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rwasp_multipleregression.wasp

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Multiple Regression

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Tue, 18 Nov 2008 05:56:00 -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/18/t1227013145av7rb18kz03aifl.htm/, Retrieved Mon, 29 Apr 2024 12:41:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25001, Retrieved Mon, 29 Apr 2024 12:41:49 +0000

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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]
F    D    [Multiple Regression] [] [2008-11-18 12:56:00] [de3f0516a1536f7c4a656924d8bc8d07] [Current]

Feedback Forum

2008-11-28 20:40:32 [Kelly Deckx] [reply] 
Je moet meer informatie geven dat dit Peter. :) 
Q1: Wanneer we logisch nadenken weten we dat we bij de the multiple regression model the seasonal dummies en de lineare trend moeten gebruiken. We kunnen zeker stellen dat er in de wintermaanden meer ongelukken gebeuren door het slechte weer. Er is ook een lange termijn trend omdat er elk jaar nieuwe technologieën worden uitgevonden die de auto veiliger maakt.  
 
De null hypothesis stellen we gelijk aan 0, dit wil zeggen dat de gordel geen effect zou hebben op het aantal slachtoffers. We kijken naar de kolom van de one-tailed p-value, omdat we met zekerheid kunnen zeggen dat het dragen van een gordel enkel een positief effect kan hebben. Hieruit kunnen we concluderen dat deze waarden allemaal 0 zijn, uitgezonderd voor M11 (November). We kunnen dus besluiten dat het niet toevallig is dat het dragen van een gordel een positief effect geeft. 
 
 
Q2: Wanneer we kijken naar de R-square van 0.7418… dan weten we dat we ongeveer 74% van de originele variabiliteit hebben verklaard. De R-square waarde geeft aan hoe goed het model de data weergeeft. (een r-square van 1 is dus ideaal). Waneer we willen weten of dit toeval is kijken we naar de F-test. Deze geeft de verdeling weer. De p-value is zeer klein, dus is hier significant verschillend van 0. Het is dus niet aan toeval te wijten.  
 
Je moet ook elke grafiek apart bespreken. De enige die je besproken hebt is wel juist.  
 
actuals en interpolations: Hier zien we inderdaad een dalende trend van het aantal slachtoffers. De verplichting van het dragen van de gordel is hier opvallend terug te vinden, namelijk het niveauverschil helemaal rechts. 
 
Het histogram en de qq-plot is vrij normaal verdeeld. Ze geeft geen perfecte normaalverdeling weer en vooral aan de 2 staarten zien we een scheefverdeling. Dit kan je ook terug vinden in de volgende QQ-plot. De theoretische kwantielen komen goed overeen met de sample kwantielen. 
2008-11-30 14:04:10 [Siem Van Opstal] [reply] 
Voor het oplossen van deze vraag hebben we gebruik gemaakt van de multiple regression software. Aan de hand van deze gegevens kunnen we de volgende formule opstellen: 
 
St = C + βt + ωGt + γ1M1,t + γ2M2,t + γ3M3,t + … + γ11M11,t + et 
 
Uit de tabel kunnen we afleiden dat: 
	C = 2325,8 
	β = -1,76 
	ω = -226 
	γ1M1,t = -454,9 
 
Vermits beta negatief is, trekken we steeds een groter getal van de constante af, en daalt het aantal slachtoffers op lange termijn. Elke maand zijn er gemiddeld 1,76 slachtoffers minder.  
 
Als G = 0, dan is er geen effect. Als G = 1, dan worden er in die maanden 226 levens gered. 
 
We kunnen besluiten dat december de onveiligste maand is, en april de veiligste want hier hebben we de hoogste parameter (-694,56). 
 
Zijn deze effecten aan het toeval te wijten? 
	 
Hiervoor gebruiken we de T-test. 
 
De null hypothese: de parameter = 0. Dit wil zeggen dat er geen enkel van de invloeden bestaat, tenzij we het tegendeel kunnen bewijzen. We gebruiken hier een eenzijdige test, omdat we ervan uit gaan dat het dragen van een gordel geen negatief effect zal hebben (voorkennis). 
 
We kiezen zelf een alfa-fout. Als we een alfa-fout van 5% kiezen, zien we dat de p-value steeds onder de alfa-fout ligt. We verwerpen dus de null hypothese, er is dus een significant verschil ten opzichte van de referentiemaand december. Uit de tabel kunnen we afleiden dat de p-value steeds zeer dicht bij 0 ligt. Dit wil zeggen dat zelfs als we een alfa-fout van 1% kiezen, het dragen van de gordel steeds nuttig is. Behalve in november is er een afwijking. Het aantal verkeersslachtoffers is in november niet significant verschillend ten opzichte van december. Dit is te wijten aan toeval.	 
 
2008-11-30 14:10:41 [Siem Van Opstal] [reply] 
Q2:Als maatstaf gebruiken we de adjusted R-squared. Deze is gelijk aan 0,7230. Dit wil zeggen dat we 72% van de wijzigingen in de verkeersslachtoffers kunnen verklaren. Het resterende gedeelte (28%) kunnen we verklaren door bijvoorbeeld uitzonderlijke weersomstandigheden. 
 
De stippellijn op de interpolation plot geeft het werkelijke aantal slachtoffers weer. De volle lijn geeft het aantal verkeersslachtoffers weer die voorspeld zijn door het model. 
 
We zien ook hier een dalende trend op lange termijn. Op het einde zien we een structurele breuk, dit is het seatbelt law effect (-226). Er treedt ook een regelmatig seizoenaal patroon op. De constante term kunnen we ook aflezen op deze grafiek. Deze zien we in de eerste piek, dit is de eerste decembermaand (2325). Op deze grafiek kunnen we een aantal outliers vaststellen (vb tussen 40 en 50), dit kan te verklaren zijn door een enorme kettingbotsing of extreem slecht weer. Dit kunnen we eventueel oplossen door een extra dummy-variabele te gebruiken, maar dit behoort niet tot de opdracht. 
 
De voorwaarden gaan we testen aan de hand van de explorative data-analyse. 
 
1e voorwaarde: Het gemiddelde moet constant zijn, en gelijk zijn aan 0.  
 
Gemiddelde gelijk aan 0? Ja, voor de hele periode, maar niet voor deelperiodes. 
Gemiddelde constant? Neen, in het begin hebben we een slechte voorspelling, dan is het gemiddelde negatief. Als we een denkbeeldige lijn zouden trekken is deze in het begin golvend en op het einde pas vlak (= constant). 
 
We zien dat het gemiddelde gelijk is aan 0, want de horizontale lijn ligt binnen het 95% betrouwbaarheidsinterval. Het gemiddelde is niet significant verschillend van 0. 
 
2e voorwaarde: Er mag geen autocorrelatie zijn. 
 
Dit wil zeggen dat er geen structuur mag zijn in de historiek van de voorspellingsfouten. Dit is wel het geval, dus er is autocorrelatie. Er is niet voldaan aan de 2e voorwaarde. 
 
Op de autocorrelation function zien we dat er autocorrelatie aanwezig is. Dit zien we aan de waarden die buiten het 95% betrouwbaarheidsinterval liggen (blauwe stippellijn). Dit wil dus zeggen dat ons model niet volledig is, en dat we eventueel een extra dummy-variabele moeten toevoegen voor andere factoren die het resultaat beïnvloeden. 
 
3e voorwaarde: De variantie moet constant zijn. 
 
4e voorwaarde: De residu’s moeten normaal verdeeld zijn. 
We zien dat de density plot een min of meer normale verdeling vertoont. 
De kwantielen van de normaalverdeling stemmen zeer goed overeen met de kwantielen van de residu’s 
 
2008-11-30 14:11:05 [Pieter Broos] [reply] 
ik zou hier willen zeggen dat de student de berekeningen correct heeft gedaan en de oplossing ook correct heeft weergegeven in het word document, één kleine bemerking: het aantal mensenlevens die gered werden is ongeveer 226, omdat we met een standaardfout rekening moeten houden.
2008-11-30 14:43:02 [Thomas Baken] [reply] 
De student heeft een correct antwoord gegeven maar hij had wel wat meer informatie kunnen geven bij zijn antwoord. Zo leek het mij belangrijk bij deze vraag te vermelden dat we gemiddeld 226 geredde levens per maand hebben na invoering van de seatbeltlaw en dat seizoenalteit een zeer grote rol speelt. We nemen een éénzijdige toets omdat we ervan uitgaan dat het dragen van een gordel geen negatief effect heeft. Het aantal geredde slachtoffers hangt van maand tot maand af. 
2008-11-30 15:14:26 [Evelyn Ongena] [reply] 
De student heeft een correct antwoord gegeven maar hij had wel wat meer informatie kunnen geven bij zijn antwoord. Zo leek het mij belangrijk bij deze vraag te vermelden dat we gemiddeld 226 geredde levens per maand hebben na invoering van de seatbeltlaw en dat seizoenalteit een zeer grote rol speelt. We nemen een éénzijdige toets omdat we ervan uitgaan dat het dragen van een gordel geen negatief effect heeft. Het aantal geredde slachtoffers hangt van maand tot maand af. 
2008-11-30 22:33:20 [Tamara Witters] [reply] 
Q1 
Dit is een correcte berekening, maar de uitleg bij de berekening van de student is zeer miniem. 
De student is er direct van uitgegaan dat dit de correcte oplossing was zonder te vergelijken met andere methoden. 
 
Er zijn een aantal werkwijzen voor het bekomen van de oplossing: 
 
1)Zonder seasonal dummies en lineaire trend 
 
http://www.freestatistics.org/blog/index.php?v=date/2008/Nov/30/t122808026316q0gpzr4c8nf79.htm 
 
In de eerste tabel zien we dat het gemiddelde aantal verkeersslachtoffers x[t] = + 1717.75147928994 wordt verminderd met 396 indien de dummy variabele 1 wordt. (dummy variabele 1 = het dragen van de autogordel) 
In de tweede tabel zien we dat de parameters 1717 en 369 geen vaste getallen zijn, maar T-verdelingen. Een T-verdeling heeft een dikkere staart en een hoge piek in het midden. A.d.H.v een T-test kunnen we zien of we te maken hebben met een T-verdeling. T-test= (geschatte parameter – nulhypothese ) / geschatte standaardfout  1717-0/20 
Indien de T-test groter is dan 2 (zien naar de absolute waarde) dan kunnen we stellen dat het resultaat SIGNIFICANT verschillend is van 0. Beide parameters zijn significant verschillend van 0.  
 
