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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationTue, 24 Nov 2009 11:27:10 -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/24/t1259087300vg6nmwb7nejh39z.htm/, Retrieved Fri, 14 Jun 2024 19:51:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59208, Retrieved Fri, 14 Jun 2024 19:51:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-   PD    [Multiple Regression] [] [2009-11-20 13:55:26] [5482608004c1d7bbf873930172393a2d]
-   PD        [Multiple Regression] [Workshop7/module3] [2009-11-24 18:27:10] [f94f05f163a3ee3ab544c4fef41db0eb] [Current]
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Dataseries X:
114.08	136.49
112.95	142.62
135.31	141.71
134.31	149.51
133.03	147.39
140.11	131.96
124.69	136.38
131.68	127.34
150.95	133.85
137.26	125.14
130.51	141.25
143.15	149.32
118.01	120.92
122.56	134.85
147.97	131.93
135.74	134.22
151.62	143.07
154.82	145.37
145.59	134.32
147.12	126.31
175.86	162.21
140.66	124.09
152.69	153.91
154.38	154.34
132.45	138.70
136.44	150.98
153.24	146.39
154.11	178.30
155.93	168.23
142.53	162.52
148.73	158.86
147.73	152.17
166.79	171.01
144.30	171.49
156.07	189.62
161.70	177.46
152.10	179.98
140.45	156.96
155.56	167.89
174.53	194.78
167.16	192.78
159.48	165.06
173.22	196.60
176.13	151.64
180.31	187.02
185.84	210.99
169.43	219.08
195.25	235.68
174.99	241.44
156.42	187.46
182.08	229.57
182.00	208.44
153.28	215.09
136.72	217.00
130.19	171.08
132.04	178.41
143.89	196.34
133.38	172.11
127.98	154.93
150.45	182.26
133.55	181.74




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=59208&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=59208&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59208&T=0

As an alternative you can also use a QR Code:  

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

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







Multiple Linear Regression - Estimated Regression Equation
InvoerEU[t] = + 82.683850593337 + 0.467262809361258InvoerAM[t] -18.0508952623992M1[t] -17.0173631257305M2[t] + 0.0395977543686826M3[t] -2.95888240981108M4[t] -6.85649107502474M5[t] -7.99701999658972M6[t] -7.7807311043623M7[t] + 0.569266808576778M8[t] + 6.64215551133062M9[t] -4.11520638896474M10[t] -10.0454795242434M11[t] -0.158814190838987t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
InvoerEU[t] =  +  82.683850593337 +  0.467262809361258InvoerAM[t] -18.0508952623992M1[t] -17.0173631257305M2[t] +  0.0395977543686826M3[t] -2.95888240981108M4[t] -6.85649107502474M5[t] -7.99701999658972M6[t] -7.7807311043623M7[t] +  0.569266808576778M8[t] +  6.64215551133062M9[t] -4.11520638896474M10[t] -10.0454795242434M11[t] -0.158814190838987t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59208&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]InvoerEU[t] =  +  82.683850593337 +  0.467262809361258InvoerAM[t] -18.0508952623992M1[t] -17.0173631257305M2[t] +  0.0395977543686826M3[t] -2.95888240981108M4[t] -6.85649107502474M5[t] -7.99701999658972M6[t] -7.7807311043623M7[t] +  0.569266808576778M8[t] +  6.64215551133062M9[t] -4.11520638896474M10[t] -10.0454795242434M11[t] -0.158814190838987t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59208&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59208&T=1

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Estimated Regression Equation
InvoerEU[t] = + 82.683850593337 + 0.467262809361258InvoerAM[t] -18.0508952623992M1[t] -17.0173631257305M2[t] + 0.0395977543686826M3[t] -2.95888240981108M4[t] -6.85649107502474M5[t] -7.99701999658972M6[t] -7.7807311043623M7[t] + 0.569266808576778M8[t] + 6.64215551133062M9[t] -4.11520638896474M10[t] -10.0454795242434M11[t] -0.158814190838987t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)82.68385059333714.7865295.59181e-061e-06
InvoerAM0.4672628093612580.0986794.73522e-051e-05
M1-18.05089526239928.131757-2.21980.0312930.015647
M2-17.01736312573058.589618-1.98120.0534420.026721
M30.03959775436868268.5075520.00470.9963060.498153
M4-2.958882409811088.494898-0.34830.7291610.36458
M5-6.856491075024748.482331-0.80830.4229750.211488
M6-7.997019996589728.502859-0.94050.3517650.175883
M7-7.78073110436238.572446-0.90760.3686970.184348
M80.5692668085767788.8793050.06410.9491530.474577
M96.642155511330628.4741430.78380.4370810.218541
M10-4.115206388964748.605814-0.47820.6347320.317366
M11-10.04547952424348.476515-1.18510.2419370.120969
t-0.1588141908389870.163431-0.97180.3361490.168075

