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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 computationThu, 19 Nov 2009 10:07:50 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/19/t1258650970f9u7lkiutefyldd.htm/, Retrieved Tue, 16 Apr 2024 15:57:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57840, Retrieved Tue, 16 Apr 2024 15:57:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact149

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:06:21] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-11-19 17:07:50] [faa1ded5041cd5a0e2be04844f08502a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
29	27	24	25	22	24
26	28	29	24	25	22
26	25	26	29	24	25
21	19	26	26	29	24
23	19	21	26	26	29
22	19	23	21	26	26
21	20	22	23	21	26
16	16	21	22	23	21
19	22	16	21	22	23
16	21	19	16	21	22
25	25	16	19	16	21
27	29	25	16	19	16
23	28	27	25	16	19
22	25	23	27	25	16
23	26	22	23	27	25
20	24	23	22	23	27
24	28	20	23	22	23
23	28	24	20	23	22
20	28	23	24	20	23
21	28	20	23	24	20
22	32	21	20	23	24
17	31	22	21	20	23
21	22	17	22	21	20
19	29	21	17	22	21
23	31	19	21	17	22
22	29	23	19	21	17
15	32	22	23	19	21
23	32	15	22	23	19
21	31	23	15	22	23
18	29	21	23	15	22
18	28	18	21	23	15
18	28	18	18	21	23
18	29	18	18	18	21
10	22	18	18	18	18
13	26	10	18	18	18
10	24	13	10	18	18
9	27	10	13	10	18
9	27	9	10	13	10
6	23	9	9	10	13
11	21	6	9	9	10
9	19	11	6	9	9
10	17	9	11	6	9
9	19	10	9	11	6
16	21	9	10	9	11
10	13	16	9	10	9
7	8	10	16	9	10
7	5	7	10	16	9
14	10	7	7	10	16
11	6	14	7	7	10
10	6	11	14	7	7
6	8	10	11	14	7
8	11	6	10	11	14
13	12	8	6	10	11
12	13	13	8	6	10
15	19	12	13	8	6
16	19	15	12	13	8
16	18	16	15	12	13

Tables (Output of Computation)





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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57840&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57840&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57840&T=0

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


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

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






Multiple Linear Regression - Estimated Regression Equation
s[t] = + 8.53757859793634 + 0.116192357805682consv[t] + 0.431844748244927`y(t-1)`[t] + 0.314619658899698`y(t-2)`[t] -0.104294325773217`y(t-3)`[t] -0.0303437661333572`y(t-4)`[t] -2.05606014705970M1[t] -3.08835545424920M2[t] -4.95092737842675M3[t] -1.76783608517104M4[t] -0.238952069021539M5[t] -2.44084765933435M6[t] -2.88724301052567M7[t] -1.28389824915988M8[t] -1.93079924912808M9[t] -6.85809143702282M10[t] -0.412018727564027M11[t] -0.0810169313766484t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
s[t] =  +  8.53757859793634 +  0.116192357805682consv[t] +  0.431844748244927`y(t-1)`[t] +  0.314619658899698`y(t-2)`[t] -0.104294325773217`y(t-3)`[t] -0.0303437661333572`y(t-4)`[t] -2.05606014705970M1[t] -3.08835545424920M2[t] -4.95092737842675M3[t] -1.76783608517104M4[t] -0.238952069021539M5[t] -2.44084765933435M6[t] -2.88724301052567M7[t] -1.28389824915988M8[t] -1.93079924912808M9[t] -6.85809143702282M10[t] -0.412018727564027M11[t] -0.0810169313766484t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57840&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]s[t] =  +  8.53757859793634 +  0.116192357805682consv[t] +  0.431844748244927`y(t-1)`[t] +  0.314619658899698`y(t-2)`[t] -0.104294325773217`y(t-3)`[t] -0.0303437661333572`y(t-4)`[t] -2.05606014705970M1[t] -3.08835545424920M2[t] -4.95092737842675M3[t] -1.76783608517104M4[t] -0.238952069021539M5[t] -2.44084765933435M6[t] -2.88724301052567M7[t] -1.28389824915988M8[t] -1.93079924912808M9[t] -6.85809143702282M10[t] -0.412018727564027M11[t] -0.0810169313766484t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57840&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57840&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
s[t] = + 8.53757859793634 + 0.116192357805682consv[t] + 0.431844748244927`y(t-1)`[t] + 0.314619658899698`y(t-2)`[t] -0.104294325773217`y(t-3)`[t] -0.0303437661333572`y(t-4)`[t] -2.05606014705970M1[t] -3.08835545424920M2[t] -4.95092737842675M3[t] -1.76783608517104M4[t] -0.238952069021539M5[t] -2.44084765933435M6[t] -2.88724301052567M7[t] -1.28389824915988M8[t] -1.93079924912808M9[t] -6.85809143702282M10[t] -0.412018727564027M11[t] -0.0810169313766484t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)8.537578597936344.843481.76270.0857880.042894
consv0.1161923578056820.0740151.56990.1245280.062264
`y(t-1)`0.4318447482449270.1562822.76320.0086890.004344
`y(t-2)`0.3146196588996980.1713181.83650.073920.03696
`y(t-3)`-0.1042943257732170.17345-0.60130.5511240.275562
`y(t-4)`-0.03034376613335720.167302-0.18140.8570160.428508
M1-2.056060147059702.379737-0.8640.3928780.196439
M2-3.088355454249202.42868-1.27160.211040.10552
M3-4.950927378426752.285318-2.16640.0364530.018226
M4-1.767836085171042.288861-0.77240.4445540.222277
M5-0.2389520690215392.121875-0.11260.9109150.455457
M6-2.440847659334352.246256-1.08660.2838710.141936
M7-2.887243010525672.359874-1.22350.2284920.114246
M8-1.283898249159882.245427-0.57180.570750.285375
M9-1.930799249128082.200794-0.87730.3856860.192843
M10-6.858091437022822.358847-2.90740.0059840.002992
M11-0.4120187275640272.528009-0.1630.8713750.435687
t-0.08101693137664840.0603-1.34360.1868570.093428

