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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 computationSun, 13 Dec 2009 07:07:06 -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/Dec/13/t1260713314xe4ynj5sru1skhr.htm/, Retrieved Sun, 28 Apr 2024 13:41:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67289, Retrieved Sun, 28 Apr 2024 13:41:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-   PD    [Multiple Regression] [] [2009-11-19 10:28:54] [74be16979710d4c4e7c6647856088456]
-   P       [Multiple Regression] [] [2009-11-20 13:18:20] [74be16979710d4c4e7c6647856088456]
-    D        [Multiple Regression] [] [2009-11-20 13:28:43] [74be16979710d4c4e7c6647856088456]
-    D            [Multiple Regression] [] [2009-12-13 14:07:06] [14869f38c4320b00c96ca15cc00142de] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
431	106,2	436	443	448	460	467
484	81	431	436	443	448	460
510	94,7	484	431	436	443	448
513	101	510	484	431	436	443
503	109,4	513	510	484	431	436
471	102,3	503	513	510	484	431
471	90,7	471	503	513	510	484
476	96,2	471	471	503	513	510
475	96,1	476	471	471	503	513
470	106	475	476	471	471	503
461	103,1	470	475	476	471	471
455	102	461	470	475	476	471
456	104,7	455	461	470	475	476
517	86	456	455	461	470	475
525	92,1	517	456	455	461	470
523	106,9	525	517	456	455	461
519	112,6	523	525	517	456	455
509	101,7	519	523	525	517	456
512	92	509	519	523	525	517
519	97,4	512	509	519	523	525
517	97	519	512	509	519	523
510	105,4	517	519	512	509	519
509	102,7	510	517	519	512	509
501	98,1	509	510	517	519	512
507	104,5	501	509	510	517	519
569	87,4	507	501	509	510	517
580	89,9	569	507	501	509	510
578	109,8	580	569	507	501	509
565	111,7	578	580	569	507	501
547	98,6	565	578	580	569	507
555	96,9	547	565	578	580	569
562	95,1	555	547	565	578	580
561	97	562	555	547	565	578
555	112,7	561	562	555	547	565
544	102,9	555	561	562	555	547
537	97,4	544	555	561	562	555
543	111,4	537	544	555	561	562
594	87,4	543	537	544	555	561
611	96,8	594	543	537	544	555
613	114,1	611	594	543	537	544
611	110,3	613	611	594	543	537
594	103,9	611	613	611	594	543
595	101,6	594	611	613	611	594
591	94,6	595	594	611	613	611
589	95,9	591	595	594	611	613
584	104,7	589	591	595	594	611
573	102,8	584	589	591	595	594
567	98,1	573	584	589	591	595
569	113,9	567	573	584	589	591
621	80,9	569	567	573	584	589
629	95,7	621	569	567	573	584
628	113,2	629	621	569	567	573
612	105,9	628	629	621	569	567
595	108,8	612	628	629	621	569
597	102,3	595	612	628	629	621
593	99	597	595	612	628	629
590	100,7	593	597	595	612	628
580	115,5	590	593	597	595	612
574	100,7	580	590	593	597	595
573	109,9	574	580	590	593	597
573	114,6	573	574	580	590	593
620	85,4	573	573	574	580	590
626	100,5	620	573	573	574	580
620	114,8	626	620	573	573	574
588	116,5	620	626	620	573	573
566	112,9	588	620	626	620	573
557	102	566	588	620	626	620

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.

\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 & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
R Framework error message & 
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67289&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67289&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67289&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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 302.521504071985 -1.72123794877019X[t] + 0.866754928207082`Y(t-1)`[t] + 0.134467604277825`Y(t-2)`[t] -0.125706630975887`Y(t-3)`[t] -0.380598880377657`Y(t-4)`[t] + 0.226892520847359`Y(t-5) `[t] + 0.764686012256499t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  302.521504071985 -1.72123794877019X[t] +  0.866754928207082`Y(t-1)`[t] +  0.134467604277825`Y(t-2)`[t] -0.125706630975887`Y(t-3)`[t] -0.380598880377657`Y(t-4)`[t] +  0.226892520847359`Y(t-5)
`[t] +  0.764686012256499t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67289&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  302.521504071985 -1.72123794877019X[t] +  0.866754928207082`Y(t-1)`[t] +  0.134467604277825`Y(t-2)`[t] -0.125706630975887`Y(t-3)`[t] -0.380598880377657`Y(t-4)`[t] +  0.226892520847359`Y(t-5)
`[t] +  0.764686012256499t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67289&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67289&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
Y[t] = + 302.521504071985 -1.72123794877019X[t] + 0.866754928207082`Y(t-1)`[t] + 0.134467604277825`Y(t-2)`[t] -0.125706630975887`Y(t-3)`[t] -0.380598880377657`Y(t-4)`[t] + 0.226892520847359`Y(t-5) `[t] + 0.764686012256499t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)302.52150407198546.1855926.550100
X-1.721237948770190.223008-7.718300
`Y(t-1)`0.8667549282070820.0945699.165300
`Y(t-2)`0.1344676042778250.148310.90670.3682720.184136
`Y(t-3)`-0.1257066309758870.137991-0.9110.3660130.183006
