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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 10:06:03 -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/t1258736865881l7wctxrwzx3z.htm/, Retrieved Thu, 28 Mar 2024 09:20:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58336, Retrieved Thu, 28 Mar 2024 09:20:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140
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: model met s...] [2009-11-20 17:06:03] [17b3de9cda9f51722106e41c76160a49] [Current]
-             [Multiple Regression] [WS 7: Model 3: Li...] [2009-11-20 17:23:23] [8cf9233b7464ea02e32be3b30fdac052]
-             [Multiple Regression] [Paper: hypotheses] [2009-12-13 16:47:34] [b97b96148b0223bc16666763988dc147]
-    D          [Multiple Regression] [paper multiple re...] [2009-12-28 14:18:34] [0f0e461427f61416e46aeda5f4901bed]
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Dataseries X:
423	114
427	116
441	153
449	162
452	161
462	149
455	139
461	135
461	130
463	127
462	122
456	117
455	112
456	113
472	149
472	157
471	157
465	147
459	137
465	132
468	125
467	123
463	117
460	114
462	111
461	112
476	144
476	150
471	149
453	134
443	123
442	116
444	117
438	111
427	105
424	102
416	95
406	93
431	124
434	130
418	124
412	115
404	106
409	105
412	105
406	101
398	95
397	93
385	84
390	87
413	116
413	120
401	117
397	109
397	105
409	107
419	109
424	109
428	108
430	107




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=58336&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=58336&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58336&T=0

As an alternative you can also use a QR Code:  

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

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







Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 210.097277375847 + 2.01219960132561X[t] + 4.33105354315315M1[t] + 1.87434713285987M2[t] -46.1727465198532M3[t] -57.4977706975701M4[t] -59.5154383836216M5[t] -42.8281894982728M6[t] -31.5653398155752M7[t] -20.1732478205662M8[t] -13.195795347148M9[t] -8.60370335213898M10[t] -3.18965207474387M11[t] + 0.244506808967836t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  210.097277375847 +  2.01219960132561X[t] +  4.33105354315315M1[t] +  1.87434713285987M2[t] -46.1727465198532M3[t] -57.4977706975701M4[t] -59.5154383836216M5[t] -42.8281894982728M6[t] -31.5653398155752M7[t] -20.1732478205662M8[t] -13.195795347148M9[t] -8.60370335213898M10[t] -3.18965207474387M11[t] +  0.244506808967836t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58336&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  210.097277375847 +  2.01219960132561X[t] +  4.33105354315315M1[t] +  1.87434713285987M2[t] -46.1727465198532M3[t] -57.4977706975701M4[t] -59.5154383836216M5[t] -42.8281894982728M6[t] -31.5653398155752M7[t] -20.1732478205662M8[t] -13.195795347148M9[t] -8.60370335213898M10[t] -3.18965207474387M11[t] +  0.244506808967836t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58336&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58336&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] = + 210.097277375847 + 2.01219960132561X[t] + 4.33105354315315M1[t] + 1.87434713285987M2[t] -46.1727465198532M3[t] -57.4977706975701M4[t] -59.5154383836216M5[t] -42.8281894982728M6[t] -31.5653398155752M7[t] -20.1732478205662M8[t] -13.195795347148M9[t] -8.60370335213898M10[t] -3.18965207474387M11[t] + 0.244506808967836t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)210.09727737584738.652525.43552e-061e-06
X2.012199601325610.2895946.948400
M14.331053543153158.8889650.48720.6284030.314201
M21.874347132859878.7143920.21510.8306510.415325
M3-46.172746519853210.885047-4.24190.0001065.3e-05
M4-57.497770697570112.353443-4.65442.8e-051.4e-05
M5-59.515438383621612.025613-4.94911e-055e-06
M6-42.828189498272810.093164-4.24330.0001065.3e-05
M7-31.56533981557528.942847-3.52970.0009570.000479
M8-20.17324782056628.700421-2.31870.0249110.012456
M9-13.1957953471488.598451-1.53470.1317150.065857
M10-8.603703352138988.427509-1.02090.3126380.156319
M11-3.189652074743878.253434-0.38650.7009350.350468
t0.2445068089678360.2225281.09880.2775870.138794

