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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 computationTue, 28 Dec 2010 10:10:04 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/28/t12935309336ec2lcrhoxsesm7.htm/, Retrieved Sun, 05 May 2024 02:05:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116259, Retrieved Sun, 05 May 2024 02:05:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [MultipleRegression2] [2010-12-28 10:10:04] [a35bd1e3fb5b4b301d5250bc2f7eb297] [Current]
-    D    [Multiple Regression] [] [2011-01-11 17:11:15] [4cec9a0c6d7fcfe819c8df12b51eb7f5]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
-6	5
-3	0
-3	-2
-7	6
-9	11
-11	9
-13	17
-11	21
-9	21
-17	41
-22	57
-25	65
-20	68
-24	73
-24	71
-22	71
-19	70
-18	69
-17	65
-11	57
-11	57
-12	57
-10	55
-15	65
-15	65
-15	64
-13	60
-8	43
-13	47
-9	40
-7	31
-4	27
-4	24
-2	23
0	17
-2	16

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116259&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]6 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=116259&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116259&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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
IndVertr[t] = -2.70086291822297 -0.224608973717344WerklHd[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
IndVertr[t] =  -2.70086291822297 -0.224608973717344WerklHd[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116259&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]IndVertr[t] =  -2.70086291822297 -0.224608973717344WerklHd[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116259&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116259&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
IndVertr[t] = -2.70086291822297 -0.224608973717344WerklHd[t] + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-2.700862918222971.375959-1.96290.0578820.028941
WerklHd-0.2246089737173440.028755-7.811100

\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) & -2.70086291822297 & 1.375959 & -1.9629 & 0.057882 & 0.028941 \tabularnewline
WerklHd & -0.224608973717344 & 0.028755 & -7.8111 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116259&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]-2.70086291822297[/C][C]1.375959[/C][C]-1.9629[/C][C]0.057882[/C][C]0.028941[/C][/ROW]
[ROW][C]WerklHd[/C][C]-0.224608973717344[/C][C]0.028755[/C][C]-7.8111[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116259&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116259&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)-2.700862918222971.375959-1.96290.0578820.028941
WerklHd-0.2246089737173440.028755-7.811100






Multiple Linear Regression - Regression Statistics
Multiple R0.80134653483524
R-squared0.642156268892446
Adjusted R-squared0.631631453271636
F-TEST (value)61.0135409519888
F-TEST (DF numerator)1
F-TEST (DF denominator)34
p-value4.31997659866568e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4.17604204093941
Sum Squared Residuals592.937122341575

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.80134653483524 \tabularnewline
R-squared & 0.642156268892446 \tabularnewline
Adjusted R-squared & 0.631631453271636 \tabularnewline
F-TEST (value) & 61.0135409519888 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 34 \tabularnewline
p-value & 4.31997659866568e-09 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 4.17604204093941 \tabularnewline
Sum Squared Residuals & 592.937122341575 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116259&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.80134653483524[/C][/ROW]
[ROW][C]R-squared[/C][C]0.642156268892446[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.631631453271636[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]61.0135409519888[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]34[/C][/ROW]
[ROW][C]p-value[/C][C]4.31997659866568e-09[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]4.17604204093941[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]592.937122341575[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116259&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116259&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 R0.80134653483524
R-squared0.642156268892446
Adjusted R-squared0.631631453271636
F-TEST (value)61.0135409519888
F-TEST (DF numerator)1
F-TEST (DF denominator)34
p-value4.31997659866568e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4.17604204093941
Sum Squared Residuals592.937122341575






