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multiple regression with monthly dummies and linear trend, index van totale...

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationThu, 19 Nov 2009 08:27:59 -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/19/t125864466433g9plaenpn1bpf.htm/, Retrieved Thu, 28 Mar 2024 21:54:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57763, Retrieved Thu, 28 Mar 2024 21:54:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143
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 14:06:21] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [multiple regressi...] [2009-11-19 15:27:59] [8f072ead2c7c0b3cf3fdae49bab9dd9b] [Current]
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Dataseries X:
95.1	117.1
97	118.7
112.7	126.5
102.9	127.5
97.4	134.6
111.4	131.8
87.4	135.9
96.8	142.7
114.1	141.7
110.3	153.4
103.9	145
101.6	137.7
94.6	148.3
95.9	152.2
104.7	169.4
102.8	168.6
98.1	161.1
113.9	174.1
80.9	179
95.7	190.6
113.2	190
105.9	181.6
108.8	174.8
102.3	180.5
99	196.8
100.7	193.8
115.5	197
100.7	216.3
109.9	221.4
114.6	217.9
85.4	229.7
100.5	227.4
114.8	204.2
116.5	196.6
112.9	198.8
102	207.5
106	190.7
105.3	201.6
118.8	210.5
106.1	223.5
109.3	223.8
117.2	231.2
92.5	244
104.2	234.7
112.5	250.2
122.4	265.7
113.3	287.6
100	283.3
110.7	295.4
112.8	312.3
109.8	333.8
117.3	347.7
109.1	383.2
115.9	407.1
96	413.6
99.8	362.7
116.8	321.9
115.7	239.4
99.4	191
94.3	159.7
91	163.4




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=57763&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=57763&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57763&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
tot.ind.prod.index[t] = + 91.8225099826307 + 0.0465801300311876prijsindex.grondst.incl.energie[t] -0.358162974657512M1[t] + 1.98362012729574M2[t] + 11.4201161248545M3[t] + 4.6702676396893M4[t] + 3.11538370796093M5[t] + 12.6237898412482M6[t] -13.8873676800777M7[t] -2.49411581167839M8[t] + 12.8750322127584M9[t] + 13.4416799885274M10[t] + 7.33207813729798M11[t] -0.0224151215242509t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
tot.ind.prod.index[t] =  +  91.8225099826307 +  0.0465801300311876prijsindex.grondst.incl.energie[t] -0.358162974657512M1[t] +  1.98362012729574M2[t] +  11.4201161248545M3[t] +  4.6702676396893M4[t] +  3.11538370796093M5[t] +  12.6237898412482M6[t] -13.8873676800777M7[t] -2.49411581167839M8[t] +  12.8750322127584M9[t] +  13.4416799885274M10[t] +  7.33207813729798M11[t] -0.0224151215242509t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57763&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]tot.ind.prod.index[t] =  +  91.8225099826307 +  0.0465801300311876prijsindex.grondst.incl.energie[t] -0.358162974657512M1[t] +  1.98362012729574M2[t] +  11.4201161248545M3[t] +  4.6702676396893M4[t] +  3.11538370796093M5[t] +  12.6237898412482M6[t] -13.8873676800777M7[t] -2.49411581167839M8[t] +  12.8750322127584M9[t] +  13.4416799885274M10[t] +  7.33207813729798M11[t] -0.0224151215242509t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57763&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57763&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
tot.ind.prod.index[t] = + 91.8225099826307 + 0.0465801300311876prijsindex.grondst.incl.energie[t] -0.358162974657512M1[t] + 1.98362012729574M2[t] + 11.4201161248545M3[t] + 4.6702676396893M4[t] + 3.11538370796093M5[t] + 12.6237898412482M6[t] -13.8873676800777M7[t] -2.49411581167839M8[t] + 12.8750322127584M9[t] + 13.4416799885274M10[t] + 7.33207813729798M11[t] -0.0224151215242509t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)91.82250998263072.60258735.281300
prijsindex.grondst.incl.energie0.04658013003118760.0144973.2130.0023740.001187
M1-0.3581629746575122.755462-0.130.8971350.448567
M21.983620127295742.9333250.67620.5022050.251103
M311.42011612485452.9532143.8670.0003380.000169
M44.67026763968932.9696761.57270.1225080.061254
M53.115383707960932.9844161.04390.3018790.150939
M612.62378984124822.9990314.20930.0001155.7e-05
M7-13.88736768007773.017088-4.60293.2e-051.6e-05
