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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 13:16:51 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/20/t1258748254p069wt8k7dh9c48.htm/, Retrieved Fri, 19 Apr 2024 19:59:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58452, Retrieved Fri, 19 Apr 2024 19:59:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140

Tree of Dependent Computations

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] [WS 7.4] [2009-11-20 20:16:51] [51118f1042b56b16d340924f16263174] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
114,91	93,13	107,18	96,31	96,21	100,00
92,56	93,88	114,91	107,18	96,31	96,21
115,00	92,55	92,56	114,91	107,18	96,31
107,12	94,43	115,00	92,56	114,91	107,18
117,78	96,25	107,12	115,00	92,56	114,91
107,37	100,44	117,78	107,12	115,00	92,56
106,30	101,50	107,37	117,78	107,12	115,00
114,51	99,40	106,30	107,37	117,78	107,12
98,00	99,69	114,51	106,30	107,37	117,78
103,06	101,69	98,00	114,51	106,30	107,37
100,29	103,67	103,06	98,00	114,51	106,30
104,61	103,05	100,29	103,06	98,00	114,51
111,15	100,95	104,61	100,29	103,06	98,00
104,99	102,35	111,15	104,61	100,29	103,06
109,93	101,65	104,99	111,15	104,61	100,29
111,54	99,57	109,93	104,99	111,15	104,61
132,50	95,68	111,54	109,93	104,99	111,15
100,34	96,58	132,50	111,54	109,93	104,99
123,10	96,33	100,34	132,50	111,54	109,93
114,24	95,37	123,10	100,34	132,50	111,54
104,57	96,00	114,24	123,10	100,34	132,50
109,08	96,88	104,57	114,24	123,10	100,34
106,98	94,85	109,08	104,57	114,24	123,10
133,68	92,47	106,98	109,08	104,57	114,24
124,85	93,99	133,68	106,98	109,08	104,57
122,51	93,45	124,85	133,68	106,98	109,08
116,80	92,27	122,51	124,85	133,68	106,98
116,01	90,40	116,80	122,51	124,85	133,68
129,76	90,43	116,01	116,80	122,51	124,85
125,20	91,05	129,76	116,01	116,80	122,51
143,79	89,08	125,20	129,76	116,01	116,80
127,95	89,69	143,79	125,20	129,76	116,01
130,30	87,92	127,95	143,79	125,20	129,76
108,44	85,88	130,30	127,95	143,79	125,20
129,37	83,21	108,44	130,30	127,95	143,79
143,68	83,86	129,37	108,44	130,30	127,95
131,88	83,01	143,68	129,37	108,44	130,30
117,62	82,85	131,88	143,68	129,37	108,44
118,96	78,69	117,62	131,88	143,68	129,37
104,82	77,57	118,96	117,62	131,88	143,68
134,62	78,54	104,82	118,96	117,62	131,88
140,40	78,56	134,62	104,82	118,96	117,62
143,80	77,48	140,40	134,62	104,82	118,96
153,43	81,59	143,80	140,40	134,62	104,82
153,29	85,02	153,43	143,80	140,40	134,62
127,31	91,71	153,29	153,43	143,80	140,40
153,55	95,96	127,31	153,29	153,43	143,80
136,93	90,85	153,55	127,31	153,29	153,43
131,77	92,29	136,93	153,55	127,31	153,29
144,34	95,57	131,77	136,93	153,55	127,31
107,42	93,62	144,34	131,77	136,93	153,55
113,62	92,63	107,42	144,34	131,77	136,93
124,22	89,51	113,62	107,42	144,34	131,77
102,06	87,17	124,22	113,62	107,42	144,34
96,37	86,73	102,06	124,22	113,62	107,42
111,68	85,63	96,37	102,06	124,22	113,62