\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) & 82.683850593337 & 14.786529 & 5.5918 & 1e-06 & 1e-06 \tabularnewline
InvoerAM & 0.467262809361258 & 0.098679 & 4.7352 & 2e-05 & 1e-05 \tabularnewline
M1 & -18.0508952623992 & 8.131757 & -2.2198 & 0.031293 & 0.015647 \tabularnewline
M2 & -17.0173631257305 & 8.589618 & -1.9812 & 0.053442 & 0.026721 \tabularnewline
M3 & 0.0395977543686826 & 8.507552 & 0.0047 & 0.996306 & 0.498153 \tabularnewline
M4 & -2.95888240981108 & 8.494898 & -0.3483 & 0.729161 & 0.36458 \tabularnewline
M5 & -6.85649107502474 & 8.482331 & -0.8083 & 0.422975 & 0.211488 \tabularnewline
M6 & -7.99701999658972 & 8.502859 & -0.9405 & 0.351765 & 0.175883 \tabularnewline
M7 & -7.7807311043623 & 8.572446 & -0.9076 & 0.368697 & 0.184348 \tabularnewline
M8 & 0.569266808576778 & 8.879305 & 0.0641 & 0.949153 & 0.474577 \tabularnewline
M9 & 6.64215551133062 & 8.474143 & 0.7838 & 0.437081 & 0.218541 \tabularnewline
M10 & -4.11520638896474 & 8.605814 & -0.4782 & 0.634732 & 0.317366 \tabularnewline
M11 & -10.0454795242434 & 8.476515 & -1.1851 & 0.241937 & 0.120969 \tabularnewline
t & -0.158814190838987 & 0.163431 & -0.9718 & 0.336149 & 0.168075 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59208&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]82.683850593337[/C][C]14.786529[/C][C]5.5918[/C][C]1e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]InvoerAM[/C][C]0.467262809361258[/C][C]0.098679[/C][C]4.7352[/C][C]2e-05[/C][C]1e-05[/C][/ROW]
[ROW][C]M1[/C][C]-18.0508952623992[/C][C]8.131757[/C][C]-2.2198[/C][C]0.031293[/C][C]0.015647[/C][/ROW]
[ROW][C]M2[/C][C]-17.0173631257305[/C][C]8.589618[/C][C]-1.9812[/C][C]0.053442[/C][C]0.026721[/C][/ROW]
[ROW][C]M3[/C][C]0.0395977543686826[/C][C]8.507552[/C][C]0.0047[/C][C]0.996306[/C][C]0.498153[/C][/ROW]
[ROW][C]M4[/C][C]-2.95888240981108[/C][C]8.494898[/C][C]-0.3483[/C][C]0.729161[/C][C]0.36458[/C][/ROW]
[ROW][C]M5[/C][C]-6.85649107502474[/C][C]8.482331[/C][C]-0.8083[/C][C]0.422975[/C][C]0.211488[/C][/ROW]
[ROW][C]M6[/C][C]-7.99701999658972[/C][C]8.502859[/C][C]-0.9405[/C][C]0.351765[/C][C]0.175883[/C][/ROW]
[ROW][C]M7[/C][C]-7.7807311043623[/C][C]8.572446[/C][C]-0.9076[/C][C]0.368697[/C][C]0.184348[/C][/ROW]
[ROW][C]M8[/C][C]0.569266808576778[/C][C]8.879305[/C][C]0.0641[/C][C]0.949153[/C][C]0.474577[/C][/ROW]
[ROW][C]M9[/C][C]6.64215551133062[/C][C]8.474143[/C][C]0.7838[/C][C]0.437081[/C][C]0.218541[/C][/ROW]
[ROW][C]M10[/C][C]-4.11520638896474[/C][C]8.605814[/C][C]-0.4782[/C][C]0.634732[/C][C]0.317366[/C][/ROW]
[ROW][C]M11[/C][C]-10.0454795242434[/C][C]8.476515[/C][C]-1.1851[/C][C]0.241937[/C][C]0.120969[/C][/ROW]
[ROW][C]t[/C][C]-0.158814190838987[/C][C]0.163431[/C][C]-0.9718[/C][C]0.336149[/C][C]0.168075[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59208&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59208&T=2

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)82.68385059333714.7865295.59181e-061e-06
InvoerAM0.4672628093612580.0986794.73522e-051e-05
M1-18.05089526239928.131757-2.21980.0312930.015647
M2-17.01736312573058.589618-1.98120.0534420.026721
M30.03959775436868268.5075520.00470.9963060.498153
M4-2.958882409811088.494898-0.34830.7291610.36458
M5-6.856491075024748.482331-0.80830.4229750.211488
M6-7.997019996589728.502859-0.94050.3517650.175883
M7-7.78073110436238.572446-0.90760.3686970.184348
M80.5692668085767788.8793050.06410.9491530.474577
M96.642155511330628.4741430.78380.4370810.218541
M10-4.115206388964748.605814-0.47820.6347320.317366
M11-10.04547952424348.476515-1.18510.2419370.120969
t-0.1588141908389870.163431-0.97180.3361490.168075







Multiple Linear Regression - Regression Statistics
Multiple R0.770106253769868
R-squared0.59306364209546
Adjusted R-squared0.480506777143141
F-TEST (value)5.26901351016386
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value1.07834850648914e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation13.3604016177259
Sum Squared Residuals8389.5155751859

