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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 04:59:59 -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/t1258718477199vs857ecg115t.htm/, Retrieved Fri, 29 Mar 2024 08:23:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58056, Retrieved Fri, 29 Mar 2024 08:23:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133
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]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 14:03:14] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [model 2] [2009-11-20 11:59:59] [986e3c28a4248c495afaef9fd432264f] [Current]
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Dataseries X:
98.71	153.4
98.54	145
98.2	137.7
96.92	148.3
99.06	152.2
99.65	169.4
99.82	168.6
99.99	161.1
100.33	174.1
99.31	179
101.1	190.6
101.1	190
100.93	181.6
100.85	174.8
100.93	180.5
99.6	196.8
101.88	193.8
101.81	197
102.38	216.3
102.74	221.4
102.82	217.9
101.72	229.7
103.47	227.4
102.98	204.2
102.68	196.6
102.9	198.8
103.03	207.5
101.29	190.7
103.69	201.6
103.68	210.5
104.2	223.5
104.08	223.8
104.16	231.2
103.05	244
104.66	234.7
104.46	250.2
104.95	265.7
105.85	287.6
106.23	283.3
104.86	295.4
107.44	312.3
108.23	333.8
108.45	347.7
109.39	383.2
110.15	407.1
109.13	413.6
110.28	362.7
110.17	321.9
109.99	239.4
109.26	191
109.11	159.7
107.06	163.4
109.53	157.6
108.92	166.2
109.24	176.7
109.12	198.3
109	226.2
107.23	216.2
109.49	235.9
109.04	226.9




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=58056&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=58056&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58056&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 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] = + 97.1336370267663 + 0.0352680312321223X[t] -0.994110622434554M1[t] -0.687493175700802M2[t] -0.466465397677703M3[t] -2.20315379946010M4[t] + 0.00931861749677947M5[t] -0.271665593540829M6[t] -0.305962182715962M7[t] -0.447910526269306M8[t] -0.704493275398668M9[t] -2.09188703780570M10[t] -0.159814522917262M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  97.1336370267663 +  0.0352680312321223X[t] -0.994110622434554M1[t] -0.687493175700802M2[t] -0.466465397677703M3[t] -2.20315379946010M4[t] +  0.00931861749677947M5[t] -0.271665593540829M6[t] -0.305962182715962M7[t] -0.447910526269306M8[t] -0.704493275398668M9[t] -2.09188703780570M10[t] -0.159814522917262M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58056&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  97.1336370267663 +  0.0352680312321223X[t] -0.994110622434554M1[t] -0.687493175700802M2[t] -0.466465397677703M3[t] -2.20315379946010M4[t] +  0.00931861749677947M5[t] -0.271665593540829M6[t] -0.305962182715962M7[t] -0.447910526269306M8[t] -0.704493275398668M9[t] -2.09188703780570M10[t] -0.159814522917262M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58056&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58056&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] = + 97.1336370267663 + 0.0352680312321223X[t] -0.994110622434554M1[t] -0.687493175700802M2[t] -0.466465397677703M3[t] -2.20315379946010M4[t] + 0.00931861749677947M5[t] -0.271665593540829M6[t] -0.305962182715962M7[t] -0.447910526269306M8[t] -0.704493275398668M9[t] -2.09188703780570M10[t] -0.159814522917262M11[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)97.13363702676632.26444242.895200
X0.03526803123212230.0070984.9699e-065e-06
M1-0.9941106224345542.137059-0.46520.6439530.321976
M2-0.6874931757008022.143613-0.32070.7498470.374923
M3-0.4664653976777032.149238-0.2170.8291190.414559
M4-2.203153799460102.144095-1.02750.3094230.154712
M50.009318617496779472.1400640.00440.9965440.498272
M6-0.2716655935408292.131882-0.12740.8991440.449572
M7-0.3059621827159622.127209-0.14380.8862480.443124
M8-0.4479105262693062.125494-0.21070.8340070.417004
M9-0.7044932753986682.127379-0.33120.7419990.371
M10-2.091887037805702.129257-0.98240.3309090.165455
M11-0.1598145229172622.12708-0.07510.9404280.470214

\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) & 97.1336370267663 & 2.264442 & 42.8952 & 0 & 0 \tabularnewline
X & 0.0352680312321223 & 0.007098 & 4.969 & 9e-06 & 5e-06 \tabularnewline