Als we dan kijken naar de Residual standard deviation bedraagt deze 260. Dit is de fout die we zouden maken als we een voorspelling maken.  
Vervolgens kijken we naar het density plot en zien we een scheve verdeling, deze is niet conform met de assumpties.  
Ten slotte zien we ook naar de autocorrelatie functie en zien we dat er veel autocorrelatie is met een significant verschillend patroon. 
We kunnen besluiten dat dit geen goede juiste methode. 
 
2)Met monthly dummies en zonder trend 
 
http://www.freestatistics.org/blog/index.php?v=date/2008/Nov/30/t1228081719xfram486cv2abli.htm 
 
De Pc gaat nu zelf reeksen toevoegen. In de eerste tabel zien we dat er gemiddeld 2165 verkeersslachtoffers zijn. Dit gemiddelde is genomen van de referentiemaand december en hiermee worden alle maanden vergeleken. Zo zien we dat is november het aantal verkeerslachtoffers: 2165 – 116 bedraagt. De seizoenseffecten zijn significant verschillend behalve voor november (twijfelgeval) 
Nu zien we dat de R-squared 0, 66 bedraagt, en bijgevolg verebetrd is vergeleken met de 1e berekening.  
De density plot heeft nu ook een minder scheve verdeling.  
Er is nu ook een andere vorm van autocorrelatie, dit heeft te maken met het LT-effect. 
We kunnen besluiten dat dit model ons al een juister beeld geeft vergeleken met het vorige.  
 
3)Met dummies en trend 
 
http://www.freestatistics.org/blog/index.php?v=date/2008/Nov/23/t1227453256tskdvxa4fmufsw4.htm 
 
Nu hebben we de variabele t toegevoegt  
De scheefheid die we duidelijk merkten in vorige berekeningen is sterk afgenomen.  
Conclusie : dit is de beste methode 
 
 
2008-11-30 22:38:47 [Tamara Witters] [reply] 
Q2 
Deze vraag moest je oplossen aan de hand van 4 assumpties. 
Voor de oplossing sluit ik mij aan bij de feedback van Siem.
2008-12-01 22:21:51 [Kristof Augustyns] [reply] 
Dit is een juiste berekening en juiste conclusie. 
De leerlingen die hiervoor een veel te lange reactie schreven, zijn slijmballen! 
In die maand zouden er 226.385033602658 minder doden vallen als er een gordel werd gedragen. 
Ook erbij zeggen dat december de gevaarlijkste maand is omdat daar de invloed van de gordel het minste is. 
April doet het beste. 
De t-waarde is de potentieele waarde die men er nog eens moet aftrekken doordat elke maand alles wel verbeterd (wegdek, auto's ...)
2008-12-01 22:24:24 [Kristof Augustyns] [reply] 
Q2: Wanneer we kijken naar de R-square van 0.7418â€¦ dan weten we dat we ongeveer 74% van de originele variabiliteit hebben verklaard. De R-square waarde geeft aan hoe goed het model de data weergeeft. (een r-square van 1 is dus ideaal). Waneer we willen weten of dit toeval is kijken we naar de F-test. Deze geeft de verdeling weer. De p-value is zeer klein, dus is hier significant verschillend van 0. Het is dus niet aan toeval te wijten.  
 
Je moet ook elke grafiek apart bespreken. De enige die je besproken hebt is wel juist.  
 
actuals en interpolations: Hier zien we inderdaad een dalende trend van het aantal slachtoffers. De verplichting van het dragen van de gordel is hier opvallend terug te vinden, namelijk het niveauverschil helemaal rechts.  
 
Het histogram en de qq-plot is vrij normaal verdeeld. Ze geeft geen perfecte normaalverdeling weer en vooral aan de 2 staarten zien we een scheefverdeling. Dit kan je ook terug vinden in de volgende QQ-plot. De theoretische kwantielen komen goed overeen met de sample kwantielen.

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Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
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Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25001&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25001&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25001&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	5 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation
y[t] = + 2324.06337310277 -226.385033602658x[t] -451.374973256311M1[t] -635.461053323769M2[t] -583.133697991392M3[t] -694.556342659015M4[t] -555.478987326638M5[t] -609.464131994261M6[t] -532.074276661884M7[t] -515.434421329507M8[t] -460.857065997131M9[t] -319.717210664754M10[t] -118.389855332377M11[t] -1.76485533237685t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  2324.06337310277 -226.385033602658x[t] -451.374973256311M1[t] -635.461053323769M2[t] -583.133697991392M3[t] -694.556342659015M4[t] -555.478987326638M5[t] -609.464131994261M6[t] -532.074276661884M7[t] -515.434421329507M8[t] -460.857065997131M9[t] -319.717210664754M10[t] -118.389855332377M11[t] -1.76485533237685t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25001&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  2324.06337310277 -226.385033602658x[t] -451.374973256311M1[t] -635.461053323769M2[t] -583.133697991392M3[t] -694.556342659015M4[t] -555.478987326638M5[t] -609.464131994261M6[t] -532.074276661884M7[t] -515.434421329507M8[t] -460.857065997131M9[t] -319.717210664754M10[t] -118.389855332377M11[t] -1.76485533237685t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25001&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25001&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
y[t] = + 2324.06337310277 -226.385033602658x[t] -451.374973256311M1[t] -635.461053323769M2[t] -583.133697991392M3[t] -694.556342659015M4[t] -555.478987326638M5[t] -609.464131994261M6[t] -532.074276661884M7[t] -515.434421329507M8[t] -460.857065997131M9[t] -319.717210664754M10[t] -118.389855332377M11[t] -1.76485533237685t + 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)	2324.06337310277	44.029939	52.7837	0	0
x	-226.385033602658	41.037226	-5.5166	0	0
M1	-451.374973256311	53.942919	-8.3676	0	0
M2	-635.461053323769	53.941479	-11.7806	0	0
M3	-583.133697991392	53.931287	-10.8125	0	0
M4	-694.556342659015	53.922166	-12.8807	0	0
M5	-555.478987326638	53.914117	-10.303	0	0
M6	-609.464131994261	53.907141	-11.3058	0	0
M7	-532.074276661884	53.901237	-9.8713	0	0
M8	-515.434421329507	53.896405	-9.5634	0	0
M9	-460.857065997131	53.892648	-8.5514	0	0
M10	-319.717210664754	53.889963	-5.9328	0	0
M11	-118.389855332377	53.888353	-2.1969	0.029316	0.014658
t	-1.76485533237685	0.240551	-7.3367	0	0

\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) & 2324.06337310277 & 44.029939 & 52.7837 & 0 & 0 \tabularnewline
x & -226.385033602658 & 41.037226 & -5.5166 & 0 & 0 \tabularnewline
M1 & -451.374973256311 & 53.942919 & -8.3676 & 0 & 0 \tabularnewline
M2 & -635.461053323769 & 53.941479 & -11.7806 & 0 & 0 \tabularnewline
M3 & -583.133697991392 & 53.931287 & -10.8125 & 0 & 0 \tabularnewline
M4 & -694.556342659015 & 53.922166 & -12.8807 & 0 & 0 \tabularnewline
M5 & -555.478987326638 & 53.914117 & -10.303 & 0 & 0 \tabularnewline
M6 & -609.464131994261 & 53.907141 & -11.3058 & 0 & 0 \tabularnewline
M7 & -532.074276661884 & 53.901237 & -9.8713 & 0 & 0 \tabularnewline
M8 & -515.434421329507 & 53.896405 & -9.5634 & 0 & 0 \tabularnewline
M9 & -460.857065997131 & 53.892648 & -8.5514 & 0 & 0 \tabularnewline
M10 & -319.717210664754 & 53.889963 & -5.9328 & 0 & 0 \tabularnewline
M11 & -118.389855332377 & 53.888353 & -2.1969 & 0.029316 & 0.014658 \tabularnewline
t & -1.76485533237685 & 0.240551 & -7.3367 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25001&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]2324.06337310277[/C][C]44.029939[/C][C]52.7837[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]x[/C][C]-226.385033602658[/C][C]41.037226[/C][C]-5.5166[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-451.374973256311[/C][C]53.942919[/C][C]-8.3676[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M2[/C][C]-635.461053323769[/C][C]53.941479[/C][C]-11.7806[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M3[/C][C]-583.133697991392[/C][C]53.931287[/C][C]-10.8125[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M4[/C][C]-694.556342659015[/C][C]53.922166[/C][C]-12.8807[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M5[/C][C]-555.478987326638[/C][C]53.914117[/C][C]-10.303[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M6[/C][C]-609.464131994261[/C][C]53.907141[/C][C]-11.3058[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M7[/C][C]-532.074276661884[/C][C]53.901237[/C][C]-9.8713[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M8[/C][C]-515.434421329507[/C][C]53.896405[/C][C]-9.5634[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M9[/C][C]-460.857065997131[/C][C]53.892648[/C][C]-8.5514[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M10[/C][C]-319.717210664754[/C][C]53.889963[/C][C]-5.9328[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M11[/C][C]-118.389855332377[/C][C]53.888353[/C][C]-2.1969[/C][C]0.029316[/C][C]0.014658[/C][/ROW]
[ROW][C]t[/C][C]-1.76485533237685[/C][C]0.240551[/C][C]-7.3367[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25001&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25001&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)	2324.06337310277	44.029939	52.7837	0	0
x	-226.385033602658	41.037226	-5.5166	0	0
M1	-451.374973256311	53.942919	-8.3676	0	0
M2	-635.461053323769	53.941479	-11.7806	0	0
M3	-583.133697991392	53.931287	-10.8125	0	0
M4	-694.556342659015	53.922166	-12.8807	0	0
M5	-555.478987326638	53.914117	-10.303	0	0
M6	-609.464131994261	53.907141	-11.3058	0	0
M7	-532.074276661884	53.901237	-9.8713	0	0
M8	-515.434421329507	53.896405	-9.5634	0	0
M9	-460.857065997131	53.892648	-8.5514	0	0
M10	-319.717210664754	53.889963	-5.9328	0	0
M11	-118.389855332377	53.888353	-2.1969	0.029316	0.014658
t	-1.76485533237685	0.240551	-7.3367	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.861322441473346
R-squared	0.741876348185605
Adjusted R-squared	0.723024620805902
F-TEST (value)	39.3532291891913
F-TEST (DF numerator)	13
F-TEST (DF denominator)	178
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	152.417759557721
Sum Squared Residuals	4135148.87028996

