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rwasp_multipleregression.wasp

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Multiple Regression

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Thu, 27 Nov 2008 05:40:35 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/27/t1227789677j2f6gp1rokwqvo4.htm/, Retrieved Sun, 19 May 2024 09:40:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25786, Retrieved Sun, 19 May 2024 09:40:28 +0000

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-     [Multiple Regression] [hk] [2008-11-27 11:32:49] [a0c3f7f6bb6d3d65b8bcf25e6a3c7584]
F   PD    [Multiple Regression] [nieuwe] [2008-11-27 12:40:35] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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2008-11-30 21:08:07 [Nathalie Daneels] [reply] 
Evaluatie opdracht 1 - Blok 11 (Q3) 
 
Bij de evaluatie in moodle heb ik staan dat wat je beschrijft in je conclusies niet ech tovereenkomt met wat je uitvoert... Ik neem deze woorden terug, ik heb gemerkt dat u er een nieuwe link hebt bijgezet, waar het wel juist werd uitgevoerd. Ik heb het hier over 'include monthly dummies'. Bij de eerste link hebt u 'Do not include seasonal dummies' om na te gaan of er de data op een bepaald moment plots dalen of stijgen. Op deze manier kon u een gebeurtenis vinden als dummie. U hebt inderdaad een datum vastgesteld vanaf dewelke de cijfergegevens een klein niveauverschil ondergaan (en dus lager liggen).  
 
Ook al heeft de student niet echt de reden gevonden waarom op die datum (oktober 2004) de cijfergegevens plots een niveauverschil ondergaan, de student heeft aan de hand van deze datum toch verder onderzoek gedaan, wat ik zeer goed vind.  
 
* Bij de conclusie over de vergelijking, ben ik het niet eens met wat de student schrijft over de variabelen M1,M2,... Dit zijn niet de dummies, maar wel de maanden.  
 
* Bij de conclusie van de tabel 'Multiple Linear Regression - Ordinary Least Squares', zou de student nog moeten bijschrijven: 
- wat voor soort dummy hij heeft gebruikt en waarom. 
- wat precies de referentiemaand is. De referentiemaand is die maand (van het jaar daarna) die net voor de maand komt waarmee de cijfferreeks begint. 
(De student heeft er wel bij vermeld waarom zij/hij bij het nagaan van de p-waarde (om te kunnen bepalen of dalingen/stijgingen in de werkloosheid te wijten zijn aan het toeval)gebruik maakt van de 2-tailed p-value, maar ik ben hier niet mee akkoord. Ik ben van mening dat de student mag gebruik maken van de one-tailed p-value omdat we er van mogen uitgaan dat deze datum een positieve invloed heeft op het indexcijfer van de werkloosheid, dat deze de werkloosheid doet dalen (wat de student helemaal in het begin geconcludeerd heeft, aangezien hij/zij daarom deze datum koos als dummie) 
- Hoe de lange termijn trend er in dit geval uitziet: We kunnen vaststellen dat deze waarde zeer klein is en positief (namelijk 0,009). Dit betekent dat de lange termijn trend stijgend is, wat betekent dat de werkloosheid gestegen is op lange termijn (een hoger cijfer van werkloosheid, betekent meer werkloosheid). Dit betekent dat de werkloosheid elke maand met 0,009 stijgt t.o.v. de vorige maand. We kunnen vaststellen dat deze stijgende lange termijn trend niet aan het toeval kan worden toegeschreven aangezien de p-waarde (3,8%) duidelijk kleiner is dan het 5% type I error. De kans dat we ons hierbij vergissen is dus kleiner dan 5%. De nul-hypothese (waarbij de parameters gelijk worden gesteld aan 0) mag dus verworpen worden. De nulhypothese heeft de student uigelegd (wat deze precies is en waaraan deze wordt gelijkgesteld: dit is goed gedaan). 
- meer uitleg geven over de dummie (d): d stelt dus de dummie voor: Door de datum oktober 2004 is het indexcijfer van de werkloosheid gedaald met 0,12 (afgerond) (d = 1, dit betekent dat de datum heeft plaatsgevonden, wat de verandering teweeg heeft gebracht; Als d = 0 dan heeft de datum nog geen invloed gehad op het indexcijfer van de werkloosheid en telt de parameter die overeenkomt met d niet mee, aangezien deze wegvalt door de waarde 0). Nu moeten we ons wel afvragen of deze daling te wijten is aan het toeval of niet. We kunnen vaststellen dat deze daling van het indexcijfer van de werkloosheid te wijten is aan het toeval. De one-tailed p-value (35%)  is groter dan 5% (type I error) en dit betekent dus dat we de nul-hypothese niet mogen verwerpen. Het is dus niet significant verschillend van de nul-hypothese en dus te wijten aan het toeval.  
- De student concludeert dat M1 en M10 positief zijn, dit klopt ook, maar dit positief cijfer wijst erop dat de werkloosheid gestegen is en niet gedaald (zoals de student concludeerde) t.o.v. het referentiejaar. In alle andere maanden is het indexcijfer van de werkloosheid wel gedaald t.o.v. het referentiejaar. (Hierbij wordt er nog geen rekening gehouden met de invloed van de datum 'oktober 2004' op de cijferreeks en de lange termijn trend, dit is omdat we de seizoenaliteit willen nagaan.)We moeten ook hierbij concluderen dat deze dalingen/stijgingen te wijten zijn aan het toeval, met uitzondering voor maand 5 en 6, aangezien de one-tail P-value telkens groter is dan het 5% type I error. De nulhypothese (die stelt dat de datum 'oktober 2004' geen invloed heeft op de cijfferreeks, tenzij het tegendeel bewezen wordt) mag niet verworpen worden, omdat de parameters niet significant verschillend zijn van nul. Enkel voor de maanden 5 en 6 mogen we concluderen dat de daling van het indexcijfer van de werkloosheid niet te wijten is aan het toeval: de one-tail p-value is hier kleiner dan 5% type I error, wat erop wijst dat de nul-hypothese mag verworpen worden, aangezien de parameters significant verschillend zijn van de nul-hypothese (die stelt dat de parameters gelijk worden gesteld aan 0). 
* Bij de conclusie van de tabel ‘multiple linear regression – regression statistics’ zou de student het volgende nog kunnen bij vermelden: 
R-squared heeft steeds een waarde tussen 0 en 1. R-squared geeft het percentage aan dat we kunnen verklaren van de spreiding/variabiliteit van het indexcijfer van de werkloosheid. Dat indexcijfer schommelt en van die schommelingen kunnen we 18,31% verklaren met behulp van dit model. Om te weten of dit te wijten is aan het toeval, moeten we  een hypothese opstellen, en nagaan of de verdeling van R-squared significant verschillend is van de Ho. Ho = R-squared = O en Ha = R-squared > 0. Vervolgens moeten we gaan kijken naar de p-value. Als we naar de p-value (10,87%) kijken kunnen we vaststellen dat deze groter is dan 5% type I error. Dit betekent dat R-squared niet significant verschillend is van de nulhypothese. Dit model verklaart niet voldoende de schommelingen van de datareeks.  
De residual Standaard deviation = 0,789 (afgerond). Dit duidt de spreiding van de voorspellingsfouten aan: De te verwachten fout die ik voorspel voor die residu’s. Als ik een voorspelling maak met dit model, kan ik voorspellen hoeveel slachtoffers er zijn. Bij deze voorspelling kan ik er 0,789 naast zitten (een afwijking van 0,789 naar boven of naar onder.), Dit is zeer weinig. Als we kijken naar de ‘Adjusted R-squared’ kunnen we besluiten dat dit geen goed beeld weergeeft van de realiteit. Aan de hand van dit model kunnen we slechts 6,65%  van de schommelingen, die bestaan in het indexcijfer van de werkloosheid, verklaren. Dit is aan toeval onderhevig, want de P-value is groter dan 5% type I error, wat wil zeggen dat onze alternatieve hypothese (>0) niet significant verschilt van onze Ho (=0). 
 
* De student heeft geen conclusie gegeven bij de grafiek ‘Actuals and interpolation’. Dit zou de conclusie kunnen zijn: Actuals zijn de werkelijke waarden (bolletjes), de interpolation stellen de voorspelde waarden (lijn) voor: het verschil hier tussen beiden zijn de residu’s.  
Op deze grafiek kunnen we waarnemen dat er zich een bepaald patroon (van de werkelijke waarden) herhaalt in de tijd (eerst een stijging met vervolgens een sterke daling). Deze herhaling van het patroon wijst erop dat we voorspellingen kunnen maken op basis van het verleden, wat op zijn beurt wijst op autocorrelatie. Dit is dus geen goed model, want er wordt niet aan alle assumpties voldaan. 
Als we deze patronen op lange termijn bekijken, kunnen we vaststellen dat er globaal een stijgende lange termijn trend is. Het patroon van de korte termijn wordt duidelijk gedurende de lange termijn stijgende trend herhaald. 
 
*Bij de conclusie van de grafiek ‘residuals’ zou de student het volgende nog kunnen bij vermelden: Residuals = werkelijke waarden – voorspelde waarden. Als deze uitkomt gelijk is aan 0, dan betekent dit dat we de waarden correct hebben voorspeld. (Deze zijn dan gelijk aan de werkelijke waarden). Als deze uitkomt groter is dan 0, dan liggen de werkelijke waarden hoger dan de voorspelde waarden. (De voorspelling was dus niet correct). Als deze uitkomt kleiner is dan 0, dan zijn de voorspelde waarden hoger dan de werkelijke waarden (DE voorspelling was dus niet correct). Deze grafiek geeft dus de voorspellingsfouten weer, wat de student ook vermeldde. Het gemiddelde van deze voorspellingsfouten moet gelijk zijn aan nul (ook dit vermeldde de student in zijn conclusie) (Dit betekent dat de te hoog voorspelde waarden en de te laag voorspelde waarden elkaar neutraliseren) en dus ook constant zijn. We kunnen afleiden uit de grafiek dat dit niet het geval is. Opdat het gemiddelde gelijk zou zijn aan nul, moet de grafiek min of meer gespiegeld worden rond de zwarte horizontale lijn (die gelijk wordt gesteld aan nul). Dit is hier niet het geval. Het zou eventueel mogelijk kunnen zijn dat het gemiddelde van deze voorspellingsfouten toch nul is: Er liggen veel meer voorspellingsfouten boven de horizontale zwarte lijn dan eronder, maar de voorspellingsfouten eronder zijn veel negatiever dan de positieve positieve voorspellingsfouten boven de horizontale as. Het is mogelijk dat deze 2 elkaar neutraliseren, maar dat is hier niet het geval, lijkt me.  We kunnen in deze grafiek mogelijk wel een patroon zien: heel vaak worden dalingen opgevolgd door stijgingen: dalingen, stijgingen, dalingen, stijgingen,...  
We kunnen ook opmerken dat als we een bepaalde periode eruit halen, de opeenvolgende residu’s vaak stijgen of dalen, dus er is waarschijnlijk sprake van autocorrelatie. Stijgende residu’s worden vaak gevolgd (of vooraf gegaan) door stijgende en dalende residu’s worden ook vaak vooraf gegaan door dalende (of gevolgd door dalende residu’s).We kunnen dus eigenlijk voorspellingen doen (op basis van het verleden, aangezien dalende/stijgende residu’s vooraf worden gegaan door dalende/stijgende residu’s). 
 
