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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 02 Nov 2012 15:46:17 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/02/t1351885763fltgogozscw4nm1.htm/, Retrieved Sun, 03 Jul 2022 14:36:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=185666, Retrieved Sun, 03 Jul 2022 14:36:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Competence to learn] [2010-11-17 07:43:53] [b98453cac15ba1066b407e146608df68]
- R PD  [Multiple Regression] [workshop 7: regre...] [2012-11-02 15:42:59] [40b341cf5fb1ddfd74e4c5704837f48c]
-   PD    [Multiple Regression] [workshop 7: Y_t m...] [2012-11-02 16:52:03] [40b341cf5fb1ddfd74e4c5704837f48c]
-           [Multiple Regression] [workshop 7: deter...] [2012-11-02 17:20:14] [40b341cf5fb1ddfd74e4c5704837f48c]
-   PD          [Multiple Regression] [workshop 7: berek...] [2012-11-02 19:46:17] [7a9100b3135ff0dae36397155af309d9] [Current]
- R P             [Multiple Regression] [WS 7 multiple reg...] [2012-11-04 13:01:29] [e01c78beec4051e03ee053d8bc2c6384]
-    D            [Multiple Regression] [Paper 2012: invoe...] [2012-12-06 20:03:52] [40b341cf5fb1ddfd74e4c5704837f48c]
-    D              [Multiple Regression] [Paper 2012: invo...] [2012-12-06 20:11:38] [40b341cf5fb1ddfd74e4c5704837f48c]
-   PD            [Multiple Regression] [Paper 2012: rfc m...] [2012-12-12 13:09:31] [40b341cf5fb1ddfd74e4c5704837f48c]
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Dataseries X:
31/12/1961	9190	0	2514	0	2550	0	1512	0	1591	0	472	0	551	0
31/12/1962	9251	1	2537	2537	2572	2572	1517	1517	1595	1595	476	476	554	554
31/12/1963	9328	2	2564	5128	2597	5194	1525	3050	1602	3204	483	966	558	1116
31/12/1964	9428	0	2595	0	2623	0	1540	0	1613	0	493	0	565	0
31/12/1965	9499	1	2617	2617	2647	2647	1547	1547	1622	1622	498	498	568	568
31/12/1966	9556	2	2638	5276	2670	5340	1547	3094	1627	3254	502	1004	572	1144
31/12/1967	9606	0	2657	0	2690	0	1547	0	1632	0	504	0	575	0
31/12/1968	9632	1	2668	2668	2705	2705	1547	1547	1634	1634	503	503	574	574
31/12/1969	9660	2	2683	5366	2721	5442	1546	3092	1637	3274	501	1002	572	1144
31/12/1970	9651	0	2687	0	2729	0	1533	0	1627	0	502	0	573	0
31/12/1971	9695	1	2705	2705	2747	2747	1538	1538	1632	1632	502	502	572	572
31/12/1972	9727	2	2717	5434	2761	5522	1543	3086	1637	3274	500	1000	569	1138
31/12/1973	9757	0	2728	0	2773	0	1549	0	1643	0	498	0	566	0
31/12/1974	9788	1	2741	2741	2786	2786	1556	1556	1650	1650	495	495	560	560
31/12/1975	9813	2	2752	5504	2796	5592	1559	3118	1654	3308	494	988	557	1114
31/12/1976	9823	0	2759	0	2807	0	1559	0	1656	0	490	0	552	0
31/12/1977	9837	1	2767	2767	2817	2817	1563	1563	1661	1661	484	484	545	545
31/12/1978	9842	2	2774	5548	2827	5654	1563	3126	1662	3324	477	954	539	1078
31/12/1979	9855	0	2781	0	2838	0	1564	0	1664	0	474	0	535	0
31/12/1980	9863	1	2788	2788	2847	2847	1564	1564	1665	1665	469	469	531	531
31/12/1981	9855	2	2789	5578	2853	5706	1557	3114	1661	3322	466	932	528	1056
31/12/1982	9858	0	2795	0	2860	0	1554	0	1659	0	464	0	526	0
31/12/1983	9853	1	2798	2798	2864	2864	1552	1552	1656	1656	460	460	523	523
31/12/1984	9858	2	2801	5602	2869	5738	1552	3104	1656	3312	458	916	521	1042
31/12/1985	9859	0	2803	0	2873	0	1551	0	1655	0	457	0	519	0
31/12/1986	9865	1	2808	2808	2877	2877	1552	1552	1654	1654	456	456	517	517
31/12/1987	9876	2	2813	5626	2883	5766	1554	3108	1656	3312	455	910	515	1030
31/12/1988	9928	0	2826	0	2896	0	1567	0	1668	0	456	0	514	0
31/12/1989	9948	1	2835	2835	2905	2905	1572	1572	1672	1672	453	453	511	511
31/12/1990	9987	2	2849	5698	2919	5838	1579	3158	1680	3360	453	906	508	1016
31/12/1991	10022	0	2862	0	2933	0	1588	0	1688	0	449	0	502	0
31/12/1992	10068	1	2877	2877	2948	2948	1597	1597	1696	1696	449	449	501	501
31/12/1993	10101	2	2888	5776	2959	5918	1603	3206	1702	3404	449	898	500	1000
31/12/1994	10131	0	2897	0	2969	0	1607	0	1706	0	452	0	500	0
31/12/1995	10143	1	2902	2902	2978	2978	1607	1607	1708	1708	450	450	498	498
31/12/1996	10170	2	2911	5822	2988	5976	1609	3218	1711	3422	452	904	499	998
31/12/1997	10192	0	2917	0	2996	0	1612	0	1714	0	454	0	499	0
31/12/1998	10214	1	2924	2924	3003	3003	1615	1615	1717	1717	455	455	500	500
31/12/1999	10239	2	2930	5860	3011	6022	1619	3238	1721	3442	458	916	501	1002
31/12/2000	10263	0	2935	0	3018	0	1622	0	1724	0	461	0	503	0
31/12/2001	10310	1	2945	2945	3028	3028	1628	1628	1730	1730	469	469	510	510
31/12/2002	10355	2	2957	5914	3038	6076	1634	3268	1735	3470	477	954	515	1030
31/12/2003	10396	0	2967	0	3049	0	1640	0	1740	0	480	0	520	0
31/12/2004	10446	1	2980	2980	3063	3063	1648	1648	1748	1748	484	484	523	523
31/12/2005	10511	2	2997	5994	3081	6162	1657	3314	1757	3514	490	980	529	1058
31/12/2006	10585	0	3017	0	3100	0	1668	0	1768	0	497	0	534	0
31/12/2007	10667	1	3040	3040	3122	3122	1678	1678	1778	1778	506	506	543	543
31/12/2008	10753	2	3064	6128	3145	6290	1687	3374	1789	3578	516	1032	553	1106
31/12/2009	10840	0	3085	0	3167	0	1700	0	1798	0	527	0	563	0
31/12/2010	10951	1	3113	3113	3193	3193	1714	1714	1811	1811	542	542	577	577





