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rwasp_multipleregression.wasp

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Multiple Regression

Date of computation

Mon, 06 Dec 2010 14:42:23 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/06/t12916464819ms5jmtsuxnfabk.htm/, Retrieved Mon, 29 Apr 2024 03:48:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105621, Retrieved Mon, 29 Apr 2024 03:48:53 +0000

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-       [Multiple Regression] [] [2010-12-06 14:42:23] [c474a97a96075919a678ad3d2290b00b] [Current]

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3484,74	13830,14	9349,44	7977	-5,6	6	1	2,77
3411,13	14153,22	9327,78	8241	-6,2	3	1	2,76
3288,18	15418,03	9753,63	8444	-7,1	2	1,2	2,76
3280,37	16666,97	10443,5	8490	-1,4	2	1,2	2,46
3173,95	16505,21	10853,87	8388	-0,1	2	0,8	2,46
3165,26	17135,96	10704,02	8099	-0,9	-8	0,7	2,47
3092,71	18033,25	11052,23	7984	0	0	0,7	2,71
3053,05	17671	10935,47	7786	0,1	-2	0,9	2,8
3181,96	17544,22	10714,03	8086	2,6	3	1,2	2,89
2999,93	17677,9	10394,48	9315	6	5	1,3	3,36
3249,57	18470,97	10817,9	9113	6,4	8	1,5	3,31
3210,52	18409,96	11251,2	9023	8,6	8	1,9	3,5
3030,29	18941,6	11281,26	9026	6,4	9	1,8	3,51
2803,47	19685,53	10539,68	9787	7,7	11	1,9	3,71
2767,63	19834,71	10483,39	9536	9,2	13	2,2	3,71
2882,6	19598,93	10947,43	9490	8,6	12	2,1	3,71
2863,36	17039,97	10580,27	9736	7,4	13	2,2	4,21
2897,06	16969,28	10582,92	9694	8,6	15	2,7	4,21
3012,61	16973,38	10654,41	9647	6,2	13	2,8	4,21
3142,95	16329,89	11014,51	9753	6	16	2,9	4,5
3032,93	16153,34	10967,87	10070	6,6	10	3,4	4,51
3045,78	15311,7	10433,56	10137	5,1	14	3	4,51
3110,52	14760,87	10665,78	9984	4,7	14	3,1	4,51
3013,24	14452,93	10666,71	9732	5	15	2,5	4,32
2987,1	13720,95	10682,74	9103	3,6	13	2,2	4,02
2995,55	13266,27	10777,22	9155	1,9	8	2,3	4,02
2833,18	12708,47	10052,6	9308	-0,1	7	2,1	3,85
2848,96	13411,84	10213,97	9394	-5,7	3	2,8	3,84
2794,83	13975,55	10546,82	9948	-5,6	3	3,1	4,02
2845,26	12974,89	10767,2	10177	-6,4	4	2,9	3,82
2915,02	12151,11	10444,5	10002	-7,7	4	2,6	3,75
2892,63	11576,21	10314,68	9728	-8	0	2,7	3,74
2604,42	9996,83	9042,56	10002	-11,9	-4	2,3	3,14
2641,65	10438,9	9220,75	10063	-15,4	-14	2,3	2,91
2659,81	10511,22	9721,84	10018	-15,5	-18	2,1	2,84
2638,53	10496,2	9978,53	9960	-13,4	-8	2,2	2,85
2720,25	10300,79	9923,81	10236	-10,9	-1	2,9	2,85
2745,88	9981,65	9892,56	10893	-10,8	1	2,6	3,08
2735,7	11448,79	10500,98	10756	-7,3	2	2,7	3,3
2811,7	11384,49	10179,35	10940	-6,5	0	1,8	3,29
2799,43	11717,46	10080,48	10997	-5,1	1	1,3	3,26
2555,28	10965,88	9492,44	10827	-5,3	0	0,9	3,26
2304,98	10352,27	8616,49	10166	-6,8	-1	1,3	3,11
2214,95	9751,2	8685,4	10186	-8,4	-3	1,3	2,84
2065,81	9354,01	8160,67	10457	-8,4	-3	1,3	2,71
1940,49	8792,5	8048,1	10368	-9,7	-3	1,3	2,69
2042	8721,14	8641,21	10244	-8,8	-4	1,1	2,65
1995,37	8692,94	8526,63	10511	-9,6	-8	1,4	2,57
1946,81	8570,73	8474,21	10812	-11,5	-9	1,2	2,32
1765,9	8538,47	7916,13	10738	-11	-13	1,7	2,12
1635,25	8169,75	7977,64	10171	-14,9	-18	1,8	2,05

