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rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 23 Nov 2009 12:19:36 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/23/t12590041247d26hs51fgzkxc2.htm/, Retrieved Thu, 02 May 2024 22:07:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58868, Retrieved Thu, 02 May 2024 22:07:11 +0000

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Estimated Impact

167

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

-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [] [2009-11-20 07:49:33] [5d885a68c2332cc44f6191ec94766bfa]
-    D        [Multiple Regression] [VerbeteringModel5] [2009-11-23 19:19:36] [82f29a5d509ab8039aab37a0145f886d] [Current]

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Dataseries X:

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Boxplots

100.49	1.9	100.16	100.03
99.72	2	100.49	100.25
100.14	2.3	99.72	99.6
98.48	2.8	100.14	100.16
100.38	2.4	98.48	100.49
101.45	2.3	100.38	99.72
98.42	2.7	101.45	100.14
98.6	2.7	98.42	98.48
100.06	2.9	98.6	100.38
98.62	3	100.06	101.45
100.84	2.2	98.62	98.42
100.02	2.3	100.84	98.6
97.95	2.8	100.02	100.06
98.32	2.8	97.95	98.62
98.27	2.8	98.32	100.84
97.22	2.2	98.27	100.02
99.28	2.6	97.22	97.95
100.38	2.8	99.28	98.32
99.02	2.5	100.38	98.27
100.32	2.4	99.02	97.22
99.81	2.3	100.32	99.28
100.6	1.9	99.81	100.38
101.19	1.7	100.6	99.02
100.47	2	101.19	100.32
101.77	2.1	100.47	99.81
102.32	1.7	101.77	100.6
102.39	1.8	102.32	101.19
101.16	1.8	102.39	100.47
100.63	1.8	101.16	101.77
101.48	1.3	100.63	102.32
101.44	1.3	101.48	102.39
100.09	1.3	101.44	101.16
100.7	1.2	100.09	100.63
100.78	1.4	100.7	101.48
99.81	2.2	100.78	101.44
98.45	2.9	99.81	100.09
98.49	3.1	98.45	100.7
97.48	3.5	98.49	100.78
97.91	3.6	97.48	99.81
96.94	4.4	97.91	98.45
98.53	4.1	96.94	98.49
96.82	5.1	98.53	97.48
95.76	5.8	96.82	97.91
95.27	5.9	95.76	96.94
97.32	5.4	95.27	98.53
96.68	5.5	97.32	96.82
97.87	4.8	96.68	95.76
97.42	3.2	97.87	95.27
97.94	2.7	97.42	97.32
99.52	2.1	97.94	96.68
100.99	1.9	99.52	97.87
99.92	0.6	100.99	97.42
101.97	0.7	99.92	97.94
101.58	-0.2	101.97	99.52
99.54	-1	101.58	100.99
100.83	-1.7	99.54	99.92

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58868&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58868&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58868&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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 57.3427945489103 -0.49999670903731X[t] + 0.571499960545084Y1[t] -0.139851953533137Y4[t] + 0.650113977389304M1[t] + 0.71191289906699M2[t] + 1.20339151560654M3[t] -0.388902182650499M4[t] + 1.70117362711875M5[t] + 1.07641684010856M6[t] -0.460083159944192M7[t] + 0.358538583379871M8[t] + 1.46442617656104M9[t] + 0.701154255385232M10[t] + 1.33629220612652M11[t] -0.00920527843402831t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  57.3427945489103 -0.49999670903731X[t] +  0.571499960545084Y1[t] -0.139851953533137Y4[t] +  0.650113977389304M1[t] +  0.71191289906699M2[t] +  1.20339151560654M3[t] -0.388902182650499M4[t] +  1.70117362711875M5[t] +  1.07641684010856M6[t] -0.460083159944192M7[t] +  0.358538583379871M8[t] +  1.46442617656104M9[t] +  0.701154255385232M10[t] +  1.33629220612652M11[t] -0.00920527843402831t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58868&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  57.3427945489103 -0.49999670903731X[t] +  0.571499960545084Y1[t] -0.139851953533137Y4[t] +  0.650113977389304M1[t] +  0.71191289906699M2[t] +  1.20339151560654M3[t] -0.388902182650499M4[t] +  1.70117362711875M5[t] +  1.07641684010856M6[t] -0.460083159944192M7[t] +  0.358538583379871M8[t] +  1.46442617656104M9[t] +  0.701154255385232M10[t] +  1.33629220612652M11[t] -0.00920527843402831t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58868&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58868&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 57.3427945489103 -0.49999670903731X[t] + 0.571499960545084Y1[t] -0.139851953533137Y4[t] + 0.650113977389304M1[t] + 0.71191289906699M2[t] + 1.20339151560654M3[t] -0.388902182650499M4[t] + 1.70117362711875M5[t] + 1.07641684010856M6[t] -0.460083159944192M7[t] + 0.358538583379871M8[t] + 1.46442617656104M9[t] + 0.701154255385232M10[t] + 1.33629220612652M11[t] -0.00920527843402831t + 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)	57.3427945489103	13.295668	4.3129	0.000102	5.1e-05
X	-0.49999670903731	0.129826	-3.8513	0.000415	0.000207
Y1	0.571499960545084	0.132264	4.3209	1e-04	5e-05
Y4	-0.139851953533137	0.101748	-1.3745	0.176942	0.088471
M1	0.650113977389304	0.606476	1.072	0.290166	0.145083
M2	0.71191289906699	0.603108	1.1804	0.24481	0.122405
M3	1.20339151560654	0.607928	1.9795	0.054671	0.027335
M4	-0.388902182650499	0.589216	-0.66	0.513015	0.256508
M5	1.70117362711875	0.625057	2.7216	0.009573	0.004787
M6	1.07641684010856	0.589786	1.8251	0.07546	0.03773
M7	-0.460083159944192	0.596563	-0.7712	0.445107	0.222553
M8	0.358538583379871	0.615889	0.5821	0.563734	0.281867
M9	1.46442617656104	0.658338	2.2244	0.031827	0.015914
M10	0.701154255385232	0.640525	1.0947	0.280215	0.140108
M11	1.33629220612652	0.623133	2.1445	0.038124	0.019062
t	-0.00920527843402831	0.008074	-1.1401	0.261005	0.130503