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.770106253769868 \tabularnewline
R-squared & 0.59306364209546 \tabularnewline
Adjusted R-squared & 0.480506777143141 \tabularnewline
F-TEST (value) & 5.26901351016386 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 1.07834850648914e-05 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 13.3604016177259 \tabularnewline
Sum Squared Residuals & 8389.5155751859 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59208&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.770106253769868[/C][/ROW]
[ROW][C]R-squared[/C][C]0.59306364209546[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.480506777143141[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]5.26901351016386[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]1.07834850648914e-05[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]13.3604016177259[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]8389.5155751859[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59208&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59208&T=3

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Regression Statistics
Multiple R0.770106253769868
R-squared0.59306364209546
Adjusted R-squared0.480506777143141
F-TEST (value)5.26901351016386
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value1.07834850648914e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation13.3604016177259
Sum Squared Residuals8389.5155751859







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1114.08128.250841989817-14.1708419898174
2112.95131.989880957031-19.0398809570312
3135.31148.462818489773-13.1528184897726
4134.31148.950174047772-14.6401740477717
5133.03143.903154035873-10.8731540358732
6140.11135.3939457750254.71605422497503
7124.69137.516722093790-12.8267220937902
8131.68141.483850019265-9.8038500192645
9150.95150.4398054201210.51019457987886
10137.26135.4537702594501.80622974054976
11130.51136.892286792142-6.38228679214242
12143.15150.549762997092-7.3997629970922
13118.01119.069789757994-1.05978975799429
14122.56126.453478638226-3.89347863822638
15147.97141.9872179241525.98278207584834
16135.74139.899955402570-4.15995540257019
17151.62139.97880840936511.6411915906353
18154.82139.75416975849215.0658302415084
19145.59134.64839041643810.9416095835619
20147.12139.0967990355558.02320096444544
21175.86161.78560840353914.0743915964614
22140.66133.0573740195537.60262598044692
23152.69140.90206366858811.7879363314119
24154.38150.9896520100183.39034798998211
25132.45125.4719522183706.97804778163037
26136.44132.0846574631564.35534253684437
27153.24146.8380678574486.40193214255241
28154.11158.591129749147-4.48112974914660
29155.93149.8293704028266.10062959717393
30142.53145.861956648969-3.33195664896934
31148.73144.2092494680964.52075053190441
32147.73149.274444995569-1.54444499556885
33166.79163.9917508358502.7982491641502
34144.3153.299860893209-8.99986089320883
35156.07155.6822483008110.387751699189206
36161.7159.8869978723821.81300212761766
37152.1142.8547906987349.2452093012655
38140.45132.9731187730687.47688122693188
39155.56154.9784479686470.581552031353204
40174.53164.38585055735210.1441494426477
41167.16159.3949020825777.76509791742287
42159.48145.14303389467914.3369661053209
43173.22159.93797760332213.2820223966784
44176.13147.12102541654029.0089745834604
45180.31169.56685812365610.7431418763443
46185.84169.85097157291115.9890284270893
47169.43167.5420403745261.8879596254744
48195.25185.18526834332710.0647316566731
49174.99169.6669926720105.32300732799045
50156.42145.31886416851911.1011358314814
51182.08181.8934477599810.186552240018664
52182168.86289024315913.1371097568408
53153.28167.913765069359-14.6337650693590
54136.72167.506893922835-30.7868939228350
55130.19146.107660418354-15.9176604183545
56132.04157.723880533073-25.6838805330726
57143.89172.015977216835-28.1259772168348
58133.38149.778023254877-16.3980232548771
59127.98135.661360863933-7.68136086393306
60150.45158.318318777181-7.86831877718068
61133.55139.865632663075-6.31563266307461

