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Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 09:50:02 -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/20/t12587358635mtsxyabyt4dqe0.htm/, Retrieved Thu, 28 Mar 2024 22:41:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58324, Retrieved Thu, 28 Mar 2024 22:41:03 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact127
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 14:06:21] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-11-20 16:50:02] [3e9f70e60513fc8919624add68d96eca] [Current]
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Dataseries X:
8	5560
8.1	3922
7.7	3759
7.5	4138
7.6	4634
7.8	3996
7.8	4308
7.8	4143
7.5	4429
7.5	5219
7.1	4929
7.5	5755
7.5	5592
7.6	4163
7.7	4962
7.7	5208
7.9	4755
8.1	4491
8.2	5732
8.2	5731
8.2	5040
7.9	6102
7.3	4904
6.9	5369
6.7	5578
6.7	4619
6.9	4731
7	5011
7.1	5299
7.2	4146
7.1	4625
6.9	4736
7	4219
6.8	5116
6.4	4205
6.7	4121
6.6	5103
6.4	4300
6.3	4578
6.2	3809
6.5	5526
6.8	4247
6.8	3830
6.4	4394
6.1	4826
5.8	4409
6.1	4569
7.2	4106
7.3	4794
6.9	3914
6.1	3793
5.8	4405
6.2	4022
7.1	4100
7.7	4788
7.9	3163
7.7	3585
7.4	3903
7.5	4178
8	3863
8.1	4187




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=58324&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=58324&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58324&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 8.55056685635983 -0.000128679428252901X[t] + 0.0738198554733517M1[t] -0.371626817583526M2[t] -0.529082118656772M3[t] -0.590577953777158M4[t] -0.308473981755963M5[t] -0.0330163030212729M6[t] + 0.165507164044993M7[t] + 0.0760396380719248M8[t] -0.0464566797393355M9[t] -0.179002860352318M10[t] -0.410294417357079M11[t] -0.0192537224129794t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  8.55056685635983 -0.000128679428252901X[t] +  0.0738198554733517M1[t] -0.371626817583526M2[t] -0.529082118656772M3[t] -0.590577953777158M4[t] -0.308473981755963M5[t] -0.0330163030212729M6[t] +  0.165507164044993M7[t] +  0.0760396380719248M8[t] -0.0464566797393355M9[t] -0.179002860352318M10[t] -0.410294417357079M11[t] -0.0192537224129794t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58324&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  8.55056685635983 -0.000128679428252901X[t] +  0.0738198554733517M1[t] -0.371626817583526M2[t] -0.529082118656772M3[t] -0.590577953777158M4[t] -0.308473981755963M5[t] -0.0330163030212729M6[t] +  0.165507164044993M7[t] +  0.0760396380719248M8[t] -0.0464566797393355M9[t] -0.179002860352318M10[t] -0.410294417357079M11[t] -0.0192537224129794t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58324&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58324&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
Y[t] = + 8.55056685635983 -0.000128679428252901X[t] + 0.0738198554733517M1[t] -0.371626817583526M2[t] -0.529082118656772M3[t] -0.590577953777158M4[t] -0.308473981755963M5[t] -0.0330163030212729M6[t] + 0.165507164044993M7[t] + 0.0760396380719248M8[t] -0.0464566797393355M9[t] -0.179002860352318M10[t] -0.410294417357079M11[t] -0.0192537224129794t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)8.550566856359830.890649.600500
X-0.0001286794282529010.00016-0.80490.4249480.212474
M10.07381985547335170.3775360.19550.845820.42291
M2-0.3716268175835260.402273-0.92380.36030.18015
M3-0.5290821186567720.395282-1.33850.1871750.093588
M4-0.5905779537771580.39124-1.50950.1378650.068932
M5-0.3084739817559630.389053-0.79290.4318290.215915
M6-0.03301630302127290.397889-0.0830.9342210.46711
M70.1655071640449930.3882550.42630.6718460.335923
M80.07603963807192480.3903050.19480.8463730.423186
M9-0.04645667973933550.390087-0.11910.9057090.452855
M10-0.1790028603523180.39007-0.45890.6484210.324211
M11-0.4102944173570790.387826-1.05790.2954930.147747
t-0.01925372241297940.005158-3.73250.0005110.000256

\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) & 8.55056685635983 & 0.89064 & 9.6005 & 0 & 0 \tabularnewline
X & -0.000128679428252901 & 0.00016 & -0.8049 & 0.424948 & 0.212474 \tabularnewline
