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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 computationFri, 27 Nov 2009 08:55:13 -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/27/t1259337555yesomtjp13p9kky.htm/, Retrieved Wed, 05 Nov 2025 00:32:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60925, Retrieved Wed, 05 Nov 2025 00:32:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact429

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 14:10:54] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [WS 7 4] [2009-11-14 13:58:56] [6e4e01d7eb22a9f33d58ebb35753a195]
-   PD      [Multiple Regression] [ws7 4] [2009-11-18 20:49:31] [6e4e01d7eb22a9f33d58ebb35753a195]
-    D          [Multiple Regression] [WS7: Correctie] [2009-11-27 15:55:13] [b9056af0304697100f456398102f1287] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
103.91	89.00	103.88	103.77	103.66	103.64	103.63
103.91	86.40	103.91	103.88	103.77	103.66	103.64
103.92	84.50	103.91	103.91	103.88	103.77	103.66
104.05	82.70	103.92	103.91	103.91	103.88	103.77
104.23	80.80	104.05	103.92	103.91	103.91	103.88
104.30	81.80	104.23	104.05	103.92	103.91	103.91
104.31	81.80	104.30	104.23	104.05	103.92	103.91
104.31	82.90	104.31	104.30	104.23	104.05	103.92
104.34	83.80	104.31	104.31	104.30	104.23	104.05
104.55	86.20	104.34	104.31	104.31	104.30	104.23
104.65	86.10	104.55	104.34	104.31	104.31	104.30
104.73	86.20	104.65	104.55	104.34	104.31	104.31
104.75	88.80	104.73	104.65	104.55	104.34	104.31
104.75	89.60	104.75	104.73	104.65	104.55	104.34
104.76	87.80	104.75	104.75	104.73	104.65	104.55
104.94	88.30	104.76	104.75	104.75	104.73	104.65
105.29	88.60	104.94	104.76	104.75	104.75	104.73
105.38	91.00	105.29	104.94	104.76	104.75	104.75
105.43	91.50	105.38	105.29	104.94	104.76	104.75
105.43	95.40	105.43	105.38	105.29	104.94	104.76
105.42	98.70	105.43	105.43	105.38	105.29	104.94
105.52	99.90	105.42	105.43	105.43	105.38	105.29
105.69	98.60	105.52	105.42	105.43	105.43	105.38
105.72	100.30	105.69	105.52	105.42	105.43	105.43
105.74	100.20	105.72	105.69	105.52	105.42	105.43
105.74	100.40	105.74	105.72	105.69	105.52	105.42
105.74	101.40	105.74	105.74	105.72	105.69	105.52
105.95	103.00	105.74	105.74	105.74	105.72	105.69
106.17	109.10	105.95	105.74	105.74	105.74	105.72
106.34	111.40	106.17	105.95	105.74	105.74	105.74
106.37	114.10	106.34	106.17	105.95	105.74	105.74
106.37	121.80	106.37	106.34	106.17	105.95	105.74
106.36	127.60	106.37	106.37	106.34	106.17	105.95
106.44	129.90	106.36	106.37	106.37	106.34	106.17
106.29	128.00	106.44	106.36	106.37	106.37	106.34
106.23	123.50	106.29	106.44	106.36	106.37	106.37
106.23	124.00	106.23	106.29	106.44	106.36	106.37
106.23	127.40	106.23	106.23	106.29	106.44	106.36
106.23	127.60	106.23	106.23	106.23	106.29	106.44
106.34	128.40	106.23	106.23	106.23	106.23	106.29
106.44	131.40	106.34	106.23	106.23	106.23	106.23
106.44	135.10	106.44	106.34	106.23	106.23	106.23
106.48	134.00	106.44	106.44	106.34	106.23	106.23
106.50	144.50	106.48	106.44	106.44	106.34	106.23
106.57	147.30	106.50	106.48	106.44	106.44	106.34
106.40	150.90	106.57	106.50	106.48	106.44	106.44
106.37	148.70	106.40	106.57	106.50	106.48	106.44
106.25	141.40	106.37	106.40	106.57	106.50	106.48
106.21	138.90	106.25	106.37	106.40	106.57	106.50
106.21	139.80	106.21	106.25	106.37	106.40	106.57
106.24	145.60	106.21	106.21	106.25	106.37	106.40
106.19	147.90	106.24	106.21	106.21	106.25	106.37
106.08	148.50	106.19	106.24	106.21	106.21	106.25
106.13	151.10	106.08	106.19	106.24	106.21	106.21
106.09	157.50	106.13	106.08	106.19	106.24	106.21

Tables (Output of Computation)