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time8 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 8 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=185666&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]8 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=185666&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185666&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time8 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Multiple Linear Regression - Estimated Regression Equation
totaal[t] = + 28077.1236605879 -21314442.052228jaar[t] -13.1476462703488pop[t] + 0.836477807566883vlaams_man[t] + 0.0471501485953764man_vlaams_pop[t] + 1.13238757187277vlaams_vrouw[t] -0.0449098556338475vrouw_vlaams_pop[t] + 1.11206792400799waals_man[t] -0.0337743960440693man_waals_pop[t] + 0.92867218471356waals_vrouw[t] + 0.0395007801556062vrouw_waals_pop[t] + 0.951118040980139brussel_man[t] -0.0226033357346419man_brussel_pop[t] + 1.10169157043926brussel_vrouw[t] + 0.0138893774853077vrouw_brussel_pop[t] -13.8206845223669t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
totaal[t] =  +  28077.1236605879 -21314442.052228jaar[t] -13.1476462703488pop[t] +  0.836477807566883vlaams_man[t] +  0.0471501485953764man_vlaams_pop[t] +  1.13238757187277vlaams_vrouw[t] -0.0449098556338475vrouw_vlaams_pop[t] +  1.11206792400799waals_man[t] -0.0337743960440693man_waals_pop[t] +  0.92867218471356waals_vrouw[t] +  0.0395007801556062vrouw_waals_pop[t] +  0.951118040980139brussel_man[t] -0.0226033357346419man_brussel_pop[t] +  1.10169157043926brussel_vrouw[t] +  0.0138893774853077vrouw_brussel_pop[t] -13.8206845223669t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185666&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]totaal[t] =  +  28077.1236605879 -21314442.052228jaar[t] -13.1476462703488pop[t] +  0.836477807566883vlaams_man[t] +  0.0471501485953764man_vlaams_pop[t] +  1.13238757187277vlaams_vrouw[t] -0.0449098556338475vrouw_vlaams_pop[t] +  1.11206792400799waals_man[t] -0.0337743960440693man_waals_pop[t] +  0.92867218471356waals_vrouw[t] +  0.0395007801556062vrouw_waals_pop[t] +  0.951118040980139brussel_man[t] -0.0226033357346419man_brussel_pop[t] +  1.10169157043926brussel_vrouw[t] +  0.0138893774853077vrouw_brussel_pop[t] -13.8206845223669t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185666&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185666&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
totaal[t] = + 28077.1236605879 -21314442.052228jaar[t] -13.1476462703488pop[t] + 0.836477807566883vlaams_man[t] + 0.0471501485953764man_vlaams_pop[t] + 1.13238757187277vlaams_vrouw[t] -0.0449098556338475vrouw_vlaams_pop[t] + 1.11206792400799waals_man[t] -0.0337743960440693man_waals_pop[t] + 0.92867218471356waals_vrouw[t] + 0.0395007801556062vrouw_waals_pop[t] + 0.951118040980139brussel_man[t] -0.0226033357346419man_brussel_pop[t] + 1.10169157043926brussel_vrouw[t] + 0.0138893774853077vrouw_brussel_pop[t] -13.8206845223669t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)28077.123660587917923.1498221.56650.1264860.063243
jaar-21314442.05222813605470.329206-1.56660.1264670.063234
pop-13.147646270348829.76534-0.44170.6614960.330748
vlaams_man0.8364778075668830.1061317.881600
man_vlaams_pop0.04715014859537640.0391471.20440.2367350.118367
vlaams_vrouw1.132387571872770.1073110.552500
vrouw_vlaams_pop-0.04490985563384750.036031-1.24640.2211260.110563
waals_man1.112067924007990.08552713.002600
man_waals_pop-0.03377439604406930.047276-0.71440.4798480.239924
waals_vrouw0.928672184713560.1072328.660400
vrouw_waals_pop0.03950078015560620.0662860.59590.5551760.277588
brussel_man0.9511180409801390.1182368.044200
man_brussel_pop-0.02260333573464190.075357-0.30.766040.38302
brussel_vrouw1.101691570439260.1116259.869600
vrouw_brussel_pop0.01388937748530770.0677210.20510.838720.41936
t-13.82068452236698.781073-1.57390.1247670.062384