\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) & 57.3427945489103 & 13.295668 & 4.3129 & 0.000102 & 5.1e-05 \tabularnewline
X & -0.49999670903731 & 0.129826 & -3.8513 & 0.000415 & 0.000207 \tabularnewline
Y1 & 0.571499960545084 & 0.132264 & 4.3209 & 1e-04 & 5e-05 \tabularnewline
Y4 & -0.139851953533137 & 0.101748 & -1.3745 & 0.176942 & 0.088471 \tabularnewline
M1 & 0.650113977389304 & 0.606476 & 1.072 & 0.290166 & 0.145083 \tabularnewline
M2 & 0.71191289906699 & 0.603108 & 1.1804 & 0.24481 & 0.122405 \tabularnewline
M3 & 1.20339151560654 & 0.607928 & 1.9795 & 0.054671 & 0.027335 \tabularnewline
M4 & -0.388902182650499 & 0.589216 & -0.66 & 0.513015 & 0.256508 \tabularnewline
M5 & 1.70117362711875 & 0.625057 & 2.7216 & 0.009573 & 0.004787 \tabularnewline
M6 & 1.07641684010856 & 0.589786 & 1.8251 & 0.07546 & 0.03773 \tabularnewline
M7 & -0.460083159944192 & 0.596563 & -0.7712 & 0.445107 & 0.222553 \tabularnewline
M8 & 0.358538583379871 & 0.615889 & 0.5821 & 0.563734 & 0.281867 \tabularnewline
M9 & 1.46442617656104 & 0.658338 & 2.2244 & 0.031827 & 0.015914 \tabularnewline
M10 & 0.701154255385232 & 0.640525 & 1.0947 & 0.280215 & 0.140108 \tabularnewline
M11 & 1.33629220612652 & 0.623133 & 2.1445 & 0.038124 & 0.019062 \tabularnewline
t & -0.00920527843402831 & 0.008074 & -1.1401 & 0.261005 & 0.130503 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58868&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]57.3427945489103[/C][C]13.295668[/C][C]4.3129[/C][C]0.000102[/C][C]5.1e-05[/C][/ROW]
[ROW][C]X[/C][C]-0.49999670903731[/C][C]0.129826[/C][C]-3.8513[/C][C]0.000415[/C][C]0.000207[/C][/ROW]
[ROW][C]Y1[/C][C]0.571499960545084[/C][C]0.132264[/C][C]4.3209[/C][C]1e-04[/C][C]5e-05[/C][/ROW]
[ROW][C]Y4[/C][C]-0.139851953533137[/C][C]0.101748[/C][C]-1.3745[/C][C]0.176942[/C][C]0.088471[/C][/ROW]
[ROW][C]M1[/C][C]0.650113977389304[/C][C]0.606476[/C][C]1.072[/C][C]0.290166[/C][C]0.145083[/C][/ROW]
[ROW][C]M2[/C][C]0.71191289906699[/C][C]0.603108[/C][C]1.1804[/C][C]0.24481[/C][C]0.122405[/C][/ROW]
[ROW][C]M3[/C][C]1.20339151560654[/C][C]0.607928[/C][C]1.9795[/C][C]0.054671[/C][C]0.027335[/C][/ROW]
[ROW][C]M4[/C][C]-0.388902182650499[/C][C]0.589216[/C][C]-0.66[/C][C]0.513015[/C][C]0.256508[/C][/ROW]
[ROW][C]M5[/C][C]1.70117362711875[/C][C]0.625057[/C][C]2.7216[/C][C]0.009573[/C][C]0.004787[/C][/ROW]
[ROW][C]M6[/C][C]1.07641684010856[/C][C]0.589786[/C][C]1.8251[/C][C]0.07546[/C][C]0.03773[/C][/ROW]
[ROW][C]M7[/C][C]-0.460083159944192[/C][C]0.596563[/C][C]-0.7712[/C][C]0.445107[/C][C]0.222553[/C][/ROW]
[ROW][C]M8[/C][C]0.358538583379871[/C][C]0.615889[/C][C]0.5821[/C][C]0.563734[/C][C]0.281867[/C][/ROW]
[ROW][C]M9[/C][C]1.46442617656104[/C][C]0.658338[/C][C]2.2244[/C][C]0.031827[/C][C]0.015914[/C][/ROW]
[ROW][C]M10[/C][C]0.701154255385232[/C][C]0.640525[/C][C]1.0947[/C][C]0.280215[/C][C]0.140108[/C][/ROW]
[ROW][C]M11[/C][C]1.33629220612652[/C][C]0.623133[/C][C]2.1445[/C][C]0.038124[/C][C]0.019062[/C][/ROW]
[ROW][C]t[/C][C]-0.00920527843402831[/C][C]0.008074[/C][C]-1.1401[/C][C]0.261005[/C][C]0.130503[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58868&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58868&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)	57.3427945489103	13.295668	4.3129	0.000102	5.1e-05
X	-0.49999670903731	0.129826	-3.8513	0.000415	0.000207
Y1	0.571499960545084	0.132264	4.3209	1e-04	5e-05
Y4	-0.139851953533137	0.101748	-1.3745	0.176942	0.088471
M1	0.650113977389304	0.606476	1.072	0.290166	0.145083
M2	0.71191289906699	0.603108	1.1804	0.24481	0.122405
M3	1.20339151560654	0.607928	1.9795	0.054671	0.027335
M4	-0.388902182650499	0.589216	-0.66	0.513015	0.256508
M5	1.70117362711875	0.625057	2.7216	0.009573	0.004787
M6	1.07641684010856	0.589786	1.8251	0.07546	0.03773
M7	-0.460083159944192	0.596563	-0.7712	0.445107	0.222553
M8	0.358538583379871	0.615889	0.5821	0.563734	0.281867
M9	1.46442617656104	0.658338	2.2244	0.031827	0.015914
M10	0.701154255385232	0.640525	1.0947	0.280215	0.140108
M11	1.33629220612652	0.623133	2.1445	0.038124	0.019062
t	-0.00920527843402831	0.008074	-1.1401	0.261005	0.130503

