599577[/C][C]0.185853254004235[/C][/ROW]
[ROW][C]20[/C][C]7.7[/C][C]7.64484638820713[/C][C]0.0551536117928682[/C][/ROW]
[ROW][C]21[/C][C]7.7[/C][C]7.77440666954256[/C][C]-0.0744066695425606[/C][/ROW]
[ROW][C]22[/C][C]7.9[/C][C]7.98370328195135[/C][C]-0.0837032819513493[/C][/ROW]
[ROW][C]23[/C][C]8.1[/C][C]8.07559268967146[/C][C]0.0244073103285375[/C][/ROW]
[ROW][C]24[/C][C]8.2[/C][C]8.06913394899696[/C][C]0.130866051003037[/C][/ROW]
[ROW][C]25[/C][C]8.2[/C][C]7.97362787019285[/C][C]0.226372129807146[/C][/ROW]
[ROW][C]26[/C][C]8.2[/C][C]7.81951354722505[/C][C]0.380486452774946[/C][/ROW]
[ROW][C]27[/C][C]7.9[/C][C]7.75569043238608[/C][C]0.14430956761392[/C][/ROW]
[ROW][C]28[/C][C]7.3[/C][C]7.45959558386951[/C][C]-0.159595583869511[/C][/ROW]
[ROW][C]29[/C][C]6.9[/C][C]7.12426421693733[/C][C]-0.224264216937335[/C][/ROW]
[ROW][C]30[/C][C]6.6[/C][C]6.47420498249763[/C][C]0.125795017502374[/C][/ROW]
[ROW][C]31[/C][C]6.7[/C][C]6.40196192517185[/C][C]0.298038074828145[/C][/ROW]
[ROW][C]32[/C][C]6.9[/C][C]6.69709388384326[/C][C]0.202906116156745[/C][/ROW]
[ROW][C]33[/C][C]7[/C][C]6.92203339006412[/C][C]0.0779666099358808[/C][/ROW]
[ROW][C]34[/C][C]7.1[/C][C]7.1913483565328[/C][C]-0.0913483565327949[/C][/ROW]
[ROW][C]35[/C][C]7.2[/C][C]7.225385686571[/C][C]-0.0253856865709956[/C][/ROW]
[ROW][C]36[/C][C]7.1[/C][C]7.15890859183661[/C][C]-0.0589085918366104[/C][/ROW]
[ROW][C]37[/C][C]6.9[/C][C]6.90800493408718[/C][C]-0.00800493408717858[/C][/ROW]
[ROW][C]38[/C][C]7[/C][C]6.73797964304114[/C][C]0.262020356958860[/C][/ROW]
[ROW][C]39[/C][C]6.8[/C][C]6.8402574947387[/C][C]-0.0402574947386995[/C][/ROW]
[ROW][C]40[/C][C]6.4[/C][C]6.60418100028201[/C][C]-0.204181000282014[/C][/ROW]
[ROW][C]41[/C][C]6.7[/C][C]6.74703700642392[/C][C]-0.0470370064239158[/C][/ROW]
[ROW][C]42[/C][C]6.6[/C][C]6.69391060453116[/C][C]-0.0939106045311558[/C][/ROW]
[ROW][C]43[/C][C]6.4[/C][C]6.56489990119741[/C][C]-0.164899901197414[/C][/ROW]
[ROW][C]44[/C][C]6.3[/C][C]6.18038264943266[/C][C]0.119617350567341[/C][/ROW]
[ROW][C]45[/C][C]6.2[/C][C]6.22526709347386[/C][C]-0.0252670934738619[/C][/ROW]
[ROW][C]46[/C][C]6.5[/C][C]6.40990622264831[/C][C]0.0900937773516862[/C][/ROW]
[ROW][C]47[/C][C]6.8[/C][C]6.88243750217909[/C][C]-0.0824375021790897[/C][/ROW]
[ROW][C]48[/C][C]6.8[/C][C]6.93599711556448[/C][C]-0.135997115564476[/C][/ROW]
[ROW][C]49[/C][C]6.4[/C][C]6.70975094104938[/C][C]-0.309750941049384[/C][/ROW]
[ROW][C]50[/C][C]6.1[/C][C]6.21989316336955[/C][C]-0.119893163369546[/C][/ROW]
[ROW][C]51[/C][C]5.8[/C][C]6.01137585717646[/C][C]-0.211375857176461[/C][/ROW]
[ROW][C]52[/C][C]6.1[/C][C]5.82136362113654[/C][C]0.278636378863464[/C][/ROW]
[ROW][C]53[/C][C]7.2[/C][C]7.11497575448062[/C][C]0.085024245519375[/C][/ROW]
[ROW][C]54[/C][C]7.3[/C][C]7.5773570558925[/C][C]-0.277357055892507[/C][/ROW]
[ROW][C]55[/C][C]6.9[/C][C]7.35621783572525[/C][C]-0.456217835725247[/C][/ROW]
[ROW][C]56[/C][C]6.1[/C][C]6.38743059840977[/C][C]-0.287430598409771[/C][/ROW]
[ROW][C]57[/C][C]5.8[/C][C]5.83538220990402[/C][C]-0.0353822099040236[/C][/ROW]
[ROW][C]58[/C][C]6.2[/C][C]6.07678898508644[/C][C]0.123211014913555[/C][/ROW]
[ROW][C]59[/C][C]7.1[/C][C]7.02779845127835[/C][C]0.0722015487216452[/C][/ROW]
[ROW][C]60[/C][C]7.7[/C][C]7.6182725431508[/C][C]0.0817274568491964[/C][/ROW]
[ROW][C]61[/C][C]7.9[/C][C]7.75213649299503[/C][C]0.147863507004969[/C][/ROW]