`Y(t-4)`-0.3805988803776570.141786-2.68430.0094190.004709
`Y(t-5) `0.2268925208473590.0941622.40960.0191080.009554
t0.7646860122564990.2262213.38030.0012890.000645

\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) & 302.521504071985 & 46.185592 & 6.5501 & 0 & 0 \tabularnewline
X & -1.72123794877019 & 0.223008 & -7.7183 & 0 & 0 \tabularnewline
`Y(t-1)` & 0.866754928207082 & 0.094569 & 9.1653 & 0 & 0 \tabularnewline
`Y(t-2)` & 0.134467604277825 & 0.14831 & 0.9067 & 0.368272 & 0.184136 \tabularnewline
`Y(t-3)` & -0.125706630975887 & 0.137991 & -0.911 & 0.366013 & 0.183006 \tabularnewline
`Y(t-4)` & -0.380598880377657 & 0.141786 & -2.6843 & 0.009419 & 0.004709 \tabularnewline
`Y(t-5)
` & 0.226892520847359 & 0.094162 & 2.4096 & 0.019108 & 0.009554 \tabularnewline
t & 0.764686012256499 & 0.226221 & 3.3803 & 0.001289 & 0.000645 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67289&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]302.521504071985[/C][C]46.185592[/C][C]6.5501[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]-1.72123794877019[/C][C]0.223008[/C][C]-7.7183[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Y(t-1)`[/C][C]0.866754928207082[/C][C]0.094569[/C][C]9.1653[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Y(t-2)`[/C][C]0.134467604277825[/C][C]0.14831[/C][C]0.9067[/C][C]0.368272[/C][C]0.184136[/C][/ROW]
[ROW][C]`Y(t-3)`[/C][C]-0.125706630975887[/C][C]0.137991[/C][C]-0.911[/C][C]0.366013[/C][C]0.183006[/C][/ROW]
[ROW][C]`Y(t-4)`[/C][C]-0.380598880377657[/C][C]0.141786[/C][C]-2.6843[/C][C]0.009419[/C][C]0.004709[/C][/ROW]
[ROW][C]`Y(t-5)
`[/C][C]0.226892520847359[/C][C]0.094162[/C][C]2.4096[/C][C]0.019108[/C][C]0.009554[/C][/ROW]
[ROW][C]t[/C][C]0.764686012256499[/C][C]0.226221[/C][C]3.3803[/C][C]0.001289[/C][C]0.000645[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67289&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67289&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)302.52150407198546.1855926.550100
X-1.721237948770190.223008-7.718300
`Y(t-1)`0.8667549282070820.0945699.165300
`Y(t-2)`0.1344676042778250.148310.90670.3682720.184136
`Y(t-3)`-0.1257066309758870.137991-0.9110.3660130.183006
`Y(t-4)`-0.3805988803776570.141786-2.68430.0094190.004709
`Y(t-5) `0.2268925208473590.0941622.40960.0191080.009554
t0.7646860122564990.2262213.38030.0012890.000645






Multiple Linear Regression - Regression Statistics
Multiple R0.975983400744419
R-squared0.95254359852864
Adjusted R-squared0.94691317801509
F-TEST (value)169.178056281247
F-TEST (DF numerator)7
F-TEST (DF denominator)59
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation11.6937803278994
Sum Squared Residuals8067.9254030729

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.975983400744419 \tabularnewline
R-squared & 0.95254359852864 \tabularnewline
Adjusted R-squared & 0.94691317801509 \tabularnewline
F-TEST (value) & 169.178056281247 \tabularnewline
F-TEST (DF numerator) & 7 \tabularnewline
F-TEST (DF denominator) & 59 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 11.6937803278994 \tabularnewline
Sum Squared Residuals & 8067.9254030729 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67289&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.975983400744419[/C][/ROW]
[ROW][C]R-squared[/C][C]0.95254359852864[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.94691317801509[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]169.178056281247[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]7[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]59[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]11.6937803278994[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]8067.9254030729[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67289&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67289&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 R0.975983400744419
R-squared0.95254359852864
Adjusted R-squared0.94691317801509
F-TEST (value)169.178056281247
F-TEST (DF numerator)7
F-TEST (DF denominator)59
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation11.6937803278994
Sum Squared Residuals8067.9254030729






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1431432.531768903009-1.53176890300867
2484475.0040754267748.99592457322623
3510497.51370528301612.4862947169842
4513519.255266091415-6.2552660914153
5503505.310271144082-2.31027114408167
6471485.457024453743-14.4570244537435
7471478.859849748493-7.85984974849263
8476471.869238916284.13076108372011
9475485.649101921996-10.6491019219959
10470479.089354298221-9.08935429822093
11461472.488294294603-11.4882942946028
12455464.895921904341-9.89592190434128
13456456.746122086669-0.746122086669211
14517492.56536860329224.4346313967077
