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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 computationThu, 19 Nov 2009 12:17:04 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/19/t1258658281701rkyjyg23soy0.htm/, Retrieved Fri, 29 Mar 2024 07:08:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57907, Retrieved Fri, 29 Mar 2024 07:08:08 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117
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] [workshop7] [2009-11-19 19:17:04] [307139c5e328127f586f26d5bcc435d8] [Current]
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Dataseries X:
5.4	2.7
5.4	2.5
5.6	2.2
5.7	2.9
5.8	3.1
5.8	3
5.8	2.8
5.9	2.5
6.1	1.9
6.4	1.9
6.4	1.8
6.3	2
6.2	2.6
6.2	2.5
6.3	2.5
6.4	1.6
6.5	1.4
6.6	0.8
6.6	1.1
6.6	1.3
6.8	1.2
7	1.3
7.2	1.1
7.3	1.3
7.5	1.2
7.6	1.6
7.6	1.7
7.7	1.5
7.7	0.9
7.7	1.5
7.7	1.4
7.6	1.6
7.7	1.7
7.9	1.4
7.9	1.8
7.9	1.7
7.8	1.4
7.6	1.2
7.4	1
7	1.7
7	2.4
7.2	2
7.5	2.1
7.8	2
7.8	1.8
7.7	2.7
7.6	2.3
7.6	1.9
7.5	2
7.5	2.3
7.6	2.8
7.6	2.4
7.9	2.3
7.6	2.7
7.5	2.7
7.5	2.9
7.6	3
7.7	2.2
7.8	2.3
7.9	2.8
7.9	2.8




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57907&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57907&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57907&T=0

As an alternative you can also use a QR Code:  

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

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







Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 6.8925548273832 -0.450048120480993X[t] -0.078750036721978M1[t] -0.120513226375429M2[t] -0.109860556364419M3[t] -0.177209811172647M4[t] -0.115558103571256M5[t] -0.162907358379485M6[t] -0.152254688368474M7[t] -0.112601055947844M8[t] -0.0939560852137923M9[t] -0.00130534002202076M10[t] -0.0176555572398699M11[t] + 0.0383482923986091t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  6.8925548273832 -0.450048120480993X[t] -0.078750036721978M1[t] -0.120513226375429M2[t] -0.109860556364419M3[t] -0.177209811172647M4[t] -0.115558103571256M5[t] -0.162907358379485M6[t] -0.152254688368474M7[t] -0.112601055947844M8[t] -0.0939560852137923M9[t] -0.00130534002202076M10[t] -0.0176555572398699M11[t] +  0.0383482923986091t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57907&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  6.8925548273832 -0.450048120480993X[t] -0.078750036721978M1[t] -0.120513226375429M2[t] -0.109860556364419M3[t] -0.177209811172647M4[t] -0.115558103571256M5[t] -0.162907358379485M6[t] -0.152254688368474M7[t] -0.112601055947844M8[t] -0.0939560852137923M9[t] -0.00130534002202076M10[t] -0.0176555572398699M11[t] +  0.0383482923986091t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57907&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57907&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] = + 6.8925548273832 -0.450048120480993X[t] -0.078750036721978M1[t] -0.120513226375429M2[t] -0.109860556364419M3[t] -0.177209811172647M4[t] -0.115558103571256M5[t] -0.162907358379485M6[t] -0.152254688368474M7[t] -0.112601055947844M8[t] -0.0939560852137923M9[t] -0.00130534002202076M10[t] -0.0176555572398699M11[t] + 0.0383482923986091t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)6.89255482738320.20104134.284300
X-0.4500481204809930.066701-6.747300
M1-0.0787500367219780.191341-0.41160.6825270.341263
M2-0.1205132263754290.200525-0.6010.5507350.275367
M3-0.1098605563644190.200315-0.54840.5859860.292993
M4-0.1772098111726470.20001-0.8860.3801270.190063
M5-0.1155581035712560.199794-0.57840.5657650.282882
M6-0.1629073583794850.19956-0.81630.4184280.209214
M7-0.1522546883684740.199444-0.76340.4490420.224521
M8-0.1126010559478440.199418-0.56460.5749980.287499
M9-0.09395608521379230.199101-0.47190.6391810.319591
M10-0.001305340022020760.199043-0.00660.9947950.497398
M11-0.01765555723986990.199055-0.08870.92970.46485
t0.03834829239860910.00234816.330500