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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=58452&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=58452&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58452&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 106.850129100590 -0.538798718918726X[t] + 0.291815822997867Y1[t] + 0.500730273935326Y2[t] + 0.260686397627196Y3[t] -0.383518985923385Y4[t] -11.1406334334353M1[t] -25.8052401812007M2[t] -25.288184371146M3[t] -20.9695688872197M4[t] -1.12377457251293M5[t] -18.6728896312874M6[t] -16.4695496880641M7[t] -16.1366071199349M8[t] -17.4192741971750M9[t] -30.11444063088M10[t] -8.84376235170137M11[t] -0.0619092178886454t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  106.850129100590 -0.538798718918726X[t] +  0.291815822997867Y1[t] +  0.500730273935326Y2[t] +  0.260686397627196Y3[t] -0.383518985923385Y4[t] -11.1406334334353M1[t] -25.8052401812007M2[t] -25.288184371146M3[t] -20.9695688872197M4[t] -1.12377457251293M5[t] -18.6728896312874M6[t] -16.4695496880641M7[t] -16.1366071199349M8[t] -17.4192741971750M9[t] -30.11444063088M10[t] -8.84376235170137M11[t] -0.0619092178886454t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58452&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  106.850129100590 -0.538798718918726X[t] +  0.291815822997867Y1[t] +  0.500730273935326Y2[t] +  0.260686397627196Y3[t] -0.383518985923385Y4[t] -11.1406334334353M1[t] -25.8052401812007M2[t] -25.288184371146M3[t] -20.9695688872197M4[t] -1.12377457251293M5[t] -18.6728896312874M6[t] -16.4695496880641M7[t] -16.1366071199349M8[t] -17.4192741971750M9[t] -30.11444063088M10[t] -8.84376235170137M11[t] -0.0619092178886454t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58452&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58452&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 106.850129100590 -0.538798718918726X[t] + 0.291815822997867Y1[t] + 0.500730273935326Y2[t] + 0.260686397627196Y3[t] -0.383518985923385Y4[t] -11.1406334334353M1[t] -25.8052401812007M2[t] -25.288184371146M3[t] -20.9695688872197M4[t] -1.12377457251293M5[t] -18.6728896312874M6[t] -16.4695496880641M7[t] -16.1366071199349M8[t] -17.4192741971750M9[t] -30.11444063088M10[t] -8.84376235170137M11[t] -0.0619092178886454t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)106.85012910059035.6211422.99960.0047510.002376
X-0.5387987189187260.283326-1.90170.0648130.032406
Y10.2918158229978670.1487861.96130.05720.0286
Y20.5007302739353260.1575353.17850.002940.00147
Y30.2606863976271960.1692091.54060.1316970.065848
Y4-0.3835189859233850.171674-2.2340.0314460.015723
M1-11.14063343343537.707668-1.44540.1565440.078272
M2-25.80524018120078.277069-3.11770.0034670.001733
M3-25.2881843711467.816939-3.2350.002520.00126
M4-20.96956888721977.452359-2.81380.0077110.003855
M5-1.123774572512937.449147-0.15090.8808850.440442
M6-18.67288963128747.636335-2.44530.019220.00961
M7-16.46954968806418.442743-1.95070.0584920.029246
M8-16.13660711993497.910961-2.03980.0483690.024184
M9-17.41927419717508.067463-2.15920.0372120.018606
M10-30.114440630888.312143-3.62290.0008490.000424
M11-8.843762351701378.077025-1.09490.280440.14022
t-0.06190921788864540.187738-0.32980.743390.371695

