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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 13:28:44 -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/t1259094574kr5saqyy8plxbeb.htm/, Retrieved Sat, 12 Oct 2024 11:42:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59267, Retrieved Sat, 12 Oct 2024 11:42:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsJSSHWR1
Estimated Impact225
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] [Ws7] [2009-11-20 12:14:35] [786e067c4f7cec17385c4742b96b6dfa]
-    D        [Multiple Regression] [Revieuw] [2009-11-24 20:28:44] [c8fd62404619100d8e91184019148412] [Current]
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Dataseries X:
132.92	138.04	136.51	131.02	126.51
129.61	132.92	138.04	136.51	131.02
122.96	129.61	132.92	138.04	136.51
124.04	122.96	129.61	132.92	138.04
121.29	124.04	122.96	129.61	132.92
124.56	121.29	124.04	122.96	129.61
118.53	124.56	121.29	124.04	122.96
113.14	118.53	124.56	121.29	124.04
114.15	113.14	118.53	124.56	121.29
122.17	114.15	113.14	118.53	124.56
129.23	122.17	114.15	113.14	118.53
131.19	129.23	122.17	114.15	113.14
129.12	131.19	129.23	122.17	114.15
128.28	129.12	131.19	129.23	122.17
126.83	128.28	129.12	131.19	129.23
138.13	126.83	128.28	129.12	131.19
140.52	138.13	126.83	128.28	129.12
146.83	140.52	138.13	126.83	128.28
135.14	146.83	140.52	138.13	126.83
131.84	135.14	146.83	140.52	138.13
125.7	131.84	135.14	146.83	140.52
128.98	125.7	131.84	135.14	146.83
133.25	128.98	125.7	131.84	135.14
136.76	133.25	128.98	125.7	131.84
133.24	136.76	133.25	128.98	125.7
128.54	133.24	136.76	133.25	128.98
121.08	128.54	133.24	136.76	133.25
120.23	121.08	128.54	133.24	136.76
119.08	120.23	121.08	128.54	133.24
125.75	119.08	120.23	121.08	128.54
126.89	125.75	119.08	120.23	121.08
126.6	126.89	125.75	119.08	120.23
121.89	126.6	126.89	125.75	119.08
123.44	121.89	126.6	126.89	125.75
126.46	123.44	121.89	126.6	126.89
129.49	126.46	123.44	121.89	126.6
127.78	129.49	126.46	123.44	121.89
125.29	127.78	129.49	126.46	123.44
119.02	125.29	127.78	129.49	126.46
119.96	119.02	125.29	127.78	129.49
122.86	119.96	119.02	125.29	127.78
131.89	122.86	119.96	119.02	125.29
132.73	131.89	122.86	119.96	119.02
135.01	132.73	131.89	122.86	119.96
136.71	135.01	132.73	131.89	122.86
142.73	136.71	135.01	132.73	131.89
144.43	142.73	136.71	135.01	132.73
144.93	144.43	142.73	136.71	135.01
138.75	144.93	144.43	142.73	136.71
130.22	138.75	144.93	144.43	142.73
122.19	130.22	138.75	144.93	144.43
128.4	122.19	130.22	138.75	144.93
140.43	128.4	122.19	130.22	138.75
153.5	140.43	128.4	122.19	130.22
149.33	153.5	140.43	128.4	122.19
142.97	149.33	153.5	140.43	128.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59267&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]4 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=59267&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59267&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 15.1051730064618 + 1.51203729325094`Y[t-1]`[t] -0.615089404620718`Y[t-2]`[t] -0.323100184191052`Y[t-3]`[t] + 0.296459446705439`Y[t-4]`[t] -2.20171905517736M1[t] + 0.712293154424418M2[t] -2.17351756400950M3[t] + 6.28391154924662M4[t] -0.573360721088252M5[t] + 4.54706471258425M6[t] -6.44161928890922M7[t] + 1.40686131961080M8[t] + 1.31742230283138M9[t] + 4.89880448576374M10[t] + 1.11412070259176M11[t] + 0.037816028123414t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  15.1051730064618 +  1.51203729325094`Y[t-1]`[t] -0.615089404620718`Y[t-2]`[t] -0.323100184191052`Y[t-3]`[t] +  0.296459446705439`Y[t-4]`[t] -2.20171905517736M1[t] +  0.712293154424418M2[t] -2.17351756400950M3[t] +  6.28391154924662M4[t] -0.573360721088252M5[t] +  4.54706471258425M6[t] -6.44161928890922M7[t] +  1.40686131961080M8[t] +  1.31742230283138M9[t] +  4.89880448576374M10[t] +  1.11412070259176M11[t] +  0.037816028123414t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59267&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  15.1051730064618 +  1.51203729325094`Y[t-1]`[t] -0.615089404620718`Y[t-2]`[t] -0.323100184191052`Y[t-3]`[t] +  0.296459446705439`Y[t-4]`[t] -2.20171905517736M1[t] +  0.712293154424418M2[t] -2.17351756400950M3[t] +  6.28391154924662M4[t] -0.573360721088252M5[t] +  4.54706471258425M6[t] -6.44161928890922M7[t] +  1.40686131961080M8[t] +  1.31742230283138M9[t] +  4.89880448576374M10[t] +  1.11412070259176M11[t] +  0.037816028123414t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59267&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59267&T=1

