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rwasp_multipleregression.wasp

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Multiple Regression

Date of computation

Fri, 16 Nov 2012 10:49:30 -0500

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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/16/t1353081194t1fv0072cm2hw3h.htm/, Retrieved Sat, 27 Apr 2024 12:53:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=189971, Retrieved Sat, 27 Apr 2024 12:53:23 +0000

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Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Mean Plot] [Colombia Coffee] [2008-01-07 13:38:24] [74be16979710d4c4e7c6647856088456]
- RMPD    [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Happiness - Depre...] [2011-11-14 20:01:00] [f2faabc3a2466a29562900bc59f67898]
- R P       [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Connected - Separ...] [2011-11-14 20:24:26] [f2faabc3a2466a29562900bc59f67898]
-             [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2012-11-06 14:08:14] [74be16979710d4c4e7c6647856088456]
- RMPD            [Multiple Regression] [WS7] [2012-11-16 15:49:30] [3335f298c0b702cf6bacf0a9219000f9] [Current]

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109.08	119.73	101.52	112.47	104.49	104	109.55	90.14	101.33	109.47	108.81	108.99
110.4	119.77	101.61	114.97	104.62	104.03	111.69	89.96	101.3	109.47	108.81	109.1
111.03	119.77	101.65	115.65	104.76	104.1	110.76	89.97	102.39	109.47	109.74	109.2
112.05	119.78	101.66	117.44	104.88	104.36	110.78	89.98	101.69	109.47	109.57	109.68
112.28	119.78	101.56	120.13	105.09	103.6	110.76	90.1	103.75	109.47	110.44	110.02
112.8	119.78	101.75	122.87	105.31	103.69	112.38	90.13	102.99	109.47	111.2	110.32
114.17	121.28	101.83	123.67	105.48	103.78	112.86	89.6	100.8	109.47	111.44	110.64
114.92	122.44	101.98	125.68	105.71	103.27	114.74	89.6	102.21	109.47	111.83	110.87
114.65	122.72	102.06	127.68	105.87	103.29	116.21	89.61	102.45	109.47	112.87	110.96
115.49	122.75	102.07	128.41	105.94	103.3	116.86	89.22	102.49	109.47	115.07	111.85
114.67	122.8	102.1	127.03	106.14	103.47	114.51	89.6	102.4	109.47	115.35	111.94
114.71	122.81	102.42	128.57	106.49	103.27	114.11	88.9	102.99	109.47	113.81	112.11
115.15	122.83	102.91	127.54	106.79	103.3	112.12	89.6	103.19	111.29	114.66	112.42
115.03	122.83	103.14	126.27	107.02	103.38	108.9	89.47	103.35	111.29	114.51	112.62
115.07	122.83	103.23	125.69	107.14	103.38	106.62	89.73	104.44	111.29	115.11	112.63
116.46	122.84	103.23	125.8	107.31	105.22	105.95	88.53	103.42	111.29	114.54	113.25
116.37	122.85	102.91	124.36	107.67	105.29	107.03	90.09	105.81	111.29	115.39	113.73
116.2	123.61	103.11	121.18	108.03	104.85	107.1	90.09	104.25	111.29	115.65	114.17
116.5	124.74	103.14	121.08	108.27	104.99	108	90.28	103.78	111.29	116.46	114.27
116.38	125.1	103.26	119.98	108.41	104.61	108.24	89.69	104.53	111.29	116.18	114.49
115.44	125.29	103.3	117.58	108.56	104.6	109.72	89.69	105.01	111.29	116.63	114.69
114.96	125.45	103.32	117.29	108.62	103.53	109.53	89.67	104.83	111.29	118.84	114.63
114.48	125.51	103.44	119.02	108.83	103.48	110.64	89.66	104.55	111.29	118.77	114.74
114.3	125.55	103.54	117.76	109	103.54	110.03	89.56	105.16	111.29	117.83	114.94
114.66	125.57	103.98	118.06	109.21	103.52	109.38	89.6	105.06	116.29	117.66	114.78
114.97	125.81	104.24	118.76	109.45	103.5	110.62	86.62	105.2	116.29	117.36	114.83
114.79	127.41	104.29	119.04	109.59	103.5	110.57	86.98	105.87	116.29	118	114.91
116.16	127.75	104.29	120.34	109.57	103.83	111.52	86.71	105.41	116.29	117.34	114.84
116.52	127.76	103.98	120.74	109.75	103.2	111.47	86.6	107.89	116.29	118.04	115.13
117.14	127.8	103.98	122.26	110.01	103.24	112.97	86.58	106.06	116.29	118.17	115.45
117.27	128.23	103.89	123.41	110.09	103.11	114.24	86.79	105.5	116.29	118.82	115.5
117.58	130.01	103.86	124.12	110.25	103.13	114.97	86.08	106.71	116.29	119	115.61
117.21	130.07	103.88	124.29	110.28	103.15	114.82	87.48	106.34	116.29	118.89	116.3
117.08	130.17	103.88	124.02	110.26	103.03	114.61	87.4	106.11	116.29	121.4	116.48
117.06	130.21	104.31	124.35	110.38	103.06	114.68	87.51	106.15	116.29	121.01	116.46
117.55	130.22	104.41	125.56	110.37	103.11	114.9	87.58	106.61	116.29	120.21	116.77
117.61	130.23	104.8	125.99	110.5	103.11	115.05	87.59	106.63	115.72	120.39	117.02
117.74	130.23	104.89	126.35	110.51	103.12	115.67	87.62	106.27	115.72	120.09	117.19
117.87	130.23	104.9	127.53	110.71	103.12	117.17	88.35	105.59	115.72	120.76	117.34
118.59	130.23	104.9	128.42	110.62	103.28	118.17	88.67	107.09	115.72	120.33	118.15
119.09	130.24	104.54	130.11	110.81	103.44	118.61	87.81	108.53	115.72	120.84	118.94
118.93	130.13	104.67	132.15	110.97	103.37	120.38	87.81	108.01	115.72	121.49	119.17
119.62	130.14	104.87	132.91	111.06	103.15	121.27	87.86	106.52	115.72	122.29	119.33
120.09	130.79	105.04	133.84	111.33	103.21	121.55	87.86	107.27	115.72	121.91	119.5
120.38	131.38	105.09	135.52	111.55	103.22	121.08	87.86	107.58	115.72	122.46	119.58
120.49	131.61	105.1	135.29	111.67	103.32	121.01	87.51	107.36	115.72	124.94	119.79
120.02	131.72	105.46	135.13	111.72	103.34	121.15	87.5	107.23	115.72	124.6	119.91
120.17	131.89	105.83	136.43	112	103.34	121.84	86.72	107.54	115.72	123.09	120.35
120.58	131.89	106.27	136.29	112.42	103.3	121.83	86.74	107.64	119.24	123.25	120.69
121.54	131.96	106.46	137.32	112.84	103.29	121.86	86.74	108.23	119.24	123.01	121.01
121.52	131.99	106.52	137.3	112.99	103.35	121.56	86.76	108.42	119.24	123.82	121.14
121.81	132	106.53	138.38	113.11	104.02	122.81	90.75	109.33	119.24	123.31	123.78
122.85	132.06	105.96	139.39	113.51	104.07	123.24	90.21	111.3	119.24	124.04	123.95
122.97	132.11	106	140.03	113.42	104.23	124.52	90.2	110.52	119.24	124.15	124.25
122.96	132.88	106.15	140.05	113.6	103.96	125.03	89.34	109.86	119.24	125.37	124.3
123.4	135.48	106.32	139.47	113.65	103.81	123.56	89.35	110.94	119.24	125.41	124.7
123.23	136.56	106.41	138.31	113.76	103.38	122.58	88.94	111.35	119.24	126.06	124.73
123.24	136.96	106.41	138.5	113.74	103.29	122.95	88.94	111.01	119.24	128.17	125.02
123.72	137.4	106.81	139.31	114.02	103.24	124.73	88.77	110.84	119.24	128.16	125.24
123.99	138.32	106.99	139.66	114.08	103.26	125.75	88.72	110.79	119.24	126.69	125.67
125.1	138.82	107.35	139.63	114.29	103.4	125.16	89.25	110.87	119.79	126.75	125.84

