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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 02 Nov 2012 13:20:14 -0400

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/02/t1351876895avn4kxvzz2prh7j.htm/, Retrieved Fri, 19 Apr 2024 08:39:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=185654, Retrieved Fri, 19 Apr 2024 08:39:13 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

185

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] [7a9100b3135ff0dae36397155af309d9] [Current]
-   PD          [Multiple Regression] [workshop 7: berek...] [2012-11-02 19:46:17] [40b341cf5fb1ddfd74e4c5704837f48c] 
- 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] 
- R             [Multiple Regression] [Multiple regressi...] [2012-12-21 15:06:33] [426d1a1037dab69a05582f8f9c03d6e4] 

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Dataseries X:

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31/12/1961	9190	2514	2550	1512	1591	472	551
31/12/1962	9251	2537	2572	1517	1595	476	554
31/12/1963	9328	2564	2597	1525	1602	483	558
31/12/1964	9428	2595	2623	1540	1613	493	565
31/12/1965	9499	2617	2647	1547	1622	498	568
31/12/1966	9556	2638	2670	1547	1627	502	572
31/12/1967	9606	2657	2690	1547	1632	504	575
31/12/1968	9632	2668	2705	1547	1634	503	574
31/12/1969	9660	2683	2721	1546	1637	501	572
31/12/1970	9651	2687	2729	1533	1627	502	573
31/12/1971	9695	2705	2747	1538	1632	502	572
31/12/1972	9727	2717	2761	1543	1637	500	569
31/12/1973	9757	2728	2773	1549	1643	498	566
31/12/1974	9788	2741	2786	1556	1650	495	560
31/12/1975	9813	2752	2796	1559	1654	494	557
31/12/1976	9823	2759	2807	1559	1656	490	552
31/12/1977	9837	2767	2817	1563	1661	484	545
31/12/1978	9842	2774	2827	1563	1662	477	539
31/12/1979	9855	2781	2838	1564	1664	474	535
31/12/1980	9863	2788	2847	1564	1665	469	531
31/12/1981	9855	2789	2853	1557	1661	466	528
31/12/1982	9858	2795	2860	1554	1659	464	526
31/12/1983	9853	2798	2864	1552	1656	460	523
31/12/1984	9858	2801	2869	1552	1656	458	521
31/12/1985	9859	2803	2873	1551	1655	457	519
31/12/1986	9865	2808	2877	1552	1654	456	517
31/12/1987	9876	2813	2883	1554	1656	455	515
31/12/1988	9928	2826	2896	1567	1668	456	514
31/12/1989	9948	2835	2905	1572	1672	453	511
31/12/1990	9987	2849	2919	1579	1680	453	508
31/12/1991	10022	2862	2933	1588	1688	449	502
31/12/1992	10068	2877	2948	1597	1696	449	501
31/12/1993	10101	2888	2959	1603	1702	449	500
31/12/1994	10131	2897	2969	1607	1706	452	500
31/12/1995	10143	2902	2978	1607	1708	450	498
31/12/1996	10170	2911	2988	1609	1711	452	499
31/12/1997	10192	2917	2996	1612	1714	454	499
31/12/1998	10214	2924	3003	1615	1717	455	500
31/12/1999	10239	2930	3011	1619	1721	458	501
31/12/2000	10263	2935	3018	1622	1724	461	503
31/12/2001	10310	2945	3028	1628	1730	469	510
31/12/2002	10355	2957	3038	1634	1735	477	515
31/12/2003	10396	2967	3049	1640	1740	480	520
31/12/2004	10446	2980	3063	1648	1748	484	523
31/12/2005	10511	2997	3081	1657	1757	490	529
31/12/2006	10585	3017	3100	1668	1768	497	534
31/12/2007	10667	3040	3122	1678	1778	506	543
31/12/2008	10753	3064	3145	1687	1789	516	553
31/12/2009	10840	3085	3167	1700	1798	527	563
31/12/2010	10951	3113	3193	1714	1811	542	577

