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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationSat, 04 Dec 2010 09:33:17 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/04/t1291455087jobi48ul2jx8qtk.htm/, Retrieved Wed, 05 Nov 2025 09:36:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105055, Retrieved Wed, 05 Nov 2025 09:36:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact427

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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F  MPD  [Multiple Regression] [ws 8: Regression ...] [2010-11-26 10:04:32] [05ab9592748364013445d860bb938e43]
-    D      [Multiple Regression] [review ws8] [2010-12-04 09:33:17] [cfd788255f1b1b5389e58d7f218c70bf] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9084	0	9700	9081
9743	0	9081	9084
8587	0	9084	9743
9731	0	9743	8587
9563	0	8587	9731
9998	0	9731	9563
9437	0	9563	9998
10038	0	9998	9437
9918	0	9437	10038
9252	0	10038	9918
9737	0	9918	9252
9035	0	9252	9737
9133	0	9737	9035
9487	0	9035	9133
8700	0	9133	9487
9627	0	9487	8700
8947	0	8700	9627
9283	0	9627	8947
8829	0	8947	9283
9947	0	9283	8829
9628	0	8829	9947
9318	0	9947	9628
9605	0	9628	9318
8640	0	9318	9605
9214	0	9605	8640
9567	0	8640	9214
8547	0	9214	9567
9185	0	9567	8547
9470	0	8547	9185
9123	0	9185	9470
9278	0	9470	9123
10170	0	9123	9278
9434	0	9278	10170
9655	0	10170	9434
9429	0	9434	9655
8739	0	9655	9429
9552	0	9429	8739
9687	0	8739	9552
9019	0	9552	9687
9672	0	9687	9019
9206	0	9019	9672
9069	0	9672	9206
9788	0	9206	9069
10312	0	9069	9788
10105	0	9788	10312
9863	0	10312	10105
9656	0	10105	9863
9295	0	9863	9656
9946	0	9656	9295
9701	0	9295	9946
9049	0	9946	9701
10190	0	9701	9049
9706	0	9049	10190
9765	0	10190	9706
9893	0	9706	9765
9994	0	9765	9893
10433	1	9893	9994
10073	1	9994	10433
10112	1	10433	10073
9266	1	10073	10112
9820	1	10112	9266
10097	1	9266	9820
9115	1	9820	10097
10411	1	10097	9115
9678	1	9115	10411
10408	1	10411	9678
10153	1	9678	10408
10368	1	10408	10153
10581	1	10153	10368
10597	1	10368	10581
10680	1	10581	10597
9738	1	10597	10680
9556	1	10680	9738

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 5 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105055&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105055&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105055&T=0

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


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Multiple Linear Regression - Estimated Regression Equation
Births[t] = + 5632.42646760897 + 233.327295316956x[t] + 0.184925679115300`y-1`[t] + 0.141855719535449`y-2`[t] + 485.518122007314M1[t] + 884.077057591996M2[t] -117.371735721934M3[t] + 921.654299160091M4[t] + 567.78584832305M5[t] + 616.785989141178M6[t] + 611.199861323609M7[t] + 1154.83556367848M8[t] + 916.246498776956M9[t] + 598.938676886247M10[t] + 725.272206498409M11[t] + 4.70384799637204t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Births[t] =  +  5632.42646760897 +  233.327295316956x[t] +  0.184925679115300`y-1`[t] +  0.141855719535449`y-2`[t] +  485.518122007314M1[t] +  884.077057591996M2[t] -117.371735721934M3[t] +  921.654299160091M4[t] +  567.78584832305M5[t] +  616.785989141178M6[t] +  611.199861323609M7[t] +  1154.83556367848M8[t] +  916.246498776956M9[t] +  598.938676886247M10[t] +  725.272206498409M11[t] +  4.70384799637204t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105055&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Births[t] =  +  5632.42646760897 +  233.327295316956x[t] +  0.184925679115300`y-1`[t] +  0.141855719535449`y-2`[t] +  485.518122007314M1[t] +  884.077057591996M2[t] -117.371735721934M3[t] +  921.654299160091M4[t] +  567.78584832305M5[t] +  616.785989141178M6[t] +  611.199861323609M7[t] +  1154.83556367848M8[t] +  916.246498776956M9[t] +  598.938676886247M10[t] +  725.272206498409M11[t] +  4.70384799637204t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105055&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105055&T=1

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


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

Multiple Linear Regression - Estimated Regression Equation
Births[t] = + 5632.42646760897 + 233.327295316956x[t] + 0.184925679115300`y-1`[t] + 0.141855719535449`y-2`[t] + 485.518122007314M1[t] + 884.077057591996M2[t] -117.371735721934M3[t] + 921.654299160091M4[t] + 567.78584832305M5[t] + 616.785989141178M6[t] + 611.199861323609M7[t] + 1154.83556367848M8[t] + 916.246498776956M9[t] + 598.938676886247M10[t] + 725.272206498409M11[t] + 4.70384799637204t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)5632.426467608971521.6957853.70140.0004850.000242
x233.327295316956122.0614091.91160.0609650.030483
`y-1`0.1849256791153000.1301781.42060.1608920.080446
`y-2`0.1418557195354490.1292051.09790.2768610.13843
M1485.518122007314176.8272972.74570.0080640.004032
M2884.077057591996177.4633224.98176e-063e-06
M3-117.371735721934157.726562-0.74410.4598440.229922
M4921.654299160091196.2524074.69631.7e-059e-06
M5567.78584832305191.7117592.96170.0044550.002228
M6616.785989141178162.795023.78870.0003670.000184
M7611.199861323609159.6182773.82910.0003220.000161
M81154.83556367848157.8430797.316400
M9916.246498776956162.9942815.62131e-060
M10598.938676886247161.3985893.71090.0004710.000235
M11725.272206498409158.072794.58822.5e-051.3e-05
t4.703847996372042.453331.91730.0602120.030106