[ROW][C]62[/C][C]7.7[/C][C]7.7577523017285[/C][C]-0.0577523017285054[/C][/ROW]
[ROW][C]63[/C][C]7.4[/C][C]7.43244899546756[/C][C]-0.0324489954675638[/C][/ROW]
[ROW][C]64[/C][C]7.5[/C][C]7.20707588860209[/C][C]0.292924111397909[/C][/ROW]
[ROW][C]65[/C][C]8[/C][C]7.93507690802579[/C][C]0.0649230919742107[/C][/ROW]
[ROW][C]66[/C][C]8.1[/C][C]7.89590460177616[/C][C]0.204095398223843[/C][/ROW]
[ROW][C]67[/C][C]8[/C][C]7.88693060656219[/C][C]0.113069393437811[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57970&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57970&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
17.57.72967726491395-0.22967726491395
26.86.95484765389596-0.154847653895955
36.56.400174318986680.0998256810133238
46.66.351605566248950.248394433751053
57.67.537759841855390.0622401581446084
687.975483660032930.0245163399670651
78.18.075842985347530.0241570146524692
87.77.79024648010718-0.0902464801071824
97.57.442910637015430.0570893629845652
107.67.6382531537811-0.0382531537810969
117.87.78878567030010.0112143296999025
127.87.81768780045115-0.0176878004511470
137.87.62680249676160.173197503238397
147.57.8100136907398-0.310013690739799
157.57.460052901244520.0399470987554803
167.17.5561783398609-0.456178339860901
177.57.440886272276940.0591137277230566
187.57.483139095269620.0168609047303809
197.67.414146745995770.185853254004235
207.77.644846388207130.0551536117928682
217.77.77440666954256-0.0744066695425606
227.97.98370328195135-0.0837032819513493
238.18.075592689671460.0244073103285375
248.28.069133948996960.130866051003037
258.27.973627870192850.226372129807146
268.27.819513547225050.380486452774946
277.97.755690432386080.14430956761392
287.37.45959558386951-0.159595583869511
296.97.12426421693733-0.224264216937335
306.66.474204982497630.125795017502374
316.76.401961925171850.298038074828145
326.96.697093883843260.202906116156745
3376.922033390064120.0779666099358808
347.17.1913483565328-0.0913483565327949
357.27.225385686571-0.0253856865709956
367.17.15890859183661-0.0589085918366104
376.96.90800493408718-0.00800493408717858
3876.737979643041140.262020356958860
396.86.8402574947387-0.0402574947386995
406.46.60418100028201-0.204181000282014
416.76.74703700642392-0.0470370064239158
426.66.69391060453116-0.0939106045311558
436.46.56489990119741-0.164899901197414
446.36.180382649432660.119617350567341
456.26.22526709347386-0.0252670934738619
466.56.409906222648310.0900937773516862
476.86.88243750217909-0.0824375021790897
486.86.93599711556448-0.135997115564476
496.46.70975094104938-0.309750941049384
506.16.21989316336955-0.119893163369546
515.86.01137585717646-0.211375857176461
526.15.821363621136540.278636378863464
537.27.114975754480620.085024245519375
547.37.5773570558925-0.277357055892507
556.97.35621783572525-0.456217835725247
566.16.38743059840977-0.287430598409771
575.85.83538220990402-0.0353822099040236
586.26.076788985086440.123211014913555
597.17.027798451278350.0722015487216452
607.77.61827254315080.0817274568491964
617.97.752136492995030.147863507004969
627.77.7577523017285-0.0577523017285054
637.47.43244899546756-0.0324489954675638
647.57.207075888602090.292924111397909
6587.935076908025790.0649230919742107
668.17.895904601776160.204095398223843
6787.886930606562190.113069393437811