\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) & 6.8925548273832 & 0.201041 & 34.2843 & 0 & 0 \tabularnewline
X & -0.450048120480993 & 0.066701 & -6.7473 & 0 & 0 \tabularnewline
M1 & -0.078750036721978 & 0.191341 & -0.4116 & 0.682527 & 0.341263 \tabularnewline
M2 & -0.120513226375429 & 0.200525 & -0.601 & 0.550735 & 0.275367 \tabularnewline
M3 & -0.109860556364419 & 0.200315 & -0.5484 & 0.585986 & 0.292993 \tabularnewline
M4 & -0.177209811172647 & 0.20001 & -0.886 & 0.380127 & 0.190063 \tabularnewline
M5 & -0.115558103571256 & 0.199794 & -0.5784 & 0.565765 & 0.282882 \tabularnewline
M6 & -0.162907358379485 & 0.19956 & -0.8163 & 0.418428 & 0.209214 \tabularnewline
M7 & -0.152254688368474 & 0.199444 & -0.7634 & 0.449042 & 0.224521 \tabularnewline
M8 & -0.112601055947844 & 0.199418 & -0.5646 & 0.574998 & 0.287499 \tabularnewline
M9 & -0.0939560852137923 & 0.199101 & -0.4719 & 0.639181 & 0.319591 \tabularnewline
M10 & -0.00130534002202076 & 0.199043 & -0.0066 & 0.994795 & 0.497398 \tabularnewline
M11 & -0.0176555572398699 & 0.199055 & -0.0887 & 0.9297 & 0.46485 \tabularnewline
t & 0.0383482923986091 & 0.002348 & 16.3305 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57907&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]6.8925548273832[/C][C]0.201041[/C][C]34.2843[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]-0.450048120480993[/C][C]0.066701[/C][C]-6.7473[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-0.078750036721978[/C][C]0.191341[/C][C]-0.4116[/C][C]0.682527[/C][C]0.341263[/C][/ROW]
[ROW][C]M2[/C][C]-0.120513226375429[/C][C]0.200525[/C][C]-0.601[/C][C]0.550735[/C][C]0.275367[/C][/ROW]
[ROW][C]M3[/C][C]-0.109860556364419[/C][C]0.200315[/C][C]-0.5484[/C][C]0.585986[/C][C]0.292993[/C][/ROW]
[ROW][C]M4[/C][C]-0.177209811172647[/C][C]0.20001[/C][C]-0.886[/C][C]0.380127[/C][C]0.190063[/C][/ROW]
[ROW][C]M5[/C][C]-0.115558103571256[/C][C]0.199794[/C][C]-0.5784[/C][C]0.565765[/C][C]0.282882[/C][/ROW]
[ROW][C]M6[/C][C]-0.162907358379485[/C][C]0.19956[/C][C]-0.8163[/C][C]0.418428[/C][C]0.209214[/C][/ROW]
[ROW][C]M7[/C][C]-0.152254688368474[/C][C]0.199444[/C][C]-0.7634[/C][C]0.449042[/C][C]0.224521[/C][/ROW]
[ROW][C]M8[/C][C]-0.112601055947844[/C][C]0.199418[/C][C]-0.5646[/C][C]0.574998[/C][C]0.287499[/C][/ROW]
[ROW][C]M9[/C][C]-0.0939560852137923[/C][C]0.199101[/C][C]-0.4719[/C][C]0.639181[/C][C]0.319591[/C][/ROW]
[ROW][C]M10[/C][C]-0.00130534002202076[/C][C]0.199043[/C][C]-0.0066[/C][C]0.994795[/C][C]0.497398[/C][/ROW]
[ROW][C]M11[/C][C]-0.0176555572398699[/C][C]0.199055[/C][C]-0.0887[/C][C]0.9297[/C][C]0.46485[/C][/ROW]
[ROW][C]t[/C][C]0.0383482923986091[/C][C]0.002348[/C][C]16.3305[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57907&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57907&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)6.89255482738320.20104134.284300
X-0.4500481204809930.066701-6.747300
M1-0.0787500367219780.191341-0.41160.6825270.341263
M2-0.1205132263754290.200525-0.6010.5507350.275367
M3-0.1098605563644190.200315-0.54840.5859860.292993
M4-0.1772098111726470.20001-0.8860.3801270.190063
M5-0.1155581035712560.199794-0.57840.5657650.282882
M6-0.1629073583794850.19956-0.81630.4184280.209214
M7-0.1522546883684740.199444-0.76340.4490420.224521
M8-0.1126010559478440.199418-0.56460.5749980.287499
M9-0.09395608521379230.199101-0.47190.6391810.319591
M10-0.001305340022020760.199043-0.00660.9947950.497398
M11-0.01765555723986990.199055-0.08870.92970.46485
t0.03834829239860910.00234816.330500







Multiple Linear Regression - Regression Statistics
Multiple R0.931216785308685
R-squared0.867164701240642
Adjusted R-squared0.830423022860394
F-TEST (value)23.6016627293439
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value2.22044604925031e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.314614031618701
Sum Squared Residuals4.65215347789455

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.931216785308685 \tabularnewline
R-squared & 0.867164701240642 \tabularnewline
Adjusted R-squared & 0.830423022860394 \tabularnewline
F-TEST (value) & 23.6016627293439 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 2.22044604925031e-16 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.314614031618701 \tabularnewline
Sum Squared Residuals & 4.65215347789455 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57907&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.931216785308685[/C][/ROW]
[ROW][C]R-squared[/C][C]0.867164701240642[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.830423022860394[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]23.6016627293439[/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]2.22044604925031e-16[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.314614031618701[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]4.65215347789455[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57907&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57907&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 R0.931216785308685
R-squared0.867164701240642
Adjusted R-squared0.830423022860394
F-TEST (value)23.6016627293439
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value2.22044604925031e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.314614031618701
Sum Squared Residuals4.65215347789455