M8-2.494115811678392.966896-0.84060.4048020.202401
M912.87503221275842.9234584.4046.1e-053.1e-05
M1013.44167998852742.8857674.65792.6e-051.3e-05
M117.332078137297982.8732892.55180.0140280.007014
t-0.02241512152425090.058184-0.38520.7017950.350898

\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) & 91.8225099826307 & 2.602587 & 35.2813 & 0 & 0 \tabularnewline
prijsindex.grondst.incl.energie & 0.0465801300311876 & 0.014497 & 3.213 & 0.002374 & 0.001187 \tabularnewline
M1 & -0.358162974657512 & 2.755462 & -0.13 & 0.897135 & 0.448567 \tabularnewline
M2 & 1.98362012729574 & 2.933325 & 0.6762 & 0.502205 & 0.251103 \tabularnewline
M3 & 11.4201161248545 & 2.953214 & 3.867 & 0.000338 & 0.000169 \tabularnewline
M4 & 4.6702676396893 & 2.969676 & 1.5727 & 0.122508 & 0.061254 \tabularnewline
M5 & 3.11538370796093 & 2.984416 & 1.0439 & 0.301879 & 0.150939 \tabularnewline
M6 & 12.6237898412482 & 2.999031 & 4.2093 & 0.000115 & 5.7e-05 \tabularnewline
M7 & -13.8873676800777 & 3.017088 & -4.6029 & 3.2e-05 & 1.6e-05 \tabularnewline
M8 & -2.49411581167839 & 2.966896 & -0.8406 & 0.404802 & 0.202401 \tabularnewline
M9 & 12.8750322127584 & 2.923458 & 4.404 & 6.1e-05 & 3.1e-05 \tabularnewline
M10 & 13.4416799885274 & 2.885767 & 4.6579 & 2.6e-05 & 1.3e-05 \tabularnewline
M11 & 7.33207813729798 & 2.873289 & 2.5518 & 0.014028 & 0.007014 \tabularnewline
t & -0.0224151215242509 & 0.058184 & -0.3852 & 0.701795 & 0.350898 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57763&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]91.8225099826307[/C][C]2.602587[/C][C]35.2813[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]prijsindex.grondst.incl.energie[/C][C]0.0465801300311876[/C][C]0.014497[/C][C]3.213[/C][C]0.002374[/C][C]0.001187[/C][/ROW]
[ROW][C]M1[/C][C]-0.358162974657512[/C][C]2.755462[/C][C]-0.13[/C][C]0.897135[/C][C]0.448567[/C][/ROW]
[ROW][C]M2[/C][C]1.98362012729574[/C][C]2.933325[/C][C]0.6762[/C][C]0.502205[/C][C]0.251103[/C][/ROW]
[ROW][C]M3[/C][C]11.4201161248545[/C][C]2.953214[/C][C]3.867[/C][C]0.000338[/C][C]0.000169[/C][/ROW]
[ROW][C]M4[/C][C]4.6702676396893[/C][C]2.969676[/C][C]1.5727[/C][C]0.122508[/C][C]0.061254[/C][/ROW]
[ROW][C]M5[/C][C]3.11538370796093[/C][C]2.984416[/C][C]1.0439[/C][C]0.301879[/C][C]0.150939[/C][/ROW]
[ROW][C]M6[/C][C]12.6237898412482[/C][C]2.999031[/C][C]4.2093[/C][C]0.000115[/C][C]5.7e-05[/C][/ROW]
[ROW][C]M7[/C][C]-13.8873676800777[/C][C]3.017088[/C][C]-4.6029[/C][C]3.2e-05[/C][C]1.6e-05[/C][/ROW]
[ROW][C]M8[/C][C]-2.49411581167839[/C][C]2.966896[/C][C]-0.8406[/C][C]0.404802[/C][C]0.202401[/C][/ROW]
[ROW][C]M9[/C][C]12.8750322127584[/C][C]2.923458[/C][C]4.404[/C][C]6.1e-05[/C][C]3.1e-05[/C][/ROW]
[ROW][C]M10[/C][C]13.4416799885274[/C][C]2.885767[/C][C]4.6579[/C][C]2.6e-05[/C][C]1.3e-05[/C][/ROW]
[ROW][C]M11[/C][C]7.33207813729798[/C][C]2.873289[/C][C]2.5518[/C][C]0.014028[/C][C]0.007014[/C][/ROW]
[ROW][C]t[/C][C]-0.0224151215242509[/C][C]0.058184[/C][C]-0.3852[/C][C]0.701795[/C][C]0.350898[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57763&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57763&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)91.82250998263072.60258735.281300
prijsindex.grondst.incl.energie0.04658013003118760.0144973.2130.0023740.001187
M1-0.3581629746575122.755462-0.130.8971350.448567
M21.983620127295742.9333250.67620.5022050.251103
M311.42011612485452.9532143.8670.0003380.000169
M44.67026763968932.9696761.57270.1225080.061254
M53.115383707960932.9844161.04390.3018790.150939
M612.62378984124822.9990314.20930.0001155.7e-05
M7-13.88736768007773.017088-4.60293.2e-051.6e-05
M8-2.494115811678392.966896-0.84060.4048020.202401
M912.87503221275842.9234584.4046.1e-053.1e-05
M1013.44167998852742.8857674.65792.6e-051.3e-05
M117.332078137297982.8732892.55180.0140280.007014
t-0.02241512152425090.058184-0.38520.7017950.350898







Multiple Linear Regression - Regression Statistics
Multiple R0.89764089211575
R-squared0.80575917119836
Adjusted R-squared0.752032984508545
F-TEST (value)14.9975127743638