\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) & 5632.42646760897 & 1521.695785 & 3.7014 & 0.000485 & 0.000242 \tabularnewline
x & 233.327295316956 & 122.061409 & 1.9116 & 0.060965 & 0.030483 \tabularnewline
`y-1` & 0.184925679115300 & 0.130178 & 1.4206 & 0.160892 & 0.080446 \tabularnewline
`y-2` & 0.141855719535449 & 0.129205 & 1.0979 & 0.276861 & 0.13843 \tabularnewline
M1 & 485.518122007314 & 176.827297 & 2.7457 & 0.008064 & 0.004032 \tabularnewline
M2 & 884.077057591996 & 177.463322 & 4.9817 & 6e-06 & 3e-06 \tabularnewline
M3 & -117.371735721934 & 157.726562 & -0.7441 & 0.459844 & 0.229922 \tabularnewline
M4 & 921.654299160091 & 196.252407 & 4.6963 & 1.7e-05 & 9e-06 \tabularnewline
M5 & 567.78584832305 & 191.711759 & 2.9617 & 0.004455 & 0.002228 \tabularnewline
M6 & 616.785989141178 & 162.79502 & 3.7887 & 0.000367 & 0.000184 \tabularnewline
M7 & 611.199861323609 & 159.618277 & 3.8291 & 0.000322 & 0.000161 \tabularnewline
M8 & 1154.83556367848 & 157.843079 & 7.3164 & 0 & 0 \tabularnewline
M9 & 916.246498776956 & 162.994281 & 5.6213 & 1e-06 & 0 \tabularnewline
M10 & 598.938676886247 & 161.398589 & 3.7109 & 0.000471 & 0.000235 \tabularnewline
M11 & 725.272206498409 & 158.07279 & 4.5882 & 2.5e-05 & 1.3e-05 \tabularnewline
t & 4.70384799637204 & 2.45333 & 1.9173 & 0.060212 & 0.030106 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105055&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]5632.42646760897[/C][C]1521.695785[/C][C]3.7014[/C][C]0.000485[/C][C]0.000242[/C][/ROW]
[ROW][C]x[/C][C]233.327295316956[/C][C]122.061409[/C][C]1.9116[/C][C]0.060965[/C][C]0.030483[/C][/ROW]
[ROW][C]`y-1`[/C][C]0.184925679115300[/C][C]0.130178[/C][C]1.4206[/C][C]0.160892[/C][C]0.080446[/C][/ROW]
[ROW][C]`y-2`[/C][C]0.141855719535449[/C][C]0.129205[/C][C]1.0979[/C][C]0.276861[/C][C]0.13843[/C][/ROW]
[ROW][C]M1[/C][C]485.518122007314[/C][C]176.827297[/C][C]2.7457[/C][C]0.008064[/C][C]0.004032[/C][/ROW]
[ROW][C]M2[/C][C]884.077057591996[/C][C]177.463322[/C][C]4.9817[/C][C]6e-06[/C][C]3e-06[/C][/ROW]
[ROW][C]M3[/C][C]-117.371735721934[/C][C]157.726562[/C][C]-0.7441[/C][C]0.459844[/C][C]0.229922[/C][/ROW]
[ROW][C]M4[/C][C]921.654299160091[/C][C]196.252407[/C][C]4.6963[/C][C]1.7e-05[/C][C]9e-06[/C][/ROW]
[ROW][C]M5[/C][C]567.78584832305[/C][C]191.711759[/C][C]2.9617[/C][C]0.004455[/C][C]0.002228[/C][/ROW]
[ROW][C]M6[/C][C]616.785989141178[/C][C]162.79502[/C][C]3.7887[/C][C]0.000367[/C][C]0.000184[/C][/ROW]
[ROW][C]M7[/C][C]611.199861323609[/C][C]159.618277[/C][C]3.8291[/C][C]0.000322[/C][C]0.000161[/C][/ROW]
[ROW][C]M8[/C][C]1154.83556367848[/C][C]157.843079[/C][C]7.3164[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M9[/C][C]916.246498776956[/C][C]162.994281[/C][C]5.6213[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]M10[/C][C]598.938676886247[/C][C]161.398589[/C][C]3.7109[/C][C]0.000471[/C][C]0.000235[/C][/ROW]
[ROW][C]M11[/C][C]725.272206498409[/C][C]158.07279[/C][C]4.5882[/C][C]2.5e-05[/C][C]1.3e-05[/C][/ROW]
[ROW][C]t[/C][C]4.70384799637204[/C][C]2.45333[/C][C]1.9173[/C][C]0.060212[/C][C]0.030106[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105055&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105055&T=2

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


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)5632.426467608971521.6957853.70140.0004850.000242
x233.327295316956122.0614091.91160.0609650.030483
`y-1`0.1849256791153000.1301781.42060.1608920.080446
`y-2`0.1418557195354490.1292051.09790.2768610.13843
M1485.518122007314176.8272972.74570.0080640.004032
M2884.077057591996177.4633224.98176e-063e-06
M3-117.371735721934157.726562-0.74410.4598440.229922
M4921.654299160091196.2524074.69631.7e-059e-06
M5567.78584832305191.7117592.96170.0044550.002228
M6616.785989141178162.795023.78870.0003670.000184
M7611.199861323609159.6182773.82910.0003220.000161
M81154.83556367848157.8430797.316400
M9916.246498776956162.9942815.62131e-060
M10598.938676886247161.3985893.71090.0004710.000235
M11725.272206498409158.072794.58822.5e-051.3e-05
t4.703847996372042.453331.91730.0602120.030106






Multiple Linear Regression - Regression Statistics
Multiple R0.882356647284765
R-squared0.77855325300761
Adjusted R-squared0.720277793272771
F-TEST (value)13.3598817847191
F-TEST (DF numerator)15
F-TEST (DF denominator)57
p-value1.54876111935209e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation267.664628275107
Sum Squared Residuals4083728.13409011