Multiple Linear Regression - Regression Statistics
Multiple R	0.899016799661889
R-squared	0.808231206074305
Adjusted R-squared	0.73631790835217
F-TEST (value)	11.2389673631324
F-TEST (DF numerator)	15
F-TEST (DF denominator)	40
p-value	5.60008373007292e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.870721422195195
Sum Squared Residuals	30.3262318027849

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.899016799661889 \tabularnewline
R-squared & 0.808231206074305 \tabularnewline
Adjusted R-squared & 0.73631790835217 \tabularnewline
F-TEST (value) & 11.2389673631324 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 40 \tabularnewline
p-value & 5.60008373007292e-10 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.870721422195195 \tabularnewline
Sum Squared Residuals & 30.3262318027849 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58868&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.899016799661889[/C][/ROW]
[ROW][C]R-squared[/C][C]0.808231206074305[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.73631790835217[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]11.2389673631324[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]40[/C][/ROW]
[ROW][C]p-value[/C][C]5.60008373007292e-10[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.870721422195195[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]30.3262318027849[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58868&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58868&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	0.899016799661889
R-squared	0.808231206074305
Adjusted R-squared	0.73631790835217
F-TEST (value)	11.2389673631324
F-TEST (DF numerator)	15
F-TEST (DF denominator)	40
p-value	5.60008373007292e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.870721422195195
Sum Squared Residuals	30.3262318027849