\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) & 106.850129100590 & 35.621142 & 2.9996 & 0.004751 & 0.002376 \tabularnewline
X & -0.538798718918726 & 0.283326 & -1.9017 & 0.064813 & 0.032406 \tabularnewline
Y1 & 0.291815822997867 & 0.148786 & 1.9613 & 0.0572 & 0.0286 \tabularnewline
Y2 & 0.500730273935326 & 0.157535 & 3.1785 & 0.00294 & 0.00147 \tabularnewline
Y3 & 0.260686397627196 & 0.169209 & 1.5406 & 0.131697 & 0.065848 \tabularnewline
Y4 & -0.383518985923385 & 0.171674 & -2.234 & 0.031446 & 0.015723 \tabularnewline
M1 & -11.1406334334353 & 7.707668 & -1.4454 & 0.156544 & 0.078272 \tabularnewline
M2 & -25.8052401812007 & 8.277069 & -3.1177 & 0.003467 & 0.001733 \tabularnewline
M3 & -25.288184371146 & 7.816939 & -3.235 & 0.00252 & 0.00126 \tabularnewline
M4 & -20.9695688872197 & 7.452359 & -2.8138 & 0.007711 & 0.003855 \tabularnewline
M5 & -1.12377457251293 & 7.449147 & -0.1509 & 0.880885 & 0.440442 \tabularnewline
M6 & -18.6728896312874 & 7.636335 & -2.4453 & 0.01922 & 0.00961 \tabularnewline
M7 & -16.4695496880641 & 8.442743 & -1.9507 & 0.058492 & 0.029246 \tabularnewline
M8 & -16.1366071199349 & 7.910961 & -2.0398 & 0.048369 & 0.024184 \tabularnewline
M9 & -17.4192741971750 & 8.067463 & -2.1592 & 0.037212 & 0.018606 \tabularnewline
M10 & -30.11444063088 & 8.312143 & -3.6229 & 0.000849 & 0.000424 \tabularnewline
M11 & -8.84376235170137 & 8.077025 & -1.0949 & 0.28044 & 0.14022 \tabularnewline
t & -0.0619092178886454 & 0.187738 & -0.3298 & 0.74339 & 0.371695 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58452&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]106.850129100590[/C][C]35.621142[/C][C]2.9996[/C][C]0.004751[/C][C]0.002376[/C][/ROW]
[ROW][C]X[/C][C]-0.538798718918726[/C][C]0.283326[/C][C]-1.9017[/C][C]0.064813[/C][C]0.032406[/C][/ROW]
[ROW][C]Y1[/C][C]0.291815822997867[/C][C]0.148786[/C][C]1.9613[/C][C]0.0572[/C][C]0.0286[/C][/ROW]
[ROW][C]Y2[/C][C]0.500730273935326[/C][C]0.157535[/C][C]3.1785[/C][C]0.00294[/C][C]0.00147[/C][/ROW]
[ROW][C]Y3[/C][C]0.260686397627196[/C][C]0.169209[/C][C]1.5406[/C][C]0.131697[/C][C]0.065848[/C][/ROW]
[ROW][C]Y4[/C][C]-0.383518985923385[/C][C]0.171674[/C][C]-2.234[/C][C]0.031446[/C][C]0.015723[/C][/ROW]
[ROW][C]M1[/C][C]-11.1406334334353[/C][C]7.707668[/C][C]-1.4454[/C][C]0.156544[/C][C]0.078272[/C][/ROW]
[ROW][C]M2[/C][C]-25.8052401812007[/C][C]8.277069[/C][C]-3.1177[/C][C]0.003467[/C][C]0.001733[/C][/ROW]
[ROW][C]M3[/C][C]-25.288184371146[/C][C]7.816939[/C][C]-3.235[/C][C]0.00252[/C][C]0.00126[/C][/ROW]
[ROW][C]M4[/C][C]-20.9695688872197[/C][C]7.452359[/C][C]-2.8138[/C][C]0.007711[/C][C]0.003855[/C][/ROW]
[ROW][C]M5[/C][C]-1.12377457251293[/C][C]7.449147[/C][C]-0.1509[/C][C]0.880885[/C][C]0.440442[/C][/ROW]
[ROW][C]M6[/C][C]-18.6728896312874[/C][C]7.636335[/C][C]-2.4453[/C][C]0.01922[/C][C]0.00961[/C][/ROW]
[ROW][C]M7[/C][C]-16.4695496880641[/C][C]8.442743[/C][C]-1.9507[/C][C]0.058492[/C][C]0.029246[/C][/ROW]
[ROW][C]M8[/C][C]-16.1366071199349[/C][C]7.910961[/C][C]-2.0398[/C][C]0.048369[/C][C]0.024184[/C][/ROW]
[ROW][C]M9[/C][C]-17.4192741971750[/C][C]8.067463[/C][C]-2.1592[/C][C]0.037212[/C][C]0.018606[/C][/ROW]
[ROW][C]M10[/C][C]-30.11444063088[/C][C]8.312143[/C][C]-3.6229[/C][C]0.000849[/C][C]0.000424[/C][/ROW]
[ROW][C]M11[/C][C]-8.84376235170137[/C][C]8.077025[/C][C]-1.0949[/C][C]0.28044[/C][C]0.14022[/C][/ROW]
[ROW][C]t[/C][C]-0.0619092178886454[/C][C]0.187738[/C][C]-0.3298[/C][C]0.74339[/C][C]0.371695[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58452&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58452&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)106.85012910059035.6211422.99960.0047510.002376
X-0.5387987189187260.283326-1.90170.0648130.032406
Y10.2918158229978670.1487861.96130.05720.0286
Y20.5007302739353260.1575353.17850.002940.00147
Y30.2606863976271960.1692091.54060.1316970.065848
Y4-0.3835189859233850.171674-2.2340.0314460.015723
M1-11.14063343343537.707668-1.44540.1565440.078272
M2-25.80524018120078.277069-3.11770.0034670.001733
M3-25.2881843711467.816939-3.2350.002520.00126
M4-20.96956888721977.452359-2.81380.0077110.003855
M5-1.123774572512937.449147-0.15090.8808850.440442
M6-18.67288963128747.636335-2.44530.019220.00961
M7-16.46954968806418.442743-1.95070.0584920.029246
M8-16.13660711993497.910961-2.03980.0483690.024184
M9-17.41927419717508.067463-2.15920.0372120.018606
M10-30.114440630888.312143-3.62290.0008490.000424
M11-8.843762351701378.077025-1.09490.280440.14022
t-0.06190921788864540.187738-0.32980.743390.371695






Multiple Linear Regression - Regression Statistics
Multiple R0.822066171071495
R-squared0.675792789620149
Adjusted R-squared0.530752721818636
F-TEST (value)4.65935241112113
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value3.97256906923271e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation10.6850633507316
Sum Squared Residuals4338.48199474764

