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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 10:20:37 -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/t1258737736c7adbqpqyqe4czs.htm/, Retrieved Fri, 19 Apr 2024 01:45:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58348, Retrieved Fri, 19 Apr 2024 01:45:12 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-   PD      [Multiple Regression] [WS 7.5] [2009-11-20 17:20:37] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9,3	7,5	9,8	9,9
8,3	6,8	9,3	9,8
8	6,5	8,3	9,3
8,5	6,6	8	8,3
10,4	7,6	8,5	8
11,1	8	10,4	8,5
10,9	8,1	11,1	10,4
10	7,7	10,9	11,1
9,2	7,5	10	10,9
9,2	7,6	9,2	10
9,5	7,8	9,2	9,2
9,6	7,8	9,5	9,2
9,5	7,8	9,6	9,5
9,1	7,5	9,5	9,6
8,9	7,5	9,1	9,5
9	7,1	8,9	9,1
10,1	7,5	9	8,9
10,3	7,5	10,1	9
10,2	7,6	10,3	10,1
9,6	7,7	10,2	10,3
9,2	7,7	9,6	10,2
9,3	7,9	9,2	9,6
9,4	8,1	9,3	9,2
9,4	8,2	9,4	9,3
9,2	8,2	9,4	9,4
9	8,2	9,2	9,4
9	7,9	9	9,2
9	7,3	9	9
9,8	6,9	9	9
10	6,6	9,8	9
9,8	6,7	10	9,8
9,3	6,9	9,8	10
9	7	9,3	9,8
9	7,1	9	9,3
9,1	7,2	9	9
9,1	7,1	9,1	9
9,1	6,9	9,1	9,1
9,2	7	9,1	9,1
8,8	6,8	9,2	9,1
8,3	6,4	8,8	9,2
8,4	6,7	8,3	8,8
8,1	6,6	8,4	8,3
7,7	6,4	8,1	8,4
7,9	6,3	7,7	8,1
7,9	6,2	7,9	7,7
8	6,5	7,9	7,9
7,9	6,8	8	7,9
7,6	6,8	7,9	8
7,1	6,4	7,6	7,9
6,8	6,1	7,1	7,6
6,5	5,8	6,8	7,1
6,9	6,1	6,5	6,8
8,2	7,2	6,9	6,5
8,7	7,3	8,2	6,9
8,3	6,9	8,7	8,2
7,9	6,1	8,3	8,7
7,5	5,8	7,9	8,3
7,8	6,2	7,5	7,9

Tables (Output of Computation)





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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58348&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=58348&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58348&T=0

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


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

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






Multiple Linear Regression - Estimated Regression Equation
WLMan[t] = + 3.65718934610865 + 0.395497505499312WLVrouw[t] + 0.191002977382953`Yt-1`[t] -0.138059867944866`Yt-2`[t] -0.099406851289696M1[t] -0.148951401377357M2[t] -0.234467327975613M3[t] -0.471178750524076M4[t] -0.448031656398712M5[t] -0.708998951622607M6[t] -0.565548945759982M7[t] -0.499274537665341M8[t] -0.394140575303057M9[t] -0.195156370453495M10[t] -0.0142767368236248M11[t] -0.00669916588971114t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
WLMan[t] =  +  3.65718934610865 +  0.395497505499312WLVrouw[t] +  0.191002977382953`Yt-1`[t] -0.138059867944866`Yt-2`[t] -0.099406851289696M1[t] -0.148951401377357M2[t] -0.234467327975613M3[t] -0.471178750524076M4[t] -0.448031656398712M5[t] -0.708998951622607M6[t] -0.565548945759982M7[t] -0.499274537665341M8[t] -0.394140575303057M9[t] -0.195156370453495M10[t] -0.0142767368236248M11[t] -0.00669916588971114t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58348&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]WLMan[t] =  +  3.65718934610865 +  0.395497505499312WLVrouw[t] +  0.191002977382953`Yt-1`[t] -0.138059867944866`Yt-2`[t] -0.099406851289696M1[t] -0.148951401377357M2[t] -0.234467327975613M3[t] -0.471178750524076M4[t] -0.448031656398712M5[t] -0.708998951622607M6[t] -0.565548945759982M7[t] -0.499274537665341M8[t] -0.394140575303057M9[t] -0.195156370453495M10[t] -0.0142767368236248M11[t] -0.00669916588971114t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58348&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58348&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
WLMan[t] = + 3.65718934610865 + 0.395497505499312WLVrouw[t] + 0.191002977382953`Yt-1`[t] -0.138059867944866`Yt-2`[t] -0.099406851289696M1[t] -0.148951401377357M2[t] -0.234467327975613M3[t] -0.471178750524076M4[t] -0.448031656398712M5[t] -0.708998951622607M6[t] -0.565548945759982M7[t] -0.499274537665341M8[t] -0.394140575303057M9[t] -0.195156370453495M10[t] -0.0142767368236248M11[t] -0.00669916588971114t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)3.657189346108651.2641522.8930.0060240.003012
WLVrouw0.3954975054993120.2546411.55320.127890.063945
`Yt-1`0.1910029773829530.4069980.46930.6412850.320642
`Yt-2`-0.1380598679448660.255103-0.54120.5912350.295617
M1-0.0994068512896960.278415-0.3570.7228450.361422
M2-0.1489514013773570.285278-0.52210.6043250.302163
M3-0.2344673279756130.290255-0.80780.4237590.21188
M4-0.4711787505240760.292672-1.60990.1149060.057453
M5-0.4480316563987120.366738-1.22170.2286470.114323
M6-0.7089989516226070.32784-2.16260.0363110.018156
M7-0.5655489457599820.285832-1.97860.0544430.027222
M8-0.4992745376653410.290653-1.71780.0932050.046602
M9-0.3941405753030570.29421-1.33970.187560.09378
M10-0.1951563704534950.306503-0.63670.5277630.263882
M11-0.01427673682362480.292262-0.04880.9612710.480636
t-0.006699165889711140.006096-1.0990.2780480.139024