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1-6-3.82390778680966-2.17609221319034
2-3-2.70086291822294-0.299137081777056
3-3-2.25164497078827-0.748355029211727
4-7-4.04851676052703-2.95148323947297
5-9-5.17156162911375-3.82843837088625
6-11-4.72234368167906-6.27765631832094
7-13-6.51921547141781-6.48078452858219
8-11-7.41765136628719-3.58234863371281
9-9-7.41765136628719-1.58234863371281
10-17-11.9098308406341-5.09016915936593
11-22-15.5035744201116-6.49642557988842
12-25-17.3004462098503-7.69955379014967
13-20-17.9742731310024-2.02572686899763
14-24-19.0973179995891-4.90268200041091
15-24-18.6481000521544-5.3518999478456
16-22-18.6481000521544-3.3518999478456
17-19-18.4234910784371-0.576508921562947
18-18-18.19888210471970.198882104719709
19-17-17.30044620985030.300446209850332
20-11-15.50357442011164.50357442011158
21-11-15.50357442011164.50357442011158
22-12-15.50357442011163.50357442011158
23-10-15.05435647267695.05435647267689
24-15-17.30044620985032.30044620985033
25-15-17.30044620985032.30044620985033
26-15-17.0758372361332.07583723613299
27-13-16.17740134126363.17740134126361
28-8-12.35904878806884.35904878806876
29-13-13.25748468293810.257484682938137
30-9-11.68522186691672.68522186691673
31-7-9.663741103460632.66374110346063
32-4-8.765305208591254.76530520859125
33-4-8.091478287439224.09147828743922
34-2-7.866869313721885.86686931372188
350-6.519215471417816.51921547141781
36-2-6.294606497700474.29460649770047