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	100.49	100.285754636971	0.204245363029248
2	99.72	100.446176166513	-0.726176166513105
3	100.14	100.429299292084	-0.289299292084255
4	98.48	98.739514850325	-0.259514850324912
5	100.38	100.025542986104	0.354457013895707
6	101.45	100.63511652082	0.814883479180028
7	98.42	99.4421796960176	-1.02217969601759
8	98.6	98.752105523321	-0.152105523321035
9	100.06	99.5859397774459	0.474060222554142
10	98.62	99.4482112590477	-0.828211259047656
11	100.84	100.074932774605	0.765067225394747
12	100.02	99.922992179915	0.0970078200848986
13	97.95	99.6410887045464	-1.69108870454636
14	98.32	98.7120642425494	-0.392064242549426
15	98.27	99.095321229213	-0.825321229213055
16	97.22	97.8799238818143	-0.659923881814293
17	99.28	99.4502143147758	-0.170214314775844
18	100.38	99.8417976034398	0.538202396560212
19	99.02	99.0817338919404	-0.0617338919404416
20	100.32	99.3107546326027	1.00924536739731
21	99.81	100.912291542684	-1.10229154268390
22	100.6	99.8945108979245	0.705489102075445
23	101.19	101.262126537675	-0.0721265376749542
24	100.47	99.9220074775317	0.547992522468268
25	101.77	100.172761030293	1.59723896970728
26	102.32	101.057820262569	1.26217973743127
27	102.39	101.721906255486	0.668093744514241
28	101.16	100.261105682577	0.898894317423284
29	100.63	101.457223722848	-0.827223722848403
30	101.48	100.693446458391	0.786553541609285
31	101.44	99.62372650962	1.81627349038006
32	100.09	100.582300878934	-0.492300878933925
33	100.7	101.031579453221	-0.3315794532215
34	100.78	100.388843727234	0.391156272766464
35	99.81	100.666093107296	-0.856093107295881
36	98.45	98.6050431019502	-0.155043101950216
37	98.49	98.2834028211015	0.206597178898490
38	97.48	98.1476696228694	-0.667669622869383
39	97.91	98.1383847248478	-0.228384724847794
40	96.94	96.5728320207663	0.367167979233672
41	98.53	98.2437525249427	0.286247475057317
42	96.82	98.1597291607963	-1.33972916079632
43	95.76	95.226624913432	0.53337508656794
44	95.27	95.5159081441677	-0.245908144167734
45	97.32	96.3601892266487	0.959810773351254
46	96.68	96.9484341157943	-0.268434115794253
47	97.87	97.706847580424	0.163152419576088
48	97.42	97.909957240603	-0.489957240602947
49	97.94	98.2569928070887	-0.316992807088660
50	99.52	98.9962697054993	0.523730294500647
51	100.99	100.315088498369	0.674911501630864
52	99.92	100.266623564518	-0.346623564517751
53	101.97	101.613266451329	0.356733548671224
54	101.58	102.379910256553	-0.799910256553205
55	99.54	100.80573498899	-1.26573498898997
56	100.83	100.948930820975	-0.118930820974616