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 15.1051730064618 + 1.51203729325094`Y[t-1]`[t] -0.615089404620718`Y[t-2]`[t] -0.323100184191052`Y[t-3]`[t] + 0.296459446705439`Y[t-4]`[t] -2.20171905517736M1[t] + 0.712293154424418M2[t] -2.17351756400950M3[t] + 6.28391154924662M4[t] -0.573360721088252M5[t] + 4.54706471258425M6[t] -6.44161928890922M7[t] + 1.40686131961080M8[t] + 1.31742230283138M9[t] + 4.89880448576374M10[t] + 1.11412070259176M11[t] + 0.037816028123414t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)15.10517300646189.337521.61770.1137910.056896
`Y[t-1]`1.512037293250940.1539069.824400
`Y[t-2]`-0.6150894046207180.280843-2.19020.0345580.017279
`Y[t-3]`-0.3231001841910520.28643-1.1280.2662020.133101
`Y[t-4]`0.2964594467054390.1609781.84160.0731460.036573
M1-2.201719055177362.115769-1.04060.3044590.152229
M20.7122931544244182.2649170.31450.7548250.377413
M3-2.173517564009502.441033-0.89040.3787060.189353
M46.283911549246622.2461452.79760.0079560.003978
M5-0.5733607210882522.484979-0.23070.818730.409365
M64.547064712584251.9432122.340.0244970.012248
M7-6.441619288909222.32824-2.76670.0086120.004306
M81.406861319610802.3357780.60230.5504540.275227
M91.317422302831382.9503690.44650.6576860.328843
M104.898804485763742.1290842.30090.0268290.013415
M111.114120702591762.3241720.47940.6343580.317179
t0.0378160281234140.0257891.46640.1505640.075282

\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) & 15.1051730064618 & 9.33752 & 1.6177 & 0.113791 & 0.056896 \tabularnewline
`Y[t-1]` & 1.51203729325094 & 0.153906 & 9.8244 & 0 & 0 \tabularnewline
`Y[t-2]` & -0.615089404620718 & 0.280843 & -2.1902 & 0.034558 & 0.017279 \tabularnewline
`Y[t-3]` & -0.323100184191052 & 0.28643 & -1.128 & 0.266202 & 0.133101 \tabularnewline
`Y[t-4]` & 0.296459446705439 & 0.160978 & 1.8416 & 0.073146 & 0.036573 \tabularnewline
M1 & -2.20171905517736 & 2.115769 & -1.0406 & 0.304459 & 0.152229 \tabularnewline
M2 & 0.712293154424418 & 2.264917 & 0.3145 & 0.754825 & 0.377413 \tabularnewline
M3 & -2.17351756400950 & 2.441033 & -0.8904 & 0.378706 & 0.189353 \tabularnewline
M4 & 6.28391154924662 & 2.246145 & 2.7976 & 0.007956 & 0.003978 \tabularnewline
M5 & -0.573360721088252 & 2.484979 & -0.2307 & 0.81873 & 0.409365 \tabularnewline
M6 & 4.54706471258425 & 1.943212 & 2.34 & 0.024497 & 0.012248 \tabularnewline
M7 & -6.44161928890922 & 2.32824 & -2.7667 & 0.008612 & 0.004306 \tabularnewline
M8 & 1.40686131961080 & 2.335778 & 0.6023 & 0.550454 & 0.275227 \tabularnewline
M9 & 1.31742230283138 & 2.950369 & 0.4465 & 0.657686 & 0.328843 \tabularnewline
M10 & 4.89880448576374 & 2.129084 & 2.3009 & 0.026829 & 0.013415 \tabularnewline
M11 & 1.11412070259176 & 2.324172 & 0.4794 & 0.634358 & 0.317179 \tabularnewline
t & 0.037816028123414 & 0.025789 & 1.4664 & 0.150564 & 0.075282 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59267&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]15.1051730064618[/C][C]9.33752[/C][C]1.6177[/C][C]0.113791[/C][C]0.056896[/C][/ROW]
[ROW][C]`Y[t-1]`[/C][C]1.51203729325094[/C][C]0.153906[/C][C]9.8244[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Y[t-2]`[/C][C]-0.615089404620718[/C][C]0.280843[/C][C]-2.1902[/C][C]0.034558[/C][C]0.017279[/C][/ROW]
[ROW][C]`Y[t-3]`[/C][C]-0.323100184191052[/C][C]0.28643[/C][C]-1.128[/C][C]0.266202[/C][C]0.133101[/C][/ROW]