\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) & 3.65718934610865 & 1.264152 & 2.893 & 0.006024 & 0.003012 \tabularnewline
WLVrouw & 0.395497505499312 & 0.254641 & 1.5532 & 0.12789 & 0.063945 \tabularnewline
`Yt-1` & 0.191002977382953 & 0.406998 & 0.4693 & 0.641285 & 0.320642 \tabularnewline
`Yt-2` & -0.138059867944866 & 0.255103 & -0.5412 & 0.591235 & 0.295617 \tabularnewline
M1 & -0.099406851289696 & 0.278415 & -0.357 & 0.722845 & 0.361422 \tabularnewline
M2 & -0.148951401377357 & 0.285278 & -0.5221 & 0.604325 & 0.302163 \tabularnewline
M3 & -0.234467327975613 & 0.290255 & -0.8078 & 0.423759 & 0.21188 \tabularnewline
M4 & -0.471178750524076 & 0.292672 & -1.6099 & 0.114906 & 0.057453 \tabularnewline
M5 & -0.448031656398712 & 0.366738 & -1.2217 & 0.228647 & 0.114323 \tabularnewline
M6 & -0.708998951622607 & 0.32784 & -2.1626 & 0.036311 & 0.018156 \tabularnewline
M7 & -0.565548945759982 & 0.285832 & -1.9786 & 0.054443 & 0.027222 \tabularnewline
M8 & -0.499274537665341 & 0.290653 & -1.7178 & 0.093205 & 0.046602 \tabularnewline
M9 & -0.394140575303057 & 0.29421 & -1.3397 & 0.18756 & 0.09378 \tabularnewline
M10 & -0.195156370453495 & 0.306503 & -0.6367 & 0.527763 & 0.263882 \tabularnewline
M11 & -0.0142767368236248 & 0.292262 & -0.0488 & 0.961271 & 0.480636 \tabularnewline
t & -0.00669916588971114 & 0.006096 & -1.099 & 0.278048 & 0.139024 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58348&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]3.65718934610865[/C][C]1.264152[/C][C]2.893[/C][C]0.006024[/C][C]0.003012[/C][/ROW]
[ROW][C]WLVrouw[/C][C]0.395497505499312[/C][C]0.254641[/C][C]1.5532[/C][C]0.12789[/C][C]0.063945[/C][/ROW]
[ROW][C]`Yt-1`[/C][C]0.191002977382953[/C][C]0.406998[/C][C]0.4693[/C][C]0.641285[/C][C]0.320642[/C][/ROW]
[ROW][C]`Yt-2`[/C][C]-0.138059867944866[/C][C]0.255103[/C][C]-0.5412[/C][C]0.591235[/C][C]0.295617[/C][/ROW]
[ROW][C]M1[/C][C]-0.099406851289696[/C][C]0.278415[/C][C]-0.357[/C][C]0.722845[/C][C]0.361422[/C][/ROW]
[ROW][C]M2[/C][C]-0.148951401377357[/C][C]0.285278[/C][C]-0.5221[/C][C]0.604325[/C][C]0.302163[/C][/ROW]
[ROW][C]M3[/C][C]-0.234467327975613[/C][C]0.290255[/C][C]-0.8078[/C][C]0.423759[/C][C]0.21188[/C][/ROW]
[ROW][C]M4[/C][C]-0.471178750524076[/C][C]0.292672[/C][C]-1.6099[/C][C]0.114906[/C][C]0.057453[/C][/ROW]
[ROW][C]M5[/C][C]-0.448031656398712[/C][C]0.366738[/C][C]-1.2217[/C][C]0.228647[/C][C]0.114323[/C][/ROW]
[ROW][C]M6[/C][C]-0.708998951622607[/C][C]0.32784[/C][C]-2.1626[/C][C]0.036311[/C][C]0.018156[/C][/ROW]
[ROW][C]M7[/C][C]-0.565548945759982[/C][C]0.285832[/C][C]-1.9786[/C][C]0.054443[/C][C]0.027222[/C][/ROW]
[ROW][C]M8[/C][C]-0.499274537665341[/C][C]0.290653[/C][C]-1.7178[/C][C]0.093205[/C][C]0.046602[/C][/ROW]
[ROW][C]M9[/C][C]-0.394140575303057[/C][C]0.29421[/C][C]-1.3397[/C][C]0.18756[/C][C]0.09378[/C][/ROW]
[ROW][C]M10[/C][C]-0.195156370453495[/C][C]0.306503[/C][C]-0.6367[/C][C]0.527763[/C][C]0.263882[/C][/ROW]
[ROW][C]M11[/C][C]-0.0142767368236248[/C][C]0.292262[/C][C]-0.0488[/C][C]0.961271[/C][C]0.480636[/C][/ROW]
[ROW][C]t[/C][C]-0.00669916588971114[/C][C]0.006096[/C][C]-1.099[/C][C]0.278048[/C][C]0.139024[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58348&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58348&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)3.657189346108651.2641522.8930.0060240.003012
WLVrouw0.3954975054993120.2546411.55320.127890.063945
`Yt-1`0.1910029773829530.4069980.46930.6412850.320642
`Yt-2`-0.1380598679448660.255103-0.54120.5912350.295617
M1-0.0994068512896960.278415-0.3570.7228450.361422
M2-0.1489514013773570.285278-0.52210.6043250.302163
M3-0.2344673279756130.290255-0.80780.4237590.21188
M4-0.4711787505240760.292672-1.60990.1149060.057453
M5-0.4480316563987120.366738-1.22170.2286470.114323
M6-0.7089989516226070.32784-2.16260.0363110.018156
M7-0.5655489457599820.285832-1.97860.0544430.027222
M8-0.4992745376653410.290653-1.71780.0932050.046602
M9-0.3941405753030570.29421-1.33970.187560.09378
M10-0.1951563704534950.306503-0.63670.5277630.263882
M11-0.01427673682362480.292262-0.04880.9612710.480636
t-0.006699165889711140.006096-1.0990.2780480.139024