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
15.45.63702315776115-0.237023157761147
25.45.7236178846025-0.323617884602503
35.65.90763328315642-0.307633283156423
45.75.563598636410110.136401363589894
55.85.573589012313910.226410987686092
65.85.609592861952390.190407138047613
75.85.74860344845820.0513965515417942
85.95.96161980942174-0.0616198094217432
96.16.288641944843-0.188641944843001
106.46.41964098243338-0.0196409824333802
116.46.48664386966224-0.08664386966224
126.36.45263809520452-0.152638095204521
136.26.142207478592550.0577925214074454
146.26.183797393385810.0162026066141876
156.36.232798355795430.067201644204567
166.46.60884070181871-0.208840701818707
176.56.79885032591491-0.298850325914906
186.67.05987823579388-0.459878235793882
196.66.9738647620592-0.373864762059204
206.66.96185706278225-0.361857062782245
216.87.063855137963-0.263855137963005
2277.14984936350529-0.149849363505286
237.27.26185706278225-0.0618570627822449
247.37.227851288324530.0721487116754742
257.57.232454356049260.267545643950744
267.67.049020210602020.550979789397982
277.67.053016360963540.546983639036462
287.77.114025022650120.585974977349883
297.77.484053894938710.215946105061288
307.77.20502406024050.494975939759504
317.77.299029834698220.400970165301784
327.67.287022135421260.312977864578743
337.77.299010586505820.400989413494182
347.97.56502406024050.334975939759503
357.97.407002887228860.492997112771141
367.97.508011548915440.391988451084562
377.87.602624240736370.197375759263633
387.67.68921896757772-0.0892189675777252
397.47.82822955408354-0.428229554083542
4077.48419490733723-0.484194907337228
4177.26916122300053-0.269161223000532
427.27.44017950878331-0.240179508783310
437.57.444175659144830.0558243408551698
447.87.567182396012170.23281760398783
457.87.714185283241030.0858147167589713
467.77.440141012398520.259858987601485
477.67.64215833577167-0.0421583357716732
487.67.87818143360255-0.278181433602549
497.57.79277487723108-0.292774877231081
507.57.65434554383194-0.154345543831942
517.67.478322446001060.121677553998935
527.67.62934073178384-0.0293407317838426
537.97.774345543831940.125654456168059
547.67.585325333229920.0146746667700755
557.57.63432629563954-0.134326295639544
567.57.62231859636259-0.122318596362585
577.67.63430704744715-0.0343070474471465
587.78.12534458142232-0.425344581422321
597.88.10233784455498-0.302337844554983
607.97.93331763395297-0.0333176339529647
617.97.89291588962960.00708411037040462