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 6 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105621&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105621&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105621&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	6 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Multiple Linear Regression - Estimated Regression Equation
BEL_20[t] = + 961.213187415473 + 0.0452365407202592Nikkei[t] + 0.249168737014703DJ_Indust[t] -0.177843191456367Goudprijs[t] -51.3749707456488Conjunct_Seizoenzuiver[t] + 29.9047276015519Cons_vertrouw[t] -105.787821541009Alg_consumptie_index_BE[t] + 127.079892680716Gem_rente_kasbon_1j[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
BEL_20[t] =  +  961.213187415473 +  0.0452365407202592Nikkei[t] +  0.249168737014703DJ_Indust[t] -0.177843191456367Goudprijs[t] -51.3749707456488Conjunct_Seizoenzuiver[t] +  29.9047276015519Cons_vertrouw[t] -105.787821541009Alg_consumptie_index_BE[t] +  127.079892680716Gem_rente_kasbon_1j[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105621&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]BEL_20[t] =  +  961.213187415473 +  0.0452365407202592Nikkei[t] +  0.249168737014703DJ_Indust[t] -0.177843191456367Goudprijs[t] -51.3749707456488Conjunct_Seizoenzuiver[t] +  29.9047276015519Cons_vertrouw[t] -105.787821541009Alg_consumptie_index_BE[t] +  127.079892680716Gem_rente_kasbon_1j[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105621&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105621&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
BEL_20[t] = + 961.213187415473 + 0.0452365407202592Nikkei[t] + 0.249168737014703DJ_Indust[t] -0.177843191456367Goudprijs[t] -51.3749707456488Conjunct_Seizoenzuiver[t] + 29.9047276015519Cons_vertrouw[t] -105.787821541009Alg_consumptie_index_BE[t] + 127.079892680716Gem_rente_kasbon_1j[t] + 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)	961.213187415473	756.282401	1.271	0.210572	0.105286
Nikkei	0.0452365407202592	0.023743	1.9053	0.063444	0.031722
DJ_Indust	0.249168737014703	0.053385	4.6674	3e-05	1.5e-05
Goudprijs	-0.177843191456367	0.045979	-3.868	0.000367	0.000183
Conjunct_Seizoenzuiver	-51.3749707456488	11.300252	-4.5464	4.4e-05	2.2e-05
Cons_vertrouw	29.9047276015519	7.37313	4.0559	0.000206	0.000103
Alg_consumptie_index_BE	-105.787821541009	63.506334	-1.6658	0.103026	0.051513
Gem_rente_kasbon_1j	127.079892680716	106.533689	1.1929	0.239465	0.119732

\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) & 961.213187415473 & 756.282401 & 1.271 & 0.210572 & 0.105286 \tabularnewline
Nikkei & 0.0452365407202592 & 0.023743 & 1.9053 & 0.063444 & 0.031722 \tabularnewline
DJ_Indust & 0.249168737014703 & 0.053385 & 4.6674 & 3e-05 & 1.5e-05 \tabularnewline
Goudprijs & -0.177843191456367 & 0.045979 & -3.868 & 0.000367 & 0.000183 \tabularnewline
Conjunct_Seizoenzuiver & -51.3749707456488 & 11.300252 & -4.5464 & 4.4e-05 & 2.2e-05 \tabularnewline
Cons_vertrouw & 29.9047276015519 & 7.37313 & 4.0559 & 0.000206 & 0.000103 \tabularnewline
Alg_consumptie_index_BE & -105.787821541009 & 63.506334 & -1.6658 & 0.103026 & 0.051513 \tabularnewline
Gem_rente_kasbon_1j & 127.079892680716 & 106.533689 & 1.1929 & 0.239465 & 0.119732 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105621&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]961.213187415473[/C][C]756.282401[/C][C]1.271[/C][C]0.210572[/C][C]0.105286[/C][/ROW]
[ROW][C]Nikkei[/C][C]0.0452365407202592[/C][C]0.023743[/C][C]1.9053[/C][C]0.063444[/C][C]0.031722[/C][/ROW]
[ROW][C]DJ_Indust[/C][C]0.249168737014703[/C][C]0.053385[/C][C]4.6674[/C][C]3e-05[/C][C]1.5e-05[/C][/ROW]
[ROW][C]Goudprijs[/C][C]-0.177843191456367[/C][C]0.045979[/C][C]-3.868[/C][C]0.000367[/C][C]0.000183[/C][/ROW]
[ROW][C]Conjunct_Seizoenzuiver[/C][C]-51.3749707456488[/C][C]11.300252[/C][C]-4.5464[/C][C]4.4e-05[/C][C]2.2e-05[/C][/ROW]
[ROW][C]Cons_vertrouw[/C][C]29.9047276015519[/C][C]7.37313[/C][C]4.0559[/C][C]0.000206[/C][C]0.000103[/C][/ROW]
[ROW][C]Alg_consumptie_index_BE[/C][C]-105.787821541009[/C][C]63.506334[/C][C]-1.6658[/C][C]0.103026[/C][C]0.051513[/C][/ROW]
[ROW][C]Gem_rente_kasbon_1j[/C][C]127.079892680716[/C][C]106.533689[/C][C]1.1929[/C][C]0.239465[/C][C]0.119732[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105621&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105621&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)	961.213187415473	756.282401	1.271	0.210572	0.105286
Nikkei	0.0452365407202592	0.023743	1.9053	0.063444	0.031722
DJ_Indust	0.249168737014703	0.053385	4.6674	3e-05	1.5e-05
Goudprijs	-0.177843191456367	0.045979	-3.868	0.000367	0.000183
Conjunct_Seizoenzuiver	-51.3749707456488	11.300252	-4.5464	4.4e-05	2.2e-05
Cons_vertrouw	29.9047276015519	7.37313	4.0559	0.000206	0.000103
Alg_consumptie_index_BE	-105.787821541009	63.506334	-1.6658	0.103026	0.051513
Gem_rente_kasbon_1j	127.079892680716	106.533689	1.1929	0.239465	0.119732