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value1.48236978247951e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4.53809224582419
Sum Squared Residuals967.931217885652

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.89764089211575 \tabularnewline
R-squared & 0.80575917119836 \tabularnewline
Adjusted R-squared & 0.752032984508545 \tabularnewline
F-TEST (value) & 14.9975127743638 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 1.48236978247951e-12 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 4.53809224582419 \tabularnewline
Sum Squared Residuals & 967.931217885652 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57763&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.89764089211575[/C][/ROW]
[ROW][C]R-squared[/C][C]0.80575917119836[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.752032984508545[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]14.9975127743638[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]1.48236978247951e-12[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]4.53809224582419[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]967.931217885652[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57763&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57763&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 R0.89764089211575
R-squared0.80575917119836
Adjusted R-squared0.752032984508545
F-TEST (value)14.9975127743638
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value1.48236978247951e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4.53809224582419
Sum Squared Residuals967.931217885652







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
195.196.896465113101-1.79646511310108
29799.29036130158-2.29036130157994
3112.7109.0677671918583.63223280814230
4102.9102.3420837151990.557916284800547
597.4101.095503585168-3.69550358516828
6111.4110.4510702328440.948929767156081
787.484.10847612312173.29152387687832
896.895.79605775420881.00394224579119
9114.1111.0962105270903.00378947290986
10110.3112.185430702700-1.88543070269976
11103.9105.662140637684-1.76214063768416
12101.697.96761242963433.63238757036573
1394.698.0807837117831-3.4807837117831
1495.9100.581814199334-4.68181419933372
15104.7110.797073311905-6.09707331190463
16102.8103.987545601190-1.18754560119027
1798.1102.060895572704-3.96089557270374
18113.9112.1524282748721.74757172512785
1980.985.8470982691749-4.94709826917484
2095.797.7582645244117-2.05826452441169
21113.2113.0770493493050.122950650694521
22105.9113.230008911288-7.33000891128824
23108.8106.7812470543232.01875294567745
24102.399.6922605366782.60773946332191
2599100.070938560005-1.07093856000468
26100.7102.25056615034-1.55056615034012
27115.5111.8137034424743.6862965575256
28100.7105.940436345387-5.2404363453869
29109.9104.6006959552935.29930404470667
30114.6113.9236565119470.676343488052836
3185.487.939729403465-2.53972940346504
32100.599.20343185126841.29656814873161
33114.8113.4695057374571.33049426254266
34116.5113.6597294034652.84027059653495
35112.9107.630188716785.26981128321996
36102100.6809425892291.31905741077086
3710699.51781830852346.48218169147658
38105.3102.3449097062922.95509029370762
39118.8112.1735537396046.62644626039557
40106.1106.0068318233200.0931681766795536
41109.3104.4435068090774.85649319092282
42117.2114.2741907830712.92580921692906
4392.588.336843804624.16315619537998
44104.299.2744853422054.92551465779495
45112.5115.343210260601-2.84321026060095
46122.4116.6094349303295.79056506967091
47113.3111.4975228052581.80247719474150
48100103.942734987302-3.94273498730215
49110.7104.1257764644986.57422353550225
50112.8107.2323486424545.56765135754617
51109.8117.647902314159-7.84790231415885
52117.3111.5231025149035.77689748509707
53109.1111.599398077757-2.49939807775748
54115.9122.198654197266-6.29865419726583
559695.96785239961840.032147600381574
5699.8104.967760527906-5.16776052790605
57116.8118.414024125546-1.61402412554610
58115.7115.1153960522180.584603947782148
5999.4106.728900785955-7.32890078595475
6094.397.9164494571563-3.61644945715635
619197.70821784209-6.70821784208998

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 95.1 & 96.896465113101 & -1.79646511310108 \tabularnewline
