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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationTue, 24 Nov 2009 05:16:30 -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/24/t1259065067wcul4jnvj5fzaei.htm/, Retrieved Sat, 28 Jun 2025 07:02:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59027, Retrieved Sat, 28 Jun 2025 07:02:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact310

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [] [2009-11-24 11:34:57] [f57b281e621ed7dff28b90886f5aa97c]
-   PD  [Multiple Regression] [] [2009-11-24 12:09:41] [f57b281e621ed7dff28b90886f5aa97c]
-    D      [Multiple Regression] [] [2009-11-24 12:16:30] [4d89445a8ea4b299af2ee123046cffa6] [Current]
- R  D        [Multiple Regression] [Vertragingen] [2010-12-18 11:45:57] [0ed8ad64bdfc801eaa95d5097964fc04]
-    D        [Multiple Regression] [2 vertragingen] [2010-12-18 12:25:58] [0ed8ad64bdfc801eaa95d5097964fc04]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
105.4	119.5	109	116.7
102.7	115.1	119.5	109
98.1	107.1	115.1	119.5
104.5	109.7	107.1	115.1
87.4	110.4	109.7	107.1
89.9	105	110.4	109.7
109.8	115.8	105	110.4
111.7	116.4	115.8	105
98.6	111.1	116.4	115.8
96.9	119.5	111.1	116.4
95.1	110.9	119.5	111.1
97	115.1	110.9	119.5
112.7	125.2	115.1	110.9
102.9	116	125.2	115.1
97.4	112.9	116	125.2
111.4	121.7	112.9	116
87.4	123.2	121.7	112.9
96.8	116.6	123.2	121.7
114.1	136.2	116.6	123.2
110.3	120.9	136.2	116.6
103.9	119.6	120.9	136.2
101.6	125.9	119.6	120.9
94.6	116.1	125.9	119.6
95.9	107.5	116.1	125.9
104.7	116.7	107.5	116.1
102.8	112.5	116.7	107.5
98.1	113	112.5	116.7
113.9	126.4	113	112.5
80.9	114.1	126.4	113
95.7	112.5	114.1	126.4
113.2	112.4	112.5	114.1
105.9	113.1	112.4	112.5
108.8	116.3	113.1	112.4
102.3	111.7	116.3	113.1
99	118.8	111.7	116.3
100.7	116.5	118.8	111.7
115.5	125.1	116.5	118.8
100.7	113.1	125.1	116.5
109.9	119.6	113.1	125.1
114.6	114.4	119.6	113.1
85.4	114	114.4	119.6
100.5	117.8	114	114.4
114.8	117	117.8	114
116.5	120.9	117	117.8
112.9	115	120.9	117
102	117.3	115	120.9
106	119.4	117.3	115
105.3	114.9	119.4	117.3
118.8	125.8	114.9	119.4
106.1	117.6	125.8	114.9
109.3	117.6	117.6	125.8
117.2	114.9	117.6	117.6
92.5	121.9	114.9	117.6
104.2	117	121.9	114.9
112.5	106.4	117	121.9
122.4	110.5	106.4	117
113.3	113.6	110.5	106.4
100	114.2	113.6	110.5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59027&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]5 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=59027&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59027&T=0

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


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
ipchn[t] = -22.3389173229912 + 0.832240299372395Tip[t] + 0.254189299923941`y(t-1)`[t] + 0.234683807228363`y(t-2)`[t] -0.0702121144545338M1[t] -2.16350805662868M2[t] -2.81444431776765M3[t] -5.41334542375707M4[t] + 14.6770191833725M5[t] + 2.36848127661478M6[t] -5.65462648983423M7[t] -7.37323493898212M8[t] -4.1666523610624M9[t] + 4.95764267217371M10[t] + 3.66500467191191M11[t] -0.151732055011969t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
ipchn[t] =  -22.3389173229912 +  0.832240299372395Tip[t] +  0.254189299923941`y(t-1)`[t] +  0.234683807228363`y(t-2)`[t] -0.0702121144545338M1[t] -2.16350805662868M2[t] -2.81444431776765M3[t] -5.41334542375707M4[t] +  14.6770191833725M5[t] +  2.36848127661478M6[t] -5.65462648983423M7[t] -7.37323493898212M8[t] -4.1666523610624M9[t] +  4.95764267217371M10[t] +  3.66500467191191M11[t] -0.151732055011969t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59027&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]ipchn[t] =  -22.3389173229912 +  0.832240299372395Tip[t] +  0.254189299923941`y(t-1)`[t] +  0.234683807228363`y(t-2)`[t] -0.0702121144545338M1[t] -2.16350805662868M2[t] -2.81444431776765M3[t] -5.41334542375707M4[t] +  14.6770191833725M5[t] +  2.36848127661478M6[t] -5.65462648983423M7[t] -7.37323493898212M8[t] -4.1666523610624M9[t] +  4.95764267217371M10[t] +  3.66500467191191M11[t] -0.151732055011969t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59027&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59027&T=1