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 5.4 & 5.63702315776115 & -0.237023157761147 \tabularnewline
2 & 5.4 & 5.7236178846025 & -0.323617884602503 \tabularnewline
3 & 5.6 & 5.90763328315642 & -0.307633283156423 \tabularnewline
4 & 5.7 & 5.56359863641011 & 0.136401363589894 \tabularnewline
5 & 5.8 & 5.57358901231391 & 0.226410987686092 \tabularnewline
6 & 5.8 & 5.60959286195239 & 0.190407138047613 \tabularnewline
7 & 5.8 & 5.7486034484582 & 0.0513965515417942 \tabularnewline
8 & 5.9 & 5.96161980942174 & -0.0616198094217432 \tabularnewline
9 & 6.1 & 6.288641944843 & -0.188641944843001 \tabularnewline
10 & 6.4 & 6.41964098243338 & -0.0196409824333802 \tabularnewline
11 & 6.4 & 6.48664386966224 & -0.08664386966224 \tabularnewline
12 & 6.3 & 6.45263809520452 & -0.152638095204521 \tabularnewline
13 & 6.2 & 6.14220747859255 & 0.0577925214074454 \tabularnewline
14 & 6.2 & 6.18379739338581 & 0.0162026066141876 \tabularnewline
15 & 6.3 & 6.23279835579543 & 0.067201644204567 \tabularnewline
16 & 6.4 & 6.60884070181871 & -0.208840701818707 \tabularnewline
17 & 6.5 & 6.79885032591491 & -0.298850325914906 \tabularnewline
18 & 6.6 & 7.05987823579388 & -0.459878235793882 \tabularnewline
19 & 6.6 & 6.9738647620592 & -0.373864762059204 \tabularnewline
20 & 6.6 & 6.96185706278225 & -0.361857062782245 \tabularnewline
21 & 6.8 & 7.063855137963 & -0.263855137963005 \tabularnewline
22 & 7 & 7.14984936350529 & -0.149849363505286 \tabularnewline
23 & 7.2 & 7.26185706278225 & -0.0618570627822449 \tabularnewline
24 & 7.3 & 7.22785128832453 & 0.0721487116754742 \tabularnewline
25 & 7.5 & 7.23245435604926 & 0.267545643950744 \tabularnewline
26 & 7.6 & 7.04902021060202 & 0.550979789397982 \tabularnewline
27 & 7.6 & 7.05301636096354 & 0.546983639036462 \tabularnewline
28 & 7.7 & 7.11402502265012 & 0.585974977349883 \tabularnewline
29 & 7.7 & 7.48405389493871 & 0.215946105061288 \tabularnewline
30 & 7.7 & 7.2050240602405 & 0.494975939759504 \tabularnewline
31 & 7.7 & 7.29902983469822 & 0.400970165301784 \tabularnewline
32 & 7.6 & 7.28702213542126 & 0.312977864578743 \tabularnewline
33 & 7.7 & 7.29901058650582 & 0.400989413494182 \tabularnewline
34 & 7.9 & 7.5650240602405 & 0.334975939759503 \tabularnewline
35 & 7.9 & 7.40700288722886 & 0.492997112771141 \tabularnewline
36 & 7.9 & 7.50801154891544 & 0.391988451084562 \tabularnewline
37 & 7.8 & 7.60262424073637 & 0.197375759263633 \tabularnewline
38 & 7.6 & 7.68921896757772 & -0.0892189675777252 \tabularnewline
39 & 7.4 & 7.82822955408354 & -0.428229554083542 \tabularnewline
40 & 7 & 7.48419490733723 & -0.484194907337228 \tabularnewline
41 & 7 & 7.26916122300053 & -0.269161223000532 \tabularnewline
42 & 7.2 & 7.44017950878331 & -0.240179508783310 \tabularnewline
43 & 7.5 & 7.44417565914483 & 0.0558243408551698 \tabularnewline
44 & 7.8 & 7.56718239601217 & 0.23281760398783 \tabularnewline
45 & 7.8 & 7.71418528324103 & 0.0858147167589713 \tabularnewline
46 & 7.7 & 7.44014101239852 & 0.259858987601485 \tabularnewline
47 & 7.6 & 7.64215833577167 & -0.0421583357716732 \tabularnewline
48 & 7.6 & 7.87818143360255 & -0.278181433602549 \tabularnewline
49 & 7.5 & 7.79277487723108 & -0.292774877231081 \tabularnewline
50 & 7.5 & 7.65434554383194 & -0.154345543831942 \tabularnewline
51 & 7.6 & 7.47832244600106 & 0.121677553998935 \tabularnewline
52 & 7.6 & 7.62934073178384 & -0.0293407317838426 \tabularnewline
53 & 7.9 & 7.77434554383194 & 0.125654456168059 \tabularnewline
54 & 7.6 & 7.58532533322992 & 0.0146746667700755 \tabularnewline
55 & 7.5 & 7.63432629563954 & -0.134326295639544 \tabularnewline
56 & 7.5 & 7.62231859636259 & -0.122318596362585 \tabularnewline
57 & 7.6 & 7.63430704744715 & -0.0343070474471465 \tabularnewline
58 & 7.7 & 8.12534458142232 & -0.425344581422321 \tabularnewline