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.822066171071495 \tabularnewline
R-squared & 0.675792789620149 \tabularnewline
Adjusted R-squared & 0.530752721818636 \tabularnewline
F-TEST (value) & 4.65935241112113 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 38 \tabularnewline
p-value & 3.97256906923271e-05 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 10.6850633507316 \tabularnewline
Sum Squared Residuals & 4338.48199474764 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58452&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.822066171071495[/C][/ROW]
[ROW][C]R-squared[/C][C]0.675792789620149[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.530752721818636[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]4.65935241112113[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]38[/C][/ROW]
[ROW][C]p-value[/C][C]3.97256906923271e-05[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]10.6850633507316[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]4338.48199474764[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58452&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58452&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Regression Statistics
Multiple R0.822066171071495
R-squared0.675792789620149
Adjusted R-squared0.530752721818636
F-TEST (value)4.65935241112113
F-TEST (DF numerator)17
F-TEST (DF denominator)38
p-value3.97256906923271e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation10.6850633507316
Sum Squared Residuals4338.48199474764






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1114.91111.7001540713613.20984592863867
292.56105.747819052381-13.1878190523812
3115107.0634385578427.93656144215788
4107.12103.5104831546013.60951684539874
5117.78122.459690496717-4.67969049671719
6107.37116.177553800474-8.80755380047352
7106.3109.387465029074-3.08746502907399
8114.51111.0661772145523.44382278544845
998104.623318015396-6.62331801539574
10103.0693.79525943528029.26474056471982
11100.29109.697338914265-9.40733891426535
12104.61113.085989310960-8.47598931096034
13111.15110.5395170955040.610482904495695
14104.9996.46760579897118.52239420102888
15109.93100.9656148450088.96438515499232
16111.54104.7481811458576.79181885414297
17132.5125.4573819102147.04261808978643
18100.34117.934341935161-17.5943419351612
19123.1119.8461033240173.25389667598318
20114.24116.01914729302-1.7791472930201
21104.57106.724028155335-2.15402815533472
22109.08104.5016733929274.57832660707274
23106.98112.239657863795-5.25965786379481
24133.68124.8264730060138.8535269939869
25124.85124.4292294478890.420770552110658
26122.51118.5093173259224.00068267407811
27116.8122.261665748833-5.46166574883334
28116.01112.146130613723.86386938627997
29129.76131.600613859887-1.84061385988741
30125.2116.6813401239168.51865987608409
31143.79127.42251659475816.3674834052421
32127.95134.393826793097-6.44382679309673
33130.3132.227021356999-1.92702135699910
34108.44119.918301444609-11.4783014446093
35129.37126.1043948516963.26560514830363
36143.68136.3853239767817.29467602321861
37131.88133.697055028054-1.8170550280537
38117.62136.618661700689-18.9986617006888
39118.96124.948670069839-5.98867006983904
40104.82114.495194217001-9.67519421700053
41134.62131.1092833900833.51071660991693
42140.4120.92156910302019.4784308969795
43143.8136.0533389614027.74666103859817
44153.43151.1877174686722.24228253132755
45153.29142.58563247227010.7043675277296
46127.31129.674765727183-2.36476572718326
47153.55142.14860837024311.4013916297565
48136.93144.602213706245-7.67221370624518
49131.77134.194044357191-2.42404435719133
50144.34124.67659612203719.663403877963
51107.42112.870610778478-5.45061077847782
52113.62118.210010868821-4.59001086882115
53124.22128.253030343099-4.03303034309875
54102.06103.655195037429-1.59519503742886
5596.37120.650576090749-24.2805760907494
56111.68109.1431312306592.53686876934082