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.3322298812975810.6644597625951620.667770118702419
200.1882390280326690.3764780560653380.811760971967331
210.2812262032050160.5624524064100310.718773796794984
220.1980392744719290.3960785489438590.80196072552807
230.1209250825988730.2418501651977460.879074917401127
240.09852204550254250.1970440910050850.901477954497458
250.07061062243145150.1412212448629030.929389377568548
260.1696646831653190.3393293663306370.830335316834681
270.1815856758865150.3631713517730310.818414324113485
280.1456967917889230.2913935835778460.854303208211077
290.3595009016240640.7190018032481280.640499098375936
300.2787629293231950.5575258586463890.721237070676805
310.4424650272471840.8849300544943680.557534972752816
320.4276822996744250.855364599348850.572317700325575
330.4206403157368470.8412806314736940.579359684263153
340.4199224160557950.839844832111590.580077583944205
350.3577946746607130.7155893493214260.642205325339287
360.3119975206993150.6239950413986310.688002479300684
370.2599694871583670.5199389743167340.740030512841633
380.3595807763801430.7191615527602870.640419223619857
390.3692977325003090.7385954650006190.63070226749969
400.4037520686039680.8075041372079360.596247931396032
410.3095376026213650.619075205242730.690462397378635
420.2577277507031990.5154555014063990.7422722492968
430.2784820088428840.5569640176857680.721517991157116
440.5749066767954540.8501866464090930.425093323204546
450.4984583127051820.9969166254103640.501541687294818
460.5661187241901530.8677625516196940.433881275809847
470.5526724270271860.8946551459456290.447327572972814
480.9195047504051780.1609904991896440.0804952495948221