15525538.882188457978-13.8821884579780
16523529.424970078703-6.42497007870345
17519510.3107722657878.68922773421258
18509502.1057047682586.89429523174182
19512521.408045175023-9.40804517502284
20519517.2127994572011.78720054279898
21517527.462344748823-10.4623447488234
22510515.4976941924-5.4976941924004
23509510.282834693893-1.28283469389343
24501515.425085774191-14.4250857741912
25507501.3347337079025.66526629209798
26569537.99349113107331.0065088689265
27580588.798697728164-8.79869772816376
28578575.2457029717152.75429702828488
29565560.59312610244.40687389759962
30547548.750731569233-1.75073156923332
31555545.2240164013949.77598359860627
32562558.4917549628553.50824503714482
33561569.885833964901-8.88583396490128
34555546.5971265111798.40287348882148
35544550.886144412758-6.88614441275765
36537550.053183942416-13.0531839424165
37543521.89719683954921.1028031604509
38594571.67032366374122.3296763362587
39611604.9718588976876.02814110231254
40613596.96594464137616.0340553586235
41611598.00791488012912.9920851198708
42594588.137748615895.86225138411006
43595582.70743725708512.2925627429148
44591597.448982921819-6.4489829218187
45589595.995503021163-6.99550302116352
46584585.232604104466-1.23260410446644
47573580.929987158916-7.92998715891604
48567581.578550603035-14.5785506030352
49569548.95016464066920.0498353593306
50621610.27438949401810.7256105059823
51629634.711310205572-5.71131020557207
52628618.8170492534479.18295074655298
53612623.696460501156-11.6964605011559
54595585.1240002206379.8759997793629
55597589.0697441239527.93025587604845
56593599.169121093612-6.16912109361154
57590601.809320380471-11.8093203804712
58580576.5500369201073.44996307989297
59574589.602548388001-15.6025483880012
60573570.3399401156842.66005988431582
61573562.83254008234910.1674599176508
62620617.6024576215072.39754237849277
63626633.254306937835-7.25430693783494
64620619.9450410082710.0549589917285095
65588607.254794387329-19.2547943873291
66566567.030586523259-1.03058652325947
67557572.31978940308-15.3197894030801

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 431 & 432.531768903009 & -1.53176890300867 \tabularnewline
2 & 484 & 475.004075426774 & 8.99592457322623 \tabularnewline
3 & 510 & 497.513705283016 & 12.4862947169842 \tabularnewline
4 & 513 & 519.255266091415 & -6.2552660914153 \tabularnewline
5 & 503 & 505.310271144082 & -2.31027114408167 \tabularnewline
6 & 471 & 485.457024453743 & -14.4570244537435 \tabularnewline
7 & 471 & 478.859849748493 & -7.85984974849263 \tabularnewline
8 & 476 & 471.86923891628 & 4.13076108372011 \tabularnewline
9 & 475 & 485.649101921996 & -10.6491019219959 \tabularnewline
10 & 470 & 479.089354298221 & -9.08935429822093 \tabularnewline
11 & 461 & 472.488294294603 & -11.4882942946028 \tabularnewline
12 & 455 & 464.895921904341 & -9.89592190434128 \tabularnewline
13 & 456 & 456.746122086669 & -0.746122086669211 \tabularnewline
14 & 517 & 492.565368603292 & 24.4346313967077 \tabularnewline
15 & 525 & 538.882188457978 & -13.8821884579780 \tabularnewline
16 & 523 & 529.424970078703 & -6.42497007870345 \tabularnewline
17 & 519 & 510.310772265787 & 8.68922773421258 \tabularnewline
18 & 509 & 502.105704768258 & 6.89429523174182 \tabularnewline
19 & 512 & 521.408045175023 & -9.40804517502284 \tabularnewline
20 & 519 & 517.212799457201 & 1.78720054279898 \tabularnewline
21 & 517 & 527.462344748823 & -10.4623447488234 \tabularnewline
22 & 510 & 515.4976941924 & -5.4976941924004 \tabularnewline
23 & 509 & 510.282834693893 & -1.28283469389343 \tabularnewline
24 & 501 & 515.425085774191 & -14.4250857741912 \tabularnewline
25 & 507 & 501.334733707902 & 5.66526629209798 \tabularnewline
26 & 569 & 537.993491131073 & 31.0065088689265 \tabularnewline
27 & 580 & 588.798697728164 & -8.79869772816376 \tabularnewline
28 & 578 & 575.245702971715 & 2.75429702828488 \tabularnewline
29 & 565 & 560.5931261024 & 4.40687389759962 \tabularnewline
30 & 547 & 548.750731569233 & -1.75073156923332 \tabularnewline
31 & 555 & 545.224016401394 & 9.77598359860627 \tabularnewline
32 & 562 & 558.491754962855 & 3.50824503714482 \tabularnewline
33 & 561 & 569.885833964901 & -8.88583396490128 \tabularnewline
34 & 555 & 546.597126511179 & 8.40287348882148 \tabularnewline
35 & 544 & 550.886144412758 & -6.88614441275765 \tabularnewline
36 & 537 & 550.053183942416 & -13.0531839424165 \tabularnewline
37 & 543 & 521.897196839549 & 21.1028031604509 \tabularnewline
38 & 594 & 571.670323663741 & 22.3296763362587 \tabularnewline
39 & 611 & 604.971858897687 & 6.02814110231254 \tabularnewline
40 & 613 & 596.965944641376 & 16.0340553586235 \tabularnewline
41 & 611 & 598.007914880129 & 12.9920851198708 \tabularnewline
42 & 594 & 588.13774861589 & 5.86225138411006 \tabularnewline
43 & 595 & 582.707437257085 & 12.2925627429148 \tabularnewline