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.861322441473346 \tabularnewline
R-squared & 0.741876348185605 \tabularnewline
Adjusted R-squared & 0.723024620805902 \tabularnewline
F-TEST (value) & 39.3532291891913 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 178 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 152.417759557721 \tabularnewline
Sum Squared Residuals & 4135148.87028996 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25001&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.861322441473346[/C][/ROW]
[ROW][C]R-squared[/C][C]0.741876348185605[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.723024620805902[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]39.3532291891913[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]178[/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]152.417759557721[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]4135148.87028996[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25001&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25001&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	0.861322441473346
R-squared	0.741876348185605
Adjusted R-squared	0.723024620805902
F-TEST (value)	39.3532291891913
F-TEST (DF numerator)	13
F-TEST (DF denominator)	178
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	152.417759557721
Sum Squared Residuals	4135148.87028996

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	1687	1870.92354451408	-183.923544514078
2	1508	1685.07260911425	-177.072609114249
3	1507	1735.63510911425	-228.635109114249
4	1385	1622.44760911425	-237.447609114250
5	1632	1759.76010911425	-127.760109114249
6	1511	1704.01010911425	-193.010109114250
7	1559	1779.63510911425	-220.635109114249
8	1630	1794.51010911425	-164.510109114249
9	1579	1847.32260911425	-268.322609114249
10	1653	1986.69760911425	-333.697609114249
11	2152	2186.26010911425	-34.2601091142491
12	2148	2302.88510911425	-154.885109114249
13	1752	1849.74528052556	-97.7452805255611
14	1765	1663.89434512573	101.105654874273
15	1717	1714.45684512573	2.54315487427314
16	1558	1601.26934512573	-43.2693451257269
17	1575	1738.58184512573	-163.581845125727
18	1520	1682.83184512573	-162.831845125727
19	1805	1758.45684512573	46.5431548742731
20	1800	1773.33184512573	26.6681548742731
21	1719	1826.14434512573	-107.144345125727
22	2008	1965.51934512573	42.4806548742732
23	2242	2165.08184512573	76.9181548742732
24	2478	2281.70684512573	196.293154874273
25	2030	1828.56701653704	201.432983462961
26	1655	1642.71608113720	12.2839188627954
27	1693	1693.27858113720	-0.278581137204616
28	1623	1580.09108113720	42.9089188627954
29	1805	1717.40358113720	87.5964188627954
30	1746	1661.65358113720	84.3464188627954
31	1795	1737.27858113720	57.7214188627954
32	1926	1752.15358113720	173.846418862795
33	1619	1804.96608113720	-185.966081137205
34	1992	1944.34108113720	47.6589188627954
35	2233	2143.90358113720	89.0964188627954
36	2192	2260.52858113720	-68.5285811372045
37	2080	1807.38875254852	272.611247451483
38	1768	1621.53781714868	146.462182851318
39	1835	1672.10031714868	162.899682851318
40	1569	1558.91281714868	10.0871828513176
41	1976	1696.22531714868	279.774682851318
42	1853	1640.47531714868	212.524682851318
43	1965	1716.10031714868	248.899682851318
44	1689	1730.97531714868	-41.9753171486824
45	1778	1783.78781714868	-5.78781714868237
46	1976	1923.16281714868	52.8371828513176
47	2397	2122.72531714868	274.274682851318
48	2654	2239.35031714868	414.649682851318
49	2097	1786.21048855999	310.789511440006
50	1963	1600.35955316016	362.64044683984
51	1677	1650.92205316016	26.0779468398399
52	1941	1537.73455316016	403.26544683984
53	2003	1675.04705316016	327.95294683984
54	1813	1619.29705316016	193.70294683984
55	2012	1694.92205316016	317.07794683984
56	1912	1709.79705316016	202.202946839840
57	2084	1762.60955316016	321.39044683984
58	2080	1901.98455316016	178.01544683984
59	2118	2101.54705316016	16.4529468398399
60	2150	2218.17205316016	-68.1720531601601
61	1608	1765.03222457147	-157.032224571472
62	1503	1579.18128917164	-76.1812891716379
63	1548	1629.74378917164	-81.7437891716379
64	1382	1516.55628917164	-134.556289171638
65	1731	1653.86878917164	77.1312108283621
66	1798	1598.11878917164	199.881210828362
67	1779	1673.74378917164	105.256210828362
68	1887	1688.61878917164	198.381210828362
69	2004	1741.43128917164	262.568710828362
70	2077	1880.80628917164	196.193710828362
71	2092	2080.36878917164	11.6312108283621
72	2051	2196.99378917164	-145.993789171638
73	1577	1743.85396058295	-166.85396058295
74	1356	1558.00302518312	-202.003025183116
75	1652	1608.56552518312	43.4344748168844
76	1382	1495.37802518312	-113.378025183116
77	1519	1632.69052518312	-113.690525183116
78	1421	1576.94052518312	-155.940525183116
79	1442	1652.56552518312	-210.565525183116
80	1543	1667.44052518312	-124.440525183116
81	1656	1720.25302518312	-64.2530251831156
82	1561	1859.62802518312	-298.628025183116
83	1905	2059.19052518312	-154.190525183116
84	2199	2175.81552518312	23.1844748168844
85	1473	1722.67569659443	-249.675696594427
86	1655	1536.82476119459	118.175238805407
87	1407	1587.38726119459	-180.387261194593
88	1395	1474.19976119459	-79.1997611945933
89	1530	1611.51226119459	-81.5122611945934
90	1309	1555.76226119459	-246.762261194593
91	1526	1631.38726119459	-105.387261194593
92	1327	1646.26226119459	-319.262261194593
93	1627	1699.07476119459	-72.0747611945934
94	1748	1838.44976119459	-90.4497611945934
95	1958	2038.01226119459	-80.0122611945934
96	2274	2154.63726119459	119.362738805407
97	1648	1701.49743260591	-53.4974326059054
98	1401	1515.64649720607	-114.646497206071
99	1411	1566.20899720607	-155.208997206071
100	1403	1453.02149720607	-50.0214972060711
101	1394	1590.33399720607	-196.333997206071
102	1520	1534.58399720607	-14.5839972060711
103	1528	1610.20899720607	-82.2089972060712
104	1643	1625.08399720607	17.9160027939289
105	1515	1677.89649720607	-162.896497206071
106	1685	1817.27149720607	-132.271497206071
107	2000	2016.83399720607	-16.8339972060712
108	2215	2133.45899720607	81.5410027939289
109	1956	1680.31916861738	275.680831382617
110	1462	1494.46823321755	-32.4682332175488
111	1563	1545.03073321755	17.9692667824511
112	1459	1431.84323321755	27.1567667824512
113	1446	1569.15573321755	-123.155733217549
114	1622	1513.40573321755	108.594266782451
115	1657	1589.03073321755	67.9692667824512
116	1638	1603.90573321755	34.0942667824511
117	1643	1656.71823321755	-13.7182332175489
118	1683	1796.09323321755	-113.093233217549
119	2050	1995.65573321755	54.3442667824512
120	2262	2112.28073321755	149.719266782451
121	1813	1659.14090462886	153.859095371139
122	1445	1473.28996922903	-28.2899692290266
123	1762	1523.85246922903	238.147530770973
124	1461	1410.66496922903	50.3350307709734
125	1556	1547.97746922903	8.02253077097338
126	1431	1492.22746922903	-61.2274692290265
127	1427	1567.85246922903	-140.852469229027
128	1554	1582.72746922903	-28.7274692290267
129	1645	1635.53996922903	9.4600307709734
130	1653	1774.91496922903	-121.914969229027
131	2016	1974.47746922903	41.5225307709734
132	2207	2091.10246922903	115.897530770973
133	1665	1637.96264064034	27.0373593596614
134	1361	1452.11170524050	-91.1117052405044
135	1506	1502.67420524050	3.32579475949564
136	1360	1389.48670524050	-29.4867052405044
137	1453	1526.79920524050	-73.7992052405043
138	1522	1471.04920524050	50.9507947594957
139	1460	1546.67420524050	-86.6742052405043
140	1552	1561.54920524050	-9.5492052405044
141	1548	1614.36170524050	-66.3617052405044
142	1827	1753.73670524050	73.2632947594957
143	1737	1953.29920524050	-216.299205240504
144	1941	2069.92420524050	-128.924205240504
145	1474	1616.78437665182	-142.784376651816
146	1458	1430.93344125198	27.0665587480179
147	1542	1481.49594125198	60.5040587480179
148	1404	1368.30844125198	35.6915587480179
149	1522	1505.62094125198	16.3790587480179
150	1385	1449.87094125198	-64.870941251982
151	1641	1525.49594125198	115.504058748018
152	1510	1540.37094125198	-30.3709412519821
153	1681	1593.18344125198	87.816558748018
154	1938	1732.55844125198	205.441558748018
155	1868	1932.12094125198	-64.1209412519821
156	1726	2048.74594125198	-322.745941251982
157	1456	1595.60611266329	-139.606112663294
158	1445	1409.75517726346	35.2448227365402
159	1456	1460.31767726346	-4.31767726345983
160	1365	1347.13017726346	17.8698227365402
161	1487	1484.44267726346	2.55732273654013
162	1558	1428.69267726346	129.307322736540
163	1488	1504.31767726346	-16.3176772634599
164	1684	1519.19267726346	164.80732273654
165	1594	1572.00517726346	21.9948227365402
166	1850	1711.38017726346	138.619822736540
167	1998	1910.94267726346	87.05732273654
168	2079	2027.56767726346	51.4323227365402
169	1494	1574.42784867477	-80.4278486747719
170	1057	1162.19187967228	-105.191879672280
171	1218	1212.75437967228	5.2456203277202
172	1168	1099.56687967228	68.4331203277202
173	1236	1236.87937967228	-0.879379672279648
174	1076	1181.12937967228	-105.129379672280
175	1174	1256.75437967228	-82.7543796722796
176	1139	1271.62937967228	-132.629379672280
177	1427	1324.44187967228	102.558120327720
178	1487	1463.81687967228	23.1831203277203
179	1483	1663.37937967228	-180.379379672280
180	1513	1780.00437967228	-267.004379672280
181	1357	1326.86455108359	30.1354489164084
182	1165	1141.01361568376	23.9863843162425
183	1282	1191.57611568376	90.4238843162424
184	1110	1078.38861568376	31.6113843162425
185	1297	1215.70111568376	81.2988843162426
186	1185	1159.95111568376	25.0488843162426
187	1222	1235.57611568376	-13.5761156837574
188	1284	1250.45111568376	33.5488843162426
189	1444	1303.26361568376	140.736384316243
190	1575	1442.63861568376	132.361384316243
191	1737	1642.20111568376	94.7988843162425
192	1763	1758.82611568376	4.17388431624252

