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Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 10:45:44 -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/t1258739324iumhzxd785mnk1f.htm/, Retrieved Thu, 28 Mar 2024 08:20:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58368, Retrieved Thu, 28 Mar 2024 08:20:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
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 14:14:11] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [blog 5] [2009-11-20 17:45:44] [9a3898f49d4e2f0208d1968305d88f0a] [Current]
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Dataseries X:
3884.3	12476.8	3983.4	3956.2
3892.2	12384.6	4152.9	3142.7
3613	12266.7	4286.1	3884.3
3730.5	12919.9	4348.1	3892.2
3481.3	11497.3	3949.3	3613
3649.5	12142	4166.7	3730.5
4215.2	13919.4	4217.9	3481.3
4066.6	12656.8	4528.2	3649.5
4196.8	12034.1	4232.2	4215.2
4536.6	13199.7	4470.9	4066.6
4441.6	10881.3	5121.2	4196.8
3548.3	11301.2	4170.8	4536.6
4735.9	13643.9	4398.6	4441.6
4130.6	12517	4491.4	3548.3
4356.2	13981.1	4251.8	4735.9
4159.6	14275.7	4901.9	4130.6
3988	13435	4745.2	4356.2
4167.8	13565.7	4666.9	4159.6
4902.2	16216.3	4210.4	3988
3909.4	12970	5273.6	4167.8
4697.6	14079.9	4095.3	4902.2
4308.9	14235	4610.1	3909.4
4420.4	12213.4	4718.1	4697.6
3544.2	12581	4185.5	4308.9
4433	14130.4	4314.7	4420.4
4479.7	14210.8	4422.6	3544.2
4533.2	14378.5	5059.2	4433
4237.5	13142.8	5043.6	4479.7
4207.4	13714.7	4436.6	4533.2
4394	13621.9	4922.6	4237.5
5148.4	15379.8	4454.8	4207.4
4202.2	13306.3	5058.7	4394
4682.5	14391.2	4768.9	5148.4
4884.3	14909.9	5171.8	4202.2
5288.9	14025.4	4989.3	4682.5
4505.2	12951.2	5202.1	4884.3
4611.5	14344.3	4838.4	5288.9
5104	16093.4	4876.5	4505.2
4586.6	15413.6	5875.5	4611.5
4529.3	14705.7	5717.9	5104
4504.1	15972.8	4778.8	4586.6
4604.9	16241.4	6195.9	4529.3
4795.4	16626.4	4625.4	4504.1
5391.1	17136.2	5549.8	4604.9
5213.9	15622.9	6397.6	4795.4
5415	18003.9	5856.7	5391.1
5990.3	16136.1	6343.8	5213.9
4241.8	14423.7	6615.5	5415
5677.6	16789.4	5904.6	5990.3
5164.2	16782.2	6861	4241.8
3962.3	14133.8	6553.5	5677.6
4011	12607	5481	5164.2
3310.3	12004.5	5435.3	3962.3
3837.3	12175.4	5278	4011
4145.3	13268	4671.8	3310.3
3796.7	12299.3	4891.5	3837.3
3849.6	11800.6	4241.6	4145.3
4285	13873.3	4152.1	3796.7
4189.6	12269.6	4484.4	3849.6




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=58368&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=58368&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58368&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] = -169.548966574492 + 0.255796082918873X[t] + 0.0207257906429053Y1[t] + 0.175892072127307Y2[t] + 320.150624530104M1[t] + 352.419180806125M2[t] -53.9281294197686M3[t] + 23.9260159457721M4[t] -86.3569691050612M5[t] + 97.5515370487508M6[t] + 273.292809663731M7[t] + 214.749768916847M8[t] + 411.976430473136M9[t] + 313.631950712519M10[t] + 891.257869708524M11[t] -3.16006754830636t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -169.548966574492 +  0.255796082918873X[t] +  0.0207257906429053Y1[t] +  0.175892072127307Y2[t] +  320.150624530104M1[t] +  352.419180806125M2[t] -53.9281294197686M3[t] +  23.9260159457721M4[t] -86.3569691050612M5[t] +  97.5515370487508M6[t] +  273.292809663731M7[t] +  214.749768916847M8[t] +  411.976430473136M9[t] +  313.631950712519M10[t] +  891.257869708524M11[t] -3.16006754830636t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58368&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -169.548966574492 +  0.255796082918873X[t] +  0.0207257906429053Y1[t] +  0.175892072127307Y2[t] +  320.150624530104M1[t] +  352.419180806125M2[t] -53.9281294197686M3[t] +  23.9260159457721M4[t] -86.3569691050612M5[t] +  97.5515370487508M6[t] +  273.292809663731M7[t] +  214.749768916847M8[t] +  411.976430473136M9[t] +  313.631950712519M10[t] +  891.257869708524M11[t] -3.16006754830636t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58368&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58368&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] = -169.548966574492 + 0.255796082918873X[t] + 0.0207257906429053Y1[t] + 0.175892072127307Y2[t] + 320.150624530104M1[t] + 352.419180806125M2[t] -53.9281294197686M3[t] + 23.9260159457721M4[t] -86.3569691050612M5[t] + 97.5515370487508M6[t] + 273.292809663731M7[t] + 214.749768916847M8[t] + 411.976430473136M9[t] + 313.631950712519M10[t] + 891.257869708524M11[t] -3.16006754830636t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-169.548966574492331.386342-0.51160.6115240.305762