Multiple Linear Regression - Regression Statistics
Multiple R	0.935503325245988
R-squared	0.875166471546301
Adjusted R-squared	0.854844734356164
F-TEST (value)	43.0655343762174
F-TEST (DF numerator)	7
F-TEST (DF denominator)	43
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	164.31351893068
Sum Squared Residuals	1160954.09764546

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.935503325245988 \tabularnewline
R-squared & 0.875166471546301 \tabularnewline
Adjusted R-squared & 0.854844734356164 \tabularnewline
F-TEST (value) & 43.0655343762174 \tabularnewline
F-TEST (DF numerator) & 7 \tabularnewline
F-TEST (DF denominator) & 43 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 164.31351893068 \tabularnewline
Sum Squared Residuals & 1160954.09764546 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105621&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.935503325245988[/C][/ROW]
[ROW][C]R-squared[/C][C]0.875166471546301[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.854844734356164[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]43.0655343762174[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]7[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]43[/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]164.31351893068[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1160954.09764546[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105621&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105621&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	0.935503325245988
R-squared	0.875166471546301
Adjusted R-squared	0.854844734356164
F-TEST (value)	43.0655343762174
F-TEST (DF numerator)	7
F-TEST (DF denominator)	43
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	164.31351893068
Sum Squared Residuals	1160954.09764546

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	3484.74	3211.12558000918	273.614419990819
2	3411.13	3113.23300491279	297.89699508721
3	3288.18	3235.63015453458	52.5498454654203
4	3280.37	3124.87982844467	155.490171555333
5	3173.95	3213.48141240209	-39.5314124020916
6	3165.26	3009.97538921254	155.284610787461
7	3092.71	3381.2802191535	-288.570219153496
8	3053.05	3296.3459662075	-243.2959662075
9	3181.96	3182.86905003614	-0.90905003613946
10	2999.93	2825.00844066043	174.921559339567
11	3249.57	3043.96417087456	205.60582912544
12	3210.52	3033.98010585727	176.539894142734
13	3030.29	3219.76538734896	-189.475387348965
14	2803.47	2941.16017600913	-137.690176009131
15	2767.63	2929.5321486251	-161.902148625098
16	2882.6	3054.17036158531	-171.570361585309
17	2863.36	2947.6935014458	-84.3335014457977
18	2897.06	2897.89102111436	-0.831021114359997
19	3012.61	2977.1598863713	35.4501136287043
20	3142.95	3145.18847236493	-2.23847236492843
21	3032.93	2807.32797961433	225.602020385666
22	3045.78	2863.20275092172	182.577249078283
23	3110.52	2933.32828574331	177.191714256686
24	3013.24	3018.26610625947	-5.02610625947204
25	2987.1	3106.73928796235	-119.63928796235
26	2995.55	3027.69978405082	-32.1497840508221
27	2833.18	2867.10337957087	-33.9233795708695
28	2848.96	3016.59390160801	-167.633901608005
29	2794.83	3012.5054151716	-217.6754151716
30	2845.26	3048.17102372439	-202.911023724388
31	2915.02	3051.25008922407	-136.230089224068
32	2892.63	2925.56955072037	-32.9395507203656
33	2604.42	2535.23296335721	69.1870366427897
34	2641.65	2440.31836976091	201.331630239087
35	2659.81	2474.22934092095	185.580659079054
36	2638.53	2729.67577051046	-91.145770510464
37	2720.25	2664.96105522495	55.2889447750484
38	2745.88	2641.53144570835	104.348554291649
39	2735.7	2751.33466849212	-15.6346684921185
40	2811.7	2628.59147947027	183.108520529727
41	2799.43	2615.94279803997	183.487201960032
42	2555.28	2488.34147236287	66.9385276371274
43	2304.98	2345.65948897455	-40.6794889745546
44	2214.95	2320.16144224852	-105.211442248525
45	2065.81	2106.73173833295	-40.9217383329518
46	1940.49	2133.35595178272	-192.86595178272
47	2042	2239.89706491664	-197.897064916639
48	1995.37	2042.16583677588	-46.7958367758845
49	1946.81	2027.14056126499	-80.3305612649878
50	1765.9	1676.16925279028	89.7307472097219
51	1635.25	1807.01746732396	-171.767467323959