\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) & 8.53757859793634 & 4.84348 & 1.7627 & 0.085788 & 0.042894 \tabularnewline
consv & 0.116192357805682 & 0.074015 & 1.5699 & 0.124528 & 0.062264 \tabularnewline
`y(t-1)` & 0.431844748244927 & 0.156282 & 2.7632 & 0.008689 & 0.004344 \tabularnewline
`y(t-2)` & 0.314619658899698 & 0.171318 & 1.8365 & 0.07392 & 0.03696 \tabularnewline
`y(t-3)` & -0.104294325773217 & 0.17345 & -0.6013 & 0.551124 & 0.275562 \tabularnewline
`y(t-4)` & -0.0303437661333572 & 0.167302 & -0.1814 & 0.857016 & 0.428508 \tabularnewline
M1 & -2.05606014705970 & 2.379737 & -0.864 & 0.392878 & 0.196439 \tabularnewline
M2 & -3.08835545424920 & 2.42868 & -1.2716 & 0.21104 & 0.10552 \tabularnewline
M3 & -4.95092737842675 & 2.285318 & -2.1664 & 0.036453 & 0.018226 \tabularnewline
M4 & -1.76783608517104 & 2.288861 & -0.7724 & 0.444554 & 0.222277 \tabularnewline
M5 & -0.238952069021539 & 2.121875 & -0.1126 & 0.910915 & 0.455457 \tabularnewline
M6 & -2.44084765933435 & 2.246256 & -1.0866 & 0.283871 & 0.141936 \tabularnewline
M7 & -2.88724301052567 & 2.359874 & -1.2235 & 0.228492 & 0.114246 \tabularnewline
M8 & -1.28389824915988 & 2.245427 & -0.5718 & 0.57075 & 0.285375 \tabularnewline
M9 & -1.93079924912808 & 2.200794 & -0.8773 & 0.385686 & 0.192843 \tabularnewline
M10 & -6.85809143702282 & 2.358847 & -2.9074 & 0.005984 & 0.002992 \tabularnewline
M11 & -0.412018727564027 & 2.528009 & -0.163 & 0.871375 & 0.435687 \tabularnewline
t & -0.0810169313766484 & 0.0603 & -1.3436 & 0.186857 & 0.093428 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57840&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]8.53757859793634[/C][C]4.84348[/C][C]1.7627[/C][C]0.085788[/C][C]0.042894[/C][/ROW]
[ROW][C]consv[/C][C]0.116192357805682[/C][C]0.074015[/C][C]1.5699[/C][C]0.124528[/C][C]0.062264[/C][/ROW]
[ROW][C]`y(t-1)`[/C][C]0.431844748244927[/C][C]0.156282[/C][C]2.7632[/C][C]0.008689[/C][C]0.004344[/C][/ROW]
[ROW][C]`y(t-2)`[/C][C]0.314619658899698[/C][C]0.171318[/C][C]1.8365[/C][C]0.07392[/C][C]0.03696[/C][/ROW]
[ROW][C]`y(t-3)`[/C][C]-0.104294325773217[/C][C]0.17345[/C][C]-0.6013[/C][C]0.551124[/C][C]0.275562[/C][/ROW]
[ROW][C]`y(t-4)`[/C][C]-0.0303437661333572[/C][C]0.167302[/C][C]-0.1814[/C][C]0.857016[/C][C]0.428508[/C][/ROW]
[ROW][C]M1[/C][C]-2.05606014705970[/C][C]2.379737[/C][C]-0.864[/C][C]0.392878[/C][C]0.196439[/C][/ROW]
[ROW][C]M2[/C][C]-3.08835545424920[/C][C]2.42868[/C][C]-1.2716[/C][C]0.21104[/C][C]0.10552[/C][/ROW]
[ROW][C]M3[/C][C]-4.95092737842675[/C][C]2.285318[/C][C]-2.1664[/C][C]0.036453[/C][C]0.018226[/C][/ROW]
[ROW][C]M4[/C][C]-1.76783608517104[/C][C]2.288861[/C][C]-0.7724[/C][C]0.444554[/C][C]0.222277[/C][/ROW]
[ROW][C]M5[/C][C]-0.238952069021539[/C][C]2.121875[/C][C]-0.1126[/C][C]0.910915[/C][C]0.455457[/C][/ROW]
[ROW][C]M6[/C][C]-2.44084765933435[/C][C]2.246256[/C][C]-1.0866[/C][C]0.283871[/C][C]0.141936[/C][/ROW]
[ROW][C]M7[/C][C]-2.88724301052567[/C][C]2.359874[/C][C]-1.2235[/C][C]0.228492[/C][C]0.114246[/C][/ROW]
[ROW][C]M8[/C][C]-1.28389824915988[/C][C]2.245427[/C][C]-0.5718[/C][C]0.57075[/C][C]0.285375[/C][/ROW]
[ROW][C]M9[/C][C]-1.93079924912808[/C][C]2.200794[/C][C]-0.8773[/C][C]0.385686[/C][C]0.192843[/C][/ROW]
[ROW][C]M10[/C][C]-6.85809143702282[/C][C]2.358847[/C][C]-2.9074[/C][C]0.005984[/C][C]0.002992[/C][/ROW]
[ROW][C]M11[/C][C]-0.412018727564027[/C][C]2.528009[/C][C]-0.163[/C][C]0.871375[/C][C]0.435687[/C][/ROW]
[ROW][C]t[/C][C]-0.0810169313766484[/C][C]0.0603[/C][C]-1.3436[/C][C]0.186857[/C][C]0.093428[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57840&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57840&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)8.537578597936344.843481.76270.0857880.042894
consv0.1161923578056820.0740151.56990.1245280.062264
`y(t-1)`0.4318447482449270.1562822.76320.0086890.004344
`y(t-2)`0.3146196588996980.1713181.83650.073920.03696
`y(t-3)`-0.1042943257732170.17345-0.60130.5511240.275562
`y(t-4)`-0.03034376613335720.167302-0.18140.8570160.428508
M1-2.056060147059702.379737-0.8640.3928780.196439
M2-3.088355454249202.42868-1.27160.211040.10552
M3-4.950927378426752.285318-2.16640.0364530.018226
M4-1.767836085171042.288861-0.77240.4445540.222277
M5-0.2389520690215392.121875-0.11260.9109150.455457
M6-2.440847659334352.246256-1.08660.2838710.141936
M7-2.887243010525672.359874-1.22350.2284920.114246
M8-1.283898249159882.245427-0.57180.570750.285375
M9-1.930799249128082.200794-0.87730.3856860.192843
M10-6.858091437022822.358847-2.90740.0059840.002992
M11-0.4120187275640272.528009-0.1630.8713750.435687
t-0.08101693137664840.0603-1.34360.1868570.093428