Multiple Linear Regression - Regression Statistics
Multiple R0.844394446216218
R-squared0.713001980800794
Adjusted R-squared0.610502688229648
F-TEST (value)6.95616489553717
F-TEST (DF numerator)15
F-TEST (DF denominator)42
p-value3.1064643501999e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.409325621372292
Sum Squared Residuals7.03699350109613

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.844394446216218 \tabularnewline
R-squared & 0.713001980800794 \tabularnewline
Adjusted R-squared & 0.610502688229648 \tabularnewline
F-TEST (value) & 6.95616489553717 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 42 \tabularnewline
p-value & 3.1064643501999e-07 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.409325621372292 \tabularnewline
Sum Squared Residuals & 7.03699350109613 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58348&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.844394446216218[/C][/ROW]
[ROW][C]R-squared[/C][C]0.713001980800794[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.610502688229648[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]6.95616489553717[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]42[/C][/ROW]
[ROW][C]p-value[/C][C]3.1064643501999e-07[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.409325621372292[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]7.03699350109613[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58348&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58348&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 R0.844394446216218
R-squared0.713001980800794
Adjusted R-squared0.610502688229648
F-TEST (value)6.95616489553717
F-TEST (DF numerator)15
F-TEST (DF denominator)42
p-value3.1064643501999e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.409325621372292
Sum Squared Residuals7.03699350109613






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
17.57.73424661577162-0.234246615771617
26.87.20080989239794-0.400809892397944
36.56.86797250484966-0.367972504849663
46.66.90306964389112-0.303069643891124
57.67.8078822816504-0.207882281650406
688.1109397974415-0.110939797441497
78.18.039979471387370.0600205286126291
87.77.608764455604920.0912355443950769
97.57.246510541622360.253489458377639
107.67.410247079826230.189752920173772
117.87.81352469357208-0.0135246935720755
127.87.9179529082708-0.117952908270805
137.87.74997947789630.0500205221036976
147.57.50263047518642-0.00263047518642345
157.57.26872067743990.231279322560101
167.17.081883191253010.0181168087469879
177.57.58009064686518-0.080090646865176
187.57.5878209751782-0.0878209751781949
197.67.571356805338420.0286431946615845
207.77.346921272916490.353078727083511
217.77.186361267554050.513638732445948
227.97.424630786877570.475369213122428
238.17.71268525008390.387314749916095
248.27.725557131961630.474442868038372
258.27.526545626887870.673454373112129
268.27.353001814334050.846998185665954
277.97.250198099958460.649801900041539
287.37.034399485109260.265600514890740
296.97.36724541774436-0.467245417744362
306.67.33148083963698-0.731480839636982
316.77.31688487963073-0.61688487963073
326.97.11289880002044-0.212898800020441
3377.02479482974072-0.0247948297407169
347.17.22880890945811-0.128808909458114
357.27.48395708813166-0.283957088131664
367.17.51063495680387-0.410634956803873
376.97.39072295282998-0.490722952829979
3877.37402898740254-0.374028987402538
396.87.14271519045314-0.342715190453143
406.46.61134867151764-0.211348671517644
416.76.62706880878970.0729311912103026
426.66.328883327737030.271116672262974
436.46.236328285500840.163671714499158
446.36.34001979823591-0.0400197982359138
456.26.53187913736302-0.331879137363024
466.56.73610195328383-0.236101953283832
476.86.88983296821236-0.0898329682123556
486.86.745855002963690.0541449970363064
496.46.398505326614230.00149467338576981
506.16.16952883067905-0.0695288306790485
515.85.97039352729883-0.170393527298835
526.15.869299008228960.230700991771041
537.26.517712844950360.682287155049642
547.36.64087506000630.659124939993699
556.96.535450558142640.364549441857359
566.16.29139567322223-0.191395673222233
575.86.21045422371985-0.410454223719846
586.26.50021127055425-0.300211270554254