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 100.49 & 100.285754636971 & 0.204245363029248 \tabularnewline
2 & 99.72 & 100.446176166513 & -0.726176166513105 \tabularnewline
3 & 100.14 & 100.429299292084 & -0.289299292084255 \tabularnewline
4 & 98.48 & 98.739514850325 & -0.259514850324912 \tabularnewline
5 & 100.38 & 100.025542986104 & 0.354457013895707 \tabularnewline
6 & 101.45 & 100.63511652082 & 0.814883479180028 \tabularnewline
7 & 98.42 & 99.4421796960176 & -1.02217969601759 \tabularnewline
8 & 98.6 & 98.752105523321 & -0.152105523321035 \tabularnewline
9 & 100.06 & 99.5859397774459 & 0.474060222554142 \tabularnewline
10 & 98.62 & 99.4482112590477 & -0.828211259047656 \tabularnewline
11 & 100.84 & 100.074932774605 & 0.765067225394747 \tabularnewline
12 & 100.02 & 99.922992179915 & 0.0970078200848986 \tabularnewline
13 & 97.95 & 99.6410887045464 & -1.69108870454636 \tabularnewline
14 & 98.32 & 98.7120642425494 & -0.392064242549426 \tabularnewline
15 & 98.27 & 99.095321229213 & -0.825321229213055 \tabularnewline
16 & 97.22 & 97.8799238818143 & -0.659923881814293 \tabularnewline
17 & 99.28 & 99.4502143147758 & -0.170214314775844 \tabularnewline
18 & 100.38 & 99.8417976034398 & 0.538202396560212 \tabularnewline
19 & 99.02 & 99.0817338919404 & -0.0617338919404416 \tabularnewline
20 & 100.32 & 99.3107546326027 & 1.00924536739731 \tabularnewline
21 & 99.81 & 100.912291542684 & -1.10229154268390 \tabularnewline
22 & 100.6 & 99.8945108979245 & 0.705489102075445 \tabularnewline
23 & 101.19 & 101.262126537675 & -0.0721265376749542 \tabularnewline
24 & 100.47 & 99.9220074775317 & 0.547992522468268 \tabularnewline
25 & 101.77 & 100.172761030293 & 1.59723896970728 \tabularnewline
26 & 102.32 & 101.057820262569 & 1.26217973743127 \tabularnewline
27 & 102.39 & 101.721906255486 & 0.668093744514241 \tabularnewline
28 & 101.16 & 100.261105682577 & 0.898894317423284 \tabularnewline
29 & 100.63 & 101.457223722848 & -0.827223722848403 \tabularnewline
30 & 101.48 & 100.693446458391 & 0.786553541609285 \tabularnewline
31 & 101.44 & 99.62372650962 & 1.81627349038006 \tabularnewline
32 & 100.09 & 100.582300878934 & -0.492300878933925 \tabularnewline
33 & 100.7 & 101.031579453221 & -0.3315794532215 \tabularnewline
34 & 100.78 & 100.388843727234 & 0.391156272766464 \tabularnewline
35 & 99.81 & 100.666093107296 & -0.856093107295881 \tabularnewline
36 & 98.45 & 98.6050431019502 & -0.155043101950216 \tabularnewline
37 & 98.49 & 98.2834028211015 & 0.206597178898490 \tabularnewline
38 & 97.48 & 98.1476696228694 & -0.667669622869383 \tabularnewline
39 & 97.91 & 98.1383847248478 & -0.228384724847794 \tabularnewline
40 & 96.94 & 96.5728320207663 & 0.367167979233672 \tabularnewline
41 & 98.53 & 98.2437525249427 & 0.286247475057317 \tabularnewline
42 & 96.82 & 98.1597291607963 & -1.33972916079632 \tabularnewline
43 & 95.76 & 95.226624913432 & 0.53337508656794 \tabularnewline
44 & 95.27 & 95.5159081441677 & -0.245908144167734 \tabularnewline
45 & 97.32 & 96.3601892266487 & 0.959810773351254 \tabularnewline
46 & 96.68 & 96.9484341157943 & -0.268434115794253 \tabularnewline
47 & 97.87 & 97.706847580424 & 0.163152419576088 \tabularnewline
48 & 97.42 & 97.909957240603 & -0.489957240602947 \tabularnewline
49 & 97.94 & 98.2569928070887 & -0.316992807088660 \tabularnewline
50 & 99.52 & 98.9962697054993 & 0.523730294500647 \tabularnewline
51 & 100.99 & 100.315088498369 & 0.674911501630864 \tabularnewline
52 & 99.92 & 100.266623564518 & -0.346623564517751 \tabularnewline
53 & 101.97 & 101.613266451329 & 0.356733548671224 \tabularnewline
54 & 101.58 & 102.379910256553 & -0.799910256553205 \tabularnewline