Multiple Linear Regression - Regression Statistics
Multiple R0.907368783699279
R-squared0.82331810963191
Adjusted R-squared0.746302926650947
F-TEST (value)10.6903350451745
F-TEST (DF numerator)17
F-TEST (DF denominator)39
p-value7.56620321951118e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.09778928349134
Sum Squared Residuals374.255639351637

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.907368783699279 \tabularnewline
R-squared & 0.82331810963191 \tabularnewline
Adjusted R-squared & 0.746302926650947 \tabularnewline
F-TEST (value) & 10.6903350451745 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 39 \tabularnewline
p-value & 7.56620321951118e-10 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.09778928349134 \tabularnewline
Sum Squared Residuals & 374.255639351637 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57840&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.907368783699279[/C][/ROW]
[ROW][C]R-squared[/C][C]0.82331810963191[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.746302926650947[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]10.6903350451745[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]39[/C][/ROW]
[ROW][C]p-value[/C][C]7.56620321951118e-10[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.09778928349134[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]374.255639351637[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57840&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57840&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 R0.907368783699279
R-squared0.82331810963191
Adjusted R-squared0.746302926650947
F-TEST (value)10.6903350451745
F-TEST (DF numerator)17
F-TEST (DF denominator)39
p-value7.56620321951118e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.09778928349134
Sum Squared Residuals374.255639351637