X0.2557960829188730.030848.294200
Y10.02072579064290530.0670250.30920.7586460.379323
Y20.1758920721273070.0988851.77870.0823510.041176
M1320.150624530104156.2345462.04920.0465790.023289
M2352.419180806125195.8106661.79980.0789120.039456
M3-53.9281294197686153.440499-0.35150.726960.36348
M423.9260159457721151.8555340.15760.8755430.437771
M5-86.3569691050612160.753804-0.53720.5938990.296949
M697.5515370487508166.5994750.58550.5612420.280621
M7273.292809663731204.915151.33370.1893280.094664
M8214.749768916847168.446071.27490.2091950.104598
M9411.976430473136152.5801362.70010.0098740.004937
M10313.631950712519178.8037761.75410.0865460.043273
M11891.257869708524150.5939465.918300
t-3.160067548306362.2056-1.43270.1591610.07958

\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) & -169.548966574492 & 331.386342 & -0.5116 & 0.611524 & 0.305762 \tabularnewline
X & 0.255796082918873 & 0.03084 & 8.2942 & 0 & 0 \tabularnewline
Y1 & 0.0207257906429053 & 0.067025 & 0.3092 & 0.758646 & 0.379323 \tabularnewline
Y2 & 0.175892072127307 & 0.098885 & 1.7787 & 0.082351 & 0.041176 \tabularnewline
M1 & 320.150624530104 & 156.234546 & 2.0492 & 0.046579 & 0.023289 \tabularnewline
M2 & 352.419180806125 & 195.810666 & 1.7998 & 0.078912 & 0.039456 \tabularnewline
M3 & -53.9281294197686 & 153.440499 & -0.3515 & 0.72696 & 0.36348 \tabularnewline
M4 & 23.9260159457721 & 151.855534 & 0.1576 & 0.875543 & 0.437771 \tabularnewline
M5 & -86.3569691050612 & 160.753804 & -0.5372 & 0.593899 & 0.296949 \tabularnewline
M6 & 97.5515370487508 & 166.599475 & 0.5855 & 0.561242 & 0.280621 \tabularnewline
M7 & 273.292809663731 & 204.91515 & 1.3337 & 0.189328 & 0.094664 \tabularnewline
M8 & 214.749768916847 & 168.44607 & 1.2749 & 0.209195 & 0.104598 \tabularnewline
M9 & 411.976430473136 & 152.580136 & 2.7001 & 0.009874 & 0.004937 \tabularnewline
M10 & 313.631950712519 & 178.803776 & 1.7541 & 0.086546 & 0.043273 \tabularnewline
M11 & 891.257869708524 & 150.593946 & 5.9183 & 0 & 0 \tabularnewline
t & -3.16006754830636 & 2.2056 & -1.4327 & 0.159161 & 0.07958 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58368&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]-169.548966574492[/C][C]331.386342[/C][C]-0.5116[/C][C]0.611524[/C][C]0.305762[/C][/ROW]
[ROW][C]X[/C][C]0.255796082918873[/C][C]0.03084[/C][C]8.2942[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y1[/C][C]0.0207257906429053[/C][C]0.067025[/C][C]0.3092[/C][C]0.758646[/C][C]0.379323[/C][/ROW]
[ROW][C]Y2[/C][C]0.175892072127307[/C][C]0.098885[/C][C]1.7787[/C][C]0.082351[/C][C]0.041176[/C][/ROW]
[ROW][C]M1[/C][C]320.150624530104[/C][C]156.234546[/C][C]2.0492[/C][C]0.046579[/C][C]0.023289[/C][/ROW]
[ROW][C]M2[/C][C]352.419180806125[/C][C]195.810666[/C][C]1.7998[/C][C]0.078912[/C][C]0.039456[/C][/ROW]
[ROW][C]M3[/C][C]-53.9281294197686[/C][C]153.440499[/C][C]-0.3515[/C][C]0.72696[/C][C]0.36348[/C][/ROW]
[ROW][C]M4[/C][C]23.9260159457721[/C][C]151.855534[/C][C]0.1576[/C][C]0.875543[/C][C]0.437771[/C][/ROW]
[ROW][C]M5[/C][C]-86.3569691050612[/C][C]160.753804[/C][C]-0.5372[/C][C]0.593899[/C][C]0.296949[/C][/ROW]
[ROW][C]M6[/C][C]97.5515370487508[/C][C]166.599475[/C][C]0.5855[/C][C]0.561242[/C][C]0.280621[/C][/ROW]
[ROW][C]M7[/C][C]273.292809663731[/C][C]204.91515[/C][C]1.3337[/C][C]0.189328[/C][C]0.094664[/C][/ROW]
[ROW][C]M8[/C][C]214.749768916847[/C][C]168.44607[/C][C]1.2749[/C][C]0.209195[/C][C]0.104598[/C][/ROW]
[ROW][C]M9[/C][C]411.976430473136[/C][C]152.580136[/C][C]2.7001[/C][C]0.009874[/C][C]0.004937[/C][/ROW]