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


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

Multiple Linear Regression - Estimated Regression Equation
ipchn[t] = -22.3389173229912 + 0.832240299372395Tip[t] + 0.254189299923941`y(t-1)`[t] + 0.234683807228363`y(t-2)`[t] -0.0702121144545338M1[t] -2.16350805662868M2[t] -2.81444431776765M3[t] -5.41334542375707M4[t] + 14.6770191833725M5[t] + 2.36848127661478M6[t] -5.65462648983423M7[t] -7.37323493898212M8[t] -4.1666523610624M9[t] + 4.95764267217371M10[t] + 3.66500467191191M11[t] -0.151732055011969t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-22.338917322991226.834303-0.83250.4098490.204925
Tip0.8322402993723950.1991774.17840.0001457.3e-05
`y(t-1)`0.2541892999239410.1277791.98930.0532080.026604
`y(t-2)`0.2346838072283630.1287521.82280.0754640.037732
M1-0.07021211445453383.98167-0.01760.9860140.493007
M2-2.163508056628683.39199-0.63780.5270480.263524
M3-2.814444317767653.206688-0.87770.3851110.192555
M4-5.413345423757074.006826-1.3510.1839190.09196
M514.67701918337254.0797723.59750.000840.00042
M62.368481276614783.1060350.76250.4499980.224999
M7-5.654626489834234.008324-1.41070.1656910.082846
M8-7.373234938982124.059724-1.81620.0764830.038242
M9-4.16665236106243.382125-1.2320.2248160.112408
M104.957642672173713.0828351.60810.1152960.057648
M113.665004671911913.285681.11540.2710.1355
t-0.1517320550119690.053097-2.85760.0066130.003307

\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) & -22.3389173229912 & 26.834303 & -0.8325 & 0.409849 & 0.204925 \tabularnewline
Tip & 0.832240299372395 & 0.199177 & 4.1784 & 0.000145 & 7.3e-05 \tabularnewline
`y(t-1)` & 0.254189299923941 & 0.127779 & 1.9893 & 0.053208 & 0.026604 \tabularnewline
`y(t-2)` & 0.234683807228363 & 0.128752 & 1.8228 & 0.075464 & 0.037732 \tabularnewline
M1 & -0.0702121144545338 & 3.98167 & -0.0176 & 0.986014 & 0.493007 \tabularnewline
M2 & -2.16350805662868 & 3.39199 & -0.6378 & 0.527048 & 0.263524 \tabularnewline
M3 & -2.81444431776765 & 3.206688 & -0.8777 & 0.385111 & 0.192555 \tabularnewline
M4 & -5.41334542375707 & 4.006826 & -1.351 & 0.183919 & 0.09196 \tabularnewline
M5 & 14.6770191833725 & 4.079772 & 3.5975 & 0.00084 & 0.00042 \tabularnewline
M6 & 2.36848127661478 & 3.106035 & 0.7625 & 0.449998 & 0.224999 \tabularnewline
M7 & -5.65462648983423 & 4.008324 & -1.4107 & 0.165691 & 0.082846 \tabularnewline
M8 & -7.37323493898212 & 4.059724 & -1.8162 & 0.076483 & 0.038242 \tabularnewline
M9 & -4.1666523610624 & 3.382125 & -1.232 & 0.224816 & 0.112408 \tabularnewline
M10 & 4.95764267217371 & 3.082835 & 1.6081 & 0.115296 & 0.057648 \tabularnewline
M11 & 3.66500467191191 & 3.28568 & 1.1154 & 0.271 & 0.1355 \tabularnewline
t & -0.151732055011969 & 0.053097 & -2.8576 & 0.006613 & 0.003307 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59027&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]-22.3389173229912[/C][C]26.834303[/C][C]-0.8325[/C][C]0.409849[/C][C]0.204925[/C][/ROW]
[ROW][C]Tip[/C][C]0.832240299372395[/C][C]0.199177[/C][C]4.1784[/C][C]0.000145[/C][C]7.3e-05[/C][/ROW]
[ROW][C]`y(t-1)`[/C][C]0.254189299923941[/C][C]0.127779[/C][C]1.9893[/C][C]0.053208[/C][C]0.026604[/C][/ROW]
[ROW][C]`y(t-2)`[/C][C]0.234683807228363[/C][C]0.128752[/C][C]1.8228[/C][C]0.075464[/C][C]0.037732[/C][/ROW]
[ROW][C]M1[/C][C]-0.0702121144545338[/C][C]3.98167[/C][C]-0.0176[/C][C]0.986014[/C][C]0.493007[/C][/ROW]
[ROW][C]M2[/C][C]-2.16350805662868[/C][C]3.39199[/C][C]-0.6378[/C][C]0.527048[/C][C]0.263524[/C][/ROW]
[ROW][C]M3[/C][C]-2.81444431776765[/C][C]3.206688[/C][C]-0.8777[/C][C]0.385111[/C][C]0.192555[/C][/ROW]
[ROW][C]M4[/C][C]-5.41334542375707[/C][C]4.006826[/C][C]-1.351[/C][C]0.183919[/C][C]0.09196[/C][/ROW]
[ROW][C]M5[/C][C]14.6770191833725[/C][C]4.079772[/C][C]3.5975[/C][C]0.00084[/C][C]0.00042[/C][/ROW]
[ROW][C]M6[/C][C]2.36848127661478[/C][C]3.106035[/C][C]0.7625[/C][C]0.449998[/C][C]0.224999[/C][/ROW]
[ROW][C]M7[/C][C]-5.65462648983423[/C][C]4.008324[/C][C]-1.4107[/C][C]0.165691[/C][C]0.082846[/C][/ROW]
[ROW][C]M8[/C][C]-7.37323493898212[/C][C]4.059724[/C][C]-1.8162[/C][C]0.076483[/C][C]0.038242[/C][/ROW]
[ROW][C]M9[/C][C]-4.1666523610624[/C][C]3.382125[/C][C]-1.232[/C][C]0.224816[/C][C]0.112408[/C][/ROW]
[ROW][C]M10[/C][C]4.95764267217371[/C][C]3.082835[/C][C]1.6081[/C][C]0.115296[/C][C]0.057648[/C][/ROW]
[ROW][C]M11[/C][C]3.66500467191191[/C][C]3.28568[/C][C]1.1154[/C][C]0.271[/C][C]0.1355[/C][/ROW]
[ROW][C]t[/C][C]-0.151732055011969[/C][C]0.053097[/C][C]-2.8576[/C][C]0.006613[/C][C]0.003307[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59027&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59027&T=2