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
12924.74473505641274.25526494358728
22625.34002381292430.659976187075723
32623.33868496108992.66131503891013
42124.308618336703-3.30861833670302
52323.7584258269041-0.758425826904108
62220.85713580560611.14286419439391
72121.1647820792644-0.164782079264363
81621.4190062500065-5.4190062500065
91918.95800585887790.041994141122085
101613.69057842394372.30942157605629
112520.72054376021234.27945623978767
122724.29789459847482.70210540152518
132325.9617432677395-2.96174326773950
142222.5540966470171-0.554096647017124
152318.55469421867824.44530578132176
162021.8980987251173-1.89809872511731
172423.05549004558450.94450995441554
182321.48214698053581.51785301946424
192022.0639077965079-2.06390779650795
202121.6499357181698-0.649935718169819
212220.85769225083331.14230774916668
221716.82288192435390.177118075646127
232120.28433937248680.715660627513198
241921.4483302798886-2.4483302798886
252320.42955491890532.57044508109473
262219.9165391674822.08346083251800
271519.2353748597117-4.23537485971172
282318.64342655415044.35657344584956
292121.2104409160189-0.210440916018926
301821.1088154999717-3.10881549997171
311817.91848905381160.0815109461883505
321818.4627964295813-0.462796429581278
331818.2246413656285-0.224641365628473
341012.4940170401174-2.49401704011738
351315.8690842634628-2.86908426346284
361014.7462783175761-4.74627831757605
37913.4404576507068-4.44045765070679
38910.8813088389438-1.88130883894384
3968.3801825721868-2.38018257218679
401110.1496635978930.850336402107004
41912.6108544977134-3.61085449771338
421011.1178490357408-1.11784903574085
43910.1949865687638-1.19498656876376
441611.88934384589874.11065615410131
451012.8965738374167-2.89657383741667
4676.992522611585040.00747738841495471
4779.12603260383803-2.12603260383803
48149.507496804060524.49250319593948
491110.42350910623570.57649089376428
501010.3080315336328-0.308031533632758
5166.49106338833338-0.49106338833338
5288.00019278613623-0.000192786136232415
53139.364788713779123.63521128622088
541210.43405267814561.56594732185440
551511.65783450165233.34216549834772
561613.57891775634372.42108224365629
571614.06308668724361.93691331275638