M1 & -0.994110622434554 & 2.137059 & -0.4652 & 0.643953 & 0.321976 \tabularnewline
M2 & -0.687493175700802 & 2.143613 & -0.3207 & 0.749847 & 0.374923 \tabularnewline
M3 & -0.466465397677703 & 2.149238 & -0.217 & 0.829119 & 0.414559 \tabularnewline
M4 & -2.20315379946010 & 2.144095 & -1.0275 & 0.309423 & 0.154712 \tabularnewline
M5 & 0.00931861749677947 & 2.140064 & 0.0044 & 0.996544 & 0.498272 \tabularnewline
M6 & -0.271665593540829 & 2.131882 & -0.1274 & 0.899144 & 0.449572 \tabularnewline
M7 & -0.305962182715962 & 2.127209 & -0.1438 & 0.886248 & 0.443124 \tabularnewline
M8 & -0.447910526269306 & 2.125494 & -0.2107 & 0.834007 & 0.417004 \tabularnewline
M9 & -0.704493275398668 & 2.127379 & -0.3312 & 0.741999 & 0.371 \tabularnewline
M10 & -2.09188703780570 & 2.129257 & -0.9824 & 0.330909 & 0.165455 \tabularnewline
M11 & -0.159814522917262 & 2.12708 & -0.0751 & 0.940428 & 0.470214 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58056&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]97.1336370267663[/C][C]2.264442[/C][C]42.8952[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]0.0352680312321223[/C][C]0.007098[/C][C]4.969[/C][C]9e-06[/C][C]5e-06[/C][/ROW]
[ROW][C]M1[/C][C]-0.994110622434554[/C][C]2.137059[/C][C]-0.4652[/C][C]0.643953[/C][C]0.321976[/C][/ROW]
[ROW][C]M2[/C][C]-0.687493175700802[/C][C]2.143613[/C][C]-0.3207[/C][C]0.749847[/C][C]0.374923[/C][/ROW]
[ROW][C]M3[/C][C]-0.466465397677703[/C][C]2.149238[/C][C]-0.217[/C][C]0.829119[/C][C]0.414559[/C][/ROW]
[ROW][C]M4[/C][C]-2.20315379946010[/C][C]2.144095[/C][C]-1.0275[/C][C]0.309423[/C][C]0.154712[/C][/ROW]
[ROW][C]M5[/C][C]0.00931861749677947[/C][C]2.140064[/C][C]0.0044[/C][C]0.996544[/C][C]0.498272[/C][/ROW]
[ROW][C]M6[/C][C]-0.271665593540829[/C][C]2.131882[/C][C]-0.1274[/C][C]0.899144[/C][C]0.449572[/C][/ROW]
[ROW][C]M7[/C][C]-0.305962182715962[/C][C]2.127209[/C][C]-0.1438[/C][C]0.886248[/C][C]0.443124[/C][/ROW]
[ROW][C]M8[/C][C]-0.447910526269306[/C][C]2.125494[/C][C]-0.2107[/C][C]0.834007[/C][C]0.417004[/C][/ROW]
[ROW][C]M9[/C][C]-0.704493275398668[/C][C]2.127379[/C][C]-0.3312[/C][C]0.741999[/C][C]0.371[/C][/ROW]
[ROW][C]M10[/C][C]-2.09188703780570[/C][C]2.129257[/C][C]-0.9824[/C][C]0.330909[/C][C]0.165455[/C][/ROW]
[ROW][C]M11[/C][C]-0.159814522917262[/C][C]2.12708[/C][C]-0.0751[/C][C]0.940428[/C][C]0.470214[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58056&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58056&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
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)97.13363702676632.26444242.895200
X0.03526803123212230.0070984.9699e-065e-06
M1-0.9941106224345542.137059-0.46520.6439530.321976
M2-0.6874931757008022.143613-0.32070.7498470.374923
M3-0.4664653976777032.149238-0.2170.8291190.414559
M4-2.203153799460102.144095-1.02750.3094230.154712
M50.009318617496779472.1400640.00440.9965440.498272
M6-0.2716655935408292.131882-0.12740.8991440.449572
M7-0.3059621827159622.127209-0.14380.8862480.443124
M8-0.4479105262693062.125494-0.21070.8340070.417004
M9-0.7044932753986682.127379-0.33120.7419990.371
M10-2.091887037805702.129257-0.98240.3309090.165455
M11-0.1598145229172622.12708-0.07510.9404280.470214







Multiple Linear Regression - Regression Statistics
Multiple R0.627797045839455
R-squared0.394129130764746
Adjusted R-squared0.239438696066384
F-TEST (value)2.54785715440825
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0.0111036875022026
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.36067973745561
Sum Squared Residuals530.825909994002

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.627797045839455 \tabularnewline
R-squared & 0.394129130764746 \tabularnewline
Adjusted R-squared & 0.239438696066384 \tabularnewline
F-TEST (value) & 2.54785715440825 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 0.0111036875022026 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.36067973745561 \tabularnewline
Sum Squared Residuals & 530.825909994002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58056&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.627797045839455[/C][/ROW]