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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=189971&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=189971&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=189971&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Multiple Linear Regression - Estimated Regression Equation
Vervoer[t] = + 571.904681422643 -1.40459287981778VoedingsmiddelenEnDranken[t] + 0.484331344917395Tabak[t] -3.36887528975686KledingEnSchoeisel[t] + 0.597116854081499`Huisvesting,water,elektriciteit,gas`[t] + 0.367282982725115StofferingEnOnderhoudVanWoning[t] -1.80583285610949Gezondheidsuitgaven[t] -0.812407529113463Communicatie[t] -1.03263668282893RecreatieEnCultuur[t] + 0.114569379912798Onderwijs[t] -0.899373119097168`Hotels,caf\303\251sEnRestaurants`[t] + 2.94648422505312DiverseGoederenEnDiensten[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Vervoer[t] =  +  571.904681422643 -1.40459287981778VoedingsmiddelenEnDranken[t] +  0.484331344917395Tabak[t] -3.36887528975686KledingEnSchoeisel[t] +  0.597116854081499`Huisvesting,water,elektriciteit,gas`[t] +  0.367282982725115StofferingEnOnderhoudVanWoning[t] -1.80583285610949Gezondheidsuitgaven[t] -0.812407529113463Communicatie[t] -1.03263668282893RecreatieEnCultuur[t] +  0.114569379912798Onderwijs[t] -0.899373119097168`Hotels,caf\303\251sEnRestaurants`[t] +  2.94648422505312DiverseGoederenEnDiensten[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=189971&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Vervoer[t] =  +  571.904681422643 -1.40459287981778VoedingsmiddelenEnDranken[t] +  0.484331344917395Tabak[t] -3.36887528975686KledingEnSchoeisel[t] +  0.597116854081499`Huisvesting,water,elektriciteit,gas`[t] +  0.367282982725115StofferingEnOnderhoudVanWoning[t] -1.80583285610949Gezondheidsuitgaven[t] -0.812407529113463Communicatie[t] -1.03263668282893RecreatieEnCultuur[t] +  0.114569379912798Onderwijs[t] -0.899373119097168`Hotels,caf\303\251sEnRestaurants`[t] +  2.94648422505312DiverseGoederenEnDiensten[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=189971&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=189971&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
Vervoer[t] = + 571.904681422643 -1.40459287981778VoedingsmiddelenEnDranken[t] + 0.484331344917395Tabak[t] -3.36887528975686KledingEnSchoeisel[t] + 0.597116854081499`Huisvesting,water,elektriciteit,gas`[t] + 0.367282982725115StofferingEnOnderhoudVanWoning[t] -1.80583285610949Gezondheidsuitgaven[t] -0.812407529113463Communicatie[t] -1.03263668282893RecreatieEnCultuur[t] + 0.114569379912798Onderwijs[t] -0.899373119097168`Hotels,caf\303\251sEnRestaurants`[t] + 2.94648422505312DiverseGoederenEnDiensten[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)	571.904681422643	107.064686	5.3417	2e-06	1e-06
VoedingsmiddelenEnDranken	-1.40459287981778	0.449075	-3.1277	0.002963	0.001481
Tabak	0.484331344917395	0.285363	1.6972	0.095994	0.047997
KledingEnSchoeisel	-3.36887528975686	0.784846	-4.2924	8.3e-05	4.2e-05
`Huisvesting,water,elektriciteit,gas`	0.597116854081499	0.136069	4.3883	6.1e-05	3e-05
StofferingEnOnderhoudVanWoning	0.367282982725115	1.027822	0.3573	0.722371	0.361186
Gezondheidsuitgaven	-1.80583285610949	0.710747	-2.5408	0.014279	0.00714
Communicatie	-0.812407529113463	0.363962	-2.2321	0.030211	0.015106
RecreatieEnCultuur	-1.03263668282893	0.317068	-3.2568	0.002048	0.001024
Onderwijs	0.114569379912798	0.254405	0.4503	0.65445	0.327225
`Hotels,caf\303\251sEnRestaurants`	-0.899373119097168	0.265902	-3.3823	0.00142	0.00071
DiverseGoederenEnDiensten	2.94648422505312	0.634157	4.6463	2.6e-05	1.3e-05