\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) & 28077.1236605879 & 17923.149822 & 1.5665 & 0.126486 & 0.063243 \tabularnewline
jaar & -21314442.052228 & 13605470.329206 & -1.5666 & 0.126467 & 0.063234 \tabularnewline
pop & -13.1476462703488 & 29.76534 & -0.4417 & 0.661496 & 0.330748 \tabularnewline
vlaams_man & 0.836477807566883 & 0.106131 & 7.8816 & 0 & 0 \tabularnewline
man_vlaams_pop & 0.0471501485953764 & 0.039147 & 1.2044 & 0.236735 & 0.118367 \tabularnewline
vlaams_vrouw & 1.13238757187277 & 0.10731 & 10.5525 & 0 & 0 \tabularnewline
vrouw_vlaams_pop & -0.0449098556338475 & 0.036031 & -1.2464 & 0.221126 & 0.110563 \tabularnewline
waals_man & 1.11206792400799 & 0.085527 & 13.0026 & 0 & 0 \tabularnewline
man_waals_pop & -0.0337743960440693 & 0.047276 & -0.7144 & 0.479848 & 0.239924 \tabularnewline
waals_vrouw & 0.92867218471356 & 0.107232 & 8.6604 & 0 & 0 \tabularnewline
vrouw_waals_pop & 0.0395007801556062 & 0.066286 & 0.5959 & 0.555176 & 0.277588 \tabularnewline
brussel_man & 0.951118040980139 & 0.118236 & 8.0442 & 0 & 0 \tabularnewline
man_brussel_pop & -0.0226033357346419 & 0.075357 & -0.3 & 0.76604 & 0.38302 \tabularnewline
brussel_vrouw & 1.10169157043926 & 0.111625 & 9.8696 & 0 & 0 \tabularnewline
vrouw_brussel_pop & 0.0138893774853077 & 0.067721 & 0.2051 & 0.83872 & 0.41936 \tabularnewline
t & -13.8206845223669 & 8.781073 & -1.5739 & 0.124767 & 0.062384 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185666&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]28077.1236605879[/C][C]17923.149822[/C][C]1.5665[/C][C]0.126486[/C][C]0.063243[/C][/ROW]
[ROW][C]jaar[/C][C]-21314442.052228[/C][C]13605470.329206[/C][C]-1.5666[/C][C]0.126467[/C][C]0.063234[/C][/ROW]
[ROW][C]pop[/C][C]-13.1476462703488[/C][C]29.76534[/C][C]-0.4417[/C][C]0.661496[/C][C]0.330748[/C][/ROW]
[ROW][C]vlaams_man[/C][C]0.836477807566883[/C][C]0.106131[/C][C]7.8816[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]man_vlaams_pop[/C][C]0.0471501485953764[/C][C]0.039147[/C][C]1.2044[/C][C]0.236735[/C][C]0.118367[/C][/ROW]
[ROW][C]vlaams_vrouw[/C][C]1.13238757187277[/C][C]0.10731[/C][C]10.5525[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]vrouw_vlaams_pop[/C][C]-0.0449098556338475[/C][C]0.036031[/C][C]-1.2464[/C][C]0.221126[/C][C]0.110563[/C][/ROW]
[ROW][C]waals_man[/C][C]1.11206792400799[/C][C]0.085527[/C][C]13.0026[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]man_waals_pop[/C][C]-0.0337743960440693[/C][C]0.047276[/C][C]-0.7144[/C][C]0.479848[/C][C]0.239924[/C][/ROW]
[ROW][C]waals_vrouw[/C][C]0.92867218471356[/C][C]0.107232[/C][C]8.6604[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]vrouw_waals_pop[/C][C]0.0395007801556062[/C][C]0.066286[/C][C]0.5959[/C][C]0.555176[/C][C]0.277588[/C][/ROW]
[ROW][C]brussel_man[/C][C]0.951118040980139[/C][C]0.118236[/C][C]8.0442[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]man_brussel_pop[/C][C]-0.0226033357346419[/C][C]0.075357[/C][C]-0.3[/C][C]0.76604[/C][C]0.38302[/C][/ROW]
[ROW][C]brussel_vrouw[/C][C]1.10169157043926[/C][C]0.111625[/C][C]9.8696[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]vrouw_brussel_pop[/C][C]0.0138893774853077[/C][C]0.067721[/C][C]0.2051[/C][C]0.83872[/C][C]0.41936[/C][/ROW]
[ROW][C]t[/C][C]-13.8206845223669[/C][C]8.781073[/C][C]-1.5739[/C][C]0.124767[/C][C]0.062384[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185666&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185666&T=2