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 7.5 & 7.73424661577162 & -0.234246615771617 \tabularnewline
2 & 6.8 & 7.20080989239794 & -0.400809892397944 \tabularnewline
3 & 6.5 & 6.86797250484966 & -0.367972504849663 \tabularnewline
4 & 6.6 & 6.90306964389112 & -0.303069643891124 \tabularnewline
5 & 7.6 & 7.8078822816504 & -0.207882281650406 \tabularnewline
6 & 8 & 8.1109397974415 & -0.110939797441497 \tabularnewline
7 & 8.1 & 8.03997947138737 & 0.0600205286126291 \tabularnewline
8 & 7.7 & 7.60876445560492 & 0.0912355443950769 \tabularnewline
9 & 7.5 & 7.24651054162236 & 0.253489458377639 \tabularnewline
10 & 7.6 & 7.41024707982623 & 0.189752920173772 \tabularnewline
11 & 7.8 & 7.81352469357208 & -0.0135246935720755 \tabularnewline
12 & 7.8 & 7.9179529082708 & -0.117952908270805 \tabularnewline
13 & 7.8 & 7.7499794778963 & 0.0500205221036976 \tabularnewline
14 & 7.5 & 7.50263047518642 & -0.00263047518642345 \tabularnewline
15 & 7.5 & 7.2687206774399 & 0.231279322560101 \tabularnewline
16 & 7.1 & 7.08188319125301 & 0.0181168087469879 \tabularnewline
17 & 7.5 & 7.58009064686518 & -0.080090646865176 \tabularnewline
18 & 7.5 & 7.5878209751782 & -0.0878209751781949 \tabularnewline
19 & 7.6 & 7.57135680533842 & 0.0286431946615845 \tabularnewline
20 & 7.7 & 7.34692127291649 & 0.353078727083511 \tabularnewline
21 & 7.7 & 7.18636126755405 & 0.513638732445948 \tabularnewline
22 & 7.9 & 7.42463078687757 & 0.475369213122428 \tabularnewline
23 & 8.1 & 7.7126852500839 & 0.387314749916095 \tabularnewline
24 & 8.2 & 7.72555713196163 & 0.474442868038372 \tabularnewline
25 & 8.2 & 7.52654562688787 & 0.673454373112129 \tabularnewline
26 & 8.2 & 7.35300181433405 & 0.846998185665954 \tabularnewline
27 & 7.9 & 7.25019809995846 & 0.649801900041539 \tabularnewline
28 & 7.3 & 7.03439948510926 & 0.265600514890740 \tabularnewline
29 & 6.9 & 7.36724541774436 & -0.467245417744362 \tabularnewline
30 & 6.6 & 7.33148083963698 & -0.731480839636982 \tabularnewline
31 & 6.7 & 7.31688487963073 & -0.61688487963073 \tabularnewline
32 & 6.9 & 7.11289880002044 & -0.212898800020441 \tabularnewline
33 & 7 & 7.02479482974072 & -0.0247948297407169 \tabularnewline
34 & 7.1 & 7.22880890945811 & -0.128808909458114 \tabularnewline
35 & 7.2 & 7.48395708813166 & -0.283957088131664 \tabularnewline
36 & 7.1 & 7.51063495680387 & -0.410634956803873 \tabularnewline
37 & 6.9 & 7.39072295282998 & -0.490722952829979 \tabularnewline
38 & 7 & 7.37402898740254 & -0.374028987402538 \tabularnewline
39 & 6.8 & 7.14271519045314 & -0.342715190453143 \tabularnewline
40 & 6.4 & 6.61134867151764 & -0.211348671517644 \tabularnewline
41 & 6.7 & 6.6270688087897 & 0.0729311912103026 \tabularnewline
42 & 6.6 & 6.32888332773703 & 0.271116672262974 \tabularnewline
43 & 6.4 & 6.23632828550084 & 0.163671714499158 \tabularnewline