\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) & 571.904681422643 & 107.064686 & 5.3417 & 2e-06 & 1e-06 \tabularnewline
VoedingsmiddelenEnDranken & -1.40459287981778 & 0.449075 & -3.1277 & 0.002963 & 0.001481 \tabularnewline
Tabak & 0.484331344917395 & 0.285363 & 1.6972 & 0.095994 & 0.047997 \tabularnewline
KledingEnSchoeisel & -3.36887528975686 & 0.784846 & -4.2924 & 8.3e-05 & 4.2e-05 \tabularnewline
`Huisvesting,water,elektriciteit,gas` & 0.597116854081499 & 0.136069 & 4.3883 & 6.1e-05 & 3e-05 \tabularnewline
StofferingEnOnderhoudVanWoning & 0.367282982725115 & 1.027822 & 0.3573 & 0.722371 & 0.361186 \tabularnewline
Gezondheidsuitgaven & -1.80583285610949 & 0.710747 & -2.5408 & 0.014279 & 0.00714 \tabularnewline
Communicatie & -0.812407529113463 & 0.363962 & -2.2321 & 0.030211 & 0.015106 \tabularnewline
RecreatieEnCultuur & -1.03263668282893 & 0.317068 & -3.2568 & 0.002048 & 0.001024 \tabularnewline
Onderwijs & 0.114569379912798 & 0.254405 & 0.4503 & 0.65445 & 0.327225 \tabularnewline
`Hotels,caf\303\251sEnRestaurants` & -0.899373119097168 & 0.265902 & -3.3823 & 0.00142 & 0.00071 \tabularnewline
DiverseGoederenEnDiensten & 2.94648422505312 & 0.634157 & 4.6463 & 2.6e-05 & 1.3e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=189971&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]571.904681422643[/C][C]107.064686[/C][C]5.3417[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]VoedingsmiddelenEnDranken[/C][C]-1.40459287981778[/C][C]0.449075[/C][C]-3.1277[/C][C]0.002963[/C][C]0.001481[/C][/ROW]
[ROW][C]Tabak[/C][C]0.484331344917395[/C][C]0.285363[/C][C]1.6972[/C][C]0.095994[/C][C]0.047997[/C][/ROW]
[ROW][C]KledingEnSchoeisel[/C][C]-3.36887528975686[/C][C]0.784846[/C][C]-4.2924[/C][C]8.3e-05[/C][C]4.2e-05[/C][/ROW]
[ROW][C]`Huisvesting,water,elektriciteit,gas`[/C][C]0.597116854081499[/C][C]0.136069[/C][C]4.3883[/C][C]6.1e-05[/C][C]3e-05[/C][/ROW]
[ROW][C]StofferingEnOnderhoudVanWoning[/C][C]0.367282982725115[/C][C]1.027822[/C][C]0.3573[/C][C]0.722371[/C][C]0.361186[/C][/ROW]
[ROW][C]Gezondheidsuitgaven[/C][C]-1.80583285610949[/C][C]0.710747[/C][C]-2.5408[/C][C]0.014279[/C][C]0.00714[/C][/ROW]
[ROW][C]Communicatie[/C][C]-0.812407529113463[/C][C]0.363962[/C][C]-2.2321[/C][C]0.030211[/C][C]0.015106[/C][/ROW]
[ROW][C]RecreatieEnCultuur[/C][C]-1.03263668282893[/C][C]0.317068[/C][C]-3.2568[/C][C]0.002048[/C][C]0.001024[/C][/ROW]
[ROW][C]Onderwijs[/C][C]0.114569379912798[/C][C]0.254405[/C][C]0.4503[/C][C]0.65445[/C][C]0.327225[/C][/ROW]
[ROW][C]`Hotels,caf\303\251sEnRestaurants`[/C][C]-0.899373119097168[/C][C]0.265902[/C][C]-3.3823[/C][C]0.00142[/C][C]0.00071[/C][/ROW]
[ROW][C]DiverseGoederenEnDiensten[/C][C]2.94648422505312[/C][C]0.634157[/C][C]4.6463[/C][C]2.6e-05[/C][C]1.3e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=189971&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=189971&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)	571.904681422643	107.064686	5.3417	2e-06	1e-06
VoedingsmiddelenEnDranken	-1.40459287981778	0.449075	-3.1277	0.002963	0.001481
Tabak	0.484331344917395	0.285363	1.6972	0.095994	0.047997
KledingEnSchoeisel	-3.36887528975686	0.784846	-4.2924	8.3e-05	4.2e-05
`Huisvesting,water,elektriciteit,gas`	0.597116854081499	0.136069	4.3883	6.1e-05	3e-05
StofferingEnOnderhoudVanWoning	0.367282982725115	1.027822	0.3573	0.722371	0.361186
Gezondheidsuitgaven	-1.80583285610949	0.710747	-2.5408	0.014279	0.00714
Communicatie	-0.812407529113463	0.363962	-2.2321	0.030211	0.015106
RecreatieEnCultuur	-1.03263668282893	0.317068	-3.2568	0.002048	0.001024
Onderwijs	0.114569379912798	0.254405	0.4503	0.65445	0.327225
`Hotels,caf\303\251sEnRestaurants`	-0.899373119097168	0.265902	-3.3823	0.00142	0.00071
DiverseGoederenEnDiensten	2.94648422505312	0.634157	4.6463	2.6e-05	1.3e-05

Multiple Linear Regression - Regression Statistics
Multiple R	0.971939109628318
R-squared	0.944665632825087
Adjusted R-squared	0.932243632030719
F-TEST (value)	76.0477839651538
F-TEST (DF numerator)	11
F-TEST (DF denominator)	49
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.49156339063183
Sum Squared Residuals	109.013306065383

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.971939109628318 \tabularnewline
R-squared & 0.944665632825087 \tabularnewline
Adjusted R-squared & 0.932243632030719 \tabularnewline
F-TEST (value) & 76.0477839651538 \tabularnewline
F-TEST (DF numerator) & 11 \tabularnewline
F-TEST (DF denominator) & 49 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 1.49156339063183 \tabularnewline
Sum Squared Residuals & 109.013306065383 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=189971&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.971939109628318[/C][/ROW]
[ROW][C]R-squared[/C][C]0.944665632825087[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.932243632030719[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]76.0477839651538[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]11[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]49[/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]1.49156339063183[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]109.013306065383[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=189971&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=189971&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	0.971939109628318
R-squared	0.944665632825087
Adjusted R-squared	0.932243632030719
F-TEST (value)	76.0477839651538
F-TEST (DF numerator)	11
F-TEST (DF denominator)	49
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.49156339063183
Sum Squared Residuals	109.013306065383