44 & 591 & 597.448982921819 & -6.4489829218187 \tabularnewline
45 & 589 & 595.995503021163 & -6.99550302116352 \tabularnewline
46 & 584 & 585.232604104466 & -1.23260410446644 \tabularnewline
47 & 573 & 580.929987158916 & -7.92998715891604 \tabularnewline
48 & 567 & 581.578550603035 & -14.5785506030352 \tabularnewline
49 & 569 & 548.950164640669 & 20.0498353593306 \tabularnewline
50 & 621 & 610.274389494018 & 10.7256105059823 \tabularnewline
51 & 629 & 634.711310205572 & -5.71131020557207 \tabularnewline
52 & 628 & 618.817049253447 & 9.18295074655298 \tabularnewline
53 & 612 & 623.696460501156 & -11.6964605011559 \tabularnewline
54 & 595 & 585.124000220637 & 9.8759997793629 \tabularnewline
55 & 597 & 589.069744123952 & 7.93025587604845 \tabularnewline
56 & 593 & 599.169121093612 & -6.16912109361154 \tabularnewline
57 & 590 & 601.809320380471 & -11.8093203804712 \tabularnewline
58 & 580 & 576.550036920107 & 3.44996307989297 \tabularnewline
59 & 574 & 589.602548388001 & -15.6025483880012 \tabularnewline
60 & 573 & 570.339940115684 & 2.66005988431582 \tabularnewline
61 & 573 & 562.832540082349 & 10.1674599176508 \tabularnewline
62 & 620 & 617.602457621507 & 2.39754237849277 \tabularnewline
63 & 626 & 633.254306937835 & -7.25430693783494 \tabularnewline
64 & 620 & 619.945041008271 & 0.0549589917285095 \tabularnewline
65 & 588 & 607.254794387329 & -19.2547943873291 \tabularnewline
66 & 566 & 567.030586523259 & -1.03058652325947 \tabularnewline
67 & 557 & 572.31978940308 & -15.3197894030801 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67289&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]431[/C][C]432.531768903009[/C][C]-1.53176890300867[/C][/ROW]
[ROW][C]2[/C][C]484[/C][C]475.004075426774[/C][C]8.99592457322623[/C][/ROW]
[ROW][C]3[/C][C]510[/C][C]497.513705283016[/C][C]12.4862947169842[/C][/ROW]
[ROW][C]4[/C][C]513[/C][C]519.255266091415[/C][C]-6.2552660914153[/C][/ROW]
[ROW][C]5[/C][C]503[/C][C]505.310271144082[/C][C]-2.31027114408167[/C][/ROW]
[ROW][C]6[/C][C]471[/C][C]485.457024453743[/C][C]-14.4570244537435[/C][/ROW]
[ROW][C]7[/C][C]471[/C][C]478.859849748493[/C][C]-7.85984974849263[/C][/ROW]
[ROW][C]8[/C][C]476[/C][C]471.86923891628[/C][C]4.13076108372011[/C][/ROW]
[ROW][C]9[/C][C]475[/C][C]485.649101921996[/C][C]-10.6491019219959[/C][/ROW]
[ROW][C]10[/C][C]470[/C][C]479.089354298221[/C][C]-9.08935429822093[/C][/ROW]
[ROW][C]11[/C][C]461[/C][C]472.488294294603[/C][C]-11.4882942946028[/C][/ROW]
[ROW][C]12[/C][C]455[/C][C]464.895921904341[/C][C]-9.89592190434128[/C][/ROW]
[ROW][C]13[/C][C]456[/C][C]456.746122086669[/C][C]-0.746122086669211[/C][/ROW]
[ROW][C]14[/C][C]517[/C][C]492.565368603292[/C][C]24.4346313967077[/C][/ROW]
[ROW][C]15[/C][C]525[/C][C]538.882188457978[/C][C]-13.8821884579780[/C][/ROW]
[ROW][C]16[/C][C]523[/C][C]529.424970078703[/C][C]-6.42497007870345[/C][/ROW]
[ROW][C]17[/C][C]519[/C][C]510.310772265787[/C][C]8.68922773421258[/C][/ROW]
[ROW][C]18[/C][C]509[/C][C]502.105704768258[/C][C]6.89429523174182[/C][/ROW]
[ROW][C]19[/C][C]512[/C][C]521.408045175023[/C][C]-9.40804517502284[/C][/ROW]
[ROW][C]20[/C][C]519[/C][C]517.212799457201[/C][C]1.78720054279898[/C][/ROW]
[ROW][C]21[/C][C]517[/C][C]527.462344748823[/C][C]-10.4623447488234[/C][/ROW]
[ROW][C]22[/C][C]510[/C][C]515.4976941924[/C][C]-5.4976941924004[/C][/ROW]
[ROW][C]23[/C][C]509[/C][C]510.282834693893[/C][C]-1.28283469389343[/C][/ROW]
[ROW][C]24[/C][C]501[/C][C]515.425085774191[/C][C]-14.4250857741912[/C][/ROW]
[ROW][C]25[/C][C]507[/C][C]501.334733707902[/C][C]5.66526629209798[/C][/ROW]
[ROW][C]26[/C][C]569[/C][C]537.993491131073[/C][C]31.0065088689265[/C][/ROW]
[ROW][C]27[/C][C]580[/C][C]588.798697728164[/C][C]-8.79869772816376[/C][/ROW]
[ROW][C]28[/C][C]578[/C][C]575.245702971715[/C][C]2.75429702828488[/C][/ROW]
[ROW][C]29[/C][C]565[/C][C]560.5931261024[/C][C]4.40687389759962[/C][/ROW]
[ROW][C]30[/C][C]547[/C][C]548.750731569233[/C][C]-1.75073156923332[/C][/ROW]
[ROW][C]31[/C][C]555[/C][C]545.224016401394[/C][C]9.77598359860627[/C][/ROW]
[ROW][C]32[/C][C]562[/C][C]558.491754962855[/C][C]3.50824503714482[/C][/ROW]
[ROW][C]33[/C][C]561[/C][C]569.885833964901[/C][C]-8.88583396490128[/C][/ROW]
[ROW][C]34[/C][C]555[/C][C]546.597126511179[/C][C]8.40287348882148[/C][/ROW]
[ROW][C]35[/C][C]544[/C][C]550.886144412758[/C][C]-6.88614441275765[/C][/ROW]
[ROW][C]36[/C][C]537[/C][C]550.053183942416[/C][C]-13.0531839424165[/C][/ROW]
[ROW][C]37[/C][C]543[/C][C]521.897196839549[/C][C]21.1028031604509[/C][/ROW]
[ROW][C]38[/C][C]594[/C][C]571.670323663741[/C][C]22.3296763362587[/C][/ROW]
[ROW][C]39[/C][C]611[/C][C]604.971858897687[/C][C]6.02814110231254[/C][/ROW]
[ROW][C]40[/C][C]613[/C][C]596.965944641376[/C][C]16.0340553586235[/C][/ROW]