44 & 6.3 & 6.34001979823591 & -0.0400197982359138 \tabularnewline
45 & 6.2 & 6.53187913736302 & -0.331879137363024 \tabularnewline
46 & 6.5 & 6.73610195328383 & -0.236101953283832 \tabularnewline
47 & 6.8 & 6.88983296821236 & -0.0898329682123556 \tabularnewline
48 & 6.8 & 6.74585500296369 & 0.0541449970363064 \tabularnewline
49 & 6.4 & 6.39850532661423 & 0.00149467338576981 \tabularnewline
50 & 6.1 & 6.16952883067905 & -0.0695288306790485 \tabularnewline
51 & 5.8 & 5.97039352729883 & -0.170393527298835 \tabularnewline
52 & 6.1 & 5.86929900822896 & 0.230700991771041 \tabularnewline
53 & 7.2 & 6.51771284495036 & 0.682287155049642 \tabularnewline
54 & 7.3 & 6.6408750600063 & 0.659124939993699 \tabularnewline
55 & 6.9 & 6.53545055814264 & 0.364549441857359 \tabularnewline
56 & 6.1 & 6.29139567322223 & -0.191395673222233 \tabularnewline
57 & 5.8 & 6.21045422371985 & -0.410454223719846 \tabularnewline
58 & 6.2 & 6.50021127055425 & -0.300211270554254 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58348&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]7.5[/C][C]7.73424661577162[/C][C]-0.234246615771617[/C][/ROW]
[ROW][C]2[/C][C]6.8[/C][C]7.20080989239794[/C][C]-0.400809892397944[/C][/ROW]
[ROW][C]3[/C][C]6.5[/C][C]6.86797250484966[/C][C]-0.367972504849663[/C][/ROW]
[ROW][C]4[/C][C]6.6[/C][C]6.90306964389112[/C][C]-0.303069643891124[/C][/ROW]
[ROW][C]5[/C][C]7.6[/C][C]7.8078822816504[/C][C]-0.207882281650406[/C][/ROW]
[ROW][C]6[/C][C]8[/C][C]8.1109397974415[/C][C]-0.110939797441497[/C][/ROW]
[ROW][C]7[/C][C]8.1[/C][C]8.03997947138737[/C][C]0.0600205286126291[/C][/ROW]
[ROW][C]8[/C][C]7.7[/C][C]7.60876445560492[/C][C]0.0912355443950769[/C][/ROW]
[ROW][C]9[/C][C]7.5[/C][C]7.24651054162236[/C][C]0.253489458377639[/C][/ROW]
[ROW][C]10[/C][C]7.6[/C][C]7.41024707982623[/C][C]0.189752920173772[/C][/ROW]
[ROW][C]11[/C][C]7.8[/C][C]7.81352469357208[/C][C]-0.0135246935720755[/C][/ROW]
[ROW][C]12[/C][C]7.8[/C][C]7.9179529082708[/C][C]-0.117952908270805[/C][/ROW]
[ROW][C]13[/C][C]7.8[/C][C]7.7499794778963[/C][C]0.0500205221036976[/C][/ROW]
[ROW][C]14[/C][C]7.5[/C][C]7.50263047518642[/C][C]-0.00263047518642345[/C][/ROW]
[ROW][C]15[/C][C]7.5[/C][C]7.2687206774399[/C][C]0.231279322560101[/C][/ROW]
[ROW][C]16[/C][C]7.1[/C][C]7.08188319125301[/C][C]0.0181168087469879[/C][/ROW]
[ROW][C]17[/C][C]7.5[/C][C]7.58009064686518[/C][C]-0.080090646865176[/C][/ROW]
[ROW][C]18[/C][C]7.5[/C][C]7.5878209751782[/C][C]-0.0878209751781949[/C][/ROW]
[ROW][C]19[/C][C]7.6[/C][C]7.57135680533842[/C][C]0.0286431946615845[/C][/ROW]
[ROW][C]20[/C][C]7.7[/C][C]7.34692127291649[/C][C]0.353078727083511[/C][/ROW]
[ROW][C]21[/C][C]7.7[/C][C]7.18636126755405[/C][C]0.513638732445948[/C][/ROW]
[ROW][C]22[/C][C]7.9[/C][C]7.42463078687757[/C][C]0.475369213122428[/C][/ROW]
[ROW][C]23[/C][C]8.1[/C][C]7.7126852500839[/C][C]0.387314749916095[/C][/ROW]