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=60925&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=60925&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60925&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = -0.882021848595453 -0.00452130769895071X[t] + 1.28776785397041Y1[t] -0.416249054274984Y2[t] -0.111638282342769Y3[t] + 0.271637226912727Y4[t] -0.0188616710391742Y5[t] + 0.0035299223429012t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -0.882021848595453 -0.00452130769895071X[t] +  1.28776785397041Y1[t] -0.416249054274984Y2[t] -0.111638282342769Y3[t] +  0.271637226912727Y4[t] -0.0188616710391742Y5[t] +  0.0035299223429012t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60925&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -0.882021848595453 -0.00452130769895071X[t] +  1.28776785397041Y1[t] -0.416249054274984Y2[t] -0.111638282342769Y3[t] +  0.271637226912727Y4[t] -0.0188616710391742Y5[t] +  0.0035299223429012t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60925&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60925&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
Y[t] = -0.882021848595453 -0.00452130769895071X[t] + 1.28776785397041Y1[t] -0.416249054274984Y2[t] -0.111638282342769Y3[t] + 0.271637226912727Y4[t] -0.0188616710391742Y5[t] + 0.0035299223429012t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-0.8820218485954534.04946-0.21780.8285180.414259
X-0.004521307698950710.001859-2.43210.0188760.009438
Y11.287767853970410.1384869.298900
Y2-0.4162490542749840.229841-1.8110.076530.038265
Y3-0.1116382823427690.243676-0.45810.6489610.32448
Y40.2716372269127270.2361051.15050.2557610.12788
Y5-0.01886167103917420.149062-0.12650.8998470.449924
t0.00352992234290120.0039910.88450.380950.190475

\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) & -0.882021848595453 & 4.04946 & -0.2178 & 0.828518 & 0.414259 \tabularnewline
X & -0.00452130769895071 & 0.001859 & -2.4321 & 0.018876 & 0.009438 \tabularnewline
Y1 & 1.28776785397041 & 0.138486 & 9.2989 & 0 & 0 \tabularnewline
Y2 & -0.416249054274984 & 0.229841 & -1.811 & 0.07653 & 0.038265 \tabularnewline
Y3 & -0.111638282342769 & 0.243676 & -0.4581 & 0.648961 & 0.32448 \tabularnewline
Y4 & 0.271637226912727 & 0.236105 & 1.1505 & 0.255761 & 0.12788 \tabularnewline
Y5 & -0.0188616710391742 & 0.149062 & -0.1265 & 0.899847 & 0.449924 \tabularnewline
t & 0.0035299223429012 & 0.003991 & 0.8845 & 0.38095 & 0.190475 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60925&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]-0.882021848595453[/C][C]4.04946[/C][C]-0.2178[/C][C]0.828518[/C][C]0.414259[/C][/ROW]
[ROW][C]X[/C][C]-0.00452130769895071[/C][C]0.001859[/C][C]-2.4321[/C][C]0.018876[/C][C]0.009438[/C][/ROW]
[ROW][C]Y1[/C][C]1.28776785397041[/C][C]0.138486[/C][C]9.2989[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Y2[/C][C]-0.416249054274984[/C][C]0.229841[/C][C]-1.811[/C][C]0.07653[/C][C]0.038265[/C][/ROW]
[ROW][C]Y3[/C][C]-0.111638282342769[/C][C]0.243676[/C][C]-0.4581[/C][C]0.648961[/C][C]0.32448[/C][/ROW]
[ROW][C]Y4[/C][C]0.271637226912727[/C][C]0.236105[/C][C]1.1505[/C][C]0.255761[/C][C]0.12788[/C][/ROW]
[ROW][C]Y5[/C][C]-0.0188616710391742[/C][C]0.149062[/C][C]-0.1265[/C][C]0.899847[/C][C]0.449924[/C][/ROW]
[ROW][C]t[/C][C]0.0035299223429012[/C][C]0.003991[/C][C]0.8845[/C][C]0.38095[/C][C]0.190475[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60925&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60925&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)-0.8820218485954534.04946-0.21780.8285180.414259
X-0.004521307698950710.001859-2.43210.0188760.009438
Y11.287767853970410.1384869.298900
Y2-0.4162490542749840.229841-1.8110.076530.038265
Y3-0.1116382823427690.243676-0.45810.6489610.32448
Y40.2716372269127270.2361051.15050.2557610.12788
Y5-0.01886167103917420.149062-0.12650.8998470.449924
t0.00352992234290120.0039910.88450.380950.190475






Multiple Linear Regression - Regression Statistics
Multiple R0.996238049982534
R-squared0.992490252233001
Adjusted R-squared0.99137177916132
F-TEST (value)887.361776838902
F-TEST (DF numerator)7
F-TEST (DF denominator)47
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.07894860758537
Sum Squared Residuals0.292945484064431

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.996238049982534 \tabularnewline
R-squared & 0.992490252233001 \tabularnewline
Adjusted R-squared & 0.99137177916132 \tabularnewline
F-TEST (value) & 887.361776838902 \tabularnewline
F-TEST (DF numerator) & 7 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.07894860758537 \tabularnewline
Sum Squared Residuals & 0.292945484064431 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60925&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.996238049982534[/C][/ROW]
[ROW][C]R-squared[/C][C]0.992490252233001[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.99137177916132[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]887.361776838902[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]7[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/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]0.07894860758537[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.292945484064431[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60925&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60925&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 R0.996238049982534
R-squared0.992490252233001
Adjusted R-squared0.99137177916132
F-TEST (value)887.361776838902
F-TEST (DF numerator)7
F-TEST (DF denominator)47
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.07894860758537
Sum Squared Residuals0.292945484064431