[ROW][C]41[/C][C]611[/C][C]598.007914880129[/C][C]12.9920851198708[/C][/ROW]
[ROW][C]42[/C][C]594[/C][C]588.13774861589[/C][C]5.86225138411006[/C][/ROW]
[ROW][C]43[/C][C]595[/C][C]582.707437257085[/C][C]12.2925627429148[/C][/ROW]
[ROW][C]44[/C][C]591[/C][C]597.448982921819[/C][C]-6.4489829218187[/C][/ROW]
[ROW][C]45[/C][C]589[/C][C]595.995503021163[/C][C]-6.99550302116352[/C][/ROW]
[ROW][C]46[/C][C]584[/C][C]585.232604104466[/C][C]-1.23260410446644[/C][/ROW]
[ROW][C]47[/C][C]573[/C][C]580.929987158916[/C][C]-7.92998715891604[/C][/ROW]
[ROW][C]48[/C][C]567[/C][C]581.578550603035[/C][C]-14.5785506030352[/C][/ROW]
[ROW][C]49[/C][C]569[/C][C]548.950164640669[/C][C]20.0498353593306[/C][/ROW]
[ROW][C]50[/C][C]621[/C][C]610.274389494018[/C][C]10.7256105059823[/C][/ROW]
[ROW][C]51[/C][C]629[/C][C]634.711310205572[/C][C]-5.71131020557207[/C][/ROW]
[ROW][C]52[/C][C]628[/C][C]618.817049253447[/C][C]9.18295074655298[/C][/ROW]
[ROW][C]53[/C][C]612[/C][C]623.696460501156[/C][C]-11.6964605011559[/C][/ROW]
[ROW][C]54[/C][C]595[/C][C]585.124000220637[/C][C]9.8759997793629[/C][/ROW]
[ROW][C]55[/C][C]597[/C][C]589.069744123952[/C][C]7.93025587604845[/C][/ROW]
[ROW][C]56[/C][C]593[/C][C]599.169121093612[/C][C]-6.16912109361154[/C][/ROW]
[ROW][C]57[/C][C]590[/C][C]601.809320380471[/C][C]-11.8093203804712[/C][/ROW]
[ROW][C]58[/C][C]580[/C][C]576.550036920107[/C][C]3.44996307989297[/C][/ROW]
[ROW][C]59[/C][C]574[/C][C]589.602548388001[/C][C]-15.6025483880012[/C][/ROW]
[ROW][C]60[/C][C]573[/C][C]570.339940115684[/C][C]2.66005988431582[/C][/ROW]
[ROW][C]61[/C][C]573[/C][C]562.832540082349[/C][C]10.1674599176508[/C][/ROW]
[ROW][C]62[/C][C]620[/C][C]617.602457621507[/C][C]2.39754237849277[/C][/ROW]
[ROW][C]63[/C][C]626[/C][C]633.254306937835[/C][C]-7.25430693783494[/C][/ROW]
[ROW][C]64[/C][C]620[/C][C]619.945041008271[/C][C]0.0549589917285095[/C][/ROW]
[ROW][C]65[/C][C]588[/C][C]607.254794387329[/C][C]-19.2547943873291[/C][/ROW]
[ROW][C]66[/C][C]566[/C][C]567.030586523259[/C][C]-1.03058652325947[/C][/ROW]
[ROW][C]67[/C][C]557[/C][C]572.31978940308[/C][C]-15.3197894030801[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67289&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67289&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
1431432.531768903009-1.53176890300867
2484475.0040754267748.99592457322623
3510497.51370528301612.4862947169842
4513519.255266091415-6.2552660914153
5503505.310271144082-2.31027114408167
6471485.457024453743-14.4570244537435
7471478.859849748493-7.85984974849263
8476471.869238916284.13076108372011
9475485.649101921996-10.6491019219959
10470479.089354298221-9.08935429822093
11461472.488294294603-11.4882942946028
12455464.895921904341-9.89592190434128
13456456.746122086669-0.746122086669211
14517492.56536860329224.4346313967077
15525538.882188457978-13.8821884579780
16523529.424970078703-6.42497007870345
17519510.3107722657878.68922773421258
18509502.1057047682586.89429523174182
19512521.408045175023-9.40804517502284
20519517.2127994572011.78720054279898
21517527.462344748823-10.4623447488234
22510515.4976941924-5.4976941924004
23509510.282834693893-1.28283469389343
24501515.425085774191-14.4250857741912
25507501.3347337079025.66526629209798
26569537.99349113107331.0065088689265
27580588.798697728164-8.79869772816376
28578575.2457029717152.75429702828488
29565560.59312610244.40687389759962
30547548.750731569233-1.75073156923332
31555545.2240164013949.77598359860627
32562558.4917549628553.50824503714482
33561569.885833964901-8.88583396490128
34555546.5971265111798.40287348882148
35544550.886144412758-6.88614441275765
36537550.053183942416-13.0531839424165
37543521.89719683954921.1028031604509
38594571.67032366374122.3296763362587
39611604.9718588976876.02814110231254
40613596.96594464137616.0340553586235
41611598.00791488012912.9920851198708
42594588.137748615895.86225138411006
43595582.70743725708512.2925627429148
44591597.448982921819-6.4489829218187
45589595.995503021163-6.99550302116352
46584585.232604104466-1.23260410446644
47573580.929987158916-7.92998715891604
48567581.578550603035-14.5785506030352
49569548.95016464066920.0498353593306
50621610.27438949401810.7256105059823
51629634.711310205572-5.71131020557207
52628618.8170492534479.18295074655298
53612623.696460501156-11.6964605011559
54595585.1240002206379.8759997793629
55597589.0697441239527.93025587604845
56593599.169121093612-6.16912109361154
57590601.809320380471-11.8093203804712
58580576.5500369201073.44996307989297
59574589.602548388001-15.6025483880012
60573570.3399401156842.66005988431582
61573562.83254008234910.1674599176508
62620617.6024576215072.39754237849277
63626633.254306937835-7.25430693783494
64620619.9450410082710.0549589917285095
65588607.254794387329-19.2547943873291
66566567.030586523259-1.03058652325947