M1 & 0.0738198554733517 & 0.377536 & 0.1955 & 0.84582 & 0.42291 \tabularnewline
M2 & -0.371626817583526 & 0.402273 & -0.9238 & 0.3603 & 0.18015 \tabularnewline
M3 & -0.529082118656772 & 0.395282 & -1.3385 & 0.187175 & 0.093588 \tabularnewline
M4 & -0.590577953777158 & 0.39124 & -1.5095 & 0.137865 & 0.068932 \tabularnewline
M5 & -0.308473981755963 & 0.389053 & -0.7929 & 0.431829 & 0.215915 \tabularnewline
M6 & -0.0330163030212729 & 0.397889 & -0.083 & 0.934221 & 0.46711 \tabularnewline
M7 & 0.165507164044993 & 0.388255 & 0.4263 & 0.671846 & 0.335923 \tabularnewline
M8 & 0.0760396380719248 & 0.390305 & 0.1948 & 0.846373 & 0.423186 \tabularnewline
M9 & -0.0464566797393355 & 0.390087 & -0.1191 & 0.905709 & 0.452855 \tabularnewline
M10 & -0.179002860352318 & 0.39007 & -0.4589 & 0.648421 & 0.324211 \tabularnewline
M11 & -0.410294417357079 & 0.387826 & -1.0579 & 0.295493 & 0.147747 \tabularnewline
t & -0.0192537224129794 & 0.005158 & -3.7325 & 0.000511 & 0.000256 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58324&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]8.55056685635983[/C][C]0.89064[/C][C]9.6005[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]-0.000128679428252901[/C][C]0.00016[/C][C]-0.8049[/C][C]0.424948[/C][C]0.212474[/C][/ROW]
[ROW][C]M1[/C][C]0.0738198554733517[/C][C]0.377536[/C][C]0.1955[/C][C]0.84582[/C][C]0.42291[/C][/ROW]
[ROW][C]M2[/C][C]-0.371626817583526[/C][C]0.402273[/C][C]-0.9238[/C][C]0.3603[/C][C]0.18015[/C][/ROW]
[ROW][C]M3[/C][C]-0.529082118656772[/C][C]0.395282[/C][C]-1.3385[/C][C]0.187175[/C][C]0.093588[/C][/ROW]
[ROW][C]M4[/C][C]-0.590577953777158[/C][C]0.39124[/C][C]-1.5095[/C][C]0.137865[/C][C]0.068932[/C][/ROW]
[ROW][C]M5[/C][C]-0.308473981755963[/C][C]0.389053[/C][C]-0.7929[/C][C]0.431829[/C][C]0.215915[/C][/ROW]
[ROW][C]M6[/C][C]-0.0330163030212729[/C][C]0.397889[/C][C]-0.083[/C][C]0.934221[/C][C]0.46711[/C][/ROW]
[ROW][C]M7[/C][C]0.165507164044993[/C][C]0.388255[/C][C]0.4263[/C][C]0.671846[/C][C]0.335923[/C][/ROW]
[ROW][C]M8[/C][C]0.0760396380719248[/C][C]0.390305[/C][C]0.1948[/C][C]0.846373[/C][C]0.423186[/C][/ROW]
[ROW][C]M9[/C][C]-0.0464566797393355[/C][C]0.390087[/C][C]-0.1191[/C][C]0.905709[/C][C]0.452855[/C][/ROW]
[ROW][C]M10[/C][C]-0.179002860352318[/C][C]0.39007[/C][C]-0.4589[/C][C]0.648421[/C][C]0.324211[/C][/ROW]
[ROW][C]M11[/C][C]-0.410294417357079[/C][C]0.387826[/C][C]-1.0579[/C][C]0.295493[/C][C]0.147747[/C][/ROW]
[ROW][C]t[/C][C]-0.0192537224129794[/C][C]0.005158[/C][C]-3.7325[/C][C]0.000511[/C][C]0.000256[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58324&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58324&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)8.550566856359830.890649.600500
X-0.0001286794282529010.00016-0.80490.4249480.212474
M10.07381985547335170.3775360.19550.845820.42291
M2-0.3716268175835260.402273-0.92380.36030.18015
M3-0.5290821186567720.395282-1.33850.1871750.093588
M4-0.5905779537771580.39124-1.50950.1378650.068932
M5-0.3084739817559630.389053-0.79290.4318290.215915
M6-0.03301630302127290.397889-0.0830.9342210.46711
M70.1655071640449930.3882550.42630.6718460.335923
M80.07603963807192480.3903050.19480.8463730.423186
M9-0.04645667973933550.390087-0.11910.9057090.452855
M10-0.1790028603523180.39007-0.45890.6484210.324211
M11-0.4102944173570790.387826-1.05790.2954930.147747
t-0.01925372241297940.005158-3.73250.0005110.000256







Multiple Linear Regression - Regression Statistics
Multiple R0.572985276305044
R-squared0.328312126862368
Adjusted R-squared0.142526119398767
F-TEST (value)1.76715206567261
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value0.0776405512042548
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.612630271023394
Sum Squared Residuals17.6398449017873

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.572985276305044 \tabularnewline
R-squared & 0.328312126862368 \tabularnewline
Adjusted R-squared & 0.142526119398767 \tabularnewline