[ROW][C]M10[/C][C]313.631950712519[/C][C]178.803776[/C][C]1.7541[/C][C]0.086546[/C][C]0.043273[/C][/ROW]
[ROW][C]M11[/C][C]891.257869708524[/C][C]150.593946[/C][C]5.9183[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]t[/C][C]-3.16006754830636[/C][C]2.2056[/C][C]-1.4327[/C][C]0.159161[/C][C]0.07958[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58368&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58368&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)-169.548966574492331.386342-0.51160.6115240.305762
X0.2557960829188730.030848.294200
Y10.02072579064290530.0670250.30920.7586460.379323
Y20.1758920721273070.0988851.77870.0823510.041176
M1320.150624530104156.2345462.04920.0465790.023289
M2352.419180806125195.8106661.79980.0789120.039456
M3-53.9281294197686153.440499-0.35150.726960.36348
M423.9260159457721151.8555340.15760.8755430.437771
M5-86.3569691050612160.753804-0.53720.5938990.296949
M697.5515370487508166.5994750.58550.5612420.280621
M7273.292809663731204.915151.33370.1893280.094664
M8214.749768916847168.446071.27490.2091950.104598
M9411.976430473136152.5801362.70010.0098740.004937
M10313.631950712519178.8037761.75410.0865460.043273
M11891.257869708524150.5939465.918300
t-3.160067548306362.2056-1.43270.1591610.07958







Multiple Linear Regression - Regression Statistics
Multiple R0.942613397058808
R-squared0.888520016314745
Adjusted R-squared0.849631649912912
F-TEST (value)22.8479645334977
F-TEST (DF numerator)15
F-TEST (DF denominator)43
p-value1.11022302462516e-15
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation218.394652553447
Sum Squared Residuals2050937.64334946

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.942613397058808 \tabularnewline
R-squared & 0.888520016314745 \tabularnewline
Adjusted R-squared & 0.849631649912912 \tabularnewline
F-TEST (value) & 22.8479645334977 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 43 \tabularnewline
p-value & 1.11022302462516e-15 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 218.394652553447 \tabularnewline
Sum Squared Residuals & 2050937.64334946 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58368&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.942613397058808[/C][/ROW]
[ROW][C]R-squared[/C][C]0.888520016314745[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.849631649912912[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]22.8479645334977[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]43[/C][/ROW]
[ROW][C]p-value[/C][C]1.11022302462516e-15[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]218.394652553447[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2050937.64334946[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58368&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58368&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 R0.942613397058808
R-squared0.888520016314745
Adjusted R-squared0.849631649912912
F-TEST (value)22.8479645334977
F-TEST (DF numerator)15
F-TEST (DF denominator)43
p-value1.11022302462516e-15
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation218.394652553447
Sum Squared Residuals2050937.64334946







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
13884.34117.38148796651-233.081487966507
23892.23983.3303986875-91.1303986875024
336133676.86689874041-63.8668987404131
43730.53921.32152430992-190.821524309920
53481.33386.6084523040694.6915476959427
63649.53757.44173092809-107.941730928087
74215.24341.90374988156-126.703749881557
84066.63993.248766661373.351233338696
94196.84121.3984510078275.401548992177
104536.64296.85950225748239.740497742519
114441.64314.66684451212126.933155487878
123548.33567.72801715477-19.4280171547682
134735.94471.98364584697263.916354153032
144130.64057.6344940737472.9655059262573
154356.24226.56168672141129.638313278585
164159.64283.61965580484-124.019655804843
1739883991.56235637398-3.56235637398397
184167.84169.54013222942-1.74013222941856
194902.24980.49003167532-78.2900316753234