55 & 99.54 & 100.80573498899 & -1.26573498898997 \tabularnewline
56 & 100.83 & 100.948930820975 & -0.118930820974616 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58868&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]100.49[/C][C]100.285754636971[/C][C]0.204245363029248[/C][/ROW]
[ROW][C]2[/C][C]99.72[/C][C]100.446176166513[/C][C]-0.726176166513105[/C][/ROW]
[ROW][C]3[/C][C]100.14[/C][C]100.429299292084[/C][C]-0.289299292084255[/C][/ROW]
[ROW][C]4[/C][C]98.48[/C][C]98.739514850325[/C][C]-0.259514850324912[/C][/ROW]
[ROW][C]5[/C][C]100.38[/C][C]100.025542986104[/C][C]0.354457013895707[/C][/ROW]
[ROW][C]6[/C][C]101.45[/C][C]100.63511652082[/C][C]0.814883479180028[/C][/ROW]
[ROW][C]7[/C][C]98.42[/C][C]99.4421796960176[/C][C]-1.02217969601759[/C][/ROW]
[ROW][C]8[/C][C]98.6[/C][C]98.752105523321[/C][C]-0.152105523321035[/C][/ROW]
[ROW][C]9[/C][C]100.06[/C][C]99.5859397774459[/C][C]0.474060222554142[/C][/ROW]
[ROW][C]10[/C][C]98.62[/C][C]99.4482112590477[/C][C]-0.828211259047656[/C][/ROW]
[ROW][C]11[/C][C]100.84[/C][C]100.074932774605[/C][C]0.765067225394747[/C][/ROW]
[ROW][C]12[/C][C]100.02[/C][C]99.922992179915[/C][C]0.0970078200848986[/C][/ROW]
[ROW][C]13[/C][C]97.95[/C][C]99.6410887045464[/C][C]-1.69108870454636[/C][/ROW]
[ROW][C]14[/C][C]98.32[/C][C]98.7120642425494[/C][C]-0.392064242549426[/C][/ROW]
[ROW][C]15[/C][C]98.27[/C][C]99.095321229213[/C][C]-0.825321229213055[/C][/ROW]
[ROW][C]16[/C][C]97.22[/C][C]97.8799238818143[/C][C]-0.659923881814293[/C][/ROW]
[ROW][C]17[/C][C]99.28[/C][C]99.4502143147758[/C][C]-0.170214314775844[/C][/ROW]
[ROW][C]18[/C][C]100.38[/C][C]99.8417976034398[/C][C]0.538202396560212[/C][/ROW]
[ROW][C]19[/C][C]99.02[/C][C]99.0817338919404[/C][C]-0.0617338919404416[/C][/ROW]
[ROW][C]20[/C][C]100.32[/C][C]99.3107546326027[/C][C]1.00924536739731[/C][/ROW]
[ROW][C]21[/C][C]99.81[/C][C]100.912291542684[/C][C]-1.10229154268390[/C][/ROW]
[ROW][C]22[/C][C]100.6[/C][C]99.8945108979245[/C][C]0.705489102075445[/C][/ROW]
[ROW][C]23[/C][C]101.19[/C][C]101.262126537675[/C][C]-0.0721265376749542[/C][/ROW]
[ROW][C]24[/C][C]100.47[/C][C]99.9220074775317[/C][C]0.547992522468268[/C][/ROW]
[ROW][C]25[/C][C]101.77[/C][C]100.172761030293[/C][C]1.59723896970728[/C][/ROW]
[ROW][C]26[/C][C]102.32[/C][C]101.057820262569[/C][C]1.26217973743127[/C][/ROW]
[ROW][C]27[/C][C]102.39[/C][C]101.721906255486[/C][C]0.668093744514241[/C][/ROW]
[ROW][C]28[/C][C]101.16[/C][C]100.261105682577[/C][C]0.898894317423284[/C][/ROW]
[ROW][C]29[/C][C]100.63[/C][C]101.457223722848[/C][C]-0.827223722848403[/C][/ROW]
[ROW][C]30[/C][C]101.48[/C][C]100.693446458391[/C][C]0.786553541609285[/C][/ROW]
[ROW][C]31[/C][C]101.44[/C][C]99.62372650962[/C][C]1.81627349038006[/C][/ROW]
[ROW][C]32[/C][C]100.09[/C][C]100.582300878934[/C][C]-0.492300878933925[/C][/ROW]
[ROW][C]33[/C][C]100.7[/C][C]101.031579453221[/C][C]-0.3315794532215[/C][/ROW]
[ROW][C]34[/C][C]100.78[/C][C]100.388843727234[/C][C]0.391156272766464[/C][/ROW]
[ROW][C]35[/C][C]99.81[/C][C]100.666093107296[/C][C]-0.856093107295881[/C][/ROW]
[ROW][C]36[/C][C]98.45[/C][C]98.6050431019502[/C][C]-0.155043101950216[/C][/ROW]
[ROW][C]37[/C][C]98.49[/C][C]98.2834028211015[/C][C]0.206597178898490[/C][/ROW]
[ROW][C]38[/C][C]97.48[/C][C]98.1476696228694[/C][C]-0.667669622869383[/C][/ROW]
[ROW][C]39[/C][C]97.91[/C][C]98.1383847248478[/C][C]-0.228384724847794[/C][/ROW]
[ROW][C]40[/C][C]96.94[/C][C]96.5728320207663[/C][C]0.367167979233672[/C][/ROW]
[ROW][C]41[/C][C]98.53[/C][C]98.2437525249427[/C][C]0.286247475057317[/C][/ROW]
[ROW][C]42[/C][C]96.82[/C][C]98.1597291607963[/C][C]-1.33972916079632[/C][/ROW]
[ROW][C]43[/C][C]95.76[/C][C]95.226624913432[/C][C]0.53337508656794[/C][/ROW]