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 3484.74 & 3211.12558000918 & 273.614419990819 \tabularnewline
2 & 3411.13 & 3113.23300491279 & 297.89699508721 \tabularnewline
3 & 3288.18 & 3235.63015453458 & 52.5498454654203 \tabularnewline
4 & 3280.37 & 3124.87982844467 & 155.490171555333 \tabularnewline
5 & 3173.95 & 3213.48141240209 & -39.5314124020916 \tabularnewline
6 & 3165.26 & 3009.97538921254 & 155.284610787461 \tabularnewline
7 & 3092.71 & 3381.2802191535 & -288.570219153496 \tabularnewline
8 & 3053.05 & 3296.3459662075 & -243.2959662075 \tabularnewline
9 & 3181.96 & 3182.86905003614 & -0.90905003613946 \tabularnewline
10 & 2999.93 & 2825.00844066043 & 174.921559339567 \tabularnewline
11 & 3249.57 & 3043.96417087456 & 205.60582912544 \tabularnewline
12 & 3210.52 & 3033.98010585727 & 176.539894142734 \tabularnewline
13 & 3030.29 & 3219.76538734896 & -189.475387348965 \tabularnewline
14 & 2803.47 & 2941.16017600913 & -137.690176009131 \tabularnewline
15 & 2767.63 & 2929.5321486251 & -161.902148625098 \tabularnewline
16 & 2882.6 & 3054.17036158531 & -171.570361585309 \tabularnewline
17 & 2863.36 & 2947.6935014458 & -84.3335014457977 \tabularnewline
18 & 2897.06 & 2897.89102111436 & -0.831021114359997 \tabularnewline
19 & 3012.61 & 2977.1598863713 & 35.4501136287043 \tabularnewline
20 & 3142.95 & 3145.18847236493 & -2.23847236492843 \tabularnewline
21 & 3032.93 & 2807.32797961433 & 225.602020385666 \tabularnewline
22 & 3045.78 & 2863.20275092172 & 182.577249078283 \tabularnewline
23 & 3110.52 & 2933.32828574331 & 177.191714256686 \tabularnewline
24 & 3013.24 & 3018.26610625947 & -5.02610625947204 \tabularnewline
25 & 2987.1 & 3106.73928796235 & -119.63928796235 \tabularnewline
26 & 2995.55 & 3027.69978405082 & -32.1497840508221 \tabularnewline
27 & 2833.18 & 2867.10337957087 & -33.9233795708695 \tabularnewline
28 & 2848.96 & 3016.59390160801 & -167.633901608005 \tabularnewline
29 & 2794.83 & 3012.5054151716 & -217.6754151716 \tabularnewline
30 & 2845.26 & 3048.17102372439 & -202.911023724388 \tabularnewline
31 & 2915.02 & 3051.25008922407 & -136.230089224068 \tabularnewline
32 & 2892.63 & 2925.56955072037 & -32.9395507203656 \tabularnewline
33 & 2604.42 & 2535.23296335721 & 69.1870366427897 \tabularnewline
34 & 2641.65 & 2440.31836976091 & 201.331630239087 \tabularnewline
35 & 2659.81 & 2474.22934092095 & 185.580659079054 \tabularnewline
36 & 2638.53 & 2729.67577051046 & -91.145770510464 \tabularnewline
37 & 2720.25 & 2664.96105522495 & 55.2889447750484 \tabularnewline
38 & 2745.88 & 2641.53144570835 & 104.348554291649 \tabularnewline
39 & 2735.7 & 2751.33466849212 & -15.6346684921185 \tabularnewline
40 & 2811.7 & 2628.59147947027 & 183.108520529727 \tabularnewline
41 & 2799.43 & 2615.94279803997 & 183.487201960032 \tabularnewline
42 & 2555.28 & 2488.34147236287 & 66.9385276371274 \tabularnewline
43 & 2304.98 & 2345.65948897455 & -40.6794889745546 \tabularnewline
44 & 2214.95 & 2320.16144224852 & -105.211442248525 \tabularnewline
45 & 2065.81 & 2106.73173833295 & -40.9217383329518 \tabularnewline
46 & 1940.49 & 2133.35595178272 & -192.86595178272 \tabularnewline
47 & 2042 & 2239.89706491664 & -197.897064916639 \tabularnewline
48 & 1995.37 & 2042.16583677588 & -46.7958367758845 \tabularnewline
49 & 1946.81 & 2027.14056126499 & -80.3305612649878 \tabularnewline
50 & 1765.9 & 1676.16925279028 & 89.7307472097219 \tabularnewline
51 & 1635.25 & 1807.01746732396 & -171.767467323959 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105621&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]3484.74[/C][C]3211.12558000918[/C][C]273.614419990819[/C][/ROW]
[ROW][C]2[/C][C]3411.13[/C][C]3113.23300491279[/C][C]297.89699508721[/C][/ROW]
[ROW][C]3[/C][C]3288.18[/C][C]3235.63015453458[/C][C]52.5498454654203[/C][/ROW]
[ROW][C]4[/C][C]3280.37[/C][C]3124.87982844467[/C][C]155.490171555333[/C][/ROW]
[ROW][C]5[/C][C]3173.95[/C][C]3213.48141240209[/C][C]-39.5314124020916[/C][/ROW]
[ROW][C]6[/C][C]3165.26[/C][C]3009.97538921254[/C][C]155.284610787461[/C][/ROW]
[ROW][C]7[/C][C]3092.71[/C][C]3381.2802191535[/C][C]-288.570219153496[/C][/ROW]
[ROW][C]8[/C][C]3053.05[/C][C]3296.3459662075[/C][C]-243.2959662075[/C][/ROW]
[ROW][C]9[/C][C]3181.96[/C][C]3182.86905003614[/C][C]-0.90905003613946[/C][/ROW]
[ROW][C]10[/C][C]2999.93[/C][C]2825.00844066043[/C][C]174.921559339567[/C][/ROW]
[ROW][C]11[/C][C]3249.57[/C][C]3043.96417087456[/C][C]205.60582912544[/C][/ROW]
[ROW][C]12[/C][C]3210.52[/C][C]3033.98010585727[/C][C]176.539894142734[/C][/ROW]
[ROW][C]13[/C][C]3030.29[/C][C]3219.76538734896[/C][C]-189.475387348965[/C][/ROW]
[ROW][C]14[/C][C]2803.47[/C][C]2941.16017600913[/C][C]-137.690176009131[/C][/ROW]
[ROW][C]15[/C][C]2767.63[/C][C]2929.5321486251[/C][C]-161.902148625098[/C][/ROW]
[ROW][C]16[/C][C]2882.6[/C][C]3054.17036158531[/C][C]-171.570361585309[/C][/ROW]
[ROW][C]17[/C][C]2863.36[/C][C]2947.6935014458[/C][C]-84.3335014457977[/C][/ROW]
[ROW][C]18[/C][C]2897.06[/C][C]2897.89102111436[/C][C]-0.831021114359997[/C][/ROW]
[ROW][C]19[/C][C]3012.61[/C][C]2977.1598863713[/C][C]35.4501136287043[/C][/ROW]