67557572.31978940308-15.3197894030801






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
110.02400893627303820.04801787254607640.975991063726962
120.01292730523091990.02585461046183980.98707269476908
130.03034711663314730.06069423326629470.969652883366853
140.1882908419187540.3765816838375080.811709158081246
150.4436669576886950.8873339153773890.556333042311305
160.414477892045950.82895578409190.58552210795405
170.4168283622367450.833656724473490.583171637763255
180.4703833219044050.940766643808810.529616678095595
190.4031433874431850.806286774886370.596856612556815
200.3441765949115460.6883531898230910.655823405088454
210.2986894616759880.5973789233519750.701310538324012
220.2445422760841630.4890845521683260.755457723915837
230.18857627804830.37715255609660.8114237219517
240.2703511061038840.5407022122077680.729648893896116
250.2691571716056720.5383143432113440.730842828394328
260.524103423151130.951793153697740.47589657684887
270.5298441425750760.9403117148498470.470155857424924
280.5656264772351410.8687470455297180.434373522764859
290.4883637638781240.9767275277562490.511636236121876
300.4662255460731780.9324510921463550.533774453926823
310.4474019260005950.894803852001190.552598073999405
320.3781630124759630.7563260249519250.621836987524037
330.4101651900006710.8203303800013420.589834809999329
340.3773318307140360.7546636614280710.622668169285964
350.4560528848593460.9121057697186920.543947115140654
360.8192920361507360.3614159276985270.180707963849264
370.8492605432826840.3014789134346310.150739456717316
380.8296962326423170.3406075347153660.170303767357683
390.7876822948731810.4246354102536380.212317705126819
400.7818289980718120.4363420038563750.218171001928188
410.7494797734571890.5010404530856210.250520226542811
420.6965797807933190.6068404384133620.303420219206681
430.678123486407340.6437530271853220.321876513592661
440.6263351880775810.7473296238448380.373664811922419
450.6024549825865370.7950900348269260.397545017413463
460.521180115665420.957639768669160.47881988433458
470.5962119252977380.8075761494045230.403788074702262
480.9070819071631060.1858361856737880.092918092836894
490.865589755151990.2688204896960190.134410244848010
500.8047833534097840.3904332931804310.195216646590216
510.7849857329299320.4300285341401350.215014267070068
520.6877314132207970.6245371735584050.312268586779202
530.6298764586366390.7402470827267230.370123541363361
540.4983816234107480.9967632468214950.501618376589252
550.6166097896313740.7667804207372520.383390210368626
560.5584455137907780.8831089724184440.441554486209222

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
11 & 0.0240089362730382 & 0.0480178725460764 & 0.975991063726962 \tabularnewline
12 & 0.0129273052309199 & 0.0258546104618398 & 0.98707269476908 \tabularnewline
13 & 0.0303471166331473 & 0.0606942332662947 & 0.969652883366853 \tabularnewline
14 & 0.188290841918754 & 0.376581683837508 & 0.811709158081246 \tabularnewline
15 & 0.443666957688695 & 0.887333915377389 & 0.556333042311305 \tabularnewline
16 & 0.41447789204595 & 0.8289557840919 & 0.58552210795405 \tabularnewline
17 & 0.416828362236745 & 0.83365672447349 & 0.583171637763255 \tabularnewline
18 & 0.470383321904405 & 0.94076664380881 & 0.529616678095595 \tabularnewline
19 & 0.403143387443185 & 0.80628677488637 & 0.596856612556815 \tabularnewline
20 & 0.344176594911546 & 0.688353189823091 & 0.655823405088454 \tabularnewline
21 & 0.298689461675988 & 0.597378923351975 & 0.701310538324012 \tabularnewline
22 & 0.244542276084163 & 0.489084552168326 & 0.755457723915837 \tabularnewline
23 & 0.1885762780483 & 0.3771525560966 & 0.8114237219517 \tabularnewline
24 & 0.270351106103884 & 0.540702212207768 & 0.729648893896116 \tabularnewline
25 & 0.269157171605672 & 0.538314343211344 & 0.730842828394328 \tabularnewline
26 & 0.52410342315113 & 0.95179315369774 & 0.47589657684887 \tabularnewline
27 & 0.529844142575076 & 0.940311714849847 & 0.470155857424924 \tabularnewline
28 & 0.565626477235141 & 0.868747045529718 & 0.434373522764859 \tabularnewline
29 & 0.488363763878124 & 0.976727527756249 & 0.511636236121876 \tabularnewline
30 & 0.466225546073178 & 0.932451092146355 & 0.533774453926823 \tabularnewline
31 & 0.447401926000595 & 0.89480385200119 & 0.552598073999405 \tabularnewline
32 & 0.378163012475963 & 0.756326024951925 & 0.621836987524037 \tabularnewline
33 & 0.410165190000671 & 0.820330380001342 & 0.589834809999329 \tabularnewline
34 & 0.377331830714036 & 0.754663661428071 & 0.622668169285964 \tabularnewline
35 & 0.456052884859346 & 0.912105769718692 & 0.543947115140654 \tabularnewline
36 & 0.819292036150736 & 0.361415927698527 & 0.180707963849264 \tabularnewline
37 & 0.849260543282684 & 0.301478913434631 & 0.150739456717316 \tabularnewline