59 & 7.8 & 8.10233784455498 & -0.302337844554983 \tabularnewline
60 & 7.9 & 7.93331763395297 & -0.0333176339529647 \tabularnewline
61 & 7.9 & 7.8929158896296 & 0.00708411037040462 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57907&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]5.4[/C][C]5.63702315776115[/C][C]-0.237023157761147[/C][/ROW]
[ROW][C]2[/C][C]5.4[/C][C]5.7236178846025[/C][C]-0.323617884602503[/C][/ROW]
[ROW][C]3[/C][C]5.6[/C][C]5.90763328315642[/C][C]-0.307633283156423[/C][/ROW]
[ROW][C]4[/C][C]5.7[/C][C]5.56359863641011[/C][C]0.136401363589894[/C][/ROW]
[ROW][C]5[/C][C]5.8[/C][C]5.57358901231391[/C][C]0.226410987686092[/C][/ROW]
[ROW][C]6[/C][C]5.8[/C][C]5.60959286195239[/C][C]0.190407138047613[/C][/ROW]
[ROW][C]7[/C][C]5.8[/C][C]5.7486034484582[/C][C]0.0513965515417942[/C][/ROW]
[ROW][C]8[/C][C]5.9[/C][C]5.96161980942174[/C][C]-0.0616198094217432[/C][/ROW]
[ROW][C]9[/C][C]6.1[/C][C]6.288641944843[/C][C]-0.188641944843001[/C][/ROW]
[ROW][C]10[/C][C]6.4[/C][C]6.41964098243338[/C][C]-0.0196409824333802[/C][/ROW]
[ROW][C]11[/C][C]6.4[/C][C]6.48664386966224[/C][C]-0.08664386966224[/C][/ROW]
[ROW][C]12[/C][C]6.3[/C][C]6.45263809520452[/C][C]-0.152638095204521[/C][/ROW]
[ROW][C]13[/C][C]6.2[/C][C]6.14220747859255[/C][C]0.0577925214074454[/C][/ROW]
[ROW][C]14[/C][C]6.2[/C][C]6.18379739338581[/C][C]0.0162026066141876[/C][/ROW]
[ROW][C]15[/C][C]6.3[/C][C]6.23279835579543[/C][C]0.067201644204567[/C][/ROW]
[ROW][C]16[/C][C]6.4[/C][C]6.60884070181871[/C][C]-0.208840701818707[/C][/ROW]
[ROW][C]17[/C][C]6.5[/C][C]6.79885032591491[/C][C]-0.298850325914906[/C][/ROW]
[ROW][C]18[/C][C]6.6[/C][C]7.05987823579388[/C][C]-0.459878235793882[/C][/ROW]
[ROW][C]19[/C][C]6.6[/C][C]6.9738647620592[/C][C]-0.373864762059204[/C][/ROW]
[ROW][C]20[/C][C]6.6[/C][C]6.96185706278225[/C][C]-0.361857062782245[/C][/ROW]
[ROW][C]21[/C][C]6.8[/C][C]7.063855137963[/C][C]-0.263855137963005[/C][/ROW]
[ROW][C]22[/C][C]7[/C][C]7.14984936350529[/C][C]-0.149849363505286[/C][/ROW]
[ROW][C]23[/C][C]7.2[/C][C]7.26185706278225[/C][C]-0.0618570627822449[/C][/ROW]
[ROW][C]24[/C][C]7.3[/C][C]7.22785128832453[/C][C]0.0721487116754742[/C][/ROW]
[ROW][C]25[/C][C]7.5[/C][C]7.23245435604926[/C][C]0.267545643950744[/C][/ROW]
[ROW][C]26[/C][C]7.6[/C][C]7.04902021060202[/C][C]0.550979789397982[/C][/ROW]
[ROW][C]27[/C][C]7.6[/C][C]7.05301636096354[/C][C]0.546983639036462[/C][/ROW]
[ROW][C]28[/C][C]7.7[/C][C]7.11402502265012[/C][C]0.585974977349883[/C][/ROW]
[ROW][C]29[/C][C]7.7[/C][C]7.48405389493871[/C][C]0.215946105061288[/C][/ROW]
[ROW][C]30[/C][C]7.7[/C][C]7.2050240602405[/C][C]0.494975939759504[/C][/ROW]
[ROW][C]31[/C][C]7.7[/C][C]7.29902983469822[/C][C]0.400970165301784[/C][/ROW]
[ROW][C]32[/C][C]7.6[/C][C]7.28702213542126[/C][C]0.312977864578743[/C][/ROW]
[ROW][C]33[/C][C]7.7[/C][C]7.29901058650582[/C][C]0.400989413494182[/C][/ROW]
[ROW][C]34[/C][C]7.9[/C][C]7.5650240602405[/C][C]0.334975939759503[/C][/ROW]
[ROW][C]35[/C][C]7.9[/C][C]7.40700288722886[/C][C]0.492997112771141[/C][/ROW]
[ROW][C]36[/C][C]7.9[/C][C]7.50801154891544[/C][C]0.391988451084562[/C][/ROW]
[ROW][C]37[/C][C]7.8[/C][C]7.60262424073637[/C][C]0.197375759263633[/C][/ROW]
[ROW][C]38[/C][C]7.6[/C][C]7.68921896757772[/C][C]-0.0892189675777252[/C][/ROW]
[ROW][C]39[/C][C]7.4[/C][C]7.82822955408354[/C][C]-0.428229554083542[/C][/ROW]
[ROW][C]40[/C][C]7[/C][C]7.48419490733723[/C][C]-0.484194907337228[/C][/ROW]
[ROW][C]41[/C][C]7[/C][C]7.26916122300053[/C][C]-0.269161223000532[/C][/ROW]
[ROW][C]42[/C][C]7.2[/C][C]7.44017950878331[/C][C]-0.240179508783310[/C][/ROW]
[ROW][C]43[/C][C]7.5[/C][C]7.44417565914483[/C][C]0.0558243408551698[/C][/ROW]
[ROW][C]44[/C][C]7.8[/C][C]7.56718239601217[/C][C]0.23281760398783[/C][/ROW]
[ROW][C]45[/C][C]7.8[/C][C]7.71418528324103[/C][C]0.0858147167589713[/C][/ROW]