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)28077.123660587917923.1498221.56650.1264860.063243
jaar-21314442.05222813605470.329206-1.56660.1264670.063234
pop-13.147646270348829.76534-0.44170.6614960.330748
vlaams_man0.8364778075668830.1061317.881600
man_vlaams_pop0.04715014859537640.0391471.20440.2367350.118367
vlaams_vrouw1.132387571872770.1073110.552500
vrouw_vlaams_pop-0.04490985563384750.036031-1.24640.2211260.110563
waals_man1.112067924007990.08552713.002600
man_waals_pop-0.03377439604406930.047276-0.71440.4798480.239924
waals_vrouw0.928672184713560.1072328.660400
vrouw_waals_pop0.03950078015560620.0662860.59590.5551760.277588
brussel_man0.9511180409801390.1182368.044200
man_brussel_pop-0.02260333573464190.075357-0.30.766040.38302
brussel_vrouw1.101691570439260.1116259.869600
vrouw_brussel_pop0.01388937748530770.0677210.20510.838720.41936
t-13.82068452236698.781073-1.57390.1247670.062384







Multiple Linear Regression - Regression Statistics
Multiple R0.999999127416479
R-squared0.999998254833719
Adjusted R-squared0.999997484907419
F-TEST (value)1298823.34762231
F-TEST (DF numerator)15
F-TEST (DF denominator)34
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.625454159930041
Sum Squared Residuals13.300558809909

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.999999127416479 \tabularnewline
R-squared & 0.999998254833719 \tabularnewline
Adjusted R-squared & 0.999997484907419 \tabularnewline
F-TEST (value) & 1298823.34762231 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 34 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.625454159930041 \tabularnewline
Sum Squared Residuals & 13.300558809909 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185666&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.999999127416479[/C][/ROW]
[ROW][C]R-squared[/C][C]0.999998254833719[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.999997484907419[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1298823.34762231[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]34[/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]0.625454159930041[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]13.300558809909[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185666&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185666&T=3

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Regression Statistics
Multiple R0.999999127416479
R-squared0.999998254833719
Adjusted R-squared0.999997484907419
F-TEST (value)1298823.34762231
F-TEST (DF numerator)15
F-TEST (DF denominator)34
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.625454159930041
Sum Squared Residuals13.300558809909







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
191909190.03166215015-0.031662150147516
292519250.72597219090.274027809101506
393289328.3339453377-0.333945337697938
494289428.84450862113-0.844508621128191
594999498.89629435840.103705641601395
695569555.855858730620.144141269378778
796069604.781732829111.21826717088526
896329631.242857535860.757142464144093
996609660.24842602742-0.248426027417757
1096519650.888191824310.111808175694669
1196959695.93415407212-0.934154072116918
1297279727.25016631417-0.250166314165801
1397579757.1816671442-0.181667144196003
1497889788.10043647916-0.100436479158595
1598139812.122129749360.877870250641633
1698239822.682704783850.317295216152959
1798379836.902525758020.0974742419762931
1898429842.24991108841-0.249911088412445
1998559856.01210009834-1.01210009833895
2098639864.22528281931-1.22528281931034
2198559854.34884137530.651158624696052
2298589858.09679191355-0.0967919135492537
2398539853.22374877865-0.223748778650978
2498589857.351708782430.648291217567291
2598599858.613717005630.386282994368908
2698659864.335668222410.664331777592909
2798769876.15155822476-0.15155822475686
2899289927.70177365820.298226341803655
2999489948.51274419602-0.512744196018935
3099879988.08478798247-1.08478798247262
311002210022.0338159539-0.0338159539116831
321006810067.94011482460.0598851753513681
331010110100.85369623770.146303762256546
341013110130.71803060350.281969396543092
351014310142.74237241680.257627583160653
361017010169.48327667030.516723329680716
371019210191.8334785260.16652147397086
381021410213.5623908510.437609149046182
391023910239.3015960772-0.301596077247167
401026310263.1713153628-0.17131536280786
411031010309.91995786910.0800421309329473
421035510355.1961176177-0.196117617745985
431039610396.491422587-0.491422587005978
441044610446.0635656821-0.0635656820742312
451051110510.7303955450.269604455042736
461058510584.44998181470.550018185337703
471066710666.98386792640.0161320735950905
481075310753.6265638849-0.626563884893406
491084010840.6560847692-0.656084769217903
501095110950.31008672810.689913271920019