[ROW][C]`Y[t-4]`[/C][C]0.296459446705439[/C][C]0.160978[/C][C]1.8416[/C][C]0.073146[/C][C]0.036573[/C][/ROW]
[ROW][C]M1[/C][C]-2.20171905517736[/C][C]2.115769[/C][C]-1.0406[/C][C]0.304459[/C][C]0.152229[/C][/ROW]
[ROW][C]M2[/C][C]0.712293154424418[/C][C]2.264917[/C][C]0.3145[/C][C]0.754825[/C][C]0.377413[/C][/ROW]
[ROW][C]M3[/C][C]-2.17351756400950[/C][C]2.441033[/C][C]-0.8904[/C][C]0.378706[/C][C]0.189353[/C][/ROW]
[ROW][C]M4[/C][C]6.28391154924662[/C][C]2.246145[/C][C]2.7976[/C][C]0.007956[/C][C]0.003978[/C][/ROW]
[ROW][C]M5[/C][C]-0.573360721088252[/C][C]2.484979[/C][C]-0.2307[/C][C]0.81873[/C][C]0.409365[/C][/ROW]
[ROW][C]M6[/C][C]4.54706471258425[/C][C]1.943212[/C][C]2.34[/C][C]0.024497[/C][C]0.012248[/C][/ROW]
[ROW][C]M7[/C][C]-6.44161928890922[/C][C]2.32824[/C][C]-2.7667[/C][C]0.008612[/C][C]0.004306[/C][/ROW]
[ROW][C]M8[/C][C]1.40686131961080[/C][C]2.335778[/C][C]0.6023[/C][C]0.550454[/C][C]0.275227[/C][/ROW]
[ROW][C]M9[/C][C]1.31742230283138[/C][C]2.950369[/C][C]0.4465[/C][C]0.657686[/C][C]0.328843[/C][/ROW]
[ROW][C]M10[/C][C]4.89880448576374[/C][C]2.129084[/C][C]2.3009[/C][C]0.026829[/C][C]0.013415[/C][/ROW]
[ROW][C]M11[/C][C]1.11412070259176[/C][C]2.324172[/C][C]0.4794[/C][C]0.634358[/C][C]0.317179[/C][/ROW]
[ROW][C]t[/C][C]0.037816028123414[/C][C]0.025789[/C][C]1.4664[/C][C]0.150564[/C][C]0.075282[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59267&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59267&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)15.10517300646189.337521.61770.1137910.056896
`Y[t-1]`1.512037293250940.1539069.824400
`Y[t-2]`-0.6150894046207180.280843-2.19020.0345580.017279
`Y[t-3]`-0.3231001841910520.28643-1.1280.2662020.133101
`Y[t-4]`0.2964594467054390.1609781.84160.0731460.036573
M1-2.201719055177362.115769-1.04060.3044590.152229
M20.7122931544244182.2649170.31450.7548250.377413
M3-2.173517564009502.441033-0.89040.3787060.189353
M46.283911549246622.2461452.79760.0079560.003978
M5-0.5733607210882522.484979-0.23070.818730.409365
M64.547064712584251.9432122.340.0244970.012248
M7-6.441619288909222.32824-2.76670.0086120.004306
M81.406861319610802.3357780.60230.5504540.275227
M91.317422302831382.9503690.44650.6576860.328843
M104.898804485763742.1290842.30090.0268290.013415
M111.114120702591762.3241720.47940.6343580.317179
t0.0378160281234140.0257891.46640.1505640.075282







Multiple Linear Regression - Regression Statistics
Multiple R0.964424788006357
R-squared0.930115171721107
Adjusted R-squared0.901444472940023
F-TEST (value)32.4413150451275
F-TEST (DF numerator)16
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.77372047228213
Sum Squared Residuals300.047485075922

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.964424788006357 \tabularnewline
R-squared & 0.930115171721107 \tabularnewline
Adjusted R-squared & 0.901444472940023 \tabularnewline
F-TEST (value) & 32.4413150451275 \tabularnewline
F-TEST (DF numerator) & 16 \tabularnewline
F-TEST (DF denominator) & 39 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 2.77372047228213 \tabularnewline
Sum Squared Residuals & 300.047485075922 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59267&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.964424788006357[/C][/ROW]
[ROW][C]R-squared[/C][C]0.930115171721107[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.901444472940023[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]32.4413150451275[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]16[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]39[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]2.77372047228213[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]300.047485075922[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59267&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59267&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 R0.964424788006357
R-squared0.930115171721107
Adjusted R-squared0.901444472940023
F-TEST (value)32.4413150451275