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 29 & 24.7447350564127 & 4.25526494358728 \tabularnewline
2 & 26 & 25.3400238129243 & 0.659976187075723 \tabularnewline
3 & 26 & 23.3386849610899 & 2.66131503891013 \tabularnewline
4 & 21 & 24.308618336703 & -3.30861833670302 \tabularnewline
5 & 23 & 23.7584258269041 & -0.758425826904108 \tabularnewline
6 & 22 & 20.8571358056061 & 1.14286419439391 \tabularnewline
7 & 21 & 21.1647820792644 & -0.164782079264363 \tabularnewline
8 & 16 & 21.4190062500065 & -5.4190062500065 \tabularnewline
9 & 19 & 18.9580058588779 & 0.041994141122085 \tabularnewline
10 & 16 & 13.6905784239437 & 2.30942157605629 \tabularnewline
11 & 25 & 20.7205437602123 & 4.27945623978767 \tabularnewline
12 & 27 & 24.2978945984748 & 2.70210540152518 \tabularnewline
13 & 23 & 25.9617432677395 & -2.96174326773950 \tabularnewline
14 & 22 & 22.5540966470171 & -0.554096647017124 \tabularnewline
15 & 23 & 18.5546942186782 & 4.44530578132176 \tabularnewline
16 & 20 & 21.8980987251173 & -1.89809872511731 \tabularnewline
17 & 24 & 23.0554900455845 & 0.94450995441554 \tabularnewline
18 & 23 & 21.4821469805358 & 1.51785301946424 \tabularnewline
19 & 20 & 22.0639077965079 & -2.06390779650795 \tabularnewline
20 & 21 & 21.6499357181698 & -0.649935718169819 \tabularnewline
21 & 22 & 20.8576922508333 & 1.14230774916668 \tabularnewline
22 & 17 & 16.8228819243539 & 0.177118075646127 \tabularnewline
23 & 21 & 20.2843393724868 & 0.715660627513198 \tabularnewline
24 & 19 & 21.4483302798886 & -2.4483302798886 \tabularnewline
25 & 23 & 20.4295549189053 & 2.57044508109473 \tabularnewline
26 & 22 & 19.916539167482 & 2.08346083251800 \tabularnewline
27 & 15 & 19.2353748597117 & -4.23537485971172 \tabularnewline
28 & 23 & 18.6434265541504 & 4.35657344584956 \tabularnewline
29 & 21 & 21.2104409160189 & -0.210440916018926 \tabularnewline
30 & 18 & 21.1088154999717 & -3.10881549997171 \tabularnewline
31 & 18 & 17.9184890538116 & 0.0815109461883505 \tabularnewline
32 & 18 & 18.4627964295813 & -0.462796429581278 \tabularnewline
33 & 18 & 18.2246413656285 & -0.224641365628473 \tabularnewline
34 & 10 & 12.4940170401174 & -2.49401704011738 \tabularnewline
35 & 13 & 15.8690842634628 & -2.86908426346284 \tabularnewline
36 & 10 & 14.7462783175761 & -4.74627831757605 \tabularnewline
37 & 9 & 13.4404576507068 & -4.44045765070679 \tabularnewline
38 & 9 & 10.8813088389438 & -1.88130883894384 \tabularnewline
39 & 6 & 8.3801825721868 & -2.38018257218679 \tabularnewline
40 & 11 & 10.149663597893 & 0.850336402107004 \tabularnewline
41 & 9 & 12.6108544977134 & -3.61085449771338 \tabularnewline
42 & 10 & 11.1178490357408 & -1.11784903574085 \tabularnewline
43 & 9 & 10.1949865687638 & -1.19498656876376 \tabularnewline
44 & 16 & 11.8893438458987 & 4.11065615410131 \tabularnewline
45 & 10 & 12.8965738374167 & -2.89657383741667 \tabularnewline
46 & 7 & 6.99252261158504 & 0.00747738841495471 \tabularnewline
47 & 7 & 9.12603260383803 & -2.12603260383803 \tabularnewline
48 & 14 & 9.50749680406052 & 4.49250319593948 \tabularnewline
49 & 11 & 10.4235091062357 & 0.57649089376428 \tabularnewline
50 & 10 & 10.3080315336328 & -0.308031533632758 \tabularnewline
51 & 6 & 6.49106338833338 & -0.49106338833338 \tabularnewline
52 & 8 & 8.00019278613623 & -0.000192786136232415 \tabularnewline
53 & 13 & 9.36478871377912 & 3.63521128622088 \tabularnewline
54 & 12 & 10.4340526781456 & 1.56594732185440 \tabularnewline