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	109.55	110.351923884357	-0.801923884357248
2	111.69	110.201725418473	1.4882745815275
3	110.76	107.837661033197	2.9223389668034
4	110.78	109.30145490144	1.47854509856033
5	110.76	110.365722355334	0.394277644665746
6	112.38	111.510478582187	0.869521417813132
7	112.86	113.83985569357	-0.979855693569853
8	114.74	113.919476952219	0.820523047780867
9	116.21	114.455580768667	1.75441923133334
10	116.86	114.619394288104	2.24060571189649
11	114.51	114.43433605778	0.0756639422197657
12	114.11	116.559597682955	-2.44959768295472
13	112.12	113.323740723213	-1.20374072321267
14	108.9	112.563714527409	-3.66371452740855
15	106.62	110.055119247637	-3.43511924763663
16	105.95	109.28060831275	-3.33060831274986
17	107.03	106.550358241496	0.479641758504378
18	107.1	108.184941803012	-1.0849418030118
19	108	107.882549737156	0.117450262844414
20	108.24	108.506896628461	-0.266896628460748
21	109.72	108.113465539267	1.60653446073319
22	109.53	108.616618985072	0.91338101492844
23	110.64	110.800383369623	-0.160383369622901
24	110.03	110.823456665713	-0.793456665712766
25	109.38	109.462636089023	-0.0826360890230147
26	110.62	111.5033320627	-0.883332062700039
27	110.57	111.257044158977	-0.68704415897735
28	111.52	110.752101248847	0.767898751153374
29	111.47	110.491619939942	0.978380060057787
30	112.97	113.302953214414	-0.332953214413522
31	114.24	114.553045331646	-0.313045331645642
32	114.97	115.016944240825	-0.0469442408254123
33	114.82	116.951447869086	-2.1314478690865
34	114.61	115.806050481387	-1.19605048138658
35	114.68	114.753002288706	-0.0730022887059389
36	114.9	115.46228168678	-0.562281686779621
37	115.05	114.854147638772	0.195852361228369
38	115.67	115.687019590986	-0.0170195909858736
39	117.17	116.197316340107	0.972683659893121
40	118.17	116.359911971293	1.81008802870705
41	118.61	118.7459478411	-0.135947841100022
42	120.38	120.512814345172	-0.132814345171606
43	121.27	121.008808281177	0.261191718823401
44	121.55	120.705077902259	0.844922097740817
45	121.08	120.901904089445	0.178095910555354
46	121.01	119.451099182288	1.55890081771225
47	121.15	119.64017978635	1.50982021365017
48	121.84	122.112501441164	-0.272501441163655
49	121.83	121.338886376253	0.491113623746687
50	121.86	120.721110499459	1.1388895005405
51	121.56	119.938501521447	1.621498478553
52	122.81	123.037569515936	-0.227569515935824
53	123.24	122.434587031555	0.805412968444895
54	124.52	123.814258415135	0.705741584865156
55	125.03	124.691836022836	0.338163977163633
56	123.56	124.72252622794	-1.16252622793953
57	122.58	124.718947845749	-2.13894784574863
58	122.95	124.47516557072	-1.52516557072043
59	124.73	124.314189970776	0.41581002922382
60	125.75	126.650367311606	-0.900367311605812
61	125.16	123.923805269058	1.23619473094239