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


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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-22.338917322991226.834303-0.83250.4098490.204925
Tip0.8322402993723950.1991774.17840.0001457.3e-05
`y(t-1)`0.2541892999239410.1277791.98930.0532080.026604
`y(t-2)`0.2346838072283630.1287521.82280.0754640.037732
M1-0.07021211445453383.98167-0.01760.9860140.493007
M2-2.163508056628683.39199-0.63780.5270480.263524
M3-2.814444317767653.206688-0.87770.3851110.192555
M4-5.413345423757074.006826-1.3510.1839190.09196
M514.67701918337254.0797723.59750.000840.00042
M62.368481276614783.1060350.76250.4499980.224999
M7-5.654626489834234.008324-1.41070.1656910.082846
M8-7.373234938982124.059724-1.81620.0764830.038242
M9-4.16665236106243.382125-1.2320.2248160.112408
M104.957642672173713.0828351.60810.1152960.057648
M113.665004671911913.285681.11540.2710.1355
t-0.1517320550119690.053097-2.85760.0066130.003307






Multiple Linear Regression - Regression Statistics
Multiple R0.7068850117758
R-squared0.499686419873272
Adjusted R-squared0.32100299839944
F-TEST (value)2.79649010384800
F-TEST (DF numerator)15
F-TEST (DF denominator)42
p-value0.00440837369515834
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4.56808646868449
Sum Squared Residuals876.431387385888

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.7068850117758 \tabularnewline
R-squared & 0.499686419873272 \tabularnewline
Adjusted R-squared & 0.32100299839944 \tabularnewline
F-TEST (value) & 2.79649010384800 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 42 \tabularnewline
p-value & 0.00440837369515834 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 4.56808646868449 \tabularnewline
Sum Squared Residuals & 876.431387385888 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59027&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.7068850117758[/C][/ROW]
[ROW][C]R-squared[/C][C]0.499686419873272[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.32100299839944[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]2.79649010384800[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]42[/C][/ROW]
[ROW][C]p-value[/C][C]0.00440837369515834[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]4.56808646868449[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]876.431387385888[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59027&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59027&T=3

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


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

Multiple Linear Regression - Regression Statistics
Multiple R0.7068850117758
R-squared0.499686419873272
Adjusted R-squared0.32100299839944
F-TEST (value)2.79649010384800
F-TEST (DF numerator)15
F-TEST (DF denominator)42
p-value0.00440837369515834
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4.56808646868449
Sum Squared Residuals876.431387385888