F-TEST (value) & 1.76715206567261 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 0.0776405512042548 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.612630271023394 \tabularnewline
Sum Squared Residuals & 17.6398449017873 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58324&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.572985276305044[/C][/ROW]
[ROW][C]R-squared[/C][C]0.328312126862368[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.142526119398767[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1.76715206567261[/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]0.0776405512042548[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.612630271023394[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]17.6398449017873[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58324&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58324&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 R0.572985276305044
R-squared0.328312126862368
Adjusted R-squared0.142526119398767
F-TEST (value)1.76715206567261
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value0.0776405512042548
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.612630271023394
Sum Squared Residuals17.6398449017873







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
187.889675368334060.110324631665942
28.17.635751876342460.464248123657535
37.77.480017599661460.219982400338537
47.57.350498538820250.149501461179753
57.67.549523792015020.0504762079849763
67.87.88782522356209-0.087825223562086
77.88.02694698660047-0.226946986600467
87.87.93945784387615-0.139457843876148
97.57.76090548717158-0.260905487171578
107.57.50744883582582-0.0074488358258244
117.17.29422059060143-0.194220590601427
127.57.57897207780863-0.0789720778086287
137.57.65451295767422-0.154512957674223
147.67.373695465177760.226304534822237
157.77.094171578517470.605828421482531
167.76.981766881633890.71823311836611
177.97.302908912240670.59709108775933
188.17.593084237621150.506915762378853
198.27.612662811812580.587337188187416
208.27.504070242854790.695929757145211
218.27.45123768755330.748762312446696
227.97.162780231722760.73721976827724
237.37.0663929073520.233607092648004
246.97.3975976681585-0.497597668158496
256.77.42526980071401-0.725269800714011
266.77.08397297693869-0.383972976938687
276.96.892851857488140.00714814251186351
2876.776072060043960.223927939956041
297.17.001862634315340.0981373656846603
307.27.40643397141265-0.206433971412645
317.17.5240662699328-0.424066269932792
326.97.40106160501067-0.501061605010672
3377.32583882919318-0.325838829193182
346.87.05861347902437-0.258613479024368
356.46.92529515874502-0.525295158745021
366.77.32714492566236-0.627144925662364
376.67.25534786017839-0.655347860178387
386.46.89397704559561-0.493977045595610
396.36.68149514105508-0.381495141055078
406.26.6997000638482-0.499700063848193
416.56.74160773514618-0.241607735146178
426.87.16239268020335-0.362392680203350
436.87.3953217464381-0.595321746438095
446.47.21402530051741-0.814025300517411
456.17.01668574728792-0.91668574728792
465.86.91854516584342-1.11854516584342
476.16.64741117790521-0.547411177905212
487.27.09803044813040.101969551869596
497.37.064065134552780.235934865447219
506.96.712602635945480.187397364054524
516.16.55146382327785-0.451463823277853
525.86.39196245565371-0.591962455653711
536.26.70409692628279-0.504096926282789
547.16.950263887200770.149736112799227
557.77.041002185216060.658997814783937
567.97.141385007740980.75861499225902
577.76.945332248794020.754667751205984
587.46.752612287583630.647387712416369
597.56.466680165396341.03331983460366
6086.89825488024011.10174511975989
618.16.911128878546541.18887112145346

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8 & 7.88967536833406 & 0.110324631665942 \tabularnewline
2 & 8.1 & 7.63575187634246 & 0.464248123657535 \tabularnewline
3 & 7.7 & 7.48001759966146 & 0.219982400338537 \tabularnewline
4 & 7.5 & 7.35049853882025 & 0.149501461179753 \tabularnewline
5 & 7.6 & 7.54952379201502 & 0.0504762079849763 \tabularnewline
6 & 7.8 & 7.88782522356209 & -0.087825223562086 \tabularnewline