[ROW][C]46[/C][C]7.7[/C][C]7.44014101239852[/C][C]0.259858987601485[/C][/ROW]
[ROW][C]47[/C][C]7.6[/C][C]7.64215833577167[/C][C]-0.0421583357716732[/C][/ROW]
[ROW][C]48[/C][C]7.6[/C][C]7.87818143360255[/C][C]-0.278181433602549[/C][/ROW]
[ROW][C]49[/C][C]7.5[/C][C]7.79277487723108[/C][C]-0.292774877231081[/C][/ROW]
[ROW][C]50[/C][C]7.5[/C][C]7.65434554383194[/C][C]-0.154345543831942[/C][/ROW]
[ROW][C]51[/C][C]7.6[/C][C]7.47832244600106[/C][C]0.121677553998935[/C][/ROW]
[ROW][C]52[/C][C]7.6[/C][C]7.62934073178384[/C][C]-0.0293407317838426[/C][/ROW]
[ROW][C]53[/C][C]7.9[/C][C]7.77434554383194[/C][C]0.125654456168059[/C][/ROW]
[ROW][C]54[/C][C]7.6[/C][C]7.58532533322992[/C][C]0.0146746667700755[/C][/ROW]
[ROW][C]55[/C][C]7.5[/C][C]7.63432629563954[/C][C]-0.134326295639544[/C][/ROW]
[ROW][C]56[/C][C]7.5[/C][C]7.62231859636259[/C][C]-0.122318596362585[/C][/ROW]
[ROW][C]57[/C][C]7.6[/C][C]7.63430704744715[/C][C]-0.0343070474471465[/C][/ROW]
[ROW][C]58[/C][C]7.7[/C][C]8.12534458142232[/C][C]-0.425344581422321[/C][/ROW]
[ROW][C]59[/C][C]7.8[/C][C]8.10233784455498[/C][C]-0.302337844554983[/C][/ROW]
[ROW][C]60[/C][C]7.9[/C][C]7.93331763395297[/C][C]-0.0333176339529647[/C][/ROW]
[ROW][C]61[/C][C]7.9[/C][C]7.8929158896296[/C][C]0.00708411037040462[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57907&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57907&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
15.45.63702315776115-0.237023157761147
25.45.7236178846025-0.323617884602503
35.65.90763328315642-0.307633283156423
45.75.563598636410110.136401363589894
55.85.573589012313910.226410987686092
65.85.609592861952390.190407138047613
75.85.74860344845820.0513965515417942
85.95.96161980942174-0.0616198094217432
96.16.288641944843-0.188641944843001
106.46.41964098243338-0.0196409824333802
116.46.48664386966224-0.08664386966224
126.36.45263809520452-0.152638095204521
136.26.142207478592550.0577925214074454
146.26.183797393385810.0162026066141876
156.36.232798355795430.067201644204567
166.46.60884070181871-0.208840701818707
176.56.79885032591491-0.298850325914906
186.67.05987823579388-0.459878235793882
196.66.9738647620592-0.373864762059204
206.66.96185706278225-0.361857062782245
216.87.063855137963-0.263855137963005
2277.14984936350529-0.149849363505286
237.27.26185706278225-0.0618570627822449
247.37.227851288324530.0721487116754742
257.57.232454356049260.267545643950744
267.67.049020210602020.550979789397982
277.67.053016360963540.546983639036462
287.77.114025022650120.585974977349883
297.77.484053894938710.215946105061288
307.77.20502406024050.494975939759504
317.77.299029834698220.400970165301784
327.67.287022135421260.312977864578743
337.77.299010586505820.400989413494182
347.97.56502406024050.334975939759503
357.97.407002887228860.492997112771141
367.97.508011548915440.391988451084562
377.87.602624240736370.197375759263633
387.67.68921896757772-0.0892189675777252
397.47.82822955408354-0.428229554083542
4077.48419490733723-0.484194907337228
4177.26916122300053-0.269161223000532
427.27.44017950878331-0.240179508783310
437.57.444175659144830.0558243408551698
447.87.567182396012170.23281760398783
457.87.714185283241030.0858147167589713
467.77.440141012398520.259858987601485
477.67.64215833577167-0.0421583357716732
487.67.87818143360255-0.278181433602549
497.57.79277487723108-0.292774877231081
507.57.65434554383194-0.154345543831942
517.67.478322446001060.121677553998935
527.67.62934073178384-0.0293407317838426
537.97.774345543831940.125654456168059
547.67.585325333229920.0146746667700755
557.57.63432629563954-0.134326295639544
567.57.62231859636259-0.122318596362585
577.67.63430704744715-0.0343070474471465
587.78.12534458142232-0.425344581422321
597.88.10233784455498-0.302337844554983
607.97.93331763395297-0.0333176339529647
617.97.89291588962960.00708411037040462