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 109.55 & 110.351923884357 & -0.801923884357248 \tabularnewline
2 & 111.69 & 110.201725418473 & 1.4882745815275 \tabularnewline
3 & 110.76 & 107.837661033197 & 2.9223389668034 \tabularnewline
4 & 110.78 & 109.30145490144 & 1.47854509856033 \tabularnewline
5 & 110.76 & 110.365722355334 & 0.394277644665746 \tabularnewline
6 & 112.38 & 111.510478582187 & 0.869521417813132 \tabularnewline
7 & 112.86 & 113.83985569357 & -0.979855693569853 \tabularnewline
8 & 114.74 & 113.919476952219 & 0.820523047780867 \tabularnewline
9 & 116.21 & 114.455580768667 & 1.75441923133334 \tabularnewline
10 & 116.86 & 114.619394288104 & 2.24060571189649 \tabularnewline
11 & 114.51 & 114.43433605778 & 0.0756639422197657 \tabularnewline
12 & 114.11 & 116.559597682955 & -2.44959768295472 \tabularnewline
13 & 112.12 & 113.323740723213 & -1.20374072321267 \tabularnewline
14 & 108.9 & 112.563714527409 & -3.66371452740855 \tabularnewline
15 & 106.62 & 110.055119247637 & -3.43511924763663 \tabularnewline
16 & 105.95 & 109.28060831275 & -3.33060831274986 \tabularnewline
17 & 107.03 & 106.550358241496 & 0.479641758504378 \tabularnewline
18 & 107.1 & 108.184941803012 & -1.0849418030118 \tabularnewline
19 & 108 & 107.882549737156 & 0.117450262844414 \tabularnewline
20 & 108.24 & 108.506896628461 & -0.266896628460748 \tabularnewline
21 & 109.72 & 108.113465539267 & 1.60653446073319 \tabularnewline
22 & 109.53 & 108.616618985072 & 0.91338101492844 \tabularnewline
23 & 110.64 & 110.800383369623 & -0.160383369622901 \tabularnewline
24 & 110.03 & 110.823456665713 & -0.793456665712766 \tabularnewline
25 & 109.38 & 109.462636089023 & -0.0826360890230147 \tabularnewline
26 & 110.62 & 111.5033320627 & -0.883332062700039 \tabularnewline
27 & 110.57 & 111.257044158977 & -0.68704415897735 \tabularnewline
28 & 111.52 & 110.752101248847 & 0.767898751153374 \tabularnewline
29 & 111.47 & 110.491619939942 & 0.978380060057787 \tabularnewline
30 & 112.97 & 113.302953214414 & -0.332953214413522 \tabularnewline
31 & 114.24 & 114.553045331646 & -0.313045331645642 \tabularnewline
32 & 114.97 & 115.016944240825 & -0.0469442408254123 \tabularnewline
33 & 114.82 & 116.951447869086 & -2.1314478690865 \tabularnewline
34 & 114.61 & 115.806050481387 & -1.19605048138658 \tabularnewline
35 & 114.68 & 114.753002288706 & -0.0730022887059389 \tabularnewline
36 & 114.9 & 115.46228168678 & -0.562281686779621 \tabularnewline
37 & 115.05 & 114.854147638772 & 0.195852361228369 \tabularnewline
38 & 115.67 & 115.687019590986 & -0.0170195909858736 \tabularnewline
39 & 117.17 & 116.197316340107 & 0.972683659893121 \tabularnewline
40 & 118.17 & 116.359911971293 & 1.81008802870705 \tabularnewline
41 & 118.61 & 118.7459478411 & -0.135947841100022 \tabularnewline
42 & 120.38 & 120.512814345172 & -0.132814345171606 \tabularnewline
43 & 121.27 & 121.008808281177 & 0.261191718823401 \tabularnewline
44 & 121.55 & 120.705077902259 & 0.844922097740817 \tabularnewline
45 & 121.08 & 120.901904089445 & 0.178095910555354 \tabularnewline
46 & 121.01 & 119.451099182288 & 1.55890081771225 \tabularnewline
47 & 121.15 & 119.64017978635 & 1.50982021365017 \tabularnewline
48 & 121.84 & 122.112501441164 & -0.272501441163655 \tabularnewline
49 & 121.83 & 121.338886376253 & 0.491113623746687 \tabularnewline
50 & 121.86 & 120.721110499459 & 1.1388895005405 \tabularnewline
51 & 121.56 & 119.938501521447 & 1.621498478553 \tabularnewline
52 & 122.81 & 123.037569515936 & -0.227569515935824 \tabularnewline
53 & 123.24 & 122.434587031555 & 0.805412968444895 \tabularnewline
54 & 124.52 & 123.814258415135 & 0.705741584865156 \tabularnewline
55 & 125.03 & 124.691836022836 & 0.338163977163633 \tabularnewline
56 & 123.56 & 124.72252622794 & -1.16252622793953 \tabularnewline
57 & 122.58 & 124.718947845749 & -2.13894784574863 \tabularnewline
58 & 122.95 & 124.47516557072 & -1.52516557072043 \tabularnewline
59 & 124.73 & 124.314189970776 & 0.41581002922382 \tabularnewline
60 & 125.75 & 126.650367311606 & -0.900367311605812 \tabularnewline
61 & 125.16 & 123.923805269058 & 1.23619473094239 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=189971&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]109.55[/C][C]110.351923884357[/C][C]-0.801923884357248[/C][/ROW]
[ROW][C]2[/C][C]111.69[/C][C]110.201725418473[/C][C]1.4882745815275[/C][/ROW]
[ROW][C]3[/C][C]110.76[/C][C]107.837661033197[/C][C]2.9223389668034[/C][/ROW]
[ROW][C]4[/C][C]110.78[/C][C]109.30145490144[/C][C]1.47854509856033[/C][/ROW]
[ROW][C]5[/C][C]110.76[/C][C]110.365722355334[/C][C]0.394277644665746[/C][/ROW]
[ROW][C]6[/C][C]112.38[/C][C]111.510478582187[/C][C]0.869521417813132[/C][/ROW]
[ROW][C]7[/C][C]112.86[/C][C]113.83985569357[/C][C]-0.979855693569853[/C][/ROW]
[ROW][C]8[/C][C]114.74[/C][C]113.919476952219[/C][C]0.820523047780867[/C][/ROW]
[ROW][C]9[/C][C]116.21[/C][C]114.455580768667[/C][C]1.75441923133334[/C][/ROW]
[ROW][C]10[/C][C]116.86[/C][C]114.619394288104[/C][C]2.24060571189649[/C][/ROW]
[ROW][C]11[/C][C]114.51[/C][C]114.43433605778[/C][C]0.0756639422197657[/C][/ROW]
[ROW][C]12[/C][C]114.11[/C][C]116.559597682955[/C][C]-2.44959768295472[/C][/ROW]
[ROW][C]13[/C][C]112.12[/C][C]113.323740723213[/C][C]-1.20374072321267[/C][/ROW]
[ROW][C]14[/C][C]108.9[/C][C]112.563714527409[/C][C]-3.66371452740855[/C][/ROW]
[ROW][C]15[/C][C]106.62[/C][C]110.055119247637[/C][C]-3.43511924763663[/C][/ROW]
[ROW][C]16[/C][C]105.95[/C][C]109.28060831275[/C][C]-3.33060831274986[/C][/ROW]
[ROW][C]17[/C][C]107.03[/C][C]106.550358241496[/C][C]0.479641758504378[/C][/ROW]
[ROW][C]18[/C][C]107.1[/C][C]108.184941803012[/C][C]-1.0849418030118[/C][/ROW]
[ROW][C]19[/C][C]108[/C][C]107.882549737156[/C][C]0.117450262844414[/C][/ROW]
[ROW][C]20[/C][C]108.24[/C][C]108.506896628461[/C][C]-0.266896628460748[/C][/ROW]
[ROW][C]21[/C][C]109.72[/C][C]108.113465539267[/C][C]1.60653446073319[/C][/ROW]
[ROW][C]22[/C][C]109.53[/C][C]108.616618985072[/C][C]0.91338101492844[/C][/ROW]
[ROW][C]23[/C][C]110.64[/C][C]110.800383369623[/C][C]-0.160383369622901[/C][/ROW]