[ROW][C]R-squared[/C][C]0.394129130764746[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.239438696066384[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]2.54785715440825[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]0.0111036875022026[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.36067973745561[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]530.825909994002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58056&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58056&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 R0.627797045839455
R-squared0.394129130764746
Adjusted R-squared0.239438696066384
F-TEST (value)2.54785715440825
F-TEST (DF numerator)12
F-TEST (DF denominator)47
p-value0.0111036875022026
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.36067973745561
Sum Squared Residuals530.825909994002







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
198.71101.549642395339-2.83964239533927
298.54101.560008379723-3.02000837972326
398.2101.523579529752-3.32357952975187
496.92100.16073225903-3.24073225902997
599.06102.510749997792-3.45074999779212
699.65102.836375923947-3.18637592394701
799.82102.773864909786-2.95386490978619
899.99102.367406331992-2.37740633199193
9100.33102.569307988880-2.23930798888015
1099.31101.354727579511-2.04472757951052
11101.1103.695909256692-2.59590925669158
12101.1103.834562960870-2.73456296086957
13100.93102.544200876085-1.61420087608518
14100.85102.610995710441-1.76099571044051
15100.93103.033051266487-2.1030512664867
1699.6101.871231773788-2.27123177378791
17101.88103.977900097048-2.09790009704842
18101.81103.809773585954-1.99977358595359
19102.38104.456149999558-2.07614999955843
20102.74104.494068615289-1.75406861528891
21102.82104.114047756847-1.29404775684712
22101.72103.142816762979-1.42281676297912
23103.47104.993772806034-1.52377280603368
24102.98104.335369004366-1.3553690043657
25102.68103.073221344567-0.393221344567015
26102.9103.457428460011-0.557428460011436
27103.03103.985288109754-0.955288109754006
28101.29101.656096783272-0.366096783271949
29103.69104.252990740659-0.562990740658968
30103.68104.285892007587-0.60589200758724
31104.2104.710079824430-0.510079824429701
32104.08104.578711890246-0.498711890245997
33104.16104.583112572234-0.423112572234342
34103.05103.647149609598-0.597149609598473
35104.66105.251229434028-0.591229434028176
36104.46105.957698441043-1.49769844104334
37104.95105.510242302707-0.56024230270667
38105.85106.589229633424-0.73922963342391
39106.23106.658604877149-0.428604877148875
40104.86105.348659653275-0.488659653275163
41107.44108.157161798055-0.71716179805491
42108.23108.634440258508-0.404440258507925
43108.45109.090369303459-0.640369303459294
44109.39110.200436068646-0.810436068646293
45110.15110.786759265965-0.636759265964651
46109.13109.628607706566-0.498607706566422
47110.28109.7655374317400.51446256826017
48110.17108.4864162803871.6835837196135
49109.99104.5826930813025.40730691869814
50109.26103.1823378164016.07766218359912
51109.11102.2994762168596.81052378314144
52107.06100.6932795306356.36672046936499
53109.53102.7011973664466.82880263355442
54108.92102.7235182240046.19648177599577
55109.24103.0595359627666.18046403723362
56109.12103.6793770938275.44062290617313
57109104.4067724160744.59322758392627
58107.23102.6666983413454.56330165865453
59109.49105.2935510715074.19644892849327
60109.04105.1359533133353.90404668666512

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 98.71 & 101.549642395339 & -2.83964239533927 \tabularnewline
2 & 98.54 & 101.560008379723 & -3.02000837972326 \tabularnewline
3 & 98.2 & 101.523579529752 & -3.32357952975187 \tabularnewline
4 & 96.92 & 100.16073225903 & -3.24073225902997 \tabularnewline
5 & 99.06 & 102.510749997792 & -3.45074999779212 \tabularnewline
6 & 99.65 & 102.836375923947 & -3.18637592394701 \tabularnewline
7 & 99.82 & 102.773864909786 & -2.95386490978619 \tabularnewline
8 & 99.99 & 102.367406331992 & -2.37740633199193 \tabularnewline
9 & 100.33 & 102.569307988880 & -2.23930798888015 \tabularnewline
10 & 99.31 & 101.354727579511 & -2.04472757951052 \tabularnewline
11 & 101.1 & 103.695909256692 & -2.59590925669158 \tabularnewline
12 & 101.1 & 103.834562960870 & -2.73456296086957 \tabularnewline