\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) & 210.097277375847 & 38.65252 & 5.4355 & 2e-06 & 1e-06 \tabularnewline
X & 2.01219960132561 & 0.289594 & 6.9484 & 0 & 0 \tabularnewline
M1 & 4.33105354315315 & 8.888965 & 0.4872 & 0.628403 & 0.314201 \tabularnewline
M2 & 1.87434713285987 & 8.714392 & 0.2151 & 0.830651 & 0.415325 \tabularnewline
M3 & -46.1727465198532 & 10.885047 & -4.2419 & 0.000106 & 5.3e-05 \tabularnewline
M4 & -57.4977706975701 & 12.353443 & -4.6544 & 2.8e-05 & 1.4e-05 \tabularnewline
M5 & -59.5154383836216 & 12.025613 & -4.9491 & 1e-05 & 5e-06 \tabularnewline
M6 & -42.8281894982728 & 10.093164 & -4.2433 & 0.000106 & 5.3e-05 \tabularnewline
M7 & -31.5653398155752 & 8.942847 & -3.5297 & 0.000957 & 0.000479 \tabularnewline
M8 & -20.1732478205662 & 8.700421 & -2.3187 & 0.024911 & 0.012456 \tabularnewline
M9 & -13.195795347148 & 8.598451 & -1.5347 & 0.131715 & 0.065857 \tabularnewline
M10 & -8.60370335213898 & 8.427509 & -1.0209 & 0.312638 & 0.156319 \tabularnewline
M11 & -3.18965207474387 & 8.253434 & -0.3865 & 0.700935 & 0.350468 \tabularnewline
t & 0.244506808967836 & 0.222528 & 1.0988 & 0.277587 & 0.138794 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58336&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]210.097277375847[/C][C]38.65252[/C][C]5.4355[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]X[/C][C]2.01219960132561[/C][C]0.289594[/C][C]6.9484[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]4.33105354315315[/C][C]8.888965[/C][C]0.4872[/C][C]0.628403[/C][C]0.314201[/C][/ROW]
[ROW][C]M2[/C][C]1.87434713285987[/C][C]8.714392[/C][C]0.2151[/C][C]0.830651[/C][C]0.415325[/C][/ROW]
[ROW][C]M3[/C][C]-46.1727465198532[/C][C]10.885047[/C][C]-4.2419[/C][C]0.000106[/C][C]5.3e-05[/C][/ROW]
[ROW][C]M4[/C][C]-57.4977706975701[/C][C]12.353443[/C][C]-4.6544[/C][C]2.8e-05[/C][C]1.4e-05[/C][/ROW]
[ROW][C]M5[/C][C]-59.5154383836216[/C][C]12.025613[/C][C]-4.9491[/C][C]1e-05[/C][C]5e-06[/C][/ROW]
[ROW][C]M6[/C][C]-42.8281894982728[/C][C]10.093164[/C][C]-4.2433[/C][C]0.000106[/C][C]5.3e-05[/C][/ROW]
[ROW][C]M7[/C][C]-31.5653398155752[/C][C]8.942847[/C][C]-3.5297[/C][C]0.000957[/C][C]0.000479[/C][/ROW]
[ROW][C]M8[/C][C]-20.1732478205662[/C][C]8.700421[/C][C]-2.3187[/C][C]0.024911[/C][C]0.012456[/C][/ROW]
[ROW][C]M9[/C][C]-13.195795347148[/C][C]8.598451[/C][C]-1.5347[/C][C]0.131715[/C][C]0.065857[/C][/ROW]
[ROW][C]M10[/C][C]-8.60370335213898[/C][C]8.427509[/C][C]-1.0209[/C][C]0.312638[/C][C]0.156319[/C][/ROW]
[ROW][C]M11[/C][C]-3.18965207474387[/C][C]8.253434[/C][C]-0.3865[/C][C]0.700935[/C][C]0.350468[/C][/ROW]
[ROW][C]t[/C][C]0.244506808967836[/C][C]0.222528[/C][C]1.0988[/C][C]0.277587[/C][C]0.138794[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58336&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58336&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)210.09727737584738.652525.43552e-061e-06
X2.012199601325610.2895946.948400
M14.331053543153158.8889650.48720.6284030.314201
M21.874347132859878.7143920.21510.8306510.415325
M3-46.172746519853210.885047-4.24190.0001065.3e-05
M4-57.497770697570112.353443-4.65442.8e-051.4e-05
M5-59.515438383621612.025613-4.94911e-055e-06
M6-42.828189498272810.093164-4.24330.0001065.3e-05
M7-31.56533981557528.942847-3.52970.0009570.000479
M8-20.17324782056628.700421-2.31870.0249110.012456
M9-13.1957953471488.598451-1.53470.1317150.065857
M10-8.603703352138988.427509-1.02090.3126380.156319
M11-3.189652074743878.253434-0.38650.7009350.350468
t0.2445068089678360.2225281.09880.2775870.138794







Multiple Linear Regression - Regression Statistics
Multiple R0.899625961873798
R-squared0.809326871277356
Adjusted R-squared0.75544098707313
F-TEST (value)15.0192742167882
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value2.02726724296554e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation13.0130086667657
Sum Squared Residuals7789.5661498207