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & -6 & -3.82390778680966 & -2.17609221319034 \tabularnewline
2 & -3 & -2.70086291822294 & -0.299137081777056 \tabularnewline
3 & -3 & -2.25164497078827 & -0.748355029211727 \tabularnewline
4 & -7 & -4.04851676052703 & -2.95148323947297 \tabularnewline
5 & -9 & -5.17156162911375 & -3.82843837088625 \tabularnewline
6 & -11 & -4.72234368167906 & -6.27765631832094 \tabularnewline
7 & -13 & -6.51921547141781 & -6.48078452858219 \tabularnewline
8 & -11 & -7.41765136628719 & -3.58234863371281 \tabularnewline
9 & -9 & -7.41765136628719 & -1.58234863371281 \tabularnewline
10 & -17 & -11.9098308406341 & -5.09016915936593 \tabularnewline
11 & -22 & -15.5035744201116 & -6.49642557988842 \tabularnewline
12 & -25 & -17.3004462098503 & -7.69955379014967 \tabularnewline
13 & -20 & -17.9742731310024 & -2.02572686899763 \tabularnewline
14 & -24 & -19.0973179995891 & -4.90268200041091 \tabularnewline
15 & -24 & -18.6481000521544 & -5.3518999478456 \tabularnewline
16 & -22 & -18.6481000521544 & -3.3518999478456 \tabularnewline
17 & -19 & -18.4234910784371 & -0.576508921562947 \tabularnewline
18 & -18 & -18.1988821047197 & 0.198882104719709 \tabularnewline
19 & -17 & -17.3004462098503 & 0.300446209850332 \tabularnewline
20 & -11 & -15.5035744201116 & 4.50357442011158 \tabularnewline
21 & -11 & -15.5035744201116 & 4.50357442011158 \tabularnewline
22 & -12 & -15.5035744201116 & 3.50357442011158 \tabularnewline
23 & -10 & -15.0543564726769 & 5.05435647267689 \tabularnewline
24 & -15 & -17.3004462098503 & 2.30044620985033 \tabularnewline
25 & -15 & -17.3004462098503 & 2.30044620985033 \tabularnewline
26 & -15 & -17.075837236133 & 2.07583723613299 \tabularnewline
27 & -13 & -16.1774013412636 & 3.17740134126361 \tabularnewline
28 & -8 & -12.3590487880688 & 4.35904878806876 \tabularnewline
29 & -13 & -13.2574846829381 & 0.257484682938137 \tabularnewline
30 & -9 & -11.6852218669167 & 2.68522186691673 \tabularnewline
31 & -7 & -9.66374110346063 & 2.66374110346063 \tabularnewline
32 & -4 & -8.76530520859125 & 4.76530520859125 \tabularnewline
33 & -4 & -8.09147828743922 & 4.09147828743922 \tabularnewline
34 & -2 & -7.86686931372188 & 5.86686931372188 \tabularnewline
35 & 0 & -6.51921547141781 & 6.51921547141781 \tabularnewline
36 & -2 & -6.29460649770047 & 4.29460649770047 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116259&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]-6[/C][C]-3.82390778680966[/C][C]-2.17609221319034[/C][/ROW]
[ROW][C]2[/C][C]-3[/C][C]-2.70086291822294[/C][C]-0.299137081777056[/C][/ROW]
[ROW][C]3[/C][C]-3[/C][C]-2.25164497078827[/C][C]-0.748355029211727[/C][/ROW]
[ROW][C]4[/C][C]-7[/C][C]-4.04851676052703[/C][C]-2.95148323947297[/C][/ROW]
[ROW][C]5[/C][C]-9[/C][C]-5.17156162911375[/C][C]-3.82843837088625[/C][/ROW]
[ROW][C]6[/C][C]-11[/C][C]-4.72234368167906[/C][C]-6.27765631832094[/C][/ROW]
[ROW][C]7[/C][C]-13[/C][C]-6.51921547141781[/C][C]-6.48078452858219[/C][/ROW]
[ROW][C]8[/C][C]-11[/C][C]-7.41765136628719[/C][C]-3.58234863371281[/C][/ROW]
[ROW][C]9[/C][C]-9[/C][C]-7.41765136628719[/C][C]-1.58234863371281[/C][/ROW]
[ROW][C]10[/C][C]-17[/C][C]-11.9098308406341[/C][C]-5.09016915936593[/C][/ROW]
[ROW][C]11[/C][C]-22[/C][C]-15.5035744201116[/C][C]-6.49642557988842[/C][/ROW]
[ROW][C]12[/C][C]-25[/C][C]-17.3004462098503[/C][C]-7.69955379014967[/C][/ROW]