7 & 7.8 & 8.02694698660047 & -0.226946986600467 \tabularnewline
8 & 7.8 & 7.93945784387615 & -0.139457843876148 \tabularnewline
9 & 7.5 & 7.76090548717158 & -0.260905487171578 \tabularnewline
10 & 7.5 & 7.50744883582582 & -0.0074488358258244 \tabularnewline
11 & 7.1 & 7.29422059060143 & -0.194220590601427 \tabularnewline
12 & 7.5 & 7.57897207780863 & -0.0789720778086287 \tabularnewline
13 & 7.5 & 7.65451295767422 & -0.154512957674223 \tabularnewline
14 & 7.6 & 7.37369546517776 & 0.226304534822237 \tabularnewline
15 & 7.7 & 7.09417157851747 & 0.605828421482531 \tabularnewline
16 & 7.7 & 6.98176688163389 & 0.71823311836611 \tabularnewline
17 & 7.9 & 7.30290891224067 & 0.59709108775933 \tabularnewline
18 & 8.1 & 7.59308423762115 & 0.506915762378853 \tabularnewline
19 & 8.2 & 7.61266281181258 & 0.587337188187416 \tabularnewline
20 & 8.2 & 7.50407024285479 & 0.695929757145211 \tabularnewline
21 & 8.2 & 7.4512376875533 & 0.748762312446696 \tabularnewline
22 & 7.9 & 7.16278023172276 & 0.73721976827724 \tabularnewline
23 & 7.3 & 7.066392907352 & 0.233607092648004 \tabularnewline
24 & 6.9 & 7.3975976681585 & -0.497597668158496 \tabularnewline
25 & 6.7 & 7.42526980071401 & -0.725269800714011 \tabularnewline
26 & 6.7 & 7.08397297693869 & -0.383972976938687 \tabularnewline
27 & 6.9 & 6.89285185748814 & 0.00714814251186351 \tabularnewline
28 & 7 & 6.77607206004396 & 0.223927939956041 \tabularnewline
29 & 7.1 & 7.00186263431534 & 0.0981373656846603 \tabularnewline
30 & 7.2 & 7.40643397141265 & -0.206433971412645 \tabularnewline
31 & 7.1 & 7.5240662699328 & -0.424066269932792 \tabularnewline
32 & 6.9 & 7.40106160501067 & -0.501061605010672 \tabularnewline
33 & 7 & 7.32583882919318 & -0.325838829193182 \tabularnewline
34 & 6.8 & 7.05861347902437 & -0.258613479024368 \tabularnewline
35 & 6.4 & 6.92529515874502 & -0.525295158745021 \tabularnewline
36 & 6.7 & 7.32714492566236 & -0.627144925662364 \tabularnewline
37 & 6.6 & 7.25534786017839 & -0.655347860178387 \tabularnewline
38 & 6.4 & 6.89397704559561 & -0.493977045595610 \tabularnewline
39 & 6.3 & 6.68149514105508 & -0.381495141055078 \tabularnewline
40 & 6.2 & 6.6997000638482 & -0.499700063848193 \tabularnewline
41 & 6.5 & 6.74160773514618 & -0.241607735146178 \tabularnewline
42 & 6.8 & 7.16239268020335 & -0.362392680203350 \tabularnewline
43 & 6.8 & 7.3953217464381 & -0.595321746438095 \tabularnewline
44 & 6.4 & 7.21402530051741 & -0.814025300517411 \tabularnewline
45 & 6.1 & 7.01668574728792 & -0.91668574728792 \tabularnewline
46 & 5.8 & 6.91854516584342 & -1.11854516584342 \tabularnewline
47 & 6.1 & 6.64741117790521 & -0.547411177905212 \tabularnewline
48 & 7.2 & 7.0980304481304 & 0.101969551869596 \tabularnewline
49 & 7.3 & 7.06406513455278 & 0.235934865447219 \tabularnewline
50 & 6.9 & 6.71260263594548 & 0.187397364054524 \tabularnewline
51 & 6.1 & 6.55146382327785 & -0.451463823277853 \tabularnewline
52 & 5.8 & 6.39196245565371 & -0.591962455653711 \tabularnewline
53 & 6.2 & 6.70409692628279 & -0.504096926282789 \tabularnewline
54 & 7.1 & 6.95026388720077 & 0.149736112799227 \tabularnewline
55 & 7.7 & 7.04100218521606 & 0.658997814783937 \tabularnewline
56 & 7.9 & 7.14138500774098 & 0.75861499225902 \tabularnewline
57 & 7.7 & 6.94533224879402 & 0.754667751205984 \tabularnewline
58 & 7.4 & 6.75261228758363 & 0.647387712416369 \tabularnewline
59 & 7.5 & 6.46668016539634 & 1.03331983460366 \tabularnewline
60 & 8 & 6.8982548802401 & 1.10174511975989 \tabularnewline
61 & 8.1 & 6.91112887854654 & 1.18887112145346 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58324&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]8[/C][C]7.88967536833406[/C][C]0.110324631665942[/C][/ROW]
[ROW][C]2[/C][C]8.1[/C][C]7.63575187634246[/C][C]0.464248123657535[/C][/ROW]
[ROW][C]3[/C][C]7.7[/C][C]7.48001759966146[/C][C]0.219982400338537[/C][/ROW]
[ROW][C]4[/C][C]7.5[/C][C]7.35049853882025[/C][C]0.149501461179753[/C][/ROW]
[ROW][C]5[/C][C]7.6[/C][C]7.54952379201502[/C][C]0.0504762079849763[/C][/ROW]