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 114.91 & 111.700154071361 & 3.20984592863867 \tabularnewline
2 & 92.56 & 105.747819052381 & -13.1878190523812 \tabularnewline
3 & 115 & 107.063438557842 & 7.93656144215788 \tabularnewline
4 & 107.12 & 103.510483154601 & 3.60951684539874 \tabularnewline
5 & 117.78 & 122.459690496717 & -4.67969049671719 \tabularnewline
6 & 107.37 & 116.177553800474 & -8.80755380047352 \tabularnewline
7 & 106.3 & 109.387465029074 & -3.08746502907399 \tabularnewline
8 & 114.51 & 111.066177214552 & 3.44382278544845 \tabularnewline
9 & 98 & 104.623318015396 & -6.62331801539574 \tabularnewline
10 & 103.06 & 93.7952594352802 & 9.26474056471982 \tabularnewline
11 & 100.29 & 109.697338914265 & -9.40733891426535 \tabularnewline
12 & 104.61 & 113.085989310960 & -8.47598931096034 \tabularnewline
13 & 111.15 & 110.539517095504 & 0.610482904495695 \tabularnewline
14 & 104.99 & 96.4676057989711 & 8.52239420102888 \tabularnewline
15 & 109.93 & 100.965614845008 & 8.96438515499232 \tabularnewline
16 & 111.54 & 104.748181145857 & 6.79181885414297 \tabularnewline
17 & 132.5 & 125.457381910214 & 7.04261808978643 \tabularnewline
18 & 100.34 & 117.934341935161 & -17.5943419351612 \tabularnewline
19 & 123.1 & 119.846103324017 & 3.25389667598318 \tabularnewline
20 & 114.24 & 116.01914729302 & -1.7791472930201 \tabularnewline
21 & 104.57 & 106.724028155335 & -2.15402815533472 \tabularnewline
22 & 109.08 & 104.501673392927 & 4.57832660707274 \tabularnewline
23 & 106.98 & 112.239657863795 & -5.25965786379481 \tabularnewline
24 & 133.68 & 124.826473006013 & 8.8535269939869 \tabularnewline
25 & 124.85 & 124.429229447889 & 0.420770552110658 \tabularnewline
26 & 122.51 & 118.509317325922 & 4.00068267407811 \tabularnewline
27 & 116.8 & 122.261665748833 & -5.46166574883334 \tabularnewline
28 & 116.01 & 112.14613061372 & 3.86386938627997 \tabularnewline
29 & 129.76 & 131.600613859887 & -1.84061385988741 \tabularnewline
30 & 125.2 & 116.681340123916 & 8.51865987608409 \tabularnewline
31 & 143.79 & 127.422516594758 & 16.3674834052421 \tabularnewline
32 & 127.95 & 134.393826793097 & -6.44382679309673 \tabularnewline
33 & 130.3 & 132.227021356999 & -1.92702135699910 \tabularnewline
34 & 108.44 & 119.918301444609 & -11.4783014446093 \tabularnewline
35 & 129.37 & 126.104394851696 & 3.26560514830363 \tabularnewline
36 & 143.68 & 136.385323976781 & 7.29467602321861 \tabularnewline
37 & 131.88 & 133.697055028054 & -1.8170550280537 \tabularnewline
38 & 117.62 & 136.618661700689 & -18.9986617006888 \tabularnewline
39 & 118.96 & 124.948670069839 & -5.98867006983904 \tabularnewline
40 & 104.82 & 114.495194217001 & -9.67519421700053 \tabularnewline
41 & 134.62 & 131.109283390083 & 3.51071660991693 \tabularnewline
42 & 140.4 & 120.921569103020 & 19.4784308969795 \tabularnewline
43 & 143.8 & 136.053338961402 & 7.74666103859817 \tabularnewline
44 & 153.43 & 151.187717468672 & 2.24228253132755 \tabularnewline
45 & 153.29 & 142.585632472270 & 10.7043675277296 \tabularnewline
46 & 127.31 & 129.674765727183 & -2.36476572718326 \tabularnewline
47 & 153.55 & 142.148608370243 & 11.4013916297565 \tabularnewline
48 & 136.93 & 144.602213706245 & -7.67221370624518 \tabularnewline
49 & 131.77 & 134.194044357191 & -2.42404435719133 \tabularnewline
50 & 144.34 & 124.676596122037 & 19.663403877963 \tabularnewline
51 & 107.42 & 112.870610778478 & -5.45061077847782 \tabularnewline
52 & 113.62 & 118.210010868821 & -4.59001086882115 \tabularnewline
53 & 124.22 & 128.253030343099 & -4.03303034309875 \tabularnewline
54 & 102.06 & 103.655195037429 & -1.59519503742886 \tabularnewline
55 & 96.37 & 120.650576090749 & -24.2805760907494 \tabularnewline
56 & 111.68 & 109.143131230659 & 2.53686876934082 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58452&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]114.91[/C][C]111.700154071361[/C][C]3.20984592863867[/C][/ROW]
[ROW][C]2[/C][C]92.56[/C][C]105.747819052381[/C][C]-13.1878190523812[/C][/ROW]
[ROW][C]3[/C][C]115[/C][C]107.063438557842[/C][C]7.93656144215788[/C][/ROW]
[ROW][C]4[/C][C]107.12[/C][C]103.510483154601[/C][C]3.60951684539874[/C][/ROW]
[ROW][C]5[/C][C]117.78[/C][C]122.459690496717[/C][C]-4.67969049671719[/C][/ROW]