13 & 100.93 & 102.544200876085 & -1.61420087608518 \tabularnewline
14 & 100.85 & 102.610995710441 & -1.76099571044051 \tabularnewline
15 & 100.93 & 103.033051266487 & -2.1030512664867 \tabularnewline
16 & 99.6 & 101.871231773788 & -2.27123177378791 \tabularnewline
17 & 101.88 & 103.977900097048 & -2.09790009704842 \tabularnewline
18 & 101.81 & 103.809773585954 & -1.99977358595359 \tabularnewline
19 & 102.38 & 104.456149999558 & -2.07614999955843 \tabularnewline
20 & 102.74 & 104.494068615289 & -1.75406861528891 \tabularnewline
21 & 102.82 & 104.114047756847 & -1.29404775684712 \tabularnewline
22 & 101.72 & 103.142816762979 & -1.42281676297912 \tabularnewline
23 & 103.47 & 104.993772806034 & -1.52377280603368 \tabularnewline
24 & 102.98 & 104.335369004366 & -1.3553690043657 \tabularnewline
25 & 102.68 & 103.073221344567 & -0.393221344567015 \tabularnewline
26 & 102.9 & 103.457428460011 & -0.557428460011436 \tabularnewline
27 & 103.03 & 103.985288109754 & -0.955288109754006 \tabularnewline
28 & 101.29 & 101.656096783272 & -0.366096783271949 \tabularnewline
29 & 103.69 & 104.252990740659 & -0.562990740658968 \tabularnewline
30 & 103.68 & 104.285892007587 & -0.60589200758724 \tabularnewline
31 & 104.2 & 104.710079824430 & -0.510079824429701 \tabularnewline
32 & 104.08 & 104.578711890246 & -0.498711890245997 \tabularnewline
33 & 104.16 & 104.583112572234 & -0.423112572234342 \tabularnewline
34 & 103.05 & 103.647149609598 & -0.597149609598473 \tabularnewline
35 & 104.66 & 105.251229434028 & -0.591229434028176 \tabularnewline
36 & 104.46 & 105.957698441043 & -1.49769844104334 \tabularnewline
37 & 104.95 & 105.510242302707 & -0.56024230270667 \tabularnewline
38 & 105.85 & 106.589229633424 & -0.73922963342391 \tabularnewline
39 & 106.23 & 106.658604877149 & -0.428604877148875 \tabularnewline
40 & 104.86 & 105.348659653275 & -0.488659653275163 \tabularnewline
41 & 107.44 & 108.157161798055 & -0.71716179805491 \tabularnewline
42 & 108.23 & 108.634440258508 & -0.404440258507925 \tabularnewline
43 & 108.45 & 109.090369303459 & -0.640369303459294 \tabularnewline
44 & 109.39 & 110.200436068646 & -0.810436068646293 \tabularnewline
45 & 110.15 & 110.786759265965 & -0.636759265964651 \tabularnewline
46 & 109.13 & 109.628607706566 & -0.498607706566422 \tabularnewline
47 & 110.28 & 109.765537431740 & 0.51446256826017 \tabularnewline
48 & 110.17 & 108.486416280387 & 1.6835837196135 \tabularnewline
49 & 109.99 & 104.582693081302 & 5.40730691869814 \tabularnewline
50 & 109.26 & 103.182337816401 & 6.07766218359912 \tabularnewline
51 & 109.11 & 102.299476216859 & 6.81052378314144 \tabularnewline
52 & 107.06 & 100.693279530635 & 6.36672046936499 \tabularnewline
53 & 109.53 & 102.701197366446 & 6.82880263355442 \tabularnewline
54 & 108.92 & 102.723518224004 & 6.19648177599577 \tabularnewline
55 & 109.24 & 103.059535962766 & 6.18046403723362 \tabularnewline
56 & 109.12 & 103.679377093827 & 5.44062290617313 \tabularnewline
57 & 109 & 104.406772416074 & 4.59322758392627 \tabularnewline
58 & 107.23 & 102.666698341345 & 4.56330165865453 \tabularnewline
59 & 109.49 & 105.293551071507 & 4.19644892849327 \tabularnewline
60 & 109.04 & 105.135953313335 & 3.90404668666512 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58056&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]98.71[/C][C]101.549642395339[/C][C]-2.83964239533927[/C][/ROW]
[ROW][C]2[/C][C]98.54[/C][C]101.560008379723[/C][C]-3.02000837972326[/C][/ROW]
[ROW][C]3[/C][C]98.2[/C][C]101.523579529752[/C][C]-3.32357952975187[/C][/ROW]
[ROW][C]4[/C][C]96.92[/C][C]100.16073225903[/C][C]-3.24073225902997[/C][/ROW]
[ROW][C]5[/C][C]99.06[/C][C]102.510749997792[/C][C]-3.45074999779212[/C][/ROW]
[ROW][C]6[/C][C]99.65[/C][C]102.836375923947[/C][C]-3.18637592394701[/C][/ROW]
[ROW][C]7[/C][C]99.82[/C][C]102.773864909786[/C][C]-2.95386490978619[/C][/ROW]
[ROW][C]8[/C][C]99.99[/C][C]102.367406331992[/C][C]-2.37740633199193[/C][/ROW]
[ROW][C]9[/C][C]100.33[/C][C]102.569307988880[/C][C]-2.23930798888015[/C][/ROW]
[ROW][C]10[/C][C]99.31[/C][C]101.354727579511[/C][C]-2.04472757951052[/C][/ROW]
[ROW][C]11[/C][C]101.1[/C][C]103.695909256692[/C][C]-2.59590925669158[/C][/ROW]