38 & 0.829696232642317 & 0.340607534715366 & 0.170303767357683 \tabularnewline
39 & 0.787682294873181 & 0.424635410253638 & 0.212317705126819 \tabularnewline
40 & 0.781828998071812 & 0.436342003856375 & 0.218171001928188 \tabularnewline
41 & 0.749479773457189 & 0.501040453085621 & 0.250520226542811 \tabularnewline
42 & 0.696579780793319 & 0.606840438413362 & 0.303420219206681 \tabularnewline
43 & 0.67812348640734 & 0.643753027185322 & 0.321876513592661 \tabularnewline
44 & 0.626335188077581 & 0.747329623844838 & 0.373664811922419 \tabularnewline
45 & 0.602454982586537 & 0.795090034826926 & 0.397545017413463 \tabularnewline
46 & 0.52118011566542 & 0.95763976866916 & 0.47881988433458 \tabularnewline
47 & 0.596211925297738 & 0.807576149404523 & 0.403788074702262 \tabularnewline
48 & 0.907081907163106 & 0.185836185673788 & 0.092918092836894 \tabularnewline
49 & 0.86558975515199 & 0.268820489696019 & 0.134410244848010 \tabularnewline
50 & 0.804783353409784 & 0.390433293180431 & 0.195216646590216 \tabularnewline
51 & 0.784985732929932 & 0.430028534140135 & 0.215014267070068 \tabularnewline
52 & 0.687731413220797 & 0.624537173558405 & 0.312268586779202 \tabularnewline
53 & 0.629876458636639 & 0.740247082726723 & 0.370123541363361 \tabularnewline
54 & 0.498381623410748 & 0.996763246821495 & 0.501618376589252 \tabularnewline
55 & 0.616609789631374 & 0.766780420737252 & 0.383390210368626 \tabularnewline
56 & 0.558445513790778 & 0.883108972418444 & 0.441554486209222 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67289&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]11[/C][C]0.0240089362730382[/C][C]0.0480178725460764[/C][C]0.975991063726962[/C][/ROW]
[ROW][C]12[/C][C]0.0129273052309199[/C][C]0.0258546104618398[/C][C]0.98707269476908[/C][/ROW]
[ROW][C]13[/C][C]0.0303471166331473[/C][C]0.0606942332662947[/C][C]0.969652883366853[/C][/ROW]
[ROW][C]14[/C][C]0.188290841918754[/C][C]0.376581683837508[/C][C]0.811709158081246[/C][/ROW]
[ROW][C]15[/C][C]0.443666957688695[/C][C]0.887333915377389[/C][C]0.556333042311305[/C][/ROW]
[ROW][C]16[/C][C]0.41447789204595[/C][C]0.8289557840919[/C][C]0.58552210795405[/C][/ROW]
[ROW][C]17[/C][C]0.416828362236745[/C][C]0.83365672447349[/C][C]0.583171637763255[/C][/ROW]
[ROW][C]18[/C][C]0.470383321904405[/C][C]0.94076664380881[/C][C]0.529616678095595[/C][/ROW]
[ROW][C]19[/C][C]0.403143387443185[/C][C]0.80628677488637[/C][C]0.596856612556815[/C][/ROW]
[ROW][C]20[/C][C]0.344176594911546[/C][C]0.688353189823091[/C][C]0.655823405088454[/C][/ROW]
[ROW][C]21[/C][C]0.298689461675988[/C][C]0.597378923351975[/C][C]0.701310538324012[/C][/ROW]
[ROW][C]22[/C][C]0.244542276084163[/C][C]0.489084552168326[/C][C]0.755457723915837[/C][/ROW]
[ROW][C]23[/C][C]0.1885762780483[/C][C]0.3771525560966[/C][C]0.8114237219517[/C][/ROW]
[ROW][C]24[/C][C]0.270351106103884[/C][C]0.540702212207768[/C][C]0.729648893896116[/C][/ROW]
[ROW][C]25[/C][C]0.269157171605672[/C][C]0.538314343211344[/C][C]0.730842828394328[/C][/ROW]
[ROW][C]26[/C][C]0.52410342315113[/C][C]0.95179315369774[/C][C]0.47589657684887[/C][/ROW]
[ROW][C]27[/C][C]0.529844142575076[/C][C]0.940311714849847[/C][C]0.470155857424924[/C][/ROW]
[ROW][C]28[/C][C]0.565626477235141[/C][C]0.868747045529718[/C][C]0.434373522764859[/C][/ROW]
[ROW][C]29[/C][C]0.488363763878124[/C][C]0.976727527756249[/C][C]0.511636236121876[/C][/ROW]
[ROW][C]30[/C][C]0.466225546073178[/C][C]0.932451092146355[/C][C]0.533774453926823[/C][/ROW]
[ROW][C]31[/C][C]0.447401926000595[/C][C]0.89480385200119[/C][C]0.552598073999405[/C][/ROW]
[ROW][C]32[/C][C]0.378163012475963[/C][C]0.756326024951925[/C][C]0.621836987524037[/C][/ROW]
[ROW][C]33[/C][C]0.410165190000671[/C][C]0.820330380001342[/C][C]0.589834809999329[/C][/ROW]
[ROW][C]34[/C][C]0.377331830714036[/C][C]0.754663661428071[/C][C]0.622668169285964[/C][/ROW]
[ROW][C]35[/C][C]0.456052884859346[/C][C]0.912105769718692[/C][C]0.543947115140654[/C][/ROW]
[ROW][C]36[/C][C]0.819292036150736[/C][C]0.361415927698527[/C][C]0.180707963849264[/C][/ROW]
[ROW][C]37[/C][C]0.849260543282684[/C][C]0.301478913434631[/C][C]0.150739456717316[/C][/ROW]
[ROW][C]38[/C][C]0.829696232642317[/C][C]0.340607534715366[/C][C]0.170303767357683[/C][/ROW]
[ROW][C]39[/C][C]0.787682294873181[/C][C]0.424635410253638[/C][C]0.212317705126819[/C][/ROW]
[ROW][C]40[/C][C]0.781828998071812[/C][C]0.436342003856375[/C][C]0.218171001928188[/C][/ROW]
[ROW][C]41[/C][C]0.749479773457189[/C][C]0.501040453085621[/C][C]0.250520226542811[/C][/ROW]
[ROW][C]42[/C][C]0.696579780793319[/C][C]0.606840438413362[/C][C]0.303420219206681[/C][/ROW]
[ROW][C]43[/C][C]0.67812348640734[/C][C]0.643753027185322[/C][C]0.321876513592661[/C][/ROW]
[ROW][C]44[/C][C]0.626335188077581[/C][C]0.747329623844838[/C][C]0.373664811922419[/C][/ROW]
[ROW][C]45[/C][C]0.602454982586537[/C][C]0.795090034826926[/C][C]0.397545017413463[/C][/ROW]