[ROW][C]6[/C][C]7.8[/C][C]7.88782522356209[/C][C]-0.087825223562086[/C][/ROW]
[ROW][C]7[/C][C]7.8[/C][C]8.02694698660047[/C][C]-0.226946986600467[/C][/ROW]
[ROW][C]8[/C][C]7.8[/C][C]7.93945784387615[/C][C]-0.139457843876148[/C][/ROW]
[ROW][C]9[/C][C]7.5[/C][C]7.76090548717158[/C][C]-0.260905487171578[/C][/ROW]
[ROW][C]10[/C][C]7.5[/C][C]7.50744883582582[/C][C]-0.0074488358258244[/C][/ROW]
[ROW][C]11[/C][C]7.1[/C][C]7.29422059060143[/C][C]-0.194220590601427[/C][/ROW]
[ROW][C]12[/C][C]7.5[/C][C]7.57897207780863[/C][C]-0.0789720778086287[/C][/ROW]
[ROW][C]13[/C][C]7.5[/C][C]7.65451295767422[/C][C]-0.154512957674223[/C][/ROW]
[ROW][C]14[/C][C]7.6[/C][C]7.37369546517776[/C][C]0.226304534822237[/C][/ROW]
[ROW][C]15[/C][C]7.7[/C][C]7.09417157851747[/C][C]0.605828421482531[/C][/ROW]
[ROW][C]16[/C][C]7.7[/C][C]6.98176688163389[/C][C]0.71823311836611[/C][/ROW]
[ROW][C]17[/C][C]7.9[/C][C]7.30290891224067[/C][C]0.59709108775933[/C][/ROW]
[ROW][C]18[/C][C]8.1[/C][C]7.59308423762115[/C][C]0.506915762378853[/C][/ROW]
[ROW][C]19[/C][C]8.2[/C][C]7.61266281181258[/C][C]0.587337188187416[/C][/ROW]
[ROW][C]20[/C][C]8.2[/C][C]7.50407024285479[/C][C]0.695929757145211[/C][/ROW]
[ROW][C]21[/C][C]8.2[/C][C]7.4512376875533[/C][C]0.748762312446696[/C][/ROW]
[ROW][C]22[/C][C]7.9[/C][C]7.16278023172276[/C][C]0.73721976827724[/C][/ROW]
[ROW][C]23[/C][C]7.3[/C][C]7.066392907352[/C][C]0.233607092648004[/C][/ROW]
[ROW][C]24[/C][C]6.9[/C][C]7.3975976681585[/C][C]-0.497597668158496[/C][/ROW]
[ROW][C]25[/C][C]6.7[/C][C]7.42526980071401[/C][C]-0.725269800714011[/C][/ROW]
[ROW][C]26[/C][C]6.7[/C][C]7.08397297693869[/C][C]-0.383972976938687[/C][/ROW]
[ROW][C]27[/C][C]6.9[/C][C]6.89285185748814[/C][C]0.00714814251186351[/C][/ROW]
[ROW][C]28[/C][C]7[/C][C]6.77607206004396[/C][C]0.223927939956041[/C][/ROW]
[ROW][C]29[/C][C]7.1[/C][C]7.00186263431534[/C][C]0.0981373656846603[/C][/ROW]
[ROW][C]30[/C][C]7.2[/C][C]7.40643397141265[/C][C]-0.206433971412645[/C][/ROW]
[ROW][C]31[/C][C]7.1[/C][C]7.5240662699328[/C][C]-0.424066269932792[/C][/ROW]
[ROW][C]32[/C][C]6.9[/C][C]7.40106160501067[/C][C]-0.501061605010672[/C][/ROW]
[ROW][C]33[/C][C]7[/C][C]7.32583882919318[/C][C]-0.325838829193182[/C][/ROW]
[ROW][C]34[/C][C]6.8[/C][C]7.05861347902437[/C][C]-0.258613479024368[/C][/ROW]
[ROW][C]35[/C][C]6.4[/C][C]6.92529515874502[/C][C]-0.525295158745021[/C][/ROW]
[ROW][C]36[/C][C]6.7[/C][C]7.32714492566236[/C][C]-0.627144925662364[/C][/ROW]
[ROW][C]37[/C][C]6.6[/C][C]7.25534786017839[/C][C]-0.655347860178387[/C][/ROW]
[ROW][C]38[/C][C]6.4[/C][C]6.89397704559561[/C][C]-0.493977045595610[/C][/ROW]
[ROW][C]39[/C][C]6.3[/C][C]6.68149514105508[/C][C]-0.381495141055078[/C][/ROW]
[ROW][C]40[/C][C]6.2[/C][C]6.6997000638482[/C][C]-0.499700063848193[/C][/ROW]
[ROW][C]41[/C][C]6.5[/C][C]6.74160773514618[/C][C]-0.241607735146178[/C][/ROW]
[ROW][C]42[/C][C]6.8[/C][C]7.16239268020335[/C][C]-0.362392680203350[/C][/ROW]
[ROW][C]43[/C][C]6.8[/C][C]7.3953217464381[/C][C]-0.595321746438095[/C][/ROW]
[ROW][C]44[/C][C]6.4[/C][C]7.21402530051741[/C][C]-0.814025300517411[/C][/ROW]
[ROW][C]45[/C][C]6.1[/C][C]7.01668574728792[/C][C]-0.91668574728792[/C][/ROW]
[ROW][C]46[/C][C]5.8[/C][C]6.91854516584342[/C][C]-1.11854516584342[/C][/ROW]
[ROW][C]47[/C][C]6.1[/C][C]6.64741117790521[/C][C]-0.547411177905212[/C][/ROW]
[ROW][C]48[/C][C]7.2[/C][C]7.0980304481304[/C][C]0.101969551869596[/C][/ROW]
[ROW][C]49[/C][C]7.3[/C][C]7.06406513455278[/C][C]0.235934865447219[/C][/ROW]
[ROW][C]50[/C][C]6.9[/C][C]6.71260263594548[/C][C]0.187397364054524[/C][/ROW]
[ROW][C]51[/C][C]6.1[/C][C]6.55146382327785[/C][C]-0.451463823277853[/C][/ROW]
[ROW][C]52[/C][C]5.8[/C][C]6.39196245565371[/C][C]-0.591962455653711[/C][/ROW]
[ROW][C]53[/C][C]6.2[/C][C]6.70409692628279[/C][C]-0.504096926282789[/C][/ROW]
[ROW][C]54[/C][C]7.1[/C][C]6.95026388720077[/C][C]0.149736112799227[/C][/ROW]
[ROW][C]55[/C][C]7.7[/C][C]7.04100218521606[/C][C]0.658997814783937[/C][/ROW]
[ROW][C]56[/C][C]7.9[/C][C]7.14138500774098[/C][C]0.75861499225902[/C][/ROW]
[ROW][C]57[/C][C]7.7[/C][C]6.94533224879402[/C][C]0.754667751205984[/C][/ROW]