203909.44142.05715458062-232.657154580623
214697.64724.78575967602-27.1857596760217
224308.94498.99917264279-190.099172642794
234420.44697.22417950188-276.824179501877
243544.23817.42907779373-273.229077793728
2544334553.03982384328-120.039823843285
264479.74450.833996850128.8660031499005
274533.24253.75053421142279.449465788581
284237.54020.24822980012217.251770199882
294207.44049.92462796085157.475372039150
3043944164.99663859589229.003361404109
315148.44772.25190159187376.148098408133
324202.24225.4933809926-23.2933809926006
334682.54823.75979044380-141.259790443795
344884.34696.85801374806187.441986251941
355288.95125.77073530443163.129264695569
364505.23996.48211418025508.717885819751
374611.54733.45015660221-121.950156602211
3851045072.9146096606531.0853903393505
394586.64528.9194468376057.6805531624048
404529.34505.8959384739423.4040615260632
414504.14606.10195442988-102.001954429879
424604.94874.84912309456-269.949123094561
434795.45108.92948566271-313.52948566271
445391.15214.52006218029176.579937819706
455213.95072.56920895445141.330791045545
4654155673.68346228286-258.683462282857
475990.35749.30084749589240.999152504114
484241.84457.86079087126-216.060790871256
495677.65466.44488574103211.155114258971
505164.25205.98650072801-41.7865007280059
513962.34365.20143348916-402.901433489158
5240113936.8146516111874.1853483888178
533310.33456.90260893123-146.602608931230
543837.33686.67237515204150.627624847958
554145.34002.92483118854142.375168811457
563796.73790.680635585186.01936441482239
573849.63897.88678991791-48.2867899179053
5842854263.3998490688121.6001509311903
594189.64443.83739318568-254.237393185684

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 3884.3 & 4117.38148796651 & -233.081487966507 \tabularnewline
2 & 3892.2 & 3983.3303986875 & -91.1303986875024 \tabularnewline
3 & 3613 & 3676.86689874041 & -63.8668987404131 \tabularnewline
4 & 3730.5 & 3921.32152430992 & -190.821524309920 \tabularnewline
5 & 3481.3 & 3386.60845230406 & 94.6915476959427 \tabularnewline
6 & 3649.5 & 3757.44173092809 & -107.941730928087 \tabularnewline
7 & 4215.2 & 4341.90374988156 & -126.703749881557 \tabularnewline
8 & 4066.6 & 3993.2487666613 & 73.351233338696 \tabularnewline
9 & 4196.8 & 4121.39845100782 & 75.401548992177 \tabularnewline
10 & 4536.6 & 4296.85950225748 & 239.740497742519 \tabularnewline
11 & 4441.6 & 4314.66684451212 & 126.933155487878 \tabularnewline
12 & 3548.3 & 3567.72801715477 & -19.4280171547682 \tabularnewline
13 & 4735.9 & 4471.98364584697 & 263.916354153032 \tabularnewline
14 & 4130.6 & 4057.63449407374 & 72.9655059262573 \tabularnewline
15 & 4356.2 & 4226.56168672141 & 129.638313278585 \tabularnewline
16 & 4159.6 & 4283.61965580484 & -124.019655804843 \tabularnewline
17 & 3988 & 3991.56235637398 & -3.56235637398397 \tabularnewline
18 & 4167.8 & 4169.54013222942 & -1.74013222941856 \tabularnewline
19 & 4902.2 & 4980.49003167532 & -78.2900316753234 \tabularnewline
20 & 3909.4 & 4142.05715458062 & -232.657154580623 \tabularnewline
21 & 4697.6 & 4724.78575967602 & -27.1857596760217 \tabularnewline
22 & 4308.9 & 4498.99917264279 & -190.099172642794 \tabularnewline
23 & 4420.4 & 4697.22417950188 & -276.824179501877 \tabularnewline
24 & 3544.2 & 3817.42907779373 & -273.229077793728 \tabularnewline
25 & 4433 & 4553.03982384328 & -120.039823843285 \tabularnewline
26 & 4479.7 & 4450.8339968501 & 28.8660031499005 \tabularnewline
27 & 4533.2 & 4253.75053421142 & 279.449465788581 \tabularnewline
28 & 4237.5 & 4020.24822980012 & 217.251770199882 \tabularnewline
29 & 4207.4 & 4049.92462796085 & 157.475372039150 \tabularnewline
30 & 4394 & 4164.99663859589 & 229.003361404109 \tabularnewline
31 & 5148.4 & 4772.25190159187 & 376.148098408133 \tabularnewline
32 & 4202.2 & 4225.4933809926 & -23.2933809926006 \tabularnewline
33 & 4682.5 & 4823.75979044380 & -141.259790443795 \tabularnewline
34 & 4884.3 & 4696.85801374806 & 187.441986251941 \tabularnewline
35 & 5288.9 & 5125.77073530443 & 163.129264695569 \tabularnewline