[ROW][C]20[/C][C]3142.95[/C][C]3145.18847236493[/C][C]-2.23847236492843[/C][/ROW]
[ROW][C]21[/C][C]3032.93[/C][C]2807.32797961433[/C][C]225.602020385666[/C][/ROW]
[ROW][C]22[/C][C]3045.78[/C][C]2863.20275092172[/C][C]182.577249078283[/C][/ROW]
[ROW][C]23[/C][C]3110.52[/C][C]2933.32828574331[/C][C]177.191714256686[/C][/ROW]
[ROW][C]24[/C][C]3013.24[/C][C]3018.26610625947[/C][C]-5.02610625947204[/C][/ROW]
[ROW][C]25[/C][C]2987.1[/C][C]3106.73928796235[/C][C]-119.63928796235[/C][/ROW]
[ROW][C]26[/C][C]2995.55[/C][C]3027.69978405082[/C][C]-32.1497840508221[/C][/ROW]
[ROW][C]27[/C][C]2833.18[/C][C]2867.10337957087[/C][C]-33.9233795708695[/C][/ROW]
[ROW][C]28[/C][C]2848.96[/C][C]3016.59390160801[/C][C]-167.633901608005[/C][/ROW]
[ROW][C]29[/C][C]2794.83[/C][C]3012.5054151716[/C][C]-217.6754151716[/C][/ROW]
[ROW][C]30[/C][C]2845.26[/C][C]3048.17102372439[/C][C]-202.911023724388[/C][/ROW]
[ROW][C]31[/C][C]2915.02[/C][C]3051.25008922407[/C][C]-136.230089224068[/C][/ROW]
[ROW][C]32[/C][C]2892.63[/C][C]2925.56955072037[/C][C]-32.9395507203656[/C][/ROW]
[ROW][C]33[/C][C]2604.42[/C][C]2535.23296335721[/C][C]69.1870366427897[/C][/ROW]
[ROW][C]34[/C][C]2641.65[/C][C]2440.31836976091[/C][C]201.331630239087[/C][/ROW]
[ROW][C]35[/C][C]2659.81[/C][C]2474.22934092095[/C][C]185.580659079054[/C][/ROW]
[ROW][C]36[/C][C]2638.53[/C][C]2729.67577051046[/C][C]-91.145770510464[/C][/ROW]
[ROW][C]37[/C][C]2720.25[/C][C]2664.96105522495[/C][C]55.2889447750484[/C][/ROW]
[ROW][C]38[/C][C]2745.88[/C][C]2641.53144570835[/C][C]104.348554291649[/C][/ROW]
[ROW][C]39[/C][C]2735.7[/C][C]2751.33466849212[/C][C]-15.6346684921185[/C][/ROW]
[ROW][C]40[/C][C]2811.7[/C][C]2628.59147947027[/C][C]183.108520529727[/C][/ROW]
[ROW][C]41[/C][C]2799.43[/C][C]2615.94279803997[/C][C]183.487201960032[/C][/ROW]
[ROW][C]42[/C][C]2555.28[/C][C]2488.34147236287[/C][C]66.9385276371274[/C][/ROW]
[ROW][C]43[/C][C]2304.98[/C][C]2345.65948897455[/C][C]-40.6794889745546[/C][/ROW]
[ROW][C]44[/C][C]2214.95[/C][C]2320.16144224852[/C][C]-105.211442248525[/C][/ROW]
[ROW][C]45[/C][C]2065.81[/C][C]2106.73173833295[/C][C]-40.9217383329518[/C][/ROW]
[ROW][C]46[/C][C]1940.49[/C][C]2133.35595178272[/C][C]-192.86595178272[/C][/ROW]
[ROW][C]47[/C][C]2042[/C][C]2239.89706491664[/C][C]-197.897064916639[/C][/ROW]
[ROW][C]48[/C][C]1995.37[/C][C]2042.16583677588[/C][C]-46.7958367758845[/C][/ROW]
[ROW][C]49[/C][C]1946.81[/C][C]2027.14056126499[/C][C]-80.3305612649878[/C][/ROW]
[ROW][C]50[/C][C]1765.9[/C][C]1676.16925279028[/C][C]89.7307472097219[/C][/ROW]
[ROW][C]51[/C][C]1635.25[/C][C]1807.01746732396[/C][C]-171.767467323959[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105621&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105621&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	3484.74	3211.12558000918	273.614419990819
2	3411.13	3113.23300491279	297.89699508721
3	3288.18	3235.63015453458	52.5498454654203
4	3280.37	3124.87982844467	155.490171555333
5	3173.95	3213.48141240209	-39.5314124020916
6	3165.26	3009.97538921254	155.284610787461
7	3092.71	3381.2802191535	-288.570219153496
8	3053.05	3296.3459662075	-243.2959662075
9	3181.96	3182.86905003614	-0.90905003613946
10	2999.93	2825.00844066043	174.921559339567
11	3249.57	3043.96417087456	205.60582912544
12	3210.52	3033.98010585727	176.539894142734
13	3030.29	3219.76538734896	-189.475387348965
14	2803.47	2941.16017600913	-137.690176009131
15	2767.63	2929.5321486251	-161.902148625098
16	2882.6	3054.17036158531	-171.570361585309
17	2863.36	2947.6935014458	-84.3335014457977
18	2897.06	2897.89102111436	-0.831021114359997
19	3012.61	2977.1598863713	35.4501136287043
20	3142.95	3145.18847236493	-2.23847236492843
21	3032.93	2807.32797961433	225.602020385666
22	3045.78	2863.20275092172	182.577249078283
23	3110.52	2933.32828574331	177.191714256686
24	3013.24	3018.26610625947	-5.02610625947204
25	2987.1	3106.73928796235	-119.63928796235
26	2995.55	3027.69978405082	-32.1497840508221
27	2833.18	2867.10337957087	-33.9233795708695
28	2848.96	3016.59390160801	-167.633901608005
29	2794.83	3012.5054151716	-217.6754151716
30	2845.26	3048.17102372439	-202.911023724388
31	2915.02	3051.25008922407	-136.230089224068
32	2892.63	2925.56955072037	-32.9395507203656
33	2604.42	2535.23296335721	69.1870366427897
34	2641.65	2440.31836976091	201.331630239087
35	2659.81	2474.22934092095	185.580659079054
36	2638.53	2729.67577051046	-91.145770510464
37	2720.25	2664.96105522495	55.2889447750484
38	2745.88	2641.53144570835	104.348554291649
39	2735.7	2751.33466849212	-15.6346684921185
40	2811.7	2628.59147947027	183.108520529727
41	2799.43	2615.94279803997	183.487201960032
42	2555.28	2488.34147236287	66.9385276371274
43	2304.98	2345.65948897455	-40.6794889745546
44	2214.95	2320.16144224852	-105.211442248525
45	2065.81	2106.73173833295	-40.9217383329518
46	1940.49	2133.35595178272	-192.86595178272
47	2042	2239.89706491664	-197.897064916639
48	1995.37	2042.16583677588	-46.7958367758845
49	1946.81	2027.14056126499	-80.3305612649878
50	1765.9	1676.16925279028	89.7307472097219
51	1635.25	1807.01746732396	-171.767467323959