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 114.08 & 128.250841989817 & -14.1708419898174 \tabularnewline
2 & 112.95 & 131.989880957031 & -19.0398809570312 \tabularnewline
3 & 135.31 & 148.462818489773 & -13.1528184897726 \tabularnewline
4 & 134.31 & 148.950174047772 & -14.6401740477717 \tabularnewline
5 & 133.03 & 143.903154035873 & -10.8731540358732 \tabularnewline
6 & 140.11 & 135.393945775025 & 4.71605422497503 \tabularnewline
7 & 124.69 & 137.516722093790 & -12.8267220937902 \tabularnewline
8 & 131.68 & 141.483850019265 & -9.8038500192645 \tabularnewline
9 & 150.95 & 150.439805420121 & 0.51019457987886 \tabularnewline
10 & 137.26 & 135.453770259450 & 1.80622974054976 \tabularnewline
11 & 130.51 & 136.892286792142 & -6.38228679214242 \tabularnewline
12 & 143.15 & 150.549762997092 & -7.3997629970922 \tabularnewline
13 & 118.01 & 119.069789757994 & -1.05978975799429 \tabularnewline
14 & 122.56 & 126.453478638226 & -3.89347863822638 \tabularnewline
15 & 147.97 & 141.987217924152 & 5.98278207584834 \tabularnewline
16 & 135.74 & 139.899955402570 & -4.15995540257019 \tabularnewline
17 & 151.62 & 139.978808409365 & 11.6411915906353 \tabularnewline
18 & 154.82 & 139.754169758492 & 15.0658302415084 \tabularnewline
19 & 145.59 & 134.648390416438 & 10.9416095835619 \tabularnewline
20 & 147.12 & 139.096799035555 & 8.02320096444544 \tabularnewline
21 & 175.86 & 161.785608403539 & 14.0743915964614 \tabularnewline
22 & 140.66 & 133.057374019553 & 7.60262598044692 \tabularnewline
23 & 152.69 & 140.902063668588 & 11.7879363314119 \tabularnewline
24 & 154.38 & 150.989652010018 & 3.39034798998211 \tabularnewline
25 & 132.45 & 125.471952218370 & 6.97804778163037 \tabularnewline
26 & 136.44 & 132.084657463156 & 4.35534253684437 \tabularnewline
27 & 153.24 & 146.838067857448 & 6.40193214255241 \tabularnewline
28 & 154.11 & 158.591129749147 & -4.48112974914660 \tabularnewline
29 & 155.93 & 149.829370402826 & 6.10062959717393 \tabularnewline
30 & 142.53 & 145.861956648969 & -3.33195664896934 \tabularnewline
31 & 148.73 & 144.209249468096 & 4.52075053190441 \tabularnewline
32 & 147.73 & 149.274444995569 & -1.54444499556885 \tabularnewline
33 & 166.79 & 163.991750835850 & 2.7982491641502 \tabularnewline
34 & 144.3 & 153.299860893209 & -8.99986089320883 \tabularnewline
35 & 156.07 & 155.682248300811 & 0.387751699189206 \tabularnewline
36 & 161.7 & 159.886997872382 & 1.81300212761766 \tabularnewline
37 & 152.1 & 142.854790698734 & 9.2452093012655 \tabularnewline
38 & 140.45 & 132.973118773068 & 7.47688122693188 \tabularnewline
39 & 155.56 & 154.978447968647 & 0.581552031353204 \tabularnewline
40 & 174.53 & 164.385850557352 & 10.1441494426477 \tabularnewline
41 & 167.16 & 159.394902082577 & 7.76509791742287 \tabularnewline
42 & 159.48 & 145.143033894679 & 14.3369661053209 \tabularnewline
43 & 173.22 & 159.937977603322 & 13.2820223966784 \tabularnewline
44 & 176.13 & 147.121025416540 & 29.0089745834604 \tabularnewline
45 & 180.31 & 169.566858123656 & 10.7431418763443 \tabularnewline
46 & 185.84 & 169.850971572911 & 15.9890284270893 \tabularnewline
47 & 169.43 & 167.542040374526 & 1.8879596254744 \tabularnewline
48 & 195.25 & 185.185268343327 & 10.0647316566731 \tabularnewline
49 & 174.99 & 169.666992672010 & 5.32300732799045 \tabularnewline
50 & 156.42 & 145.318864168519 & 11.1011358314814 \tabularnewline
51 & 182.08 & 181.893447759981 & 0.186552240018664 \tabularnewline
52 & 182 & 168.862890243159 & 13.1371097568408 \tabularnewline
53 & 153.28 & 167.913765069359 & -14.6337650693590 \tabularnewline
54 & 136.72 & 167.506893922835 & -30.7868939228350 \tabularnewline
55 & 130.19 & 146.107660418354 & -15.9176604183545 \tabularnewline
56 & 132.04 & 157.723880533073 & -25.6838805330726 \tabularnewline
57 & 143.89 & 172.015977216835 & -28.1259772168348 \tabularnewline
58 & 133.38 & 149.778023254877 & -16.3980232548771 \tabularnewline
59 & 127.98 & 135.661360863933 & -7.68136086393306 \tabularnewline
60 & 150.45 & 158.318318777181 & -7.86831877718068 \tabularnewline
61 & 133.55 & 139.865632663075 & -6.31563266307461 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59208&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]114.08[/C][C]128.250841989817[/C][C]-14.1708419898174[/C][/ROW]
[ROW][C]2[/C][C]112.95[/C][C]131.989880957031[/C][C]-19.0398809570312[/C][/ROW]
[ROW][C]3[/C][C]135.31[/C][C]148.462818489773[/C][C]-13.1528184897726[/C][/ROW]
[ROW][C]4[/C][C]134.31[/C][C]148.950174047772[/C][C]-14.6401740477717[/C][/ROW]
[ROW][C]5[/C][C]133.03[/C][C]143.903154035873[/C][C]-10.8731540358732[/C][/ROW]
[ROW][C]6[/C][C]140.11[/C][C]135.393945775025[/C][C]4.71605422497503[/C][/ROW]
[ROW][C]7[/C][C]124.69[/C][C]137.516722093790[/C][C]-12.8267220937902[/C][/ROW]
[ROW][C]8[/C][C]131.68[/C][C]141.483850019265[/C][C]-9.8038500192645[/C][/ROW]
[ROW][C]9[/C][C]150.95[/C][C]150.439805420121[/C][C]0.51019457987886[/C][/ROW]
[ROW][C]10[/C][C]137.26[/C][C]135.453770259450[/C][C]1.80622974054976[/C][/ROW]
[ROW][C]11[/C][C]130.51[/C][C]136.892286792142[/C][C]-6.38228679214242[/C][/ROW]
[ROW][C]12[/C][C]143.15[/C][C]150.549762997092[/C][C]-7.3997629970922[/C][/ROW]
[ROW][C]13[/C][C]118.01[/C][C]119.069789757994[/C][C]-1.05978975799429[/C][/ROW]
[ROW][C]14[/C][C]122.56[/C][C]126.453478638226[/C][C]-3.89347863822638[/C][/ROW]
[ROW][C]15[/C][C]147.97[/C][C]141.987217924152[/C][C]5.98278207584834[/C][/ROW]
[ROW][C]16[/C][C]135.74[/C][C]139.899955402570[/C][C]-4.15995540257019[/C][/ROW]
[ROW][C]17[/C][C]151.62[/C][C]139.978808409365[/C][C]11.6411915906353[/C][/ROW]
[ROW][C]18[/C][C]154.82[/C][C]139.754169758492[/C][C]15.0658302415084[/C][/ROW]
[ROW][C]19[/C][C]145.59[/C][C]134.648390416438[/C][C]10.9416095835619[/C][/ROW]
[ROW][C]20[/C][C]147.12[/C][C]139.096799035555[/C][C]8.02320096444544[/C][/ROW]
[ROW][C]21[/C][C]175.86[/C][C]161.785608403539[/C][C]14.0743915964614[/C][/ROW]
[ROW][C]22[/C][C]140.66[/C][C]133.057374019553[/C][C]7.60262598044692[/C][/ROW]
[ROW][C]23[/C][C]152.69[/C][C]140.902063668588[/C][C]11.7879363314119[/C][/ROW]
[ROW][C]24[/C][C]154.38[/C][C]150.989652010018[/C][C]3.39034798998211[/C][/ROW]
[ROW][C]25[/C][C]132.45[/C][C]125.471952218370[/C][C]6.97804778163037[/C][/ROW]
[ROW][C]26[/C][C]136.44[/C][C]132.084657463156[/C][C]4.35534253684437[/C][/ROW]
[ROW][C]27[/C][C]153.24[/C][C]146.838067857448[/C][C]6.40193214255241[/C][/ROW]
[ROW][C]28[/C][C]154.11[/C][C]158.591129749147[/C][C]-4.48112974914660[/C][/ROW]
[ROW][C]29[/C][C]155.93[/C][C]149.829370402826[/C][C]6.10062959717393[/C][/ROW]
[ROW][C]30[/C][C]142.53[/C][C]145.861956648969[/C][C]-3.33195664896934[/C][/ROW]
[ROW][C]31[/C][C]148.73[/C][C]144.209249468096[/C][C]4.52075053190441[/C][/ROW]
[ROW][C]32[/C][C]147.73[/C][C]149.274444995569[/C][C]-1.54444499556885[/C][/ROW]
[ROW][C]33[/C][C]166.79[/C][C]163.991750835850[/C][C]2.7982491641502[/C][/ROW]
[ROW][C]34[/C][C]144.3[/C][C]153.299860893209[/C][C]-8.99986089320883[/C][/ROW]
[ROW][C]35[/C][C]156.07[/C][C]155.682248300811[/C][C]0.387751699189206[/C][/ROW]
[ROW][C]36[/C][C]161.7[/C][C]159.886997872382[/C][C]1.81300212761766[/C][/ROW]
[ROW][C]37[/C][C]152.1[/C][C]142.854790698734[/C][C]9.2452093012655[/C][/ROW]
[ROW][C]38[/C][C]140.45[/C][C]132.973118773068[/C][C]7.47688122693188[/C][/ROW]
[ROW][C]39[/C][C]155.56[/C][C]154.978447968647[/C][C]0.581552031353204[/C][/ROW]
[ROW][C]40[/C][C]174.53[/C][C]164.385850557352[/C][C]10.1441494426477[/C][/ROW]
[ROW][C]41[/C][C]167.16[/C][C]159.394902082577[/C][C]7.76509791742287[/C][/ROW]
[ROW][C]42[/C][C]159.48[/C][C]145.143033894679[/C][C]14.3369661053209[/C][/ROW]
[ROW][C]43[/C][C]173.22[/C][C]159.937977603322[/C][C]13.2820223966784[/C][/ROW]
[ROW][C]44[/C][C]176.13[/C][C]147.121025416540[/C][C]29.0089745834604[/C][/ROW]
[ROW][C]45[/C][C]180.31[/C][C]169.566858123656[/C][C]10.7431418763443[/C][/ROW]
[ROW][C]46[/C][C]185.84[/C][C]169.850971572911[/C][C]15.9890284270893[/C][/ROW]
[ROW][C]47[/C][C]169.43[/C][C]167.542040374526[/C][C]1.8879596254744[/C][/ROW]
[ROW][C]48[/C][C]195.25[/C][C]185.185268343327[/C][C]10.0647316566731[/C][/ROW]
[ROW][C]49[/C][C]174.99[/C][C]169.666992672010[/C][C]5.32300732799045[/C][/ROW]
[ROW][C]50[/C][C]156.42[/C][C]145.318864168519[/C][C]11.1011358314814[/C][/ROW]
[ROW][C]51[/C][C]182.08[/C][C]181.893447759981[/C][C]0.186552240018664[/C][/ROW]
[ROW][C]52[/C][C]182[/C][C]168.862890243159[/C][C]13.1371097568408[/C][/ROW]
[ROW][C]53[/C][C]153.28[/C][C]167.913765069359[/C][C]-14.6337650693590[/C][/ROW]
[ROW][C]54[/C][C]136.72[/C][C]167.506893922835[/C][C]-30.7868939228350[/C][/ROW]
[ROW][C]55[/C][C]130.19[/C][C]146.107660418354[/C][C]-15.9176604183545[/C][/ROW]
[ROW][C]56[/C][C]132.04[/C][C]157.723880533073[/C][C]-25.6838805330726[/C][/ROW]
[ROW][C]57[/C][C]143.89[/C][C]172.015977216835[/C][C]-28.1259772168348[/C][/ROW]
[ROW][C]58[/C][C]133.38[/C][C]149.778023254877[/C][C]-16.3980232548771[/C][/ROW]
[ROW][C]59[/C][C]127.98[/C][C]135.661360863933[/C][C]-7.68136086393306[/C][/ROW]
[ROW][C]60[/C][C]150.45[/C][C]158.318318777181[/C][C]-7.86831877718068[/C][/ROW]
[ROW][C]61[/C][C]133.55[/C][C]139.865632663075[/C][C]-6.31563266307461[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59208&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59208&T=4