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.882356647284765 \tabularnewline
R-squared & 0.77855325300761 \tabularnewline
Adjusted R-squared & 0.720277793272771 \tabularnewline
F-TEST (value) & 13.3598817847191 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 57 \tabularnewline
p-value & 1.54876111935209e-13 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 267.664628275107 \tabularnewline
Sum Squared Residuals & 4083728.13409011 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105055&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.882356647284765[/C][/ROW]
[ROW][C]R-squared[/C][C]0.77855325300761[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.720277793272771[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]13.3598817847191[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]57[/C][/ROW]
[ROW][C]p-value[/C][C]1.54876111935209e-13[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]267.664628275107[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]4083728.13409011[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105055&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105055&T=3

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


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

Multiple Linear Regression - Regression Statistics
Multiple R0.882356647284765
R-squared0.77855325300761
Adjusted R-squared0.720277793272771
F-TEST (value)13.3598817847191
F-TEST (DF numerator)15
F-TEST (DF denominator)57
p-value1.54876111935209e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation267.664628275107
Sum Squared Residuals4083728.13409011






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
190849204.61931413246-120.619314132463
297439493.83866949976249.161330500238
385878591.13142039341-4.13142039341149
497319592.74211402581138.257885974188
595639192.08636927641370.91363072359
699989433.51357411686564.486425883143
794379463.2710182022-26.2710182022101
81003810012.472180309225.5278196907818
999189760.0989448612157.901055138809
1092529541.6126177709-289.612617770896
1197379555.98300467498181.016995325014
1290358781.05416785685253.945832143149
1391339261.38237711757-128.382377117572
1494879548.72919447416-61.7291944741601
1587008620.3238904254579.6761095745493
1696279617.877012436279.12298756373444
1789479254.67615214122-307.676152141217
1892839383.3443562115-100.344356211494
1988299304.3761363558-475.376136355804
2099479850.448218220796.5517817793093
2196289691.20143743783-63.2014374378281
2293189540.09239826259-222.092398262588
2396059568.1632111773536.8367888226475
2486408830.98048365625-190.980483656246
2592149237.38535421432-23.385354214315
2695679543.6200404624523.3799595375478
2785478703.09750395309-156.09750395309
2891859667.41331763303-482.413317633031
2994709220.12847115837249.871528841628
3091239432.24392331603-309.243923316035
3192789434.8415273639-156.841527363899
32101709940.99950359012229.000496409876
3394349862.31306877347-428.313068773467
3496559610.2569910718944.7430089281129
3594299636.5391828689-207.539182868895
3687398924.78000683633-185.780006836327
3795529275.3283268805276.671673119504
3896879666.3210918543120.6789081456868
3990198839.07124579478179.92875420522
4096729813.00647470406-141.006474704063
4192069432.94330307102-226.943303071022
4290699541.2989950443-472.298995044292
4397889434.80711517901353.192884820990
441031210059.8061098374252.193890162559
451010510033.214853252871.7851467472319
4698639788.1478012710174.8521987289898
4796569846.5764791751-190.576479175099
4892959051.89197238332243.108027616679
4999469452.62441205784493.375587942157
5097019881.47709889585-180.477098895851
5190498970.3641193961778.6358806038313
52101909876.2972817542313.702718245795
5397069568.4185121203137.581487879692
5497659764.46453255020.535467449793721
5598939682.4477114898210.552288510204
56999410259.8554090094-265.855409009376
571043310297.2954020210135.704597978978
581007310065.64358259347.35641740660755
591011210226.7952743008-114.795274300782
6092669445.18604437912-179.186044379119
6198209822.61017714131-2.61017714131218
621009710148.0139048135-51.0139048134611
6391159293.0118200371-178.011820037099
641041110248.6637994466162.336200553376
6596789901.74719223267-223.747192232672
661040810091.1346187611316.865381238885
671015310058.256491409394.7435085907183
681036810705.4185790332-337.418579033151
691058110454.8762936537126.123706346277
701059710212.2466090302384.753390969774
711068010384.9428478029295.057152197114
7297389679.1073248881358.8926751118645
73955610051.050038456-495.050038455999