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.899625961873798 \tabularnewline
R-squared & 0.809326871277356 \tabularnewline
Adjusted R-squared & 0.75544098707313 \tabularnewline
F-TEST (value) & 15.0192742167882 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 2.02726724296554e-12 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 13.0130086667657 \tabularnewline
Sum Squared Residuals & 7789.5661498207 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58336&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.899625961873798[/C][/ROW]
[ROW][C]R-squared[/C][C]0.809326871277356[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.75544098707313[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]15.0192742167882[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/C][/ROW]
[ROW][C]p-value[/C][C]2.02726724296554e-12[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]13.0130086667657[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]7789.5661498207[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58336&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58336&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 R0.899625961873798
R-squared0.809326871277356
Adjusted R-squared0.75544098707313
F-TEST (value)15.0192742167882
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value2.02726724296554e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation13.0130086667657
Sum Squared Residuals7789.5661498207







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1423444.063592279089-21.0635922790891
2427445.875791880414-18.875791880414
3441472.524590285717-31.5245902857167
4449479.553869328898-30.5538693288981
5452475.768508850489-23.7685088504889
6462468.553869328898-6.55386932889807
7455459.939229807307-4.93922980730737
8461463.527030205982-2.52703020598172
9461460.687991481740.312008518260225
10463459.487991481743.51200851826021
11462455.0855515614756.91444843852534
12456448.4587124385587.54128756144169
13455442.97327478405112.0267252159488
14456442.77327478405113.2267252159486
15472467.4098735880284.5901264119718
16472472.426953029884-0.42695302988406
17471470.65379215280.346207847199586
18465467.463551833861-2.46355183386091
19459458.848912312270.151087687729826
20465460.4245131096194.57548689038106
21468453.56107518272614.4389248172743
22467454.37327478405112.6267252159486
23463447.95863526246115.0413647375394
24460445.35619534219614.6438046578045
25462443.8951568903418.1048431096604
26461443.6951568903417.3048431096602
27476460.28295728901415.7170427109858
28476461.27563752821914.7243624717812
29471457.49027704981013.5097229501905
30453444.2390387242428.76096127575803
31443433.6121996013269.38780039867439
32442431.16340119602310.8365988039768
33444440.3975600797353.60243992026513
34438433.1609612757584.83903872424196
35427426.7463217541670.253678245832703
36424424.143881833902-0.143881833902165
37416414.6340449767441.36595502325616
38406408.397446172767-2.39744617276718
39431422.9730469701168.02695302988407
40434423.96572720932110.0342727906794
41418410.1193687242837.88063127571678
42412408.9413280066693.05867199333065
43404402.3388880864041.66111191359578
44409411.963287289055-2.96328728905545
45412419.185246571442-7.18524657144154
46406415.973046970116-9.97304697011593
47398409.558407448525-11.5584074485252
48397408.968167129586-11.9681671295857
49385395.433931069776-10.4339310697761
50390399.258330272428-9.25833027242754
51413409.8095318671253.19046813287494
52413406.7778129036786.22218709632153
53401398.9680532226182.03194677738203
54397399.80221210633-2.8022121063297
55397403.260770192693-6.26077019269264
56409418.921768199321-9.92176819932071
57419430.168126684358-11.1681266843580
58424435.004725488335-11.0047254883349
59428438.651083973372-10.6510839733722
60430440.073043255758-10.0730432557583