2 & 97 & 99.29036130158 & -2.29036130157994 \tabularnewline
3 & 112.7 & 109.067767191858 & 3.63223280814230 \tabularnewline
4 & 102.9 & 102.342083715199 & 0.557916284800547 \tabularnewline
5 & 97.4 & 101.095503585168 & -3.69550358516828 \tabularnewline
6 & 111.4 & 110.451070232844 & 0.948929767156081 \tabularnewline
7 & 87.4 & 84.1084761231217 & 3.29152387687832 \tabularnewline
8 & 96.8 & 95.7960577542088 & 1.00394224579119 \tabularnewline
9 & 114.1 & 111.096210527090 & 3.00378947290986 \tabularnewline
10 & 110.3 & 112.185430702700 & -1.88543070269976 \tabularnewline
11 & 103.9 & 105.662140637684 & -1.76214063768416 \tabularnewline
12 & 101.6 & 97.9676124296343 & 3.63238757036573 \tabularnewline
13 & 94.6 & 98.0807837117831 & -3.4807837117831 \tabularnewline
14 & 95.9 & 100.581814199334 & -4.68181419933372 \tabularnewline
15 & 104.7 & 110.797073311905 & -6.09707331190463 \tabularnewline
16 & 102.8 & 103.987545601190 & -1.18754560119027 \tabularnewline
17 & 98.1 & 102.060895572704 & -3.96089557270374 \tabularnewline
18 & 113.9 & 112.152428274872 & 1.74757172512785 \tabularnewline
19 & 80.9 & 85.8470982691749 & -4.94709826917484 \tabularnewline
20 & 95.7 & 97.7582645244117 & -2.05826452441169 \tabularnewline
21 & 113.2 & 113.077049349305 & 0.122950650694521 \tabularnewline
22 & 105.9 & 113.230008911288 & -7.33000891128824 \tabularnewline
23 & 108.8 & 106.781247054323 & 2.01875294567745 \tabularnewline
24 & 102.3 & 99.692260536678 & 2.60773946332191 \tabularnewline
25 & 99 & 100.070938560005 & -1.07093856000468 \tabularnewline
26 & 100.7 & 102.25056615034 & -1.55056615034012 \tabularnewline
27 & 115.5 & 111.813703442474 & 3.6862965575256 \tabularnewline
28 & 100.7 & 105.940436345387 & -5.2404363453869 \tabularnewline
29 & 109.9 & 104.600695955293 & 5.29930404470667 \tabularnewline
30 & 114.6 & 113.923656511947 & 0.676343488052836 \tabularnewline
31 & 85.4 & 87.939729403465 & -2.53972940346504 \tabularnewline
32 & 100.5 & 99.2034318512684 & 1.29656814873161 \tabularnewline
33 & 114.8 & 113.469505737457 & 1.33049426254266 \tabularnewline
34 & 116.5 & 113.659729403465 & 2.84027059653495 \tabularnewline
35 & 112.9 & 107.63018871678 & 5.26981128321996 \tabularnewline
36 & 102 & 100.680942589229 & 1.31905741077086 \tabularnewline
37 & 106 & 99.5178183085234 & 6.48218169147658 \tabularnewline
38 & 105.3 & 102.344909706292 & 2.95509029370762 \tabularnewline
39 & 118.8 & 112.173553739604 & 6.62644626039557 \tabularnewline
40 & 106.1 & 106.006831823320 & 0.0931681766795536 \tabularnewline
41 & 109.3 & 104.443506809077 & 4.85649319092282 \tabularnewline
42 & 117.2 & 114.274190783071 & 2.92580921692906 \tabularnewline
43 & 92.5 & 88.33684380462 & 4.16315619537998 \tabularnewline
44 & 104.2 & 99.274485342205 & 4.92551465779495 \tabularnewline
45 & 112.5 & 115.343210260601 & -2.84321026060095 \tabularnewline
46 & 122.4 & 116.609434930329 & 5.79056506967091 \tabularnewline
47 & 113.3 & 111.497522805258 & 1.80247719474150 \tabularnewline
48 & 100 & 103.942734987302 & -3.94273498730215 \tabularnewline
49 & 110.7 & 104.125776464498 & 6.57422353550225 \tabularnewline
50 & 112.8 & 107.232348642454 & 5.56765135754617 \tabularnewline
51 & 109.8 & 117.647902314159 & -7.84790231415885 \tabularnewline
52 & 117.3 & 111.523102514903 & 5.77689748509707 \tabularnewline
53 & 109.1 & 111.599398077757 & -2.49939807775748 \tabularnewline
54 & 115.9 & 122.198654197266 & -6.29865419726583 \tabularnewline
55 & 96 & 95.9678523996184 & 0.032147600381574 \tabularnewline
56 & 99.8 & 104.967760527906 & -5.16776052790605 \tabularnewline
57 & 116.8 & 118.414024125546 & -1.61402412554610 \tabularnewline
58 & 115.7 & 115.115396052218 & 0.584603947782148 \tabularnewline
59 & 99.4 & 106.728900785955 & -7.32890078595475 \tabularnewline
60 & 94.3 & 97.9164494571563 & -3.61644945715635 \tabularnewline
61 & 91 & 97.70821784209 & -6.70821784208998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57763&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]95.1[/C][C]96.896465113101[/C][C]-1.79646511310108[/C][/ROW]