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 9084 & 9204.61931413246 & -120.619314132463 \tabularnewline
2 & 9743 & 9493.83866949976 & 249.161330500238 \tabularnewline
3 & 8587 & 8591.13142039341 & -4.13142039341149 \tabularnewline
4 & 9731 & 9592.74211402581 & 138.257885974188 \tabularnewline
5 & 9563 & 9192.08636927641 & 370.91363072359 \tabularnewline
6 & 9998 & 9433.51357411686 & 564.486425883143 \tabularnewline
7 & 9437 & 9463.2710182022 & -26.2710182022101 \tabularnewline
8 & 10038 & 10012.4721803092 & 25.5278196907818 \tabularnewline
9 & 9918 & 9760.0989448612 & 157.901055138809 \tabularnewline
10 & 9252 & 9541.6126177709 & -289.612617770896 \tabularnewline
11 & 9737 & 9555.98300467498 & 181.016995325014 \tabularnewline
12 & 9035 & 8781.05416785685 & 253.945832143149 \tabularnewline
13 & 9133 & 9261.38237711757 & -128.382377117572 \tabularnewline
14 & 9487 & 9548.72919447416 & -61.7291944741601 \tabularnewline
15 & 8700 & 8620.32389042545 & 79.6761095745493 \tabularnewline
16 & 9627 & 9617.87701243627 & 9.12298756373444 \tabularnewline
17 & 8947 & 9254.67615214122 & -307.676152141217 \tabularnewline
18 & 9283 & 9383.3443562115 & -100.344356211494 \tabularnewline
19 & 8829 & 9304.3761363558 & -475.376136355804 \tabularnewline
20 & 9947 & 9850.4482182207 & 96.5517817793093 \tabularnewline
21 & 9628 & 9691.20143743783 & -63.2014374378281 \tabularnewline
22 & 9318 & 9540.09239826259 & -222.092398262588 \tabularnewline
23 & 9605 & 9568.16321117735 & 36.8367888226475 \tabularnewline
24 & 8640 & 8830.98048365625 & -190.980483656246 \tabularnewline
25 & 9214 & 9237.38535421432 & -23.385354214315 \tabularnewline
26 & 9567 & 9543.62004046245 & 23.3799595375478 \tabularnewline
27 & 8547 & 8703.09750395309 & -156.09750395309 \tabularnewline
28 & 9185 & 9667.41331763303 & -482.413317633031 \tabularnewline
29 & 9470 & 9220.12847115837 & 249.871528841628 \tabularnewline
30 & 9123 & 9432.24392331603 & -309.243923316035 \tabularnewline
31 & 9278 & 9434.8415273639 & -156.841527363899 \tabularnewline
32 & 10170 & 9940.99950359012 & 229.000496409876 \tabularnewline
33 & 9434 & 9862.31306877347 & -428.313068773467 \tabularnewline
34 & 9655 & 9610.25699107189 & 44.7430089281129 \tabularnewline
35 & 9429 & 9636.5391828689 & -207.539182868895 \tabularnewline
36 & 8739 & 8924.78000683633 & -185.780006836327 \tabularnewline
37 & 9552 & 9275.3283268805 & 276.671673119504 \tabularnewline
38 & 9687 & 9666.32109185431 & 20.6789081456868 \tabularnewline
39 & 9019 & 8839.07124579478 & 179.92875420522 \tabularnewline
40 & 9672 & 9813.00647470406 & -141.006474704063 \tabularnewline
41 & 9206 & 9432.94330307102 & -226.943303071022 \tabularnewline
42 & 9069 & 9541.2989950443 & -472.298995044292 \tabularnewline
43 & 9788 & 9434.80711517901 & 353.192884820990 \tabularnewline
44 & 10312 & 10059.8061098374 & 252.193890162559 \tabularnewline
45 & 10105 & 10033.2148532528 & 71.7851467472319 \tabularnewline
46 & 9863 & 9788.14780127101 & 74.8521987289898 \tabularnewline
47 & 9656 & 9846.5764791751 & -190.576479175099 \tabularnewline
48 & 9295 & 9051.89197238332 & 243.108027616679 \tabularnewline
49 & 9946 & 9452.62441205784 & 493.375587942157 \tabularnewline
50 & 9701 & 9881.47709889585 & -180.477098895851 \tabularnewline
51 & 9049 & 8970.36411939617 & 78.6358806038313 \tabularnewline
52 & 10190 & 9876.2972817542 & 313.702718245795 \tabularnewline
53 & 9706 & 9568.4185121203 & 137.581487879692 \tabularnewline
54 & 9765 & 9764.4645325502 & 0.535467449793721 \tabularnewline
55 & 9893 & 9682.4477114898 & 210.552288510204 \tabularnewline
56 & 9994 & 10259.8554090094 & -265.855409009376 \tabularnewline
57 & 10433 & 10297.2954020210 & 135.704597978978 \tabularnewline
58 & 10073 & 10065.6435825934 & 7.35641740660755 \tabularnewline
59 & 10112 & 10226.7952743008 & -114.795274300782 \tabularnewline
60 & 9266 & 9445.18604437912 & -179.186044379119 \tabularnewline
61 & 9820 & 9822.61017714131 & -2.61017714131218 \tabularnewline
62 & 10097 & 10148.0139048135 & -51.0139048134611 \tabularnewline
63 & 9115 & 9293.0118200371 & -178.011820037099 \tabularnewline
64 & 10411 & 10248.6637994466 & 162.336200553376 \tabularnewline
65 & 9678 & 9901.74719223267 & -223.747192232672 \tabularnewline
66 & 10408 & 10091.1346187611 & 316.865381238885 \tabularnewline
67 & 10153 & 10058.2564914093 & 94.7435085907183 \tabularnewline
68 & 10368 & 10705.4185790332 & -337.418579033151 \tabularnewline
69 & 10581 & 10454.8762936537 & 126.123706346277 \tabularnewline
70 & 10597 & 10212.2466090302 & 384.753390969774 \tabularnewline
71 & 10680 & 10384.9428478029 & 295.057152197114 \tabularnewline
72 & 9738 & 9679.10732488813 & 58.8926751118645 \tabularnewline
73 & 9556 & 10051.050038456 & -495.050038455999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105055&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]9084[/C][C]9204.61931413246[/C][C]-120.619314132463[/C][/ROW]
[ROW][C]2[/C][C]9743[/C][C]9493.83866949976[/C][C]249.161330500238[/C][/ROW]
[ROW][C]3[/C][C]8587[/C][C]8591.13142039341[/C][C]-4.13142039341149[/C][/ROW]
[ROW][C]4[/C][C]9731[/C][C]9592.74211402581[/C][C]138.257885974188[/C][/ROW]
[ROW][C]5[/C][C]9563[/C][C]9192.08636927641[/C][C]370.91363072359[/C][/ROW]
[ROW][C]6[/C][C]9998[/C][C]9433.51357411686[/C][C]564.486425883143[/C][/ROW]
[ROW][C]7[/C][C]9437[/C][C]9463.2710182022[/C][C]-26.2710182022101[/C][/ROW]