[ROW][C]6[/C][C]107.37[/C][C]116.177553800474[/C][C]-8.80755380047352[/C][/ROW]
[ROW][C]7[/C][C]106.3[/C][C]109.387465029074[/C][C]-3.08746502907399[/C][/ROW]
[ROW][C]8[/C][C]114.51[/C][C]111.066177214552[/C][C]3.44382278544845[/C][/ROW]
[ROW][C]9[/C][C]98[/C][C]104.623318015396[/C][C]-6.62331801539574[/C][/ROW]
[ROW][C]10[/C][C]103.06[/C][C]93.7952594352802[/C][C]9.26474056471982[/C][/ROW]
[ROW][C]11[/C][C]100.29[/C][C]109.697338914265[/C][C]-9.40733891426535[/C][/ROW]
[ROW][C]12[/C][C]104.61[/C][C]113.085989310960[/C][C]-8.47598931096034[/C][/ROW]
[ROW][C]13[/C][C]111.15[/C][C]110.539517095504[/C][C]0.610482904495695[/C][/ROW]
[ROW][C]14[/C][C]104.99[/C][C]96.4676057989711[/C][C]8.52239420102888[/C][/ROW]
[ROW][C]15[/C][C]109.93[/C][C]100.965614845008[/C][C]8.96438515499232[/C][/ROW]
[ROW][C]16[/C][C]111.54[/C][C]104.748181145857[/C][C]6.79181885414297[/C][/ROW]
[ROW][C]17[/C][C]132.5[/C][C]125.457381910214[/C][C]7.04261808978643[/C][/ROW]
[ROW][C]18[/C][C]100.34[/C][C]117.934341935161[/C][C]-17.5943419351612[/C][/ROW]
[ROW][C]19[/C][C]123.1[/C][C]119.846103324017[/C][C]3.25389667598318[/C][/ROW]
[ROW][C]20[/C][C]114.24[/C][C]116.01914729302[/C][C]-1.7791472930201[/C][/ROW]
[ROW][C]21[/C][C]104.57[/C][C]106.724028155335[/C][C]-2.15402815533472[/C][/ROW]
[ROW][C]22[/C][C]109.08[/C][C]104.501673392927[/C][C]4.57832660707274[/C][/ROW]
[ROW][C]23[/C][C]106.98[/C][C]112.239657863795[/C][C]-5.25965786379481[/C][/ROW]
[ROW][C]24[/C][C]133.68[/C][C]124.826473006013[/C][C]8.8535269939869[/C][/ROW]
[ROW][C]25[/C][C]124.85[/C][C]124.429229447889[/C][C]0.420770552110658[/C][/ROW]
[ROW][C]26[/C][C]122.51[/C][C]118.509317325922[/C][C]4.00068267407811[/C][/ROW]
[ROW][C]27[/C][C]116.8[/C][C]122.261665748833[/C][C]-5.46166574883334[/C][/ROW]
[ROW][C]28[/C][C]116.01[/C][C]112.14613061372[/C][C]3.86386938627997[/C][/ROW]
[ROW][C]29[/C][C]129.76[/C][C]131.600613859887[/C][C]-1.84061385988741[/C][/ROW]
[ROW][C]30[/C][C]125.2[/C][C]116.681340123916[/C][C]8.51865987608409[/C][/ROW]
[ROW][C]31[/C][C]143.79[/C][C]127.422516594758[/C][C]16.3674834052421[/C][/ROW]
[ROW][C]32[/C][C]127.95[/C][C]134.393826793097[/C][C]-6.44382679309673[/C][/ROW]
[ROW][C]33[/C][C]130.3[/C][C]132.227021356999[/C][C]-1.92702135699910[/C][/ROW]
[ROW][C]34[/C][C]108.44[/C][C]119.918301444609[/C][C]-11.4783014446093[/C][/ROW]
[ROW][C]35[/C][C]129.37[/C][C]126.104394851696[/C][C]3.26560514830363[/C][/ROW]
[ROW][C]36[/C][C]143.68[/C][C]136.385323976781[/C][C]7.29467602321861[/C][/ROW]
[ROW][C]37[/C][C]131.88[/C][C]133.697055028054[/C][C]-1.8170550280537[/C][/ROW]
[ROW][C]38[/C][C]117.62[/C][C]136.618661700689[/C][C]-18.9986617006888[/C][/ROW]
[ROW][C]39[/C][C]118.96[/C][C]124.948670069839[/C][C]-5.98867006983904[/C][/ROW]
[ROW][C]40[/C][C]104.82[/C][C]114.495194217001[/C][C]-9.67519421700053[/C][/ROW]
[ROW][C]41[/C][C]134.62[/C][C]131.109283390083[/C][C]3.51071660991693[/C][/ROW]
[ROW][C]42[/C][C]140.4[/C][C]120.921569103020[/C][C]19.4784308969795[/C][/ROW]
[ROW][C]43[/C][C]143.8[/C][C]136.053338961402[/C][C]7.74666103859817[/C][/ROW]
[ROW][C]44[/C][C]153.43[/C][C]151.187717468672[/C][C]2.24228253132755[/C][/ROW]
[ROW][C]45[/C][C]153.29[/C][C]142.585632472270[/C][C]10.7043675277296[/C][/ROW]
[ROW][C]46[/C][C]127.31[/C][C]129.674765727183[/C][C]-2.36476572718326[/C][/ROW]
[ROW][C]47[/C][C]153.55[/C][C]142.148608370243[/C][C]11.4013916297565[/C][/ROW]
[ROW][C]48[/C][C]136.93[/C][C]144.602213706245[/C][C]-7.67221370624518[/C][/ROW]
[ROW][C]49[/C][C]131.77[/C][C]134.194044357191[/C][C]-2.42404435719133[/C][/ROW]
[ROW][C]50[/C][C]144.34[/C][C]124.676596122037[/C][C]19.663403877963[/C][/ROW]
[ROW][C]51[/C][C]107.42[/C][C]112.870610778478[/C][C]-5.45061077847782[/C][/ROW]
[ROW][C]52[/C][C]113.62[/C][C]118.210010868821[/C][C]-4.59001086882115[/C][/ROW]
[ROW][C]53[/C][C]124.22[/C][C]128.253030343099[/C][C]-4.03303034309875[/C][/ROW]
[ROW][C]54[/C][C]102.06[/C][C]103.655195037429[/C][C]-1.59519503742886[/C][/ROW]
[ROW][C]55[/C][C]96.37[/C][C]120.650576090749[/C][C]-24.2805760907494[/C][/ROW]
[ROW][C]56[/C][C]111.68[/C][C]109.143131230659[/C][C]2.53686876934082[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58452&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58452&T=4