* Ik ben het eens met de student zijn conclusie bij de grafiek ‘residual histogram’. De grafiek is duidelijk geen normaalverdeling, terwijl dit wel zo zou moeten zijn.  
 
* Ik ben het eveneens eens met de conclusie bij de grafiek ‘residual density plot’: Deze grafiek zou ook een normaalverdeling moeten zijn, wat hier duidelijk niet het geval is. De grafiek lijkt wel twee toppen te hebben, bovendien is er links een duidelijk zichtbare uitstulping.  
 
* De conclusie bij de grafiek ‘residual normal QQ plot’ is ook correct, maar ik zou er nog iets meer uitleg bij zetten: 
Deze grafiek toont het verband aan tussen de steekproefkwantielen en de theoretische kwantielen en we kunnen uit deze grafiek eveneens afleiden of (het verband tussen) deze quantielen van de residu’s de normaalcurve (de diagonale rechte) benaderen of niet. We kunnen vaststellen dat de quantielen van de residu’s de normaalcurve niet echt benaderen: We kunnen dus concluderen dat de voorspellingsfouten niet echt normaal verdeeld zijn. 
 
* De student concludeerde bij de grafiek ‘residual lag plot, lowess and regression line’ dat deze grafiek het verband toont tussen de voorspellingsfouten nu en de voorspellingsfouten een periode vroeger. Hij concludeerde eveneens dat de correlatie zeer goed is: Dit is correct. Ik zou dit er nog bij aanvullen: 
We kunnen vaststellen dat het in dit geval om een positief verband gaat: Dit zien we aan de schuine rechte die van links beneden naar rechts boven gaat, wat wijst op een positief verband. Een positief verband betekent dat als de x-waarde toeneemt, de y-waarde ook gaat toenemen. Hoe sterk de y-waarde gaat toenemen, als de x-waarde stijgt, hangt af van de grootte van het verband. Een positieve correlatie betekent dat er voorspelbaarheid is op basis van het verleden. Dit is een indicator dat het model niet juist kan zijn.  
 
* Ik ben het eveneens eens met wat de student concludeert bij de grafiek ‘Residual autocorrelation function’: De twee blauwe horizontale lijnen stellen het betrouwbaarheidsinterval van 95% voor. Alle verticale lijntjes die boven of onder dit betrouwbaarheidsinterval uitkomen, stellen een significant verschil voor. Dit wil zeggen dat de voorspellingsfout niet aan het toeval kan worden toegeschreven.  
De student zou wel eventueel iets specifieker kunnen zijn dan ‘Hier valt op dat er nog heel veel verticale lijnen zijn die buiten het betrouwbaarheidinterval vallen.’: Tot en met het verticale lijntje dat overeenkomt met 15 overschrijden alle verticale lijntjes het betrouwbaarheidsinterval (bovenaan). Deze zijn dus allemaal significant verschillend en dus niet te wijten aan het toeval. En vanaf verticaal lijntje 37 ongeveer overschrijden ook weer de verdere verticale lijntjes het betrouwbaarheidsinterval van 95% langs beneden. Dit betekent dat deze autocorrelaties ook niet aan het toeval te wijten zijn. We kunnen hier eigenlijk wel een patroon in zien, wat voornamelijk niet aan het toeval kan worden toegeschreven: Dat wijst erop dat er voorspellingen kunnen gedaan worden op basis van het verleden.  
 
We moeten hierbij inderdaad concluderen dat er niet aan de assumpties voldaan is (Het gemiddelde van de voorspellingsfouten is verschillend van 0: Dit moet gelijk zijn aan 0 en er is autocorrelatie: Dit mag eigenlijk niet). Dit betekent dat het model nog niet helemaal in orde is. 
2008-12-01 11:33:34 [Vincent Dolhain] [reply] 
De student heeft zijn best gedaan om zijn model te verklaren. Hij heeft gezocht naar een goede dummy, ook al kan hij deze niet verklaren. Zijn conclusies zijn goed, wel heeft hij een paar foutjes gemaakt. M1,M2,…. Zijn geen dummievariabelen, maar de verschillende maanden. Hij zou ook de one-tail p value mogen gebruiken in plaats van de two-tail p value, omdat we er van uit gaan dat het enkel een positief verband heeft, moeten we kijken of het ook geen negatieve invloed heeft (index cijfer vergroten). 
2008-12-01 14:23:16 [Alexander Hendrickx] [reply] 
De vraag werd vrij goed beantwoord, in tabel 3 werd de t- stat niet verklaard, deze was hier op vele plaatsen kleiner dan 2 dwz dat de kans dat de nulhypothese foutief verworpen zal worden hier vaak groter dan 5 % is  niet betrouwbaar. In het besluit staat er dat er geen patroon en dus ook geen autocorrelatie merkbaar is, laar dit is helemaal niet waar. we kunnen zeer duidelijk een patroon herkennen, er is dus autocorrelatie, het model is dus ook op dit vlak niet betrouwbaar.
2008-12-01 17:58:41 [Peter Van Doninck] [reply] 
De conclusie van de student mbt de r-waarde is correct. Slechts 18% van de schommelingen kunnen verklaard worden! De student analyseert ook hier de one en two tailed p waarden niet. Dit zou hij echter wel moeten doen, aangezien ze in praktisch alle gevallen verschillend zijn van nul!  
Vervolgens beschrijft de student de grafieken behoorlijk. het valt duidelijk op dat het histogram en de density plot helemaal niet normaal verdeeld zijn. Ook de residual auto correlation van de functie komt in praktisc alle gevallen buiten de stippellijnen. Dit model dient grondig aangepast te worden!

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25786&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25786&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25786&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
w[t] = + 7.41527777777778 -0.118472222222222d[t] + 0.0891550925925951M1[t] -0.0311033950617277M2[t] -0.218028549382717M3[t] -0.416064814814815M4[t] -0.658545524691358M5[t] -0.778804012345679M6[t] -0.243506944444444M7[t] -0.108209876543209M8[t] -0.0951350308641968M9[t] + 0.0557947530864199M10[t] -0.0533526234567892M11[t] + 0.00914737654320988t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
w[t] =  +  7.41527777777778 -0.118472222222222d[t] +  0.0891550925925951M1[t] -0.0311033950617277M2[t] -0.218028549382717M3[t] -0.416064814814815M4[t] -0.658545524691358M5[t] -0.778804012345679M6[t] -0.243506944444444M7[t] -0.108209876543209M8[t] -0.0951350308641968M9[t] +  0.0557947530864199M10[t] -0.0533526234567892M11[t] +  0.00914737654320988t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25786&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]w[t] =  +  7.41527777777778 -0.118472222222222d[t] +  0.0891550925925951M1[t] -0.0311033950617277M2[t] -0.218028549382717M3[t] -0.416064814814815M4[t] -0.658545524691358M5[t] -0.778804012345679M6[t] -0.243506944444444M7[t] -0.108209876543209M8[t] -0.0951350308641968M9[t] +  0.0557947530864199M10[t] -0.0533526234567892M11[t] +  0.00914737654320988t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25786&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25786&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
w[t] = + 7.41527777777778 -0.118472222222222d[t] + 0.0891550925925951M1[t] -0.0311033950617277M2[t] -0.218028549382717M3[t] -0.416064814814815M4[t] -0.658545524691358M5[t] -0.778804012345679M6[t] -0.243506944444444M7[t] -0.108209876543209M8[t] -0.0951350308641968M9[t] + 0.0557947530864199M10[t] -0.0533526234567892M11[t] + 0.00914737654320988t + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	7.41527777777778	0.322124	23.0199	0	0
d	-0.118472222222222	0.309809	-0.3824	0.703053	0.351527
M1	0.0891550925925951	0.383647	0.2324	0.816758	0.408379
M2	-0.0311033950617277	0.38354	-0.0811	0.935544	0.467772
M3	-0.218028549382717	0.383501	-0.5685	0.571081	0.285541
M4	-0.416064814814815	0.38353	-1.0848	0.280862	0.140431
M5	-0.658545524691358	0.383626	-1.7166	0.089448	0.044724
M6	-0.778804012345679	0.38379	-2.0292	0.045355	0.022677
M7	-0.243506944444444	0.384023	-0.6341	0.527609	0.263805
M8	-0.108209876543209	0.384322	-0.2816	0.77892	0.38946
M9	-0.0951350308641968	0.384689	-0.2473	0.80523	0.402615
M10	0.0557947530864199	0.394652	0.1414	0.887884	0.443942
M11	-0.0533526234567892	0.394553	-0.1352	0.892734	0.446367
t	0.00914737654320988	0.005101	1.7932	0.076259	0.03813

\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) & 7.41527777777778 & 0.322124 & 23.0199 & 0 & 0 \tabularnewline
d & -0.118472222222222 & 0.309809 & -0.3824 & 0.703053 & 0.351527 \tabularnewline
M1 & 0.0891550925925951 & 0.383647 & 0.2324 & 0.816758 & 0.408379 \tabularnewline
M2 & -0.0311033950617277 & 0.38354 & -0.0811 & 0.935544 & 0.467772 \tabularnewline
M3 & -0.218028549382717 & 0.383501 & -0.5685 & 0.571081 & 0.285541 \tabularnewline
M4 & -0.416064814814815 & 0.38353 & -1.0848 & 0.280862 & 0.140431 \tabularnewline
M5 & -0.658545524691358 & 0.383626 & -1.7166 & 0.089448 & 0.044724 \tabularnewline
M6 & -0.778804012345679 & 0.38379 & -2.0292 & 0.045355 & 0.022677 \tabularnewline
M7 & -0.243506944444444 & 0.384023 & -0.6341 & 0.527609 & 0.263805 \tabularnewline
M8 & -0.108209876543209 & 0.384322 & -0.2816 & 0.77892 & 0.38946 \tabularnewline
M9 & -0.0951350308641968 & 0.384689 & -0.2473 & 0.80523 & 0.402615 \tabularnewline
M10 & 0.0557947530864199 & 0.394652 & 0.1414 & 0.887884 & 0.443942 \tabularnewline
M11 & -0.0533526234567892 & 0.394553 & -0.1352 & 0.892734 & 0.446367 \tabularnewline
t & 0.00914737654320988 & 0.005101 & 1.7932 & 0.076259 & 0.03813 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25786&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]7.41527777777778[/C][C]0.322124[/C][C]23.0199[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]d[/C][C]-0.118472222222222[/C][C]0.309809[/C][C]-0.3824[/C][C]0.703053[/C][C]0.351527[/C][/ROW]
[ROW][C]M1[/C][C]0.0891550925925951[/C][C]0.383647[/C][C]0.2324[/C][C]0.816758[/C][C]0.408379[/C][/ROW]
[ROW][C]M2[/C][C]-0.0311033950617277[/C][C]0.38354[/C][C]-0.0811[/C][C]0.935544[/C][C]0.467772[/C][/ROW]
[ROW][C]M3[/C][C]-0.218028549382717[/C][C]0.383501[/C][C]-0.5685[/C][C]0.571081[/C][C]0.285541[/C][/ROW]
[ROW][C]M4[/C][C]-0.416064814814815[/C][C]0.38353[/C][C]-1.0848[/C][C]0.280862[/C][C]0.140431[/C][/ROW]
[ROW][C]M5[/C][C]-0.658545524691358[/C][C]0.383626[/C][C]-1.7166[/C][C]0.089448[/C][C]0.044724[/C][/ROW]
[ROW][C]M6[/C][C]-0.778804012345679[/C][C]0.38379[/C][C]-2.0292[/C][C]0.045355[/C][C]0.022677[/C][/ROW]
[ROW][C]M7[/C][C]-0.243506944444444[/C][C]0.384023[/C][C]-0.6341[/C][C]0.527609[/C][C]0.263805[/C][/ROW]
[ROW][C]M8[/C][C]-0.108209876543209[/C][C]0.384322[/C][C]-0.2816[/C][C]0.77892[/C][C]0.38946[/C][/ROW]
[ROW][C]M9[/C][C]-0.0951350308641968[/C][C]0.384689[/C][C]-0.2473[/C][C]0.80523[/C][C]0.402615[/C][/ROW]
[ROW][C]M10[/C][C]0.0557947530864199[/C][C]0.394652[/C][C]0.1414[/C][C]0.887884[/C][C]0.443942[/C][/ROW]
[ROW][C]M11[/C][C]-0.0533526234567892[/C][C]0.394553[/C][C]-0.1352[/C][C]0.892734[/C][C]0.446367[/C][/ROW]
[ROW][C]t[/C][C]0.00914737654320988[/C][C]0.005101[/C][C]1.7932[/C][C]0.076259[/C][C]0.03813[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25786&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25786&T=2