[ROW][C]13[/C][C]-20[/C][C]-17.9742731310024[/C][C]-2.02572686899763[/C][/ROW]
[ROW][C]14[/C][C]-24[/C][C]-19.0973179995891[/C][C]-4.90268200041091[/C][/ROW]
[ROW][C]15[/C][C]-24[/C][C]-18.6481000521544[/C][C]-5.3518999478456[/C][/ROW]
[ROW][C]16[/C][C]-22[/C][C]-18.6481000521544[/C][C]-3.3518999478456[/C][/ROW]
[ROW][C]17[/C][C]-19[/C][C]-18.4234910784371[/C][C]-0.576508921562947[/C][/ROW]
[ROW][C]18[/C][C]-18[/C][C]-18.1988821047197[/C][C]0.198882104719709[/C][/ROW]
[ROW][C]19[/C][C]-17[/C][C]-17.3004462098503[/C][C]0.300446209850332[/C][/ROW]
[ROW][C]20[/C][C]-11[/C][C]-15.5035744201116[/C][C]4.50357442011158[/C][/ROW]
[ROW][C]21[/C][C]-11[/C][C]-15.5035744201116[/C][C]4.50357442011158[/C][/ROW]
[ROW][C]22[/C][C]-12[/C][C]-15.5035744201116[/C][C]3.50357442011158[/C][/ROW]
[ROW][C]23[/C][C]-10[/C][C]-15.0543564726769[/C][C]5.05435647267689[/C][/ROW]
[ROW][C]24[/C][C]-15[/C][C]-17.3004462098503[/C][C]2.30044620985033[/C][/ROW]
[ROW][C]25[/C][C]-15[/C][C]-17.3004462098503[/C][C]2.30044620985033[/C][/ROW]
[ROW][C]26[/C][C]-15[/C][C]-17.075837236133[/C][C]2.07583723613299[/C][/ROW]
[ROW][C]27[/C][C]-13[/C][C]-16.1774013412636[/C][C]3.17740134126361[/C][/ROW]
[ROW][C]28[/C][C]-8[/C][C]-12.3590487880688[/C][C]4.35904878806876[/C][/ROW]
[ROW][C]29[/C][C]-13[/C][C]-13.2574846829381[/C][C]0.257484682938137[/C][/ROW]
[ROW][C]30[/C][C]-9[/C][C]-11.6852218669167[/C][C]2.68522186691673[/C][/ROW]
[ROW][C]31[/C][C]-7[/C][C]-9.66374110346063[/C][C]2.66374110346063[/C][/ROW]
[ROW][C]32[/C][C]-4[/C][C]-8.76530520859125[/C][C]4.76530520859125[/C][/ROW]
[ROW][C]33[/C][C]-4[/C][C]-8.09147828743922[/C][C]4.09147828743922[/C][/ROW]
[ROW][C]34[/C][C]-2[/C][C]-7.86686931372188[/C][C]5.86686931372188[/C][/ROW]
[ROW][C]35[/C][C]0[/C][C]-6.51921547141781[/C][C]6.51921547141781[/C][/ROW]
[ROW][C]36[/C][C]-2[/C][C]-6.29460649770047[/C][C]4.29460649770047[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116259&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116259&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
1-6-3.82390778680966-2.17609221319034
2-3-2.70086291822294-0.299137081777056
3-3-2.25164497078827-0.748355029211727
4-7-4.04851676052703-2.95148323947297
5-9-5.17156162911375-3.82843837088625
6-11-4.72234368167906-6.27765631832094
7-13-6.51921547141781-6.48078452858219
8-11-7.41765136628719-3.58234863371281
9-9-7.41765136628719-1.58234863371281
10-17-11.9098308406341-5.09016915936593
11-22-15.5035744201116-6.49642557988842
12-25-17.3004462098503-7.69955379014967
13-20-17.9742731310024-2.02572686899763
14-24-19.0973179995891-4.90268200041091
15-24-18.6481000521544-5.3518999478456
16-22-18.6481000521544-3.3518999478456
17-19-18.4234910784371-0.576508921562947
18-18-18.19888210471970.198882104719709
19-17-17.30044620985030.300446209850332
20-11-15.50357442011164.50357442011158
21-11-15.50357442011164.50357442011158
22-12-15.50357442011163.50357442011158
23-10-15.05435647267695.05435647267689
24-15-17.30044620985032.30044620985033
25-15-17.30044620985032.30044620985033
26-15-17.0758372361332.07583723613299
27-13-16.17740134126363.17740134126361
28-8-12.35904878806884.35904878806876
29-13-13.25748468293810.257484682938137
30-9-11.68522186691672.68522186691673
31-7-9.663741103460632.66374110346063
32-4-8.765305208591254.76530520859125
33-4-8.091478287439224.09147828743922
34-2-7.866869313721885.86686931372188
350-6.519215471417816.51921547141781
36-2-6.294606497700474.29460649770047