[ROW][C]12[/C][C]101.1[/C][C]103.834562960870[/C][C]-2.73456296086957[/C][/ROW]
[ROW][C]13[/C][C]100.93[/C][C]102.544200876085[/C][C]-1.61420087608518[/C][/ROW]
[ROW][C]14[/C][C]100.85[/C][C]102.610995710441[/C][C]-1.76099571044051[/C][/ROW]
[ROW][C]15[/C][C]100.93[/C][C]103.033051266487[/C][C]-2.1030512664867[/C][/ROW]
[ROW][C]16[/C][C]99.6[/C][C]101.871231773788[/C][C]-2.27123177378791[/C][/ROW]
[ROW][C]17[/C][C]101.88[/C][C]103.977900097048[/C][C]-2.09790009704842[/C][/ROW]
[ROW][C]18[/C][C]101.81[/C][C]103.809773585954[/C][C]-1.99977358595359[/C][/ROW]
[ROW][C]19[/C][C]102.38[/C][C]104.456149999558[/C][C]-2.07614999955843[/C][/ROW]
[ROW][C]20[/C][C]102.74[/C][C]104.494068615289[/C][C]-1.75406861528891[/C][/ROW]
[ROW][C]21[/C][C]102.82[/C][C]104.114047756847[/C][C]-1.29404775684712[/C][/ROW]
[ROW][C]22[/C][C]101.72[/C][C]103.142816762979[/C][C]-1.42281676297912[/C][/ROW]
[ROW][C]23[/C][C]103.47[/C][C]104.993772806034[/C][C]-1.52377280603368[/C][/ROW]
[ROW][C]24[/C][C]102.98[/C][C]104.335369004366[/C][C]-1.3553690043657[/C][/ROW]
[ROW][C]25[/C][C]102.68[/C][C]103.073221344567[/C][C]-0.393221344567015[/C][/ROW]
[ROW][C]26[/C][C]102.9[/C][C]103.457428460011[/C][C]-0.557428460011436[/C][/ROW]
[ROW][C]27[/C][C]103.03[/C][C]103.985288109754[/C][C]-0.955288109754006[/C][/ROW]
[ROW][C]28[/C][C]101.29[/C][C]101.656096783272[/C][C]-0.366096783271949[/C][/ROW]
[ROW][C]29[/C][C]103.69[/C][C]104.252990740659[/C][C]-0.562990740658968[/C][/ROW]
[ROW][C]30[/C][C]103.68[/C][C]104.285892007587[/C][C]-0.60589200758724[/C][/ROW]
[ROW][C]31[/C][C]104.2[/C][C]104.710079824430[/C][C]-0.510079824429701[/C][/ROW]
[ROW][C]32[/C][C]104.08[/C][C]104.578711890246[/C][C]-0.498711890245997[/C][/ROW]
[ROW][C]33[/C][C]104.16[/C][C]104.583112572234[/C][C]-0.423112572234342[/C][/ROW]
[ROW][C]34[/C][C]103.05[/C][C]103.647149609598[/C][C]-0.597149609598473[/C][/ROW]
[ROW][C]35[/C][C]104.66[/C][C]105.251229434028[/C][C]-0.591229434028176[/C][/ROW]
[ROW][C]36[/C][C]104.46[/C][C]105.957698441043[/C][C]-1.49769844104334[/C][/ROW]
[ROW][C]37[/C][C]104.95[/C][C]105.510242302707[/C][C]-0.56024230270667[/C][/ROW]
[ROW][C]38[/C][C]105.85[/C][C]106.589229633424[/C][C]-0.73922963342391[/C][/ROW]
[ROW][C]39[/C][C]106.23[/C][C]106.658604877149[/C][C]-0.428604877148875[/C][/ROW]
[ROW][C]40[/C][C]104.86[/C][C]105.348659653275[/C][C]-0.488659653275163[/C][/ROW]
[ROW][C]41[/C][C]107.44[/C][C]108.157161798055[/C][C]-0.71716179805491[/C][/ROW]
[ROW][C]42[/C][C]108.23[/C][C]108.634440258508[/C][C]-0.404440258507925[/C][/ROW]
[ROW][C]43[/C][C]108.45[/C][C]109.090369303459[/C][C]-0.640369303459294[/C][/ROW]
[ROW][C]44[/C][C]109.39[/C][C]110.200436068646[/C][C]-0.810436068646293[/C][/ROW]
[ROW][C]45[/C][C]110.15[/C][C]110.786759265965[/C][C]-0.636759265964651[/C][/ROW]
[ROW][C]46[/C][C]109.13[/C][C]109.628607706566[/C][C]-0.498607706566422[/C][/ROW]
[ROW][C]47[/C][C]110.28[/C][C]109.765537431740[/C][C]0.51446256826017[/C][/ROW]
[ROW][C]48[/C][C]110.17[/C][C]108.486416280387[/C][C]1.6835837196135[/C][/ROW]
[ROW][C]49[/C][C]109.99[/C][C]104.582693081302[/C][C]5.40730691869814[/C][/ROW]
[ROW][C]50[/C][C]109.26[/C][C]103.182337816401[/C][C]6.07766218359912[/C][/ROW]
[ROW][C]51[/C][C]109.11[/C][C]102.299476216859[/C][C]6.81052378314144[/C][/ROW]
[ROW][C]52[/C][C]107.06[/C][C]100.693279530635[/C][C]6.36672046936499[/C][/ROW]
[ROW][C]53[/C][C]109.53[/C][C]102.701197366446[/C][C]6.82880263355442[/C][/ROW]
[ROW][C]54[/C][C]108.92[/C][C]102.723518224004[/C][C]6.19648177599577[/C][/ROW]
[ROW][C]55[/C][C]109.24[/C][C]103.059535962766[/C][C]6.18046403723362[/C][/ROW]
[ROW][C]56[/C][C]109.12[/C][C]103.679377093827[/C][C]5.44062290617313[/C][/ROW]
[ROW][C]57[/C][C]109[/C][C]104.406772416074[/C][C]4.59322758392627[/C][/ROW]
[ROW][C]58[/C][C]107.23[/C][C]102.666698341345[/C][C]4.56330165865453[/C][/ROW]
[ROW][C]59[/C][C]109.49[/C][C]105.293551071507[/C][C]4.19644892849327[/C][/ROW]
[ROW][C]60[/C][C]109.04[/C][C]105.135953313335[/C][C]3.90404668666512[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58056&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58056&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 IndexActualsInterpolationForecastResidualsPrediction Error