[ROW][C]8[/C][C]10038[/C][C]10012.4721803092[/C][C]25.5278196907818[/C][/ROW]
[ROW][C]9[/C][C]9918[/C][C]9760.0989448612[/C][C]157.901055138809[/C][/ROW]
[ROW][C]10[/C][C]9252[/C][C]9541.6126177709[/C][C]-289.612617770896[/C][/ROW]
[ROW][C]11[/C][C]9737[/C][C]9555.98300467498[/C][C]181.016995325014[/C][/ROW]
[ROW][C]12[/C][C]9035[/C][C]8781.05416785685[/C][C]253.945832143149[/C][/ROW]
[ROW][C]13[/C][C]9133[/C][C]9261.38237711757[/C][C]-128.382377117572[/C][/ROW]
[ROW][C]14[/C][C]9487[/C][C]9548.72919447416[/C][C]-61.7291944741601[/C][/ROW]
[ROW][C]15[/C][C]8700[/C][C]8620.32389042545[/C][C]79.6761095745493[/C][/ROW]
[ROW][C]16[/C][C]9627[/C][C]9617.87701243627[/C][C]9.12298756373444[/C][/ROW]
[ROW][C]17[/C][C]8947[/C][C]9254.67615214122[/C][C]-307.676152141217[/C][/ROW]
[ROW][C]18[/C][C]9283[/C][C]9383.3443562115[/C][C]-100.344356211494[/C][/ROW]
[ROW][C]19[/C][C]8829[/C][C]9304.3761363558[/C][C]-475.376136355804[/C][/ROW]
[ROW][C]20[/C][C]9947[/C][C]9850.4482182207[/C][C]96.5517817793093[/C][/ROW]
[ROW][C]21[/C][C]9628[/C][C]9691.20143743783[/C][C]-63.2014374378281[/C][/ROW]
[ROW][C]22[/C][C]9318[/C][C]9540.09239826259[/C][C]-222.092398262588[/C][/ROW]
[ROW][C]23[/C][C]9605[/C][C]9568.16321117735[/C][C]36.8367888226475[/C][/ROW]
[ROW][C]24[/C][C]8640[/C][C]8830.98048365625[/C][C]-190.980483656246[/C][/ROW]
[ROW][C]25[/C][C]9214[/C][C]9237.38535421432[/C][C]-23.385354214315[/C][/ROW]
[ROW][C]26[/C][C]9567[/C][C]9543.62004046245[/C][C]23.3799595375478[/C][/ROW]
[ROW][C]27[/C][C]8547[/C][C]8703.09750395309[/C][C]-156.09750395309[/C][/ROW]
[ROW][C]28[/C][C]9185[/C][C]9667.41331763303[/C][C]-482.413317633031[/C][/ROW]
[ROW][C]29[/C][C]9470[/C][C]9220.12847115837[/C][C]249.871528841628[/C][/ROW]
[ROW][C]30[/C][C]9123[/C][C]9432.24392331603[/C][C]-309.243923316035[/C][/ROW]
[ROW][C]31[/C][C]9278[/C][C]9434.8415273639[/C][C]-156.841527363899[/C][/ROW]
[ROW][C]32[/C][C]10170[/C][C]9940.99950359012[/C][C]229.000496409876[/C][/ROW]
[ROW][C]33[/C][C]9434[/C][C]9862.31306877347[/C][C]-428.313068773467[/C][/ROW]
[ROW][C]34[/C][C]9655[/C][C]9610.25699107189[/C][C]44.7430089281129[/C][/ROW]
[ROW][C]35[/C][C]9429[/C][C]9636.5391828689[/C][C]-207.539182868895[/C][/ROW]
[ROW][C]36[/C][C]8739[/C][C]8924.78000683633[/C][C]-185.780006836327[/C][/ROW]
[ROW][C]37[/C][C]9552[/C][C]9275.3283268805[/C][C]276.671673119504[/C][/ROW]
[ROW][C]38[/C][C]9687[/C][C]9666.32109185431[/C][C]20.6789081456868[/C][/ROW]
[ROW][C]39[/C][C]9019[/C][C]8839.07124579478[/C][C]179.92875420522[/C][/ROW]
[ROW][C]40[/C][C]9672[/C][C]9813.00647470406[/C][C]-141.006474704063[/C][/ROW]
[ROW][C]41[/C][C]9206[/C][C]9432.94330307102[/C][C]-226.943303071022[/C][/ROW]
[ROW][C]42[/C][C]9069[/C][C]9541.2989950443[/C][C]-472.298995044292[/C][/ROW]
[ROW][C]43[/C][C]9788[/C][C]9434.80711517901[/C][C]353.192884820990[/C][/ROW]
[ROW][C]44[/C][C]10312[/C][C]10059.8061098374[/C][C]252.193890162559[/C][/ROW]
[ROW][C]45[/C][C]10105[/C][C]10033.2148532528[/C][C]71.7851467472319[/C][/ROW]
[ROW][C]46[/C][C]9863[/C][C]9788.14780127101[/C][C]74.8521987289898[/C][/ROW]
[ROW][C]47[/C][C]9656[/C][C]9846.5764791751[/C][C]-190.576479175099[/C][/ROW]
[ROW][C]48[/C][C]9295[/C][C]9051.89197238332[/C][C]243.108027616679[/C][/ROW]
[ROW][C]49[/C][C]9946[/C][C]9452.62441205784[/C][C]493.375587942157[/C][/ROW]
[ROW][C]50[/C][C]9701[/C][C]9881.47709889585[/C][C]-180.477098895851[/C][/ROW]
[ROW][C]51[/C][C]9049[/C][C]8970.36411939617[/C][C]78.6358806038313[/C][/ROW]
[ROW][C]52[/C][C]10190[/C][C]9876.2972817542[/C][C]313.702718245795[/C][/ROW]
[ROW][C]53[/C][C]9706[/C][C]9568.4185121203[/C][C]137.581487879692[/C][/ROW]
[ROW][C]54[/C][C]9765[/C][C]9764.4645325502[/C][C]0.535467449793721[/C][/ROW]
[ROW][C]55[/C][C]9893[/C][C]9682.4477114898[/C][C]210.552288510204[/C][/ROW]
[ROW][C]56[/C][C]9994[/C][C]10259.8554090094[/C][C]-265.855409009376[/C][/ROW]
[ROW][C]57[/C][C]10433[/C][C]10297.2954020210[/C][C]135.704597978978[/C][/ROW]
[ROW][C]58[/C][C]10073[/C][C]10065.6435825934[/C][C]7.35641740660755[/C][/ROW]
[ROW][C]59[/C][C]10112[/C][C]10226.7952743008[/C][C]-114.795274300782[/C][/ROW]
[ROW][C]60[/C][C]9266[/C][C]9445.18604437912[/C][C]-179.186044379119[/C][/ROW]
[ROW][C]61[/C][C]9820[/C][C]9822.61017714131[/C][C]-2.61017714131218[/C][/ROW]
[ROW][C]62[/C][C]10097[/C][C]10148.0139048135[/C][C]-51.0139048134611[/C][/ROW]
[ROW][C]63[/C][C]9115[/C][C]9293.0118200371[/C][C]-178.011820037099[/C][/ROW]
[ROW][C]64[/C][C]10411[/C][C]10248.6637994466[/C][C]162.336200553376[/C][/ROW]
[ROW][C]65[/C][C]9678[/C][C]9901.74719223267[/C][C]-223.747192232672[/C][/ROW]
[ROW][C]66[/C][C]10408[/C][C]10091.1346187611[/C][C]316.865381238885[/C][/ROW]
[ROW][C]67[/C][C]10153[/C][C]10058.2564914093[/C][C]94.7435085907183[/C][/ROW]
[ROW][C]68[/C][C]10368[/C][C]10705.4185790332[/C][C]-337.418579033151[/C][/ROW]
[ROW][C]69[/C][C]10581[/C][C]10454.8762936537[/C][C]126.123706346277[/C][/ROW]
[ROW][C]70[/C][C]10597[/C][C]10212.2466090302[/C][C]384.753390969774[/C][/ROW]
[ROW][C]71[/C][C]10680[/C][C]10384.9428478029[/C][C]295.057152197114[/C][/ROW]
[ROW][C]72[/C][C]9738[/C][C]9679.10732488813[/C][C]58.8926751118645[/C][/ROW]
[ROW][C]73[/C][C]9556[/C][C]10051.050038456[/C][C]-495.050038455999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105055&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105055&T=4