36 & 4505.2 & 3996.48211418025 & 508.717885819751 \tabularnewline
37 & 4611.5 & 4733.45015660221 & -121.950156602211 \tabularnewline
38 & 5104 & 5072.91460966065 & 31.0853903393505 \tabularnewline
39 & 4586.6 & 4528.91944683760 & 57.6805531624048 \tabularnewline
40 & 4529.3 & 4505.89593847394 & 23.4040615260632 \tabularnewline
41 & 4504.1 & 4606.10195442988 & -102.001954429879 \tabularnewline
42 & 4604.9 & 4874.84912309456 & -269.949123094561 \tabularnewline
43 & 4795.4 & 5108.92948566271 & -313.52948566271 \tabularnewline
44 & 5391.1 & 5214.52006218029 & 176.579937819706 \tabularnewline
45 & 5213.9 & 5072.56920895445 & 141.330791045545 \tabularnewline
46 & 5415 & 5673.68346228286 & -258.683462282857 \tabularnewline
47 & 5990.3 & 5749.30084749589 & 240.999152504114 \tabularnewline
48 & 4241.8 & 4457.86079087126 & -216.060790871256 \tabularnewline
49 & 5677.6 & 5466.44488574103 & 211.155114258971 \tabularnewline
50 & 5164.2 & 5205.98650072801 & -41.7865007280059 \tabularnewline
51 & 3962.3 & 4365.20143348916 & -402.901433489158 \tabularnewline
52 & 4011 & 3936.81465161118 & 74.1853483888178 \tabularnewline
53 & 3310.3 & 3456.90260893123 & -146.602608931230 \tabularnewline
54 & 3837.3 & 3686.67237515204 & 150.627624847958 \tabularnewline
55 & 4145.3 & 4002.92483118854 & 142.375168811457 \tabularnewline
56 & 3796.7 & 3790.68063558518 & 6.01936441482239 \tabularnewline
57 & 3849.6 & 3897.88678991791 & -48.2867899179053 \tabularnewline
58 & 4285 & 4263.39984906881 & 21.6001509311903 \tabularnewline
59 & 4189.6 & 4443.83739318568 & -254.237393185684 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58368&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]3884.3[/C][C]4117.38148796651[/C][C]-233.081487966507[/C][/ROW]
[ROW][C]2[/C][C]3892.2[/C][C]3983.3303986875[/C][C]-91.1303986875024[/C][/ROW]
[ROW][C]3[/C][C]3613[/C][C]3676.86689874041[/C][C]-63.8668987404131[/C][/ROW]
[ROW][C]4[/C][C]3730.5[/C][C]3921.32152430992[/C][C]-190.821524309920[/C][/ROW]
[ROW][C]5[/C][C]3481.3[/C][C]3386.60845230406[/C][C]94.6915476959427[/C][/ROW]
[ROW][C]6[/C][C]3649.5[/C][C]3757.44173092809[/C][C]-107.941730928087[/C][/ROW]
[ROW][C]7[/C][C]4215.2[/C][C]4341.90374988156[/C][C]-126.703749881557[/C][/ROW]
[ROW][C]8[/C][C]4066.6[/C][C]3993.2487666613[/C][C]73.351233338696[/C][/ROW]
[ROW][C]9[/C][C]4196.8[/C][C]4121.39845100782[/C][C]75.401548992177[/C][/ROW]
[ROW][C]10[/C][C]4536.6[/C][C]4296.85950225748[/C][C]239.740497742519[/C][/ROW]
[ROW][C]11[/C][C]4441.6[/C][C]4314.66684451212[/C][C]126.933155487878[/C][/ROW]
[ROW][C]12[/C][C]3548.3[/C][C]3567.72801715477[/C][C]-19.4280171547682[/C][/ROW]
[ROW][C]13[/C][C]4735.9[/C][C]4471.98364584697[/C][C]263.916354153032[/C][/ROW]
[ROW][C]14[/C][C]4130.6[/C][C]4057.63449407374[/C][C]72.9655059262573[/C][/ROW]
[ROW][C]15[/C][C]4356.2[/C][C]4226.56168672141[/C][C]129.638313278585[/C][/ROW]
[ROW][C]16[/C][C]4159.6[/C][C]4283.61965580484[/C][C]-124.019655804843[/C][/ROW]
[ROW][C]17[/C][C]3988[/C][C]3991.56235637398[/C][C]-3.56235637398397[/C][/ROW]
[ROW][C]18[/C][C]4167.8[/C][C]4169.54013222942[/C][C]-1.74013222941856[/C][/ROW]
[ROW][C]19[/C][C]4902.2[/C][C]4980.49003167532[/C][C]-78.2900316753234[/C][/ROW]
[ROW][C]20[/C][C]3909.4[/C][C]4142.05715458062[/C][C]-232.657154580623[/C][/ROW]
[ROW][C]21[/C][C]4697.6[/C][C]4724.78575967602[/C][C]-27.1857596760217[/C][/ROW]
[ROW][C]22[/C][C]4308.9[/C][C]4498.99917264279[/C][C]-190.099172642794[/C][/ROW]
[ROW][C]23[/C][C]4420.4[/C][C]4697.22417950188[/C][C]-276.824179501877[/C][/ROW]
[ROW][C]24[/C][C]3544.2[/C][C]3817.42907779373[/C][C]-273.229077793728[/C][/ROW]
[ROW][C]25[/C][C]4433[/C][C]4553.03982384328[/C][C]-120.039823843285[/C][/ROW]
[ROW][C]26[/C][C]4479.7[/C][C]4450.8339968501[/C][C]28.8660031499005[/C][/ROW]
[ROW][C]27[/C][C]4533.2[/C][C]4253.75053421142[/C][C]279.449465788581[/C][/ROW]
[ROW][C]28[/C][C]4237.5[/C][C]4020.24822980012[/C][C]217.251770199882[/C][/ROW]
[ROW][C]29[/C][C]4207.4[/C][C]4049.92462796085[/C][C]157.475372039150[/C][/ROW]