F-TEST (DF numerator)16
F-TEST (DF denominator)39
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.77372047228213
Sum Squared Residuals300.047485075922







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1132.92132.8695417849870.0504582150127606
2129.61126.7018643856302.90813561436963
3122.96123.131503086918-0.171503086917884
4124.04125.715502053991-1.67550205399069
5121.29124.170979871759-2.88097987175857
6124.56125.674157676400-1.11415767639953
7118.53119.038743995150-0.508743995149505
8113.14117.004815109347-3.86481510934728
9114.15110.6404991391873.50950086081307
10122.17122.0199034087310.150096591269331
11129.23129.732193976044-0.502193976043713
12131.19132.473607963094-1.28360796309354
13129.12126.6389273981492.48107260185056
14128.28125.3517806679772.92821933202262
15126.83123.9666370516272.86336294837310
16138.13132.0359811144926.09401888550788
17140.52142.852159022757-2.33215902275655
18146.83144.8931286750531.93687132494742
19135.14137.932254065971-2.7922540659707
20131.84126.8394029089095.00059709109134
21125.7127.658227907921-1.95822790792126
22128.98129.671012435569-0.691012435569362
23133.25132.2608956225990.989104377401063
24136.76136.6290158999610.130984100038700
25133.24134.265902407570-1.02590240756961
26128.54129.329144761531-0.789144761530856
27121.08121.671489688127-0.591489688127453
28120.23123.955742129861-3.72574212986093
29119.08120.914654760152-1.83465476015155
30125.75125.873847303186-0.12384730318616
31126.89123.7786685752543.11133142474646
32126.6129.405616079503-2.80561607950294
33121.89125.718293762271-3.82829376227096
34123.44124.003222549002-0.5632225490023
35126.46125.9287465169160.531253483084114
36129.49129.901234518899-0.41123451889852
37127.78128.564105208962-0.784105208961647
38125.29126.550378365363-1.26037836536338
39119.02120.905527667711-1.88552766771102
40119.96122.902645036397-2.9426450363969
41122.86121.6586882215831.20131177841736
42131.89131.911307926044-0.0213079260441995
43132.73130.6678625333472.06213746665265
44135.01133.6116945183461.39830548165445
45136.71134.4329791906212.27702080937915
46142.73141.6258616066981.10413839330233
47144.43145.448163884441-1.01816388444147
48144.93143.3661416180471.56385838195336
49138.75139.471523200332-0.721523200332063
50130.22134.006831819498-3.78683181949801
51122.19122.404842505617-0.214842505616743
52128.4126.1501296652592.24987033474065
53140.43134.5835181237515.84648187624932
54153.5154.177558419318-0.677558419317529
55149.33151.202470830279-1.87247083027891
56142.97142.6984713838960.271528616104431

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 132.92 & 132.869541784987 & 0.0504582150127606 \tabularnewline
2 & 129.61 & 126.701864385630 & 2.90813561436963 \tabularnewline
3 & 122.96 & 123.131503086918 & -0.171503086917884 \tabularnewline
4 & 124.04 & 125.715502053991 & -1.67550205399069 \tabularnewline
5 & 121.29 & 124.170979871759 & -2.88097987175857 \tabularnewline
6 & 124.56 & 125.674157676400 & -1.11415767639953 \tabularnewline
7 & 118.53 & 119.038743995150 & -0.508743995149505 \tabularnewline
8 & 113.14 & 117.004815109347 & -3.86481510934728 \tabularnewline
9 & 114.15 & 110.640499139187 & 3.50950086081307 \tabularnewline
10 & 122.17 & 122.019903408731 & 0.150096591269331 \tabularnewline
11 & 129.23 & 129.732193976044 & -0.502193976043713 \tabularnewline
12 & 131.19 & 132.473607963094 & -1.28360796309354 \tabularnewline
13 & 129.12 & 126.638927398149 & 2.48107260185056 \tabularnewline
14 & 128.28 & 125.351780667977 & 2.92821933202262 \tabularnewline
15 & 126.83 & 123.966637051627 & 2.86336294837310 \tabularnewline
16 & 138.13 & 132.035981114492 & 6.09401888550788 \tabularnewline
17 & 140.52 & 142.852159022757 & -2.33215902275655 \tabularnewline
18 & 146.83 & 144.893128675053 & 1.93687132494742 \tabularnewline
19 & 135.14 & 137.932254065971 & -2.7922540659707 \tabularnewline
20 & 131.84 & 126.839402908909 & 5.00059709109134 \tabularnewline