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1114.08128.250841989817-14.1708419898174
2112.95131.989880957031-19.0398809570312
3135.31148.462818489773-13.1528184897726
4134.31148.950174047772-14.6401740477717
5133.03143.903154035873-10.8731540358732
6140.11135.3939457750254.71605422497503
7124.69137.516722093790-12.8267220937902
8131.68141.483850019265-9.8038500192645
9150.95150.4398054201210.51019457987886
10137.26135.4537702594501.80622974054976
11130.51136.892286792142-6.38228679214242
12143.15150.549762997092-7.3997629970922
13118.01119.069789757994-1.05978975799429
14122.56126.453478638226-3.89347863822638
15147.97141.9872179241525.98278207584834
16135.74139.899955402570-4.15995540257019
17151.62139.97880840936511.6411915906353
18154.82139.75416975849215.0658302415084
19145.59134.64839041643810.9416095835619
20147.12139.0967990355558.02320096444544
21175.86161.78560840353914.0743915964614
22140.66133.0573740195537.60262598044692
23152.69140.90206366858811.7879363314119
24154.38150.9896520100183.39034798998211
25132.45125.4719522183706.97804778163037
26136.44132.0846574631564.35534253684437
27153.24146.8380678574486.40193214255241
28154.11158.591129749147-4.48112974914660
29155.93149.8293704028266.10062959717393
30142.53145.861956648969-3.33195664896934
31148.73144.2092494680964.52075053190441
32147.73149.274444995569-1.54444499556885
33166.79163.9917508358502.7982491641502
34144.3153.299860893209-8.99986089320883
35156.07155.6822483008110.387751699189206
36161.7159.8869978723821.81300212761766
37152.1142.8547906987349.2452093012655
38140.45132.9731187730687.47688122693188
39155.56154.9784479686470.581552031353204
40174.53164.38585055735210.1441494426477
41167.16159.3949020825777.76509791742287
42159.48145.14303389467914.3369661053209
43173.22159.93797760332213.2820223966784
44176.13147.12102541654029.0089745834604
45180.31169.56685812365610.7431418763443
46185.84169.85097157291115.9890284270893
47169.43167.5420403745261.8879596254744
48195.25185.18526834332710.0647316566731
49174.99169.6669926720105.32300732799045
50156.42145.31886416851911.1011358314814
51182.08181.8934477599810.186552240018664
52182168.86289024315913.1371097568408
53153.28167.913765069359-14.6337650693590
54136.72167.506893922835-30.7868939228350
55130.19146.107660418354-15.9176604183545
56132.04157.723880533073-25.6838805330726
57143.89172.015977216835-28.1259772168348
58133.38149.778023254877-16.3980232548771
59127.98135.661360863933-7.68136086393306
60150.45158.318318777181-7.86831877718068
61133.55139.865632663075-6.31563266307461