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.001984641674131350.003969283348262710.998015358325869
180.0006175765023728090.001235153004745620.999382423497627
190.0001256030394148160.0002512060788296330.999874396960585
203.82999762714679e-057.65999525429358e-050.999961700023729
211.26262254316843e-052.52524508633686e-050.999987373774568
223.25860107898704e-056.51720215797408e-050.99996741398921
231.61640286270093e-053.23280572540187e-050.999983835971373
240.0003301995040449680.0006603990080899370.999669800495955
250.04720129811358720.09440259622717450.952798701886413
260.1593153920886760.3186307841773520.840684607911324
270.1455921633325350.2911843266650700.854407836667465
280.1587733723094740.3175467446189490.841226627690526
290.1227929733767300.2455859467534590.87720702662327
300.09980579293543510.1996115858708700.900194207064565
310.07219783023148720.1443956604629740.927802169768513
320.04823643571799440.09647287143598870.951763564282006
330.03788713037962050.0757742607592410.96211286962038
340.03627053518062550.0725410703612510.963729464819374
350.04951489746971470.09902979493942930.950485102530285
360.06462745187801880.1292549037560380.935372548121981
370.1065927364105580.2131854728211160.893407263589442
380.1838952023705130.3677904047410250.816104797629488
390.3355919865724420.6711839731448840.664408013427558
400.6629110440702970.6741779118594060.337088955929703
410.8959434020097740.2081131959804530.104056597990226
420.8972218595865640.2055562808268730.102778140413436
430.8046569572083920.3906860855832170.195343042791608
440.7995291334743220.4009417330513560.200470866525678