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	8 seconds
R Server	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.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=185654&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]'George Udny Yule' @ yule.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=185654&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185654&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	8 seconds
R Server	'George Udny Yule' @ yule.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] = + 30804.5369680775 -23401252.9732768jaar[t] + 0.870436647176309vlaams_man[t] + 1.09619421051282vlaams_vrouw[t] + 1.08567272568283waals_man[t] + 0.972768756511784waals_vrouw[t] + 0.909537250570316brussel_man[t] + 1.13627288054705brussel_vrouw[t] -15.1769126220416t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
totaal[t] =  +  30804.5369680775 -23401252.9732768jaar[t] +  0.870436647176309vlaams_man[t] +  1.09619421051282vlaams_vrouw[t] +  1.08567272568283waals_man[t] +  0.972768756511784waals_vrouw[t] +  0.909537250570316brussel_man[t] +  1.13627288054705brussel_vrouw[t] -15.1769126220416t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185654&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]totaal[t] =  +  30804.5369680775 -23401252.9732768jaar[t] +  0.870436647176309vlaams_man[t] +  1.09619421051282vlaams_vrouw[t] +  1.08567272568283waals_man[t] +  0.972768756511784waals_vrouw[t] +  0.909537250570316brussel_man[t] +  1.13627288054705brussel_vrouw[t] -15.1769126220416t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185654&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185654&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] = + 30804.5369680775 -23401252.9732768jaar[t] + 0.870436647176309vlaams_man[t] + 1.09619421051282vlaams_vrouw[t] + 1.08567272568283waals_man[t] + 0.972768756511784waals_vrouw[t] + 0.909537250570316brussel_man[t] + 1.13627288054705brussel_vrouw[t] -15.1769126220416t + 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)	30804.5369680775	17412.998433	1.7691	0.084323	0.042162
jaar	-23401252.9732768	13217986.10236	-1.7704	0.084094	0.042047
vlaams_man	0.870436647176309	0.08397	10.3661	0	0
vlaams_vrouw	1.09619421051282	0.083069	13.1961	0	0
waals_man	1.08567272568283	0.065387	16.6037	0	0
waals_vrouw	0.972768756511784	0.073952	13.1541	0	0
brussel_man	0.909537250570316	0.067987	13.3781	0	0
brussel_vrouw	1.13627288054705	0.072378	15.6992	0	0
t	-15.1769126220416	8.526204	-1.78	0.082483	0.041242

\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) & 30804.5369680775 & 17412.998433 & 1.7691 & 0.084323 & 0.042162 \tabularnewline
jaar & -23401252.9732768 & 13217986.10236 & -1.7704 & 0.084094 & 0.042047 \tabularnewline
vlaams_man & 0.870436647176309 & 0.08397 & 10.3661 & 0 & 0 \tabularnewline
vlaams_vrouw & 1.09619421051282 & 0.083069 & 13.1961 & 0 & 0 \tabularnewline
waals_man & 1.08567272568283 & 0.065387 & 16.6037 & 0 & 0 \tabularnewline
waals_vrouw & 0.972768756511784 & 0.073952 & 13.1541 & 0 & 0 \tabularnewline
brussel_man & 0.909537250570316 & 0.067987 & 13.3781 & 0 & 0 \tabularnewline
brussel_vrouw & 1.13627288054705 & 0.072378 & 15.6992 & 0 & 0 \tabularnewline
t & -15.1769126220416 & 8.526204 & -1.78 & 0.082483 & 0.041242 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185654&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]30804.5369680775[/C][C]17412.998433[/C][C]1.7691[/C][C]0.084323[/C][C]0.042162[/C][/ROW]
[ROW][C]jaar[/C][C]-23401252.9732768[/C][C]13217986.10236[/C][C]-1.7704[/C][C]0.084094[/C][C]0.042047[/C][/ROW]
[ROW][C]vlaams_man[/C][C]0.870436647176309[/C][C]0.08397[/C][C]10.3661[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]vlaams_vrouw[/C][C]1.09619421051282[/C][C]0.083069[/C][C]13.1961[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]waals_man[/C][C]1.08567272568283[/C][C]0.065387[/C][C]16.6037[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]waals_vrouw[/C][C]0.972768756511784[/C][C]0.073952[/C][C]13.1541[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]brussel_man[/C][C]0.909537250570316[/C][C]0.067987[/C][C]13.3781[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]brussel_vrouw[/C][C]1.13627288054705[/C][C]0.072378[/C][C]15.6992[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]t[/C][C]-15.1769126220416[/C][C]8.526204[/C][C]-1.78[/C][C]0.082483[/C][C]0.041242[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185654&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185654&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)	30804.5369680775	17412.998433	1.7691	0.084323	0.042162
jaar	-23401252.9732768	13217986.10236	-1.7704	0.084094	0.042047
vlaams_man	0.870436647176309	0.08397	10.3661	0	0
vlaams_vrouw	1.09619421051282	0.083069	13.1961	0	0
waals_man	1.08567272568283	0.065387	16.6037	0	0
waals_vrouw	0.972768756511784	0.073952	13.1541	0	0
brussel_man	0.909537250570316	0.067987	13.3781	0	0
brussel_vrouw	1.13627288054705	0.072378	15.6992	0	0
t	-15.1769126220416	8.526204	-1.78	0.082483	0.041242