21 & 125.7 & 127.658227907921 & -1.95822790792126 \tabularnewline
22 & 128.98 & 129.671012435569 & -0.691012435569362 \tabularnewline
23 & 133.25 & 132.260895622599 & 0.989104377401063 \tabularnewline
24 & 136.76 & 136.629015899961 & 0.130984100038700 \tabularnewline
25 & 133.24 & 134.265902407570 & -1.02590240756961 \tabularnewline
26 & 128.54 & 129.329144761531 & -0.789144761530856 \tabularnewline
27 & 121.08 & 121.671489688127 & -0.591489688127453 \tabularnewline
28 & 120.23 & 123.955742129861 & -3.72574212986093 \tabularnewline
29 & 119.08 & 120.914654760152 & -1.83465476015155 \tabularnewline
30 & 125.75 & 125.873847303186 & -0.12384730318616 \tabularnewline
31 & 126.89 & 123.778668575254 & 3.11133142474646 \tabularnewline
32 & 126.6 & 129.405616079503 & -2.80561607950294 \tabularnewline
33 & 121.89 & 125.718293762271 & -3.82829376227096 \tabularnewline
34 & 123.44 & 124.003222549002 & -0.5632225490023 \tabularnewline
35 & 126.46 & 125.928746516916 & 0.531253483084114 \tabularnewline
36 & 129.49 & 129.901234518899 & -0.41123451889852 \tabularnewline
37 & 127.78 & 128.564105208962 & -0.784105208961647 \tabularnewline
38 & 125.29 & 126.550378365363 & -1.26037836536338 \tabularnewline
39 & 119.02 & 120.905527667711 & -1.88552766771102 \tabularnewline
40 & 119.96 & 122.902645036397 & -2.9426450363969 \tabularnewline
41 & 122.86 & 121.658688221583 & 1.20131177841736 \tabularnewline
42 & 131.89 & 131.911307926044 & -0.0213079260441995 \tabularnewline
43 & 132.73 & 130.667862533347 & 2.06213746665265 \tabularnewline
44 & 135.01 & 133.611694518346 & 1.39830548165445 \tabularnewline
45 & 136.71 & 134.432979190621 & 2.27702080937915 \tabularnewline
46 & 142.73 & 141.625861606698 & 1.10413839330233 \tabularnewline
47 & 144.43 & 145.448163884441 & -1.01816388444147 \tabularnewline
48 & 144.93 & 143.366141618047 & 1.56385838195336 \tabularnewline
49 & 138.75 & 139.471523200332 & -0.721523200332063 \tabularnewline
50 & 130.22 & 134.006831819498 & -3.78683181949801 \tabularnewline
51 & 122.19 & 122.404842505617 & -0.214842505616743 \tabularnewline
52 & 128.4 & 126.150129665259 & 2.24987033474065 \tabularnewline
53 & 140.43 & 134.583518123751 & 5.84648187624932 \tabularnewline
54 & 153.5 & 154.177558419318 & -0.677558419317529 \tabularnewline
55 & 149.33 & 151.202470830279 & -1.87247083027891 \tabularnewline
56 & 142.97 & 142.698471383896 & 0.271528616104431 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59267&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]132.92[/C][C]132.869541784987[/C][C]0.0504582150127606[/C][/ROW]
[ROW][C]2[/C][C]129.61[/C][C]126.701864385630[/C][C]2.90813561436963[/C][/ROW]
[ROW][C]3[/C][C]122.96[/C][C]123.131503086918[/C][C]-0.171503086917884[/C][/ROW]
[ROW][C]4[/C][C]124.04[/C][C]125.715502053991[/C][C]-1.67550205399069[/C][/ROW]
[ROW][C]5[/C][C]121.29[/C][C]124.170979871759[/C][C]-2.88097987175857[/C][/ROW]
[ROW][C]6[/C][C]124.56[/C][C]125.674157676400[/C][C]-1.11415767639953[/C][/ROW]
[ROW][C]7[/C][C]118.53[/C][C]119.038743995150[/C][C]-0.508743995149505[/C][/ROW]
[ROW][C]8[/C][C]113.14[/C][C]117.004815109347[/C][C]-3.86481510934728[/C][/ROW]
[ROW][C]9[/C][C]114.15[/C][C]110.640499139187[/C][C]3.50950086081307[/C][/ROW]
[ROW][C]10[/C][C]122.17[/C][C]122.019903408731[/C][C]0.150096591269331[/C][/ROW]
[ROW][C]11[/C][C]129.23[/C][C]129.732193976044[/C][C]-0.502193976043713[/C][/ROW]
[ROW][C]12[/C][C]131.19[/C][C]132.473607963094[/C][C]-1.28360796309354[/C][/ROW]
[ROW][C]13[/C][C]129.12[/C][C]126.638927398149[/C][C]2.48107260185056[/C][/ROW]
[ROW][C]14[/C][C]128.28[/C][C]125.351780667977[/C][C]2.92821933202262[/C][/ROW]
[ROW][C]15[/C][C]126.83[/C][C]123.966637051627[/C][C]2.86336294837310[/C][/ROW]
[ROW][C]16[/C][C]138.13[/C][C]132.035981114492[/C][C]6.09401888550788[/C][/ROW]
[ROW][C]17[/C][C]140.52[/C][C]142.852159022757[/C][C]-2.33215902275655[/C][/ROW]
[ROW][C]18[/C][C]146.83[/C][C]144.893128675053[/C][C]1.93687132494742[/C][/ROW]