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1119.5120.251500056653-0.751500056652636
2115.1116.621345584704-1.52134558470371
3107.1113.336118947672-6.23611894767218
4109.7112.845700551458-3.14570055145780
5110.4117.336445706283-6.93644570628282
6105107.744886901685-2.74488690168459
7115.8114.9232854832050.876714516795172
8116.4116.1121534279980.287846572002082
9111.1110.9517547271480.148245272852022
10119.5117.3031161911792.19688380882081
11110.9115.252079538086-4.35207953808588
12115.1112.8019153813422.29808461865809
13125.2124.6954582295390.504541770461356
14116117.847459218094-1.84745921809399
15112.9112.4992341491010.400765850898923
16121.7118.4528873230483.24711267695193
17123.2119.9270987271513.27290127284901
18116.6117.736389032977-1.13638903297727
19136.2122.63368272200313.5663172779967
20120.9121.034026231030-0.134026231030336
21119.6119.4732451707940.126754829205624
22125.9122.6105471199673.28945288003306
23116.1116.636798609210-0.536798609210364
24107.5112.889427117755-5.38942711775466
25116.7115.5052682925811.19473170741862
26112.5111.9992445437240.500755456275935
27113108.3765427873434.62345721265675
28126.4117.9167290160298.48327098397145
29114.1113.9149102114520.185089788547831
30112.5113.790031308189-1.29003130818944
31112.4116.886083016958-4.48608301695821
32113.1108.5394753058224.56052469417789
33116.3114.1622868261342.13771317386629
34111.7118.702972283254-7.00297228325375
35118.8114.0939266435324.70607335646829
36116.5112.4171969417504.08280305824957
37125.1125.594028844492-0.494028844491673
38113.1112.6780996393150.42190036068522
39119.6118.5000512204661.09994877953351
40114.4118.496972229281-4.09697222928062
41114114.337848427104-0.337848427104201
42117.8113.1223754683014.67762453169943
43117117.720617744684-0.720617744684468
44120.9117.9535327769862.94646722301371
45115118.815909446074-3.81590944607412
46117.3118.132603139779-0.832603139778518
47119.4119.2171952091720.182804790827963
48114.9115.891460559153-0.991460559152996
49125.8126.253744576736-0.453744576735659
50117.6115.1538510141632.44614898583654
51117.6117.4880528954170.111947104582988
52114.9119.387710880185-4.48771088018497
53121.9118.0836969280103.81630307199018
54117116.5063172888480.493682711151877
55106.4115.636331033149-9.23633103314923
56110.5118.160812258163-7.66081225816334
57113.6112.1968038298501.40319617015018
58114.2111.8507612658222.34923873417839