198.71101.549642395339-2.83964239533927
298.54101.560008379723-3.02000837972326
398.2101.523579529752-3.32357952975187
496.92100.16073225903-3.24073225902997
599.06102.510749997792-3.45074999779212
699.65102.836375923947-3.18637592394701
799.82102.773864909786-2.95386490978619
899.99102.367406331992-2.37740633199193
9100.33102.569307988880-2.23930798888015
1099.31101.354727579511-2.04472757951052
11101.1103.695909256692-2.59590925669158
12101.1103.834562960870-2.73456296086957
13100.93102.544200876085-1.61420087608518
14100.85102.610995710441-1.76099571044051
15100.93103.033051266487-2.1030512664867
1699.6101.871231773788-2.27123177378791
17101.88103.977900097048-2.09790009704842
18101.81103.809773585954-1.99977358595359
19102.38104.456149999558-2.07614999955843
20102.74104.494068615289-1.75406861528891
21102.82104.114047756847-1.29404775684712
22101.72103.142816762979-1.42281676297912
23103.47104.993772806034-1.52377280603368
24102.98104.335369004366-1.3553690043657
25102.68103.073221344567-0.393221344567015
26102.9103.457428460011-0.557428460011436
27103.03103.985288109754-0.955288109754006
28101.29101.656096783272-0.366096783271949
29103.69104.252990740659-0.562990740658968
30103.68104.285892007587-0.60589200758724
31104.2104.710079824430-0.510079824429701
32104.08104.578711890246-0.498711890245997
33104.16104.583112572234-0.423112572234342
34103.05103.647149609598-0.597149609598473
35104.66105.251229434028-0.591229434028176
36104.46105.957698441043-1.49769844104334
37104.95105.510242302707-0.56024230270667
38105.85106.589229633424-0.73922963342391
39106.23106.658604877149-0.428604877148875
40104.86105.348659653275-0.488659653275163
41107.44108.157161798055-0.71716179805491
42108.23108.634440258508-0.404440258507925
43108.45109.090369303459-0.640369303459294
44109.39110.200436068646-0.810436068646293
45110.15110.786759265965-0.636759265964651
46109.13109.628607706566-0.498607706566422
47110.28109.7655374317400.51446256826017
48110.17108.4864162803871.6835837196135
49109.99104.5826930813025.40730691869814
50109.26103.1823378164016.07766218359912
51109.11102.2994762168596.81052378314144
52107.06100.6932795306356.36672046936499
53109.53102.7011973664466.82880263355442
54108.92102.7235182240046.19648177599577
55109.24103.0595359627666.18046403723362
56109.12103.6793770938275.44062290617313
57109104.4067724160744.59322758392627
58107.23102.6666983413454.56330165865453
59109.49105.2935510715074.19644892849327
60109.04105.1359533133353.90404668666512







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.00106999462164790.00213998924329580.998930005378352
179.03722580906049e-050.0001807445161812100.99990962774191
181.13370937557175e-052.26741875114349e-050.999988662906244
192.75200155473553e-065.50400310947105e-060.999997247998445
202.52730321115333e-065.05460642230665e-060.999997472696789
213.15259649148898e-076.30519298297797e-070.99999968474035
227.1782861872708e-081.43565723745416e-070.999999928217138
231.08193775816879e-082.16387551633758e-080.999999989180622
241.37238712068433e-082.74477424136866e-080.99999998627613
252.54795327754182e-085.09590655508363e-080.999999974520467
261.45513626366300e-082.91027252732601e-080.999999985448637
274.56497269100838e-099.12994538201676e-090.999999995435027
286.42818989219183e-081.28563797843837e-070.999999935718101
291.03680137988326e-072.07360275976653e-070.999999896319862
301.17627070202785e-072.3525414040557e-070.99999988237293
311.1307243890761e-072.2614487781522e-070.999999886927561
329.79050966051753e-081.95810193210351e-070.999999902094903
331.24347037638512e-072.48694075277024e-070.999999875652962
342.46677310881236e-074.93354621762471e-070.99999975332269
351.56085044927271e-063.12170089854542e-060.99999843914955
366.95325746222679e-050.0001390651492445360.999930467425378
370.004248437339609810.008496874679219620.99575156266039
380.03663969326706280.07327938653412550.963360306732937
390.09721956955012080.1944391391002420.90278043044988
400.1978305343597310.3956610687194620.802169465640269
410.5134307246907080.9731385506185850.486569275309292
420.5816471901484370.8367056197031260.418352809851563
430.8618143198710530.2763713602578940.138185680128947