[ROW][C]24[/C][C]8.2[/C][C]7.72555713196163[/C][C]0.474442868038372[/C][/ROW]
[ROW][C]25[/C][C]8.2[/C][C]7.52654562688787[/C][C]0.673454373112129[/C][/ROW]
[ROW][C]26[/C][C]8.2[/C][C]7.35300181433405[/C][C]0.846998185665954[/C][/ROW]
[ROW][C]27[/C][C]7.9[/C][C]7.25019809995846[/C][C]0.649801900041539[/C][/ROW]
[ROW][C]28[/C][C]7.3[/C][C]7.03439948510926[/C][C]0.265600514890740[/C][/ROW]
[ROW][C]29[/C][C]6.9[/C][C]7.36724541774436[/C][C]-0.467245417744362[/C][/ROW]
[ROW][C]30[/C][C]6.6[/C][C]7.33148083963698[/C][C]-0.731480839636982[/C][/ROW]
[ROW][C]31[/C][C]6.7[/C][C]7.31688487963073[/C][C]-0.61688487963073[/C][/ROW]
[ROW][C]32[/C][C]6.9[/C][C]7.11289880002044[/C][C]-0.212898800020441[/C][/ROW]
[ROW][C]33[/C][C]7[/C][C]7.02479482974072[/C][C]-0.0247948297407169[/C][/ROW]
[ROW][C]34[/C][C]7.1[/C][C]7.22880890945811[/C][C]-0.128808909458114[/C][/ROW]
[ROW][C]35[/C][C]7.2[/C][C]7.48395708813166[/C][C]-0.283957088131664[/C][/ROW]
[ROW][C]36[/C][C]7.1[/C][C]7.51063495680387[/C][C]-0.410634956803873[/C][/ROW]
[ROW][C]37[/C][C]6.9[/C][C]7.39072295282998[/C][C]-0.490722952829979[/C][/ROW]
[ROW][C]38[/C][C]7[/C][C]7.37402898740254[/C][C]-0.374028987402538[/C][/ROW]
[ROW][C]39[/C][C]6.8[/C][C]7.14271519045314[/C][C]-0.342715190453143[/C][/ROW]
[ROW][C]40[/C][C]6.4[/C][C]6.61134867151764[/C][C]-0.211348671517644[/C][/ROW]
[ROW][C]41[/C][C]6.7[/C][C]6.6270688087897[/C][C]0.0729311912103026[/C][/ROW]
[ROW][C]42[/C][C]6.6[/C][C]6.32888332773703[/C][C]0.271116672262974[/C][/ROW]
[ROW][C]43[/C][C]6.4[/C][C]6.23632828550084[/C][C]0.163671714499158[/C][/ROW]
[ROW][C]44[/C][C]6.3[/C][C]6.34001979823591[/C][C]-0.0400197982359138[/C][/ROW]
[ROW][C]45[/C][C]6.2[/C][C]6.53187913736302[/C][C]-0.331879137363024[/C][/ROW]
[ROW][C]46[/C][C]6.5[/C][C]6.73610195328383[/C][C]-0.236101953283832[/C][/ROW]
[ROW][C]47[/C][C]6.8[/C][C]6.88983296821236[/C][C]-0.0898329682123556[/C][/ROW]
[ROW][C]48[/C][C]6.8[/C][C]6.74585500296369[/C][C]0.0541449970363064[/C][/ROW]
[ROW][C]49[/C][C]6.4[/C][C]6.39850532661423[/C][C]0.00149467338576981[/C][/ROW]
[ROW][C]50[/C][C]6.1[/C][C]6.16952883067905[/C][C]-0.0695288306790485[/C][/ROW]
[ROW][C]51[/C][C]5.8[/C][C]5.97039352729883[/C][C]-0.170393527298835[/C][/ROW]
[ROW][C]52[/C][C]6.1[/C][C]5.86929900822896[/C][C]0.230700991771041[/C][/ROW]
[ROW][C]53[/C][C]7.2[/C][C]6.51771284495036[/C][C]0.682287155049642[/C][/ROW]
[ROW][C]54[/C][C]7.3[/C][C]6.6408750600063[/C][C]0.659124939993699[/C][/ROW]
[ROW][C]55[/C][C]6.9[/C][C]6.53545055814264[/C][C]0.364549441857359[/C][/ROW]
[ROW][C]56[/C][C]6.1[/C][C]6.29139567322223[/C][C]-0.191395673222233[/C][/ROW]
[ROW][C]57[/C][C]5.8[/C][C]6.21045422371985[/C][C]-0.410454223719846[/C][/ROW]
[ROW][C]58[/C][C]6.2[/C][C]6.50021127055425[/C][C]-0.300211270554254[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58348&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58348&T=4