[ROW][C]58[/C][C]7.4[/C][C]6.75261228758363[/C][C]0.647387712416369[/C][/ROW]
[ROW][C]59[/C][C]7.5[/C][C]6.46668016539634[/C][C]1.03331983460366[/C][/ROW]
[ROW][C]60[/C][C]8[/C][C]6.8982548802401[/C][C]1.10174511975989[/C][/ROW]
[ROW][C]61[/C][C]8.1[/C][C]6.91112887854654[/C][C]1.18887112145346[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58324&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58324&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
187.889675368334060.110324631665942
28.17.635751876342460.464248123657535
37.77.480017599661460.219982400338537
47.57.350498538820250.149501461179753
57.67.549523792015020.0504762079849763
67.87.88782522356209-0.087825223562086
77.88.02694698660047-0.226946986600467
87.87.93945784387615-0.139457843876148
97.57.76090548717158-0.260905487171578
107.57.50744883582582-0.0074488358258244
117.17.29422059060143-0.194220590601427
127.57.57897207780863-0.0789720778086287
137.57.65451295767422-0.154512957674223
147.67.373695465177760.226304534822237
157.77.094171578517470.605828421482531
167.76.981766881633890.71823311836611
177.97.302908912240670.59709108775933
188.17.593084237621150.506915762378853
198.27.612662811812580.587337188187416
208.27.504070242854790.695929757145211
218.27.45123768755330.748762312446696
227.97.162780231722760.73721976827724
237.37.0663929073520.233607092648004
246.97.3975976681585-0.497597668158496
256.77.42526980071401-0.725269800714011
266.77.08397297693869-0.383972976938687
276.96.892851857488140.00714814251186351
2876.776072060043960.223927939956041
297.17.001862634315340.0981373656846603
307.27.40643397141265-0.206433971412645
317.17.5240662699328-0.424066269932792
326.97.40106160501067-0.501061605010672
3377.32583882919318-0.325838829193182
346.87.05861347902437-0.258613479024368
356.46.92529515874502-0.525295158745021
366.77.32714492566236-0.627144925662364
376.67.25534786017839-0.655347860178387
386.46.89397704559561-0.493977045595610
396.36.68149514105508-0.381495141055078
406.26.6997000638482-0.499700063848193
416.56.74160773514618-0.241607735146178
426.87.16239268020335-0.362392680203350
436.87.3953217464381-0.595321746438095
446.47.21402530051741-0.814025300517411
456.17.01668574728792-0.91668574728792
465.86.91854516584342-1.11854516584342
476.16.64741117790521-0.547411177905212
487.27.09803044813040.101969551869596
497.37.064065134552780.235934865447219
506.96.712602635945480.187397364054524
516.16.55146382327785-0.451463823277853
525.86.39196245565371-0.591962455653711
536.26.70409692628279-0.504096926282789
547.16.950263887200770.149736112799227
557.77.041002185216060.658997814783937
567.97.141385007740980.75861499225902
577.76.945332248794020.754667751205984
587.46.752612287583630.647387712416369
597.56.466680165396341.03331983460366
6086.89825488024011.10174511975989
618.16.911128878546541.18887112145346







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.0799372277762150.159874455552430.920062772223785
180.04505693466035460.09011386932070930.954943065339645
190.01721981569822250.0344396313964450.982780184301777
200.006380936533198080.01276187306639620.993619063466802
210.01298745570056990.02597491140113980.98701254429943
220.009585846667489670.01917169333497930.99041415333251
230.006041430759321190.01208286151864240.993958569240679
240.003809860672899280.007619721345798560.9961901393271
250.008619419998954750.01723883999790950.991380580001045
260.02441496650770970.04882993301541940.97558503349229
270.02122393536235860.04244787072471730.97877606463764
280.0269863671182930.0539727342365860.973013632881707
290.03621454640139210.07242909280278420.963785453598608
300.02733764583975560.05467529167951110.972662354160244
310.01704888291591410.03409776583182820.982951117084086
320.01188752480321090.02377504960642170.988112475196789
330.01069919301696110.02139838603392230.989300806983039
340.02091007890662540.04182015781325090.979089921093375
350.01628552157020960.03257104314041920.98371447842979
360.0248338223247230.0496676446494460.975166177675277