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	7.41527777777778	0.322124	23.0199	0	0
d	-0.118472222222222	0.309809	-0.3824	0.703053	0.351527
M1	0.0891550925925951	0.383647	0.2324	0.816758	0.408379
M2	-0.0311033950617277	0.38354	-0.0811	0.935544	0.467772
M3	-0.218028549382717	0.383501	-0.5685	0.571081	0.285541
M4	-0.416064814814815	0.38353	-1.0848	0.280862	0.140431
M5	-0.658545524691358	0.383626	-1.7166	0.089448	0.044724
M6	-0.778804012345679	0.38379	-2.0292	0.045355	0.022677
M7	-0.243506944444444	0.384023	-0.6341	0.527609	0.263805
M8	-0.108209876543209	0.384322	-0.2816	0.77892	0.38946
M9	-0.0951350308641968	0.384689	-0.2473	0.80523	0.402615
M10	0.0557947530864199	0.394652	0.1414	0.887884	0.443942
M11	-0.0533526234567892	0.394553	-0.1352	0.892734	0.446367
t	0.00914737654320988	0.005101	1.7932	0.076259	0.03813

Multiple Linear Regression - Regression Statistics
Multiple R	0.427982147905556
R-squared	0.183168718925853
Adjusted R-squared	0.0664785359152604
F-TEST (value)	1.56970118822443
F-TEST (DF numerator)	13
F-TEST (DF denominator)	91
p-value	0.108650123530041
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.78903966168285
Sum Squared Residuals	56.6551064814815

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.427982147905556 \tabularnewline
R-squared & 0.183168718925853 \tabularnewline
Adjusted R-squared & 0.0664785359152604 \tabularnewline
F-TEST (value) & 1.56970118822443 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 91 \tabularnewline
p-value & 0.108650123530041 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.78903966168285 \tabularnewline
Sum Squared Residuals & 56.6551064814815 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25786&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.427982147905556[/C][/ROW]
[ROW][C]R-squared[/C][C]0.183168718925853[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.0664785359152604[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1.56970118822443[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]91[/C][/ROW]
[ROW][C]p-value[/C][C]0.108650123530041[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.78903966168285[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]56.6551064814815[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25786&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25786&T=3

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Regression Statistics
Multiple R	0.427982147905556
R-squared	0.183168718925853
Adjusted R-squared	0.0664785359152604
F-TEST (value)	1.56970118822443
F-TEST (DF numerator)	13
F-TEST (DF denominator)	91
p-value	0.108650123530041
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.78903966168285
Sum Squared Residuals	56.6551064814815

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	7.5	7.51358024691357	-0.0135802469135677
2	7.2	7.40246913580247	-0.202469135802471
3	6.9	7.22469135802469	-0.324691358024693
4	6.7	7.0358024691358	-0.335802469135804
5	6.4	6.80246913580247	-0.402469135802467
6	6.3	6.69135802469136	-0.391358024691359
7	6.8	7.2358024691358	-0.435802469135802
8	7.3	7.38024691358025	-0.080246913580246
9	7.1	7.40246913580247	-0.30246913580247
10	7.1	7.5625462962963	-0.462546296296297
11	6.8	7.4625462962963	-0.662546296296297
12	6.5	7.5250462962963	-1.02504629629629
13	6.3	7.6233487654321	-1.3233487654321
14	6.1	7.51223765432099	-1.41223765432099
15	6.1	7.33445987654321	-1.23445987654321
16	6.3	7.14557098765432	-0.845570987654321
17	6.3	6.91223765432099	-0.612237654320989
18	6	6.80112654320988	-0.801126543209877
19	6.2	7.34557098765432	-1.14557098765432
20	6.4	7.49001543209877	-1.09001543209877
21	6.8	7.51223765432099	-0.712237654320988
22	7.5	7.67231481481481	-0.172314814814815
23	7.5	7.57231481481482	-0.072314814814815
24	7.6	7.63481481481481	-0.0348148148148148
25	7.6	7.73311728395062	-0.133117283950619
26	7.4	7.6220061728395	-0.222006172839506
27	7.3	7.44422839506173	-0.144228395061729
28	7.1	7.25533950617284	-0.155339506172840
29	6.9	7.02200617283951	-0.122006172839506
30	6.8	6.9108950617284	-0.110895061728395
31	7.5	7.45533950617284	0.0446604938271603
32	7.6	7.59978395061728	0.000216049382715459
33	7.8	7.6220061728395	0.177993827160493
34	8	7.78208333333333	0.217916666666666
35	8.1	7.68208333333333	0.417916666666666
36	8.2	7.74458333333333	0.455416666666666
37	8.3	7.84288580246914	0.457114197530863
38	8.2	7.73177469135802	0.468225308641975
39	8	7.55399691358025	0.446003086419753
40	7.9	7.36510802469136	0.534891975308642
41	7.6	7.13177469135803	0.468225308641974
42	7.6	7.02066358024691	0.579336419753086
43	8.2	7.56510802469136	0.634891975308641
44	8.3	7.7095524691358	0.590447530864198
45	8.4	7.73177469135802	0.668225308641976
46	8.4	7.89185185185185	0.508148148148148
47	8.4	7.79185185185185	0.608148148148148
48	8.6	7.85435185185185	0.745648148148148
49	8.9	7.95265432098766	0.947345679012345
50	8.8	7.84154320987654	0.958456790123458
51	8.3	7.66376543209877	0.636234567901236
52	7.5	7.47487654320988	0.0251234567901237
53	7.2	7.24154320987654	-0.0415432098765432
54	7.5	7.13043209876543	0.369567901234568
55	8.8	7.67487654320988	1.12512345679012
56	9.3	7.81932098765432	1.48067901234568
57	9.3	7.84154320987654	1.45845679012346
58	8.7	7.88314814814815	0.81685185185185
59	8.2	7.78314814814815	0.416851851851851
60	8.3	7.84564814814815	0.454351851851853
61	8.5	7.94395061728395	0.556049382716048
62	8.6	7.83283950617284	0.76716049382716
63	8.6	7.65506172839506	0.944938271604938
64	8.2	7.46617283950617	0.733827160493827
65	8.1	7.23283950617284	0.86716049382716
66	8	7.12172839506173	0.878271604938271
67	8.6	7.66617283950617	0.933827160493827
68	8.7	7.81061728395062	0.889382716049382
69	8.8	7.83283950617284	0.96716049382716
70	8.5	7.99291666666667	0.507083333333333
71	8.4	7.89291666666667	0.507083333333334
72	8.5	7.95541666666667	0.544583333333334
73	8.7	8.05371913580247	0.646280864197529
74	8.7	7.94260802469136	0.757391975308642
75	8.6	7.76483024691358	0.83516975308642
76	8.5	7.57594135802469	0.924058641975309
77	8.3	7.34260802469136	0.957391975308642
78	8.1	7.23149691358025	0.868503086419753
79	8.2	7.77594135802469	0.424058641975308
80	8.1	7.92038580246914	0.179614197530864
81	8.1	7.94260802469136	0.157391975308642
82	7.9	8.10268518518519	-0.202685185185185
83	7.9	8.00268518518518	-0.102685185185185
84	7.9	8.06518518518518	-0.165185185185184
85	8	8.16348765432099	-0.163487654320989
86	8	8.05237654320988	-0.0523765432098761
87	7.9	7.8745987654321	0.0254012345679019
88	8	7.68570987654321	0.314290123456791
89	7.7	7.45237654320988	0.247623456790124
90	7.2	7.34126543209876	-0.141265432098765
91	7.5	7.88570987654321	-0.385709876543209
92	7.3	8.03015432098765	-0.730154320987654
93	7	8.05237654320988	-1.05237654320988
94	7	8.2124537037037	-1.21245370370370
95	7	8.1124537037037	-1.11245370370370
96	7.2	8.1749537037037	-0.974953703703703
97	7.3	8.2732561728395	-0.973256172839508
98	7.1	8.1621450617284	-1.06214506172839
99	6.8	7.98436728395062	-1.18436728395062
100	6.6	7.79547839506173	-1.19547839506173
101	6.2	7.5621450617284	-1.36214506172839
102	6.2	7.45103395061728	-1.25103395061728
103	6.8	7.99547839506173	-1.19547839506173
104	6.9	8.13992283950617	-1.23992283950617
105	6.8	8.1621450617284	-1.36214506172839