Multiple Linear Regression - Regression Statistics
Multiple R	0.999998996517776
R-squared	0.999997993036559
Adjusted R-squared	0.999997601433936
F-TEST (value)	2553603.92142985
F-TEST (DF numerator)	8
F-TEST (DF denominator)	41
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.61079340580206
Sum Squared Residuals	15.2958119674225

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.999998996517776 \tabularnewline
R-squared & 0.999997993036559 \tabularnewline
Adjusted R-squared & 0.999997601433936 \tabularnewline
F-TEST (value) & 2553603.92142985 \tabularnewline
F-TEST (DF numerator) & 8 \tabularnewline
F-TEST (DF denominator) & 41 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.61079340580206 \tabularnewline
Sum Squared Residuals & 15.2958119674225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185654&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.999998996517776[/C][/ROW]
[ROW][C]R-squared[/C][C]0.999997993036559[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.999997601433936[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]2553603.92142985[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]8[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]41[/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]0.61079340580206[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]15.2958119674225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185654&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185654&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	0.999998996517776
R-squared	0.999997993036559
Adjusted R-squared	0.999997601433936
F-TEST (value)	2553603.92142985
F-TEST (DF numerator)	8
F-TEST (DF denominator)	41
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.61079340580206
Sum Squared Residuals	15.2958119674225

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	9190	9189.77347683671	0.226523163287704
2	9251	9250.81170179836	0.188298201637033
3	9328	9328.6444564847	-0.644456484702895
4	9428	9428.66738234806	-0.66738234806104
5	9499	9498.92433315414	0.0756668458610427
6	9556	9555.93466926213	0.0653307378749467
7	9606	9604.94429100204	1.0557089979562
8	9632	9631.30155216273	0.698447837264957
9	9660	9660.06217742192	-0.0621774219207797
10	9651	9650.92597128438	0.0740287156173079
11	9695	9695.87356337378	-0.873563373777729
12	9727	9727.10634819719	-0.106348197191145
13	9757	9757.31898316549	-0.318983165493528
14	9788	9788.09302892045	-0.0930289204474411
15	9813	9811.78879632419	1.21120367581114
16	9823	9822.87960361499	0.120396385009302
17	9837	9836.89835953629	0.101640463713074
18	9842	9842.02400156293	-0.024001562932786
19	9855	9856.19935081646	-1.19935081645882
20	9863	9864.28919610798	-1.28919610797912
21	9855	9854.34405747037	0.655942529625127
22	9858	9858.16578246824	-0.165782468244185
23	9853	9853.22964265127	-0.229642651268907
24	9858	9857.41919079922	0.58080920078305
25	9859	9858.47772194346	0.522278056542202
26	9865	9864.30344995278	0.696550047222603
27	9876	9876.31011019002	-0.310110190018058
28	9928	9927.5636461118	0.436353888201801
29	9948	9948.5570433318	-0.55704333179597
30	9987	9988.15926161825	-1.1592616182492
31	10022	10022.0000787662	-7.8766211996077e-05
32	10068	10067.9821576312	0.0178423688248848
33	10101	10100.8798612419	0.120138758075812
34	10131	10130.6732258955	0.326774104470233
35	10143	10142.7649391672	0.235060832832552
36	10170	10169.6104478578	0.389552142152874
37	10192	10191.5864536743	0.413546325707174
38	10214	10213.5482560299	0.451743970071526
39	10239	10239.5981731885	-0.598173188471221
40	10263	10262.744154882	0.255845117979388
41	10310	10309.9201642322	0.0798357678287411
42	10355	10355.5766416934	-0.576641693397184
43	10396	10396.0256857544	-0.0256857543607167
44	10446	10446.0862200922	-0.0862200921823565
45	10511	10511.2845894911	-0.284589491120514
46	10585	10584.065609849	0.934390151005746
47	10667	10667.0372692159	-0.0372692158626008
48	10753	10753.8935098748	-0.89350987480154
49	10840	10840.3340036275	-0.334003627516723
50	10951	10950.3974079229	0.602592077110022