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
11	0.604761025160254	0.790477949679492	0.395238974839746
12	0.544759977868897	0.910480044262207	0.455240022131103
13	0.46558543702144	0.93117087404288	0.53441456297856
14	0.525522315562066	0.948955368875868	0.474477684437934
15	0.548025164340219	0.903949671319563	0.451974835659782
16	0.448378039982623	0.896756079965246	0.551621960017377
17	0.661661392662711	0.676677214674577	0.338338607337289
18	0.649281931488045	0.701436137023909	0.350718068511955
19	0.578020799816308	0.843958400367384	0.421979200183692
20	0.537592459032903	0.924815081934194	0.462407540967097
21	0.438099511654557	0.876199023309114	0.561900488345443
22	0.362625028527326	0.725250057054652	0.637374971472674
23	0.315486114313821	0.630972228627641	0.68451388568618
24	0.340258038167381	0.680516076334762	0.659741961832619
25	0.441599884356019	0.883199768712039	0.55840011564398
26	0.444342394866198	0.888684789732397	0.555657605133802
27	0.750917403669371	0.498165192661258	0.249082596330629
28	0.837475958702918	0.325048082594164	0.162524041297082
29	0.847597250499707	0.304805499000585	0.152402749500293
30	0.950561710992003	0.0988765780159936	0.0494382890079968
31	0.976221833896062	0.0475563322078766	0.0237781661039383
32	0.962414377055056	0.075171245889889	0.0375856229449445
33	0.959775505168185	0.0804489896636296	0.0402244948318148
34	0.934270905894135	0.13145818821173	0.0657290941058652
35	0.947358633471692	0.105282733056615	0.0526413665283075
36	0.910881581400713	0.178236837198575	0.0891184185992875
37	0.944511131340806	0.110977737318388	0.0554888686591938
38	0.98982971694671	0.0203405661065814	0.0101702830532907
39	0.998671205719855	0.00265758856028921	0.0013287942801446
40	0.993078460984684	0.0138430780306329	0.00692153901531646