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 7.5 & 7.51358024691357 & -0.0135802469135677 \tabularnewline
2 & 7.2 & 7.40246913580247 & -0.202469135802471 \tabularnewline
3 & 6.9 & 7.22469135802469 & -0.324691358024693 \tabularnewline
4 & 6.7 & 7.0358024691358 & -0.335802469135804 \tabularnewline
5 & 6.4 & 6.80246913580247 & -0.402469135802467 \tabularnewline
6 & 6.3 & 6.69135802469136 & -0.391358024691359 \tabularnewline
7 & 6.8 & 7.2358024691358 & -0.435802469135802 \tabularnewline
8 & 7.3 & 7.38024691358025 & -0.080246913580246 \tabularnewline
9 & 7.1 & 7.40246913580247 & -0.30246913580247 \tabularnewline
10 & 7.1 & 7.5625462962963 & -0.462546296296297 \tabularnewline
11 & 6.8 & 7.4625462962963 & -0.662546296296297 \tabularnewline
12 & 6.5 & 7.5250462962963 & -1.02504629629629 \tabularnewline
13 & 6.3 & 7.6233487654321 & -1.3233487654321 \tabularnewline
14 & 6.1 & 7.51223765432099 & -1.41223765432099 \tabularnewline
15 & 6.1 & 7.33445987654321 & -1.23445987654321 \tabularnewline
16 & 6.3 & 7.14557098765432 & -0.845570987654321 \tabularnewline
17 & 6.3 & 6.91223765432099 & -0.612237654320989 \tabularnewline
18 & 6 & 6.80112654320988 & -0.801126543209877 \tabularnewline
19 & 6.2 & 7.34557098765432 & -1.14557098765432 \tabularnewline
20 & 6.4 & 7.49001543209877 & -1.09001543209877 \tabularnewline
21 & 6.8 & 7.51223765432099 & -0.712237654320988 \tabularnewline
22 & 7.5 & 7.67231481481481 & -0.172314814814815 \tabularnewline
23 & 7.5 & 7.57231481481482 & -0.072314814814815 \tabularnewline
24 & 7.6 & 7.63481481481481 & -0.0348148148148148 \tabularnewline
25 & 7.6 & 7.73311728395062 & -0.133117283950619 \tabularnewline
26 & 7.4 & 7.6220061728395 & -0.222006172839506 \tabularnewline
27 & 7.3 & 7.44422839506173 & -0.144228395061729 \tabularnewline
28 & 7.1 & 7.25533950617284 & -0.155339506172840 \tabularnewline
29 & 6.9 & 7.02200617283951 & -0.122006172839506 \tabularnewline
30 & 6.8 & 6.9108950617284 & -0.110895061728395 \tabularnewline
31 & 7.5 & 7.45533950617284 & 0.0446604938271603 \tabularnewline
32 & 7.6 & 7.59978395061728 & 0.000216049382715459 \tabularnewline
33 & 7.8 & 7.6220061728395 & 0.177993827160493 \tabularnewline
34 & 8 & 7.78208333333333 & 0.217916666666666 \tabularnewline
35 & 8.1 & 7.68208333333333 & 0.417916666666666 \tabularnewline
36 & 8.2 & 7.74458333333333 & 0.455416666666666 \tabularnewline
37 & 8.3 & 7.84288580246914 & 0.457114197530863 \tabularnewline
38 & 8.2 & 7.73177469135802 & 0.468225308641975 \tabularnewline
39 & 8 & 7.55399691358025 & 0.446003086419753 \tabularnewline
40 & 7.9 & 7.36510802469136 & 0.534891975308642 \tabularnewline
41 & 7.6 & 7.13177469135803 & 0.468225308641974 \tabularnewline
42 & 7.6 & 7.02066358024691 & 0.579336419753086 \tabularnewline
43 & 8.2 & 7.56510802469136 & 0.634891975308641 \tabularnewline
44 & 8.3 & 7.7095524691358 & 0.590447530864198 \tabularnewline
45 & 8.4 & 7.73177469135802 & 0.668225308641976 \tabularnewline
46 & 8.4 & 7.89185185185185 & 0.508148148148148 \tabularnewline
47 & 8.4 & 7.79185185185185 & 0.608148148148148 \tabularnewline
48 & 8.6 & 7.85435185185185 & 0.745648148148148 \tabularnewline
49 & 8.9 & 7.95265432098766 & 0.947345679012345 \tabularnewline
50 & 8.8 & 7.84154320987654 & 0.958456790123458 \tabularnewline
51 & 8.3 & 7.66376543209877 & 0.636234567901236 \tabularnewline
52 & 7.5 & 7.47487654320988 & 0.0251234567901237 \tabularnewline
53 & 7.2 & 7.24154320987654 & -0.0415432098765432 \tabularnewline
54 & 7.5 & 7.13043209876543 & 0.369567901234568 \tabularnewline
55 & 8.8 & 7.67487654320988 & 1.12512345679012 \tabularnewline
56 & 9.3 & 7.81932098765432 & 1.48067901234568 \tabularnewline
57 & 9.3 & 7.84154320987654 & 1.45845679012346 \tabularnewline
58 & 8.7 & 7.88314814814815 & 0.81685185185185 \tabularnewline
59 & 8.2 & 7.78314814814815 & 0.416851851851851 \tabularnewline
60 & 8.3 & 7.84564814814815 & 0.454351851851853 \tabularnewline
61 & 8.5 & 7.94395061728395 & 0.556049382716048 \tabularnewline
62 & 8.6 & 7.83283950617284 & 0.76716049382716 \tabularnewline
63 & 8.6 & 7.65506172839506 & 0.944938271604938 \tabularnewline
64 & 8.2 & 7.46617283950617 & 0.733827160493827 \tabularnewline
65 & 8.1 & 7.23283950617284 & 0.86716049382716 \tabularnewline
66 & 8 & 7.12172839506173 & 0.878271604938271 \tabularnewline
67 & 8.6 & 7.66617283950617 & 0.933827160493827 \tabularnewline
68 & 8.7 & 7.81061728395062 & 0.889382716049382 \tabularnewline
69 & 8.8 & 7.83283950617284 & 0.96716049382716 \tabularnewline
70 & 8.5 & 7.99291666666667 & 0.507083333333333 \tabularnewline
71 & 8.4 & 7.89291666666667 & 0.507083333333334 \tabularnewline
72 & 8.5 & 7.95541666666667 & 0.544583333333334 \tabularnewline
73 & 8.7 & 8.05371913580247 & 0.646280864197529 \tabularnewline
74 & 8.7 & 7.94260802469136 & 0.757391975308642 \tabularnewline
75 & 8.6 & 7.76483024691358 & 0.83516975308642 \tabularnewline
76 & 8.5 & 7.57594135802469 & 0.924058641975309 \tabularnewline
77 & 8.3 & 7.34260802469136 & 0.957391975308642 \tabularnewline
78 & 8.1 & 7.23149691358025 & 0.868503086419753 \tabularnewline
79 & 8.2 & 7.77594135802469 & 0.424058641975308 \tabularnewline
80 & 8.1 & 7.92038580246914 & 0.179614197530864 \tabularnewline
81 & 8.1 & 7.94260802469136 & 0.157391975308642 \tabularnewline
82 & 7.9 & 8.10268518518519 & -0.202685185185185 \tabularnewline
83 & 7.9 & 8.00268518518518 & -0.102685185185185 \tabularnewline
84 & 7.9 & 8.06518518518518 & -0.165185185185184 \tabularnewline
85 & 8 & 8.16348765432099 & -0.163487654320989 \tabularnewline
86 & 8 & 8.05237654320988 & -0.0523765432098761 \tabularnewline
87 & 7.9 & 7.8745987654321 & 0.0254012345679019 \tabularnewline
88 & 8 & 7.68570987654321 & 0.314290123456791 \tabularnewline
89 & 7.7 & 7.45237654320988 & 0.247623456790124 \tabularnewline
90 & 7.2 & 7.34126543209876 & -0.141265432098765 \tabularnewline
91 & 7.5 & 7.88570987654321 & -0.385709876543209 \tabularnewline
92 & 7.3 & 8.03015432098765 & -0.730154320987654 \tabularnewline
93 & 7 & 8.05237654320988 & -1.05237654320988 \tabularnewline
94 & 7 & 8.2124537037037 & -1.21245370370370 \tabularnewline
95 & 7 & 8.1124537037037 & -1.11245370370370 \tabularnewline
96 & 7.2 & 8.1749537037037 & -0.974953703703703 \tabularnewline
97 & 7.3 & 8.2732561728395 & -0.973256172839508 \tabularnewline
98 & 7.1 & 8.1621450617284 & -1.06214506172839 \tabularnewline
99 & 6.8 & 7.98436728395062 & -1.18436728395062 \tabularnewline
100 & 6.6 & 7.79547839506173 & -1.19547839506173 \tabularnewline
101 & 6.2 & 7.5621450617284 & -1.36214506172839 \tabularnewline
102 & 6.2 & 7.45103395061728 & -1.25103395061728 \tabularnewline
103 & 6.8 & 7.99547839506173 & -1.19547839506173 \tabularnewline
104 & 6.9 & 8.13992283950617 & -1.23992283950617 \tabularnewline
105 & 6.8 & 8.1621450617284 & -1.36214506172839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25786&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]7.5[/C][C]7.51358024691357[/C][C]-0.0135802469135677[/C][/ROW]
[ROW][C]2[/C][C]7.2[/C][C]7.40246913580247[/C][C]-0.202469135802471[/C][/ROW]
[ROW][C]3[/C][C]6.9[/C][C]7.22469135802469[/C][C]-0.324691358024693[/C][/ROW]
[ROW][C]4[/C][C]6.7[/C][C]7.0358024691358[/C][C]-0.335802469135804[/C][/ROW]
[ROW][C]5[/C][C]6.4[/C][C]6.80246913580247[/C][C]-0.402469135802467[/C][/ROW]
[ROW][C]6[/C][C]6.3[/C][C]6.69135802469136[/C][C]-0.391358024691359[/C][/ROW]
[ROW][C]7[/C][C]6.8[/C][C]7.2358024691358[/C][C]-0.435802469135802[/C][/ROW]
[ROW][C]8[/C][C]7.3[/C][C]7.38024691358025[/C][C]-0.080246913580246[/C][/ROW]
[ROW][C]9[/C][C]7.1[/C][C]7.40246913580247[/C][C]-0.30246913580247[/C][/ROW]
[ROW][C]10[/C][C]7.1[/C][C]7.5625462962963[/C][C]-0.462546296296297[/C][/ROW]
[ROW][C]11[/C][C]6.8[/C][C]7.4625462962963[/C][C]-0.662546296296297[/C][/ROW]
[ROW][C]12[/C][C]6.5[/C][C]7.5250462962963[/C][C]-1.02504629629629[/C][/ROW]
[ROW][C]13[/C][C]6.3[/C][C]7.6233487654321[/C][C]-1.3233487654321[/C][/ROW]
[ROW][C]14[/C][C]6.1[/C][C]7.51223765432099[/C][C]-1.41223765432099[/C][/ROW]
[ROW][C]15[/C][C]6.1[/C][C]7.33445987654321[/C][C]-1.23445987654321[/C][/ROW]
[ROW][C]16[/C][C]6.3[/C][C]7.14557098765432[/C][C]-0.845570987654321[/C][/ROW]
[ROW][C]17[/C][C]6.3[/C][C]6.91223765432099[/C][C]-0.612237654320989[/C][/ROW]
[ROW][C]18[/C][C]6[/C][C]6.80112654320988[/C][C]-0.801126543209877[/C][/ROW]
[ROW][C]19[/C][C]6.2[/C][C]7.34557098765432[/C][C]-1.14557098765432[/C][/ROW]
[ROW][C]20[/C][C]6.4[/C][C]7.49001543209877[/C][C]-1.09001543209877[/C][/ROW]
[ROW][C]21[/C][C]6.8[/C][C]7.51223765432099[/C][C]-0.712237654320988[/C][/ROW]
[ROW][C]22[/C][C]7.5[/C][C]7.67231481481481[/C][C]-0.172314814814815[/C][/ROW]
[ROW][C]23[/C][C]7.5[/C][C]7.57231481481482[/C][C]-0.072314814814815[/C][/ROW]
[ROW][C]24[/C][C]7.6[/C][C]7.63481481481481[/C][C]-0.0348148148148148[/C][/ROW]
[ROW][C]25[/C][C]7.6[/C][C]7.73311728395062[/C][C]-0.133117283950619[/C][/ROW]
[ROW][C]26[/C][C]7.4[/C][C]7.6220061728395[/C][C]-0.222006172839506[/C][/ROW]
[ROW][C]27[/C][C]7.3[/C][C]7.44422839506173[/C][C]-0.144228395061729[/C][/ROW]
[ROW][C]28[/C][C]7.1[/C][C]7.25533950617284[/C][C]-0.155339506172840[/C][/ROW]
[ROW][C]29[/C][C]6.9[/C][C]7.02200617283951[/C][C]-0.122006172839506[/C][/ROW]
[ROW][C]30[/C][C]6.8[/C][C]6.9108950617284[/C][C]-0.110895061728395[/C][/ROW]
[ROW][C]31[/C][C]7.5[/C][C]7.45533950617284[/C][C]0.0446604938271603[/C][/ROW]
[ROW][C]32[/C][C]7.6[/C][C]7.59978395061728[/C][C]0.000216049382715459[/C][/ROW]
[ROW][C]33[/C][C]7.8[/C][C]7.6220061728395[/C][C]0.177993827160493[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]7.78208333333333[/C][C]0.217916666666666[/C][/ROW]
[ROW][C]35[/C][C]8.1[/C][C]7.68208333333333[/C][C]0.417916666666666[/C][/ROW]
[ROW][C]36[/C][C]8.2[/C][C]7.74458333333333[/C][C]0.455416666666666[/C][/ROW]
[ROW][C]37[/C][C]8.3[/C][C]7.84288580246914[/C][C]0.457114197530863[/C][/ROW]
[ROW][C]38[/C][C]8.2[/C][C]7.73177469135802[/C][C]0.468225308641975[/C][/ROW]
[ROW][C]39[/C][C]8[/C][C]7.55399691358025[/C][C]0.446003086419753[/C][/ROW]
[ROW][C]40[/C][C]7.9[/C][C]7.36510802469136[/C][C]0.534891975308642[/C][/ROW]
[ROW][C]41[/C][C]7.6[/C][C]7.13177469135803[/C][C]0.468225308641974[/C][/ROW]
[ROW][C]42[/C][C]7.6[/C][C]7.02066358024691[/C][C]0.579336419753086[/C][/ROW]
[ROW][C]43[/C][C]8.2[/C][C]7.56510802469136[/C][C]0.634891975308641[/C][/ROW]
[ROW][C]44[/C][C]8.3[/C][C]7.7095524691358[/C][C]0.590447530864198[/C][/ROW]
[ROW][C]45[/C][C]8.4[/C][C]7.73177469135802[/C][C]0.668225308641976[/C][/ROW]
[ROW][C]46[/C][C]8.4[/C][C]7.89185185185185[/C][C]0.508148148148148[/C][/ROW]
[ROW][C]47[/C][C]8.4[/C][C]7.79185185185185[/C][C]0.608148148148148[/C][/ROW]
[ROW][C]48[/C][C]8.6[/C][C]7.85435185185185[/C][C]0.745648148148148[/C][/ROW]
[ROW][C]49[/C][C]8.9[/C][C]7.95265432098766[/C][C]0.947345679012345[/C][/ROW]
[ROW][C]50[/C][C]8.8[/C][C]7.84154320987654[/C][C]0.958456790123458[/C][/ROW]
[ROW][C]51[/C][C]8.3[/C][C]7.66376543209877[/C][C]0.636234567901236[/C][/ROW]
[ROW][C]52[/C][C]7.5[/C][C]7.47487654320988[/C][C]0.0251234567901237[/C][/ROW]
[ROW][C]53[/C][C]7.2[/C][C]7.24154320987654[/C][C]-0.0415432098765432[/C][/ROW]
[ROW][C]54[/C][C]7.5[/C][C]7.13043209876543[/C][C]0.369567901234568[/C][/ROW]
[ROW][C]55[/C][C]8.8[/C][C]7.67487654320988[/C][C]1.12512345679012[/C][/ROW]
[ROW][C]56[/C][C]9.3[/C][C]7.81932098765432[/C][C]1.48067901234568[/C][/ROW]
[ROW][C]57[/C][C]9.3[/C][C]7.84154320987654[/C][C]1.45845679012346[/C][/ROW]
[ROW][C]58[/C][C]8.7[/C][C]7.88314814814815[/C][C]0.81685185185185[/C][/ROW]
[ROW][C]59[/C][C]8.2[/C][C]7.78314814814815[/C][C]0.416851851851851[/C][/ROW]
[ROW][C]60[/C][C]8.3[/C][C]7.84564814814815[/C][C]0.454351851851853[/C][/ROW]
[ROW][C]61[/C][C]8.5[/C][C]7.94395061728395[/C][C]0.556049382716048[/C][/ROW]
[ROW][C]62[/C][C]8.6[/C][C]7.83283950617284[/C][C]0.76716049382716[/C][/ROW]
[ROW][C]63[/C][C]8.6[/C][C]7.65506172839506[/C][C]0.944938271604938[/C][/ROW]
[ROW][C]64[/C][C]8.2[/C][C]7.46617283950617[/C][C]0.733827160493827[/C][/ROW]
[ROW][C]65[/C][C]8.1[/C][C]7.23283950617284[/C][C]0.86716049382716[/C][/ROW]
[ROW][C]66[/C][C]8[/C][C]7.12172839506173[/C][C]0.878271604938271[/C][/ROW]
[ROW][C]67[/C][C]8.6[/C][C]7.66617283950617[/C][C]0.933827160493827[/C][/ROW]
[ROW][C]68[/C][C]8.7[/C][C]7.81061728395062[/C][C]0.889382716049382[/C][/ROW]
[ROW][C]69[/C][C]8.8[/C][C]7.83283950617284[/C][C]0.96716049382716[/C][/ROW]
[ROW][C]70[/C][C]8.5[/C][C]7.99291666666667[/C][C]0.507083333333333[/C][/ROW]
[ROW][C]71[/C][C]8.4[/C][C]7.89291666666667[/C][C]0.507083333333334[/C][/ROW]
[ROW][C]72[/C][C]8.5[/C][C]7.95541666666667[/C][C]0.544583333333334[/C][/ROW]
[ROW][C]73[/C][C]8.7[/C][C]8.05371913580247[/C][C]0.646280864197529[/C][/ROW]
[ROW][C]74[/C][C]8.7[/C][C]7.94260802469136[/C][C]0.757391975308642[/C][/ROW]
[ROW][C]75[/C][C]8.6[/C][C]7.76483024691358[/C][C]0.83516975308642[/C][/ROW]
[ROW][C]76[/C][C]8.5[/C][C]7.57594135802469[/C][C]0.924058641975309[/C][/ROW]
[ROW][C]77[/C][C]8.3[/C][C]7.34260802469136[/C][C]0.957391975308642[/C][/ROW]
[ROW][C]78[/C][C]8.1[/C][C]7.23149691358025[/C][C]0.868503086419753[/C][/ROW]
[ROW][C]79[/C][C]8.2[/C][C]7.77594135802469[/C][C]0.424058641975308[/C][/ROW]
[ROW][C]80[/C][C]8.1[/C][C]7.92038580246914[/C][C]0.179614197530864[/C][/ROW]
[ROW][C]81[/C][C]8.1[/C][C]7.94260802469136[/C][C]0.157391975308642[/C][/ROW]
[ROW][C]82[/C][C]7.9[/C][C]8.10268518518519[/C][C]-0.202685185185185[/C][/ROW]
[ROW][C]83[/C][C]7.9[/C][C]8.00268518518518[/C][C]-0.102685185185185[/C][/ROW]
[ROW][C]84[/C][C]7.9[/C][C]8.06518518518518[/C][C]-0.165185185185184[/C][/ROW]
[ROW][C]85[/C][C]8[/C][C]8.16348765432099[/C][C]-0.163487654320989[/C][/ROW]
[ROW][C]86[/C][C]8[/C][C]8.05237654320988[/C][C]-0.0523765432098761[/C][/ROW]
[ROW][C]87[/C][C]7.9[/C][C]7.8745987654321[/C][C]0.0254012345679019[/C][/ROW]
[ROW][C]88[/C][C]8[/C][C]7.68570987654321[/C][C]0.314290123456791[/C][/ROW]
[ROW][C]89[/C][C]7.7[/C][C]7.45237654320988[/C][C]0.247623456790124[/C][/ROW]
[ROW][C]90[/C][C]7.2[/C][C]7.34126543209876[/C][C]-0.141265432098765[/C][/ROW]
[ROW][C]91[/C][C]7.5[/C][C]7.88570987654321[/C][C]-0.385709876543209[/C][/ROW]
[ROW][C]92[/C][C]7.3[/C][C]8.03015432098765[/C][C]-0.730154320987654[/C][/ROW]
[ROW][C]93[/C][C]7[/C][C]8.05237654320988[/C][C]-1.05237654320988[/C][/ROW]
[ROW][C]94[/C][C]7[/C][C]8.2124537037037[/C][C]-1.21245370370370[/C][/ROW]
[ROW][C]95[/C][C]7[/C][C]8.1124537037037[/C][C]-1.11245370370370[/C][/ROW]
[ROW][C]96[/C][C]7.2[/C][C]8.1749537037037[/C][C]-0.974953703703703[/C][/ROW]
[ROW][C]97[/C][C]7.3[/C][C]8.2732561728395[/C][C]-0.973256172839508[/C][/ROW]
[ROW][C]98[/C][C]7.1[/C][C]8.1621450617284[/C][C]-1.06214506172839[/C][/ROW]
[ROW][C]99[/C][C]6.8[/C][C]7.98436728395062[/C][C]-1.18436728395062[/C][/ROW]
[ROW][C]100[/C][C]6.6[/C][C]7.79547839506173[/C][C]-1.19547839506173[/C][/ROW]
[ROW][C]101[/C][C]6.2[/C][C]7.5621450617284[/C][C]-1.36214506172839[/C][/ROW]
[ROW][C]102[/C][C]6.2[/C][C]7.45103395061728[/C][C]-1.25103395061728[/C][/ROW]
[ROW][C]103[/C][C]6.8[/C][C]7.99547839506173[/C][C]-1.19547839506173[/C][/ROW]
[ROW][C]104[/C][C]6.9[/C][C]8.13992283950617[/C][C]-1.23992283950617[/C][/ROW]
[ROW][C]105[/C][C]6.8[/C][C]8.1621450617284[/C][C]-1.36214506172839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25786&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25786&T=4