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.005290334391127270.01058066878225450.994709665608873
180.01706180363882470.03412360727764950.982938196361175
190.01215685568430050.02431371136860100.9878431443157
200.003598910497748350.00719782099549670.996401089502252
210.001041638433758730.002083276867517460.998958361566241
220.001181091646546240.002362183293092470.998818908353454
230.0003936977069784380.0007873954139568770.999606302293021
240.0001444224658246390.0002888449316492780.999855577534175
258.87137090871153e-050.0001774274181742310.999911286290913
263.69589071457293e-057.39178142914585e-050.999963041092854
273.6496548818841e-057.2993097637682e-050.999963503451181
284.59821952321633e-059.19643904643266e-050.999954017804768
292.75024263123857e-055.50048526247715e-050.999972497573688
300.001031390318216660.002062780636433320.998968609681783
310.0004504514477214350.000900902895442870.999549548552279
320.0003555462431918370.0007110924863836750.999644453756808
330.00028456408688860.00056912817377720.999715435913111
340.0004102256524355750.000820451304871150.999589774347564
350.0002913000581278020.0005826001162556030.999708699941872
360.00033292905400570.00066585810801140.999667070945994
370.000792608856666070.001585217713332140.999207391143334
380.001409580561792930.002819161123585850.998590419438207
390.01230605651327560.02461211302655130.987693943486724
400.4034384558346570.8068769116693140.596561544165343
410.7423143364997430.5153713270005130.257685663500257
420.8956507877601740.2086984244796520.104349212239826
430.8193442993123230.3613114013753540.180655700687677
440.7411717782599620.5176564434800760.258828221740038