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.00198464167413135 & 0.00396928334826271 & 0.998015358325869 \tabularnewline
18 & 0.000617576502372809 & 0.00123515300474562 & 0.999382423497627 \tabularnewline
19 & 0.000125603039414816 & 0.000251206078829633 & 0.999874396960585 \tabularnewline
20 & 3.82999762714679e-05 & 7.65999525429358e-05 & 0.999961700023729 \tabularnewline
21 & 1.26262254316843e-05 & 2.52524508633686e-05 & 0.999987373774568 \tabularnewline
22 & 3.25860107898704e-05 & 6.51720215797408e-05 & 0.99996741398921 \tabularnewline
23 & 1.61640286270093e-05 & 3.23280572540187e-05 & 0.999983835971373 \tabularnewline
24 & 0.000330199504044968 & 0.000660399008089937 & 0.999669800495955 \tabularnewline
25 & 0.0472012981135872 & 0.0944025962271745 & 0.952798701886413 \tabularnewline
26 & 0.159315392088676 & 0.318630784177352 & 0.840684607911324 \tabularnewline
27 & 0.145592163332535 & 0.291184326665070 & 0.854407836667465 \tabularnewline
28 & 0.158773372309474 & 0.317546744618949 & 0.841226627690526 \tabularnewline
29 & 0.122792973376730 & 0.245585946753459 & 0.87720702662327 \tabularnewline
30 & 0.0998057929354351 & 0.199611585870870 & 0.900194207064565 \tabularnewline
31 & 0.0721978302314872 & 0.144395660462974 & 0.927802169768513 \tabularnewline
32 & 0.0482364357179944 & 0.0964728714359887 & 0.951763564282006 \tabularnewline
33 & 0.0378871303796205 & 0.075774260759241 & 0.96211286962038 \tabularnewline
34 & 0.0362705351806255 & 0.072541070361251 & 0.963729464819374 \tabularnewline
35 & 0.0495148974697147 & 0.0990297949394293 & 0.950485102530285 \tabularnewline
36 & 0.0646274518780188 & 0.129254903756038 & 0.935372548121981 \tabularnewline
37 & 0.106592736410558 & 0.213185472821116 & 0.893407263589442 \tabularnewline
38 & 0.183895202370513 & 0.367790404741025 & 0.816104797629488 \tabularnewline
39 & 0.335591986572442 & 0.671183973144884 & 0.664408013427558 \tabularnewline
40 & 0.662911044070297 & 0.674177911859406 & 0.337088955929703 \tabularnewline
41 & 0.895943402009774 & 0.208113195980453 & 0.104056597990226 \tabularnewline
42 & 0.897221859586564 & 0.205556280826873 & 0.102778140413436 \tabularnewline
43 & 0.804656957208392 & 0.390686085583217 & 0.195343042791608 \tabularnewline
44 & 0.799529133474322 & 0.400941733051356 & 0.200470866525678 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57907&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]0.00198464167413135[/C][C]0.00396928334826271[/C][C]0.998015358325869[/C][/ROW]
[ROW][C]18[/C][C]0.000617576502372809[/C][C]0.00123515300474562[/C][C]0.999382423497627[/C][/ROW]
[ROW][C]19[/C][C]0.000125603039414816[/C][C]0.000251206078829633[/C][C]0.999874396960585[/C][/ROW]
[ROW][C]20[/C][C]3.82999762714679e-05[/C][C]7.65999525429358e-05[/C][C]0.999961700023729[/C][/ROW]
[ROW][C]21[/C][C]1.26262254316843e-05[/C][C]2.52524508633686e-05[/C][C]0.999987373774568[/C][/ROW]
[ROW][C]22[/C][C]3.25860107898704e-05[/C][C]6.51720215797408e-05[/C][C]0.99996741398921[/C][/ROW]
[ROW][C]23[/C][C]1.61640286270093e-05[/C][C]3.23280572540187e-05[/C][C]0.999983835971373[/C][/ROW]
[ROW][C]24[/C][C]0.000330199504044968[/C][C]0.000660399008089937[/C][C]0.999669800495955[/C][/ROW]
[ROW][C]25[/C][C]0.0472012981135872[/C][C]0.0944025962271745[/C][C]0.952798701886413[/C][/ROW]
[ROW][C]26[/C][C]0.159315392088676[/C][C]0.318630784177352[/C][C]0.840684607911324[/C][/ROW]
[ROW][C]27[/C][C]0.145592163332535[/C][C]0.291184326665070[/C][C]0.854407836667465[/C][/ROW]
[ROW][C]28[/C][C]0.158773372309474[/C][C]0.317546744618949[/C][C]0.841226627690526[/C][/ROW]
[ROW][C]29[/C][C]0.122792973376730[/C][C]0.245585946753459[/C][C]0.87720702662327[/C][/ROW]
[ROW][C]30[/C][C]0.0998057929354351[/C][C]0.199611585870870[/C][C]0.900194207064565[/C][/ROW]
[ROW][C]31[/C][C]0.0721978302314872[/C][C]0.144395660462974[/C][C]0.927802169768513[/C][/ROW]
[ROW][C]32[/C][C]0.0482364357179944[/C][C]0.0964728714359887[/C][C]0.951763564282006[/C][/ROW]
[ROW][C]33[/C][C]0.0378871303796205[/C][C]0.075774260759241[/C][C]0.96211286962038[/C][/ROW]
[ROW][C]34[/C][C]0.0362705351806255[/C][C]0.072541070361251[/C][C]0.963729464819374[/C][/ROW]
[ROW][C]35[/C][C]0.0495148974697147[/C][C]0.0990297949394293[/C][C]0.950485102530285[/C][/ROW]
[ROW][C]36[/C][C]0.0646274518780188[/C][C]0.129254903756038[/C][C]0.935372548121981[/C][/ROW]
[ROW][C]37[/C][C]0.106592736410558[/C][C]0.213185472821116[/C][C]0.893407263589442[/C][/ROW]
[ROW][C]38[/C][C]0.183895202370513[/C][C]0.367790404741025[/C][C]0.816104797629488[/C][/ROW]
[ROW][C]39[/C][C]0.335591986572442[/C][C]0.671183973144884[/C][C]0.664408013427558[/C][/ROW]
[ROW][C]40[/C][C]0.662911044070297[/C][C]0.674177911859406[/C][C]0.337088955929703[/C][/ROW]
[ROW][C]41[/C][C]0.895943402009774[/C][C]0.208113195980453[/C][C]0.104056597990226[/C][/ROW]
[ROW][C]42[/C][C]0.897221859586564[/C][C]0.205556280826873[/C][C]0.102778140413436[/C][/ROW]
[ROW][C]43[/C][C]0.804656957208392[/C][C]0.390686085583217[/C][C]0.195343042791608[/C][/ROW]
[ROW][C]44[/C][C]0.799529133474322[/C][C]0.400941733051356[/C][C]0.200470866525678[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57907&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57907&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
170.001984641674131350.003969283348262710.998015358325869
180.0006175765023728090.001235153004745620.999382423497627
190.0001256030394148160.0002512060788296330.999874396960585
203.82999762714679e-057.65999525429358e-050.999961700023729
211.26262254316843e-052.52524508633686e-050.999987373774568
223.25860107898704e-056.51720215797408e-050.99996741398921
231.61640286270093e-053.23280572540187e-050.999983835971373
240.0003301995040449680.0006603990080899370.999669800495955
250.04720129811358720.09440259622717450.952798701886413
260.1593153920886760.3186307841773520.840684607911324
270.1455921633325350.2911843266650700.854407836667465
280.1587733723094740.3175467446189490.841226627690526
290.1227929733767300.2455859467534590.87720702662327
300.09980579293543510.1996115858708700.900194207064565
310.07219783023148720.1443956604629740.927802169768513
320.04823643571799440.09647287143598870.951763564282006
330.03788713037962050.0757742607592410.96211286962038
340.03627053518062550.0725410703612510.963729464819374
350.04951489746971470.09902979493942930.950485102530285
360.06462745187801880.1292549037560380.935372548121981
370.1065927364105580.2131854728211160.893407263589442
380.1838952023705130.3677904047410250.816104797629488
390.3355919865724420.6711839731448840.664408013427558
400.6629110440702970.6741779118594060.337088955929703
410.8959434020097740.2081131959804530.104056597990226
420.8972218595865640.2055562808268730.102778140413436
430.8046569572083920.3906860855832170.195343042791608
440.7995291334743220.4009417330513560.200470866525678







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level80.285714285714286NOK
5% type I error level80.285714285714286NOK
10% type I error level130.464285714285714NOK

\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 & 8 & 0.285714285714286 & NOK \tabularnewline
5% type I error level & 8 & 0.285714285714286 & NOK \tabularnewline
10% type I error level & 13 & 0.464285714285714 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57907&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]8[/C][C]0.285714285714286[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]8[/C][C]0.285714285714286[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]13[/C][C]0.464285714285714[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57907&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57907&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 level80.285714285714286NOK
5% type I error level80.285714285714286NOK
10% type I error level130.464285714285714NOK



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')
}