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	7.5	7.51358024691357	-0.0135802469135677
2	7.2	7.40246913580247	-0.202469135802471
3	6.9	7.22469135802469	-0.324691358024693
4	6.7	7.0358024691358	-0.335802469135804
5	6.4	6.80246913580247	-0.402469135802467
6	6.3	6.69135802469136	-0.391358024691359
7	6.8	7.2358024691358	-0.435802469135802
8	7.3	7.38024691358025	-0.080246913580246
9	7.1	7.40246913580247	-0.30246913580247
10	7.1	7.5625462962963	-0.462546296296297
11	6.8	7.4625462962963	-0.662546296296297
12	6.5	7.5250462962963	-1.02504629629629
13	6.3	7.6233487654321	-1.3233487654321
14	6.1	7.51223765432099	-1.41223765432099
15	6.1	7.33445987654321	-1.23445987654321
16	6.3	7.14557098765432	-0.845570987654321
17	6.3	6.91223765432099	-0.612237654320989
18	6	6.80112654320988	-0.801126543209877
19	6.2	7.34557098765432	-1.14557098765432
20	6.4	7.49001543209877	-1.09001543209877
21	6.8	7.51223765432099	-0.712237654320988
22	7.5	7.67231481481481	-0.172314814814815
23	7.5	7.57231481481482	-0.072314814814815
24	7.6	7.63481481481481	-0.0348148148148148
25	7.6	7.73311728395062	-0.133117283950619
26	7.4	7.6220061728395	-0.222006172839506
27	7.3	7.44422839506173	-0.144228395061729
28	7.1	7.25533950617284	-0.155339506172840
29	6.9	7.02200617283951	-0.122006172839506
30	6.8	6.9108950617284	-0.110895061728395
31	7.5	7.45533950617284	0.0446604938271603
32	7.6	7.59978395061728	0.000216049382715459
33	7.8	7.6220061728395	0.177993827160493
34	8	7.78208333333333	0.217916666666666
35	8.1	7.68208333333333	0.417916666666666
36	8.2	7.74458333333333	0.455416666666666
37	8.3	7.84288580246914	0.457114197530863
38	8.2	7.73177469135802	0.468225308641975
39	8	7.55399691358025	0.446003086419753
40	7.9	7.36510802469136	0.534891975308642
41	7.6	7.13177469135803	0.468225308641974
42	7.6	7.02066358024691	0.579336419753086
43	8.2	7.56510802469136	0.634891975308641
44	8.3	7.7095524691358	0.590447530864198
45	8.4	7.73177469135802	0.668225308641976
46	8.4	7.89185185185185	0.508148148148148
47	8.4	7.79185185185185	0.608148148148148
48	8.6	7.85435185185185	0.745648148148148
49	8.9	7.95265432098766	0.947345679012345
50	8.8	7.84154320987654	0.958456790123458
51	8.3	7.66376543209877	0.636234567901236
52	7.5	7.47487654320988	0.0251234567901237
53	7.2	7.24154320987654	-0.0415432098765432
54	7.5	7.13043209876543	0.369567901234568
55	8.8	7.67487654320988	1.12512345679012
56	9.3	7.81932098765432	1.48067901234568
57	9.3	7.84154320987654	1.45845679012346
58	8.7	7.88314814814815	0.81685185185185
59	8.2	7.78314814814815	0.416851851851851
60	8.3	7.84564814814815	0.454351851851853
61	8.5	7.94395061728395	0.556049382716048
62	8.6	7.83283950617284	0.76716049382716
63	8.6	7.65506172839506	0.944938271604938
64	8.2	7.46617283950617	0.733827160493827
65	8.1	7.23283950617284	0.86716049382716
66	8	7.12172839506173	0.878271604938271
67	8.6	7.66617283950617	0.933827160493827
68	8.7	7.81061728395062	0.889382716049382
69	8.8	7.83283950617284	0.96716049382716
70	8.5	7.99291666666667	0.507083333333333
71	8.4	7.89291666666667	0.507083333333334
72	8.5	7.95541666666667	0.544583333333334
73	8.7	8.05371913580247	0.646280864197529
74	8.7	7.94260802469136	0.757391975308642
75	8.6	7.76483024691358	0.83516975308642
76	8.5	7.57594135802469	0.924058641975309
77	8.3	7.34260802469136	0.957391975308642
78	8.1	7.23149691358025	0.868503086419753
79	8.2	7.77594135802469	0.424058641975308
80	8.1	7.92038580246914	0.179614197530864
81	8.1	7.94260802469136	0.157391975308642
82	7.9	8.10268518518519	-0.202685185185185
83	7.9	8.00268518518518	-0.102685185185185
84	7.9	8.06518518518518	-0.165185185185184
85	8	8.16348765432099	-0.163487654320989
86	8	8.05237654320988	-0.0523765432098761
87	7.9	7.8745987654321	0.0254012345679019
88	8	7.68570987654321	0.314290123456791
89	7.7	7.45237654320988	0.247623456790124
90	7.2	7.34126543209876	-0.141265432098765
91	7.5	7.88570987654321	-0.385709876543209
92	7.3	8.03015432098765	-0.730154320987654
93	7	8.05237654320988	-1.05237654320988
94	7	8.2124537037037	-1.21245370370370
95	7	8.1124537037037	-1.11245370370370
96	7.2	8.1749537037037	-0.974953703703703
97	7.3	8.2732561728395	-0.973256172839508
98	7.1	8.1621450617284	-1.06214506172839
99	6.8	7.98436728395062	-1.18436728395062
100	6.6	7.79547839506173	-1.19547839506173
101	6.2	7.5621450617284	-1.36214506172839
102	6.2	7.45103395061728	-1.25103395061728
103	6.8	7.99547839506173	-1.19547839506173
104	6.9	8.13992283950617	-1.23992283950617
105	6.8	8.1621450617284	-1.36214506172839