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 9190 & 9190.03166215015 & -0.031662150147516 \tabularnewline
2 & 9251 & 9250.7259721909 & 0.274027809101506 \tabularnewline
3 & 9328 & 9328.3339453377 & -0.333945337697938 \tabularnewline
4 & 9428 & 9428.84450862113 & -0.844508621128191 \tabularnewline
5 & 9499 & 9498.8962943584 & 0.103705641601395 \tabularnewline
6 & 9556 & 9555.85585873062 & 0.144141269378778 \tabularnewline
7 & 9606 & 9604.78173282911 & 1.21826717088526 \tabularnewline
8 & 9632 & 9631.24285753586 & 0.757142464144093 \tabularnewline
9 & 9660 & 9660.24842602742 & -0.248426027417757 \tabularnewline
10 & 9651 & 9650.88819182431 & 0.111808175694669 \tabularnewline
11 & 9695 & 9695.93415407212 & -0.934154072116918 \tabularnewline
12 & 9727 & 9727.25016631417 & -0.250166314165801 \tabularnewline
13 & 9757 & 9757.1816671442 & -0.181667144196003 \tabularnewline
14 & 9788 & 9788.10043647916 & -0.100436479158595 \tabularnewline
15 & 9813 & 9812.12212974936 & 0.877870250641633 \tabularnewline
16 & 9823 & 9822.68270478385 & 0.317295216152959 \tabularnewline
17 & 9837 & 9836.90252575802 & 0.0974742419762931 \tabularnewline
18 & 9842 & 9842.24991108841 & -0.249911088412445 \tabularnewline
19 & 9855 & 9856.01210009834 & -1.01210009833895 \tabularnewline
20 & 9863 & 9864.22528281931 & -1.22528281931034 \tabularnewline
21 & 9855 & 9854.3488413753 & 0.651158624696052 \tabularnewline
22 & 9858 & 9858.09679191355 & -0.0967919135492537 \tabularnewline
23 & 9853 & 9853.22374877865 & -0.223748778650978 \tabularnewline
24 & 9858 & 9857.35170878243 & 0.648291217567291 \tabularnewline
25 & 9859 & 9858.61371700563 & 0.386282994368908 \tabularnewline
26 & 9865 & 9864.33566822241 & 0.664331777592909 \tabularnewline
27 & 9876 & 9876.15155822476 & -0.15155822475686 \tabularnewline
28 & 9928 & 9927.7017736582 & 0.298226341803655 \tabularnewline
29 & 9948 & 9948.51274419602 & -0.512744196018935 \tabularnewline
30 & 9987 & 9988.08478798247 & -1.08478798247262 \tabularnewline
31 & 10022 & 10022.0338159539 & -0.0338159539116831 \tabularnewline
32 & 10068 & 10067.9401148246 & 0.0598851753513681 \tabularnewline
33 & 10101 & 10100.8536962377 & 0.146303762256546 \tabularnewline
34 & 10131 & 10130.7180306035 & 0.281969396543092 \tabularnewline
35 & 10143 & 10142.7423724168 & 0.257627583160653 \tabularnewline
36 & 10170 & 10169.4832766703 & 0.516723329680716 \tabularnewline
37 & 10192 & 10191.833478526 & 0.16652147397086 \tabularnewline
38 & 10214 & 10213.562390851 & 0.437609149046182 \tabularnewline
39 & 10239 & 10239.3015960772 & -0.301596077247167 \tabularnewline
40 & 10263 & 10263.1713153628 & -0.17131536280786 \tabularnewline
41 & 10310 & 10309.9199578691 & 0.0800421309329473 \tabularnewline
42 & 10355 & 10355.1961176177 & -0.196117617745985 \tabularnewline
43 & 10396 & 10396.491422587 & -0.491422587005978 \tabularnewline
44 & 10446 & 10446.0635656821 & -0.0635656820742312 \tabularnewline
45 & 10511 & 10510.730395545 & 0.269604455042736 \tabularnewline
46 & 10585 & 10584.4499818147 & 0.550018185337703 \tabularnewline
47 & 10667 & 10666.9838679264 & 0.0161320735950905 \tabularnewline
48 & 10753 & 10753.6265638849 & -0.626563884893406 \tabularnewline
49 & 10840 & 10840.6560847692 & -0.656084769217903 \tabularnewline
50 & 10951 & 10950.3100867281 & 0.689913271920019 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185666&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]9190[/C][C]9190.03166215015[/C][C]-0.031662150147516[/C][/ROW]
[ROW][C]2[/C][C]9251[/C][C]9250.7259721909[/C][C]0.274027809101506[/C][/ROW]
[ROW][C]3[/C][C]9328[/C][C]9328.3339453377[/C][C]-0.333945337697938[/C][/ROW]
[ROW][C]4[/C][C]9428[/C][C]9428.84450862113[/C][C]-0.844508621128191[/C][/ROW]