[ROW][C]24[/C][C]110.03[/C][C]110.823456665713[/C][C]-0.793456665712766[/C][/ROW]
[ROW][C]25[/C][C]109.38[/C][C]109.462636089023[/C][C]-0.0826360890230147[/C][/ROW]
[ROW][C]26[/C][C]110.62[/C][C]111.5033320627[/C][C]-0.883332062700039[/C][/ROW]
[ROW][C]27[/C][C]110.57[/C][C]111.257044158977[/C][C]-0.68704415897735[/C][/ROW]
[ROW][C]28[/C][C]111.52[/C][C]110.752101248847[/C][C]0.767898751153374[/C][/ROW]
[ROW][C]29[/C][C]111.47[/C][C]110.491619939942[/C][C]0.978380060057787[/C][/ROW]
[ROW][C]30[/C][C]112.97[/C][C]113.302953214414[/C][C]-0.332953214413522[/C][/ROW]
[ROW][C]31[/C][C]114.24[/C][C]114.553045331646[/C][C]-0.313045331645642[/C][/ROW]
[ROW][C]32[/C][C]114.97[/C][C]115.016944240825[/C][C]-0.0469442408254123[/C][/ROW]
[ROW][C]33[/C][C]114.82[/C][C]116.951447869086[/C][C]-2.1314478690865[/C][/ROW]
[ROW][C]34[/C][C]114.61[/C][C]115.806050481387[/C][C]-1.19605048138658[/C][/ROW]
[ROW][C]35[/C][C]114.68[/C][C]114.753002288706[/C][C]-0.0730022887059389[/C][/ROW]
[ROW][C]36[/C][C]114.9[/C][C]115.46228168678[/C][C]-0.562281686779621[/C][/ROW]
[ROW][C]37[/C][C]115.05[/C][C]114.854147638772[/C][C]0.195852361228369[/C][/ROW]
[ROW][C]38[/C][C]115.67[/C][C]115.687019590986[/C][C]-0.0170195909858736[/C][/ROW]
[ROW][C]39[/C][C]117.17[/C][C]116.197316340107[/C][C]0.972683659893121[/C][/ROW]
[ROW][C]40[/C][C]118.17[/C][C]116.359911971293[/C][C]1.81008802870705[/C][/ROW]
[ROW][C]41[/C][C]118.61[/C][C]118.7459478411[/C][C]-0.135947841100022[/C][/ROW]
[ROW][C]42[/C][C]120.38[/C][C]120.512814345172[/C][C]-0.132814345171606[/C][/ROW]
[ROW][C]43[/C][C]121.27[/C][C]121.008808281177[/C][C]0.261191718823401[/C][/ROW]
[ROW][C]44[/C][C]121.55[/C][C]120.705077902259[/C][C]0.844922097740817[/C][/ROW]
[ROW][C]45[/C][C]121.08[/C][C]120.901904089445[/C][C]0.178095910555354[/C][/ROW]
[ROW][C]46[/C][C]121.01[/C][C]119.451099182288[/C][C]1.55890081771225[/C][/ROW]
[ROW][C]47[/C][C]121.15[/C][C]119.64017978635[/C][C]1.50982021365017[/C][/ROW]
[ROW][C]48[/C][C]121.84[/C][C]122.112501441164[/C][C]-0.272501441163655[/C][/ROW]
[ROW][C]49[/C][C]121.83[/C][C]121.338886376253[/C][C]0.491113623746687[/C][/ROW]
[ROW][C]50[/C][C]121.86[/C][C]120.721110499459[/C][C]1.1388895005405[/C][/ROW]
[ROW][C]51[/C][C]121.56[/C][C]119.938501521447[/C][C]1.621498478553[/C][/ROW]
[ROW][C]52[/C][C]122.81[/C][C]123.037569515936[/C][C]-0.227569515935824[/C][/ROW]
[ROW][C]53[/C][C]123.24[/C][C]122.434587031555[/C][C]0.805412968444895[/C][/ROW]
[ROW][C]54[/C][C]124.52[/C][C]123.814258415135[/C][C]0.705741584865156[/C][/ROW]
[ROW][C]55[/C][C]125.03[/C][C]124.691836022836[/C][C]0.338163977163633[/C][/ROW]
[ROW][C]56[/C][C]123.56[/C][C]124.72252622794[/C][C]-1.16252622793953[/C][/ROW]
[ROW][C]57[/C][C]122.58[/C][C]124.718947845749[/C][C]-2.13894784574863[/C][/ROW]
[ROW][C]58[/C][C]122.95[/C][C]124.47516557072[/C][C]-1.52516557072043[/C][/ROW]
[ROW][C]59[/C][C]124.73[/C][C]124.314189970776[/C][C]0.41581002922382[/C][/ROW]
[ROW][C]60[/C][C]125.75[/C][C]126.650367311606[/C][C]-0.900367311605812[/C][/ROW]
[ROW][C]61[/C][C]125.16[/C][C]123.923805269058[/C][C]1.23619473094239[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=189971&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=189971&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	109.55	110.351923884357	-0.801923884357248
2	111.69	110.201725418473	1.4882745815275
3	110.76	107.837661033197	2.9223389668034
4	110.78	109.30145490144	1.47854509856033
5	110.76	110.365722355334	0.394277644665746
6	112.38	111.510478582187	0.869521417813132
7	112.86	113.83985569357	-0.979855693569853
8	114.74	113.919476952219	0.820523047780867
9	116.21	114.455580768667	1.75441923133334
10	116.86	114.619394288104	2.24060571189649
11	114.51	114.43433605778	0.0756639422197657
12	114.11	116.559597682955	-2.44959768295472
13	112.12	113.323740723213	-1.20374072321267
14	108.9	112.563714527409	-3.66371452740855
15	106.62	110.055119247637	-3.43511924763663
16	105.95	109.28060831275	-3.33060831274986
17	107.03	106.550358241496	0.479641758504378
18	107.1	108.184941803012	-1.0849418030118
19	108	107.882549737156	0.117450262844414
20	108.24	108.506896628461	-0.266896628460748
21	109.72	108.113465539267	1.60653446073319
22	109.53	108.616618985072	0.91338101492844
23	110.64	110.800383369623	-0.160383369622901
24	110.03	110.823456665713	-0.793456665712766
25	109.38	109.462636089023	-0.0826360890230147
26	110.62	111.5033320627	-0.883332062700039
27	110.57	111.257044158977	-0.68704415897735
28	111.52	110.752101248847	0.767898751153374
29	111.47	110.491619939942	0.978380060057787
30	112.97	113.302953214414	-0.332953214413522
31	114.24	114.553045331646	-0.313045331645642
32	114.97	115.016944240825	-0.0469442408254123
33	114.82	116.951447869086	-2.1314478690865
34	114.61	115.806050481387	-1.19605048138658
35	114.68	114.753002288706	-0.0730022887059389
36	114.9	115.46228168678	-0.562281686779621
37	115.05	114.854147638772	0.195852361228369
38	115.67	115.687019590986	-0.0170195909858736
39	117.17	116.197316340107	0.972683659893121
40	118.17	116.359911971293	1.81008802870705
41	118.61	118.7459478411	-0.135947841100022
42	120.38	120.512814345172	-0.132814345171606
43	121.27	121.008808281177	0.261191718823401
44	121.55	120.705077902259	0.844922097740817
45	121.08	120.901904089445	0.178095910555354
46	121.01	119.451099182288	1.55890081771225
47	121.15	119.64017978635	1.50982021365017
48	121.84	122.112501441164	-0.272501441163655
49	121.83	121.338886376253	0.491113623746687
50	121.86	120.721110499459	1.1388895005405
51	121.56	119.938501521447	1.621498478553
52	122.81	123.037569515936	-0.227569515935824
53	123.24	122.434587031555	0.805412968444895
54	124.52	123.814258415135	0.705741584865156
55	125.03	124.691836022836	0.338163977163633
56	123.56	124.72252622794	-1.16252622793953
57	122.58	124.718947845749	-2.13894784574863
58	122.95	124.47516557072	-1.52516557072043
59	124.73	124.314189970776	0.41581002922382
60	125.75	126.650367311606	-0.900367311605812
61	125.16	123.923805269058	1.23619473094239