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.151585144786521	0.303170289573042	0.848414855213479
18	0.0881437344944234	0.176287468988847	0.911856265505577
19	0.0447972958640183	0.0895945917280367	0.955202704135982
20	0.0270910150305235	0.054182030061047	0.972908984969477
21	0.0194156041873198	0.0388312083746396	0.98058439581268
22	0.055181939721467	0.110363879442934	0.944818060278533
23	0.136735212048949	0.273470424097898	0.863264787951051
24	0.318612728494636	0.637225456989273	0.681387271505364
25	0.425356665968091	0.850713331936183	0.574643334031909
26	0.506277500715142	0.987444998569715	0.493722499284858
27	0.566464192411252	0.867071615177497	0.433535807588748
28	0.583231577900499	0.833536844199003	0.416768422099501
29	0.59615596904592	0.80768806190816	0.40384403095408
30	0.635863609553686	0.728272780892627	0.364136390446314
31	0.721456115155505	0.55708776968899	0.278543884844495
32	0.778720575975944	0.442558848048112	0.221279424024056
33	0.825355876104633	0.349288247790734	0.174644123895367
34	0.812479640560808	0.375040718878383	0.187520359439192
35	0.804286526944307	0.391426946111387	0.195713473055693
36	0.816377352931465	0.367245294137071	0.183622647068535
37	0.819215720507429	0.361568558985142	0.180784279492571
38	0.8380996234401	0.3238007531198	0.1619003765599
39	0.851374763885152	0.297250472229696	0.148625236114848
40	0.849191562372128	0.301616875255745	0.150808437627872
41	0.847877106907051	0.304245786185898	0.152122893092949
42	0.84941297575506	0.301174048489879	0.150587024244940
43	0.860808109963881	0.278383780072237	0.139191890036119
44	0.86565462093524	0.268690758129520	0.134345379064760
45	0.859363947817064	0.281272104365873	0.140636052182936
46	0.82376252255398	0.352474954892039	0.176237477446020
47	0.778654773147274	0.442690453705452	0.221345226852726
48	0.732290191695654	0.535419616608691	0.267709808304346
49	0.68901543380249	0.62196913239502	0.31098456619751
50	0.646799993074065	0.706400013851869	0.353200006925935
51	0.593285536627855	0.81342892674429	0.406714463372145
52	0.728300848177229	0.543398303645542	0.271699151822771
53	0.909686291182709	0.180627417634582	0.0903137088172912
54	0.966631079217883	0.0667378415642334	0.0333689207821167
55	0.968379537969797	0.063240924060405	0.0316204620302025
56	0.966946453222484	0.0661070935550317	0.0330535467775159
57	0.960443900438982	0.0791121991220356	0.0395560995610178
58	0.946724385815333	0.106551228369333	0.0532756141846667
59	0.960538378235054	0.0789232435298916	0.0394616217649458
60	0.97390590353028	0.0521881929394418	0.0260940964697209
61	0.983798493103602	0.0324030137927958	0.0162015068963979
62	0.987666704674057	0.0246665906518852	0.0123332953259426
63	0.98855260100954	0.0228947979809204	0.0114473989904602
64	0.997190282699057	0.00561943460188682	0.00280971730094341
65	0.999216590796074	0.00156681840785303	0.000783409203926513
66	0.99977924848677	0.000441503026459424	0.000220751513229712
67	0.999828529139304	0.000342941721391756	0.000171470860695878
68	0.999777520194101	0.000444959611798428	0.000222479805899214
69	0.999548526564705	0.000902946870588947	0.000451473435294474
70	0.99929713565299	0.00140572869402232	0.000702864347011158
71	0.999071062020645	0.00185787595870941	0.000928937979354707
72	0.9987705566887	0.00245888662259995	0.00122944331129997
73	0.998055447254462	0.00388910549107566	0.00194455274553783
74	0.996403564599355	0.00719287080128997	0.00359643540064498
75	0.993173977412649	0.0136520451747025	0.00682602258735126
76	0.987419724269496	0.0251605514610084	0.0125802757305042
77	0.97844793767628	0.0431041246474407	0.0215520623237203
78	0.966677440435817	0.0666451191283668	0.0333225595641834
79	0.955282679586529	0.0894346408269418	0.0447173204134709
80	0.952866466266667	0.0942670674666652	0.0471335337333326
81	0.93934113855267	0.121317722894659	0.0606588614473294
82	0.926241895910755	0.147516208178491	0.0737581040892454
83	0.8980375204885	0.203924959022999	0.101962479511499
84	0.862355252730716	0.275289494538568	0.137644747269284
85	0.8148571313767	0.370285737246598	0.185142868623299
86	0.727875751018087	0.544248497963827	0.272124248981913
87	0.619979758795087	0.760040482409826	0.380020241204913
88	0.575729097058612	0.848541805882777	0.424270902941388