[ROW][C]2[/C][C]97[/C][C]99.29036130158[/C][C]-2.29036130157994[/C][/ROW]
[ROW][C]3[/C][C]112.7[/C][C]109.067767191858[/C][C]3.63223280814230[/C][/ROW]
[ROW][C]4[/C][C]102.9[/C][C]102.342083715199[/C][C]0.557916284800547[/C][/ROW]
[ROW][C]5[/C][C]97.4[/C][C]101.095503585168[/C][C]-3.69550358516828[/C][/ROW]
[ROW][C]6[/C][C]111.4[/C][C]110.451070232844[/C][C]0.948929767156081[/C][/ROW]
[ROW][C]7[/C][C]87.4[/C][C]84.1084761231217[/C][C]3.29152387687832[/C][/ROW]
[ROW][C]8[/C][C]96.8[/C][C]95.7960577542088[/C][C]1.00394224579119[/C][/ROW]
[ROW][C]9[/C][C]114.1[/C][C]111.096210527090[/C][C]3.00378947290986[/C][/ROW]
[ROW][C]10[/C][C]110.3[/C][C]112.185430702700[/C][C]-1.88543070269976[/C][/ROW]
[ROW][C]11[/C][C]103.9[/C][C]105.662140637684[/C][C]-1.76214063768416[/C][/ROW]
[ROW][C]12[/C][C]101.6[/C][C]97.9676124296343[/C][C]3.63238757036573[/C][/ROW]
[ROW][C]13[/C][C]94.6[/C][C]98.0807837117831[/C][C]-3.4807837117831[/C][/ROW]
[ROW][C]14[/C][C]95.9[/C][C]100.581814199334[/C][C]-4.68181419933372[/C][/ROW]
[ROW][C]15[/C][C]104.7[/C][C]110.797073311905[/C][C]-6.09707331190463[/C][/ROW]
[ROW][C]16[/C][C]102.8[/C][C]103.987545601190[/C][C]-1.18754560119027[/C][/ROW]
[ROW][C]17[/C][C]98.1[/C][C]102.060895572704[/C][C]-3.96089557270374[/C][/ROW]
[ROW][C]18[/C][C]113.9[/C][C]112.152428274872[/C][C]1.74757172512785[/C][/ROW]
[ROW][C]19[/C][C]80.9[/C][C]85.8470982691749[/C][C]-4.94709826917484[/C][/ROW]
[ROW][C]20[/C][C]95.7[/C][C]97.7582645244117[/C][C]-2.05826452441169[/C][/ROW]
[ROW][C]21[/C][C]113.2[/C][C]113.077049349305[/C][C]0.122950650694521[/C][/ROW]
[ROW][C]22[/C][C]105.9[/C][C]113.230008911288[/C][C]-7.33000891128824[/C][/ROW]
[ROW][C]23[/C][C]108.8[/C][C]106.781247054323[/C][C]2.01875294567745[/C][/ROW]
[ROW][C]24[/C][C]102.3[/C][C]99.692260536678[/C][C]2.60773946332191[/C][/ROW]
[ROW][C]25[/C][C]99[/C][C]100.070938560005[/C][C]-1.07093856000468[/C][/ROW]
[ROW][C]26[/C][C]100.7[/C][C]102.25056615034[/C][C]-1.55056615034012[/C][/ROW]
[ROW][C]27[/C][C]115.5[/C][C]111.813703442474[/C][C]3.6862965575256[/C][/ROW]
[ROW][C]28[/C][C]100.7[/C][C]105.940436345387[/C][C]-5.2404363453869[/C][/ROW]
[ROW][C]29[/C][C]109.9[/C][C]104.600695955293[/C][C]5.29930404470667[/C][/ROW]
[ROW][C]30[/C][C]114.6[/C][C]113.923656511947[/C][C]0.676343488052836[/C][/ROW]
[ROW][C]31[/C][C]85.4[/C][C]87.939729403465[/C][C]-2.53972940346504[/C][/ROW]
[ROW][C]32[/C][C]100.5[/C][C]99.2034318512684[/C][C]1.29656814873161[/C][/ROW]
[ROW][C]33[/C][C]114.8[/C][C]113.469505737457[/C][C]1.33049426254266[/C][/ROW]
[ROW][C]34[/C][C]116.5[/C][C]113.659729403465[/C][C]2.84027059653495[/C][/ROW]
[ROW][C]35[/C][C]112.9[/C][C]107.63018871678[/C][C]5.26981128321996[/C][/ROW]
[ROW][C]36[/C][C]102[/C][C]100.680942589229[/C][C]1.31905741077086[/C][/ROW]
[ROW][C]37[/C][C]106[/C][C]99.5178183085234[/C][C]6.48218169147658[/C][/ROW]
[ROW][C]38[/C][C]105.3[/C][C]102.344909706292[/C][C]2.95509029370762[/C][/ROW]
[ROW][C]39[/C][C]118.8[/C][C]112.173553739604[/C][C]6.62644626039557[/C][/ROW]
[ROW][C]40[/C][C]106.1[/C][C]106.006831823320[/C][C]0.0931681766795536[/C][/ROW]
[ROW][C]41[/C][C]109.3[/C][C]104.443506809077[/C][C]4.85649319092282[/C][/ROW]
[ROW][C]42[/C][C]117.2[/C][C]114.274190783071[/C][C]2.92580921692906[/C][/ROW]
[ROW][C]43[/C][C]92.5[/C][C]88.33684380462[/C][C]4.16315619537998[/C][/ROW]
[ROW][C]44[/C][C]104.2[/C][C]99.274485342205[/C][C]4.92551465779495[/C][/ROW]
[ROW][C]45[/C][C]112.5[/C][C]115.343210260601[/C][C]-2.84321026060095[/C][/ROW]
[ROW][C]46[/C][C]122.4[/C][C]116.609434930329[/C][C]5.79056506967091[/C][/ROW]
[ROW][C]47[/C][C]113.3[/C][C]111.497522805258[/C][C]1.80247719474150[/C][/ROW]
[ROW][C]48[/C][C]100[/C][C]103.942734987302[/C][C]-3.94273498730215[/C][/ROW]
[ROW][C]49[/C][C]110.7[/C][C]104.125776464498[/C][C]6.57422353550225[/C][/ROW]
[ROW][C]50[/C][C]112.8[/C][C]107.232348642454[/C][C]5.56765135754617[/C][/ROW]
[ROW][C]51[/C][C]109.8[/C][C]117.647902314159[/C][C]-7.84790231415885[/C][/ROW]
[ROW][C]52[/C][C]117.3[/C][C]111.523102514903[/C][C]5.77689748509707[/C][/ROW]
[ROW][C]53[/C][C]109.1[/C][C]111.599398077757[/C][C]-2.49939807775748[/C][/ROW]