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 119.5 & 120.251500056653 & -0.751500056652636 \tabularnewline
2 & 115.1 & 116.621345584704 & -1.52134558470371 \tabularnewline
3 & 107.1 & 113.336118947672 & -6.23611894767218 \tabularnewline
4 & 109.7 & 112.845700551458 & -3.14570055145780 \tabularnewline
5 & 110.4 & 117.336445706283 & -6.93644570628282 \tabularnewline
6 & 105 & 107.744886901685 & -2.74488690168459 \tabularnewline
7 & 115.8 & 114.923285483205 & 0.876714516795172 \tabularnewline
8 & 116.4 & 116.112153427998 & 0.287846572002082 \tabularnewline
9 & 111.1 & 110.951754727148 & 0.148245272852022 \tabularnewline
10 & 119.5 & 117.303116191179 & 2.19688380882081 \tabularnewline
11 & 110.9 & 115.252079538086 & -4.35207953808588 \tabularnewline
12 & 115.1 & 112.801915381342 & 2.29808461865809 \tabularnewline
13 & 125.2 & 124.695458229539 & 0.504541770461356 \tabularnewline
14 & 116 & 117.847459218094 & -1.84745921809399 \tabularnewline
15 & 112.9 & 112.499234149101 & 0.400765850898923 \tabularnewline
16 & 121.7 & 118.452887323048 & 3.24711267695193 \tabularnewline
17 & 123.2 & 119.927098727151 & 3.27290127284901 \tabularnewline
18 & 116.6 & 117.736389032977 & -1.13638903297727 \tabularnewline
19 & 136.2 & 122.633682722003 & 13.5663172779967 \tabularnewline
20 & 120.9 & 121.034026231030 & -0.134026231030336 \tabularnewline
21 & 119.6 & 119.473245170794 & 0.126754829205624 \tabularnewline
22 & 125.9 & 122.610547119967 & 3.28945288003306 \tabularnewline
23 & 116.1 & 116.636798609210 & -0.536798609210364 \tabularnewline
24 & 107.5 & 112.889427117755 & -5.38942711775466 \tabularnewline
25 & 116.7 & 115.505268292581 & 1.19473170741862 \tabularnewline
26 & 112.5 & 111.999244543724 & 0.500755456275935 \tabularnewline
27 & 113 & 108.376542787343 & 4.62345721265675 \tabularnewline
28 & 126.4 & 117.916729016029 & 8.48327098397145 \tabularnewline
29 & 114.1 & 113.914910211452 & 0.185089788547831 \tabularnewline
30 & 112.5 & 113.790031308189 & -1.29003130818944 \tabularnewline
31 & 112.4 & 116.886083016958 & -4.48608301695821 \tabularnewline
32 & 113.1 & 108.539475305822 & 4.56052469417789 \tabularnewline
33 & 116.3 & 114.162286826134 & 2.13771317386629 \tabularnewline
34 & 111.7 & 118.702972283254 & -7.00297228325375 \tabularnewline
35 & 118.8 & 114.093926643532 & 4.70607335646829 \tabularnewline
36 & 116.5 & 112.417196941750 & 4.08280305824957 \tabularnewline
37 & 125.1 & 125.594028844492 & -0.494028844491673 \tabularnewline
38 & 113.1 & 112.678099639315 & 0.42190036068522 \tabularnewline
39 & 119.6 & 118.500051220466 & 1.09994877953351 \tabularnewline
40 & 114.4 & 118.496972229281 & -4.09697222928062 \tabularnewline
41 & 114 & 114.337848427104 & -0.337848427104201 \tabularnewline
42 & 117.8 & 113.122375468301 & 4.67762453169943 \tabularnewline
43 & 117 & 117.720617744684 & -0.720617744684468 \tabularnewline
44 & 120.9 & 117.953532776986 & 2.94646722301371 \tabularnewline
45 & 115 & 118.815909446074 & -3.81590944607412 \tabularnewline
46 & 117.3 & 118.132603139779 & -0.832603139778518 \tabularnewline
47 & 119.4 & 119.217195209172 & 0.182804790827963 \tabularnewline
48 & 114.9 & 115.891460559153 & -0.991460559152996 \tabularnewline
49 & 125.8 & 126.253744576736 & -0.453744576735659 \tabularnewline
50 & 117.6 & 115.153851014163 & 2.44614898583654 \tabularnewline
51 & 117.6 & 117.488052895417 & 0.111947104582988 \tabularnewline
52 & 114.9 & 119.387710880185 & -4.48771088018497 \tabularnewline
53 & 121.9 & 118.083696928010 & 3.81630307199018 \tabularnewline
54 & 117 & 116.506317288848 & 0.493682711151877 \tabularnewline
55 & 106.4 & 115.636331033149 & -9.23633103314923 \tabularnewline
56 & 110.5 & 118.160812258163 & -7.66081225816334 \tabularnewline
57 & 113.6 & 112.196803829850 & 1.40319617015018 \tabularnewline
58 & 114.2 & 111.850761265822 & 2.34923873417839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59027&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]119.5[/C][C]120.251500056653[/C][C]-0.751500056652636[/C][/ROW]
[ROW][C]2[/C][C]115.1[/C][C]116.621345584704[/C][C]-1.52134558470371[/C][/ROW]
[ROW][C]3[/C][C]107.1[/C][C]113.336118947672[/C][C]-6.23611894767218[/C][/ROW]
[ROW][C]4[/C][C]109.7[/C][C]112.845700551458[/C][C]-3.14570055145780[/C][/ROW]
[ROW][C]5[/C][C]110.4[/C][C]117.336445706283[/C][C]-6.93644570628282[/C][/ROW]