[ROW][C]44[/C][C]95.27[/C][C]95.5159081441677[/C][C]-0.245908144167734[/C][/ROW]
[ROW][C]45[/C][C]97.32[/C][C]96.3601892266487[/C][C]0.959810773351254[/C][/ROW]
[ROW][C]46[/C][C]96.68[/C][C]96.9484341157943[/C][C]-0.268434115794253[/C][/ROW]
[ROW][C]47[/C][C]97.87[/C][C]97.706847580424[/C][C]0.163152419576088[/C][/ROW]
[ROW][C]48[/C][C]97.42[/C][C]97.909957240603[/C][C]-0.489957240602947[/C][/ROW]
[ROW][C]49[/C][C]97.94[/C][C]98.2569928070887[/C][C]-0.316992807088660[/C][/ROW]
[ROW][C]50[/C][C]99.52[/C][C]98.9962697054993[/C][C]0.523730294500647[/C][/ROW]
[ROW][C]51[/C][C]100.99[/C][C]100.315088498369[/C][C]0.674911501630864[/C][/ROW]
[ROW][C]52[/C][C]99.92[/C][C]100.266623564518[/C][C]-0.346623564517751[/C][/ROW]
[ROW][C]53[/C][C]101.97[/C][C]101.613266451329[/C][C]0.356733548671224[/C][/ROW]
[ROW][C]54[/C][C]101.58[/C][C]102.379910256553[/C][C]-0.799910256553205[/C][/ROW]
[ROW][C]55[/C][C]99.54[/C][C]100.80573498899[/C][C]-1.26573498898997[/C][/ROW]
[ROW][C]56[/C][C]100.83[/C][C]100.948930820975[/C][C]-0.118930820974616[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58868&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58868&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	100.49	100.285754636971	0.204245363029248
2	99.72	100.446176166513	-0.726176166513105
3	100.14	100.429299292084	-0.289299292084255
4	98.48	98.739514850325	-0.259514850324912
5	100.38	100.025542986104	0.354457013895707
6	101.45	100.63511652082	0.814883479180028
7	98.42	99.4421796960176	-1.02217969601759
8	98.6	98.752105523321	-0.152105523321035
9	100.06	99.5859397774459	0.474060222554142
10	98.62	99.4482112590477	-0.828211259047656
11	100.84	100.074932774605	0.765067225394747
12	100.02	99.922992179915	0.0970078200848986
13	97.95	99.6410887045464	-1.69108870454636
14	98.32	98.7120642425494	-0.392064242549426
15	98.27	99.095321229213	-0.825321229213055
16	97.22	97.8799238818143	-0.659923881814293
17	99.28	99.4502143147758	-0.170214314775844
18	100.38	99.8417976034398	0.538202396560212
19	99.02	99.0817338919404	-0.0617338919404416
20	100.32	99.3107546326027	1.00924536739731
21	99.81	100.912291542684	-1.10229154268390
22	100.6	99.8945108979245	0.705489102075445
23	101.19	101.262126537675	-0.0721265376749542
24	100.47	99.9220074775317	0.547992522468268
25	101.77	100.172761030293	1.59723896970728
26	102.32	101.057820262569	1.26217973743127
27	102.39	101.721906255486	0.668093744514241
28	101.16	100.261105682577	0.898894317423284
29	100.63	101.457223722848	-0.827223722848403
30	101.48	100.693446458391	0.786553541609285
31	101.44	99.62372650962	1.81627349038006
32	100.09	100.582300878934	-0.492300878933925
33	100.7	101.031579453221	-0.3315794532215
34	100.78	100.388843727234	0.391156272766464
35	99.81	100.666093107296	-0.856093107295881
36	98.45	98.6050431019502	-0.155043101950216
37	98.49	98.2834028211015	0.206597178898490
38	97.48	98.1476696228694	-0.667669622869383
39	97.91	98.1383847248478	-0.228384724847794
40	96.94	96.5728320207663	0.367167979233672
41	98.53	98.2437525249427	0.286247475057317
42	96.82	98.1597291607963	-1.33972916079632
43	95.76	95.226624913432	0.53337508656794
44	95.27	95.5159081441677	-0.245908144167734
45	97.32	96.3601892266487	0.959810773351254
46	96.68	96.9484341157943	-0.268434115794253
47	97.87	97.706847580424	0.163152419576088
48	97.42	97.909957240603	-0.489957240602947
49	97.94	98.2569928070887	-0.316992807088660
50	99.52	98.9962697054993	0.523730294500647
51	100.99	100.315088498369	0.674911501630864
52	99.92	100.266623564518	-0.346623564517751
53	101.97	101.613266451329	0.356733548671224
54	101.58	102.379910256553	-0.799910256553205
55	99.54	100.80573498899	-1.26573498898997
56	100.83	100.948930820975	-0.118930820974616