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 9190 & 9189.77347683671 & 0.226523163287704 \tabularnewline
2 & 9251 & 9250.81170179836 & 0.188298201637033 \tabularnewline
3 & 9328 & 9328.6444564847 & -0.644456484702895 \tabularnewline
4 & 9428 & 9428.66738234806 & -0.66738234806104 \tabularnewline
5 & 9499 & 9498.92433315414 & 0.0756668458610427 \tabularnewline
6 & 9556 & 9555.93466926213 & 0.0653307378749467 \tabularnewline
7 & 9606 & 9604.94429100204 & 1.0557089979562 \tabularnewline
8 & 9632 & 9631.30155216273 & 0.698447837264957 \tabularnewline
9 & 9660 & 9660.06217742192 & -0.0621774219207797 \tabularnewline
10 & 9651 & 9650.92597128438 & 0.0740287156173079 \tabularnewline
11 & 9695 & 9695.87356337378 & -0.873563373777729 \tabularnewline
12 & 9727 & 9727.10634819719 & -0.106348197191145 \tabularnewline
13 & 9757 & 9757.31898316549 & -0.318983165493528 \tabularnewline
14 & 9788 & 9788.09302892045 & -0.0930289204474411 \tabularnewline
15 & 9813 & 9811.78879632419 & 1.21120367581114 \tabularnewline
16 & 9823 & 9822.87960361499 & 0.120396385009302 \tabularnewline
17 & 9837 & 9836.89835953629 & 0.101640463713074 \tabularnewline
18 & 9842 & 9842.02400156293 & -0.024001562932786 \tabularnewline
19 & 9855 & 9856.19935081646 & -1.19935081645882 \tabularnewline
20 & 9863 & 9864.28919610798 & -1.28919610797912 \tabularnewline
21 & 9855 & 9854.34405747037 & 0.655942529625127 \tabularnewline
22 & 9858 & 9858.16578246824 & -0.165782468244185 \tabularnewline
23 & 9853 & 9853.22964265127 & -0.229642651268907 \tabularnewline
24 & 9858 & 9857.41919079922 & 0.58080920078305 \tabularnewline
25 & 9859 & 9858.47772194346 & 0.522278056542202 \tabularnewline
26 & 9865 & 9864.30344995278 & 0.696550047222603 \tabularnewline
27 & 9876 & 9876.31011019002 & -0.310110190018058 \tabularnewline
28 & 9928 & 9927.5636461118 & 0.436353888201801 \tabularnewline
29 & 9948 & 9948.5570433318 & -0.55704333179597 \tabularnewline
30 & 9987 & 9988.15926161825 & -1.1592616182492 \tabularnewline
31 & 10022 & 10022.0000787662 & -7.8766211996077e-05 \tabularnewline
32 & 10068 & 10067.9821576312 & 0.0178423688248848 \tabularnewline
33 & 10101 & 10100.8798612419 & 0.120138758075812 \tabularnewline
34 & 10131 & 10130.6732258955 & 0.326774104470233 \tabularnewline
35 & 10143 & 10142.7649391672 & 0.235060832832552 \tabularnewline
36 & 10170 & 10169.6104478578 & 0.389552142152874 \tabularnewline
37 & 10192 & 10191.5864536743 & 0.413546325707174 \tabularnewline
38 & 10214 & 10213.5482560299 & 0.451743970071526 \tabularnewline
39 & 10239 & 10239.5981731885 & -0.598173188471221 \tabularnewline
40 & 10263 & 10262.744154882 & 0.255845117979388 \tabularnewline
41 & 10310 & 10309.9201642322 & 0.0798357678287411 \tabularnewline
42 & 10355 & 10355.5766416934 & -0.576641693397184 \tabularnewline
43 & 10396 & 10396.0256857544 & -0.0256857543607167 \tabularnewline
44 & 10446 & 10446.0862200922 & -0.0862200921823565 \tabularnewline
45 & 10511 & 10511.2845894911 & -0.284589491120514 \tabularnewline
46 & 10585 & 10584.065609849 & 0.934390151005746 \tabularnewline
47 & 10667 & 10667.0372692159 & -0.0372692158626008 \tabularnewline
48 & 10753 & 10753.8935098748 & -0.89350987480154 \tabularnewline
49 & 10840 & 10840.3340036275 & -0.334003627516723 \tabularnewline
50 & 10951 & 10950.3974079229 & 0.602592077110022 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185654&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]9189.77347683671[/C][C]0.226523163287704[/C][/ROW]
[ROW][C]2[/C][C]9251[/C][C]9250.81170179836[/C][C]0.188298201637033[/C][/ROW]
[ROW][C]3[/C][C]9328[/C][C]9328.6444564847[/C][C]-0.644456484702895[/C][/ROW]
[ROW][C]4[/C][C]9428[/C][C]9428.66738234806[/C][C]-0.66738234806104[/C][/ROW]
[ROW][C]5[/C][C]9499[/C][C]9498.92433315414[/C][C]0.0756668458610427[/C][/ROW]
[ROW][C]6[/C][C]9556[/C][C]9555.93466926213[/C][C]0.0653307378749467[/C][/ROW]
[ROW][C]7[/C][C]9606[/C][C]9604.94429100204[/C][C]1.0557089979562[/C][/ROW]
[ROW][C]8[/C][C]9632[/C][C]9631.30155216273[/C][C]0.698447837264957[/C][/ROW]
[ROW][C]9[/C][C]9660[/C][C]9660.06217742192[/C][C]-0.0621774219207797[/C][/ROW]
[ROW][C]10[/C][C]9651[/C][C]9650.92597128438[/C][C]0.0740287156173079[/C][/ROW]
[ROW][C]11[/C][C]9695[/C][C]9695.87356337378[/C][C]-0.873563373777729[/C][/ROW]
[ROW][C]12[/C][C]9727[/C][C]9727.10634819719[/C][C]-0.106348197191145[/C][/ROW]
[ROW][C]13[/C][C]9757[/C][C]9757.31898316549[/C][C]-0.318983165493528[/C][/ROW]
[ROW][C]14[/C][C]9788[/C][C]9788.09302892045[/C][C]-0.0930289204474411[/C][/ROW]
[ROW][C]15[/C][C]9813[/C][C]9811.78879632419[/C][C]1.21120367581114[/C][/ROW]
[ROW][C]16[/C][C]9823[/C][C]9822.87960361499[/C][C]0.120396385009302[/C][/ROW]
[ROW][C]17[/C][C]9837[/C][C]9836.89835953629[/C][C]0.101640463713074[/C][/ROW]
[ROW][C]18[/C][C]9842[/C][C]9842.02400156293[/C][C]-0.024001562932786[/C][/ROW]
[ROW][C]19[/C][C]9855[/C][C]9856.19935081646[/C][C]-1.19935081645882[/C][/ROW]