[ROW][C]30[/C][C]4394[/C][C]4164.99663859589[/C][C]229.003361404109[/C][/ROW]
[ROW][C]31[/C][C]5148.4[/C][C]4772.25190159187[/C][C]376.148098408133[/C][/ROW]
[ROW][C]32[/C][C]4202.2[/C][C]4225.4933809926[/C][C]-23.2933809926006[/C][/ROW]
[ROW][C]33[/C][C]4682.5[/C][C]4823.75979044380[/C][C]-141.259790443795[/C][/ROW]
[ROW][C]34[/C][C]4884.3[/C][C]4696.85801374806[/C][C]187.441986251941[/C][/ROW]
[ROW][C]35[/C][C]5288.9[/C][C]5125.77073530443[/C][C]163.129264695569[/C][/ROW]
[ROW][C]36[/C][C]4505.2[/C][C]3996.48211418025[/C][C]508.717885819751[/C][/ROW]
[ROW][C]37[/C][C]4611.5[/C][C]4733.45015660221[/C][C]-121.950156602211[/C][/ROW]
[ROW][C]38[/C][C]5104[/C][C]5072.91460966065[/C][C]31.0853903393505[/C][/ROW]
[ROW][C]39[/C][C]4586.6[/C][C]4528.91944683760[/C][C]57.6805531624048[/C][/ROW]
[ROW][C]40[/C][C]4529.3[/C][C]4505.89593847394[/C][C]23.4040615260632[/C][/ROW]
[ROW][C]41[/C][C]4504.1[/C][C]4606.10195442988[/C][C]-102.001954429879[/C][/ROW]
[ROW][C]42[/C][C]4604.9[/C][C]4874.84912309456[/C][C]-269.949123094561[/C][/ROW]
[ROW][C]43[/C][C]4795.4[/C][C]5108.92948566271[/C][C]-313.52948566271[/C][/ROW]
[ROW][C]44[/C][C]5391.1[/C][C]5214.52006218029[/C][C]176.579937819706[/C][/ROW]
[ROW][C]45[/C][C]5213.9[/C][C]5072.56920895445[/C][C]141.330791045545[/C][/ROW]
[ROW][C]46[/C][C]5415[/C][C]5673.68346228286[/C][C]-258.683462282857[/C][/ROW]
[ROW][C]47[/C][C]5990.3[/C][C]5749.30084749589[/C][C]240.999152504114[/C][/ROW]
[ROW][C]48[/C][C]4241.8[/C][C]4457.86079087126[/C][C]-216.060790871256[/C][/ROW]
[ROW][C]49[/C][C]5677.6[/C][C]5466.44488574103[/C][C]211.155114258971[/C][/ROW]
[ROW][C]50[/C][C]5164.2[/C][C]5205.98650072801[/C][C]-41.7865007280059[/C][/ROW]
[ROW][C]51[/C][C]3962.3[/C][C]4365.20143348916[/C][C]-402.901433489158[/C][/ROW]
[ROW][C]52[/C][C]4011[/C][C]3936.81465161118[/C][C]74.1853483888178[/C][/ROW]
[ROW][C]53[/C][C]3310.3[/C][C]3456.90260893123[/C][C]-146.602608931230[/C][/ROW]
[ROW][C]54[/C][C]3837.3[/C][C]3686.67237515204[/C][C]150.627624847958[/C][/ROW]
[ROW][C]55[/C][C]4145.3[/C][C]4002.92483118854[/C][C]142.375168811457[/C][/ROW]
[ROW][C]56[/C][C]3796.7[/C][C]3790.68063558518[/C][C]6.01936441482239[/C][/ROW]
[ROW][C]57[/C][C]3849.6[/C][C]3897.88678991791[/C][C]-48.2867899179053[/C][/ROW]
[ROW][C]58[/C][C]4285[/C][C]4263.39984906881[/C][C]21.6001509311903[/C][/ROW]
[ROW][C]59[/C][C]4189.6[/C][C]4443.83739318568[/C][C]-254.237393185684[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58368&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58368&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
13884.34117.38148796651-233.081487966507
23892.23983.3303986875-91.1303986875024
336133676.86689874041-63.8668987404131
43730.53921.32152430992-190.821524309920
53481.33386.6084523040694.6915476959427
63649.53757.44173092809-107.941730928087
74215.24341.90374988156-126.703749881557
84066.63993.248766661373.351233338696
94196.84121.3984510078275.401548992177
104536.64296.85950225748239.740497742519
114441.64314.66684451212126.933155487878
123548.33567.72801715477-19.4280171547682
134735.94471.98364584697263.916354153032
144130.64057.6344940737472.9655059262573
154356.24226.56168672141129.638313278585
164159.64283.61965580484-124.019655804843
1739883991.56235637398-3.56235637398397
184167.84169.54013222942-1.74013222941856
194902.24980.49003167532-78.2900316753234
203909.44142.05715458062-232.657154580623
214697.64724.78575967602-27.1857596760217
224308.94498.99917264279-190.099172642794
234420.44697.22417950188-276.824179501877
243544.23817.42907779373-273.229077793728
2544334553.03982384328-120.039823843285
264479.74450.833996850128.8660031499005
274533.24253.75053421142279.449465788581
284237.54020.24822980012217.251770199882
294207.44049.92462796085157.475372039150
3043944164.99663859589229.003361404109
315148.44772.25190159187376.148098408133
324202.24225.4933809926-23.2933809926006
334682.54823.75979044380-141.259790443795
344884.34696.85801374806187.441986251941
355288.95125.77073530443163.129264695569