55 & 15 & 11.6578345016523 & 3.34216549834772 \tabularnewline
56 & 16 & 13.5789177563437 & 2.42108224365629 \tabularnewline
57 & 16 & 14.0630866872436 & 1.93691331275638 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57840&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]29[/C][C]24.7447350564127[/C][C]4.25526494358728[/C][/ROW]
[ROW][C]2[/C][C]26[/C][C]25.3400238129243[/C][C]0.659976187075723[/C][/ROW]
[ROW][C]3[/C][C]26[/C][C]23.3386849610899[/C][C]2.66131503891013[/C][/ROW]
[ROW][C]4[/C][C]21[/C][C]24.308618336703[/C][C]-3.30861833670302[/C][/ROW]
[ROW][C]5[/C][C]23[/C][C]23.7584258269041[/C][C]-0.758425826904108[/C][/ROW]
[ROW][C]6[/C][C]22[/C][C]20.8571358056061[/C][C]1.14286419439391[/C][/ROW]
[ROW][C]7[/C][C]21[/C][C]21.1647820792644[/C][C]-0.164782079264363[/C][/ROW]
[ROW][C]8[/C][C]16[/C][C]21.4190062500065[/C][C]-5.4190062500065[/C][/ROW]
[ROW][C]9[/C][C]19[/C][C]18.9580058588779[/C][C]0.041994141122085[/C][/ROW]
[ROW][C]10[/C][C]16[/C][C]13.6905784239437[/C][C]2.30942157605629[/C][/ROW]
[ROW][C]11[/C][C]25[/C][C]20.7205437602123[/C][C]4.27945623978767[/C][/ROW]
[ROW][C]12[/C][C]27[/C][C]24.2978945984748[/C][C]2.70210540152518[/C][/ROW]
[ROW][C]13[/C][C]23[/C][C]25.9617432677395[/C][C]-2.96174326773950[/C][/ROW]
[ROW][C]14[/C][C]22[/C][C]22.5540966470171[/C][C]-0.554096647017124[/C][/ROW]
[ROW][C]15[/C][C]23[/C][C]18.5546942186782[/C][C]4.44530578132176[/C][/ROW]
[ROW][C]16[/C][C]20[/C][C]21.8980987251173[/C][C]-1.89809872511731[/C][/ROW]
[ROW][C]17[/C][C]24[/C][C]23.0554900455845[/C][C]0.94450995441554[/C][/ROW]
[ROW][C]18[/C][C]23[/C][C]21.4821469805358[/C][C]1.51785301946424[/C][/ROW]
[ROW][C]19[/C][C]20[/C][C]22.0639077965079[/C][C]-2.06390779650795[/C][/ROW]
[ROW][C]20[/C][C]21[/C][C]21.6499357181698[/C][C]-0.649935718169819[/C][/ROW]
[ROW][C]21[/C][C]22[/C][C]20.8576922508333[/C][C]1.14230774916668[/C][/ROW]
[ROW][C]22[/C][C]17[/C][C]16.8228819243539[/C][C]0.177118075646127[/C][/ROW]
[ROW][C]23[/C][C]21[/C][C]20.2843393724868[/C][C]0.715660627513198[/C][/ROW]
[ROW][C]24[/C][C]19[/C][C]21.4483302798886[/C][C]-2.4483302798886[/C][/ROW]
[ROW][C]25[/C][C]23[/C][C]20.4295549189053[/C][C]2.57044508109473[/C][/ROW]
[ROW][C]26[/C][C]22[/C][C]19.916539167482[/C][C]2.08346083251800[/C][/ROW]
[ROW][C]27[/C][C]15[/C][C]19.2353748597117[/C][C]-4.23537485971172[/C][/ROW]
[ROW][C]28[/C][C]23[/C][C]18.6434265541504[/C][C]4.35657344584956[/C][/ROW]
[ROW][C]29[/C][C]21[/C][C]21.2104409160189[/C][C]-0.210440916018926[/C][/ROW]
[ROW][C]30[/C][C]18[/C][C]21.1088154999717[/C][C]-3.10881549997171[/C][/ROW]
[ROW][C]31[/C][C]18[/C][C]17.9184890538116[/C][C]0.0815109461883505[/C][/ROW]
[ROW][C]32[/C][C]18[/C][C]18.4627964295813[/C][C]-0.462796429581278[/C][/ROW]
[ROW][C]33[/C][C]18[/C][C]18.2246413656285[/C][C]-0.224641365628473[/C][/ROW]
[ROW][C]34[/C][C]10[/C][C]12.4940170401174[/C][C]-2.49401704011738[/C][/ROW]
[ROW][C]35[/C][C]13[/C][C]15.8690842634628[/C][C]-2.86908426346284[/C][/ROW]
[ROW][C]36[/C][C]10[/C][C]14.7462783175761[/C][C]-4.74627831757605[/C][/ROW]
[ROW][C]37[/C][C]9[/C][C]13.4404576507068[/C][C]-4.44045765070679[/C][/ROW]
[ROW][C]38[/C][C]9[/C][C]10.8813088389438[/C][C]-1.88130883894384[/C][/ROW]
[ROW][C]39[/C][C]6[/C][C]8.3801825721868[/C][C]-2.38018257218679[/C][/ROW]
[ROW][C]40[/C][C]11[/C][C]10.149663597893[/C][C]0.850336402107004[/C][/ROW]
[ROW][C]41[/C][C]9[/C][C]12.6108544977134[/C][C]-3.61085449771338[/C][/ROW]
[ROW][C]42[/C][C]10[/C][C]11.1178490357408[/C][C]-1.11784903574085[/C][/ROW]