[ROW][C]54[/C][C]115.9[/C][C]122.198654197266[/C][C]-6.29865419726583[/C][/ROW]
[ROW][C]55[/C][C]96[/C][C]95.9678523996184[/C][C]0.032147600381574[/C][/ROW]
[ROW][C]56[/C][C]99.8[/C][C]104.967760527906[/C][C]-5.16776052790605[/C][/ROW]
[ROW][C]57[/C][C]116.8[/C][C]118.414024125546[/C][C]-1.61402412554610[/C][/ROW]
[ROW][C]58[/C][C]115.7[/C][C]115.115396052218[/C][C]0.584603947782148[/C][/ROW]
[ROW][C]59[/C][C]99.4[/C][C]106.728900785955[/C][C]-7.32890078595475[/C][/ROW]
[ROW][C]60[/C][C]94.3[/C][C]97.9164494571563[/C][C]-3.61644945715635[/C][/ROW]
[ROW][C]61[/C][C]91[/C][C]97.70821784209[/C][C]-6.70821784208998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57763&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57763&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
195.196.896465113101-1.79646511310108
29799.29036130158-2.29036130157994
3112.7109.0677671918583.63223280814230
4102.9102.3420837151990.557916284800547
597.4101.095503585168-3.69550358516828
6111.4110.4510702328440.948929767156081
787.484.10847612312173.29152387687832
896.895.79605775420881.00394224579119
9114.1111.0962105270903.00378947290986
10110.3112.185430702700-1.88543070269976
11103.9105.662140637684-1.76214063768416
12101.697.96761242963433.63238757036573
1394.698.0807837117831-3.4807837117831
1495.9100.581814199334-4.68181419933372
15104.7110.797073311905-6.09707331190463
16102.8103.987545601190-1.18754560119027
1798.1102.060895572704-3.96089557270374
18113.9112.1524282748721.74757172512785
1980.985.8470982691749-4.94709826917484
2095.797.7582645244117-2.05826452441169
21113.2113.0770493493050.122950650694521
22105.9113.230008911288-7.33000891128824
23108.8106.7812470543232.01875294567745
24102.399.6922605366782.60773946332191
2599100.070938560005-1.07093856000468
26100.7102.25056615034-1.55056615034012
27115.5111.8137034424743.6862965575256
28100.7105.940436345387-5.2404363453869
29109.9104.6006959552935.29930404470667
30114.6113.9236565119470.676343488052836
3185.487.939729403465-2.53972940346504
32100.599.20343185126841.29656814873161
33114.8113.4695057374571.33049426254266
34116.5113.6597294034652.84027059653495
35112.9107.630188716785.26981128321996
36102100.6809425892291.31905741077086
3710699.51781830852346.48218169147658
38105.3102.3449097062922.95509029370762
39118.8112.1735537396046.62644626039557
40106.1106.0068318233200.0931681766795536
41109.3104.4435068090774.85649319092282
42117.2114.2741907830712.92580921692906
4392.588.336843804624.16315619537998
44104.299.2744853422054.92551465779495
45112.5115.343210260601-2.84321026060095
46122.4116.6094349303295.79056506967091
47113.3111.4975228052581.80247719474150
48100103.942734987302-3.94273498730215
49110.7104.1257764644986.57422353550225
50112.8107.2323486424545.56765135754617
51109.8117.647902314159-7.84790231415885
52117.3111.5231025149035.77689748509707
53109.1111.599398077757-2.49939807775748
54115.9122.198654197266-6.29865419726583
559695.96785239961840.032147600381574
5699.8104.967760527906-5.16776052790605
57116.8118.414024125546-1.61402412554610
58115.7115.1153960522180.584603947782148
5999.4106.728900785955-7.32890078595475
6094.397.9164494571563-3.61644945715635
619197.70821784209-6.70821784208998







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.09377934265442450.1875586853088490.906220657345576
180.1191961817184740.2383923634369480.880803818281526
190.08596241970778430.1719248394155690.914037580292216
200.0517869560218490.1035739120436980.948213043978151
210.02649643878034040.05299287756068070.97350356121966
220.03241225361720820.06482450723441640.967587746382792
230.0391329067642540.0782658135285080.960867093235746
240.02284127593259230.04568255186518460.977158724067408
250.03967846340267490.07935692680534990.960321536597325
260.05217971532271620.1043594306454320.947820284677284
270.05424688909278480.1084937781855700.945753110907215
280.08151674013013340.1630334802602670.918483259869867
290.2611776511812260.5223553023624510.738822348818774
300.1895534240830170.3791068481660350.810446575916983
310.2286057242578150.4572114485156300.771394275742185