364505.23996.48211418025508.717885819751
374611.54733.45015660221-121.950156602211
3851045072.9146096606531.0853903393505
394586.64528.9194468376057.6805531624048
404529.34505.8959384739423.4040615260632
414504.14606.10195442988-102.001954429879
424604.94874.84912309456-269.949123094561
434795.45108.92948566271-313.52948566271
445391.15214.52006218029176.579937819706
455213.95072.56920895445141.330791045545
4654155673.68346228286-258.683462282857
475990.35749.30084749589240.999152504114
484241.84457.86079087126-216.060790871256
495677.65466.44488574103211.155114258971
505164.25205.98650072801-41.7865007280059
513962.34365.20143348916-402.901433489158
5240113936.8146516111874.1853483888178
533310.33456.90260893123-146.602608931230
543837.33686.67237515204150.627624847958
554145.34002.92483118854142.375168811457
563796.73790.680635585186.01936441482239
573849.63897.88678991791-48.2867899179053
5842854263.3998490688121.6001509311903
594189.64443.83739318568-254.237393185684







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.2252255373745280.4504510747490560.774774462625472
200.2840925933443170.5681851866886340.715907406655683
210.2443296484841890.4886592969683770.755670351515811
220.3002329220108810.6004658440217620.699767077989119
230.3345151000239820.6690302000479650.665484899976017
240.3138689067333870.6277378134667740.686131093266613
250.2939276032357110.5878552064714220.706072396764289
260.2676392001268740.5352784002537470.732360799873126
270.2456576329339170.4913152658678340.754342367066083
280.2142723857256210.4285447714512430.785727614274379
290.1534806837088340.3069613674176670.846519316291166
300.1146393992285070.2292787984570130.885360600771493
310.1397821307267630.2795642614535250.860217869273237
320.1023106659057030.2046213318114060.897689334094297
330.0986957896700410.1973915793400820.90130421032996
340.05958247425457730.1191649485091550.940417525745423
350.05160226136402180.1032045227280440.948397738635978
360.1594816338655990.3189632677311970.840518366134401
370.2216262806146180.4432525612292370.778373719385382
380.1462841397780110.2925682795560230.853715860221989
390.14220775946790.28441551893580.8577922405321
400.08185896077254940.1637179215450990.91814103922745

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.225225537374528 & 0.450451074749056 & 0.774774462625472 \tabularnewline
20 & 0.284092593344317 & 0.568185186688634 & 0.715907406655683 \tabularnewline
21 & 0.244329648484189 & 0.488659296968377 & 0.755670351515811 \tabularnewline
22 & 0.300232922010881 & 0.600465844021762 & 0.699767077989119 \tabularnewline
23 & 0.334515100023982 & 0.669030200047965 & 0.665484899976017 \tabularnewline
24 & 0.313868906733387 & 0.627737813466774 & 0.686131093266613 \tabularnewline
25 & 0.293927603235711 & 0.587855206471422 & 0.706072396764289 \tabularnewline
26 & 0.267639200126874 & 0.535278400253747 & 0.732360799873126 \tabularnewline
27 & 0.245657632933917 & 0.491315265867834 & 0.754342367066083 \tabularnewline
28 & 0.214272385725621 & 0.428544771451243 & 0.785727614274379 \tabularnewline
29 & 0.153480683708834 & 0.306961367417667 & 0.846519316291166 \tabularnewline
30 & 0.114639399228507 & 0.229278798457013 & 0.885360600771493 \tabularnewline
31 & 0.139782130726763 & 0.279564261453525 & 0.860217869273237 \tabularnewline
32 & 0.102310665905703 & 0.204621331811406 & 0.897689334094297 \tabularnewline
33 & 0.098695789670041 & 0.197391579340082 & 0.90130421032996 \tabularnewline
34 & 0.0595824742545773 & 0.119164948509155 & 0.940417525745423 \tabularnewline
35 & 0.0516022613640218 & 0.103204522728044 & 0.948397738635978 \tabularnewline
36 & 0.159481633865599 & 0.318963267731197 & 0.840518366134401 \tabularnewline
37 & 0.221626280614618 & 0.443252561229237 & 0.778373719385382 \tabularnewline
38 & 0.146284139778011 & 0.292568279556023 & 0.853715860221989 \tabularnewline
39 & 0.1422077594679 & 0.2844155189358 & 0.8577922405321 \tabularnewline