[ROW][C]46[/C][C]0.52118011566542[/C][C]0.95763976866916[/C][C]0.47881988433458[/C][/ROW]
[ROW][C]47[/C][C]0.596211925297738[/C][C]0.807576149404523[/C][C]0.403788074702262[/C][/ROW]
[ROW][C]48[/C][C]0.907081907163106[/C][C]0.185836185673788[/C][C]0.092918092836894[/C][/ROW]
[ROW][C]49[/C][C]0.86558975515199[/C][C]0.268820489696019[/C][C]0.134410244848010[/C][/ROW]
[ROW][C]50[/C][C]0.804783353409784[/C][C]0.390433293180431[/C][C]0.195216646590216[/C][/ROW]
[ROW][C]51[/C][C]0.784985732929932[/C][C]0.430028534140135[/C][C]0.215014267070068[/C][/ROW]
[ROW][C]52[/C][C]0.687731413220797[/C][C]0.624537173558405[/C][C]0.312268586779202[/C][/ROW]
[ROW][C]53[/C][C]0.629876458636639[/C][C]0.740247082726723[/C][C]0.370123541363361[/C][/ROW]
[ROW][C]54[/C][C]0.498381623410748[/C][C]0.996763246821495[/C][C]0.501618376589252[/C][/ROW]
[ROW][C]55[/C][C]0.616609789631374[/C][C]0.766780420737252[/C][C]0.383390210368626[/C][/ROW]
[ROW][C]56[/C][C]0.558445513790778[/C][C]0.883108972418444[/C][C]0.441554486209222[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67289&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67289&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
110.02400893627303820.04801787254607640.975991063726962
120.01292730523091990.02585461046183980.98707269476908
130.03034711663314730.06069423326629470.969652883366853
140.1882908419187540.3765816838375080.811709158081246
150.4436669576886950.8873339153773890.556333042311305
160.414477892045950.82895578409190.58552210795405
170.4168283622367450.833656724473490.583171637763255
180.4703833219044050.940766643808810.529616678095595
190.4031433874431850.806286774886370.596856612556815
200.3441765949115460.6883531898230910.655823405088454
210.2986894616759880.5973789233519750.701310538324012
220.2445422760841630.4890845521683260.755457723915837
230.18857627804830.37715255609660.8114237219517
240.2703511061038840.5407022122077680.729648893896116
250.2691571716056720.5383143432113440.730842828394328
260.524103423151130.951793153697740.47589657684887
270.5298441425750760.9403117148498470.470155857424924
280.5656264772351410.8687470455297180.434373522764859
290.4883637638781240.9767275277562490.511636236121876
300.4662255460731780.9324510921463550.533774453926823
310.4474019260005950.894803852001190.552598073999405
320.3781630124759630.7563260249519250.621836987524037
330.4101651900006710.8203303800013420.589834809999329
340.3773318307140360.7546636614280710.622668169285964
350.4560528848593460.9121057697186920.543947115140654
360.8192920361507360.3614159276985270.180707963849264
370.8492605432826840.3014789134346310.150739456717316
380.8296962326423170.3406075347153660.170303767357683
390.7876822948731810.4246354102536380.212317705126819
400.7818289980718120.4363420038563750.218171001928188
410.7494797734571890.5010404530856210.250520226542811
420.6965797807933190.6068404384133620.303420219206681
430.678123486407340.6437530271853220.321876513592661
440.6263351880775810.7473296238448380.373664811922419
450.6024549825865370.7950900348269260.397545017413463
460.521180115665420.957639768669160.47881988433458
470.5962119252977380.8075761494045230.403788074702262
480.9070819071631060.1858361856737880.092918092836894
490.865589755151990.2688204896960190.134410244848010
500.8047833534097840.3904332931804310.195216646590216
510.7849857329299320.4300285341401350.215014267070068
520.6877314132207970.6245371735584050.312268586779202
530.6298764586366390.7402470827267230.370123541363361
540.4983816234107480.9967632468214950.501618376589252
550.6166097896313740.7667804207372520.383390210368626
560.5584455137907780.8831089724184440.441554486209222






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level20.0434782608695652OK
10% type I error level30.0652173913043478OK

\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 & 2 & 0.0434782608695652 & OK \tabularnewline
10% type I error level & 3 & 0.0652173913043478 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67289&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]2[/C][C]0.0434782608695652[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]3[/C][C]0.0652173913043478[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67289&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67289&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 level20.0434782608695652OK
10% type I error level30.0652173913043478OK


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 6
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Figure 7
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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 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal 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')
}