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1687 & 1870.92354451408 & -183.923544514078 \tabularnewline
2 & 1508 & 1685.07260911425 & -177.072609114249 \tabularnewline
3 & 1507 & 1735.63510911425 & -228.635109114249 \tabularnewline
4 & 1385 & 1622.44760911425 & -237.447609114250 \tabularnewline
5 & 1632 & 1759.76010911425 & -127.760109114249 \tabularnewline
6 & 1511 & 1704.01010911425 & -193.010109114250 \tabularnewline
7 & 1559 & 1779.63510911425 & -220.635109114249 \tabularnewline
8 & 1630 & 1794.51010911425 & -164.510109114249 \tabularnewline
9 & 1579 & 1847.32260911425 & -268.322609114249 \tabularnewline
10 & 1653 & 1986.69760911425 & -333.697609114249 \tabularnewline
11 & 2152 & 2186.26010911425 & -34.2601091142491 \tabularnewline
12 & 2148 & 2302.88510911425 & -154.885109114249 \tabularnewline
13 & 1752 & 1849.74528052556 & -97.7452805255611 \tabularnewline
14 & 1765 & 1663.89434512573 & 101.105654874273 \tabularnewline
15 & 1717 & 1714.45684512573 & 2.54315487427314 \tabularnewline
16 & 1558 & 1601.26934512573 & -43.2693451257269 \tabularnewline
17 & 1575 & 1738.58184512573 & -163.581845125727 \tabularnewline
18 & 1520 & 1682.83184512573 & -162.831845125727 \tabularnewline
19 & 1805 & 1758.45684512573 & 46.5431548742731 \tabularnewline
20 & 1800 & 1773.33184512573 & 26.6681548742731 \tabularnewline
21 & 1719 & 1826.14434512573 & -107.144345125727 \tabularnewline
22 & 2008 & 1965.51934512573 & 42.4806548742732 \tabularnewline
23 & 2242 & 2165.08184512573 & 76.9181548742732 \tabularnewline
24 & 2478 & 2281.70684512573 & 196.293154874273 \tabularnewline
25 & 2030 & 1828.56701653704 & 201.432983462961 \tabularnewline
26 & 1655 & 1642.71608113720 & 12.2839188627954 \tabularnewline
27 & 1693 & 1693.27858113720 & -0.278581137204616 \tabularnewline
28 & 1623 & 1580.09108113720 & 42.9089188627954 \tabularnewline
29 & 1805 & 1717.40358113720 & 87.5964188627954 \tabularnewline
30 & 1746 & 1661.65358113720 & 84.3464188627954 \tabularnewline
31 & 1795 & 1737.27858113720 & 57.7214188627954 \tabularnewline
32 & 1926 & 1752.15358113720 & 173.846418862795 \tabularnewline
33 & 1619 & 1804.96608113720 & -185.966081137205 \tabularnewline
34 & 1992 & 1944.34108113720 & 47.6589188627954 \tabularnewline
35 & 2233 & 2143.90358113720 & 89.0964188627954 \tabularnewline
36 & 2192 & 2260.52858113720 & -68.5285811372045 \tabularnewline
37 & 2080 & 1807.38875254852 & 272.611247451483 \tabularnewline
38 & 1768 & 1621.53781714868 & 146.462182851318 \tabularnewline
39 & 1835 & 1672.10031714868 & 162.899682851318 \tabularnewline
40 & 1569 & 1558.91281714868 & 10.0871828513176 \tabularnewline
41 & 1976 & 1696.22531714868 & 279.774682851318 \tabularnewline
42 & 1853 & 1640.47531714868 & 212.524682851318 \tabularnewline
43 & 1965 & 1716.10031714868 & 248.899682851318 \tabularnewline
44 & 1689 & 1730.97531714868 & -41.9753171486824 \tabularnewline
45 & 1778 & 1783.78781714868 & -5.78781714868237 \tabularnewline
46 & 1976 & 1923.16281714868 & 52.8371828513176 \tabularnewline
47 & 2397 & 2122.72531714868 & 274.274682851318 \tabularnewline
48 & 2654 & 2239.35031714868 & 414.649682851318 \tabularnewline
49 & 2097 & 1786.21048855999 & 310.789511440006 \tabularnewline
50 & 1963 & 1600.35955316016 & 362.64044683984 \tabularnewline
51 & 1677 & 1650.92205316016 & 26.0779468398399 \tabularnewline
52 & 1941 & 1537.73455316016 & 403.26544683984 \tabularnewline
53 & 2003 & 1675.04705316016 & 327.95294683984 \tabularnewline
54 & 1813 & 1619.29705316016 & 193.70294683984 \tabularnewline
55 & 2012 & 1694.92205316016 & 317.07794683984 \tabularnewline
56 & 1912 & 1709.79705316016 & 202.202946839840 \tabularnewline
57 & 2084 & 1762.60955316016 & 321.39044683984 \tabularnewline
58 & 2080 & 1901.98455316016 & 178.01544683984 \tabularnewline
59 & 2118 & 2101.54705316016 & 16.4529468398399 \tabularnewline
60 & 2150 & 2218.17205316016 & -68.1720531601601 \tabularnewline
61 & 1608 & 1765.03222457147 & -157.032224571472 \tabularnewline
62 & 1503 & 1579.18128917164 & -76.1812891716379 \tabularnewline
63 & 1548 & 1629.74378917164 & -81.7437891716379 \tabularnewline
64 & 1382 & 1516.55628917164 & -134.556289171638 \tabularnewline
65 & 1731 & 1653.86878917164 & 77.1312108283621 \tabularnewline
66 & 1798 & 1598.11878917164 & 199.881210828362 \tabularnewline
67 & 1779 & 1673.74378917164 & 105.256210828362 \tabularnewline
68 & 1887 & 1688.61878917164 & 198.381210828362 \tabularnewline
69 & 2004 & 1741.43128917164 & 262.568710828362 \tabularnewline
70 & 2077 & 1880.80628917164 & 196.193710828362 \tabularnewline
71 & 2092 & 2080.36878917164 & 11.6312108283621 \tabularnewline
72 & 2051 & 2196.99378917164 & -145.993789171638 \tabularnewline
73 & 1577 & 1743.85396058295 & -166.85396058295 \tabularnewline
74 & 1356 & 1558.00302518312 & -202.003025183116 \tabularnewline
75 & 1652 & 1608.56552518312 & 43.4344748168844 \tabularnewline
76 & 1382 & 1495.37802518312 & -113.378025183116 \tabularnewline
77 & 1519 & 1632.69052518312 & -113.690525183116 \tabularnewline
78 & 1421 & 1576.94052518312 & -155.940525183116 \tabularnewline
79 & 1442 & 1652.56552518312 & -210.565525183116 \tabularnewline
80 & 1543 & 1667.44052518312 & -124.440525183116 \tabularnewline
81 & 1656 & 1720.25302518312 & -64.2530251831156 \tabularnewline
82 & 1561 & 1859.62802518312 & -298.628025183116 \tabularnewline
83 & 1905 & 2059.19052518312 & -154.190525183116 \tabularnewline
84 & 2199 & 2175.81552518312 & 23.1844748168844 \tabularnewline
85 & 1473 & 1722.67569659443 & -249.675696594427 \tabularnewline
86 & 1655 & 1536.82476119459 & 118.175238805407 \tabularnewline
87 & 1407 & 1587.38726119459 & -180.387261194593 \tabularnewline
88 & 1395 & 1474.19976119459 & -79.1997611945933 \tabularnewline
89 & 1530 & 1611.51226119459 & -81.5122611945934 \tabularnewline
90 & 1309 & 1555.76226119459 & -246.762261194593 \tabularnewline
91 & 1526 & 1631.38726119459 & -105.387261194593 \tabularnewline
92 & 1327 & 1646.26226119459 & -319.262261194593 \tabularnewline
93 & 1627 & 1699.07476119459 & -72.0747611945934 \tabularnewline
94 & 1748 & 1838.44976119459 & -90.4497611945934 \tabularnewline
95 & 1958 & 2038.01226119459 & -80.0122611945934 \tabularnewline
96 & 2274 & 2154.63726119459 & 119.362738805407 \tabularnewline
97 & 1648 & 1701.49743260591 & -53.4974326059054 \tabularnewline
98 & 1401 & 1515.64649720607 & -114.646497206071 \tabularnewline
99 & 1411 & 1566.20899720607 & -155.208997206071 \tabularnewline
100 & 1403 & 1453.02149720607 & -50.0214972060711 \tabularnewline
101 & 1394 & 1590.33399720607 & -196.333997206071 \tabularnewline
102 & 1520 & 1534.58399720607 & -14.5839972060711 \tabularnewline
103 & 1528 & 1610.20899720607 & -82.2089972060712 \tabularnewline
104 & 1643 & 1625.08399720607 & 17.9160027939289 \tabularnewline
105 & 1515 & 1677.89649720607 & -162.896497206071 \tabularnewline
106 & 1685 & 1817.27149720607 & -132.271497206071 \tabularnewline
107 & 2000 & 2016.83399720607 & -16.8339972060712 \tabularnewline
108 & 2215 & 2133.45899720607 & 81.5410027939289 \tabularnewline
109 & 1956 & 1680.31916861738 & 275.680831382617 \tabularnewline
110 & 1462 & 1494.46823321755 & -32.4682332175488 \tabularnewline
111 & 1563 & 1545.03073321755 & 17.9692667824511 \tabularnewline
112 & 1459 & 1431.84323321755 & 27.1567667824512 \tabularnewline
113 & 1446 & 1569.15573321755 & -123.155733217549 \tabularnewline