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


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
17.57.73424661577162-0.234246615771617
26.87.20080989239794-0.400809892397944
36.56.86797250484966-0.367972504849663
46.66.90306964389112-0.303069643891124
57.67.8078822816504-0.207882281650406
688.1109397974415-0.110939797441497
78.18.039979471387370.0600205286126291
87.77.608764455604920.0912355443950769
97.57.246510541622360.253489458377639
107.67.410247079826230.189752920173772
117.87.81352469357208-0.0135246935720755
127.87.9179529082708-0.117952908270805
137.87.74997947789630.0500205221036976
147.57.50263047518642-0.00263047518642345
157.57.26872067743990.231279322560101
167.17.081883191253010.0181168087469879
177.57.58009064686518-0.080090646865176
187.57.5878209751782-0.0878209751781949
197.67.571356805338420.0286431946615845
207.77.346921272916490.353078727083511
217.77.186361267554050.513638732445948
227.97.424630786877570.475369213122428
238.17.71268525008390.387314749916095
248.27.725557131961630.474442868038372
258.27.526545626887870.673454373112129
268.27.353001814334050.846998185665954
277.97.250198099958460.649801900041539
287.37.034399485109260.265600514890740
296.97.36724541774436-0.467245417744362
306.67.33148083963698-0.731480839636982
316.77.31688487963073-0.61688487963073
326.97.11289880002044-0.212898800020441
3377.02479482974072-0.0247948297407169
347.17.22880890945811-0.128808909458114
357.27.48395708813166-0.283957088131664
367.17.51063495680387-0.410634956803873
376.97.39072295282998-0.490722952829979
3877.37402898740254-0.374028987402538
396.87.14271519045314-0.342715190453143
406.46.61134867151764-0.211348671517644
416.76.62706880878970.0729311912103026
426.66.328883327737030.271116672262974
436.46.236328285500840.163671714499158
446.36.34001979823591-0.0400197982359138
456.26.53187913736302-0.331879137363024
466.56.73610195328383-0.236101953283832
476.86.88983296821236-0.0898329682123556
486.86.745855002963690.0541449970363064
496.46.398505326614230.00149467338576981
506.16.16952883067905-0.0695288306790485
515.85.97039352729883-0.170393527298835
526.15.869299008228960.230700991771041
537.26.517712844950360.682287155049642
547.36.64087506000630.659124939993699
556.96.535450558142640.364549441857359
566.16.29139567322223-0.191395673222233
575.86.21045422371985-0.410454223719846
586.26.50021127055425-0.300211270554254






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.002037127577158940.004074255154317880.99796287242284
200.0001932692125464710.0003865384250929420.999806730787454
213.23686810988154e-056.47373621976308e-050.999967631318901
226.40359514837804e-061.28071902967561e-050.999993596404852
232.85492669698133e-065.70985339396266e-060.999997145073303
240.0001415147886432730.0002830295772865460.999858485211357
250.0004765340411344360.0009530680822688710.999523465958866
260.003799990302088070.007599980604176150.996200009697912
270.009320782546225540.01864156509245110.990679217453774
280.007513430797856430.01502686159571290.992486569202144
290.03674584057988680.07349168115977360.963254159420113
300.4343975367813520.8687950735627040.565602463218648
310.8040408144490240.3919183711019530.195959185550976
320.7823672464782760.4352655070434480.217632753521724
330.9765011490660280.04699770186794480.0234988509339724
340.9974604035942630.005079192811473930.00253959640573697
350.9953999829531860.009200034093627810.00460001704681391
360.9951667098720650.009666580255870570.00483329012793528
370.99852131135190.002957377296201570.00147868864810078
380.9989266839915560.002146632016887540.00107331600844377
390.9946113372004770.01077732559904600.00538866279952299