[ROW][C]19[/C][C]135.14[/C][C]137.932254065971[/C][C]-2.7922540659707[/C][/ROW]
[ROW][C]20[/C][C]131.84[/C][C]126.839402908909[/C][C]5.00059709109134[/C][/ROW]
[ROW][C]21[/C][C]125.7[/C][C]127.658227907921[/C][C]-1.95822790792126[/C][/ROW]
[ROW][C]22[/C][C]128.98[/C][C]129.671012435569[/C][C]-0.691012435569362[/C][/ROW]
[ROW][C]23[/C][C]133.25[/C][C]132.260895622599[/C][C]0.989104377401063[/C][/ROW]
[ROW][C]24[/C][C]136.76[/C][C]136.629015899961[/C][C]0.130984100038700[/C][/ROW]
[ROW][C]25[/C][C]133.24[/C][C]134.265902407570[/C][C]-1.02590240756961[/C][/ROW]
[ROW][C]26[/C][C]128.54[/C][C]129.329144761531[/C][C]-0.789144761530856[/C][/ROW]
[ROW][C]27[/C][C]121.08[/C][C]121.671489688127[/C][C]-0.591489688127453[/C][/ROW]
[ROW][C]28[/C][C]120.23[/C][C]123.955742129861[/C][C]-3.72574212986093[/C][/ROW]
[ROW][C]29[/C][C]119.08[/C][C]120.914654760152[/C][C]-1.83465476015155[/C][/ROW]
[ROW][C]30[/C][C]125.75[/C][C]125.873847303186[/C][C]-0.12384730318616[/C][/ROW]
[ROW][C]31[/C][C]126.89[/C][C]123.778668575254[/C][C]3.11133142474646[/C][/ROW]
[ROW][C]32[/C][C]126.6[/C][C]129.405616079503[/C][C]-2.80561607950294[/C][/ROW]
[ROW][C]33[/C][C]121.89[/C][C]125.718293762271[/C][C]-3.82829376227096[/C][/ROW]
[ROW][C]34[/C][C]123.44[/C][C]124.003222549002[/C][C]-0.5632225490023[/C][/ROW]
[ROW][C]35[/C][C]126.46[/C][C]125.928746516916[/C][C]0.531253483084114[/C][/ROW]
[ROW][C]36[/C][C]129.49[/C][C]129.901234518899[/C][C]-0.41123451889852[/C][/ROW]
[ROW][C]37[/C][C]127.78[/C][C]128.564105208962[/C][C]-0.784105208961647[/C][/ROW]
[ROW][C]38[/C][C]125.29[/C][C]126.550378365363[/C][C]-1.26037836536338[/C][/ROW]
[ROW][C]39[/C][C]119.02[/C][C]120.905527667711[/C][C]-1.88552766771102[/C][/ROW]
[ROW][C]40[/C][C]119.96[/C][C]122.902645036397[/C][C]-2.9426450363969[/C][/ROW]
[ROW][C]41[/C][C]122.86[/C][C]121.658688221583[/C][C]1.20131177841736[/C][/ROW]
[ROW][C]42[/C][C]131.89[/C][C]131.911307926044[/C][C]-0.0213079260441995[/C][/ROW]
[ROW][C]43[/C][C]132.73[/C][C]130.667862533347[/C][C]2.06213746665265[/C][/ROW]
[ROW][C]44[/C][C]135.01[/C][C]133.611694518346[/C][C]1.39830548165445[/C][/ROW]
[ROW][C]45[/C][C]136.71[/C][C]134.432979190621[/C][C]2.27702080937915[/C][/ROW]
[ROW][C]46[/C][C]142.73[/C][C]141.625861606698[/C][C]1.10413839330233[/C][/ROW]
[ROW][C]47[/C][C]144.43[/C][C]145.448163884441[/C][C]-1.01816388444147[/C][/ROW]
[ROW][C]48[/C][C]144.93[/C][C]143.366141618047[/C][C]1.56385838195336[/C][/ROW]
[ROW][C]49[/C][C]138.75[/C][C]139.471523200332[/C][C]-0.721523200332063[/C][/ROW]
[ROW][C]50[/C][C]130.22[/C][C]134.006831819498[/C][C]-3.78683181949801[/C][/ROW]
[ROW][C]51[/C][C]122.19[/C][C]122.404842505617[/C][C]-0.214842505616743[/C][/ROW]
[ROW][C]52[/C][C]128.4[/C][C]126.150129665259[/C][C]2.24987033474065[/C][/ROW]
[ROW][C]53[/C][C]140.43[/C][C]134.583518123751[/C][C]5.84648187624932[/C][/ROW]
[ROW][C]54[/C][C]153.5[/C][C]154.177558419318[/C][C]-0.677558419317529[/C][/ROW]
[ROW][C]55[/C][C]149.33[/C][C]151.202470830279[/C][C]-1.87247083027891[/C][/ROW]
[ROW][C]56[/C][C]142.97[/C][C]142.698471383896[/C][C]0.271528616104431[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59267&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59267&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
1132.92132.8695417849870.0504582150127606
2129.61126.7018643856302.90813561436963
3122.96123.131503086918-0.171503086917884
4124.04125.715502053991-1.67550205399069
5121.29124.170979871759-2.88097987175857
6124.56125.674157676400-1.11415767639953
7118.53119.038743995150-0.508743995149505
8113.14117.004815109347-3.86481510934728
9114.15110.6404991391873.50950086081307
10122.17122.0199034087310.150096591269331
11129.23129.732193976044-0.502193976043713
12131.19132.473607963094-1.28360796309354
13129.12126.6389273981492.48107260185056
14128.28125.3517806679772.92821933202262
15126.83123.9666370516272.86336294837310
16138.13132.0359811144926.09401888550788
17140.52142.852159022757-2.33215902275655
18146.83144.8931286750531.93687132494742