370.01405736972859980.02811473945719970.9859426302714
380.008202360456989020.01640472091397800.99179763954301
390.01375341874968920.02750683749937840.98624658125031
400.03294358212325180.06588716424650360.967056417876748
410.4246585035123610.8493170070247210.57534149648764
420.6842948717558390.6314102564883220.315705128244161
430.5888473116899320.8223053766201370.411152688310068
440.4209713253569860.8419426507139730.579028674643014

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.079937227776215 & 0.15987445555243 & 0.920062772223785 \tabularnewline
18 & 0.0450569346603546 & 0.0901138693207093 & 0.954943065339645 \tabularnewline
19 & 0.0172198156982225 & 0.034439631396445 & 0.982780184301777 \tabularnewline
20 & 0.00638093653319808 & 0.0127618730663962 & 0.993619063466802 \tabularnewline
21 & 0.0129874557005699 & 0.0259749114011398 & 0.98701254429943 \tabularnewline
22 & 0.00958584666748967 & 0.0191716933349793 & 0.99041415333251 \tabularnewline
23 & 0.00604143075932119 & 0.0120828615186424 & 0.993958569240679 \tabularnewline
24 & 0.00380986067289928 & 0.00761972134579856 & 0.9961901393271 \tabularnewline
25 & 0.00861941999895475 & 0.0172388399979095 & 0.991380580001045 \tabularnewline
26 & 0.0244149665077097 & 0.0488299330154194 & 0.97558503349229 \tabularnewline
27 & 0.0212239353623586 & 0.0424478707247173 & 0.97877606463764 \tabularnewline
28 & 0.026986367118293 & 0.053972734236586 & 0.973013632881707 \tabularnewline
29 & 0.0362145464013921 & 0.0724290928027842 & 0.963785453598608 \tabularnewline
30 & 0.0273376458397556 & 0.0546752916795111 & 0.972662354160244 \tabularnewline
31 & 0.0170488829159141 & 0.0340977658318282 & 0.982951117084086 \tabularnewline
32 & 0.0118875248032109 & 0.0237750496064217 & 0.988112475196789 \tabularnewline
33 & 0.0106991930169611 & 0.0213983860339223 & 0.989300806983039 \tabularnewline
34 & 0.0209100789066254 & 0.0418201578132509 & 0.979089921093375 \tabularnewline
35 & 0.0162855215702096 & 0.0325710431404192 & 0.98371447842979 \tabularnewline
36 & 0.024833822324723 & 0.049667644649446 & 0.975166177675277 \tabularnewline
37 & 0.0140573697285998 & 0.0281147394571997 & 0.9859426302714 \tabularnewline
38 & 0.00820236045698902 & 0.0164047209139780 & 0.99179763954301 \tabularnewline
39 & 0.0137534187496892 & 0.0275068374993784 & 0.98624658125031 \tabularnewline
40 & 0.0329435821232518 & 0.0658871642465036 & 0.967056417876748 \tabularnewline
41 & 0.424658503512361 & 0.849317007024721 & 0.57534149648764 \tabularnewline
42 & 0.684294871755839 & 0.631410256488322 & 0.315705128244161 \tabularnewline
43 & 0.588847311689932 & 0.822305376620137 & 0.411152688310068 \tabularnewline
44 & 0.420971325356986 & 0.841942650713973 & 0.579028674643014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58324&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]0.079937227776215[/C][C]0.15987445555243[/C][C]0.920062772223785[/C][/ROW]
[ROW][C]18[/C][C]0.0450569346603546[/C][C]0.0901138693207093[/C][C]0.954943065339645[/C][/ROW]
[ROW][C]19[/C][C]0.0172198156982225[/C][C]0.034439631396445[/C][C]0.982780184301777[/C][/ROW]
[ROW][C]20[/C][C]0.00638093653319808[/C][C]0.0127618730663962[/C][C]0.993619063466802[/C][/ROW]
[ROW][C]21[/C][C]0.0129874557005699[/C][C]0.0259749114011398[/C][C]0.98701254429943[/C][/ROW]
[ROW][C]22[/C][C]0.00958584666748967[/C][C]0.0191716933349793[/C][C]0.99041415333251[/C][/ROW]
[ROW][C]23[/C][C]0.00604143075932119[/C][C]0.0120828615186424[/C][C]0.993958569240679[/C][/ROW]
[ROW][C]24[/C][C]0.00380986067289928[/C][C]0.00761972134579856[/C][C]0.9961901393271[/C][/ROW]
[ROW][C]25[/C][C]0.00861941999895475[/C][C]0.0172388399979095[/C][C]0.991380580001045[/C][/ROW]
[ROW][C]26[/C][C]0.0244149665077097[/C][C]0.0488299330154194[/C][C]0.97558503349229[/C][/ROW]
[ROW][C]27[/C][C]0.0212239353623586[/C][C]0.0424478707247173[/C][C]0.97877606463764[/C][/ROW]
[ROW][C]28[/C][C]0.026986367118293[/C][C]0.053972734236586[/C][C]0.973013632881707[/C][/ROW]
[ROW][C]29[/C][C]0.0362145464013921[/C][C]0.0724290928027842[/C][C]0.963785453598608[/C][/ROW]