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.00203712757715894 & 0.00407425515431788 & 0.99796287242284 \tabularnewline
20 & 0.000193269212546471 & 0.000386538425092942 & 0.999806730787454 \tabularnewline
21 & 3.23686810988154e-05 & 6.47373621976308e-05 & 0.999967631318901 \tabularnewline
22 & 6.40359514837804e-06 & 1.28071902967561e-05 & 0.999993596404852 \tabularnewline
23 & 2.85492669698133e-06 & 5.70985339396266e-06 & 0.999997145073303 \tabularnewline
24 & 0.000141514788643273 & 0.000283029577286546 & 0.999858485211357 \tabularnewline
25 & 0.000476534041134436 & 0.000953068082268871 & 0.999523465958866 \tabularnewline
26 & 0.00379999030208807 & 0.00759998060417615 & 0.996200009697912 \tabularnewline
27 & 0.00932078254622554 & 0.0186415650924511 & 0.990679217453774 \tabularnewline
28 & 0.00751343079785643 & 0.0150268615957129 & 0.992486569202144 \tabularnewline
29 & 0.0367458405798868 & 0.0734916811597736 & 0.963254159420113 \tabularnewline
30 & 0.434397536781352 & 0.868795073562704 & 0.565602463218648 \tabularnewline
31 & 0.804040814449024 & 0.391918371101953 & 0.195959185550976 \tabularnewline
32 & 0.782367246478276 & 0.435265507043448 & 0.217632753521724 \tabularnewline
33 & 0.976501149066028 & 0.0469977018679448 & 0.0234988509339724 \tabularnewline
34 & 0.997460403594263 & 0.00507919281147393 & 0.00253959640573697 \tabularnewline
35 & 0.995399982953186 & 0.00920003409362781 & 0.00460001704681391 \tabularnewline
36 & 0.995166709872065 & 0.00966658025587057 & 0.00483329012793528 \tabularnewline
37 & 0.9985213113519 & 0.00295737729620157 & 0.00147868864810078 \tabularnewline
38 & 0.998926683991556 & 0.00214663201688754 & 0.00107331600844377 \tabularnewline
39 & 0.994611337200477 & 0.0107773255990460 & 0.00538866279952299 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58348&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]19[/C][C]0.00203712757715894[/C][C]0.00407425515431788[/C][C]0.99796287242284[/C][/ROW]
[ROW][C]20[/C][C]0.000193269212546471[/C][C]0.000386538425092942[/C][C]0.999806730787454[/C][/ROW]
[ROW][C]21[/C][C]3.23686810988154e-05[/C][C]6.47373621976308e-05[/C][C]0.999967631318901[/C][/ROW]
[ROW][C]22[/C][C]6.40359514837804e-06[/C][C]1.28071902967561e-05[/C][C]0.999993596404852[/C][/ROW]
[ROW][C]23[/C][C]2.85492669698133e-06[/C][C]5.70985339396266e-06[/C][C]0.999997145073303[/C][/ROW]
[ROW][C]24[/C][C]0.000141514788643273[/C][C]0.000283029577286546[/C][C]0.999858485211357[/C][/ROW]
[ROW][C]25[/C][C]0.000476534041134436[/C][C]0.000953068082268871[/C][C]0.999523465958866[/C][/ROW]
[ROW][C]26[/C][C]0.00379999030208807[/C][C]0.00759998060417615[/C][C]0.996200009697912[/C][/ROW]
[ROW][C]27[/C][C]0.00932078254622554[/C][C]0.0186415650924511[/C][C]0.990679217453774[/C][/ROW]
[ROW][C]28[/C][C]0.00751343079785643[/C][C]0.0150268615957129[/C][C]0.992486569202144[/C][/ROW]
[ROW][C]29[/C][C]0.0367458405798868[/C][C]0.0734916811597736[/C][C]0.963254159420113[/C][/ROW]
[ROW][C]30[/C][C]0.434397536781352[/C][C]0.868795073562704[/C][C]0.565602463218648[/C][/ROW]
[ROW][C]31[/C][C]0.804040814449024[/C][C]0.391918371101953[/C][C]0.195959185550976[/C][/ROW]
[ROW][C]32[/C][C]0.782367246478276[/C][C]0.435265507043448[/C][C]0.217632753521724[/C][/ROW]
[ROW][C]33[/C][C]0.976501149066028[/C][C]0.0469977018679448[/C][C]0.0234988509339724[/C][/ROW]
[ROW][C]34[/C][C]0.997460403594263[/C][C]0.00507919281147393[/C][C]0.00253959640573697[/C][/ROW]
[ROW][C]35[/C][C]0.995399982953186[/C][C]0.00920003409362781[/C][C]0.00460001704681391[/C][/ROW]
[ROW][C]36[/C][C]0.995166709872065[/C][C]0.00966658025587057[/C][C]0.00483329012793528[/C][/ROW]
[ROW][C]37[/C][C]0.9985213113519[/C][C]0.00295737729620157[/C][C]0.00147868864810078[/C][/ROW]
[ROW][C]38[/C][C]0.998926683991556[/C][C]0.00214663201688754[/C][C]0.00107331600844377[/C][/ROW]
[ROW][C]39[/C][C]0.994611337200477[/C][C]0.0107773255990460[/C][C]0.00538866279952299[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58348&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58348&T=5

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


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.002037127577158940.004074255154317880.99796287242284
200.0001932692125464710.0003865384250929420.999806730787454
213.23686810988154e-056.47373621976308e-050.999967631318901
226.40359514837804e-061.28071902967561e-050.999993596404852
232.85492669698133e-065.70985339396266e-060.999997145073303
240.0001415147886432730.0002830295772865460.999858485211357
250.0004765340411344360.0009530680822688710.999523465958866
260.003799990302088070.007599980604176150.996200009697912
270.009320782546225540.01864156509245110.990679217453774
280.007513430797856430.01502686159571290.992486569202144
290.03674584057988680.07349168115977360.963254159420113
300.4343975367813520.8687950735627040.565602463218648
310.8040408144490240.3919183711019530.195959185550976
320.7823672464782760.4352655070434480.217632753521724
330.9765011490660280.04699770186794480.0234988509339724
340.9974604035942630.005079192811473930.00253959640573697
350.9953999829531860.009200034093627810.00460001704681391
360.9951667098720650.009666580255870570.00483329012793528
370.99852131135190.002957377296201570.00147868864810078
380.9989266839915560.002146632016887540.00107331600844377
390.9946113372004770.01077732559904600.00538866279952299






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level130.619047619047619NOK
5% type I error level170.80952380952381NOK
10% type I error level180.857142857142857NOK

\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 & 13 & 0.619047619047619 & NOK \tabularnewline
5% type I error level & 17 & 0.80952380952381 & NOK \tabularnewline
10% type I error level & 18 & 0.857142857142857 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58348&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]13[/C][C]0.619047619047619[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]17[/C][C]0.80952380952381[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]18[/C][C]0.857142857142857[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58348&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58348&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 level130.619047619047619NOK
5% type I error level170.80952380952381NOK
10% type I error level180.857142857142857NOK


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 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 2 ; 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')
}