320.1907188829971100.3814377659942190.80928111700289
330.1365475451795780.2730950903591570.863452454820422
340.1875666323826880.3751332647653760.812433367617312
350.1359588404395620.2719176808791250.864041159560438
360.1025185711854570.2050371423709130.897481428814543
370.071203073275960.142406146551920.92879692672404
380.07489532496210220.1497906499242040.925104675037898
390.1065834595987860.2131669191975710.893416540401214
400.2707136469709080.5414272939418170.729286353029092
410.1842331099162530.3684662198325070.815766890083747
420.1445902321976920.2891804643953840.855409767802308
430.08470028589237250.1694005717847450.915299714107628
440.1533183517183730.3066367034367450.846681648281627

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.0937793426544245 & 0.187558685308849 & 0.906220657345576 \tabularnewline
18 & 0.119196181718474 & 0.238392363436948 & 0.880803818281526 \tabularnewline
19 & 0.0859624197077843 & 0.171924839415569 & 0.914037580292216 \tabularnewline
20 & 0.051786956021849 & 0.103573912043698 & 0.948213043978151 \tabularnewline
21 & 0.0264964387803404 & 0.0529928775606807 & 0.97350356121966 \tabularnewline
22 & 0.0324122536172082 & 0.0648245072344164 & 0.967587746382792 \tabularnewline
23 & 0.039132906764254 & 0.078265813528508 & 0.960867093235746 \tabularnewline
24 & 0.0228412759325923 & 0.0456825518651846 & 0.977158724067408 \tabularnewline
25 & 0.0396784634026749 & 0.0793569268053499 & 0.960321536597325 \tabularnewline
26 & 0.0521797153227162 & 0.104359430645432 & 0.947820284677284 \tabularnewline
27 & 0.0542468890927848 & 0.108493778185570 & 0.945753110907215 \tabularnewline
28 & 0.0815167401301334 & 0.163033480260267 & 0.918483259869867 \tabularnewline
29 & 0.261177651181226 & 0.522355302362451 & 0.738822348818774 \tabularnewline
30 & 0.189553424083017 & 0.379106848166035 & 0.810446575916983 \tabularnewline
31 & 0.228605724257815 & 0.457211448515630 & 0.771394275742185 \tabularnewline
32 & 0.190718882997110 & 0.381437765994219 & 0.80928111700289 \tabularnewline
33 & 0.136547545179578 & 0.273095090359157 & 0.863452454820422 \tabularnewline
34 & 0.187566632382688 & 0.375133264765376 & 0.812433367617312 \tabularnewline
35 & 0.135958840439562 & 0.271917680879125 & 0.864041159560438 \tabularnewline
36 & 0.102518571185457 & 0.205037142370913 & 0.897481428814543 \tabularnewline
37 & 0.07120307327596 & 0.14240614655192 & 0.92879692672404 \tabularnewline
38 & 0.0748953249621022 & 0.149790649924204 & 0.925104675037898 \tabularnewline
39 & 0.106583459598786 & 0.213166919197571 & 0.893416540401214 \tabularnewline
40 & 0.270713646970908 & 0.541427293941817 & 0.729286353029092 \tabularnewline
41 & 0.184233109916253 & 0.368466219832507 & 0.815766890083747 \tabularnewline
42 & 0.144590232197692 & 0.289180464395384 & 0.855409767802308 \tabularnewline
43 & 0.0847002858923725 & 0.169400571784745 & 0.915299714107628 \tabularnewline
44 & 0.153318351718373 & 0.306636703436745 & 0.846681648281627 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57763&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]17[/C][C]0.0937793426544245[/C][C]0.187558685308849[/C][C]0.906220657345576[/C][/ROW]
[ROW][C]18[/C][C]0.119196181718474[/C][C]0.238392363436948[/C][C]0.880803818281526[/C][/ROW]
[ROW][C]19[/C][C]0.0859624197077843[/C][C]0.171924839415569[/C][C]0.914037580292216[/C][/ROW]
[ROW][C]20[/C][C]0.051786956021849[/C][C]0.103573912043698[/C][C]0.948213043978151[/C][/ROW]
[ROW][C]21[/C][C]0.0264964387803404[/C][C]0.0529928775606807[/C][C]0.97350356121966[/C][/ROW]
[ROW][C]22[/C][C]0.0324122536172082[/C][C]0.0648245072344164[/C][C]0.967587746382792[/C][/ROW]
[ROW][C]23[/C][C]0.039132906764254[/C][C]0.078265813528508[/C][C]0.960867093235746[/C][/ROW]
[ROW][C]24[/C][C]0.0228412759325923[/C][C]0.0456825518651846[/C][C]0.977158724067408[/C][/ROW]
[ROW][C]25[/C][C]0.0396784634026749[/C][C]0.0793569268053499[/C][C]0.960321536597325[/C][/ROW]
[ROW][C]26[/C][C]0.0521797153227162[/C][C]0.104359430645432[/C][C]0.947820284677284[/C][/ROW]
[ROW][C]27[/C][C]0.0542468890927848[/C][C]0.108493778185570[/C][C]0.945753110907215[/C][/ROW]