[ROW][C]43[/C][C]9[/C][C]10.1949865687638[/C][C]-1.19498656876376[/C][/ROW]
[ROW][C]44[/C][C]16[/C][C]11.8893438458987[/C][C]4.11065615410131[/C][/ROW]
[ROW][C]45[/C][C]10[/C][C]12.8965738374167[/C][C]-2.89657383741667[/C][/ROW]
[ROW][C]46[/C][C]7[/C][C]6.99252261158504[/C][C]0.00747738841495471[/C][/ROW]
[ROW][C]47[/C][C]7[/C][C]9.12603260383803[/C][C]-2.12603260383803[/C][/ROW]
[ROW][C]48[/C][C]14[/C][C]9.50749680406052[/C][C]4.49250319593948[/C][/ROW]
[ROW][C]49[/C][C]11[/C][C]10.4235091062357[/C][C]0.57649089376428[/C][/ROW]
[ROW][C]50[/C][C]10[/C][C]10.3080315336328[/C][C]-0.308031533632758[/C][/ROW]
[ROW][C]51[/C][C]6[/C][C]6.49106338833338[/C][C]-0.49106338833338[/C][/ROW]
[ROW][C]52[/C][C]8[/C][C]8.00019278613623[/C][C]-0.000192786136232415[/C][/ROW]
[ROW][C]53[/C][C]13[/C][C]9.36478871377912[/C][C]3.63521128622088[/C][/ROW]
[ROW][C]54[/C][C]12[/C][C]10.4340526781456[/C][C]1.56594732185440[/C][/ROW]
[ROW][C]55[/C][C]15[/C][C]11.6578345016523[/C][C]3.34216549834772[/C][/ROW]
[ROW][C]56[/C][C]16[/C][C]13.5789177563437[/C][C]2.42108224365629[/C][/ROW]
[ROW][C]57[/C][C]16[/C][C]14.0630866872436[/C][C]1.93691331275638[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57840&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57840&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
12924.74473505641274.25526494358728
22625.34002381292430.659976187075723
32623.33868496108992.66131503891013
42124.308618336703-3.30861833670302
52323.7584258269041-0.758425826904108
62220.85713580560611.14286419439391
72121.1647820792644-0.164782079264363
81621.4190062500065-5.4190062500065
91918.95800585887790.041994141122085
101613.69057842394372.30942157605629
112520.72054376021234.27945623978767
122724.29789459847482.70210540152518
132325.9617432677395-2.96174326773950
142222.5540966470171-0.554096647017124
152318.55469421867824.44530578132176
162021.8980987251173-1.89809872511731
172423.05549004558450.94450995441554
182321.48214698053581.51785301946424
192022.0639077965079-2.06390779650795
202121.6499357181698-0.649935718169819
212220.85769225083331.14230774916668
221716.82288192435390.177118075646127
232120.28433937248680.715660627513198
241921.4483302798886-2.4483302798886
252320.42955491890532.57044508109473
262219.9165391674822.08346083251800
271519.2353748597117-4.23537485971172
282318.64342655415044.35657344584956
292121.2104409160189-0.210440916018926
301821.1088154999717-3.10881549997171
311817.91848905381160.0815109461883505
321818.4627964295813-0.462796429581278
331818.2246413656285-0.224641365628473
341012.4940170401174-2.49401704011738
351315.8690842634628-2.86908426346284
361014.7462783175761-4.74627831757605
37913.4404576507068-4.44045765070679
38910.8813088389438-1.88130883894384
3968.3801825721868-2.38018257218679
401110.1496635978930.850336402107004
41912.6108544977134-3.61085449771338
421011.1178490357408-1.11784903574085
43910.1949865687638-1.19498656876376
441611.88934384589874.11065615410131
451012.8965738374167-2.89657383741667
4676.992522611585040.00747738841495471
4779.12603260383803-2.12603260383803
48149.507496804060524.49250319593948
491110.42350910623570.57649089376428
501010.3080315336328-0.308031533632758
5166.49106338833338-0.49106338833338
5288.00019278613623-0.000192786136232415
53139.364788713779123.63521128622088
541210.43405267814561.56594732185440
551511.65783450165233.34216549834772
561613.57891775634372.42108224365629
571614.06308668724361.93691331275638