[ROW][C]6[/C][C]105[/C][C]107.744886901685[/C][C]-2.74488690168459[/C][/ROW]
[ROW][C]7[/C][C]115.8[/C][C]114.923285483205[/C][C]0.876714516795172[/C][/ROW]
[ROW][C]8[/C][C]116.4[/C][C]116.112153427998[/C][C]0.287846572002082[/C][/ROW]
[ROW][C]9[/C][C]111.1[/C][C]110.951754727148[/C][C]0.148245272852022[/C][/ROW]
[ROW][C]10[/C][C]119.5[/C][C]117.303116191179[/C][C]2.19688380882081[/C][/ROW]
[ROW][C]11[/C][C]110.9[/C][C]115.252079538086[/C][C]-4.35207953808588[/C][/ROW]
[ROW][C]12[/C][C]115.1[/C][C]112.801915381342[/C][C]2.29808461865809[/C][/ROW]
[ROW][C]13[/C][C]125.2[/C][C]124.695458229539[/C][C]0.504541770461356[/C][/ROW]
[ROW][C]14[/C][C]116[/C][C]117.847459218094[/C][C]-1.84745921809399[/C][/ROW]
[ROW][C]15[/C][C]112.9[/C][C]112.499234149101[/C][C]0.400765850898923[/C][/ROW]
[ROW][C]16[/C][C]121.7[/C][C]118.452887323048[/C][C]3.24711267695193[/C][/ROW]
[ROW][C]17[/C][C]123.2[/C][C]119.927098727151[/C][C]3.27290127284901[/C][/ROW]
[ROW][C]18[/C][C]116.6[/C][C]117.736389032977[/C][C]-1.13638903297727[/C][/ROW]
[ROW][C]19[/C][C]136.2[/C][C]122.633682722003[/C][C]13.5663172779967[/C][/ROW]
[ROW][C]20[/C][C]120.9[/C][C]121.034026231030[/C][C]-0.134026231030336[/C][/ROW]
[ROW][C]21[/C][C]119.6[/C][C]119.473245170794[/C][C]0.126754829205624[/C][/ROW]
[ROW][C]22[/C][C]125.9[/C][C]122.610547119967[/C][C]3.28945288003306[/C][/ROW]
[ROW][C]23[/C][C]116.1[/C][C]116.636798609210[/C][C]-0.536798609210364[/C][/ROW]
[ROW][C]24[/C][C]107.5[/C][C]112.889427117755[/C][C]-5.38942711775466[/C][/ROW]
[ROW][C]25[/C][C]116.7[/C][C]115.505268292581[/C][C]1.19473170741862[/C][/ROW]
[ROW][C]26[/C][C]112.5[/C][C]111.999244543724[/C][C]0.500755456275935[/C][/ROW]
[ROW][C]27[/C][C]113[/C][C]108.376542787343[/C][C]4.62345721265675[/C][/ROW]
[ROW][C]28[/C][C]126.4[/C][C]117.916729016029[/C][C]8.48327098397145[/C][/ROW]
[ROW][C]29[/C][C]114.1[/C][C]113.914910211452[/C][C]0.185089788547831[/C][/ROW]
[ROW][C]30[/C][C]112.5[/C][C]113.790031308189[/C][C]-1.29003130818944[/C][/ROW]
[ROW][C]31[/C][C]112.4[/C][C]116.886083016958[/C][C]-4.48608301695821[/C][/ROW]
[ROW][C]32[/C][C]113.1[/C][C]108.539475305822[/C][C]4.56052469417789[/C][/ROW]
[ROW][C]33[/C][C]116.3[/C][C]114.162286826134[/C][C]2.13771317386629[/C][/ROW]
[ROW][C]34[/C][C]111.7[/C][C]118.702972283254[/C][C]-7.00297228325375[/C][/ROW]
[ROW][C]35[/C][C]118.8[/C][C]114.093926643532[/C][C]4.70607335646829[/C][/ROW]
[ROW][C]36[/C][C]116.5[/C][C]112.417196941750[/C][C]4.08280305824957[/C][/ROW]
[ROW][C]37[/C][C]125.1[/C][C]125.594028844492[/C][C]-0.494028844491673[/C][/ROW]
[ROW][C]38[/C][C]113.1[/C][C]112.678099639315[/C][C]0.42190036068522[/C][/ROW]
[ROW][C]39[/C][C]119.6[/C][C]118.500051220466[/C][C]1.09994877953351[/C][/ROW]
[ROW][C]40[/C][C]114.4[/C][C]118.496972229281[/C][C]-4.09697222928062[/C][/ROW]
[ROW][C]41[/C][C]114[/C][C]114.337848427104[/C][C]-0.337848427104201[/C][/ROW]
[ROW][C]42[/C][C]117.8[/C][C]113.122375468301[/C][C]4.67762453169943[/C][/ROW]
[ROW][C]43[/C][C]117[/C][C]117.720617744684[/C][C]-0.720617744684468[/C][/ROW]
[ROW][C]44[/C][C]120.9[/C][C]117.953532776986[/C][C]2.94646722301371[/C][/ROW]
[ROW][C]45[/C][C]115[/C][C]118.815909446074[/C][C]-3.81590944607412[/C][/ROW]
[ROW][C]46[/C][C]117.3[/C][C]118.132603139779[/C][C]-0.832603139778518[/C][/ROW]
[ROW][C]47[/C][C]119.4[/C][C]119.217195209172[/C][C]0.182804790827963[/C][/ROW]
[ROW][C]48[/C][C]114.9[/C][C]115.891460559153[/C][C]-0.991460559152996[/C][/ROW]
[ROW][C]49[/C][C]125.8[/C][C]126.253744576736[/C][C]-0.453744576735659[/C][/ROW]
[ROW][C]50[/C][C]117.6[/C][C]115.153851014163[/C][C]2.44614898583654[/C][/ROW]
[ROW][C]51[/C][C]117.6[/C][C]117.488052895417[/C][C]0.111947104582988[/C][/ROW]
[ROW][C]52[/C][C]114.9[/C][C]119.387710880185[/C][C]-4.48771088018497[/C][/ROW]
[ROW][C]53[/C][C]121.9[/C][C]118.083696928010[/C][C]3.81630307199018[/C][/ROW]
[ROW][C]54[/C][C]117[/C][C]116.506317288848[/C][C]0.493682711151877[/C][/ROW]
[ROW][C]55[/C][C]106.4[/C][C]115.636331033149[/C][C]-9.23633103314923[/C][/ROW]
[ROW][C]56[/C][C]110.5[/C][C]118.160812258163[/C][C]-7.66081225816334[/C][/ROW]
[ROW][C]57[/C][C]113.6[/C][C]112.196803829850[/C][C]1.40319617015018[/C][/ROW]
[ROW][C]58[/C][C]114.2[/C][C]111.850761265822[/C][C]2.34923873417839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59027&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59027&T=4