40 & 0.0818589607725494 & 0.163717921545099 & 0.91814103922745 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58368&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]19[/C][C]0.225225537374528[/C][C]0.450451074749056[/C][C]0.774774462625472[/C][/ROW]
[ROW][C]20[/C][C]0.284092593344317[/C][C]0.568185186688634[/C][C]0.715907406655683[/C][/ROW]
[ROW][C]21[/C][C]0.244329648484189[/C][C]0.488659296968377[/C][C]0.755670351515811[/C][/ROW]
[ROW][C]22[/C][C]0.300232922010881[/C][C]0.600465844021762[/C][C]0.699767077989119[/C][/ROW]
[ROW][C]23[/C][C]0.334515100023982[/C][C]0.669030200047965[/C][C]0.665484899976017[/C][/ROW]
[ROW][C]24[/C][C]0.313868906733387[/C][C]0.627737813466774[/C][C]0.686131093266613[/C][/ROW]
[ROW][C]25[/C][C]0.293927603235711[/C][C]0.587855206471422[/C][C]0.706072396764289[/C][/ROW]
[ROW][C]26[/C][C]0.267639200126874[/C][C]0.535278400253747[/C][C]0.732360799873126[/C][/ROW]
[ROW][C]27[/C][C]0.245657632933917[/C][C]0.491315265867834[/C][C]0.754342367066083[/C][/ROW]
[ROW][C]28[/C][C]0.214272385725621[/C][C]0.428544771451243[/C][C]0.785727614274379[/C][/ROW]
[ROW][C]29[/C][C]0.153480683708834[/C][C]0.306961367417667[/C][C]0.846519316291166[/C][/ROW]
[ROW][C]30[/C][C]0.114639399228507[/C][C]0.229278798457013[/C][C]0.885360600771493[/C][/ROW]
[ROW][C]31[/C][C]0.139782130726763[/C][C]0.279564261453525[/C][C]0.860217869273237[/C][/ROW]
[ROW][C]32[/C][C]0.102310665905703[/C][C]0.204621331811406[/C][C]0.897689334094297[/C][/ROW]
[ROW][C]33[/C][C]0.098695789670041[/C][C]0.197391579340082[/C][C]0.90130421032996[/C][/ROW]
[ROW][C]34[/C][C]0.0595824742545773[/C][C]0.119164948509155[/C][C]0.940417525745423[/C][/ROW]
[ROW][C]35[/C][C]0.0516022613640218[/C][C]0.103204522728044[/C][C]0.948397738635978[/C][/ROW]
[ROW][C]36[/C][C]0.159481633865599[/C][C]0.318963267731197[/C][C]0.840518366134401[/C][/ROW]
[ROW][C]37[/C][C]0.221626280614618[/C][C]0.443252561229237[/C][C]0.778373719385382[/C][/ROW]
[ROW][C]38[/C][C]0.146284139778011[/C][C]0.292568279556023[/C][C]0.853715860221989[/C][/ROW]
[ROW][C]39[/C][C]0.1422077594679[/C][C]0.2844155189358[/C][C]0.8577922405321[/C][/ROW]
[ROW][C]40[/C][C]0.0818589607725494[/C][C]0.163717921545099[/C][C]0.91814103922745[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58368&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58368&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
190.2252255373745280.4504510747490560.774774462625472
200.2840925933443170.5681851866886340.715907406655683
210.2443296484841890.4886592969683770.755670351515811
220.3002329220108810.6004658440217620.699767077989119
230.3345151000239820.6690302000479650.665484899976017
240.3138689067333870.6277378134667740.686131093266613
250.2939276032357110.5878552064714220.706072396764289
260.2676392001268740.5352784002537470.732360799873126
270.2456576329339170.4913152658678340.754342367066083
280.2142723857256210.4285447714512430.785727614274379
290.1534806837088340.3069613674176670.846519316291166
300.1146393992285070.2292787984570130.885360600771493
310.1397821307267630.2795642614535250.860217869273237
320.1023106659057030.2046213318114060.897689334094297
330.0986957896700410.1973915793400820.90130421032996
340.05958247425457730.1191649485091550.940417525745423
350.05160226136402180.1032045227280440.948397738635978
360.1594816338655990.3189632677311970.840518366134401
370.2216262806146180.4432525612292370.778373719385382
380.1462841397780110.2925682795560230.853715860221989
390.14220775946790.28441551893580.8577922405321
400.08185896077254940.1637179215450990.91814103922745







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK

\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 & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58368&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]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58368&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58368&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 level00OK
5% type I error level00OK
10% type I error level00OK



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')
}