[ROW][C]5[/C][C]9499[/C][C]9498.8962943584[/C][C]0.103705641601395[/C][/ROW]
[ROW][C]6[/C][C]9556[/C][C]9555.85585873062[/C][C]0.144141269378778[/C][/ROW]
[ROW][C]7[/C][C]9606[/C][C]9604.78173282911[/C][C]1.21826717088526[/C][/ROW]
[ROW][C]8[/C][C]9632[/C][C]9631.24285753586[/C][C]0.757142464144093[/C][/ROW]
[ROW][C]9[/C][C]9660[/C][C]9660.24842602742[/C][C]-0.248426027417757[/C][/ROW]
[ROW][C]10[/C][C]9651[/C][C]9650.88819182431[/C][C]0.111808175694669[/C][/ROW]
[ROW][C]11[/C][C]9695[/C][C]9695.93415407212[/C][C]-0.934154072116918[/C][/ROW]
[ROW][C]12[/C][C]9727[/C][C]9727.25016631417[/C][C]-0.250166314165801[/C][/ROW]
[ROW][C]13[/C][C]9757[/C][C]9757.1816671442[/C][C]-0.181667144196003[/C][/ROW]
[ROW][C]14[/C][C]9788[/C][C]9788.10043647916[/C][C]-0.100436479158595[/C][/ROW]
[ROW][C]15[/C][C]9813[/C][C]9812.12212974936[/C][C]0.877870250641633[/C][/ROW]
[ROW][C]16[/C][C]9823[/C][C]9822.68270478385[/C][C]0.317295216152959[/C][/ROW]
[ROW][C]17[/C][C]9837[/C][C]9836.90252575802[/C][C]0.0974742419762931[/C][/ROW]
[ROW][C]18[/C][C]9842[/C][C]9842.24991108841[/C][C]-0.249911088412445[/C][/ROW]
[ROW][C]19[/C][C]9855[/C][C]9856.01210009834[/C][C]-1.01210009833895[/C][/ROW]
[ROW][C]20[/C][C]9863[/C][C]9864.22528281931[/C][C]-1.22528281931034[/C][/ROW]
[ROW][C]21[/C][C]9855[/C][C]9854.3488413753[/C][C]0.651158624696052[/C][/ROW]
[ROW][C]22[/C][C]9858[/C][C]9858.09679191355[/C][C]-0.0967919135492537[/C][/ROW]
[ROW][C]23[/C][C]9853[/C][C]9853.22374877865[/C][C]-0.223748778650978[/C][/ROW]
[ROW][C]24[/C][C]9858[/C][C]9857.35170878243[/C][C]0.648291217567291[/C][/ROW]
[ROW][C]25[/C][C]9859[/C][C]9858.61371700563[/C][C]0.386282994368908[/C][/ROW]
[ROW][C]26[/C][C]9865[/C][C]9864.33566822241[/C][C]0.664331777592909[/C][/ROW]
[ROW][C]27[/C][C]9876[/C][C]9876.15155822476[/C][C]-0.15155822475686[/C][/ROW]
[ROW][C]28[/C][C]9928[/C][C]9927.7017736582[/C][C]0.298226341803655[/C][/ROW]
[ROW][C]29[/C][C]9948[/C][C]9948.51274419602[/C][C]-0.512744196018935[/C][/ROW]
[ROW][C]30[/C][C]9987[/C][C]9988.08478798247[/C][C]-1.08478798247262[/C][/ROW]
[ROW][C]31[/C][C]10022[/C][C]10022.0338159539[/C][C]-0.0338159539116831[/C][/ROW]
[ROW][C]32[/C][C]10068[/C][C]10067.9401148246[/C][C]0.0598851753513681[/C][/ROW]
[ROW][C]33[/C][C]10101[/C][C]10100.8536962377[/C][C]0.146303762256546[/C][/ROW]
[ROW][C]34[/C][C]10131[/C][C]10130.7180306035[/C][C]0.281969396543092[/C][/ROW]
[ROW][C]35[/C][C]10143[/C][C]10142.7423724168[/C][C]0.257627583160653[/C][/ROW]
[ROW][C]36[/C][C]10170[/C][C]10169.4832766703[/C][C]0.516723329680716[/C][/ROW]
[ROW][C]37[/C][C]10192[/C][C]10191.833478526[/C][C]0.16652147397086[/C][/ROW]
[ROW][C]38[/C][C]10214[/C][C]10213.562390851[/C][C]0.437609149046182[/C][/ROW]
[ROW][C]39[/C][C]10239[/C][C]10239.3015960772[/C][C]-0.301596077247167[/C][/ROW]
[ROW][C]40[/C][C]10263[/C][C]10263.1713153628[/C][C]-0.17131536280786[/C][/ROW]
[ROW][C]41[/C][C]10310[/C][C]10309.9199578691[/C][C]0.0800421309329473[/C][/ROW]
[ROW][C]42[/C][C]10355[/C][C]10355.1961176177[/C][C]-0.196117617745985[/C][/ROW]
[ROW][C]43[/C][C]10396[/C][C]10396.491422587[/C][C]-0.491422587005978[/C][/ROW]
[ROW][C]44[/C][C]10446[/C][C]10446.0635656821[/C][C]-0.0635656820742312[/C][/ROW]
[ROW][C]45[/C][C]10511[/C][C]10510.730395545[/C][C]0.269604455042736[/C][/ROW]
[ROW][C]46[/C][C]10585[/C][C]10584.4499818147[/C][C]0.550018185337703[/C][/ROW]
[ROW][C]47[/C][C]10667[/C][C]10666.9838679264[/C][C]0.0161320735950905[/C][/ROW]
[ROW][C]48[/C][C]10753[/C][C]10753.6265638849[/C][C]-0.626563884893406[/C][/ROW]
[ROW][C]49[/C][C]10840[/C][C]10840.6560847692[/C][C]-0.656084769217903[/C][/ROW]
[ROW][C]50[/C][C]10951[/C][C]10950.3100867281[/C][C]0.689913271920019[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185666&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185666&T=4