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
15	0.411954290484346	0.823908580968692	0.588045709515654
16	0.438480909080976	0.876961818161951	0.561519090919024
17	0.94223958632214	0.11552082735572	0.0577604136778598
18	0.991922356311582	0.0161552873768356	0.00807764368841781
19	0.991408723838584	0.0171825523228319	0.00859127616141594
20	0.999802837069831	0.000394325860338328	0.000197162930169164
21	0.999912472233093	0.000175055533814662	8.75277669073311e-05
22	0.999851952887851	0.000296094224297828	0.000148047112148914
23	0.999710164651362	0.000579670697275073	0.000289835348637537
24	0.999439855331897	0.00112028933620608	0.000560144668103042
25	0.999160065214558	0.00167986957088491	0.000839934785442457
26	0.998392138274965	0.00321572345007074	0.00160786172503537
27	0.998325028025902	0.00334994394819616	0.00167497197409808
28	0.996854884919245	0.00629023016151069	0.00314511508075534
29	0.997822430084716	0.00435513983056882	0.00217756991528441
30	0.998434603134694	0.00313079373061128	0.00156539686530564
31	0.998861380589547	0.00227723882090547	0.00113861941045273
32	0.999211211517541	0.00157757696491805	0.000788788482459027
33	0.998512958042585	0.00297408391483075	0.00148704195741537
34	0.997858852132172	0.00428229573565679	0.00214114786782839
35	0.996760658110484	0.00647868377903182	0.00323934188951591
36	0.99517639694831	0.00964720610338097	0.00482360305169048
37	0.995585276351346	0.00882944729730854	0.00441472364865427
38	0.997120059611454	0.00575988077709139	0.0028799403885457
39	0.996783571260913	0.00643285747817385	0.00321642873908692
40	0.995841390384951	0.00831721923009866	0.00415860961504933
41	0.990676772763132	0.0186464544737362	0.00932322723686812
42	0.992201423692312	0.0155971526153759	0.00779857630768795
43	0.983530277215796	0.0329394455684089	0.0164697227842044
44	0.972726296447211	0.0545474071055775	0.0272737035527887
45	0.940132190467732	0.119735619064537	0.0598678095322683
46	0.894008968564947	0.211982062870106	0.105991031435053