114 & 1622 & 1513.40573321755 & 108.594266782451 \tabularnewline
115 & 1657 & 1589.03073321755 & 67.9692667824512 \tabularnewline
116 & 1638 & 1603.90573321755 & 34.0942667824511 \tabularnewline
117 & 1643 & 1656.71823321755 & -13.7182332175489 \tabularnewline
118 & 1683 & 1796.09323321755 & -113.093233217549 \tabularnewline
119 & 2050 & 1995.65573321755 & 54.3442667824512 \tabularnewline
120 & 2262 & 2112.28073321755 & 149.719266782451 \tabularnewline
121 & 1813 & 1659.14090462886 & 153.859095371139 \tabularnewline
122 & 1445 & 1473.28996922903 & -28.2899692290266 \tabularnewline
123 & 1762 & 1523.85246922903 & 238.147530770973 \tabularnewline
124 & 1461 & 1410.66496922903 & 50.3350307709734 \tabularnewline
125 & 1556 & 1547.97746922903 & 8.02253077097338 \tabularnewline
126 & 1431 & 1492.22746922903 & -61.2274692290265 \tabularnewline
127 & 1427 & 1567.85246922903 & -140.852469229027 \tabularnewline
128 & 1554 & 1582.72746922903 & -28.7274692290267 \tabularnewline
129 & 1645 & 1635.53996922903 & 9.4600307709734 \tabularnewline
130 & 1653 & 1774.91496922903 & -121.914969229027 \tabularnewline
131 & 2016 & 1974.47746922903 & 41.5225307709734 \tabularnewline
132 & 2207 & 2091.10246922903 & 115.897530770973 \tabularnewline
133 & 1665 & 1637.96264064034 & 27.0373593596614 \tabularnewline
134 & 1361 & 1452.11170524050 & -91.1117052405044 \tabularnewline
135 & 1506 & 1502.67420524050 & 3.32579475949564 \tabularnewline
136 & 1360 & 1389.48670524050 & -29.4867052405044 \tabularnewline
137 & 1453 & 1526.79920524050 & -73.7992052405043 \tabularnewline
138 & 1522 & 1471.04920524050 & 50.9507947594957 \tabularnewline
139 & 1460 & 1546.67420524050 & -86.6742052405043 \tabularnewline
140 & 1552 & 1561.54920524050 & -9.5492052405044 \tabularnewline
141 & 1548 & 1614.36170524050 & -66.3617052405044 \tabularnewline
142 & 1827 & 1753.73670524050 & 73.2632947594957 \tabularnewline
143 & 1737 & 1953.29920524050 & -216.299205240504 \tabularnewline
144 & 1941 & 2069.92420524050 & -128.924205240504 \tabularnewline
145 & 1474 & 1616.78437665182 & -142.784376651816 \tabularnewline
146 & 1458 & 1430.93344125198 & 27.0665587480179 \tabularnewline
147 & 1542 & 1481.49594125198 & 60.5040587480179 \tabularnewline
148 & 1404 & 1368.30844125198 & 35.6915587480179 \tabularnewline
149 & 1522 & 1505.62094125198 & 16.3790587480179 \tabularnewline
150 & 1385 & 1449.87094125198 & -64.870941251982 \tabularnewline
151 & 1641 & 1525.49594125198 & 115.504058748018 \tabularnewline
152 & 1510 & 1540.37094125198 & -30.3709412519821 \tabularnewline
153 & 1681 & 1593.18344125198 & 87.816558748018 \tabularnewline
154 & 1938 & 1732.55844125198 & 205.441558748018 \tabularnewline
155 & 1868 & 1932.12094125198 & -64.1209412519821 \tabularnewline
156 & 1726 & 2048.74594125198 & -322.745941251982 \tabularnewline
157 & 1456 & 1595.60611266329 & -139.606112663294 \tabularnewline
158 & 1445 & 1409.75517726346 & 35.2448227365402 \tabularnewline
159 & 1456 & 1460.31767726346 & -4.31767726345983 \tabularnewline
160 & 1365 & 1347.13017726346 & 17.8698227365402 \tabularnewline
161 & 1487 & 1484.44267726346 & 2.55732273654013 \tabularnewline
162 & 1558 & 1428.69267726346 & 129.307322736540 \tabularnewline
163 & 1488 & 1504.31767726346 & -16.3176772634599 \tabularnewline
164 & 1684 & 1519.19267726346 & 164.80732273654 \tabularnewline
165 & 1594 & 1572.00517726346 & 21.9948227365402 \tabularnewline
166 & 1850 & 1711.38017726346 & 138.619822736540 \tabularnewline
167 & 1998 & 1910.94267726346 & 87.05732273654 \tabularnewline
168 & 2079 & 2027.56767726346 & 51.4323227365402 \tabularnewline
169 & 1494 & 1574.42784867477 & -80.4278486747719 \tabularnewline
170 & 1057 & 1162.19187967228 & -105.191879672280 \tabularnewline
171 & 1218 & 1212.75437967228 & 5.2456203277202 \tabularnewline
172 & 1168 & 1099.56687967228 & 68.4331203277202 \tabularnewline
173 & 1236 & 1236.87937967228 & -0.879379672279648 \tabularnewline
174 & 1076 & 1181.12937967228 & -105.129379672280 \tabularnewline
175 & 1174 & 1256.75437967228 & -82.7543796722796 \tabularnewline
176 & 1139 & 1271.62937967228 & -132.629379672280 \tabularnewline
177 & 1427 & 1324.44187967228 & 102.558120327720 \tabularnewline
178 & 1487 & 1463.81687967228 & 23.1831203277203 \tabularnewline
179 & 1483 & 1663.37937967228 & -180.379379672280 \tabularnewline
180 & 1513 & 1780.00437967228 & -267.004379672280 \tabularnewline
181 & 1357 & 1326.86455108359 & 30.1354489164084 \tabularnewline
182 & 1165 & 1141.01361568376 & 23.9863843162425 \tabularnewline
183 & 1282 & 1191.57611568376 & 90.4238843162424 \tabularnewline
184 & 1110 & 1078.38861568376 & 31.6113843162425 \tabularnewline
185 & 1297 & 1215.70111568376 & 81.2988843162426 \tabularnewline
186 & 1185 & 1159.95111568376 & 25.0488843162426 \tabularnewline
187 & 1222 & 1235.57611568376 & -13.5761156837574 \tabularnewline
188 & 1284 & 1250.45111568376 & 33.5488843162426 \tabularnewline
189 & 1444 & 1303.26361568376 & 140.736384316243 \tabularnewline
190 & 1575 & 1442.63861568376 & 132.361384316243 \tabularnewline
191 & 1737 & 1642.20111568376 & 94.7988843162425 \tabularnewline
192 & 1763 & 1758.82611568376 & 4.17388431624252 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25001&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]1687[/C][C]1870.92354451408[/C][C]-183.923544514078[/C][/ROW]
[ROW][C]2[/C][C]1508[/C][C]1685.07260911425[/C][C]-177.072609114249[/C][/ROW]
[ROW][C]3[/C][C]1507[/C][C]1735.63510911425[/C][C]-228.635109114249[/C][/ROW]
[ROW][C]4[/C][C]1385[/C][C]1622.44760911425[/C][C]-237.447609114250[/C][/ROW]
[ROW][C]5[/C][C]1632[/C][C]1759.76010911425[/C][C]-127.760109114249[/C][/ROW]
[ROW][C]6[/C][C]1511[/C][C]1704.01010911425[/C][C]-193.010109114250[/C][/ROW]
[ROW][C]7[/C][C]1559[/C][C]1779.63510911425[/C][C]-220.635109114249[/C][/ROW]
[ROW][C]8[/C][C]1630[/C][C]1794.51010911425[/C][C]-164.510109114249[/C][/ROW]
[ROW][C]9[/C][C]1579[/C][C]1847.32260911425[/C][C]-268.322609114249[/C][/ROW]
[ROW][C]10[/C][C]1653[/C][C]1986.69760911425[/C][C]-333.697609114249[/C][/ROW]
[ROW][C]11[/C][C]2152[/C][C]2186.26010911425[/C][C]-34.2601091142491[/C][/ROW]
[ROW][C]12[/C][C]2148[/C][C]2302.88510911425[/C][C]-154.885109114249[/C][/ROW]
[ROW][C]13[/C][C]1752[/C][C]1849.74528052556[/C][C]-97.7452805255611[/C][/ROW]
[ROW][C]14[/C][C]1765[/C][C]1663.89434512573[/C][C]101.105654874273[/C][/ROW]
[ROW][C]15[/C][C]1717[/C][C]1714.45684512573[/C][C]2.54315487427314[/C][/ROW]
[ROW][C]16[/C][C]1558[/C][C]1601.26934512573[/C][C]-43.2693451257269[/C][/ROW]
[ROW][C]17[/C][C]1575[/C][C]1738.58184512573[/C][C]-163.581845125727[/C][/ROW]
[ROW][C]18[/C][C]1520[/C][C]1682.83184512573[/C][C]-162.831845125727[/C][/ROW]
[ROW][C]19[/C][C]1805[/C][C]1758.45684512573[/C][C]46.5431548742731[/C][/ROW]
[ROW][C]20[/C][C]1800[/C][C]1773.33184512573[/C][C]26.6681548742731[/C][/ROW]
[ROW][C]21[/C][C]1719[/C][C]1826.14434512573[/C][C]-107.144345125727[/C][/ROW]
[ROW][C]22[/C][C]2008[/C][C]1965.51934512573[/C][C]42.4806548742732[/C][/ROW]
[ROW][C]23[/C][C]2242[/C][C]2165.08184512573[/C][C]76.9181548742732[/C][/ROW]
[ROW][C]24[/C][C]2478[/C][C]2281.70684512573[/C][C]196.293154874273[/C][/ROW]
[ROW][C]25[/C][C]2030[/C][C]1828.56701653704[/C][C]201.432983462961[/C][/ROW]
[ROW][C]26[/C][C]1655[/C][C]1642.71608113720[/C][C]12.2839188627954[/C][/ROW]
[ROW][C]27[/C][C]1693[/C][C]1693.27858113720[/C][C]-0.278581137204616[/C][/ROW]