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.332229881297581 & 0.664459762595162 & 0.667770118702419 \tabularnewline
20 & 0.188239028032669 & 0.376478056065338 & 0.811760971967331 \tabularnewline
21 & 0.281226203205016 & 0.562452406410031 & 0.718773796794984 \tabularnewline
22 & 0.198039274471929 & 0.396078548943859 & 0.80196072552807 \tabularnewline
23 & 0.120925082598873 & 0.241850165197746 & 0.879074917401127 \tabularnewline
24 & 0.0985220455025425 & 0.197044091005085 & 0.901477954497458 \tabularnewline
25 & 0.0706106224314515 & 0.141221244862903 & 0.929389377568548 \tabularnewline
26 & 0.169664683165319 & 0.339329366330637 & 0.830335316834681 \tabularnewline
27 & 0.181585675886515 & 0.363171351773031 & 0.818414324113485 \tabularnewline
28 & 0.145696791788923 & 0.291393583577846 & 0.854303208211077 \tabularnewline
29 & 0.359500901624064 & 0.719001803248128 & 0.640499098375936 \tabularnewline
30 & 0.278762929323195 & 0.557525858646389 & 0.721237070676805 \tabularnewline
31 & 0.442465027247184 & 0.884930054494368 & 0.557534972752816 \tabularnewline
32 & 0.427682299674425 & 0.85536459934885 & 0.572317700325575 \tabularnewline
33 & 0.420640315736847 & 0.841280631473694 & 0.579359684263153 \tabularnewline
34 & 0.419922416055795 & 0.83984483211159 & 0.580077583944205 \tabularnewline
35 & 0.357794674660713 & 0.715589349321426 & 0.642205325339287 \tabularnewline
36 & 0.311997520699315 & 0.623995041398631 & 0.688002479300684 \tabularnewline
37 & 0.259969487158367 & 0.519938974316734 & 0.740030512841633 \tabularnewline
38 & 0.359580776380143 & 0.719161552760287 & 0.640419223619857 \tabularnewline
39 & 0.369297732500309 & 0.738595465000619 & 0.63070226749969 \tabularnewline
40 & 0.403752068603968 & 0.807504137207936 & 0.596247931396032 \tabularnewline
41 & 0.309537602621365 & 0.61907520524273 & 0.690462397378635 \tabularnewline
42 & 0.257727750703199 & 0.515455501406399 & 0.7422722492968 \tabularnewline
43 & 0.278482008842884 & 0.556964017685768 & 0.721517991157116 \tabularnewline
44 & 0.574906676795454 & 0.850186646409093 & 0.425093323204546 \tabularnewline
45 & 0.498458312705182 & 0.996916625410364 & 0.501541687294818 \tabularnewline
46 & 0.566118724190153 & 0.867762551619694 & 0.433881275809847 \tabularnewline
47 & 0.552672427027186 & 0.894655145945629 & 0.447327572972814 \tabularnewline
48 & 0.919504750405178 & 0.160990499189644 & 0.0804952495948221 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57970&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]0.332229881297581[/C][C]0.664459762595162[/C][C]0.667770118702419[/C][/ROW]
[ROW][C]20[/C][C]0.188239028032669[/C][C]0.376478056065338[/C][C]0.811760971967331[/C][/ROW]
[ROW][C]21[/C][C]0.281226203205016[/C][C]0.562452406410031[/C][C]0.718773796794984[/C][/ROW]
[ROW][C]22[/C][C]0.198039274471929[/C][C]0.396078548943859[/C][C]0.80196072552807[/C][/ROW]
[ROW][C]23[/C][C]0.120925082598873[/C][C]0.241850165197746[/C][C]0.879074917401127[/C][/ROW]
[ROW][C]24[/C][C]0.0985220455025425[/C][C]0.197044091005085[/C][C]0.901477954497458[/C][/ROW]
[ROW][C]25[/C][C]0.0706106224314515[/C][C]0.141221244862903[/C][C]0.929389377568548[/C][/ROW]
[ROW][C]26[/C][C]0.169664683165319[/C][C]0.339329366330637[/C][C]0.830335316834681[/C][/ROW]
[ROW][C]27[/C][C]0.181585675886515[/C][C]0.363171351773031[/C][C]0.818414324113485[/C][/ROW]
[ROW][C]28[/C][C]0.145696791788923[/C][C]0.291393583577846[/C][C]0.854303208211077[/C][/ROW]
[ROW][C]29[/C][C]0.359500901624064[/C][C]0.719001803248128[/C][C]0.640499098375936[/C][/ROW]
[ROW][C]30[/C][C]0.278762929323195[/C][C]0.557525858646389[/C][C]0.721237070676805[/C][/ROW]
[ROW][C]31[/C][C]0.442465027247184[/C][C]0.884930054494368[/C][C]0.557534972752816[/C][/ROW]
[ROW][C]32[/C][C]0.427682299674425[/C][C]0.85536459934885[/C][C]0.572317700325575[/C][/ROW]