19135.14137.932254065971-2.7922540659707
20131.84126.8394029089095.00059709109134
21125.7127.658227907921-1.95822790792126
22128.98129.671012435569-0.691012435569362
23133.25132.2608956225990.989104377401063
24136.76136.6290158999610.130984100038700
25133.24134.265902407570-1.02590240756961
26128.54129.329144761531-0.789144761530856
27121.08121.671489688127-0.591489688127453
28120.23123.955742129861-3.72574212986093
29119.08120.914654760152-1.83465476015155
30125.75125.873847303186-0.12384730318616
31126.89123.7786685752543.11133142474646
32126.6129.405616079503-2.80561607950294
33121.89125.718293762271-3.82829376227096
34123.44124.003222549002-0.5632225490023
35126.46125.9287465169160.531253483084114
36129.49129.901234518899-0.41123451889852
37127.78128.564105208962-0.784105208961647
38125.29126.550378365363-1.26037836536338
39119.02120.905527667711-1.88552766771102
40119.96122.902645036397-2.9426450363969
41122.86121.6586882215831.20131177841736
42131.89131.911307926044-0.0213079260441995
43132.73130.6678625333472.06213746665265
44135.01133.6116945183461.39830548165445
45136.71134.4329791906212.27702080937915
46142.73141.6258616066981.10413839330233
47144.43145.448163884441-1.01816388444147
48144.93143.3661416180471.56385838195336
49138.75139.471523200332-0.721523200332063
50130.22134.006831819498-3.78683181949801
51122.19122.404842505617-0.214842505616743
52128.4126.1501296652592.24987033474065
53140.43134.5835181237515.84648187624932
54153.5154.177558419318-0.677558419317529
55149.33151.202470830279-1.87247083027891
56142.97142.6984713838960.271528616104431







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
200.876393027049560.2472139459008790.123606972950440
210.9358675016112080.1282649967775830.0641324983887917
220.9795522728684940.04089545426301270.0204477271315063
230.9628881592660920.0742236814678170.0371118407339085
240.9478813452098140.1042373095803720.0521186547901859
250.9484366085880080.1031267828239830.0515633914119915
260.9863857610984320.02722847780313520.0136142389015676
270.9864051776058710.02718964478825730.0135948223941287
280.985906245186740.02818750962651890.0140937548132594
290.9715691195006790.05686176099864180.0284308804993209
300.9846890941247720.03062181175045650.0153109058752282
310.9971197041281380.005760591743724550.00288029587186228
320.9952188926340770.009562214731846120.00478110736592306
330.993368512260780.01326297547844130.00663148773922064
340.981505465316390.03698906936721740.0184945346836087
350.9463184515356340.1073630969287320.0536815484643659
360.9949540980832640.01009180383347160.00504590191673582

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
20 & 0.87639302704956 & 0.247213945900879 & 0.123606972950440 \tabularnewline
21 & 0.935867501611208 & 0.128264996777583 & 0.0641324983887917 \tabularnewline
22 & 0.979552272868494 & 0.0408954542630127 & 0.0204477271315063 \tabularnewline
23 & 0.962888159266092 & 0.074223681467817 & 0.0371118407339085 \tabularnewline
24 & 0.947881345209814 & 0.104237309580372 & 0.0521186547901859 \tabularnewline
25 & 0.948436608588008 & 0.103126782823983 & 0.0515633914119915 \tabularnewline
26 & 0.986385761098432 & 0.0272284778031352 & 0.0136142389015676 \tabularnewline
27 & 0.986405177605871 & 0.0271896447882573 & 0.0135948223941287 \tabularnewline
28 & 0.98590624518674 & 0.0281875096265189 & 0.0140937548132594 \tabularnewline
29 & 0.971569119500679 & 0.0568617609986418 & 0.0284308804993209 \tabularnewline
30 & 0.984689094124772 & 0.0306218117504565 & 0.0153109058752282 \tabularnewline
31 & 0.997119704128138 & 0.00576059174372455 & 0.00288029587186228 \tabularnewline
32 & 0.995218892634077 & 0.00956221473184612 & 0.00478110736592306 \tabularnewline
33 & 0.99336851226078 & 0.0132629754784413 & 0.00663148773922064 \tabularnewline
34 & 0.98150546531639 & 0.0369890693672174 & 0.0184945346836087 \tabularnewline
35 & 0.946318451535634 & 0.107363096928732 & 0.0536815484643659 \tabularnewline