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 423 & 444.063592279089 & -21.0635922790891 \tabularnewline
2 & 427 & 445.875791880414 & -18.875791880414 \tabularnewline
3 & 441 & 472.524590285717 & -31.5245902857167 \tabularnewline
4 & 449 & 479.553869328898 & -30.5538693288981 \tabularnewline
5 & 452 & 475.768508850489 & -23.7685088504889 \tabularnewline
6 & 462 & 468.553869328898 & -6.55386932889807 \tabularnewline
7 & 455 & 459.939229807307 & -4.93922980730737 \tabularnewline
8 & 461 & 463.527030205982 & -2.52703020598172 \tabularnewline
9 & 461 & 460.68799148174 & 0.312008518260225 \tabularnewline
10 & 463 & 459.48799148174 & 3.51200851826021 \tabularnewline
11 & 462 & 455.085551561475 & 6.91444843852534 \tabularnewline
12 & 456 & 448.458712438558 & 7.54128756144169 \tabularnewline
13 & 455 & 442.973274784051 & 12.0267252159488 \tabularnewline
14 & 456 & 442.773274784051 & 13.2267252159486 \tabularnewline
15 & 472 & 467.409873588028 & 4.5901264119718 \tabularnewline
16 & 472 & 472.426953029884 & -0.42695302988406 \tabularnewline
17 & 471 & 470.6537921528 & 0.346207847199586 \tabularnewline
18 & 465 & 467.463551833861 & -2.46355183386091 \tabularnewline
19 & 459 & 458.84891231227 & 0.151087687729826 \tabularnewline
20 & 465 & 460.424513109619 & 4.57548689038106 \tabularnewline
21 & 468 & 453.561075182726 & 14.4389248172743 \tabularnewline
22 & 467 & 454.373274784051 & 12.6267252159486 \tabularnewline
23 & 463 & 447.958635262461 & 15.0413647375394 \tabularnewline
24 & 460 & 445.356195342196 & 14.6438046578045 \tabularnewline
25 & 462 & 443.89515689034 & 18.1048431096604 \tabularnewline
26 & 461 & 443.69515689034 & 17.3048431096602 \tabularnewline
27 & 476 & 460.282957289014 & 15.7170427109858 \tabularnewline
28 & 476 & 461.275637528219 & 14.7243624717812 \tabularnewline
29 & 471 & 457.490277049810 & 13.5097229501905 \tabularnewline
30 & 453 & 444.239038724242 & 8.76096127575803 \tabularnewline
31 & 443 & 433.612199601326 & 9.38780039867439 \tabularnewline
32 & 442 & 431.163401196023 & 10.8365988039768 \tabularnewline
33 & 444 & 440.397560079735 & 3.60243992026513 \tabularnewline
34 & 438 & 433.160961275758 & 4.83903872424196 \tabularnewline
35 & 427 & 426.746321754167 & 0.253678245832703 \tabularnewline
36 & 424 & 424.143881833902 & -0.143881833902165 \tabularnewline
37 & 416 & 414.634044976744 & 1.36595502325616 \tabularnewline
38 & 406 & 408.397446172767 & -2.39744617276718 \tabularnewline
39 & 431 & 422.973046970116 & 8.02695302988407 \tabularnewline
40 & 434 & 423.965727209321 & 10.0342727906794 \tabularnewline
41 & 418 & 410.119368724283 & 7.88063127571678 \tabularnewline
42 & 412 & 408.941328006669 & 3.05867199333065 \tabularnewline
43 & 404 & 402.338888086404 & 1.66111191359578 \tabularnewline
44 & 409 & 411.963287289055 & -2.96328728905545 \tabularnewline
45 & 412 & 419.185246571442 & -7.18524657144154 \tabularnewline
46 & 406 & 415.973046970116 & -9.97304697011593 \tabularnewline
47 & 398 & 409.558407448525 & -11.5584074485252 \tabularnewline
48 & 397 & 408.968167129586 & -11.9681671295857 \tabularnewline
49 & 385 & 395.433931069776 & -10.4339310697761 \tabularnewline
50 & 390 & 399.258330272428 & -9.25833027242754 \tabularnewline
51 & 413 & 409.809531867125 & 3.19046813287494 \tabularnewline
52 & 413 & 406.777812903678 & 6.22218709632153 \tabularnewline
53 & 401 & 398.968053222618 & 2.03194677738203 \tabularnewline
54 & 397 & 399.80221210633 & -2.8022121063297 \tabularnewline
55 & 397 & 403.260770192693 & -6.26077019269264 \tabularnewline
56 & 409 & 418.921768199321 & -9.92176819932071 \tabularnewline
57 & 419 & 430.168126684358 & -11.1681266843580 \tabularnewline