[ROW][C]20[/C][C]9863[/C][C]9864.28919610798[/C][C]-1.28919610797912[/C][/ROW]
[ROW][C]21[/C][C]9855[/C][C]9854.34405747037[/C][C]0.655942529625127[/C][/ROW]
[ROW][C]22[/C][C]9858[/C][C]9858.16578246824[/C][C]-0.165782468244185[/C][/ROW]
[ROW][C]23[/C][C]9853[/C][C]9853.22964265127[/C][C]-0.229642651268907[/C][/ROW]
[ROW][C]24[/C][C]9858[/C][C]9857.41919079922[/C][C]0.58080920078305[/C][/ROW]
[ROW][C]25[/C][C]9859[/C][C]9858.47772194346[/C][C]0.522278056542202[/C][/ROW]
[ROW][C]26[/C][C]9865[/C][C]9864.30344995278[/C][C]0.696550047222603[/C][/ROW]
[ROW][C]27[/C][C]9876[/C][C]9876.31011019002[/C][C]-0.310110190018058[/C][/ROW]
[ROW][C]28[/C][C]9928[/C][C]9927.5636461118[/C][C]0.436353888201801[/C][/ROW]
[ROW][C]29[/C][C]9948[/C][C]9948.5570433318[/C][C]-0.55704333179597[/C][/ROW]
[ROW][C]30[/C][C]9987[/C][C]9988.15926161825[/C][C]-1.1592616182492[/C][/ROW]
[ROW][C]31[/C][C]10022[/C][C]10022.0000787662[/C][C]-7.8766211996077e-05[/C][/ROW]
[ROW][C]32[/C][C]10068[/C][C]10067.9821576312[/C][C]0.0178423688248848[/C][/ROW]
[ROW][C]33[/C][C]10101[/C][C]10100.8798612419[/C][C]0.120138758075812[/C][/ROW]
[ROW][C]34[/C][C]10131[/C][C]10130.6732258955[/C][C]0.326774104470233[/C][/ROW]
[ROW][C]35[/C][C]10143[/C][C]10142.7649391672[/C][C]0.235060832832552[/C][/ROW]
[ROW][C]36[/C][C]10170[/C][C]10169.6104478578[/C][C]0.389552142152874[/C][/ROW]
[ROW][C]37[/C][C]10192[/C][C]10191.5864536743[/C][C]0.413546325707174[/C][/ROW]
[ROW][C]38[/C][C]10214[/C][C]10213.5482560299[/C][C]0.451743970071526[/C][/ROW]
[ROW][C]39[/C][C]10239[/C][C]10239.5981731885[/C][C]-0.598173188471221[/C][/ROW]
[ROW][C]40[/C][C]10263[/C][C]10262.744154882[/C][C]0.255845117979388[/C][/ROW]
[ROW][C]41[/C][C]10310[/C][C]10309.9201642322[/C][C]0.0798357678287411[/C][/ROW]
[ROW][C]42[/C][C]10355[/C][C]10355.5766416934[/C][C]-0.576641693397184[/C][/ROW]
[ROW][C]43[/C][C]10396[/C][C]10396.0256857544[/C][C]-0.0256857543607167[/C][/ROW]
[ROW][C]44[/C][C]10446[/C][C]10446.0862200922[/C][C]-0.0862200921823565[/C][/ROW]
[ROW][C]45[/C][C]10511[/C][C]10511.2845894911[/C][C]-0.284589491120514[/C][/ROW]
[ROW][C]46[/C][C]10585[/C][C]10584.065609849[/C][C]0.934390151005746[/C][/ROW]
[ROW][C]47[/C][C]10667[/C][C]10667.0372692159[/C][C]-0.0372692158626008[/C][/ROW]
[ROW][C]48[/C][C]10753[/C][C]10753.8935098748[/C][C]-0.89350987480154[/C][/ROW]
[ROW][C]49[/C][C]10840[/C][C]10840.3340036275[/C][C]-0.334003627516723[/C][/ROW]
[ROW][C]50[/C][C]10951[/C][C]10950.3974079229[/C][C]0.602592077110022[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185654&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185654&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	9190	9189.77347683671	0.226523163287704
2	9251	9250.81170179836	0.188298201637033
3	9328	9328.6444564847	-0.644456484702895
4	9428	9428.66738234806	-0.66738234806104
5	9499	9498.92433315414	0.0756668458610427
6	9556	9555.93466926213	0.0653307378749467
7	9606	9604.94429100204	1.0557089979562
8	9632	9631.30155216273	0.698447837264957
9	9660	9660.06217742192	-0.0621774219207797
10	9651	9650.92597128438	0.0740287156173079
11	9695	9695.87356337378	-0.873563373777729
12	9727	9727.10634819719	-0.106348197191145
13	9757	9757.31898316549	-0.318983165493528
14	9788	9788.09302892045	-0.0930289204474411
15	9813	9811.78879632419	1.21120367581114
16	9823	9822.87960361499	0.120396385009302
17	9837	9836.89835953629	0.101640463713074
18	9842	9842.02400156293	-0.024001562932786
19	9855	9856.19935081646	-1.19935081645882
20	9863	9864.28919610798	-1.28919610797912
21	9855	9854.34405747037	0.655942529625127
22	9858	9858.16578246824	-0.165782468244185
23	9853	9853.22964265127	-0.229642651268907
24	9858	9857.41919079922	0.58080920078305
25	9859	9858.47772194346	0.522278056542202
26	9865	9864.30344995278	0.696550047222603
27	9876	9876.31011019002	-0.310110190018058
28	9928	9927.5636461118	0.436353888201801
29	9948	9948.5570433318	-0.55704333179597
30	9987	9988.15926161825	-1.1592616182492
31	10022	10022.0000787662	-7.8766211996077e-05
32	10068	10067.9821576312	0.0178423688248848
33	10101	10100.8798612419	0.120138758075812
34	10131	10130.6732258955	0.326774104470233
35	10143	10142.7649391672	0.235060832832552
36	10170	10169.6104478578	0.389552142152874
37	10192	10191.5864536743	0.413546325707174
38	10214	10213.5482560299	0.451743970071526
39	10239	10239.5981731885	-0.598173188471221
40	10263	10262.744154882	0.255845117979388
41	10310	10309.9201642322	0.0798357678287411
42	10355	10355.5766416934	-0.576641693397184
43	10396	10396.0256857544	-0.0256857543607167
44	10446	10446.0862200922	-0.0862200921823565
45	10511	10511.2845894911	-0.284589491120514
46	10585	10584.065609849	0.934390151005746
47	10667	10667.0372692159	-0.0372692158626008
48	10753	10753.8935098748	-0.89350987480154
49	10840	10840.3340036275	-0.334003627516723
50	10951	10950.3974079229	0.602592077110022