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.05287159428378690.1057431885675740.947128405716213
220.02423912125649650.04847824251299310.975760878743503
230.009892404452400870.01978480890480170.990107595547599
240.05186472646543280.1037294529308660.948135273534567
250.04110529850874760.08221059701749510.958894701491252
260.05390784590125710.1078156918025140.946092154098743
270.2516902945050520.5033805890101050.748309705494948
280.346103569782540.692207139565080.65389643021746
290.3123789697730040.6247579395460090.687621030226996
300.2307917531937290.4615835063874580.769208246806271
310.211404932097380.422809864194760.78859506790262
320.1614916254458530.3229832508917060.838508374554147
330.2478430830742160.4956861661484330.752156916925784
340.3313749815237090.6627499630474170.668625018476291
350.7614141594994190.4771716810011610.238585840500581
360.9464651900386630.1070696199226740.053534809961337

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.0528715942837869 & 0.105743188567574 & 0.947128405716213 \tabularnewline
22 & 0.0242391212564965 & 0.0484782425129931 & 0.975760878743503 \tabularnewline
23 & 0.00989240445240087 & 0.0197848089048017 & 0.990107595547599 \tabularnewline
24 & 0.0518647264654328 & 0.103729452930866 & 0.948135273534567 \tabularnewline
25 & 0.0411052985087476 & 0.0822105970174951 & 0.958894701491252 \tabularnewline
26 & 0.0539078459012571 & 0.107815691802514 & 0.946092154098743 \tabularnewline
27 & 0.251690294505052 & 0.503380589010105 & 0.748309705494948 \tabularnewline
28 & 0.34610356978254 & 0.69220713956508 & 0.65389643021746 \tabularnewline
29 & 0.312378969773004 & 0.624757939546009 & 0.687621030226996 \tabularnewline
30 & 0.230791753193729 & 0.461583506387458 & 0.769208246806271 \tabularnewline
31 & 0.21140493209738 & 0.42280986419476 & 0.78859506790262 \tabularnewline
32 & 0.161491625445853 & 0.322983250891706 & 0.838508374554147 \tabularnewline
33 & 0.247843083074216 & 0.495686166148433 & 0.752156916925784 \tabularnewline
34 & 0.331374981523709 & 0.662749963047417 & 0.668625018476291 \tabularnewline
35 & 0.761414159499419 & 0.477171681001161 & 0.238585840500581 \tabularnewline
36 & 0.946465190038663 & 0.107069619922674 & 0.053534809961337 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57840&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]21[/C][C]0.0528715942837869[/C][C]0.105743188567574[/C][C]0.947128405716213[/C][/ROW]
[ROW][C]22[/C][C]0.0242391212564965[/C][C]0.0484782425129931[/C][C]0.975760878743503[/C][/ROW]
[ROW][C]23[/C][C]0.00989240445240087[/C][C]0.0197848089048017[/C][C]0.990107595547599[/C][/ROW]
[ROW][C]24[/C][C]0.0518647264654328[/C][C]0.103729452930866[/C][C]0.948135273534567[/C][/ROW]
[ROW][C]25[/C][C]0.0411052985087476[/C][C]0.0822105970174951[/C][C]0.958894701491252[/C][/ROW]
[ROW][C]26[/C][C]0.0539078459012571[/C][C]0.107815691802514[/C][C]0.946092154098743[/C][/ROW]
[ROW][C]27[/C][C]0.251690294505052[/C][C]0.503380589010105[/C][C]0.748309705494948[/C][/ROW]
[ROW][C]28[/C][C]0.34610356978254[/C][C]0.69220713956508[/C][C]0.65389643021746[/C][/ROW]
[ROW][C]29[/C][C]0.312378969773004[/C][C]0.624757939546009[/C][C]0.687621030226996[/C][/ROW]
[ROW][C]30[/C][C]0.230791753193729[/C][C]0.461583506387458[/C][C]0.769208246806271[/C][/ROW]
[ROW][C]31[/C][C]0.21140493209738[/C][C]0.42280986419476[/C][C]0.78859506790262[/C][/ROW]
[ROW][C]32[/C][C]0.161491625445853[/C][C]0.322983250891706[/C][C]0.838508374554147[/C][/ROW]
[ROW][C]33[/C][C]0.247843083074216[/C][C]0.495686166148433[/C][C]0.752156916925784[/C][/ROW]
[ROW][C]34[/C][C]0.331374981523709[/C][C]0.662749963047417[/C][C]0.668625018476291[/C][/ROW]
[ROW][C]35[/C][C]0.761414159499419[/C][C]0.477171681001161[/C][C]0.238585840500581[/C][/ROW]
[ROW][C]36[/C][C]0.946465190038663[/C][C]0.107069619922674[/C][C]0.053534809961337[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57840&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57840&T=5

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


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.05287159428378690.1057431885675740.947128405716213
220.02423912125649650.04847824251299310.975760878743503
230.009892404452400870.01978480890480170.990107595547599
240.05186472646543280.1037294529308660.948135273534567
250.04110529850874760.08221059701749510.958894701491252
260.05390784590125710.1078156918025140.946092154098743
270.2516902945050520.5033805890101050.748309705494948
280.346103569782540.692207139565080.65389643021746
290.3123789697730040.6247579395460090.687621030226996
300.2307917531937290.4615835063874580.769208246806271
310.211404932097380.422809864194760.78859506790262
320.1614916254458530.3229832508917060.838508374554147
330.2478430830742160.4956861661484330.752156916925784
340.3313749815237090.6627499630474170.668625018476291
350.7614141594994190.4771716810011610.238585840500581
360.9464651900386630.1070696199226740.053534809961337






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level20.125NOK
10% type I error level30.1875NOK

\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 & 2 & 0.125 & NOK \tabularnewline
10% type I error level & 3 & 0.1875 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57840&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]2[/C][C]0.125[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]3[/C][C]0.1875[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57840&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57840&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 level20.125NOK
10% type I error level30.1875NOK


Figures (Output of Computation)

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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}