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


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1119.5120.251500056653-0.751500056652636
2115.1116.621345584704-1.52134558470371
3107.1113.336118947672-6.23611894767218
4109.7112.845700551458-3.14570055145780
5110.4117.336445706283-6.93644570628282
6105107.744886901685-2.74488690168459
7115.8114.9232854832050.876714516795172
8116.4116.1121534279980.287846572002082
9111.1110.9517547271480.148245272852022
10119.5117.3031161911792.19688380882081
11110.9115.252079538086-4.35207953808588
12115.1112.8019153813422.29808461865809
13125.2124.6954582295390.504541770461356
14116117.847459218094-1.84745921809399
15112.9112.4992341491010.400765850898923
16121.7118.4528873230483.24711267695193
17123.2119.9270987271513.27290127284901
18116.6117.736389032977-1.13638903297727
19136.2122.63368272200313.5663172779967
20120.9121.034026231030-0.134026231030336
21119.6119.4732451707940.126754829205624
22125.9122.6105471199673.28945288003306
23116.1116.636798609210-0.536798609210364
24107.5112.889427117755-5.38942711775466
25116.7115.5052682925811.19473170741862
26112.5111.9992445437240.500755456275935
27113108.3765427873434.62345721265675
28126.4117.9167290160298.48327098397145
29114.1113.9149102114520.185089788547831
30112.5113.790031308189-1.29003130818944
31112.4116.886083016958-4.48608301695821
32113.1108.5394753058224.56052469417789
33116.3114.1622868261342.13771317386629
34111.7118.702972283254-7.00297228325375
35118.8114.0939266435324.70607335646829
36116.5112.4171969417504.08280305824957
37125.1125.594028844492-0.494028844491673
38113.1112.6780996393150.42190036068522
39119.6118.5000512204661.09994877953351
40114.4118.496972229281-4.09697222928062
41114114.337848427104-0.337848427104201
42117.8113.1223754683014.67762453169943
43117117.720617744684-0.720617744684468
44120.9117.9535327769862.94646722301371
45115118.815909446074-3.81590944607412
46117.3118.132603139779-0.832603139778518
47119.4119.2171952091720.182804790827963
48114.9115.891460559153-0.991460559152996
49125.8126.253744576736-0.453744576735659
50117.6115.1538510141632.44614898583654
51117.6117.4880528954170.111947104582988
52114.9119.387710880185-4.48771088018497
53121.9118.0836969280103.81630307199018
54117116.5063172888480.493682711151877
55106.4115.636331033149-9.23633103314923
56110.5118.160812258163-7.66081225816334
57113.6112.1968038298501.40319617015018
58114.2111.8507612658222.34923873417839






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.6910866797338190.6178266405323630.308913320266181
200.6647366799992580.6705266400014850.335263320000742
210.6752888379967950.649422324006410.324711162003205
220.6418972755477510.7162054489044980.358102724452249
230.516099073156440.967801853687120.48390092684356
240.6958288860276410.6083422279447170.304171113972359
250.5999404671401290.8001190657197410.400059532859871
260.5373152555387780.9253694889224440.462684744461222
270.4947814288622890.9895628577245780.505218571137711
280.6439279659872260.7121440680255480.356072034012774
290.6419051723187400.7161896553625190.358094827681260
300.5438737116132850.9122525767734290.456126288386714
310.816215872765090.3675682544698210.183784127234910
320.7515895261251740.4968209477496510.248410473874825
330.6703318066495240.6593363867009520.329668193350476
340.9083538137681950.1832923724636090.0916461862318046
350.899201711590730.2015965768185390.100798288409269
360.8307250890111130.3385498219777750.169274910988887
370.7496698610100740.5006602779798510.250330138989926
380.6228687096359980.7542625807280040.377131290364002
390.4475200002518920.8950400005037840.552479999748108