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
12	0.426155624448077	0.852311248896154	0.573844375551923
13	0.279084312238462	0.558168624476924	0.720915687761538
14	0.288219859976913	0.576439719953826	0.711780140023087
15	0.30745934464137	0.614918689282739	0.69254065535863
16	0.276177609322577	0.552355218645155	0.723822390677423
17	0.224257766897938	0.448515533795875	0.775742233102062
18	0.307821109235839	0.615642218471678	0.692178890764161
19	0.269643415191122	0.539286830382244	0.730356584808878
20	0.292667936291326	0.585335872582653	0.707332063708674
21	0.563491788957937	0.873016422084127	0.436508211042064
22	0.554098226757133	0.891803546485734	0.445901773242867
23	0.620463255931296	0.759073488137407	0.379536744068704
24	0.556634964384487	0.886730071231027	0.443365035615513
25	0.606655680740953	0.786688638518093	0.393344319259047
26	0.595472278661484	0.809055442677032	0.404527721338516
27	0.76358543229852	0.47282913540296	0.23641456770148
28	0.868559884791257	0.262880230417485	0.131440115208743
29	0.870960914547067	0.258078170905865	0.129039085452933
30	0.80812310596933	0.383753788061341	0.19187689403067
31	0.86744197116106	0.26511605767788	0.13255802883894
32	0.875295288383251	0.249409423233497	0.124704711616749
33	0.833362315600216	0.333275368799568	0.166637684399784
34	0.760634505220777	0.478730989558446	0.239365494779223
35	0.693326222989381	0.613347554021238	0.306673777010619
36	0.575783531385641	0.848432937228717	0.424216468614359
37	0.50487749289238	0.990245014215239	0.49512250710762
38	0.360342707844356	0.720685415688711	0.639657292155644