[ROW][C]28[/C][C]1623[/C][C]1580.09108113720[/C][C]42.9089188627954[/C][/ROW]
[ROW][C]29[/C][C]1805[/C][C]1717.40358113720[/C][C]87.5964188627954[/C][/ROW]
[ROW][C]30[/C][C]1746[/C][C]1661.65358113720[/C][C]84.3464188627954[/C][/ROW]
[ROW][C]31[/C][C]1795[/C][C]1737.27858113720[/C][C]57.7214188627954[/C][/ROW]
[ROW][C]32[/C][C]1926[/C][C]1752.15358113720[/C][C]173.846418862795[/C][/ROW]
[ROW][C]33[/C][C]1619[/C][C]1804.96608113720[/C][C]-185.966081137205[/C][/ROW]
[ROW][C]34[/C][C]1992[/C][C]1944.34108113720[/C][C]47.6589188627954[/C][/ROW]
[ROW][C]35[/C][C]2233[/C][C]2143.90358113720[/C][C]89.0964188627954[/C][/ROW]
[ROW][C]36[/C][C]2192[/C][C]2260.52858113720[/C][C]-68.5285811372045[/C][/ROW]
[ROW][C]37[/C][C]2080[/C][C]1807.38875254852[/C][C]272.611247451483[/C][/ROW]
[ROW][C]38[/C][C]1768[/C][C]1621.53781714868[/C][C]146.462182851318[/C][/ROW]
[ROW][C]39[/C][C]1835[/C][C]1672.10031714868[/C][C]162.899682851318[/C][/ROW]
[ROW][C]40[/C][C]1569[/C][C]1558.91281714868[/C][C]10.0871828513176[/C][/ROW]
[ROW][C]41[/C][C]1976[/C][C]1696.22531714868[/C][C]279.774682851318[/C][/ROW]
[ROW][C]42[/C][C]1853[/C][C]1640.47531714868[/C][C]212.524682851318[/C][/ROW]
[ROW][C]43[/C][C]1965[/C][C]1716.10031714868[/C][C]248.899682851318[/C][/ROW]
[ROW][C]44[/C][C]1689[/C][C]1730.97531714868[/C][C]-41.9753171486824[/C][/ROW]
[ROW][C]45[/C][C]1778[/C][C]1783.78781714868[/C][C]-5.78781714868237[/C][/ROW]
[ROW][C]46[/C][C]1976[/C][C]1923.16281714868[/C][C]52.8371828513176[/C][/ROW]
[ROW][C]47[/C][C]2397[/C][C]2122.72531714868[/C][C]274.274682851318[/C][/ROW]
[ROW][C]48[/C][C]2654[/C][C]2239.35031714868[/C][C]414.649682851318[/C][/ROW]
[ROW][C]49[/C][C]2097[/C][C]1786.21048855999[/C][C]310.789511440006[/C][/ROW]
[ROW][C]50[/C][C]1963[/C][C]1600.35955316016[/C][C]362.64044683984[/C][/ROW]
[ROW][C]51[/C][C]1677[/C][C]1650.92205316016[/C][C]26.0779468398399[/C][/ROW]
[ROW][C]52[/C][C]1941[/C][C]1537.73455316016[/C][C]403.26544683984[/C][/ROW]
[ROW][C]53[/C][C]2003[/C][C]1675.04705316016[/C][C]327.95294683984[/C][/ROW]
[ROW][C]54[/C][C]1813[/C][C]1619.29705316016[/C][C]193.70294683984[/C][/ROW]
[ROW][C]55[/C][C]2012[/C][C]1694.92205316016[/C][C]317.07794683984[/C][/ROW]
[ROW][C]56[/C][C]1912[/C][C]1709.79705316016[/C][C]202.202946839840[/C][/ROW]
[ROW][C]57[/C][C]2084[/C][C]1762.60955316016[/C][C]321.39044683984[/C][/ROW]
[ROW][C]58[/C][C]2080[/C][C]1901.98455316016[/C][C]178.01544683984[/C][/ROW]
[ROW][C]59[/C][C]2118[/C][C]2101.54705316016[/C][C]16.4529468398399[/C][/ROW]
[ROW][C]60[/C][C]2150[/C][C]2218.17205316016[/C][C]-68.1720531601601[/C][/ROW]
[ROW][C]61[/C][C]1608[/C][C]1765.03222457147[/C][C]-157.032224571472[/C][/ROW]
[ROW][C]62[/C][C]1503[/C][C]1579.18128917164[/C][C]-76.1812891716379[/C][/ROW]
[ROW][C]63[/C][C]1548[/C][C]1629.74378917164[/C][C]-81.7437891716379[/C][/ROW]
[ROW][C]64[/C][C]1382[/C][C]1516.55628917164[/C][C]-134.556289171638[/C][/ROW]
[ROW][C]65[/C][C]1731[/C][C]1653.86878917164[/C][C]77.1312108283621[/C][/ROW]
[ROW][C]66[/C][C]1798[/C][C]1598.11878917164[/C][C]199.881210828362[/C][/ROW]
[ROW][C]67[/C][C]1779[/C][C]1673.74378917164[/C][C]105.256210828362[/C][/ROW]
[ROW][C]68[/C][C]1887[/C][C]1688.61878917164[/C][C]198.381210828362[/C][/ROW]
[ROW][C]69[/C][C]2004[/C][C]1741.43128917164[/C][C]262.568710828362[/C][/ROW]
[ROW][C]70[/C][C]2077[/C][C]1880.80628917164[/C][C]196.193710828362[/C][/ROW]
[ROW][C]71[/C][C]2092[/C][C]2080.36878917164[/C][C]11.6312108283621[/C][/ROW]
[ROW][C]72[/C][C]2051[/C][C]2196.99378917164[/C][C]-145.993789171638[/C][/ROW]
[ROW][C]73[/C][C]1577[/C][C]1743.85396058295[/C][C]-166.85396058295[/C][/ROW]
[ROW][C]74[/C][C]1356[/C][C]1558.00302518312[/C][C]-202.003025183116[/C][/ROW]
[ROW][C]75[/C][C]1652[/C][C]1608.56552518312[/C][C]43.4344748168844[/C][/ROW]
[ROW][C]76[/C][C]1382[/C][C]1495.37802518312[/C][C]-113.378025183116[/C][/ROW]
[ROW][C]77[/C][C]1519[/C][C]1632.69052518312[/C][C]-113.690525183116[/C][/ROW]
[ROW][C]78[/C][C]1421[/C][C]1576.94052518312[/C][C]-155.940525183116[/C][/ROW]
[ROW][C]79[/C][C]1442[/C][C]1652.56552518312[/C][C]-210.565525183116[/C][/ROW]
[ROW][C]80[/C][C]1543[/C][C]1667.44052518312[/C][C]-124.440525183116[/C][/ROW]
[ROW][C]81[/C][C]1656[/C][C]1720.25302518312[/C][C]-64.2530251831156[/C][/ROW]
[ROW][C]82[/C][C]1561[/C][C]1859.62802518312[/C][C]-298.628025183116[/C][/ROW]
[ROW][C]83[/C][C]1905[/C][C]2059.19052518312[/C][C]-154.190525183116[/C][/ROW]
[ROW][C]84[/C][C]2199[/C][C]2175.81552518312[/C][C]23.1844748168844[/C][/ROW]
[ROW][C]85[/C][C]1473[/C][C]1722.67569659443[/C][C]-249.675696594427[/C][/ROW]
[ROW][C]86[/C][C]1655[/C][C]1536.82476119459[/C][C]118.175238805407[/C][/ROW]
[ROW][C]87[/C][C]1407[/C][C]1587.38726119459[/C][C]-180.387261194593[/C][/ROW]
[ROW][C]88[/C][C]1395[/C][C]1474.19976119459[/C][C]-79.1997611945933[/C][/ROW]
[ROW][C]89[/C][C]1530[/C][C]1611.51226119459[/C][C]-81.5122611945934[/C][/ROW]
[ROW][C]90[/C][C]1309[/C][C]1555.76226119459[/C][C]-246.762261194593[/C][/ROW]
[ROW][C]91[/C][C]1526[/C][C]1631.38726119459[/C][C]-105.387261194593[/C][/ROW]
[ROW][C]92[/C][C]1327[/C][C]1646.26226119459[/C][C]-319.262261194593[/C][/ROW]
[ROW][C]93[/C][C]1627[/C][C]1699.07476119459[/C][C]-72.0747611945934[/C][/ROW]
[ROW][C]94[/C][C]1748[/C][C]1838.44976119459[/C][C]-90.4497611945934[/C][/ROW]
[ROW][C]95[/C][C]1958[/C][C]2038.01226119459[/C][C]-80.0122611945934[/C][/ROW]
[ROW][C]96[/C][C]2274[/C][C]2154.63726119459[/C][C]119.362738805407[/C][/ROW]
[ROW][C]97[/C][C]1648[/C][C]1701.49743260591[/C][C]-53.4974326059054[/C][/ROW]
[ROW][C]98[/C][C]1401[/C][C]1515.64649720607[/C][C]-114.646497206071[/C][/ROW]
[ROW][C]99[/C][C]1411[/C][C]1566.20899720607[/C][C]-155.208997206071[/C][/ROW]
[ROW][C]100[/C][C]1403[/C][C]1453.02149720607[/C][C]-50.0214972060711[/C][/ROW]
[ROW][C]101[/C][C]1394[/C][C]1590.33399720607[/C][C]-196.333997206071[/C][/ROW]
[ROW][C]102[/C][C]1520[/C][C]1534.58399720607[/C][C]-14.5839972060711[/C][/ROW]
[ROW][C]103[/C][C]1528[/C][C]1610.20899720607[/C][C]-82.2089972060712[/C][/ROW]
[ROW][C]104[/C][C]1643[/C][C]1625.08399720607[/C][C]17.9160027939289[/C][/ROW]
[ROW][C]105[/C][C]1515[/C][C]1677.89649720607[/C][C]-162.896497206071[/C][/ROW]
[ROW][C]106[/C][C]1685[/C][C]1817.27149720607[/C][C]-132.271497206071[/C][/ROW]
[ROW][C]107[/C][C]2000[/C][C]2016.83399720607[/C][C]-16.8339972060712[/C][/ROW]
[ROW][C]108[/C][C]2215[/C][C]2133.45899720607[/C][C]81.5410027939289[/C][/ROW]
[ROW][C]109[/C][C]1956[/C][C]1680.31916861738[/C][C]275.680831382617[/C][/ROW]
[ROW][C]110[/C][C]1462[/C][C]1494.46823321755[/C][C]-32.4682332175488[/C][/ROW]
[ROW][C]111[/C][C]1563[/C][C]1545.03073321755[/C][C]17.9692667824511[/C][/ROW]
[ROW][C]112[/C][C]1459[/C][C]1431.84323321755[/C][C]27.1567667824512[/C][/ROW]
[ROW][C]113[/C][C]1446[/C][C]1569.15573321755[/C][C]-123.155733217549[/C][/ROW]
[ROW][C]114[/C][C]1622[/C][C]1513.40573321755[/C][C]108.594266782451[/C][/ROW]
[ROW][C]115[/C][C]1657[/C][C]1589.03073321755[/C][C]67.9692667824512[/C][/ROW]
[ROW][C]116[/C][C]1638[/C][C]1603.90573321755[/C][C]34.0942667824511[/C][/ROW]
[ROW][C]117[/C][C]1643[/C][C]1656.71823321755[/C][C]-13.7182332175489[/C][/ROW]
[ROW][C]118[/C][C]1683[/C][C]1796.09323321755[/C][C]-113.093233217549[/C][/ROW]
[ROW][C]119[/C][C]2050[/C][C]1995.65573321755[/C][C]54.3442667824512[/C][/ROW]
[ROW][C]120[/C][C]2262[/C][C]2112.28073321755[/C][C]149.719266782451[/C][/ROW]