36 & 0.994954098083264 & 0.0100918038334716 & 0.00504590191673582 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59267&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]20[/C][C]0.87639302704956[/C][C]0.247213945900879[/C][C]0.123606972950440[/C][/ROW]
[ROW][C]21[/C][C]0.935867501611208[/C][C]0.128264996777583[/C][C]0.0641324983887917[/C][/ROW]
[ROW][C]22[/C][C]0.979552272868494[/C][C]0.0408954542630127[/C][C]0.0204477271315063[/C][/ROW]
[ROW][C]23[/C][C]0.962888159266092[/C][C]0.074223681467817[/C][C]0.0371118407339085[/C][/ROW]
[ROW][C]24[/C][C]0.947881345209814[/C][C]0.104237309580372[/C][C]0.0521186547901859[/C][/ROW]
[ROW][C]25[/C][C]0.948436608588008[/C][C]0.103126782823983[/C][C]0.0515633914119915[/C][/ROW]
[ROW][C]26[/C][C]0.986385761098432[/C][C]0.0272284778031352[/C][C]0.0136142389015676[/C][/ROW]
[ROW][C]27[/C][C]0.986405177605871[/C][C]0.0271896447882573[/C][C]0.0135948223941287[/C][/ROW]
[ROW][C]28[/C][C]0.98590624518674[/C][C]0.0281875096265189[/C][C]0.0140937548132594[/C][/ROW]
[ROW][C]29[/C][C]0.971569119500679[/C][C]0.0568617609986418[/C][C]0.0284308804993209[/C][/ROW]
[ROW][C]30[/C][C]0.984689094124772[/C][C]0.0306218117504565[/C][C]0.0153109058752282[/C][/ROW]
[ROW][C]31[/C][C]0.997119704128138[/C][C]0.00576059174372455[/C][C]0.00288029587186228[/C][/ROW]
[ROW][C]32[/C][C]0.995218892634077[/C][C]0.00956221473184612[/C][C]0.00478110736592306[/C][/ROW]
[ROW][C]33[/C][C]0.99336851226078[/C][C]0.0132629754784413[/C][C]0.00663148773922064[/C][/ROW]
[ROW][C]34[/C][C]0.98150546531639[/C][C]0.0369890693672174[/C][C]0.0184945346836087[/C][/ROW]
[ROW][C]35[/C][C]0.946318451535634[/C][C]0.107363096928732[/C][C]0.0536815484643659[/C][/ROW]
[ROW][C]36[/C][C]0.994954098083264[/C][C]0.0100918038334716[/C][C]0.00504590191673582[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59267&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59267&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
200.876393027049560.2472139459008790.123606972950440
210.9358675016112080.1282649967775830.0641324983887917
220.9795522728684940.04089545426301270.0204477271315063
230.9628881592660920.0742236814678170.0371118407339085
240.9478813452098140.1042373095803720.0521186547901859
250.9484366085880080.1031267828239830.0515633914119915
260.9863857610984320.02722847780313520.0136142389015676
270.9864051776058710.02718964478825730.0135948223941287
280.985906245186740.02818750962651890.0140937548132594
290.9715691195006790.05686176099864180.0284308804993209
300.9846890941247720.03062181175045650.0153109058752282
310.9971197041281380.005760591743724550.00288029587186228
320.9952188926340770.009562214731846120.00478110736592306
330.993368512260780.01326297547844130.00663148773922064
340.981505465316390.03698906936721740.0184945346836087
350.9463184515356340.1073630969287320.0536815484643659
360.9949540980832640.01009180383347160.00504590191673582







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level20.117647058823529NOK
5% type I error level100.588235294117647NOK
10% type I error level120.705882352941177NOK

\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 & 2 & 0.117647058823529 & NOK \tabularnewline
5% type I error level & 10 & 0.588235294117647 & NOK \tabularnewline
10% type I error level & 12 & 0.705882352941177 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59267&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]2[/C][C]0.117647058823529[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]10[/C][C]0.588235294117647[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]12[/C][C]0.705882352941177[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59267&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59267&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 level20.117647058823529NOK
5% type I error level100.588235294117647NOK
10% type I error level120.705882352941177NOK



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')
}