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


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
190849204.61931413246-120.619314132463
297439493.83866949976249.161330500238
385878591.13142039341-4.13142039341149
497319592.74211402581138.257885974188
595639192.08636927641370.91363072359
699989433.51357411686564.486425883143
794379463.2710182022-26.2710182022101
81003810012.472180309225.5278196907818
999189760.0989448612157.901055138809
1092529541.6126177709-289.612617770896
1197379555.98300467498181.016995325014
1290358781.05416785685253.945832143149
1391339261.38237711757-128.382377117572
1494879548.72919447416-61.7291944741601
1587008620.3238904254579.6761095745493
1696279617.877012436279.12298756373444
1789479254.67615214122-307.676152141217
1892839383.3443562115-100.344356211494
1988299304.3761363558-475.376136355804
2099479850.448218220796.5517817793093
2196289691.20143743783-63.2014374378281
2293189540.09239826259-222.092398262588
2396059568.1632111773536.8367888226475
2486408830.98048365625-190.980483656246
2592149237.38535421432-23.385354214315
2695679543.6200404624523.3799595375478
2785478703.09750395309-156.09750395309
2891859667.41331763303-482.413317633031
2994709220.12847115837249.871528841628
3091239432.24392331603-309.243923316035
3192789434.8415273639-156.841527363899
32101709940.99950359012229.000496409876
3394349862.31306877347-428.313068773467
3496559610.2569910718944.7430089281129
3594299636.5391828689-207.539182868895
3687398924.78000683633-185.780006836327
3795529275.3283268805276.671673119504
3896879666.3210918543120.6789081456868
3990198839.07124579478179.92875420522
4096729813.00647470406-141.006474704063
4192069432.94330307102-226.943303071022
4290699541.2989950443-472.298995044292
4397889434.80711517901353.192884820990
441031210059.8061098374252.193890162559
451010510033.214853252871.7851467472319
4698639788.1478012710174.8521987289898
4796569846.5764791751-190.576479175099
4892959051.89197238332243.108027616679
4999469452.62441205784493.375587942157
5097019881.47709889585-180.477098895851
5190498970.3641193961778.6358806038313
52101909876.2972817542313.702718245795
5397069568.4185121203137.581487879692
5497659764.46453255020.535467449793721
5598939682.4477114898210.552288510204
56999410259.8554090094-265.855409009376
571043310297.2954020210135.704597978978
581007310065.64358259347.35641740660755
591011210226.7952743008-114.795274300782
6092669445.18604437912-179.186044379119
6198209822.61017714131-2.61017714131218
621009710148.0139048135-51.0139048134611
6391159293.0118200371-178.011820037099
641041110248.6637994466162.336200553376
6596789901.74719223267-223.747192232672
661040810091.1346187611316.865381238885
671015310058.256491409394.7435085907183
681036810705.4185790332-337.418579033151
691058110454.8762936537126.123706346277
701059710212.2466090302384.753390969774
711068010384.9428478029295.057152197114
7297389679.1073248881358.8926751118645
73955610051.050038456-495.050038455999