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
191909190.03166215015-0.031662150147516
292519250.72597219090.274027809101506
393289328.3339453377-0.333945337697938
494289428.84450862113-0.844508621128191
594999498.89629435840.103705641601395
695569555.855858730620.144141269378778
796069604.781732829111.21826717088526
896329631.242857535860.757142464144093
996609660.24842602742-0.248426027417757
1096519650.888191824310.111808175694669
1196959695.93415407212-0.934154072116918
1297279727.25016631417-0.250166314165801
1397579757.1816671442-0.181667144196003
1497889788.10043647916-0.100436479158595
1598139812.122129749360.877870250641633
1698239822.682704783850.317295216152959
1798379836.902525758020.0974742419762931
1898429842.24991108841-0.249911088412445
1998559856.01210009834-1.01210009833895
2098639864.22528281931-1.22528281931034
2198559854.34884137530.651158624696052
2298589858.09679191355-0.0967919135492537
2398539853.22374877865-0.223748778650978
2498589857.351708782430.648291217567291
2598599858.613717005630.386282994368908
2698659864.335668222410.664331777592909
2798769876.15155822476-0.15155822475686
2899289927.70177365820.298226341803655
2999489948.51274419602-0.512744196018935
3099879988.08478798247-1.08478798247262
311002210022.0338159539-0.0338159539116831
321006810067.94011482460.0598851753513681
331010110100.85369623770.146303762256546
341013110130.71803060350.281969396543092
351014310142.74237241680.257627583160653
361017010169.48327667030.516723329680716
371019210191.8334785260.16652147397086
381021410213.5623908510.437609149046182
391023910239.3015960772-0.301596077247167
401026310263.1713153628-0.17131536280786
411031010309.91995786910.0800421309329473
421035510355.1961176177-0.196117617745985
431039610396.491422587-0.491422587005978
441044610446.0635656821-0.0635656820742312
451051110510.7303955450.269604455042736
461058510584.44998181470.550018185337703
471066710666.98386792640.0161320735950905
481075310753.6265638849-0.626563884893406
491084010840.6560847692-0.656084769217903
501095110950.31008672810.689913271920019