[ROW][C]30[/C][C]0.0273376458397556[/C][C]0.0546752916795111[/C][C]0.972662354160244[/C][/ROW]
[ROW][C]31[/C][C]0.0170488829159141[/C][C]0.0340977658318282[/C][C]0.982951117084086[/C][/ROW]
[ROW][C]32[/C][C]0.0118875248032109[/C][C]0.0237750496064217[/C][C]0.988112475196789[/C][/ROW]
[ROW][C]33[/C][C]0.0106991930169611[/C][C]0.0213983860339223[/C][C]0.989300806983039[/C][/ROW]
[ROW][C]34[/C][C]0.0209100789066254[/C][C]0.0418201578132509[/C][C]0.979089921093375[/C][/ROW]
[ROW][C]35[/C][C]0.0162855215702096[/C][C]0.0325710431404192[/C][C]0.98371447842979[/C][/ROW]
[ROW][C]36[/C][C]0.024833822324723[/C][C]0.049667644649446[/C][C]0.975166177675277[/C][/ROW]
[ROW][C]37[/C][C]0.0140573697285998[/C][C]0.0281147394571997[/C][C]0.9859426302714[/C][/ROW]
[ROW][C]38[/C][C]0.00820236045698902[/C][C]0.0164047209139780[/C][C]0.99179763954301[/C][/ROW]
[ROW][C]39[/C][C]0.0137534187496892[/C][C]0.0275068374993784[/C][C]0.98624658125031[/C][/ROW]
[ROW][C]40[/C][C]0.0329435821232518[/C][C]0.0658871642465036[/C][C]0.967056417876748[/C][/ROW]
[ROW][C]41[/C][C]0.424658503512361[/C][C]0.849317007024721[/C][C]0.57534149648764[/C][/ROW]
[ROW][C]42[/C][C]0.684294871755839[/C][C]0.631410256488322[/C][C]0.315705128244161[/C][/ROW]
[ROW][C]43[/C][C]0.588847311689932[/C][C]0.822305376620137[/C][C]0.411152688310068[/C][/ROW]
[ROW][C]44[/C][C]0.420971325356986[/C][C]0.841942650713973[/C][C]0.579028674643014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58324&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58324&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
170.0799372277762150.159874455552430.920062772223785
180.04505693466035460.09011386932070930.954943065339645
190.01721981569822250.0344396313964450.982780184301777
200.006380936533198080.01276187306639620.993619063466802
210.01298745570056990.02597491140113980.98701254429943
220.009585846667489670.01917169333497930.99041415333251
230.006041430759321190.01208286151864240.993958569240679
240.003809860672899280.007619721345798560.9961901393271
250.008619419998954750.01723883999790950.991380580001045
260.02441496650770970.04882993301541940.97558503349229
270.02122393536235860.04244787072471730.97877606463764
280.0269863671182930.0539727342365860.973013632881707
290.03621454640139210.07242909280278420.963785453598608
300.02733764583975560.05467529167951110.972662354160244
310.01704888291591410.03409776583182820.982951117084086
320.01188752480321090.02377504960642170.988112475196789
330.01069919301696110.02139838603392230.989300806983039
340.02091007890662540.04182015781325090.979089921093375
350.01628552157020960.03257104314041920.98371447842979
360.0248338223247230.0496676446494460.975166177675277
370.01405736972859980.02811473945719970.9859426302714
380.008202360456989020.01640472091397800.99179763954301
390.01375341874968920.02750683749937840.98624658125031
400.03294358212325180.06588716424650360.967056417876748
410.4246585035123610.8493170070247210.57534149648764
420.6842948717558390.6314102564883220.315705128244161
430.5888473116899320.8223053766201370.411152688310068
440.4209713253569860.8419426507139730.579028674643014







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level10.0357142857142857NOK
5% type I error level180.642857142857143NOK
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 & 1 & 0.0357142857142857 & NOK \tabularnewline
5% type I error level & 18 & 0.642857142857143 & NOK \tabularnewline
10% type I error level & 23 & 0.821428571428571 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58324&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]1[/C][C]0.0357142857142857[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]18[/C][C]0.642857142857143[/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=58324&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58324&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 level10.0357142857142857NOK
5% type I error level180.642857142857143NOK
10% type I error level230.821428571428571NOK



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