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
12 & 0.426155624448077 & 0.852311248896154 & 0.573844375551923 \tabularnewline
13 & 0.279084312238462 & 0.558168624476924 & 0.720915687761538 \tabularnewline
14 & 0.288219859976913 & 0.576439719953826 & 0.711780140023087 \tabularnewline
15 & 0.30745934464137 & 0.614918689282739 & 0.69254065535863 \tabularnewline
16 & 0.276177609322577 & 0.552355218645155 & 0.723822390677423 \tabularnewline
17 & 0.224257766897938 & 0.448515533795875 & 0.775742233102062 \tabularnewline
18 & 0.307821109235839 & 0.615642218471678 & 0.692178890764161 \tabularnewline
19 & 0.269643415191122 & 0.539286830382244 & 0.730356584808878 \tabularnewline
20 & 0.292667936291326 & 0.585335872582653 & 0.707332063708674 \tabularnewline
21 & 0.563491788957937 & 0.873016422084127 & 0.436508211042064 \tabularnewline
22 & 0.554098226757133 & 0.891803546485734 & 0.445901773242867 \tabularnewline
23 & 0.620463255931296 & 0.759073488137407 & 0.379536744068704 \tabularnewline
24 & 0.556634964384487 & 0.886730071231027 & 0.443365035615513 \tabularnewline
25 & 0.606655680740953 & 0.786688638518093 & 0.393344319259047 \tabularnewline
26 & 0.595472278661484 & 0.809055442677032 & 0.404527721338516 \tabularnewline
27 & 0.76358543229852 & 0.47282913540296 & 0.23641456770148 \tabularnewline
28 & 0.868559884791257 & 0.262880230417485 & 0.131440115208743 \tabularnewline
29 & 0.870960914547067 & 0.258078170905865 & 0.129039085452933 \tabularnewline
30 & 0.80812310596933 & 0.383753788061341 & 0.19187689403067 \tabularnewline
31 & 0.86744197116106 & 0.26511605767788 & 0.13255802883894 \tabularnewline
32 & 0.875295288383251 & 0.249409423233497 & 0.124704711616749 \tabularnewline
33 & 0.833362315600216 & 0.333275368799568 & 0.166637684399784 \tabularnewline
34 & 0.760634505220777 & 0.478730989558446 & 0.239365494779223 \tabularnewline
35 & 0.693326222989381 & 0.613347554021238 & 0.306673777010619 \tabularnewline
36 & 0.575783531385641 & 0.848432937228717 & 0.424216468614359 \tabularnewline
37 & 0.50487749289238 & 0.990245014215239 & 0.49512250710762 \tabularnewline
38 & 0.360342707844356 & 0.720685415688711 & 0.639657292155644 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185654&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]12[/C][C]0.426155624448077[/C][C]0.852311248896154[/C][C]0.573844375551923[/C][/ROW]
[ROW][C]13[/C][C]0.279084312238462[/C][C]0.558168624476924[/C][C]0.720915687761538[/C][/ROW]
[ROW][C]14[/C][C]0.288219859976913[/C][C]0.576439719953826[/C][C]0.711780140023087[/C][/ROW]
[ROW][C]15[/C][C]0.30745934464137[/C][C]0.614918689282739[/C][C]0.69254065535863[/C][/ROW]
[ROW][C]16[/C][C]0.276177609322577[/C][C]0.552355218645155[/C][C]0.723822390677423[/C][/ROW]
[ROW][C]17[/C][C]0.224257766897938[/C][C]0.448515533795875[/C][C]0.775742233102062[/C][/ROW]
[ROW][C]18[/C][C]0.307821109235839[/C][C]0.615642218471678[/C][C]0.692178890764161[/C][/ROW]
[ROW][C]19[/C][C]0.269643415191122[/C][C]0.539286830382244[/C][C]0.730356584808878[/C][/ROW]
[ROW][C]20[/C][C]0.292667936291326[/C][C]0.585335872582653[/C][C]0.707332063708674[/C][/ROW]
[ROW][C]21[/C][C]0.563491788957937[/C][C]0.873016422084127[/C][C]0.436508211042064[/C][/ROW]
[ROW][C]22[/C][C]0.554098226757133[/C][C]0.891803546485734[/C][C]0.445901773242867[/C][/ROW]
[ROW][C]23[/C][C]0.620463255931296[/C][C]0.759073488137407[/C][C]0.379536744068704[/C][/ROW]
[ROW][C]24[/C][C]0.556634964384487[/C][C]0.886730071231027[/C][C]0.443365035615513[/C][/ROW]
[ROW][C]25[/C][C]0.606655680740953[/C][C]0.786688638518093[/C][C]0.393344319259047[/C][/ROW]
[ROW][C]26[/C][C]0.595472278661484[/C][C]0.809055442677032[/C][C]0.404527721338516[/C][/ROW]
[ROW][C]27[/C][C]0.76358543229852[/C][C]0.47282913540296[/C][C]0.23641456770148[/C][/ROW]
[ROW][C]28[/C][C]0.868559884791257[/C][C]0.262880230417485[/C][C]0.131440115208743[/C][/ROW]
[ROW][C]29[/C][C]0.870960914547067[/C][C]0.258078170905865[/C][C]0.129039085452933[/C][/ROW]
[ROW][C]30[/C][C]0.80812310596933[/C][C]0.383753788061341[/C][C]0.19187689403067[/C][/ROW]
[ROW][C]31[/C][C]0.86744197116106[/C][C]0.26511605767788[/C][C]0.13255802883894[/C][/ROW]
[ROW][C]32[/C][C]0.875295288383251[/C][C]0.249409423233497[/C][C]0.124704711616749[/C][/ROW]
[ROW][C]33[/C][C]0.833362315600216[/C][C]0.333275368799568[/C][C]0.166637684399784[/C][/ROW]
[ROW][C]34[/C][C]0.760634505220777[/C][C]0.478730989558446[/C][C]0.239365494779223[/C][/ROW]
[ROW][C]35[/C][C]0.693326222989381[/C][C]0.613347554021238[/C][C]0.306673777010619[/C][/ROW]
[ROW][C]36[/C][C]0.575783531385641[/C][C]0.848432937228717[/C][C]0.424216468614359[/C][/ROW]
[ROW][C]37[/C][C]0.50487749289238[/C][C]0.990245014215239[/C][C]0.49512250710762[/C][/ROW]
[ROW][C]38[/C][C]0.360342707844356[/C][C]0.720685415688711[/C][C]0.639657292155644[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185654&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185654&T=5