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1114.91111.7001540713613.20984592863867
292.56105.747819052381-13.1878190523812
3115107.0634385578427.93656144215788
4107.12103.5104831546013.60951684539874
5117.78122.459690496717-4.67969049671719
6107.37116.177553800474-8.80755380047352
7106.3109.387465029074-3.08746502907399
8114.51111.0661772145523.44382278544845
998104.623318015396-6.62331801539574
10103.0693.79525943528029.26474056471982
11100.29109.697338914265-9.40733891426535
12104.61113.085989310960-8.47598931096034
13111.15110.5395170955040.610482904495695
14104.9996.46760579897118.52239420102888
15109.93100.9656148450088.96438515499232
16111.54104.7481811458576.79181885414297
17132.5125.4573819102147.04261808978643
18100.34117.934341935161-17.5943419351612
19123.1119.8461033240173.25389667598318
20114.24116.01914729302-1.7791472930201
21104.57106.724028155335-2.15402815533472
22109.08104.5016733929274.57832660707274
23106.98112.239657863795-5.25965786379481
24133.68124.8264730060138.8535269939869
25124.85124.4292294478890.420770552110658
26122.51118.5093173259224.00068267407811
27116.8122.261665748833-5.46166574883334
28116.01112.146130613723.86386938627997
29129.76131.600613859887-1.84061385988741
30125.2116.6813401239168.51865987608409
31143.79127.42251659475816.3674834052421
32127.95134.393826793097-6.44382679309673
33130.3132.227021356999-1.92702135699910
34108.44119.918301444609-11.4783014446093
35129.37126.1043948516963.26560514830363
36143.68136.3853239767817.29467602321861
37131.88133.697055028054-1.8170550280537
38117.62136.618661700689-18.9986617006888
39118.96124.948670069839-5.98867006983904
40104.82114.495194217001-9.67519421700053
41134.62131.1092833900833.51071660991693
42140.4120.92156910302019.4784308969795
43143.8136.0533389614027.74666103859817
44153.43151.1877174686722.24228253132755
45153.29142.58563247227010.7043675277296
46127.31129.674765727183-2.36476572718326
47153.55142.14860837024311.4013916297565
48136.93144.602213706245-7.67221370624518
49131.77134.194044357191-2.42404435719133
50144.34124.67659612203719.663403877963
51107.42112.870610778478-5.45061077847782
52113.62118.210010868821-4.59001086882115
53124.22128.253030343099-4.03303034309875
54102.06103.655195037429-1.59519503742886
5596.37120.650576090749-24.2805760907494
56111.68109.1431312306592.53686876934082