58 & 424 & 435.004725488335 & -11.0047254883349 \tabularnewline
59 & 428 & 438.651083973372 & -10.6510839733722 \tabularnewline
60 & 430 & 440.073043255758 & -10.0730432557583 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58336&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]423[/C][C]444.063592279089[/C][C]-21.0635922790891[/C][/ROW]
[ROW][C]2[/C][C]427[/C][C]445.875791880414[/C][C]-18.875791880414[/C][/ROW]
[ROW][C]3[/C][C]441[/C][C]472.524590285717[/C][C]-31.5245902857167[/C][/ROW]
[ROW][C]4[/C][C]449[/C][C]479.553869328898[/C][C]-30.5538693288981[/C][/ROW]
[ROW][C]5[/C][C]452[/C][C]475.768508850489[/C][C]-23.7685088504889[/C][/ROW]
[ROW][C]6[/C][C]462[/C][C]468.553869328898[/C][C]-6.55386932889807[/C][/ROW]
[ROW][C]7[/C][C]455[/C][C]459.939229807307[/C][C]-4.93922980730737[/C][/ROW]
[ROW][C]8[/C][C]461[/C][C]463.527030205982[/C][C]-2.52703020598172[/C][/ROW]
[ROW][C]9[/C][C]461[/C][C]460.68799148174[/C][C]0.312008518260225[/C][/ROW]
[ROW][C]10[/C][C]463[/C][C]459.48799148174[/C][C]3.51200851826021[/C][/ROW]
[ROW][C]11[/C][C]462[/C][C]455.085551561475[/C][C]6.91444843852534[/C][/ROW]
[ROW][C]12[/C][C]456[/C][C]448.458712438558[/C][C]7.54128756144169[/C][/ROW]
[ROW][C]13[/C][C]455[/C][C]442.973274784051[/C][C]12.0267252159488[/C][/ROW]
[ROW][C]14[/C][C]456[/C][C]442.773274784051[/C][C]13.2267252159486[/C][/ROW]
[ROW][C]15[/C][C]472[/C][C]467.409873588028[/C][C]4.5901264119718[/C][/ROW]
[ROW][C]16[/C][C]472[/C][C]472.426953029884[/C][C]-0.42695302988406[/C][/ROW]
[ROW][C]17[/C][C]471[/C][C]470.6537921528[/C][C]0.346207847199586[/C][/ROW]
[ROW][C]18[/C][C]465[/C][C]467.463551833861[/C][C]-2.46355183386091[/C][/ROW]
[ROW][C]19[/C][C]459[/C][C]458.84891231227[/C][C]0.151087687729826[/C][/ROW]
[ROW][C]20[/C][C]465[/C][C]460.424513109619[/C][C]4.57548689038106[/C][/ROW]
[ROW][C]21[/C][C]468[/C][C]453.561075182726[/C][C]14.4389248172743[/C][/ROW]
[ROW][C]22[/C][C]467[/C][C]454.373274784051[/C][C]12.6267252159486[/C][/ROW]
[ROW][C]23[/C][C]463[/C][C]447.958635262461[/C][C]15.0413647375394[/C][/ROW]
[ROW][C]24[/C][C]460[/C][C]445.356195342196[/C][C]14.6438046578045[/C][/ROW]
[ROW][C]25[/C][C]462[/C][C]443.89515689034[/C][C]18.1048431096604[/C][/ROW]
[ROW][C]26[/C][C]461[/C][C]443.69515689034[/C][C]17.3048431096602[/C][/ROW]
[ROW][C]27[/C][C]476[/C][C]460.282957289014[/C][C]15.7170427109858[/C][/ROW]
[ROW][C]28[/C][C]476[/C][C]461.275637528219[/C][C]14.7243624717812[/C][/ROW]
[ROW][C]29[/C][C]471[/C][C]457.490277049810[/C][C]13.5097229501905[/C][/ROW]
[ROW][C]30[/C][C]453[/C][C]444.239038724242[/C][C]8.76096127575803[/C][/ROW]
[ROW][C]31[/C][C]443[/C][C]433.612199601326[/C][C]9.38780039867439[/C][/ROW]
[ROW][C]32[/C][C]442[/C][C]431.163401196023[/C][C]10.8365988039768[/C][/ROW]
[ROW][C]33[/C][C]444[/C][C]440.397560079735[/C][C]3.60243992026513[/C][/ROW]
[ROW][C]34[/C][C]438[/C][C]433.160961275758[/C][C]4.83903872424196[/C][/ROW]
[ROW][C]35[/C][C]427[/C][C]426.746321754167[/C][C]0.253678245832703[/C][/ROW]
[ROW][C]36[/C][C]424[/C][C]424.143881833902[/C][C]-0.143881833902165[/C][/ROW]
[ROW][C]37[/C][C]416[/C][C]414.634044976744[/C][C]1.36595502325616[/C][/ROW]
[ROW][C]38[/C][C]406[/C][C]408.397446172767[/C][C]-2.39744617276718[/C][/ROW]
[ROW][C]39[/C][C]431[/C][C]422.973046970116[/C][C]8.02695302988407[/C][/ROW]
[ROW][C]40[/C][C]434[/C][C]423.965727209321[/C][C]10.0342727906794[/C][/ROW]
[ROW][C]41[/C][C]418[/C][C]410.119368724283[/C][C]7.88063127571678[/C][/ROW]
[ROW][C]42[/C][C]412[/C][C]408.941328006669[/C][C]3.05867199333065[/C][/ROW]
[ROW][C]43[/C][C]404[/C][C]402.338888086404[/C][C]1.66111191359578[/C][/ROW]
[ROW][C]44[/C][C]409[/C][C]411.963287289055[/C][C]-2.96328728905545[/C][/ROW]