[ROW][C]33[/C][C]0.420640315736847[/C][C]0.841280631473694[/C][C]0.579359684263153[/C][/ROW]
[ROW][C]34[/C][C]0.419922416055795[/C][C]0.83984483211159[/C][C]0.580077583944205[/C][/ROW]
[ROW][C]35[/C][C]0.357794674660713[/C][C]0.715589349321426[/C][C]0.642205325339287[/C][/ROW]
[ROW][C]36[/C][C]0.311997520699315[/C][C]0.623995041398631[/C][C]0.688002479300684[/C][/ROW]
[ROW][C]37[/C][C]0.259969487158367[/C][C]0.519938974316734[/C][C]0.740030512841633[/C][/ROW]
[ROW][C]38[/C][C]0.359580776380143[/C][C]0.719161552760287[/C][C]0.640419223619857[/C][/ROW]
[ROW][C]39[/C][C]0.369297732500309[/C][C]0.738595465000619[/C][C]0.63070226749969[/C][/ROW]
[ROW][C]40[/C][C]0.403752068603968[/C][C]0.807504137207936[/C][C]0.596247931396032[/C][/ROW]
[ROW][C]41[/C][C]0.309537602621365[/C][C]0.61907520524273[/C][C]0.690462397378635[/C][/ROW]
[ROW][C]42[/C][C]0.257727750703199[/C][C]0.515455501406399[/C][C]0.7422722492968[/C][/ROW]
[ROW][C]43[/C][C]0.278482008842884[/C][C]0.556964017685768[/C][C]0.721517991157116[/C][/ROW]
[ROW][C]44[/C][C]0.574906676795454[/C][C]0.850186646409093[/C][C]0.425093323204546[/C][/ROW]
[ROW][C]45[/C][C]0.498458312705182[/C][C]0.996916625410364[/C][C]0.501541687294818[/C][/ROW]
[ROW][C]46[/C][C]0.566118724190153[/C][C]0.867762551619694[/C][C]0.433881275809847[/C][/ROW]
[ROW][C]47[/C][C]0.552672427027186[/C][C]0.894655145945629[/C][C]0.447327572972814[/C][/ROW]
[ROW][C]48[/C][C]0.919504750405178[/C][C]0.160990499189644[/C][C]0.0804952495948221[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57970&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57970&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
190.3322298812975810.6644597625951620.667770118702419
200.1882390280326690.3764780560653380.811760971967331
210.2812262032050160.5624524064100310.718773796794984
220.1980392744719290.3960785489438590.80196072552807
230.1209250825988730.2418501651977460.879074917401127
240.09852204550254250.1970440910050850.901477954497458
250.07061062243145150.1412212448629030.929389377568548
260.1696646831653190.3393293663306370.830335316834681
270.1815856758865150.3631713517730310.818414324113485
280.1456967917889230.2913935835778460.854303208211077
290.3595009016240640.7190018032481280.640499098375936
300.2787629293231950.5575258586463890.721237070676805
310.4424650272471840.8849300544943680.557534972752816
320.4276822996744250.855364599348850.572317700325575
330.4206403157368470.8412806314736940.579359684263153
340.4199224160557950.839844832111590.580077583944205
350.3577946746607130.7155893493214260.642205325339287
360.3119975206993150.6239950413986310.688002479300684
370.2599694871583670.5199389743167340.740030512841633
380.3595807763801430.7191615527602870.640419223619857
390.3692977325003090.7385954650006190.63070226749969
400.4037520686039680.8075041372079360.596247931396032
410.3095376026213650.619075205242730.690462397378635
420.2577277507031990.5154555014063990.7422722492968
430.2784820088428840.5569640176857680.721517991157116
440.5749066767954540.8501866464090930.425093323204546
450.4984583127051820.9969166254103640.501541687294818
460.5661187241901530.8677625516196940.433881275809847
470.5526724270271860.8946551459456290.447327572972814
480.9195047504051780.1609904991896440.0804952495948221






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

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57970&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57970&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57970&T=6

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


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

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


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 10
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Input Parameters & R Code

Parameters (Session):
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')
}