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.00529033439112727 & 0.0105806687822545 & 0.994709665608873 \tabularnewline
18 & 0.0170618036388247 & 0.0341236072776495 & 0.982938196361175 \tabularnewline
19 & 0.0121568556843005 & 0.0243137113686010 & 0.9878431443157 \tabularnewline
20 & 0.00359891049774835 & 0.0071978209954967 & 0.996401089502252 \tabularnewline
21 & 0.00104163843375873 & 0.00208327686751746 & 0.998958361566241 \tabularnewline
22 & 0.00118109164654624 & 0.00236218329309247 & 0.998818908353454 \tabularnewline
23 & 0.000393697706978438 & 0.000787395413956877 & 0.999606302293021 \tabularnewline
24 & 0.000144422465824639 & 0.000288844931649278 & 0.999855577534175 \tabularnewline
25 & 8.87137090871153e-05 & 0.000177427418174231 & 0.999911286290913 \tabularnewline
26 & 3.69589071457293e-05 & 7.39178142914585e-05 & 0.999963041092854 \tabularnewline
27 & 3.6496548818841e-05 & 7.2993097637682e-05 & 0.999963503451181 \tabularnewline
28 & 4.59821952321633e-05 & 9.19643904643266e-05 & 0.999954017804768 \tabularnewline
29 & 2.75024263123857e-05 & 5.50048526247715e-05 & 0.999972497573688 \tabularnewline
30 & 0.00103139031821666 & 0.00206278063643332 & 0.998968609681783 \tabularnewline
31 & 0.000450451447721435 & 0.00090090289544287 & 0.999549548552279 \tabularnewline
32 & 0.000355546243191837 & 0.000711092486383675 & 0.999644453756808 \tabularnewline
33 & 0.0002845640868886 & 0.0005691281737772 & 0.999715435913111 \tabularnewline
34 & 0.000410225652435575 & 0.00082045130487115 & 0.999589774347564 \tabularnewline
35 & 0.000291300058127802 & 0.000582600116255603 & 0.999708699941872 \tabularnewline
36 & 0.0003329290540057 & 0.0006658581080114 & 0.999667070945994 \tabularnewline
37 & 0.00079260885666607 & 0.00158521771333214 & 0.999207391143334 \tabularnewline
38 & 0.00140958056179293 & 0.00281916112358585 & 0.998590419438207 \tabularnewline
39 & 0.0123060565132756 & 0.0246121130265513 & 0.987693943486724 \tabularnewline
40 & 0.403438455834657 & 0.806876911669314 & 0.596561544165343 \tabularnewline
41 & 0.742314336499743 & 0.515371327000513 & 0.257685663500257 \tabularnewline
42 & 0.895650787760174 & 0.208698424479652 & 0.104349212239826 \tabularnewline
43 & 0.819344299312323 & 0.361311401375354 & 0.180655700687677 \tabularnewline
44 & 0.741171778259962 & 0.517656443480076 & 0.258828221740038 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59208&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]17[/C][C]0.00529033439112727[/C][C]0.0105806687822545[/C][C]0.994709665608873[/C][/ROW]
[ROW][C]18[/C][C]0.0170618036388247[/C][C]0.0341236072776495[/C][C]0.982938196361175[/C][/ROW]
[ROW][C]19[/C][C]0.0121568556843005[/C][C]0.0243137113686010[/C][C]0.9878431443157[/C][/ROW]
[ROW][C]20[/C][C]0.00359891049774835[/C][C]0.0071978209954967[/C][C]0.996401089502252[/C][/ROW]
[ROW][C]21[/C][C]0.00104163843375873[/C][C]0.00208327686751746[/C][C]0.998958361566241[/C][/ROW]
[ROW][C]22[/C][C]0.00118109164654624[/C][C]0.00236218329309247[/C][C]0.998818908353454[/C][/ROW]
[ROW][C]23[/C][C]0.000393697706978438[/C][C]0.000787395413956877[/C][C]0.999606302293021[/C][/ROW]
[ROW][C]24[/C][C]0.000144422465824639[/C][C]0.000288844931649278[/C][C]0.999855577534175[/C][/ROW]
[ROW][C]25[/C][C]8.87137090871153e-05[/C][C]0.000177427418174231[/C][C]0.999911286290913[/C][/ROW]
[ROW][C]26[/C][C]3.69589071457293e-05[/C][C]7.39178142914585e-05[/C][C]0.999963041092854[/C][/ROW]
[ROW][C]27[/C][C]3.6496548818841e-05[/C][C]7.2993097637682e-05[/C][C]0.999963503451181[/C][/ROW]
[ROW][C]28[/C][C]4.59821952321633e-05[/C][C]9.19643904643266e-05[/C][C]0.999954017804768[/C][/ROW]
[ROW][C]29[/C][C]2.75024263123857e-05[/C][C]5.50048526247715e-05[/C][C]0.999972497573688[/C][/ROW]
[ROW][C]30[/C][C]0.00103139031821666[/C][C]0.00206278063643332[/C][C]0.998968609681783[/C][/ROW]
[ROW][C]31[/C][C]0.000450451447721435[/C][C]0.00090090289544287[/C][C]0.999549548552279[/C][/ROW]
[ROW][C]32[/C][C]0.000355546243191837[/C][C]0.000711092486383675[/C][C]0.999644453756808[/C][/ROW]
[ROW][C]33[/C][C]0.0002845640868886[/C][C]0.0005691281737772[/C][C]0.999715435913111[/C][/ROW]
[ROW][C]34[/C][C]0.000410225652435575[/C][C]0.00082045130487115[/C][C]0.999589774347564[/C][/ROW]
[ROW][C]35[/C][C]0.000291300058127802[/C][C]0.000582600116255603[/C][C]0.999708699941872[/C][/ROW]
[ROW][C]36[/C][C]0.0003329290540057[/C][C]0.0006658581080114[/C][C]0.999667070945994[/C][/ROW]
[ROW][C]37[/C][C]0.00079260885666607[/C][C]0.00158521771333214[/C][C]0.999207391143334[/C][/ROW]
[ROW][C]38[/C][C]0.00140958056179293[/C][C]0.00281916112358585[/C][C]0.998590419438207[/C][/ROW]
[ROW][C]39[/C][C]0.0123060565132756[/C][C]0.0246121130265513[/C][C]0.987693943486724[/C][/ROW]
[ROW][C]40[/C][C]0.403438455834657[/C][C]0.806876911669314[/C][C]0.596561544165343[/C][/ROW]
[ROW][C]41[/C][C]0.742314336499743[/C][C]0.515371327000513[/C][C]0.257685663500257[/C][/ROW]
[ROW][C]42[/C][C]0.895650787760174[/C][C]0.208698424479652[/C][C]0.104349212239826[/C][/ROW]
[ROW][C]43[/C][C]0.819344299312323[/C][C]0.361311401375354[/C][C]0.180655700687677[/C][/ROW]
[ROW][C]44[/C][C]0.741171778259962[/C][C]0.517656443480076[/C][C]0.258828221740038[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59208&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59208&T=5