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
11 & 0.604761025160254 & 0.790477949679492 & 0.395238974839746 \tabularnewline
12 & 0.544759977868897 & 0.910480044262207 & 0.455240022131103 \tabularnewline
13 & 0.46558543702144 & 0.93117087404288 & 0.53441456297856 \tabularnewline
14 & 0.525522315562066 & 0.948955368875868 & 0.474477684437934 \tabularnewline
15 & 0.548025164340219 & 0.903949671319563 & 0.451974835659782 \tabularnewline
16 & 0.448378039982623 & 0.896756079965246 & 0.551621960017377 \tabularnewline
17 & 0.661661392662711 & 0.676677214674577 & 0.338338607337289 \tabularnewline
18 & 0.649281931488045 & 0.701436137023909 & 0.350718068511955 \tabularnewline
19 & 0.578020799816308 & 0.843958400367384 & 0.421979200183692 \tabularnewline
20 & 0.537592459032903 & 0.924815081934194 & 0.462407540967097 \tabularnewline
21 & 0.438099511654557 & 0.876199023309114 & 0.561900488345443 \tabularnewline
22 & 0.362625028527326 & 0.725250057054652 & 0.637374971472674 \tabularnewline
23 & 0.315486114313821 & 0.630972228627641 & 0.68451388568618 \tabularnewline
24 & 0.340258038167381 & 0.680516076334762 & 0.659741961832619 \tabularnewline
25 & 0.441599884356019 & 0.883199768712039 & 0.55840011564398 \tabularnewline
26 & 0.444342394866198 & 0.888684789732397 & 0.555657605133802 \tabularnewline
27 & 0.750917403669371 & 0.498165192661258 & 0.249082596330629 \tabularnewline
28 & 0.837475958702918 & 0.325048082594164 & 0.162524041297082 \tabularnewline
29 & 0.847597250499707 & 0.304805499000585 & 0.152402749500293 \tabularnewline
30 & 0.950561710992003 & 0.0988765780159936 & 0.0494382890079968 \tabularnewline
31 & 0.976221833896062 & 0.0475563322078766 & 0.0237781661039383 \tabularnewline
32 & 0.962414377055056 & 0.075171245889889 & 0.0375856229449445 \tabularnewline
33 & 0.959775505168185 & 0.0804489896636296 & 0.0402244948318148 \tabularnewline
34 & 0.934270905894135 & 0.13145818821173 & 0.0657290941058652 \tabularnewline
35 & 0.947358633471692 & 0.105282733056615 & 0.0526413665283075 \tabularnewline
36 & 0.910881581400713 & 0.178236837198575 & 0.0891184185992875 \tabularnewline
37 & 0.944511131340806 & 0.110977737318388 & 0.0554888686591938 \tabularnewline
38 & 0.98982971694671 & 0.0203405661065814 & 0.0101702830532907 \tabularnewline
39 & 0.998671205719855 & 0.00265758856028921 & 0.0013287942801446 \tabularnewline
40 & 0.993078460984684 & 0.0138430780306329 & 0.00692153901531646 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105621&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]11[/C][C]0.604761025160254[/C][C]0.790477949679492[/C][C]0.395238974839746[/C][/ROW]
[ROW][C]12[/C][C]0.544759977868897[/C][C]0.910480044262207[/C][C]0.455240022131103[/C][/ROW]
[ROW][C]13[/C][C]0.46558543702144[/C][C]0.93117087404288[/C][C]0.53441456297856[/C][/ROW]
[ROW][C]14[/C][C]0.525522315562066[/C][C]0.948955368875868[/C][C]0.474477684437934[/C][/ROW]
[ROW][C]15[/C][C]0.548025164340219[/C][C]0.903949671319563[/C][C]0.451974835659782[/C][/ROW]
[ROW][C]16[/C][C]0.448378039982623[/C][C]0.896756079965246[/C][C]0.551621960017377[/C][/ROW]
[ROW][C]17[/C][C]0.661661392662711[/C][C]0.676677214674577[/C][C]0.338338607337289[/C][/ROW]
[ROW][C]18[/C][C]0.649281931488045[/C][C]0.701436137023909[/C][C]0.350718068511955[/C][/ROW]
[ROW][C]19[/C][C]0.578020799816308[/C][C]0.843958400367384[/C][C]0.421979200183692[/C][/ROW]
[ROW][C]20[/C][C]0.537592459032903[/C][C]0.924815081934194[/C][C]0.462407540967097[/C][/ROW]
[ROW][C]21[/C][C]0.438099511654557[/C][C]0.876199023309114[/C][C]0.561900488345443[/C][/ROW]
[ROW][C]22[/C][C]0.362625028527326[/C][C]0.725250057054652[/C][C]0.637374971472674[/C][/ROW]
[ROW][C]23[/C][C]0.315486114313821[/C][C]0.630972228627641[/C][C]0.68451388568618[/C][/ROW]
[ROW][C]24[/C][C]0.340258038167381[/C][C]0.680516076334762[/C][C]0.659741961832619[/C][/ROW]
[ROW][C]25[/C][C]0.441599884356019[/C][C]0.883199768712039[/C][C]0.55840011564398[/C][/ROW]
[ROW][C]26[/C][C]0.444342394866198[/C][C]0.888684789732397[/C][C]0.555657605133802[/C][/ROW]
[ROW][C]27[/C][C]0.750917403669371[/C][C]0.498165192661258[/C][C]0.249082596330629[/C][/ROW]
[ROW][C]28[/C][C]0.837475958702918[/C][C]0.325048082594164[/C][C]0.162524041297082[/C][/ROW]