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.001919412404734230.003838824809468470.998080587595266
60.01716148499575420.03432296999150830.982838515004246
70.007672698675521720.01534539735104340.992327301324478
80.03536733393481690.07073466786963370.964632666065183
90.08358454544715410.1671690908943080.916415454552846
100.08706825178382630.1741365035676530.912931748216174
110.09694732724175540.1938946544835110.903052672758245
120.1674712996325010.3349425992650020.8325287003675
130.4004050035491260.8008100070982520.599594996450874
140.4555054930922560.9110109861845110.544494506907744
150.6841709974612820.6316580050774360.315829002538718
160.8738282218859880.2523435562280240.126171778114012
170.9521791411317930.09564171773641350.0478208588682068
180.9781514136969310.04369717260613830.0218485863030691
190.9901351834752380.01972963304952410.00986481652476204
200.9981184190373030.003763161925394090.00188158096269704
210.999263327629670.001473344740661640.000736672370330822
220.9990978365178830.001804326964234610.000902163482117303
230.9996875604789130.0006248790421734550.000312439521086727
240.9992271006554160.001545798689168250.000772899344584125
250.9981378042021740.003724391595651510.00186219579782576
260.9953870201386380.009225959722723820.00461297986136191
270.99561623439360.008767531212798460.00438376560639923
280.9981727409614980.003654518077003370.00182725903850168
290.9947338472167180.01053230556656450.00526615278328223
300.9819649770695070.03607004586098650.0180350229304932
310.962565965366520.07486806926695820.0374340346334791