As an alternative you can also use a QR Code:

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

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
12	0.426155624448077	0.852311248896154	0.573844375551923
13	0.279084312238462	0.558168624476924	0.720915687761538
14	0.288219859976913	0.576439719953826	0.711780140023087
15	0.30745934464137	0.614918689282739	0.69254065535863
16	0.276177609322577	0.552355218645155	0.723822390677423
17	0.224257766897938	0.448515533795875	0.775742233102062
18	0.307821109235839	0.615642218471678	0.692178890764161
19	0.269643415191122	0.539286830382244	0.730356584808878
20	0.292667936291326	0.585335872582653	0.707332063708674
21	0.563491788957937	0.873016422084127	0.436508211042064
22	0.554098226757133	0.891803546485734	0.445901773242867
23	0.620463255931296	0.759073488137407	0.379536744068704
24	0.556634964384487	0.886730071231027	0.443365035615513
25	0.606655680740953	0.786688638518093	0.393344319259047
26	0.595472278661484	0.809055442677032	0.404527721338516
27	0.76358543229852	0.47282913540296	0.23641456770148
28	0.868559884791257	0.262880230417485	0.131440115208743
29	0.870960914547067	0.258078170905865	0.129039085452933
30	0.80812310596933	0.383753788061341	0.19187689403067
31	0.86744197116106	0.26511605767788	0.13255802883894
32	0.875295288383251	0.249409423233497	0.124704711616749
33	0.833362315600216	0.333275368799568	0.166637684399784
34	0.760634505220777	0.478730989558446	0.239365494779223
35	0.693326222989381	0.613347554021238	0.306673777010619
36	0.575783531385641	0.848432937228717	0.424216468614359
37	0.50487749289238	0.990245014215239	0.49512250710762
38	0.360342707844356	0.720685415688711	0.639657292155644

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	0	0	OK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185654&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185654&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185654&T=6

As an alternative you can also use a QR Code:

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	0	0	OK

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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Figure 10

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No 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')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code