As an alternative you can also use a QR Code:  

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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.005290334391127270.01058066878225450.994709665608873
180.01706180363882470.03412360727764950.982938196361175
190.01215685568430050.02431371136860100.9878431443157
200.003598910497748350.00719782099549670.996401089502252
210.001041638433758730.002083276867517460.998958361566241
220.001181091646546240.002362183293092470.998818908353454
230.0003936977069784380.0007873954139568770.999606302293021
240.0001444224658246390.0002888449316492780.999855577534175
258.87137090871153e-050.0001774274181742310.999911286290913
263.69589071457293e-057.39178142914585e-050.999963041092854
273.6496548818841e-057.2993097637682e-050.999963503451181
284.59821952321633e-059.19643904643266e-050.999954017804768
292.75024263123857e-055.50048526247715e-050.999972497573688
300.001031390318216660.002062780636433320.998968609681783
310.0004504514477214350.000900902895442870.999549548552279
320.0003555462431918370.0007110924863836750.999644453756808
330.00028456408688860.00056912817377720.999715435913111
340.0004102256524355750.000820451304871150.999589774347564
350.0002913000581278020.0005826001162556030.999708699941872
360.00033292905400570.00066585810801140.999667070945994
370.000792608856666070.001585217713332140.999207391143334
380.001409580561792930.002819161123585850.998590419438207
390.01230605651327560.02461211302655130.987693943486724
400.4034384558346570.8068769116693140.596561544165343
410.7423143364997430.5153713270005130.257685663500257
420.8956507877601740.2086984244796520.104349212239826
430.8193442993123230.3613114013753540.180655700687677
440.7411717782599620.5176564434800760.258828221740038







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level190.678571428571429NOK
5% type I error level230.821428571428571NOK
10% type I error level230.821428571428571NOK

\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 & 19 & 0.678571428571429 & NOK \tabularnewline
5% type I error level & 23 & 0.821428571428571 & NOK \tabularnewline
10% type I error level & 23 & 0.821428571428571 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59208&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]19[/C][C]0.678571428571429[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]23[/C][C]0.821428571428571[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]23[/C][C]0.821428571428571[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59208&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59208&T=6

As an alternative you can also use a QR Code:  

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level190.678571428571429NOK
5% type I error level230.821428571428571NOK
10% type I error level230.821428571428571NOK



Parameters (Session):
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')
}