[ROW][C]28[/C][C]0.0815167401301334[/C][C]0.163033480260267[/C][C]0.918483259869867[/C][/ROW]
[ROW][C]29[/C][C]0.261177651181226[/C][C]0.522355302362451[/C][C]0.738822348818774[/C][/ROW]
[ROW][C]30[/C][C]0.189553424083017[/C][C]0.379106848166035[/C][C]0.810446575916983[/C][/ROW]
[ROW][C]31[/C][C]0.228605724257815[/C][C]0.457211448515630[/C][C]0.771394275742185[/C][/ROW]
[ROW][C]32[/C][C]0.190718882997110[/C][C]0.381437765994219[/C][C]0.80928111700289[/C][/ROW]
[ROW][C]33[/C][C]0.136547545179578[/C][C]0.273095090359157[/C][C]0.863452454820422[/C][/ROW]
[ROW][C]34[/C][C]0.187566632382688[/C][C]0.375133264765376[/C][C]0.812433367617312[/C][/ROW]
[ROW][C]35[/C][C]0.135958840439562[/C][C]0.271917680879125[/C][C]0.864041159560438[/C][/ROW]
[ROW][C]36[/C][C]0.102518571185457[/C][C]0.205037142370913[/C][C]0.897481428814543[/C][/ROW]
[ROW][C]37[/C][C]0.07120307327596[/C][C]0.14240614655192[/C][C]0.92879692672404[/C][/ROW]
[ROW][C]38[/C][C]0.0748953249621022[/C][C]0.149790649924204[/C][C]0.925104675037898[/C][/ROW]
[ROW][C]39[/C][C]0.106583459598786[/C][C]0.213166919197571[/C][C]0.893416540401214[/C][/ROW]
[ROW][C]40[/C][C]0.270713646970908[/C][C]0.541427293941817[/C][C]0.729286353029092[/C][/ROW]
[ROW][C]41[/C][C]0.184233109916253[/C][C]0.368466219832507[/C][C]0.815766890083747[/C][/ROW]
[ROW][C]42[/C][C]0.144590232197692[/C][C]0.289180464395384[/C][C]0.855409767802308[/C][/ROW]
[ROW][C]43[/C][C]0.0847002858923725[/C][C]0.169400571784745[/C][C]0.915299714107628[/C][/ROW]
[ROW][C]44[/C][C]0.153318351718373[/C][C]0.306636703436745[/C][C]0.846681648281627[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57763&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57763&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
170.09377934265442450.1875586853088490.906220657345576
180.1191961817184740.2383923634369480.880803818281526
190.08596241970778430.1719248394155690.914037580292216
200.0517869560218490.1035739120436980.948213043978151
210.02649643878034040.05299287756068070.97350356121966
220.03241225361720820.06482450723441640.967587746382792
230.0391329067642540.0782658135285080.960867093235746
240.02284127593259230.04568255186518460.977158724067408
250.03967846340267490.07935692680534990.960321536597325
260.05217971532271620.1043594306454320.947820284677284
270.05424688909278480.1084937781855700.945753110907215
280.08151674013013340.1630334802602670.918483259869867
290.2611776511812260.5223553023624510.738822348818774
300.1895534240830170.3791068481660350.810446575916983
310.2286057242578150.4572114485156300.771394275742185
320.1907188829971100.3814377659942190.80928111700289
330.1365475451795780.2730950903591570.863452454820422
340.1875666323826880.3751332647653760.812433367617312
350.1359588404395620.2719176808791250.864041159560438
360.1025185711854570.2050371423709130.897481428814543
370.071203073275960.142406146551920.92879692672404
380.07489532496210220.1497906499242040.925104675037898
390.1065834595987860.2131669191975710.893416540401214
400.2707136469709080.5414272939418170.729286353029092
410.1842331099162530.3684662198325070.815766890083747
420.1445902321976920.2891804643953840.855409767802308
430.08470028589237250.1694005717847450.915299714107628
440.1533183517183730.3066367034367450.846681648281627







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level10.0357142857142857OK
10% type I error level50.178571428571429NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 1 & 0.0357142857142857 & OK \tabularnewline
10% type I error level & 5 & 0.178571428571429 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57763&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]1[/C][C]0.0357142857142857[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]5[/C][C]0.178571428571429[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57763&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57763&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 level00OK
5% type I error level10.0357142857142857OK
10% type I error level50.178571428571429NOK



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')
}