440.9616491996549060.0767016006901880.038350800345094

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.0010699946216479 & 0.0021399892432958 & 0.998930005378352 \tabularnewline
17 & 9.03722580906049e-05 & 0.000180744516181210 & 0.99990962774191 \tabularnewline
18 & 1.13370937557175e-05 & 2.26741875114349e-05 & 0.999988662906244 \tabularnewline
19 & 2.75200155473553e-06 & 5.50400310947105e-06 & 0.999997247998445 \tabularnewline
20 & 2.52730321115333e-06 & 5.05460642230665e-06 & 0.999997472696789 \tabularnewline
21 & 3.15259649148898e-07 & 6.30519298297797e-07 & 0.99999968474035 \tabularnewline
22 & 7.1782861872708e-08 & 1.43565723745416e-07 & 0.999999928217138 \tabularnewline
23 & 1.08193775816879e-08 & 2.16387551633758e-08 & 0.999999989180622 \tabularnewline
24 & 1.37238712068433e-08 & 2.74477424136866e-08 & 0.99999998627613 \tabularnewline
25 & 2.54795327754182e-08 & 5.09590655508363e-08 & 0.999999974520467 \tabularnewline
26 & 1.45513626366300e-08 & 2.91027252732601e-08 & 0.999999985448637 \tabularnewline
27 & 4.56497269100838e-09 & 9.12994538201676e-09 & 0.999999995435027 \tabularnewline
28 & 6.42818989219183e-08 & 1.28563797843837e-07 & 0.999999935718101 \tabularnewline
29 & 1.03680137988326e-07 & 2.07360275976653e-07 & 0.999999896319862 \tabularnewline
30 & 1.17627070202785e-07 & 2.3525414040557e-07 & 0.99999988237293 \tabularnewline
31 & 1.1307243890761e-07 & 2.2614487781522e-07 & 0.999999886927561 \tabularnewline
32 & 9.79050966051753e-08 & 1.95810193210351e-07 & 0.999999902094903 \tabularnewline
33 & 1.24347037638512e-07 & 2.48694075277024e-07 & 0.999999875652962 \tabularnewline
34 & 2.46677310881236e-07 & 4.93354621762471e-07 & 0.99999975332269 \tabularnewline
35 & 1.56085044927271e-06 & 3.12170089854542e-06 & 0.99999843914955 \tabularnewline
36 & 6.95325746222679e-05 & 0.000139065149244536 & 0.999930467425378 \tabularnewline
37 & 0.00424843733960981 & 0.00849687467921962 & 0.99575156266039 \tabularnewline
38 & 0.0366396932670628 & 0.0732793865341255 & 0.963360306732937 \tabularnewline
39 & 0.0972195695501208 & 0.194439139100242 & 0.90278043044988 \tabularnewline
40 & 0.197830534359731 & 0.395661068719462 & 0.802169465640269 \tabularnewline
41 & 0.513430724690708 & 0.973138550618585 & 0.486569275309292 \tabularnewline
42 & 0.581647190148437 & 0.836705619703126 & 0.418352809851563 \tabularnewline
43 & 0.861814319871053 & 0.276371360257894 & 0.138185680128947 \tabularnewline
44 & 0.961649199654906 & 0.076701600690188 & 0.038350800345094 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58056&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]16[/C][C]0.0010699946216479[/C][C]0.0021399892432958[/C][C]0.998930005378352[/C][/ROW]
[ROW][C]17[/C][C]9.03722580906049e-05[/C][C]0.000180744516181210[/C][C]0.99990962774191[/C][/ROW]
[ROW][C]18[/C][C]1.13370937557175e-05[/C][C]2.26741875114349e-05[/C][C]0.999988662906244[/C][/ROW]
[ROW][C]19[/C][C]2.75200155473553e-06[/C][C]5.50400310947105e-06[/C][C]0.999997247998445[/C][/ROW]
[ROW][C]20[/C][C]2.52730321115333e-06[/C][C]5.05460642230665e-06[/C][C]0.999997472696789[/C][/ROW]
[ROW][C]21[/C][C]3.15259649148898e-07[/C][C]6.30519298297797e-07[/C][C]0.99999968474035[/C][/ROW]
[ROW][C]22[/C][C]7.1782861872708e-08[/C][C]1.43565723745416e-07[/C][C]0.999999928217138[/C][/ROW]
[ROW][C]23[/C][C]1.08193775816879e-08[/C][C]2.16387551633758e-08[/C][C]0.999999989180622[/C][/ROW]
[ROW][C]24[/C][C]1.37238712068433e-08[/C][C]2.74477424136866e-08[/C][C]0.99999998627613[/C][/ROW]
[ROW][C]25[/C][C]2.54795327754182e-08[/C][C]5.09590655508363e-08[/C][C]0.999999974520467[/C][/ROW]
[ROW][C]26[/C][C]1.45513626366300e-08[/C][C]2.91027252732601e-08[/C][C]0.999999985448637[/C][/ROW]
[ROW][C]27[/C][C]4.56497269100838e-09[/C][C]9.12994538201676e-09[/C][C]0.999999995435027[/C][/ROW]
[ROW][C]28[/C][C]6.42818989219183e-08[/C][C]1.28563797843837e-07[/C][C]0.999999935718101[/C][/ROW]
[ROW][C]29[/C][C]1.03680137988326e-07[/C][C]2.07360275976653e-07[/C][C]0.999999896319862[/C][/ROW]
[ROW][C]30[/C][C]1.17627070202785e-07[/C][C]2.3525414040557e-07[/C][C]0.99999988237293[/C][/ROW]
[ROW][C]31[/C][C]1.1307243890761e-07[/C][C]2.2614487781522e-07[/C][C]0.999999886927561[/C][/ROW]