[ROW][C]121[/C][C]1813[/C][C]1659.14090462886[/C][C]153.859095371139[/C][/ROW]
[ROW][C]122[/C][C]1445[/C][C]1473.28996922903[/C][C]-28.2899692290266[/C][/ROW]
[ROW][C]123[/C][C]1762[/C][C]1523.85246922903[/C][C]238.147530770973[/C][/ROW]
[ROW][C]124[/C][C]1461[/C][C]1410.66496922903[/C][C]50.3350307709734[/C][/ROW]
[ROW][C]125[/C][C]1556[/C][C]1547.97746922903[/C][C]8.02253077097338[/C][/ROW]
[ROW][C]126[/C][C]1431[/C][C]1492.22746922903[/C][C]-61.2274692290265[/C][/ROW]
[ROW][C]127[/C][C]1427[/C][C]1567.85246922903[/C][C]-140.852469229027[/C][/ROW]
[ROW][C]128[/C][C]1554[/C][C]1582.72746922903[/C][C]-28.7274692290267[/C][/ROW]
[ROW][C]129[/C][C]1645[/C][C]1635.53996922903[/C][C]9.4600307709734[/C][/ROW]
[ROW][C]130[/C][C]1653[/C][C]1774.91496922903[/C][C]-121.914969229027[/C][/ROW]
[ROW][C]131[/C][C]2016[/C][C]1974.47746922903[/C][C]41.5225307709734[/C][/ROW]
[ROW][C]132[/C][C]2207[/C][C]2091.10246922903[/C][C]115.897530770973[/C][/ROW]
[ROW][C]133[/C][C]1665[/C][C]1637.96264064034[/C][C]27.0373593596614[/C][/ROW]
[ROW][C]134[/C][C]1361[/C][C]1452.11170524050[/C][C]-91.1117052405044[/C][/ROW]
[ROW][C]135[/C][C]1506[/C][C]1502.67420524050[/C][C]3.32579475949564[/C][/ROW]
[ROW][C]136[/C][C]1360[/C][C]1389.48670524050[/C][C]-29.4867052405044[/C][/ROW]
[ROW][C]137[/C][C]1453[/C][C]1526.79920524050[/C][C]-73.7992052405043[/C][/ROW]
[ROW][C]138[/C][C]1522[/C][C]1471.04920524050[/C][C]50.9507947594957[/C][/ROW]
[ROW][C]139[/C][C]1460[/C][C]1546.67420524050[/C][C]-86.6742052405043[/C][/ROW]
[ROW][C]140[/C][C]1552[/C][C]1561.54920524050[/C][C]-9.5492052405044[/C][/ROW]
[ROW][C]141[/C][C]1548[/C][C]1614.36170524050[/C][C]-66.3617052405044[/C][/ROW]
[ROW][C]142[/C][C]1827[/C][C]1753.73670524050[/C][C]73.2632947594957[/C][/ROW]
[ROW][C]143[/C][C]1737[/C][C]1953.29920524050[/C][C]-216.299205240504[/C][/ROW]
[ROW][C]144[/C][C]1941[/C][C]2069.92420524050[/C][C]-128.924205240504[/C][/ROW]
[ROW][C]145[/C][C]1474[/C][C]1616.78437665182[/C][C]-142.784376651816[/C][/ROW]
[ROW][C]146[/C][C]1458[/C][C]1430.93344125198[/C][C]27.0665587480179[/C][/ROW]
[ROW][C]147[/C][C]1542[/C][C]1481.49594125198[/C][C]60.5040587480179[/C][/ROW]
[ROW][C]148[/C][C]1404[/C][C]1368.30844125198[/C][C]35.6915587480179[/C][/ROW]
[ROW][C]149[/C][C]1522[/C][C]1505.62094125198[/C][C]16.3790587480179[/C][/ROW]
[ROW][C]150[/C][C]1385[/C][C]1449.87094125198[/C][C]-64.870941251982[/C][/ROW]
[ROW][C]151[/C][C]1641[/C][C]1525.49594125198[/C][C]115.504058748018[/C][/ROW]
[ROW][C]152[/C][C]1510[/C][C]1540.37094125198[/C][C]-30.3709412519821[/C][/ROW]
[ROW][C]153[/C][C]1681[/C][C]1593.18344125198[/C][C]87.816558748018[/C][/ROW]
[ROW][C]154[/C][C]1938[/C][C]1732.55844125198[/C][C]205.441558748018[/C][/ROW]
[ROW][C]155[/C][C]1868[/C][C]1932.12094125198[/C][C]-64.1209412519821[/C][/ROW]
[ROW][C]156[/C][C]1726[/C][C]2048.74594125198[/C][C]-322.745941251982[/C][/ROW]
[ROW][C]157[/C][C]1456[/C][C]1595.60611266329[/C][C]-139.606112663294[/C][/ROW]
[ROW][C]158[/C][C]1445[/C][C]1409.75517726346[/C][C]35.2448227365402[/C][/ROW]
[ROW][C]159[/C][C]1456[/C][C]1460.31767726346[/C][C]-4.31767726345983[/C][/ROW]
[ROW][C]160[/C][C]1365[/C][C]1347.13017726346[/C][C]17.8698227365402[/C][/ROW]
[ROW][C]161[/C][C]1487[/C][C]1484.44267726346[/C][C]2.55732273654013[/C][/ROW]
[ROW][C]162[/C][C]1558[/C][C]1428.69267726346[/C][C]129.307322736540[/C][/ROW]
[ROW][C]163[/C][C]1488[/C][C]1504.31767726346[/C][C]-16.3176772634599[/C][/ROW]
[ROW][C]164[/C][C]1684[/C][C]1519.19267726346[/C][C]164.80732273654[/C][/ROW]
[ROW][C]165[/C][C]1594[/C][C]1572.00517726346[/C][C]21.9948227365402[/C][/ROW]
[ROW][C]166[/C][C]1850[/C][C]1711.38017726346[/C][C]138.619822736540[/C][/ROW]
[ROW][C]167[/C][C]1998[/C][C]1910.94267726346[/C][C]87.05732273654[/C][/ROW]
[ROW][C]168[/C][C]2079[/C][C]2027.56767726346[/C][C]51.4323227365402[/C][/ROW]
[ROW][C]169[/C][C]1494[/C][C]1574.42784867477[/C][C]-80.4278486747719[/C][/ROW]
[ROW][C]170[/C][C]1057[/C][C]1162.19187967228[/C][C]-105.191879672280[/C][/ROW]
[ROW][C]171[/C][C]1218[/C][C]1212.75437967228[/C][C]5.2456203277202[/C][/ROW]
[ROW][C]172[/C][C]1168[/C][C]1099.56687967228[/C][C]68.4331203277202[/C][/ROW]
[ROW][C]173[/C][C]1236[/C][C]1236.87937967228[/C][C]-0.879379672279648[/C][/ROW]
[ROW][C]174[/C][C]1076[/C][C]1181.12937967228[/C][C]-105.129379672280[/C][/ROW]
[ROW][C]175[/C][C]1174[/C][C]1256.75437967228[/C][C]-82.7543796722796[/C][/ROW]
[ROW][C]176[/C][C]1139[/C][C]1271.62937967228[/C][C]-132.629379672280[/C][/ROW]
[ROW][C]177[/C][C]1427[/C][C]1324.44187967228[/C][C]102.558120327720[/C][/ROW]
[ROW][C]178[/C][C]1487[/C][C]1463.81687967228[/C][C]23.1831203277203[/C][/ROW]
[ROW][C]179[/C][C]1483[/C][C]1663.37937967228[/C][C]-180.379379672280[/C][/ROW]
[ROW][C]180[/C][C]1513[/C][C]1780.00437967228[/C][C]-267.004379672280[/C][/ROW]
[ROW][C]181[/C][C]1357[/C][C]1326.86455108359[/C][C]30.1354489164084[/C][/ROW]
[ROW][C]182[/C][C]1165[/C][C]1141.01361568376[/C][C]23.9863843162425[/C][/ROW]
[ROW][C]183[/C][C]1282[/C][C]1191.57611568376[/C][C]90.4238843162424[/C][/ROW]
[ROW][C]184[/C][C]1110[/C][C]1078.38861568376[/C][C]31.6113843162425[/C][/ROW]
[ROW][C]185[/C][C]1297[/C][C]1215.70111568376[/C][C]81.2988843162426[/C][/ROW]
[ROW][C]186[/C][C]1185[/C][C]1159.95111568376[/C][C]25.0488843162426[/C][/ROW]
[ROW][C]187[/C][C]1222[/C][C]1235.57611568376[/C][C]-13.5761156837574[/C][/ROW]
[ROW][C]188[/C][C]1284[/C][C]1250.45111568376[/C][C]33.5488843162426[/C][/ROW]
[ROW][C]189[/C][C]1444[/C][C]1303.26361568376[/C][C]140.736384316243[/C][/ROW]
[ROW][C]190[/C][C]1575[/C][C]1442.63861568376[/C][C]132.361384316243[/C][/ROW]
[ROW][C]191[/C][C]1737[/C][C]1642.20111568376[/C][C]94.7988843162425[/C][/ROW]
[ROW][C]192[/C][C]1763[/C][C]1758.82611568376[/C][C]4.17388431624252[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25001&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25001&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	1687	1870.92354451408	-183.923544514078
2	1508	1685.07260911425	-177.072609114249
3	1507	1735.63510911425	-228.635109114249
4	1385	1622.44760911425	-237.447609114250
5	1632	1759.76010911425	-127.760109114249
6	1511	1704.01010911425	-193.010109114250
7	1559	1779.63510911425	-220.635109114249
8	1630	1794.51010911425	-164.510109114249
9	1579	1847.32260911425	-268.322609114249
10	1653	1986.69760911425	-333.697609114249
11	2152	2186.26010911425	-34.2601091142491
12	2148	2302.88510911425	-154.885109114249
13	1752	1849.74528052556	-97.7452805255611
14	1765	1663.89434512573	101.105654874273
15	1717	1714.45684512573	2.54315487427314
16	1558	1601.26934512573	-43.2693451257269
17	1575	1738.58184512573	-163.581845125727
18	1520	1682.83184512573	-162.831845125727
19	1805	1758.45684512573	46.5431548742731
20	1800	1773.33184512573	26.6681548742731
21	1719	1826.14434512573	-107.144345125727
22	2008	1965.51934512573	42.4806548742732
23	2242	2165.08184512573	76.9181548742732
24	2478	2281.70684512573	196.293154874273
25	2030	1828.56701653704	201.432983462961
26	1655	1642.71608113720	12.2839188627954
27	1693	1693.27858113720	-0.278581137204616
28	1623	1580.09108113720	42.9089188627954
29	1805	1717.40358113720	87.5964188627954
30	1746	1661.65358113720	84.3464188627954
31	1795	1737.27858113720	57.7214188627954
32	1926	1752.15358113720	173.846418862795
33	1619	1804.96608113720	-185.966081137205
34	1992	1944.34108113720	47.6589188627954
35	2233	2143.90358113720	89.0964188627954