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
5 & 0.00191941240473423 & 0.00383882480946847 & 0.998080587595266 \tabularnewline
6 & 0.0171614849957542 & 0.0343229699915083 & 0.982838515004246 \tabularnewline
7 & 0.00767269867552172 & 0.0153453973510434 & 0.992327301324478 \tabularnewline
8 & 0.0353673339348169 & 0.0707346678696337 & 0.964632666065183 \tabularnewline
9 & 0.0835845454471541 & 0.167169090894308 & 0.916415454552846 \tabularnewline
10 & 0.0870682517838263 & 0.174136503567653 & 0.912931748216174 \tabularnewline
11 & 0.0969473272417554 & 0.193894654483511 & 0.903052672758245 \tabularnewline
12 & 0.167471299632501 & 0.334942599265002 & 0.8325287003675 \tabularnewline
13 & 0.400405003549126 & 0.800810007098252 & 0.599594996450874 \tabularnewline
14 & 0.455505493092256 & 0.911010986184511 & 0.544494506907744 \tabularnewline
15 & 0.684170997461282 & 0.631658005077436 & 0.315829002538718 \tabularnewline
16 & 0.873828221885988 & 0.252343556228024 & 0.126171778114012 \tabularnewline
17 & 0.952179141131793 & 0.0956417177364135 & 0.0478208588682068 \tabularnewline
18 & 0.978151413696931 & 0.0436971726061383 & 0.0218485863030691 \tabularnewline
19 & 0.990135183475238 & 0.0197296330495241 & 0.00986481652476204 \tabularnewline
20 & 0.998118419037303 & 0.00376316192539409 & 0.00188158096269704 \tabularnewline
21 & 0.99926332762967 & 0.00147334474066164 & 0.000736672370330822 \tabularnewline
22 & 0.999097836517883 & 0.00180432696423461 & 0.000902163482117303 \tabularnewline
23 & 0.999687560478913 & 0.000624879042173455 & 0.000312439521086727 \tabularnewline
24 & 0.999227100655416 & 0.00154579868916825 & 0.000772899344584125 \tabularnewline
25 & 0.998137804202174 & 0.00372439159565151 & 0.00186219579782576 \tabularnewline
26 & 0.995387020138638 & 0.00922595972272382 & 0.00461297986136191 \tabularnewline
27 & 0.9956162343936 & 0.00876753121279846 & 0.00438376560639923 \tabularnewline
28 & 0.998172740961498 & 0.00365451807700337 & 0.00182725903850168 \tabularnewline
29 & 0.994733847216718 & 0.0105323055665645 & 0.00526615278328223 \tabularnewline
30 & 0.981964977069507 & 0.0360700458609865 & 0.0180350229304932 \tabularnewline
31 & 0.96256596536652 & 0.0748680692669582 & 0.0374340346334791 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116259&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]5[/C][C]0.00191941240473423[/C][C]0.00383882480946847[/C][C]0.998080587595266[/C][/ROW]
[ROW][C]6[/C][C]0.0171614849957542[/C][C]0.0343229699915083[/C][C]0.982838515004246[/C][/ROW]
[ROW][C]7[/C][C]0.00767269867552172[/C][C]0.0153453973510434[/C][C]0.992327301324478[/C][/ROW]
[ROW][C]8[/C][C]0.0353673339348169[/C][C]0.0707346678696337[/C][C]0.964632666065183[/C][/ROW]
[ROW][C]9[/C][C]0.0835845454471541[/C][C]0.167169090894308[/C][C]0.916415454552846[/C][/ROW]
[ROW][C]10[/C][C]0.0870682517838263[/C][C]0.174136503567653[/C][C]0.912931748216174[/C][/ROW]
[ROW][C]11[/C][C]0.0969473272417554[/C][C]0.193894654483511[/C][C]0.903052672758245[/C][/ROW]
[ROW][C]12[/C][C]0.167471299632501[/C][C]0.334942599265002[/C][C]0.8325287003675[/C][/ROW]
[ROW][C]13[/C][C]0.400405003549126[/C][C]0.800810007098252[/C][C]0.599594996450874[/C][/ROW]
[ROW][C]14[/C][C]0.455505493092256[/C][C]0.911010986184511[/C][C]0.544494506907744[/C][/ROW]
[ROW][C]15[/C][C]0.684170997461282[/C][C]0.631658005077436[/C][C]0.315829002538718[/C][/ROW]
[ROW][C]16[/C][C]0.873828221885988[/C][C]0.252343556228024[/C][C]0.126171778114012[/C][/ROW]
[ROW][C]17[/C][C]0.952179141131793[/C][C]0.0956417177364135[/C][C]0.0478208588682068[/C][/ROW]
[ROW][C]18[/C][C]0.978151413696931[/C][C]0.0436971726061383[/C][C]0.0218485863030691[/C][/ROW]
[ROW][C]19[/C][C]0.990135183475238[/C][C]0.0197296330495241[/C][C]0.00986481652476204[/C][/ROW]
[ROW][C]20[/C][C]0.998118419037303[/C][C]0.00376316192539409[/C][C]0.00188158096269704[/C][/ROW]
[ROW][C]21[/C][C]0.99926332762967[/C][C]0.00147334474066164[/C][C]0.000736672370330822[/C][/ROW]
[ROW][C]22[/C][C]0.999097836517883[/C][C]0.00180432696423461[/C][C]0.000902163482117303[/C][/ROW]
[ROW][C]23[/C][C]0.999687560478913[/C][C]0.000624879042173455[/C][C]0.000312439521086727[/C][/ROW]
[ROW][C]24[/C][C]0.999227100655416[/C][C]0.00154579868916825[/C][C]0.000772899344584125[/C][/ROW]
[ROW][C]25[/C][C]0.998137804202174[/C][C]0.00372439159565151[/C][C]0.00186219579782576[/C][/ROW]
[ROW][C]26[/C][C]0.995387020138638[/C][C]0.00922595972272382[/C][C]0.00461297986136191[/C][/ROW]
[ROW][C]27[/C][C]0.9956162343936[/C][C]0.00876753121279846[/C][C]0.00438376560639923[/C][/ROW]
[ROW][C]28[/C][C]0.998172740961498[/C][C]0.00365451807700337[/C][C]0.00182725903850168[/C][/ROW]
[ROW][C]29[/C][C]0.994733847216718[/C][C]0.0105323055665645[/C][C]0.00526615278328223[/C][/ROW]
[ROW][C]30[/C][C]0.981964977069507[/C][C]0.0360700458609865[/C][C]0.0180350229304932[/C][/ROW]
[ROW][C]31[/C][C]0.96256596536652[/C][C]0.0748680692669582[/C][C]0.0374340346334791[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116259&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116259&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
50.001919412404734230.003838824809468470.998080587595266
60.01716148499575420.03432296999150830.982838515004246
70.007672698675521720.01534539735104340.992327301324478
80.03536733393481690.07073466786963370.964632666065183
90.08358454544715410.1671690908943080.916415454552846
100.08706825178382630.1741365035676530.912931748216174
110.09694732724175540.1938946544835110.903052672758245
120.1674712996325010.3349425992650020.8325287003675
130.4004050035491260.8008100070982520.599594996450874
140.4555054930922560.9110109861845110.544494506907744
150.6841709974612820.6316580050774360.315829002538718
160.8738282218859880.2523435562280240.126171778114012
170.9521791411317930.09564171773641350.0478208588682068
180.9781514136969310.04369717260613830.0218485863030691
190.9901351834752380.01972963304952410.00986481652476204
200.9981184190373030.003763161925394090.00188158096269704
210.999263327629670.001473344740661640.000736672370330822
220.9990978365178830.001804326964234610.000902163482117303
230.9996875604789130.0006248790421734550.000312439521086727
240.9992271006554160.001545798689168250.000772899344584125
250.9981378042021740.003724391595651510.00186219579782576
260.9953870201386380.009225959722723820.00461297986136191
270.99561623439360.008767531212798460.00438376560639923
280.9981727409614980.003654518077003370.00182725903850168
290.9947338472167180.01053230556656450.00526615278328223
300.9819649770695070.03607004586098650.0180350229304932
310.962565965366520.07486806926695820.0374340346334791






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level100.370370370370370NOK
5% type I error level160.592592592592593NOK
10% type I error level190.703703703703704NOK

\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 & 10 & 0.370370370370370 & NOK \tabularnewline
5% type I error level & 16 & 0.592592592592593 & NOK \tabularnewline
10% type I error level & 19 & 0.703703703703704 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116259&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]10[/C][C]0.370370370370370[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]16[/C][C]0.592592592592593[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]19[/C][C]0.703703703703704[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116259&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116259&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 level100.370370370370370NOK
5% type I error level160.592592592592593NOK
10% type I error level190.703703703703704NOK


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):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}