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.151585144786521 & 0.303170289573042 & 0.848414855213479 \tabularnewline
18 & 0.0881437344944234 & 0.176287468988847 & 0.911856265505577 \tabularnewline
19 & 0.0447972958640183 & 0.0895945917280367 & 0.955202704135982 \tabularnewline
20 & 0.0270910150305235 & 0.054182030061047 & 0.972908984969477 \tabularnewline
21 & 0.0194156041873198 & 0.0388312083746396 & 0.98058439581268 \tabularnewline
22 & 0.055181939721467 & 0.110363879442934 & 0.944818060278533 \tabularnewline
23 & 0.136735212048949 & 0.273470424097898 & 0.863264787951051 \tabularnewline
24 & 0.318612728494636 & 0.637225456989273 & 0.681387271505364 \tabularnewline
25 & 0.425356665968091 & 0.850713331936183 & 0.574643334031909 \tabularnewline
26 & 0.506277500715142 & 0.987444998569715 & 0.493722499284858 \tabularnewline
27 & 0.566464192411252 & 0.867071615177497 & 0.433535807588748 \tabularnewline
28 & 0.583231577900499 & 0.833536844199003 & 0.416768422099501 \tabularnewline
29 & 0.59615596904592 & 0.80768806190816 & 0.40384403095408 \tabularnewline
30 & 0.635863609553686 & 0.728272780892627 & 0.364136390446314 \tabularnewline
31 & 0.721456115155505 & 0.55708776968899 & 0.278543884844495 \tabularnewline
32 & 0.778720575975944 & 0.442558848048112 & 0.221279424024056 \tabularnewline
33 & 0.825355876104633 & 0.349288247790734 & 0.174644123895367 \tabularnewline
34 & 0.812479640560808 & 0.375040718878383 & 0.187520359439192 \tabularnewline
35 & 0.804286526944307 & 0.391426946111387 & 0.195713473055693 \tabularnewline
36 & 0.816377352931465 & 0.367245294137071 & 0.183622647068535 \tabularnewline
37 & 0.819215720507429 & 0.361568558985142 & 0.180784279492571 \tabularnewline
38 & 0.8380996234401 & 0.3238007531198 & 0.1619003765599 \tabularnewline
39 & 0.851374763885152 & 0.297250472229696 & 0.148625236114848 \tabularnewline
40 & 0.849191562372128 & 0.301616875255745 & 0.150808437627872 \tabularnewline
41 & 0.847877106907051 & 0.304245786185898 & 0.152122893092949 \tabularnewline
42 & 0.84941297575506 & 0.301174048489879 & 0.150587024244940 \tabularnewline
43 & 0.860808109963881 & 0.278383780072237 & 0.139191890036119 \tabularnewline
44 & 0.86565462093524 & 0.268690758129520 & 0.134345379064760 \tabularnewline
45 & 0.859363947817064 & 0.281272104365873 & 0.140636052182936 \tabularnewline
46 & 0.82376252255398 & 0.352474954892039 & 0.176237477446020 \tabularnewline
47 & 0.778654773147274 & 0.442690453705452 & 0.221345226852726 \tabularnewline
48 & 0.732290191695654 & 0.535419616608691 & 0.267709808304346 \tabularnewline
49 & 0.68901543380249 & 0.62196913239502 & 0.31098456619751 \tabularnewline
50 & 0.646799993074065 & 0.706400013851869 & 0.353200006925935 \tabularnewline
51 & 0.593285536627855 & 0.81342892674429 & 0.406714463372145 \tabularnewline
52 & 0.728300848177229 & 0.543398303645542 & 0.271699151822771 \tabularnewline
53 & 0.909686291182709 & 0.180627417634582 & 0.0903137088172912 \tabularnewline
54 & 0.966631079217883 & 0.0667378415642334 & 0.0333689207821167 \tabularnewline
55 & 0.968379537969797 & 0.063240924060405 & 0.0316204620302025 \tabularnewline
56 & 0.966946453222484 & 0.0661070935550317 & 0.0330535467775159 \tabularnewline
57 & 0.960443900438982 & 0.0791121991220356 & 0.0395560995610178 \tabularnewline
58 & 0.946724385815333 & 0.106551228369333 & 0.0532756141846667 \tabularnewline
59 & 0.960538378235054 & 0.0789232435298916 & 0.0394616217649458 \tabularnewline
60 & 0.97390590353028 & 0.0521881929394418 & 0.0260940964697209 \tabularnewline
61 & 0.983798493103602 & 0.0324030137927958 & 0.0162015068963979 \tabularnewline
62 & 0.987666704674057 & 0.0246665906518852 & 0.0123332953259426 \tabularnewline
63 & 0.98855260100954 & 0.0228947979809204 & 0.0114473989904602 \tabularnewline
64 & 0.997190282699057 & 0.00561943460188682 & 0.00280971730094341 \tabularnewline
65 & 0.999216590796074 & 0.00156681840785303 & 0.000783409203926513 \tabularnewline
66 & 0.99977924848677 & 0.000441503026459424 & 0.000220751513229712 \tabularnewline
67 & 0.999828529139304 & 0.000342941721391756 & 0.000171470860695878 \tabularnewline
68 & 0.999777520194101 & 0.000444959611798428 & 0.000222479805899214 \tabularnewline
69 & 0.999548526564705 & 0.000902946870588947 & 0.000451473435294474 \tabularnewline
70 & 0.99929713565299 & 0.00140572869402232 & 0.000702864347011158 \tabularnewline
71 & 0.999071062020645 & 0.00185787595870941 & 0.000928937979354707 \tabularnewline
72 & 0.9987705566887 & 0.00245888662259995 & 0.00122944331129997 \tabularnewline
73 & 0.998055447254462 & 0.00388910549107566 & 0.00194455274553783 \tabularnewline
74 & 0.996403564599355 & 0.00719287080128997 & 0.00359643540064498 \tabularnewline
75 & 0.993173977412649 & 0.0136520451747025 & 0.00682602258735126 \tabularnewline
76 & 0.987419724269496 & 0.0251605514610084 & 0.0125802757305042 \tabularnewline
77 & 0.97844793767628 & 0.0431041246474407 & 0.0215520623237203 \tabularnewline
78 & 0.966677440435817 & 0.0666451191283668 & 0.0333225595641834 \tabularnewline
79 & 0.955282679586529 & 0.0894346408269418 & 0.0447173204134709 \tabularnewline
80 & 0.952866466266667 & 0.0942670674666652 & 0.0471335337333326 \tabularnewline
81 & 0.93934113855267 & 0.121317722894659 & 0.0606588614473294 \tabularnewline
82 & 0.926241895910755 & 0.147516208178491 & 0.0737581040892454 \tabularnewline
83 & 0.8980375204885 & 0.203924959022999 & 0.101962479511499 \tabularnewline
84 & 0.862355252730716 & 0.275289494538568 & 0.137644747269284 \tabularnewline
85 & 0.8148571313767 & 0.370285737246598 & 0.185142868623299 \tabularnewline
86 & 0.727875751018087 & 0.544248497963827 & 0.272124248981913 \tabularnewline
87 & 0.619979758795087 & 0.760040482409826 & 0.380020241204913 \tabularnewline
88 & 0.575729097058612 & 0.848541805882777 & 0.424270902941388 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25786&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]17[/C][C]0.151585144786521[/C][C]0.303170289573042[/C][C]0.848414855213479[/C][/ROW]
[ROW][C]18[/C][C]0.0881437344944234[/C][C]0.176287468988847[/C][C]0.911856265505577[/C][/ROW]
[ROW][C]19[/C][C]0.0447972958640183[/C][C]0.0895945917280367[/C][C]0.955202704135982[/C][/ROW]
[ROW][C]20[/C][C]0.0270910150305235[/C][C]0.054182030061047[/C][C]0.972908984969477[/C][/ROW]
[ROW][C]21[/C][C]0.0194156041873198[/C][C]0.0388312083746396[/C][C]0.98058439581268[/C][/ROW]
[ROW][C]22[/C][C]0.055181939721467[/C][C]0.110363879442934[/C][C]0.944818060278533[/C][/ROW]
[ROW][C]23[/C][C]0.136735212048949[/C][C]0.273470424097898[/C][C]0.863264787951051[/C][/ROW]
[ROW][C]24[/C][C]0.318612728494636[/C][C]0.637225456989273[/C][C]0.681387271505364[/C][/ROW]
[ROW][C]25[/C][C]0.425356665968091[/C][C]0.850713331936183[/C][C]0.574643334031909[/C][/ROW]
[ROW][C]26[/C][C]0.506277500715142[/C][C]0.987444998569715[/C][C]0.493722499284858[/C][/ROW]
[ROW][C]27[/C][C]0.566464192411252[/C][C]0.867071615177497[/C][C]0.433535807588748[/C][/ROW]
[ROW][C]28[/C][C]0.583231577900499[/C][C]0.833536844199003[/C][C]0.416768422099501[/C][/ROW]
[ROW][C]29[/C][C]0.59615596904592[/C][C]0.80768806190816[/C][C]0.40384403095408[/C][/ROW]
[ROW][C]30[/C][C]0.635863609553686[/C][C]0.728272780892627[/C][C]0.364136390446314[/C][/ROW]
[ROW][C]31[/C][C]0.721456115155505[/C][C]0.55708776968899[/C][C]0.278543884844495[/C][/ROW]
[ROW][C]32[/C][C]0.778720575975944[/C][C]0.442558848048112[/C][C]0.221279424024056[/C][/ROW]
[ROW][C]33[/C][C]0.825355876104633[/C][C]0.349288247790734[/C][C]0.174644123895367[/C][/ROW]
[ROW][C]34[/C][C]0.812479640560808[/C][C]0.375040718878383[/C][C]0.187520359439192[/C][/ROW]
[ROW][C]35[/C][C]0.804286526944307[/C][C]0.391426946111387[/C][C]0.195713473055693[/C][/ROW]
[ROW][C]36[/C][C]0.816377352931465[/C][C]0.367245294137071[/C][C]0.183622647068535[/C][/ROW]
[ROW][C]37[/C][C]0.819215720507429[/C][C]0.361568558985142[/C][C]0.180784279492571[/C][/ROW]
[ROW][C]38[/C][C]0.8380996234401[/C][C]0.3238007531198[/C][C]0.1619003765599[/C][/ROW]
[ROW][C]39[/C][C]0.851374763885152[/C][C]0.297250472229696[/C][C]0.148625236114848[/C][/ROW]
[ROW][C]40[/C][C]0.849191562372128[/C][C]0.301616875255745[/C][C]0.150808437627872[/C][/ROW]
[ROW][C]41[/C][C]0.847877106907051[/C][C]0.304245786185898[/C][C]0.152122893092949[/C][/ROW]
[ROW][C]42[/C][C]0.84941297575506[/C][C]0.301174048489879[/C][C]0.150587024244940[/C][/ROW]
[ROW][C]43[/C][C]0.860808109963881[/C][C]0.278383780072237[/C][C]0.139191890036119[/C][/ROW]
[ROW][C]44[/C][C]0.86565462093524[/C][C]0.268690758129520[/C][C]0.134345379064760[/C][/ROW]
[ROW][C]45[/C][C]0.859363947817064[/C][C]0.281272104365873[/C][C]0.140636052182936[/C][/ROW]
[ROW][C]46[/C][C]0.82376252255398[/C][C]0.352474954892039[/C][C]0.176237477446020[/C][/ROW]
[ROW][C]47[/C][C]0.778654773147274[/C][C]0.442690453705452[/C][C]0.221345226852726[/C][/ROW]
[ROW][C]48[/C][C]0.732290191695654[/C][C]0.535419616608691[/C][C]0.267709808304346[/C][/ROW]
[ROW][C]49[/C][C]0.68901543380249[/C][C]0.62196913239502[/C][C]0.31098456619751[/C][/ROW]
[ROW][C]50[/C][C]0.646799993074065[/C][C]0.706400013851869[/C][C]0.353200006925935[/C][/ROW]
[ROW][C]51[/C][C]0.593285536627855[/C][C]0.81342892674429[/C][C]0.406714463372145[/C][/ROW]
[ROW][C]52[/C][C]0.728300848177229[/C][C]0.543398303645542[/C][C]0.271699151822771[/C][/ROW]
[ROW][C]53[/C][C]0.909686291182709[/C][C]0.180627417634582[/C][C]0.0903137088172912[/C][/ROW]
[ROW][C]54[/C][C]0.966631079217883[/C][C]0.0667378415642334[/C][C]0.0333689207821167[/C][/ROW]
[ROW][C]55[/C][C]0.968379537969797[/C][C]0.063240924060405[/C][C]0.0316204620302025[/C][/ROW]
[ROW][C]56[/C][C]0.966946453222484[/C][C]0.0661070935550317[/C][C]0.0330535467775159[/C][/ROW]
[ROW][C]57[/C][C]0.960443900438982[/C][C]0.0791121991220356[/C][C]0.0395560995610178[/C][/ROW]
[ROW][C]58[/C][C]0.946724385815333[/C][C]0.106551228369333[/C][C]0.0532756141846667[/C][/ROW]
[ROW][C]59[/C][C]0.960538378235054[/C][C]0.0789232435298916[/C][C]0.0394616217649458[/C][/ROW]
[ROW][C]60[/C][C]0.97390590353028[/C][C]0.0521881929394418[/C][C]0.0260940964697209[/C][/ROW]
[ROW][C]61[/C][C]0.983798493103602[/C][C]0.0324030137927958[/C][C]0.0162015068963979[/C][/ROW]
[ROW][C]62[/C][C]0.987666704674057[/C][C]0.0246665906518852[/C][C]0.0123332953259426[/C][/ROW]
[ROW][C]63[/C][C]0.98855260100954[/C][C]0.0228947979809204[/C][C]0.0114473989904602[/C][/ROW]
[ROW][C]64[/C][C]0.997190282699057[/C][C]0.00561943460188682[/C][C]0.00280971730094341[/C][/ROW]
[ROW][C]65[/C][C]0.999216590796074[/C][C]0.00156681840785303[/C][C]0.000783409203926513[/C][/ROW]
[ROW][C]66[/C][C]0.99977924848677[/C][C]0.000441503026459424[/C][C]0.000220751513229712[/C][/ROW]
[ROW][C]67[/C][C]0.999828529139304[/C][C]0.000342941721391756[/C][C]0.000171470860695878[/C][/ROW]
[ROW][C]68[/C][C]0.999777520194101[/C][C]0.000444959611798428[/C][C]0.000222479805899214[/C][/ROW]
[ROW][C]69[/C][C]0.999548526564705[/C][C]0.000902946870588947[/C][C]0.000451473435294474[/C][/ROW]
[ROW][C]70[/C][C]0.99929713565299[/C][C]0.00140572869402232[/C][C]0.000702864347011158[/C][/ROW]
[ROW][C]71[/C][C]0.999071062020645[/C][C]0.00185787595870941[/C][C]0.000928937979354707[/C][/ROW]
[ROW][C]72[/C][C]0.9987705566887[/C][C]0.00245888662259995[/C][C]0.00122944331129997[/C][/ROW]
[ROW][C]73[/C][C]0.998055447254462[/C][C]0.00388910549107566[/C][C]0.00194455274553783[/C][/ROW]
[ROW][C]74[/C][C]0.996403564599355[/C][C]0.00719287080128997[/C][C]0.00359643540064498[/C][/ROW]
[ROW][C]75[/C][C]0.993173977412649[/C][C]0.0136520451747025[/C][C]0.00682602258735126[/C][/ROW]
[ROW][C]76[/C][C]0.987419724269496[/C][C]0.0251605514610084[/C][C]0.0125802757305042[/C][/ROW]
[ROW][C]77[/C][C]0.97844793767628[/C][C]0.0431041246474407[/C][C]0.0215520623237203[/C][/ROW]
[ROW][C]78[/C][C]0.966677440435817[/C][C]0.0666451191283668[/C][C]0.0333225595641834[/C][/ROW]
[ROW][C]79[/C][C]0.955282679586529[/C][C]0.0894346408269418[/C][C]0.0447173204134709[/C][/ROW]
[ROW][C]80[/C][C]0.952866466266667[/C][C]0.0942670674666652[/C][C]0.0471335337333326[/C][/ROW]
[ROW][C]81[/C][C]0.93934113855267[/C][C]0.121317722894659[/C][C]0.0606588614473294[/C][/ROW]
[ROW][C]82[/C][C]0.926241895910755[/C][C]0.147516208178491[/C][C]0.0737581040892454[/C][/ROW]
[ROW][C]83[/C][C]0.8980375204885[/C][C]0.203924959022999[/C][C]0.101962479511499[/C][/ROW]
[ROW][C]84[/C][C]0.862355252730716[/C][C]0.275289494538568[/C][C]0.137644747269284[/C][/ROW]
[ROW][C]85[/C][C]0.8148571313767[/C][C]0.370285737246598[/C][C]0.185142868623299[/C][/ROW]
[ROW][C]86[/C][C]0.727875751018087[/C][C]0.544248497963827[/C][C]0.272124248981913[/C][/ROW]
[ROW][C]87[/C][C]0.619979758795087[/C][C]0.760040482409826[/C][C]0.380020241204913[/C][/ROW]
[ROW][C]88[/C][C]0.575729097058612[/C][C]0.848541805882777[/C][C]0.424270902941388[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25786&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25786&T=5