[ROW][C]32[/C][C]9.79050966051753e-08[/C][C]1.95810193210351e-07[/C][C]0.999999902094903[/C][/ROW]
[ROW][C]33[/C][C]1.24347037638512e-07[/C][C]2.48694075277024e-07[/C][C]0.999999875652962[/C][/ROW]
[ROW][C]34[/C][C]2.46677310881236e-07[/C][C]4.93354621762471e-07[/C][C]0.99999975332269[/C][/ROW]
[ROW][C]35[/C][C]1.56085044927271e-06[/C][C]3.12170089854542e-06[/C][C]0.99999843914955[/C][/ROW]
[ROW][C]36[/C][C]6.95325746222679e-05[/C][C]0.000139065149244536[/C][C]0.999930467425378[/C][/ROW]
[ROW][C]37[/C][C]0.00424843733960981[/C][C]0.00849687467921962[/C][C]0.99575156266039[/C][/ROW]
[ROW][C]38[/C][C]0.0366396932670628[/C][C]0.0732793865341255[/C][C]0.963360306732937[/C][/ROW]
[ROW][C]39[/C][C]0.0972195695501208[/C][C]0.194439139100242[/C][C]0.90278043044988[/C][/ROW]
[ROW][C]40[/C][C]0.197830534359731[/C][C]0.395661068719462[/C][C]0.802169465640269[/C][/ROW]
[ROW][C]41[/C][C]0.513430724690708[/C][C]0.973138550618585[/C][C]0.486569275309292[/C][/ROW]
[ROW][C]42[/C][C]0.581647190148437[/C][C]0.836705619703126[/C][C]0.418352809851563[/C][/ROW]
[ROW][C]43[/C][C]0.861814319871053[/C][C]0.276371360257894[/C][C]0.138185680128947[/C][/ROW]
[ROW][C]44[/C][C]0.961649199654906[/C][C]0.076701600690188[/C][C]0.038350800345094[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58056&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58056&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-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.00106999462164790.00213998924329580.998930005378352
179.03722580906049e-050.0001807445161812100.99990962774191
181.13370937557175e-052.26741875114349e-050.999988662906244
192.75200155473553e-065.50400310947105e-060.999997247998445
202.52730321115333e-065.05460642230665e-060.999997472696789
213.15259649148898e-076.30519298297797e-070.99999968474035
227.1782861872708e-081.43565723745416e-070.999999928217138
231.08193775816879e-082.16387551633758e-080.999999989180622
241.37238712068433e-082.74477424136866e-080.99999998627613
252.54795327754182e-085.09590655508363e-080.999999974520467
261.45513626366300e-082.91027252732601e-080.999999985448637
274.56497269100838e-099.12994538201676e-090.999999995435027
286.42818989219183e-081.28563797843837e-070.999999935718101
291.03680137988326e-072.07360275976653e-070.999999896319862
301.17627070202785e-072.3525414040557e-070.99999988237293
311.1307243890761e-072.2614487781522e-070.999999886927561
329.79050966051753e-081.95810193210351e-070.999999902094903
331.24347037638512e-072.48694075277024e-070.999999875652962
342.46677310881236e-074.93354621762471e-070.99999975332269
351.56085044927271e-063.12170089854542e-060.99999843914955
366.95325746222679e-050.0001390651492445360.999930467425378
370.004248437339609810.008496874679219620.99575156266039
380.03663969326706280.07327938653412550.963360306732937
390.09721956955012080.1944391391002420.90278043044988
400.1978305343597310.3956610687194620.802169465640269
410.5134307246907080.9731385506185850.486569275309292
420.5816471901484370.8367056197031260.418352809851563
430.8618143198710530.2763713602578940.138185680128947
440.9616491996549060.0767016006901880.038350800345094







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level220.758620689655172NOK
5% type I error level220.758620689655172NOK
10% type I error level240.827586206896552NOK

\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 & 22 & 0.758620689655172 & NOK \tabularnewline
5% type I error level & 22 & 0.758620689655172 & NOK \tabularnewline
10% type I error level & 24 & 0.827586206896552 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58056&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]22[/C][C]0.758620689655172[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]22[/C][C]0.758620689655172[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]24[/C][C]0.827586206896552[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58056&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58056&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 testsOK/NOK
1% type I error level220.758620689655172NOK
5% type I error level220.758620689655172NOK
10% type I error level240.827586206896552NOK



Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}