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.7224169581326890.5551660837346220.277583041867311
200.6947572757015640.6104854485968720.305242724298436
210.5973929112437310.8052141775125370.402607088756269
220.5839222380972660.8321555238054670.416077761902734
230.4765264609634690.9530529219269390.523473539036531
240.3836829460826480.7673658921652950.616317053917352
250.5099189477509970.9801621044980060.490081052249003
260.4313908234016170.8627816468032330.568609176598383
270.3360677723548450.6721355447096890.663932227645155
280.3445185561014320.6890371122028650.655481443898568
290.4978217835781870.9956435671563730.502178216421813
300.4629611577243570.9259223154487140.537038842275643
310.4071675224648350.814335044929670.592832477535165
320.5325596604797880.9348806790404240.467440339520212
330.531612460765550.93677507846890.46838753923445
340.5640350484060480.8719299031879040.435964951593952
350.5321931769386360.9356136461227280.467806823061364
360.4652823945518280.9305647891036560.534717605448172
370.5746058581586260.8507882836827480.425394141841374
380.5132674481299860.9734651037400270.486732551870014
390.5520885458377630.8958229083244740.447911454162237
400.4684357324812620.9368714649625240.531564267518738
410.4069842182526470.8139684365052930.593015781747353
420.694465028399640.6110699432007210.305534971600361
430.7444969653575790.5110060692848420.255503034642421
440.7285284430014070.5429431139971860.271471556998593
450.661224874519980.6775502509600390.338775125480020
460.5919435907826320.8161128184347370.408056409217368
470.6349658790461980.7300682419076040.365034120953802
480.5508373401445580.8983253197108840.449162659855442
490.785905115687970.4281897686240610.214094884312031
500.6951630371459050.609673925708190.304836962854095
510.605151700201580.789696599596840.39484829979842
520.5150269006034770.9699461987930460.484973099396523
530.5820996732887380.8358006534225240.417900326711262
540.4083644864098240.8167289728196490.591635513590176

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.722416958132689 & 0.555166083734622 & 0.277583041867311 \tabularnewline
20 & 0.694757275701564 & 0.610485448596872 & 0.305242724298436 \tabularnewline
21 & 0.597392911243731 & 0.805214177512537 & 0.402607088756269 \tabularnewline
22 & 0.583922238097266 & 0.832155523805467 & 0.416077761902734 \tabularnewline
23 & 0.476526460963469 & 0.953052921926939 & 0.523473539036531 \tabularnewline
24 & 0.383682946082648 & 0.767365892165295 & 0.616317053917352 \tabularnewline
25 & 0.509918947750997 & 0.980162104498006 & 0.490081052249003 \tabularnewline
26 & 0.431390823401617 & 0.862781646803233 & 0.568609176598383 \tabularnewline
27 & 0.336067772354845 & 0.672135544709689 & 0.663932227645155 \tabularnewline
28 & 0.344518556101432 & 0.689037112202865 & 0.655481443898568 \tabularnewline
29 & 0.497821783578187 & 0.995643567156373 & 0.502178216421813 \tabularnewline
30 & 0.462961157724357 & 0.925922315448714 & 0.537038842275643 \tabularnewline
31 & 0.407167522464835 & 0.81433504492967 & 0.592832477535165 \tabularnewline
32 & 0.532559660479788 & 0.934880679040424 & 0.467440339520212 \tabularnewline
33 & 0.53161246076555 & 0.9367750784689 & 0.46838753923445 \tabularnewline
34 & 0.564035048406048 & 0.871929903187904 & 0.435964951593952 \tabularnewline
35 & 0.532193176938636 & 0.935613646122728 & 0.467806823061364 \tabularnewline
36 & 0.465282394551828 & 0.930564789103656 & 0.534717605448172 \tabularnewline
37 & 0.574605858158626 & 0.850788283682748 & 0.425394141841374 \tabularnewline
38 & 0.513267448129986 & 0.973465103740027 & 0.486732551870014 \tabularnewline
39 & 0.552088545837763 & 0.895822908324474 & 0.447911454162237 \tabularnewline
40 & 0.468435732481262 & 0.936871464962524 & 0.531564267518738 \tabularnewline
41 & 0.406984218252647 & 0.813968436505293 & 0.593015781747353 \tabularnewline
42 & 0.69446502839964 & 0.611069943200721 & 0.305534971600361 \tabularnewline
43 & 0.744496965357579 & 0.511006069284842 & 0.255503034642421 \tabularnewline
44 & 0.728528443001407 & 0.542943113997186 & 0.271471556998593 \tabularnewline
45 & 0.66122487451998 & 0.677550250960039 & 0.338775125480020 \tabularnewline
46 & 0.591943590782632 & 0.816112818434737 & 0.408056409217368 \tabularnewline
47 & 0.634965879046198 & 0.730068241907604 & 0.365034120953802 \tabularnewline
48 & 0.550837340144558 & 0.898325319710884 & 0.449162659855442 \tabularnewline
49 & 0.78590511568797 & 0.428189768624061 & 0.214094884312031 \tabularnewline
50 & 0.695163037145905 & 0.60967392570819 & 0.304836962854095 \tabularnewline
51 & 0.60515170020158 & 0.78969659959684 & 0.39484829979842 \tabularnewline
52 & 0.515026900603477 & 0.969946198793046 & 0.484973099396523 \tabularnewline
53 & 0.582099673288738 & 0.835800653422524 & 0.417900326711262 \tabularnewline
54 & 0.408364486409824 & 0.816728972819649 & 0.591635513590176 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105055&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]0.722416958132689[/C][C]0.555166083734622[/C][C]0.277583041867311[/C][/ROW]
[ROW][C]20[/C][C]0.694757275701564[/C][C]0.610485448596872[/C][C]0.305242724298436[/C][/ROW]
[ROW][C]21[/C][C]0.597392911243731[/C][C]0.805214177512537[/C][C]0.402607088756269[/C][/ROW]
[ROW][C]22[/C][C]0.583922238097266[/C][C]0.832155523805467[/C][C]0.416077761902734[/C][/ROW]
[ROW][C]23[/C][C]0.476526460963469[/C][C]0.953052921926939[/C][C]0.523473539036531[/C][/ROW]
[ROW][C]24[/C][C]0.383682946082648[/C][C]0.767365892165295[/C][C]0.616317053917352[/C][/ROW]
[ROW][C]25[/C][C]0.509918947750997[/C][C]0.980162104498006[/C][C]0.490081052249003[/C][/ROW]
[ROW][C]26[/C][C]0.431390823401617[/C][C]0.862781646803233[/C][C]0.568609176598383[/C][/ROW]
[ROW][C]27[/C][C]0.336067772354845[/C][C]0.672135544709689[/C][C]0.663932227645155[/C][/ROW]
[ROW][C]28[/C][C]0.344518556101432[/C][C]0.689037112202865[/C][C]0.655481443898568[/C][/ROW]
[ROW][C]29[/C][C]0.497821783578187[/C][C]0.995643567156373[/C][C]0.502178216421813[/C][/ROW]
[ROW][C]30[/C][C]0.462961157724357[/C][C]0.925922315448714[/C][C]0.537038842275643[/C][/ROW]
[ROW][C]31[/C][C]0.407167522464835[/C][C]0.81433504492967[/C][C]0.592832477535165[/C][/ROW]
[ROW][C]32[/C][C]0.532559660479788[/C][C]0.934880679040424[/C][C]0.467440339520212[/C][/ROW]
[ROW][C]33[/C][C]0.53161246076555[/C][C]0.9367750784689[/C][C]0.46838753923445[/C][/ROW]
[ROW][C]34[/C][C]0.564035048406048[/C][C]0.871929903187904[/C][C]0.435964951593952[/C][/ROW]
[ROW][C]35[/C][C]0.532193176938636[/C][C]0.935613646122728[/C][C]0.467806823061364[/C][/ROW]
[ROW][C]36[/C][C]0.465282394551828[/C][C]0.930564789103656[/C][C]0.534717605448172[/C][/ROW]
[ROW][C]37[/C][C]0.574605858158626[/C][C]0.850788283682748[/C][C]0.425394141841374[/C][/ROW]
[ROW][C]38[/C][C]0.513267448129986[/C][C]0.973465103740027[/C][C]0.486732551870014[/C][/ROW]
[ROW][C]39[/C][C]0.552088545837763[/C][C]0.895822908324474[/C][C]0.447911454162237[/C][/ROW]
[ROW][C]40[/C][C]0.468435732481262[/C][C]0.936871464962524[/C][C]0.531564267518738[/C][/ROW]
[ROW][C]41[/C][C]0.406984218252647[/C][C]0.813968436505293[/C][C]0.593015781747353[/C][/ROW]
[ROW][C]42[/C][C]0.69446502839964[/C][C]0.611069943200721[/C][C]0.305534971600361[/C][/ROW]
[ROW][C]43[/C][C]0.744496965357579[/C][C]0.511006069284842[/C][C]0.255503034642421[/C][/ROW]
[ROW][C]44[/C][C]0.728528443001407[/C][C]0.542943113997186[/C][C]0.271471556998593[/C][/ROW]
[ROW][C]45[/C][C]0.66122487451998[/C][C]0.677550250960039[/C][C]0.338775125480020[/C][/ROW]
[ROW][C]46[/C][C]0.591943590782632[/C][C]0.816112818434737[/C][C]0.408056409217368[/C][/ROW]
[ROW][C]47[/C][C]0.634965879046198[/C][C]0.730068241907604[/C][C]0.365034120953802[/C][/ROW]
[ROW][C]48[/C][C]0.550837340144558[/C][C]0.898325319710884[/C][C]0.449162659855442[/C][/ROW]
[ROW][C]49[/C][C]0.78590511568797[/C][C]0.428189768624061[/C][C]0.214094884312031[/C][/ROW]
[ROW][C]50[/C][C]0.695163037145905[/C][C]0.60967392570819[/C][C]0.304836962854095[/C][/ROW]
[ROW][C]51[/C][C]0.60515170020158[/C][C]0.78969659959684[/C][C]0.39484829979842[/C][/ROW]
[ROW][C]52[/C][C]0.515026900603477[/C][C]0.969946198793046[/C][C]0.484973099396523[/C][/ROW]
[ROW][C]53[/C][C]0.582099673288738[/C][C]0.835800653422524[/C][C]0.417900326711262[/C][/ROW]
[ROW][C]54[/C][C]0.408364486409824[/C][C]0.816728972819649[/C][C]0.591635513590176[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105055&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105055&T=5