[ROW][C]45[/C][C]412[/C][C]419.185246571442[/C][C]-7.18524657144154[/C][/ROW]
[ROW][C]46[/C][C]406[/C][C]415.973046970116[/C][C]-9.97304697011593[/C][/ROW]
[ROW][C]47[/C][C]398[/C][C]409.558407448525[/C][C]-11.5584074485252[/C][/ROW]
[ROW][C]48[/C][C]397[/C][C]408.968167129586[/C][C]-11.9681671295857[/C][/ROW]
[ROW][C]49[/C][C]385[/C][C]395.433931069776[/C][C]-10.4339310697761[/C][/ROW]
[ROW][C]50[/C][C]390[/C][C]399.258330272428[/C][C]-9.25833027242754[/C][/ROW]
[ROW][C]51[/C][C]413[/C][C]409.809531867125[/C][C]3.19046813287494[/C][/ROW]
[ROW][C]52[/C][C]413[/C][C]406.777812903678[/C][C]6.22218709632153[/C][/ROW]
[ROW][C]53[/C][C]401[/C][C]398.968053222618[/C][C]2.03194677738203[/C][/ROW]
[ROW][C]54[/C][C]397[/C][C]399.80221210633[/C][C]-2.8022121063297[/C][/ROW]
[ROW][C]55[/C][C]397[/C][C]403.260770192693[/C][C]-6.26077019269264[/C][/ROW]
[ROW][C]56[/C][C]409[/C][C]418.921768199321[/C][C]-9.92176819932071[/C][/ROW]
[ROW][C]57[/C][C]419[/C][C]430.168126684358[/C][C]-11.1681266843580[/C][/ROW]
[ROW][C]58[/C][C]424[/C][C]435.004725488335[/C][C]-11.0047254883349[/C][/ROW]
[ROW][C]59[/C][C]428[/C][C]438.651083973372[/C][C]-10.6510839733722[/C][/ROW]
[ROW][C]60[/C][C]430[/C][C]440.073043255758[/C][C]-10.0730432557583[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58336&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58336&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
1423444.063592279089-21.0635922790891
2427445.875791880414-18.875791880414
3441472.524590285717-31.5245902857167
4449479.553869328898-30.5538693288981
5452475.768508850489-23.7685088504889
6462468.553869328898-6.55386932889807
7455459.939229807307-4.93922980730737
8461463.527030205982-2.52703020598172
9461460.687991481740.312008518260225
10463459.487991481743.51200851826021
11462455.0855515614756.91444843852534
12456448.4587124385587.54128756144169
13455442.97327478405112.0267252159488
14456442.77327478405113.2267252159486
15472467.4098735880284.5901264119718
16472472.426953029884-0.42695302988406
17471470.65379215280.346207847199586
18465467.463551833861-2.46355183386091
19459458.848912312270.151087687729826
20465460.4245131096194.57548689038106
21468453.56107518272614.4389248172743
22467454.37327478405112.6267252159486
23463447.95863526246115.0413647375394
24460445.35619534219614.6438046578045
25462443.8951568903418.1048431096604
26461443.6951568903417.3048431096602
27476460.28295728901415.7170427109858
28476461.27563752821914.7243624717812
29471457.49027704981013.5097229501905
30453444.2390387242428.76096127575803
31443433.6121996013269.38780039867439
32442431.16340119602310.8365988039768
33444440.3975600797353.60243992026513
34438433.1609612757584.83903872424196
35427426.7463217541670.253678245832703
36424424.143881833902-0.143881833902165
37416414.6340449767441.36595502325616
38406408.397446172767-2.39744617276718
39431422.9730469701168.02695302988407
40434423.96572720932110.0342727906794
41418410.1193687242837.88063127571678
42412408.9413280066693.05867199333065
43404402.3388880864041.66111191359578
44409411.963287289055-2.96328728905545
45412419.185246571442-7.18524657144154
46406415.973046970116-9.97304697011593
47398409.558407448525-11.5584074485252
48397408.968167129586-11.9681671295857
49385395.433931069776-10.4339310697761
50390399.258330272428-9.25833027242754
51413409.8095318671253.19046813287494
52413406.7778129036786.22218709632153
53401398.9680532226182.03194677738203
54397399.80221210633-2.8022121063297
55397403.260770192693-6.26077019269264
56409418.921768199321-9.92176819932071
57419430.168126684358-11.1681266843580
58424435.004725488335-11.0047254883349
59428438.651083973372-10.6510839733722
60430440.073043255758-10.0730432557583