As an alternative you can also use a QR Code:

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

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.151585144786521	0.303170289573042	0.848414855213479
18	0.0881437344944234	0.176287468988847	0.911856265505577
19	0.0447972958640183	0.0895945917280367	0.955202704135982
20	0.0270910150305235	0.054182030061047	0.972908984969477
21	0.0194156041873198	0.0388312083746396	0.98058439581268
22	0.055181939721467	0.110363879442934	0.944818060278533
23	0.136735212048949	0.273470424097898	0.863264787951051
24	0.318612728494636	0.637225456989273	0.681387271505364
25	0.425356665968091	0.850713331936183	0.574643334031909
26	0.506277500715142	0.987444998569715	0.493722499284858
27	0.566464192411252	0.867071615177497	0.433535807588748
28	0.583231577900499	0.833536844199003	0.416768422099501
29	0.59615596904592	0.80768806190816	0.40384403095408
30	0.635863609553686	0.728272780892627	0.364136390446314
31	0.721456115155505	0.55708776968899	0.278543884844495
32	0.778720575975944	0.442558848048112	0.221279424024056
33	0.825355876104633	0.349288247790734	0.174644123895367
34	0.812479640560808	0.375040718878383	0.187520359439192
35	0.804286526944307	0.391426946111387	0.195713473055693
36	0.816377352931465	0.367245294137071	0.183622647068535
37	0.819215720507429	0.361568558985142	0.180784279492571
38	0.8380996234401	0.3238007531198	0.1619003765599
39	0.851374763885152	0.297250472229696	0.148625236114848
40	0.849191562372128	0.301616875255745	0.150808437627872
41	0.847877106907051	0.304245786185898	0.152122893092949
42	0.84941297575506	0.301174048489879	0.150587024244940
43	0.860808109963881	0.278383780072237	0.139191890036119
44	0.86565462093524	0.268690758129520	0.134345379064760
45	0.859363947817064	0.281272104365873	0.140636052182936
46	0.82376252255398	0.352474954892039	0.176237477446020
47	0.778654773147274	0.442690453705452	0.221345226852726
48	0.732290191695654	0.535419616608691	0.267709808304346
49	0.68901543380249	0.62196913239502	0.31098456619751
50	0.646799993074065	0.706400013851869	0.353200006925935
51	0.593285536627855	0.81342892674429	0.406714463372145
52	0.728300848177229	0.543398303645542	0.271699151822771
53	0.909686291182709	0.180627417634582	0.0903137088172912
54	0.966631079217883	0.0667378415642334	0.0333689207821167
55	0.968379537969797	0.063240924060405	0.0316204620302025
56	0.966946453222484	0.0661070935550317	0.0330535467775159
57	0.960443900438982	0.0791121991220356	0.0395560995610178
58	0.946724385815333	0.106551228369333	0.0532756141846667
59	0.960538378235054	0.0789232435298916	0.0394616217649458
60	0.97390590353028	0.0521881929394418	0.0260940964697209
61	0.983798493103602	0.0324030137927958	0.0162015068963979
62	0.987666704674057	0.0246665906518852	0.0123332953259426
63	0.98855260100954	0.0228947979809204	0.0114473989904602
64	0.997190282699057	0.00561943460188682	0.00280971730094341
65	0.999216590796074	0.00156681840785303	0.000783409203926513
66	0.99977924848677	0.000441503026459424	0.000220751513229712
67	0.999828529139304	0.000342941721391756	0.000171470860695878
68	0.999777520194101	0.000444959611798428	0.000222479805899214
69	0.999548526564705	0.000902946870588947	0.000451473435294474
70	0.99929713565299	0.00140572869402232	0.000702864347011158
71	0.999071062020645	0.00185787595870941	0.000928937979354707
72	0.9987705566887	0.00245888662259995	0.00122944331129997
73	0.998055447254462	0.00388910549107566	0.00194455274553783
74	0.996403564599355	0.00719287080128997	0.00359643540064498
75	0.993173977412649	0.0136520451747025	0.00682602258735126
76	0.987419724269496	0.0251605514610084	0.0125802757305042
77	0.97844793767628	0.0431041246474407	0.0215520623237203
78	0.966677440435817	0.0666451191283668	0.0333225595641834
79	0.955282679586529	0.0894346408269418	0.0447173204134709
80	0.952866466266667	0.0942670674666652	0.0471335337333326
81	0.93934113855267	0.121317722894659	0.0606588614473294
82	0.926241895910755	0.147516208178491	0.0737581040892454
83	0.8980375204885	0.203924959022999	0.101962479511499
84	0.862355252730716	0.275289494538568	0.137644747269284
85	0.8148571313767	0.370285737246598	0.185142868623299
86	0.727875751018087	0.544248497963827	0.272124248981913
87	0.619979758795087	0.760040482409826	0.380020241204913
88	0.575729097058612	0.848541805882777	0.424270902941388

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	11	0.152777777777778	NOK
5% type I error level	18	0.25	NOK
10% type I error level	29	0.402777777777778	NOK

\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 & 11 & 0.152777777777778 & NOK \tabularnewline
5% type I error level & 18 & 0.25 & NOK \tabularnewline
10% type I error level & 29 & 0.402777777777778 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25786&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]11[/C][C]0.152777777777778[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]18[/C][C]0.25[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]29[/C][C]0.402777777777778[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25786&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25786&T=6

As an alternative you can also use a QR Code:

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	11	0.152777777777778	NOK
5% type I error level	18	0.25	NOK
10% type I error level	29	0.402777777777778	NOK

Figure 1

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Figure 3

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Figure 4

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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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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')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code