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.691086679733819 & 0.617826640532363 & 0.308913320266181 \tabularnewline
20 & 0.664736679999258 & 0.670526640001485 & 0.335263320000742 \tabularnewline
21 & 0.675288837996795 & 0.64942232400641 & 0.324711162003205 \tabularnewline
22 & 0.641897275547751 & 0.716205448904498 & 0.358102724452249 \tabularnewline
23 & 0.51609907315644 & 0.96780185368712 & 0.48390092684356 \tabularnewline
24 & 0.695828886027641 & 0.608342227944717 & 0.304171113972359 \tabularnewline
25 & 0.599940467140129 & 0.800119065719741 & 0.400059532859871 \tabularnewline
26 & 0.537315255538778 & 0.925369488922444 & 0.462684744461222 \tabularnewline
27 & 0.494781428862289 & 0.989562857724578 & 0.505218571137711 \tabularnewline
28 & 0.643927965987226 & 0.712144068025548 & 0.356072034012774 \tabularnewline
29 & 0.641905172318740 & 0.716189655362519 & 0.358094827681260 \tabularnewline
30 & 0.543873711613285 & 0.912252576773429 & 0.456126288386714 \tabularnewline
31 & 0.81621587276509 & 0.367568254469821 & 0.183784127234910 \tabularnewline
32 & 0.751589526125174 & 0.496820947749651 & 0.248410473874825 \tabularnewline
33 & 0.670331806649524 & 0.659336386700952 & 0.329668193350476 \tabularnewline
34 & 0.908353813768195 & 0.183292372463609 & 0.0916461862318046 \tabularnewline
35 & 0.89920171159073 & 0.201596576818539 & 0.100798288409269 \tabularnewline
36 & 0.830725089011113 & 0.338549821977775 & 0.169274910988887 \tabularnewline
37 & 0.749669861010074 & 0.500660277979851 & 0.250330138989926 \tabularnewline
38 & 0.622868709635998 & 0.754262580728004 & 0.377131290364002 \tabularnewline
39 & 0.447520000251892 & 0.895040000503784 & 0.552479999748108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59027&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]19[/C][C]0.691086679733819[/C][C]0.617826640532363[/C][C]0.308913320266181[/C][/ROW]
[ROW][C]20[/C][C]0.664736679999258[/C][C]0.670526640001485[/C][C]0.335263320000742[/C][/ROW]
[ROW][C]21[/C][C]0.675288837996795[/C][C]0.64942232400641[/C][C]0.324711162003205[/C][/ROW]
[ROW][C]22[/C][C]0.641897275547751[/C][C]0.716205448904498[/C][C]0.358102724452249[/C][/ROW]
[ROW][C]23[/C][C]0.51609907315644[/C][C]0.96780185368712[/C][C]0.48390092684356[/C][/ROW]
[ROW][C]24[/C][C]0.695828886027641[/C][C]0.608342227944717[/C][C]0.304171113972359[/C][/ROW]
[ROW][C]25[/C][C]0.599940467140129[/C][C]0.800119065719741[/C][C]0.400059532859871[/C][/ROW]
[ROW][C]26[/C][C]0.537315255538778[/C][C]0.925369488922444[/C][C]0.462684744461222[/C][/ROW]
[ROW][C]27[/C][C]0.494781428862289[/C][C]0.989562857724578[/C][C]0.505218571137711[/C][/ROW]
[ROW][C]28[/C][C]0.643927965987226[/C][C]0.712144068025548[/C][C]0.356072034012774[/C][/ROW]
[ROW][C]29[/C][C]0.641905172318740[/C][C]0.716189655362519[/C][C]0.358094827681260[/C][/ROW]
[ROW][C]30[/C][C]0.543873711613285[/C][C]0.912252576773429[/C][C]0.456126288386714[/C][/ROW]
[ROW][C]31[/C][C]0.81621587276509[/C][C]0.367568254469821[/C][C]0.183784127234910[/C][/ROW]
[ROW][C]32[/C][C]0.751589526125174[/C][C]0.496820947749651[/C][C]0.248410473874825[/C][/ROW]
[ROW][C]33[/C][C]0.670331806649524[/C][C]0.659336386700952[/C][C]0.329668193350476[/C][/ROW]
[ROW][C]34[/C][C]0.908353813768195[/C][C]0.183292372463609[/C][C]0.0916461862318046[/C][/ROW]
[ROW][C]35[/C][C]0.89920171159073[/C][C]0.201596576818539[/C][C]0.100798288409269[/C][/ROW]
[ROW][C]36[/C][C]0.830725089011113[/C][C]0.338549821977775[/C][C]0.169274910988887[/C][/ROW]
[ROW][C]37[/C][C]0.749669861010074[/C][C]0.500660277979851[/C][C]0.250330138989926[/C][/ROW]
[ROW][C]38[/C][C]0.622868709635998[/C][C]0.754262580728004[/C][C]0.377131290364002[/C][/ROW]
[ROW][C]39[/C][C]0.447520000251892[/C][C]0.895040000503784[/C][C]0.552479999748108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59027&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59027&T=5

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


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.6910866797338190.6178266405323630.308913320266181
200.6647366799992580.6705266400014850.335263320000742
210.6752888379967950.649422324006410.324711162003205
220.6418972755477510.7162054489044980.358102724452249
230.516099073156440.967801853687120.48390092684356
240.6958288860276410.6083422279447170.304171113972359
250.5999404671401290.8001190657197410.400059532859871
260.5373152555387780.9253694889224440.462684744461222
270.4947814288622890.9895628577245780.505218571137711
280.6439279659872260.7121440680255480.356072034012774
290.6419051723187400.7161896553625190.358094827681260
300.5438737116132850.9122525767734290.456126288386714
310.816215872765090.3675682544698210.183784127234910
320.7515895261251740.4968209477496510.248410473874825
330.6703318066495240.6593363867009520.329668193350476
340.9083538137681950.1832923724636090.0916461862318046
350.899201711590730.2015965768185390.100798288409269
360.8307250890111130.3385498219777750.169274910988887
370.7496698610100740.5006602779798510.250330138989926
380.6228687096359980.7542625807280040.377131290364002
390.4475200002518920.8950400005037840.552479999748108






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

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59027&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59027&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59027&T=6

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


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

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


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 2 ; 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')
}