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
19	0.303963966758769	0.607927933517538	0.696036033241231
20	0.365638215830075	0.73127643166015	0.634361784169925
21	0.517645400948254	0.964709198103492	0.482354599051746
22	0.469888852319322	0.939777704638644	0.530111147680678
23	0.407348377867632	0.814696755735263	0.592651622132368
24	0.372634449459053	0.745268898918107	0.627365550540947
25	0.711305071737905	0.57738985652419	0.288694928262095
26	0.718494030811575	0.56301193837685	0.281505969188425
27	0.624431433943117	0.751137132113766	0.375568566056883
28	0.550201835912548	0.899596328174904	0.449798164087452
29	0.626577771299234	0.746844457401533	0.373422228700766
30	0.566666647168356	0.866666705663287	0.433333352831644
31	0.821574191812326	0.356851616375347	0.178425808187673
32	0.800072654544613	0.399854690910774	0.199927345455387
33	0.80722012553282	0.38555974893436	0.19277987446718
34	0.729837799786123	0.540324400427754	0.270162200213877
35	0.625255334815668	0.749489330368665	0.374744665184333
36	0.524650119011385	0.95069976197723	0.475349880988615
37	0.807635883135567	0.384728233728866	0.192364116864433

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.303963966758769 & 0.607927933517538 & 0.696036033241231 \tabularnewline
20 & 0.365638215830075 & 0.73127643166015 & 0.634361784169925 \tabularnewline
21 & 0.517645400948254 & 0.964709198103492 & 0.482354599051746 \tabularnewline
22 & 0.469888852319322 & 0.939777704638644 & 0.530111147680678 \tabularnewline
23 & 0.407348377867632 & 0.814696755735263 & 0.592651622132368 \tabularnewline
24 & 0.372634449459053 & 0.745268898918107 & 0.627365550540947 \tabularnewline
25 & 0.711305071737905 & 0.57738985652419 & 0.288694928262095 \tabularnewline
26 & 0.718494030811575 & 0.56301193837685 & 0.281505969188425 \tabularnewline
27 & 0.624431433943117 & 0.751137132113766 & 0.375568566056883 \tabularnewline
28 & 0.550201835912548 & 0.899596328174904 & 0.449798164087452 \tabularnewline
29 & 0.626577771299234 & 0.746844457401533 & 0.373422228700766 \tabularnewline
30 & 0.566666647168356 & 0.866666705663287 & 0.433333352831644 \tabularnewline
31 & 0.821574191812326 & 0.356851616375347 & 0.178425808187673 \tabularnewline
32 & 0.800072654544613 & 0.399854690910774 & 0.199927345455387 \tabularnewline
33 & 0.80722012553282 & 0.38555974893436 & 0.19277987446718 \tabularnewline
34 & 0.729837799786123 & 0.540324400427754 & 0.270162200213877 \tabularnewline
35 & 0.625255334815668 & 0.749489330368665 & 0.374744665184333 \tabularnewline
36 & 0.524650119011385 & 0.95069976197723 & 0.475349880988615 \tabularnewline
37 & 0.807635883135567 & 0.384728233728866 & 0.192364116864433 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58868&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]19[/C][C]0.303963966758769[/C][C]0.607927933517538[/C][C]0.696036033241231[/C][/ROW]
[ROW][C]20[/C][C]0.365638215830075[/C][C]0.73127643166015[/C][C]0.634361784169925[/C][/ROW]
[ROW][C]21[/C][C]0.517645400948254[/C][C]0.964709198103492[/C][C]0.482354599051746[/C][/ROW]
[ROW][C]22[/C][C]0.469888852319322[/C][C]0.939777704638644[/C][C]0.530111147680678[/C][/ROW]
[ROW][C]23[/C][C]0.407348377867632[/C][C]0.814696755735263[/C][C]0.592651622132368[/C][/ROW]
[ROW][C]24[/C][C]0.372634449459053[/C][C]0.745268898918107[/C][C]0.627365550540947[/C][/ROW]
[ROW][C]25[/C][C]0.711305071737905[/C][C]0.57738985652419[/C][C]0.288694928262095[/C][/ROW]
[ROW][C]26[/C][C]0.718494030811575[/C][C]0.56301193837685[/C][C]0.281505969188425[/C][/ROW]
[ROW][C]27[/C][C]0.624431433943117[/C][C]0.751137132113766[/C][C]0.375568566056883[/C][/ROW]
[ROW][C]28[/C][C]0.550201835912548[/C][C]0.899596328174904[/C][C]0.449798164087452[/C][/ROW]
[ROW][C]29[/C][C]0.626577771299234[/C][C]0.746844457401533[/C][C]0.373422228700766[/C][/ROW]
[ROW][C]30[/C][C]0.566666647168356[/C][C]0.866666705663287[/C][C]0.433333352831644[/C][/ROW]
[ROW][C]31[/C][C]0.821574191812326[/C][C]0.356851616375347[/C][C]0.178425808187673[/C][/ROW]
[ROW][C]32[/C][C]0.800072654544613[/C][C]0.399854690910774[/C][C]0.199927345455387[/C][/ROW]
[ROW][C]33[/C][C]0.80722012553282[/C][C]0.38555974893436[/C][C]0.19277987446718[/C][/ROW]
[ROW][C]34[/C][C]0.729837799786123[/C][C]0.540324400427754[/C][C]0.270162200213877[/C][/ROW]
[ROW][C]35[/C][C]0.625255334815668[/C][C]0.749489330368665[/C][C]0.374744665184333[/C][/ROW]
[ROW][C]36[/C][C]0.524650119011385[/C][C]0.95069976197723[/C][C]0.475349880988615[/C][/ROW]
[ROW][C]37[/C][C]0.807635883135567[/C][C]0.384728233728866[/C][C]0.192364116864433[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58868&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58868&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
19	0.303963966758769	0.607927933517538	0.696036033241231
20	0.365638215830075	0.73127643166015	0.634361784169925
21	0.517645400948254	0.964709198103492	0.482354599051746
22	0.469888852319322	0.939777704638644	0.530111147680678
23	0.407348377867632	0.814696755735263	0.592651622132368
24	0.372634449459053	0.745268898918107	0.627365550540947
25	0.711305071737905	0.57738985652419	0.288694928262095
26	0.718494030811575	0.56301193837685	0.281505969188425
27	0.624431433943117	0.751137132113766	0.375568566056883
28	0.550201835912548	0.899596328174904	0.449798164087452
29	0.626577771299234	0.746844457401533	0.373422228700766
30	0.566666647168356	0.866666705663287	0.433333352831644
31	0.821574191812326	0.356851616375347	0.178425808187673
32	0.800072654544613	0.399854690910774	0.199927345455387
33	0.80722012553282	0.38555974893436	0.19277987446718
34	0.729837799786123	0.540324400427754	0.270162200213877
35	0.625255334815668	0.749489330368665	0.374744665184333
36	0.524650119011385	0.95069976197723	0.475349880988615
37	0.807635883135567	0.384728233728866	0.192364116864433

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

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58868&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58868&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58868&T=6

As an alternative you can also use a QR Code:

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

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

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice)
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