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.2038605612617070.4077211225234130.796139438738293
180.9479244875389120.1041510249221760.0520755124610878
190.9932150654153650.01356986916926940.0067849345846347
200.9991783634333360.001643273133328950.000821636566664476
210.9995573502519420.0008852994961161070.000442649748058053
220.9995319689324880.0009360621350248190.000468031067512409
230.9997205033965420.0005589932069158580.000279496603457929
240.9997650791807050.0004698416385890920.000234920819294546
250.999869079630050.0002618407399008870.000130920369950443
260.9999821316852133.57366295740064e-051.78683147870032e-05
270.9999484579693020.000103084061396585.154203069829e-05
280.999947926767190.0001041464656213015.20732328106504e-05
290.999968082477026.38350459611116e-053.19175229805558e-05
300.999995964732878.07053426188669e-064.03526713094334e-06
310.9999959862714148.02745717195955e-064.01372858597977e-06
320.9999962070259887.58594802362209e-063.79297401181105e-06
330.9999971627978195.67440436255619e-062.83720218127809e-06
340.999998976315182.04736963938165e-061.02368481969082e-06
350.9999986956512742.60869745158581e-061.30434872579290e-06
360.999998516423682.96715264074869e-061.48357632037435e-06
370.999998082421853.8351562993739e-061.91757814968695e-06
380.999989548018832.09039623387719e-051.04519811693860e-05
390.9999615555462647.68889074714701e-053.84444537357351e-05
400.9999670871042876.58257914263479e-053.29128957131740e-05
410.999899383291640.0002012334167215520.000100616708360776
420.9999806495109073.87009781866758e-051.93504890933379e-05
430.9996234586389530.0007530827220949440.000376541361047472