36	2192	2260.52858113720	-68.5285811372045
37	2080	1807.38875254852	272.611247451483
38	1768	1621.53781714868	146.462182851318
39	1835	1672.10031714868	162.899682851318
40	1569	1558.91281714868	10.0871828513176
41	1976	1696.22531714868	279.774682851318
42	1853	1640.47531714868	212.524682851318
43	1965	1716.10031714868	248.899682851318
44	1689	1730.97531714868	-41.9753171486824
45	1778	1783.78781714868	-5.78781714868237
46	1976	1923.16281714868	52.8371828513176
47	2397	2122.72531714868	274.274682851318
48	2654	2239.35031714868	414.649682851318
49	2097	1786.21048855999	310.789511440006
50	1963	1600.35955316016	362.64044683984
51	1677	1650.92205316016	26.0779468398399
52	1941	1537.73455316016	403.26544683984
53	2003	1675.04705316016	327.95294683984
54	1813	1619.29705316016	193.70294683984
55	2012	1694.92205316016	317.07794683984
56	1912	1709.79705316016	202.202946839840
57	2084	1762.60955316016	321.39044683984
58	2080	1901.98455316016	178.01544683984
59	2118	2101.54705316016	16.4529468398399
60	2150	2218.17205316016	-68.1720531601601
61	1608	1765.03222457147	-157.032224571472
62	1503	1579.18128917164	-76.1812891716379
63	1548	1629.74378917164	-81.7437891716379
64	1382	1516.55628917164	-134.556289171638
65	1731	1653.86878917164	77.1312108283621
66	1798	1598.11878917164	199.881210828362
67	1779	1673.74378917164	105.256210828362
68	1887	1688.61878917164	198.381210828362
69	2004	1741.43128917164	262.568710828362
70	2077	1880.80628917164	196.193710828362
71	2092	2080.36878917164	11.6312108283621
72	2051	2196.99378917164	-145.993789171638
73	1577	1743.85396058295	-166.85396058295
74	1356	1558.00302518312	-202.003025183116
75	1652	1608.56552518312	43.4344748168844
76	1382	1495.37802518312	-113.378025183116
77	1519	1632.69052518312	-113.690525183116
78	1421	1576.94052518312	-155.940525183116
79	1442	1652.56552518312	-210.565525183116
80	1543	1667.44052518312	-124.440525183116
81	1656	1720.25302518312	-64.2530251831156
82	1561	1859.62802518312	-298.628025183116
83	1905	2059.19052518312	-154.190525183116
84	2199	2175.81552518312	23.1844748168844
85	1473	1722.67569659443	-249.675696594427
86	1655	1536.82476119459	118.175238805407
87	1407	1587.38726119459	-180.387261194593
88	1395	1474.19976119459	-79.1997611945933
89	1530	1611.51226119459	-81.5122611945934
90	1309	1555.76226119459	-246.762261194593
91	1526	1631.38726119459	-105.387261194593
92	1327	1646.26226119459	-319.262261194593
93	1627	1699.07476119459	-72.0747611945934
94	1748	1838.44976119459	-90.4497611945934
95	1958	2038.01226119459	-80.0122611945934
96	2274	2154.63726119459	119.362738805407
97	1648	1701.49743260591	-53.4974326059054
98	1401	1515.64649720607	-114.646497206071
99	1411	1566.20899720607	-155.208997206071
100	1403	1453.02149720607	-50.0214972060711
101	1394	1590.33399720607	-196.333997206071
102	1520	1534.58399720607	-14.5839972060711
103	1528	1610.20899720607	-82.2089972060712
104	1643	1625.08399720607	17.9160027939289
105	1515	1677.89649720607	-162.896497206071
106	1685	1817.27149720607	-132.271497206071
107	2000	2016.83399720607	-16.8339972060712
108	2215	2133.45899720607	81.5410027939289
109	1956	1680.31916861738	275.680831382617
110	1462	1494.46823321755	-32.4682332175488
111	1563	1545.03073321755	17.9692667824511
112	1459	1431.84323321755	27.1567667824512
113	1446	1569.15573321755	-123.155733217549
114	1622	1513.40573321755	108.594266782451
115	1657	1589.03073321755	67.9692667824512
116	1638	1603.90573321755	34.0942667824511
117	1643	1656.71823321755	-13.7182332175489
118	1683	1796.09323321755	-113.093233217549
119	2050	1995.65573321755	54.3442667824512
120	2262	2112.28073321755	149.719266782451
121	1813	1659.14090462886	153.859095371139
122	1445	1473.28996922903	-28.2899692290266
123	1762	1523.85246922903	238.147530770973
124	1461	1410.66496922903	50.3350307709734
125	1556	1547.97746922903	8.02253077097338
126	1431	1492.22746922903	-61.2274692290265
127	1427	1567.85246922903	-140.852469229027
128	1554	1582.72746922903	-28.7274692290267
129	1645	1635.53996922903	9.4600307709734
130	1653	1774.91496922903	-121.914969229027
131	2016	1974.47746922903	41.5225307709734
132	2207	2091.10246922903	115.897530770973
133	1665	1637.96264064034	27.0373593596614
134	1361	1452.11170524050	-91.1117052405044
135	1506	1502.67420524050	3.32579475949564
136	1360	1389.48670524050	-29.4867052405044
137	1453	1526.79920524050	-73.7992052405043
138	1522	1471.04920524050	50.9507947594957
139	1460	1546.67420524050	-86.6742052405043
140	1552	1561.54920524050	-9.5492052405044
141	1548	1614.36170524050	-66.3617052405044
142	1827	1753.73670524050	73.2632947594957
143	1737	1953.29920524050	-216.299205240504
144	1941	2069.92420524050	-128.924205240504
145	1474	1616.78437665182	-142.784376651816
146	1458	1430.93344125198	27.0665587480179
147	1542	1481.49594125198	60.5040587480179
148	1404	1368.30844125198	35.6915587480179
149	1522	1505.62094125198	16.3790587480179
150	1385	1449.87094125198	-64.870941251982
151	1641	1525.49594125198	115.504058748018
152	1510	1540.37094125198	-30.3709412519821
153	1681	1593.18344125198	87.816558748018
154	1938	1732.55844125198	205.441558748018
155	1868	1932.12094125198	-64.1209412519821
156	1726	2048.74594125198	-322.745941251982
157	1456	1595.60611266329	-139.606112663294
158	1445	1409.75517726346	35.2448227365402
159	1456	1460.31767726346	-4.31767726345983
160	1365	1347.13017726346	17.8698227365402
161	1487	1484.44267726346	2.55732273654013
162	1558	1428.69267726346	129.307322736540
163	1488	1504.31767726346	-16.3176772634599
164	1684	1519.19267726346	164.80732273654
165	1594	1572.00517726346	21.9948227365402
166	1850	1711.38017726346	138.619822736540
167	1998	1910.94267726346	87.05732273654
168	2079	2027.56767726346	51.4323227365402
169	1494	1574.42784867477	-80.4278486747719
170	1057	1162.19187967228	-105.191879672280
171	1218	1212.75437967228	5.2456203277202
172	1168	1099.56687967228	68.4331203277202
173	1236	1236.87937967228	-0.879379672279648
174	1076	1181.12937967228	-105.129379672280
175	1174	1256.75437967228	-82.7543796722796
176	1139	1271.62937967228	-132.629379672280
177	1427	1324.44187967228	102.558120327720
178	1487	1463.81687967228	23.1831203277203
179	1483	1663.37937967228	-180.379379672280
180	1513	1780.00437967228	-267.004379672280
181	1357	1326.86455108359	30.1354489164084
182	1165	1141.01361568376	23.9863843162425
183	1282	1191.57611568376	90.4238843162424
184	1110	1078.38861568376	31.6113843162425
185	1297	1215.70111568376	81.2988843162426
186	1185	1159.95111568376	25.0488843162426
187	1222	1235.57611568376	-13.5761156837574
188	1284	1250.45111568376	33.5488843162426
189	1444	1303.26361568376	140.736384316243
190	1575	1442.63861568376	132.361384316243
191	1737	1642.20111568376	94.7988843162425
192	1763	1758.82611568376	4.17388431624252

Figure 1

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Figure 2

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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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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)
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))
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$resid, main='Residual Normal Q-Q Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$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()
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code