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.02454008472396810.04908016944793610.975459915276032
220.005407069710637440.01081413942127490.994592930289363
230.002481349632390240.004962699264780490.99751865036761
240.01205362187006940.02410724374013890.98794637812993
250.05860951091586210.1172190218317240.941390489084138
260.03322154868752450.0664430973750490.966778451312476
270.02333597398812880.04667194797625760.976664026011871
280.01109689799056680.02219379598113370.988903102009433
290.004863416523136870.009726833046273740.995136583476863
300.004169543540950260.008339087081900520.99583045645905
310.005527719244015560.01105543848803110.994472280755984
320.002875495894347240.005750991788694470.997124504105653
330.002292752712416930.004585505424833850.997707247287583
340.01110329219925750.02220658439851490.988896707800742
350.01109986104938380.02219972209876750.988900138950616

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.0245400847239681 & 0.0490801694479361 & 0.975459915276032 \tabularnewline
22 & 0.00540706971063744 & 0.0108141394212749 & 0.994592930289363 \tabularnewline
23 & 0.00248134963239024 & 0.00496269926478049 & 0.99751865036761 \tabularnewline
24 & 0.0120536218700694 & 0.0241072437401389 & 0.98794637812993 \tabularnewline
25 & 0.0586095109158621 & 0.117219021831724 & 0.941390489084138 \tabularnewline
26 & 0.0332215486875245 & 0.066443097375049 & 0.966778451312476 \tabularnewline
27 & 0.0233359739881288 & 0.0466719479762576 & 0.976664026011871 \tabularnewline
28 & 0.0110968979905668 & 0.0221937959811337 & 0.988903102009433 \tabularnewline
29 & 0.00486341652313687 & 0.00972683304627374 & 0.995136583476863 \tabularnewline
30 & 0.00416954354095026 & 0.00833908708190052 & 0.99583045645905 \tabularnewline
31 & 0.00552771924401556 & 0.0110554384880311 & 0.994472280755984 \tabularnewline
32 & 0.00287549589434724 & 0.00575099178869447 & 0.997124504105653 \tabularnewline
33 & 0.00229275271241693 & 0.00458550542483385 & 0.997707247287583 \tabularnewline
34 & 0.0111032921992575 & 0.0222065843985149 & 0.988896707800742 \tabularnewline
35 & 0.0110998610493838 & 0.0221997220987675 & 0.988900138950616 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58452&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]21[/C][C]0.0245400847239681[/C][C]0.0490801694479361[/C][C]0.975459915276032[/C][/ROW]
[ROW][C]22[/C][C]0.00540706971063744[/C][C]0.0108141394212749[/C][C]0.994592930289363[/C][/ROW]
[ROW][C]23[/C][C]0.00248134963239024[/C][C]0.00496269926478049[/C][C]0.99751865036761[/C][/ROW]
[ROW][C]24[/C][C]0.0120536218700694[/C][C]0.0241072437401389[/C][C]0.98794637812993[/C][/ROW]
[ROW][C]25[/C][C]0.0586095109158621[/C][C]0.117219021831724[/C][C]0.941390489084138[/C][/ROW]
[ROW][C]26[/C][C]0.0332215486875245[/C][C]0.066443097375049[/C][C]0.966778451312476[/C][/ROW]
[ROW][C]27[/C][C]0.0233359739881288[/C][C]0.0466719479762576[/C][C]0.976664026011871[/C][/ROW]
[ROW][C]28[/C][C]0.0110968979905668[/C][C]0.0221937959811337[/C][C]0.988903102009433[/C][/ROW]
[ROW][C]29[/C][C]0.00486341652313687[/C][C]0.00972683304627374[/C][C]0.995136583476863[/C][/ROW]
[ROW][C]30[/C][C]0.00416954354095026[/C][C]0.00833908708190052[/C][C]0.99583045645905[/C][/ROW]
[ROW][C]31[/C][C]0.00552771924401556[/C][C]0.0110554384880311[/C][C]0.994472280755984[/C][/ROW]
[ROW][C]32[/C][C]0.00287549589434724[/C][C]0.00575099178869447[/C][C]0.997124504105653[/C][/ROW]
[ROW][C]33[/C][C]0.00229275271241693[/C][C]0.00458550542483385[/C][C]0.997707247287583[/C][/ROW]
[ROW][C]34[/C][C]0.0111032921992575[/C][C]0.0222065843985149[/C][C]0.988896707800742[/C][/ROW]
[ROW][C]35[/C][C]0.0110998610493838[/C][C]0.0221997220987675[/C][C]0.988900138950616[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58452&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58452&T=5

As an alternative you can also use a QR Code:  
QR Code


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.02454008472396810.04908016944793610.975459915276032
220.005407069710637440.01081413942127490.994592930289363
230.002481349632390240.004962699264780490.99751865036761
240.01205362187006940.02410724374013890.98794637812993
250.05860951091586210.1172190218317240.941390489084138
260.03322154868752450.0664430973750490.966778451312476
270.02333597398812880.04667194797625760.976664026011871
280.01109689799056680.02219379598113370.988903102009433
290.004863416523136870.009726833046273740.995136583476863
300.004169543540950260.008339087081900520.99583045645905
310.005527719244015560.01105543848803110.994472280755984
320.002875495894347240.005750991788694470.997124504105653
330.002292752712416930.004585505424833850.997707247287583
340.01110329219925750.02220658439851490.988896707800742
350.01109986104938380.02219972209876750.988900138950616






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level50.333333333333333NOK
5% type I error level130.866666666666667NOK
10% type I error level140.933333333333333NOK

\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 & 5 & 0.333333333333333 & NOK \tabularnewline
5% type I error level & 13 & 0.866666666666667 & NOK \tabularnewline
10% type I error level & 14 & 0.933333333333333 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58452&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]5[/C][C]0.333333333333333[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]13[/C][C]0.866666666666667[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]14[/C][C]0.933333333333333[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58452&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58452&T=6

As an alternative you can also use a QR Code:  
QR Code


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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level50.333333333333333NOK
5% type I error level130.866666666666667NOK
10% type I error level140.933333333333333NOK


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

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')
}