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
15 & 0.411954290484346 & 0.823908580968692 & 0.588045709515654 \tabularnewline
16 & 0.438480909080976 & 0.876961818161951 & 0.561519090919024 \tabularnewline
17 & 0.94223958632214 & 0.11552082735572 & 0.0577604136778598 \tabularnewline
18 & 0.991922356311582 & 0.0161552873768356 & 0.00807764368841781 \tabularnewline
19 & 0.991408723838584 & 0.0171825523228319 & 0.00859127616141594 \tabularnewline
20 & 0.999802837069831 & 0.000394325860338328 & 0.000197162930169164 \tabularnewline
21 & 0.999912472233093 & 0.000175055533814662 & 8.75277669073311e-05 \tabularnewline
22 & 0.999851952887851 & 0.000296094224297828 & 0.000148047112148914 \tabularnewline
23 & 0.999710164651362 & 0.000579670697275073 & 0.000289835348637537 \tabularnewline
24 & 0.999439855331897 & 0.00112028933620608 & 0.000560144668103042 \tabularnewline
25 & 0.999160065214558 & 0.00167986957088491 & 0.000839934785442457 \tabularnewline
26 & 0.998392138274965 & 0.00321572345007074 & 0.00160786172503537 \tabularnewline
27 & 0.998325028025902 & 0.00334994394819616 & 0.00167497197409808 \tabularnewline
28 & 0.996854884919245 & 0.00629023016151069 & 0.00314511508075534 \tabularnewline
29 & 0.997822430084716 & 0.00435513983056882 & 0.00217756991528441 \tabularnewline
30 & 0.998434603134694 & 0.00313079373061128 & 0.00156539686530564 \tabularnewline
31 & 0.998861380589547 & 0.00227723882090547 & 0.00113861941045273 \tabularnewline
32 & 0.999211211517541 & 0.00157757696491805 & 0.000788788482459027 \tabularnewline
33 & 0.998512958042585 & 0.00297408391483075 & 0.00148704195741537 \tabularnewline
34 & 0.997858852132172 & 0.00428229573565679 & 0.00214114786782839 \tabularnewline
35 & 0.996760658110484 & 0.00647868377903182 & 0.00323934188951591 \tabularnewline
36 & 0.99517639694831 & 0.00964720610338097 & 0.00482360305169048 \tabularnewline
37 & 0.995585276351346 & 0.00882944729730854 & 0.00441472364865427 \tabularnewline
38 & 0.997120059611454 & 0.00575988077709139 & 0.0028799403885457 \tabularnewline
39 & 0.996783571260913 & 0.00643285747817385 & 0.00321642873908692 \tabularnewline
40 & 0.995841390384951 & 0.00831721923009866 & 0.00415860961504933 \tabularnewline
41 & 0.990676772763132 & 0.0186464544737362 & 0.00932322723686812 \tabularnewline
42 & 0.992201423692312 & 0.0155971526153759 & 0.00779857630768795 \tabularnewline
43 & 0.983530277215796 & 0.0329394455684089 & 0.0164697227842044 \tabularnewline
44 & 0.972726296447211 & 0.0545474071055775 & 0.0272737035527887 \tabularnewline
45 & 0.940132190467732 & 0.119735619064537 & 0.0598678095322683 \tabularnewline
46 & 0.894008968564947 & 0.211982062870106 & 0.105991031435053 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=189971&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]15[/C][C]0.411954290484346[/C][C]0.823908580968692[/C][C]0.588045709515654[/C][/ROW]
[ROW][C]16[/C][C]0.438480909080976[/C][C]0.876961818161951[/C][C]0.561519090919024[/C][/ROW]
[ROW][C]17[/C][C]0.94223958632214[/C][C]0.11552082735572[/C][C]0.0577604136778598[/C][/ROW]
[ROW][C]18[/C][C]0.991922356311582[/C][C]0.0161552873768356[/C][C]0.00807764368841781[/C][/ROW]
[ROW][C]19[/C][C]0.991408723838584[/C][C]0.0171825523228319[/C][C]0.00859127616141594[/C][/ROW]
[ROW][C]20[/C][C]0.999802837069831[/C][C]0.000394325860338328[/C][C]0.000197162930169164[/C][/ROW]
[ROW][C]21[/C][C]0.999912472233093[/C][C]0.000175055533814662[/C][C]8.75277669073311e-05[/C][/ROW]
[ROW][C]22[/C][C]0.999851952887851[/C][C]0.000296094224297828[/C][C]0.000148047112148914[/C][/ROW]
[ROW][C]23[/C][C]0.999710164651362[/C][C]0.000579670697275073[/C][C]0.000289835348637537[/C][/ROW]
[ROW][C]24[/C][C]0.999439855331897[/C][C]0.00112028933620608[/C][C]0.000560144668103042[/C][/ROW]
[ROW][C]25[/C][C]0.999160065214558[/C][C]0.00167986957088491[/C][C]0.000839934785442457[/C][/ROW]
[ROW][C]26[/C][C]0.998392138274965[/C][C]0.00321572345007074[/C][C]0.00160786172503537[/C][/ROW]
[ROW][C]27[/C][C]0.998325028025902[/C][C]0.00334994394819616[/C][C]0.00167497197409808[/C][/ROW]
[ROW][C]28[/C][C]0.996854884919245[/C][C]0.00629023016151069[/C][C]0.00314511508075534[/C][/ROW]
[ROW][C]29[/C][C]0.997822430084716[/C][C]0.00435513983056882[/C][C]0.00217756991528441[/C][/ROW]
[ROW][C]30[/C][C]0.998434603134694[/C][C]0.00313079373061128[/C][C]0.00156539686530564[/C][/ROW]
[ROW][C]31[/C][C]0.998861380589547[/C][C]0.00227723882090547[/C][C]0.00113861941045273[/C][/ROW]
[ROW][C]32[/C][C]0.999211211517541[/C][C]0.00157757696491805[/C][C]0.000788788482459027[/C][/ROW]
[ROW][C]33[/C][C]0.998512958042585[/C][C]0.00297408391483075[/C][C]0.00148704195741537[/C][/ROW]
[ROW][C]34[/C][C]0.997858852132172[/C][C]0.00428229573565679[/C][C]0.00214114786782839[/C][/ROW]
[ROW][C]35[/C][C]0.996760658110484[/C][C]0.00647868377903182[/C][C]0.00323934188951591[/C][/ROW]
[ROW][C]36[/C][C]0.99517639694831[/C][C]0.00964720610338097[/C][C]0.00482360305169048[/C][/ROW]
[ROW][C]37[/C][C]0.995585276351346[/C][C]0.00882944729730854[/C][C]0.00441472364865427[/C][/ROW]
[ROW][C]38[/C][C]0.997120059611454[/C][C]0.00575988077709139[/C][C]0.0028799403885457[/C][/ROW]
[ROW][C]39[/C][C]0.996783571260913[/C][C]0.00643285747817385[/C][C]0.00321642873908692[/C][/ROW]
[ROW][C]40[/C][C]0.995841390384951[/C][C]0.00831721923009866[/C][C]0.00415860961504933[/C][/ROW]
[ROW][C]41[/C][C]0.990676772763132[/C][C]0.0186464544737362[/C][C]0.00932322723686812[/C][/ROW]
[ROW][C]42[/C][C]0.992201423692312[/C][C]0.0155971526153759[/C][C]0.00779857630768795[/C][/ROW]
[ROW][C]43[/C][C]0.983530277215796[/C][C]0.0329394455684089[/C][C]0.0164697227842044[/C][/ROW]
[ROW][C]44[/C][C]0.972726296447211[/C][C]0.0545474071055775[/C][C]0.0272737035527887[/C][/ROW]
[ROW][C]45[/C][C]0.940132190467732[/C][C]0.119735619064537[/C][C]0.0598678095322683[/C][/ROW]
[ROW][C]46[/C][C]0.894008968564947[/C][C]0.211982062870106[/C][C]0.105991031435053[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=189971&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=189971&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
15	0.411954290484346	0.823908580968692	0.588045709515654
16	0.438480909080976	0.876961818161951	0.561519090919024
17	0.94223958632214	0.11552082735572	0.0577604136778598
18	0.991922356311582	0.0161552873768356	0.00807764368841781
19	0.991408723838584	0.0171825523228319	0.00859127616141594
20	0.999802837069831	0.000394325860338328	0.000197162930169164
21	0.999912472233093	0.000175055533814662	8.75277669073311e-05
22	0.999851952887851	0.000296094224297828	0.000148047112148914
23	0.999710164651362	0.000579670697275073	0.000289835348637537
24	0.999439855331897	0.00112028933620608	0.000560144668103042
25	0.999160065214558	0.00167986957088491	0.000839934785442457
26	0.998392138274965	0.00321572345007074	0.00160786172503537
27	0.998325028025902	0.00334994394819616	0.00167497197409808
28	0.996854884919245	0.00629023016151069	0.00314511508075534
29	0.997822430084716	0.00435513983056882	0.00217756991528441
30	0.998434603134694	0.00313079373061128	0.00156539686530564
31	0.998861380589547	0.00227723882090547	0.00113861941045273
32	0.999211211517541	0.00157757696491805	0.000788788482459027
33	0.998512958042585	0.00297408391483075	0.00148704195741537
34	0.997858852132172	0.00428229573565679	0.00214114786782839
35	0.996760658110484	0.00647868377903182	0.00323934188951591
36	0.99517639694831	0.00964720610338097	0.00482360305169048
37	0.995585276351346	0.00882944729730854	0.00441472364865427
38	0.997120059611454	0.00575988077709139	0.0028799403885457
39	0.996783571260913	0.00643285747817385	0.00321642873908692
40	0.995841390384951	0.00831721923009866	0.00415860961504933
41	0.990676772763132	0.0186464544737362	0.00932322723686812
42	0.992201423692312	0.0155971526153759	0.00779857630768795
43	0.983530277215796	0.0329394455684089	0.0164697227842044
44	0.972726296447211	0.0545474071055775	0.0272737035527887
45	0.940132190467732	0.119735619064537	0.0598678095322683
46	0.894008968564947	0.211982062870106	0.105991031435053

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	21	0.65625	NOK
5% type I error level	26	0.8125	NOK
10% type I error level	27	0.84375	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 & 21 & 0.65625 & NOK \tabularnewline
5% type I error level & 26 & 0.8125 & NOK \tabularnewline
10% type I error level & 27 & 0.84375 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=189971&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]21[/C][C]0.65625[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]26[/C][C]0.8125[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]27[/C][C]0.84375[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=189971&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=189971&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	21	0.65625	NOK
5% type I error level	26	0.8125	NOK
10% type I error level	27	0.84375	NOK

Figure 1

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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 = 7 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 7 ; 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