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


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.7224169581326890.5551660837346220.277583041867311
200.6947572757015640.6104854485968720.305242724298436
210.5973929112437310.8052141775125370.402607088756269
220.5839222380972660.8321555238054670.416077761902734
230.4765264609634690.9530529219269390.523473539036531
240.3836829460826480.7673658921652950.616317053917352
250.5099189477509970.9801621044980060.490081052249003
260.4313908234016170.8627816468032330.568609176598383
270.3360677723548450.6721355447096890.663932227645155
280.3445185561014320.6890371122028650.655481443898568
290.4978217835781870.9956435671563730.502178216421813
300.4629611577243570.9259223154487140.537038842275643
310.4071675224648350.814335044929670.592832477535165
320.5325596604797880.9348806790404240.467440339520212
330.531612460765550.93677507846890.46838753923445
340.5640350484060480.8719299031879040.435964951593952
350.5321931769386360.9356136461227280.467806823061364
360.4652823945518280.9305647891036560.534717605448172
370.5746058581586260.8507882836827480.425394141841374
380.5132674481299860.9734651037400270.486732551870014
390.5520885458377630.8958229083244740.447911454162237
400.4684357324812620.9368714649625240.531564267518738
410.4069842182526470.8139684365052930.593015781747353
420.694465028399640.6110699432007210.305534971600361
430.7444969653575790.5110060692848420.255503034642421
440.7285284430014070.5429431139971860.271471556998593
450.661224874519980.6775502509600390.338775125480020
460.5919435907826320.8161128184347370.408056409217368
470.6349658790461980.7300682419076040.365034120953802
480.5508373401445580.8983253197108840.449162659855442
490.785905115687970.4281897686240610.214094884312031
500.6951630371459050.609673925708190.304836962854095
510.605151700201580.789696599596840.39484829979842
520.5150269006034770.9699461987930460.484973099396523
530.5820996732887380.8358006534225240.417900326711262
540.4083644864098240.8167289728196490.591635513590176






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=105055&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=105055&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105055&T=6

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


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

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


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 5
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Figure 6
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Figure 7
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Figure 8
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Figure 9
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Figure 10
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Input Parameters & R Code

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')
}