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.203860561261707 & 0.407721122523413 & 0.796139438738293 \tabularnewline
18 & 0.947924487538912 & 0.104151024922176 & 0.0520755124610878 \tabularnewline
19 & 0.993215065415365 & 0.0135698691692694 & 0.0067849345846347 \tabularnewline
20 & 0.999178363433336 & 0.00164327313332895 & 0.000821636566664476 \tabularnewline
21 & 0.999557350251942 & 0.000885299496116107 & 0.000442649748058053 \tabularnewline
22 & 0.999531968932488 & 0.000936062135024819 & 0.000468031067512409 \tabularnewline
23 & 0.999720503396542 & 0.000558993206915858 & 0.000279496603457929 \tabularnewline
24 & 0.999765079180705 & 0.000469841638589092 & 0.000234920819294546 \tabularnewline
25 & 0.99986907963005 & 0.000261840739900887 & 0.000130920369950443 \tabularnewline
26 & 0.999982131685213 & 3.57366295740064e-05 & 1.78683147870032e-05 \tabularnewline
27 & 0.999948457969302 & 0.00010308406139658 & 5.154203069829e-05 \tabularnewline
28 & 0.99994792676719 & 0.000104146465621301 & 5.20732328106504e-05 \tabularnewline
29 & 0.99996808247702 & 6.38350459611116e-05 & 3.19175229805558e-05 \tabularnewline
30 & 0.99999596473287 & 8.07053426188669e-06 & 4.03526713094334e-06 \tabularnewline
31 & 0.999995986271414 & 8.02745717195955e-06 & 4.01372858597977e-06 \tabularnewline
32 & 0.999996207025988 & 7.58594802362209e-06 & 3.79297401181105e-06 \tabularnewline
33 & 0.999997162797819 & 5.67440436255619e-06 & 2.83720218127809e-06 \tabularnewline
34 & 0.99999897631518 & 2.04736963938165e-06 & 1.02368481969082e-06 \tabularnewline
35 & 0.999998695651274 & 2.60869745158581e-06 & 1.30434872579290e-06 \tabularnewline
36 & 0.99999851642368 & 2.96715264074869e-06 & 1.48357632037435e-06 \tabularnewline
37 & 0.99999808242185 & 3.8351562993739e-06 & 1.91757814968695e-06 \tabularnewline
38 & 0.99998954801883 & 2.09039623387719e-05 & 1.04519811693860e-05 \tabularnewline
39 & 0.999961555546264 & 7.68889074714701e-05 & 3.84444537357351e-05 \tabularnewline
40 & 0.999967087104287 & 6.58257914263479e-05 & 3.29128957131740e-05 \tabularnewline
41 & 0.99989938329164 & 0.000201233416721552 & 0.000100616708360776 \tabularnewline
42 & 0.999980649510907 & 3.87009781866758e-05 & 1.93504890933379e-05 \tabularnewline
43 & 0.999623458638953 & 0.000753082722094944 & 0.000376541361047472 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58336&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]0.203860561261707[/C][C]0.407721122523413[/C][C]0.796139438738293[/C][/ROW]
[ROW][C]18[/C][C]0.947924487538912[/C][C]0.104151024922176[/C][C]0.0520755124610878[/C][/ROW]
[ROW][C]19[/C][C]0.993215065415365[/C][C]0.0135698691692694[/C][C]0.0067849345846347[/C][/ROW]
[ROW][C]20[/C][C]0.999178363433336[/C][C]0.00164327313332895[/C][C]0.000821636566664476[/C][/ROW]
[ROW][C]21[/C][C]0.999557350251942[/C][C]0.000885299496116107[/C][C]0.000442649748058053[/C][/ROW]
[ROW][C]22[/C][C]0.999531968932488[/C][C]0.000936062135024819[/C][C]0.000468031067512409[/C][/ROW]
[ROW][C]23[/C][C]0.999720503396542[/C][C]0.000558993206915858[/C][C]0.000279496603457929[/C][/ROW]
[ROW][C]24[/C][C]0.999765079180705[/C][C]0.000469841638589092[/C][C]0.000234920819294546[/C][/ROW]
[ROW][C]25[/C][C]0.99986907963005[/C][C]0.000261840739900887[/C][C]0.000130920369950443[/C][/ROW]
[ROW][C]26[/C][C]0.999982131685213[/C][C]3.57366295740064e-05[/C][C]1.78683147870032e-05[/C][/ROW]
[ROW][C]27[/C][C]0.999948457969302[/C][C]0.00010308406139658[/C][C]5.154203069829e-05[/C][/ROW]
[ROW][C]28[/C][C]0.99994792676719[/C][C]0.000104146465621301[/C][C]5.20732328106504e-05[/C][/ROW]
[ROW][C]29[/C][C]0.99996808247702[/C][C]6.38350459611116e-05[/C][C]3.19175229805558e-05[/C][/ROW]
[ROW][C]30[/C][C]0.99999596473287[/C][C]8.07053426188669e-06[/C][C]4.03526713094334e-06[/C][/ROW]
[ROW][C]31[/C][C]0.999995986271414[/C][C]8.02745717195955e-06[/C][C]4.01372858597977e-06[/C][/ROW]
[ROW][C]32[/C][C]0.999996207025988[/C][C]7.58594802362209e-06[/C][C]3.79297401181105e-06[/C][/ROW]
[ROW][C]33[/C][C]0.999997162797819[/C][C]5.67440436255619e-06[/C][C]2.83720218127809e-06[/C][/ROW]
[ROW][C]34[/C][C]0.99999897631518[/C][C]2.04736963938165e-06[/C][C]1.02368481969082e-06[/C][/ROW]
[ROW][C]35[/C][C]0.999998695651274[/C][C]2.60869745158581e-06[/C][C]1.30434872579290e-06[/C][/ROW]
[ROW][C]36[/C][C]0.99999851642368[/C][C]2.96715264074869e-06[/C][C]1.48357632037435e-06[/C][/ROW]
[ROW][C]37[/C][C]0.99999808242185[/C][C]3.8351562993739e-06[/C][C]1.91757814968695e-06[/C][/ROW]
[ROW][C]38[/C][C]0.99998954801883[/C][C]2.09039623387719e-05[/C][C]1.04519811693860e-05[/C][/ROW]
[ROW][C]39[/C][C]0.999961555546264[/C][C]7.68889074714701e-05[/C][C]3.84444537357351e-05[/C][/ROW]
[ROW][C]40[/C][C]0.999967087104287[/C][C]6.58257914263479e-05[/C][C]3.29128957131740e-05[/C][/ROW]
[ROW][C]41[/C][C]0.99989938329164[/C][C]0.000201233416721552[/C][C]0.000100616708360776[/C][/ROW]
[ROW][C]42[/C][C]0.999980649510907[/C][C]3.87009781866758e-05[/C][C]1.93504890933379e-05[/C][/ROW]
[ROW][C]43[/C][C]0.999623458638953[/C][C]0.000753082722094944[/C][C]0.000376541361047472[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58336&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58336&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
170.2038605612617070.4077211225234130.796139438738293
180.9479244875389120.1041510249221760.0520755124610878
190.9932150654153650.01356986916926940.0067849345846347
200.9991783634333360.001643273133328950.000821636566664476
210.9995573502519420.0008852994961161070.000442649748058053
220.9995319689324880.0009360621350248190.000468031067512409
230.9997205033965420.0005589932069158580.000279496603457929
240.9997650791807050.0004698416385890920.000234920819294546
250.999869079630050.0002618407399008870.000130920369950443
260.9999821316852133.57366295740064e-051.78683147870032e-05
270.9999484579693020.000103084061396585.154203069829e-05
280.999947926767190.0001041464656213015.20732328106504e-05
290.999968082477026.38350459611116e-053.19175229805558e-05
300.999995964732878.07053426188669e-064.03526713094334e-06
310.9999959862714148.02745717195955e-064.01372858597977e-06
320.9999962070259887.58594802362209e-063.79297401181105e-06
330.9999971627978195.67440436255619e-062.83720218127809e-06
340.999998976315182.04736963938165e-061.02368481969082e-06
350.9999986956512742.60869745158581e-061.30434872579290e-06
360.999998516423682.96715264074869e-061.48357632037435e-06
370.999998082421853.8351562993739e-061.91757814968695e-06
380.999989548018832.09039623387719e-051.04519811693860e-05
390.9999615555462647.68889074714701e-053.84444537357351e-05
400.9999670871042876.58257914263479e-053.29128957131740e-05
410.999899383291640.0002012334167215520.000100616708360776
420.9999806495109073.87009781866758e-051.93504890933379e-05
430.9996234586389530.0007530827220949440.000376541361047472







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level240.888888888888889NOK
5% type I error level250.925925925925926NOK
10% type I error level250.925925925925926NOK

\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 & 24 & 0.888888888888889 & NOK \tabularnewline
5% type I error level & 25 & 0.925925925925926 & NOK \tabularnewline
10% type I error level & 25 & 0.925925925925926 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58336&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]24[/C][C]0.888888888888889[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]25[/C][C]0.925925925925926[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]25[/C][C]0.925925925925926[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58336&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58336&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 level240.888888888888889NOK
5% type I error level250.925925925925926NOK
10% type I error level250.925925925925926NOK



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')
}