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.2814684976018110.5629369952036220.718531502398189
200.3065884978928810.6131769957857610.693411502107119
210.1766513348121350.353302669624270.823348665187865
220.176425847463290.3528516949265790.82357415253671
230.4427707467245120.8855414934490250.557229253275488
240.5894891539931810.8210216920136380.410510846006819
250.8285228372540480.3429543254919040.171477162745952
260.9509780747330150.0980438505339710.0490219252669855
270.9955756790369130.008848641926174320.00442432096308716
280.9971164716329630.005767056734073820.00288352836703691
290.9916005011577010.01679899768459810.00839949884229906
300.983421457940880.03315708411823910.0165785420591196
310.9981109648894650.003778070221070240.00188903511053512

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.281468497601811 & 0.562936995203622 & 0.718531502398189 \tabularnewline
20 & 0.306588497892881 & 0.613176995785761 & 0.693411502107119 \tabularnewline
21 & 0.176651334812135 & 0.35330266962427 & 0.823348665187865 \tabularnewline
22 & 0.17642584746329 & 0.352851694926579 & 0.82357415253671 \tabularnewline
23 & 0.442770746724512 & 0.885541493449025 & 0.557229253275488 \tabularnewline
24 & 0.589489153993181 & 0.821021692013638 & 0.410510846006819 \tabularnewline
25 & 0.828522837254048 & 0.342954325491904 & 0.171477162745952 \tabularnewline
26 & 0.950978074733015 & 0.098043850533971 & 0.0490219252669855 \tabularnewline
27 & 0.995575679036913 & 0.00884864192617432 & 0.00442432096308716 \tabularnewline
28 & 0.997116471632963 & 0.00576705673407382 & 0.00288352836703691 \tabularnewline
29 & 0.991600501157701 & 0.0167989976845981 & 0.00839949884229906 \tabularnewline
30 & 0.98342145794088 & 0.0331570841182391 & 0.0165785420591196 \tabularnewline
31 & 0.998110964889465 & 0.00377807022107024 & 0.00188903511053512 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185666&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]19[/C][C]0.281468497601811[/C][C]0.562936995203622[/C][C]0.718531502398189[/C][/ROW]
[ROW][C]20[/C][C]0.306588497892881[/C][C]0.613176995785761[/C][C]0.693411502107119[/C][/ROW]
[ROW][C]21[/C][C]0.176651334812135[/C][C]0.35330266962427[/C][C]0.823348665187865[/C][/ROW]
[ROW][C]22[/C][C]0.17642584746329[/C][C]0.352851694926579[/C][C]0.82357415253671[/C][/ROW]
[ROW][C]23[/C][C]0.442770746724512[/C][C]0.885541493449025[/C][C]0.557229253275488[/C][/ROW]
[ROW][C]24[/C][C]0.589489153993181[/C][C]0.821021692013638[/C][C]0.410510846006819[/C][/ROW]
[ROW][C]25[/C][C]0.828522837254048[/C][C]0.342954325491904[/C][C]0.171477162745952[/C][/ROW]
[ROW][C]26[/C][C]0.950978074733015[/C][C]0.098043850533971[/C][C]0.0490219252669855[/C][/ROW]
[ROW][C]27[/C][C]0.995575679036913[/C][C]0.00884864192617432[/C][C]0.00442432096308716[/C][/ROW]
[ROW][C]28[/C][C]0.997116471632963[/C][C]0.00576705673407382[/C][C]0.00288352836703691[/C][/ROW]
[ROW][C]29[/C][C]0.991600501157701[/C][C]0.0167989976845981[/C][C]0.00839949884229906[/C][/ROW]
[ROW][C]30[/C][C]0.98342145794088[/C][C]0.0331570841182391[/C][C]0.0165785420591196[/C][/ROW]
[ROW][C]31[/C][C]0.998110964889465[/C][C]0.00377807022107024[/C][C]0.00188903511053512[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185666&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185666&T=5

As an alternative you can also use a QR Code:  

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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.2814684976018110.5629369952036220.718531502398189
200.3065884978928810.6131769957857610.693411502107119
210.1766513348121350.353302669624270.823348665187865
220.176425847463290.3528516949265790.82357415253671
230.4427707467245120.8855414934490250.557229253275488
240.5894891539931810.8210216920136380.410510846006819
250.8285228372540480.3429543254919040.171477162745952
260.9509780747330150.0980438505339710.0490219252669855
270.9955756790369130.008848641926174320.00442432096308716
280.9971164716329630.005767056734073820.00288352836703691
290.9916005011577010.01679899768459810.00839949884229906
300.983421457940880.03315708411823910.0165785420591196
310.9981109648894650.003778070221070240.00188903511053512







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level30.230769230769231NOK
5% type I error level50.384615384615385NOK
10% type I error level60.461538461538462NOK

\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 & 3 & 0.230769230769231 & NOK \tabularnewline
5% type I error level & 5 & 0.384615384615385 & NOK \tabularnewline
10% type I error level & 6 & 0.461538461538462 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185666&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]3[/C][C]0.230769230769231[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]5[/C][C]0.384615384615385[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]6[/C][C]0.461538461538462[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185666&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185666&T=6

As an alternative you can also use a QR Code:  

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level30.230769230769231NOK
5% type I error level50.384615384615385NOK
10% type I error level60.461538461538462NOK



Parameters (Session):
par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}