[ROW][C]29[/C][C]0.847597250499707[/C][C]0.304805499000585[/C][C]0.152402749500293[/C][/ROW]
[ROW][C]30[/C][C]0.950561710992003[/C][C]0.0988765780159936[/C][C]0.0494382890079968[/C][/ROW]
[ROW][C]31[/C][C]0.976221833896062[/C][C]0.0475563322078766[/C][C]0.0237781661039383[/C][/ROW]
[ROW][C]32[/C][C]0.962414377055056[/C][C]0.075171245889889[/C][C]0.0375856229449445[/C][/ROW]
[ROW][C]33[/C][C]0.959775505168185[/C][C]0.0804489896636296[/C][C]0.0402244948318148[/C][/ROW]
[ROW][C]34[/C][C]0.934270905894135[/C][C]0.13145818821173[/C][C]0.0657290941058652[/C][/ROW]
[ROW][C]35[/C][C]0.947358633471692[/C][C]0.105282733056615[/C][C]0.0526413665283075[/C][/ROW]
[ROW][C]36[/C][C]0.910881581400713[/C][C]0.178236837198575[/C][C]0.0891184185992875[/C][/ROW]
[ROW][C]37[/C][C]0.944511131340806[/C][C]0.110977737318388[/C][C]0.0554888686591938[/C][/ROW]
[ROW][C]38[/C][C]0.98982971694671[/C][C]0.0203405661065814[/C][C]0.0101702830532907[/C][/ROW]
[ROW][C]39[/C][C]0.998671205719855[/C][C]0.00265758856028921[/C][C]0.0013287942801446[/C][/ROW]
[ROW][C]40[/C][C]0.993078460984684[/C][C]0.0138430780306329[/C][C]0.00692153901531646[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105621&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105621&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
11	0.604761025160254	0.790477949679492	0.395238974839746
12	0.544759977868897	0.910480044262207	0.455240022131103
13	0.46558543702144	0.93117087404288	0.53441456297856
14	0.525522315562066	0.948955368875868	0.474477684437934
15	0.548025164340219	0.903949671319563	0.451974835659782
16	0.448378039982623	0.896756079965246	0.551621960017377
17	0.661661392662711	0.676677214674577	0.338338607337289
18	0.649281931488045	0.701436137023909	0.350718068511955
19	0.578020799816308	0.843958400367384	0.421979200183692
20	0.537592459032903	0.924815081934194	0.462407540967097
21	0.438099511654557	0.876199023309114	0.561900488345443
22	0.362625028527326	0.725250057054652	0.637374971472674
23	0.315486114313821	0.630972228627641	0.68451388568618
24	0.340258038167381	0.680516076334762	0.659741961832619
25	0.441599884356019	0.883199768712039	0.55840011564398
26	0.444342394866198	0.888684789732397	0.555657605133802
27	0.750917403669371	0.498165192661258	0.249082596330629
28	0.837475958702918	0.325048082594164	0.162524041297082
29	0.847597250499707	0.304805499000585	0.152402749500293
30	0.950561710992003	0.0988765780159936	0.0494382890079968
31	0.976221833896062	0.0475563322078766	0.0237781661039383
32	0.962414377055056	0.075171245889889	0.0375856229449445
33	0.959775505168185	0.0804489896636296	0.0402244948318148
34	0.934270905894135	0.13145818821173	0.0657290941058652
35	0.947358633471692	0.105282733056615	0.0526413665283075
36	0.910881581400713	0.178236837198575	0.0891184185992875
37	0.944511131340806	0.110977737318388	0.0554888686591938
38	0.98982971694671	0.0203405661065814	0.0101702830532907
39	0.998671205719855	0.00265758856028921	0.0013287942801446
40	0.993078460984684	0.0138430780306329	0.00692153901531646

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	1	0.0333333333333333	NOK
5% type I error level	4	0.133333333333333	NOK
10% type I error level	7	0.233333333333333	NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 1 & 0.0333333333333333 & NOK \tabularnewline
5% type I error level & 4 & 0.133333333333333 & NOK \tabularnewline
10% type I error level & 7 & 0.233333333333333 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105621&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]1[/C][C]0.0333333333333333[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]4[/C][C]0.133333333333333[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]7[/C][C]0.233333333333333[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105621&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105621&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	1	0.0333333333333333	NOK
5% type I error level	4	0.133333333333333	NOK
10% type I error level	7	0.233333333333333	NOK

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 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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