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1103.91103.923694876667-0.0136948766666860
2103.91103.924789755446-0.0147897554456499
3103.92103.941645341270-0.0216453412702114
4104.05103.9906474586870.0593525413132544
5104.23104.1720895291240.0579104708758845
6104.3104.347101747472-0.0471017474724066
7104.31104.354053985388-0.0440539853882922
8104.31104.351380045969-0.0413800459693747
9104.34104.385306304686-0.0453063046856742
10104.55104.4311212464440.118878753556377
11104.65104.694443132558-0.0444431325583265
12104.73104.73534764295-0.0053476429499675
13104.75104.773223765681-0.0232237656811312
14104.75104.810906213889-0.0609062138884949
15104.76104.828521218190-0.0685212181896317
16104.94104.8602802106250.0797197893749793
17105.29105.0940132746850.195986725314739
18105.38105.460992361427-0.0809923614266413
19105.43105.4150950492290.0149049507714379
20105.43105.437550534673-0.00755053467327394
21105.42105.486978172117-0.0669781721174468
22105.52105.4844686981230.0355313018768063
23105.69105.6386999073670.051300092633371
24105.72105.812012535640-0.0920125356402588
25105.74105.769985084642-0.02998508464202
26105.74105.794252462300-0.0542524622996764
27105.74105.825879108859-0.0858791088590926
28105.95105.8248848059680.125115194032468
29106.17106.0761328950880.0938671049122893
30106.34106.2647832027780.0752167972220204
31106.37106.3600072982760.00999270172379286
32106.37106.3290772432660.0409227567341805
33106.36106.3307168403310.0292831596691363
34106.44106.3496496889030.090350311097268
35106.29106.473896647465-0.183896647464736
36106.23106.271857884708-0.0418578847076219
37106.23106.246651005248-0.0166510052475141
38106.23106.298448761885-0.0684487618853065
39106.23106.265518201909-0.0355182019089434
40106.34106.2519620951340.0880379048662037
41106.44106.3847142585790.0552857414210537
42106.44106.454504731863-0.0145047318625162
43106.48106.4091029761890.0708970238109437
44106.5106.4353861485780.064613851422073
45106.57106.4604507431490.109549256850864
46106.4106.523171028071-0.123171028070596
47106.37106.2972225818070.0727774181933546
48106.25106.362750951892-0.112750951892213
49106.21106.273155353096-0.0631553530956664
50106.21106.226905773786-0.0169057737860680
51106.24106.2293160347960.0106839652035338
52106.19106.233514899246-0.0435148992462501
53106.08106.148854084091-0.0688540840912035
54106.13106.0171919135650.112808086434877
55106.09106.115692286228-0.0256922862280168

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 103.91 & 103.923694876667 & -0.0136948766666860 \tabularnewline
2 & 103.91 & 103.924789755446 & -0.0147897554456499 \tabularnewline
3 & 103.92 & 103.941645341270 & -0.0216453412702114 \tabularnewline
4 & 104.05 & 103.990647458687 & 0.0593525413132544 \tabularnewline
5 & 104.23 & 104.172089529124 & 0.0579104708758845 \tabularnewline
6 & 104.3 & 104.347101747472 & -0.0471017474724066 \tabularnewline
7 & 104.31 & 104.354053985388 & -0.0440539853882922 \tabularnewline
8 & 104.31 & 104.351380045969 & -0.0413800459693747 \tabularnewline
9 & 104.34 & 104.385306304686 & -0.0453063046856742 \tabularnewline
10 & 104.55 & 104.431121246444 & 0.118878753556377 \tabularnewline
11 & 104.65 & 104.694443132558 & -0.0444431325583265 \tabularnewline
12 & 104.73 & 104.73534764295 & -0.0053476429499675 \tabularnewline
13 & 104.75 & 104.773223765681 & -0.0232237656811312 \tabularnewline
14 & 104.75 & 104.810906213889 & -0.0609062138884949 \tabularnewline
15 & 104.76 & 104.828521218190 & -0.0685212181896317 \tabularnewline
16 & 104.94 & 104.860280210625 & 0.0797197893749793 \tabularnewline
17 & 105.29 & 105.094013274685 & 0.195986725314739 \tabularnewline
18 & 105.38 & 105.460992361427 & -0.0809923614266413 \tabularnewline
19 & 105.43 & 105.415095049229 & 0.0149049507714379 \tabularnewline
20 & 105.43 & 105.437550534673 & -0.00755053467327394 \tabularnewline
21 & 105.42 & 105.486978172117 & -0.0669781721174468 \tabularnewline
22 & 105.52 & 105.484468698123 & 0.0355313018768063 \tabularnewline
23 & 105.69 & 105.638699907367 & 0.051300092633371 \tabularnewline
24 & 105.72 & 105.812012535640 & -0.0920125356402588 \tabularnewline
25 & 105.74 & 105.769985084642 & -0.02998508464202 \tabularnewline
26 & 105.74 & 105.794252462300 & -0.0542524622996764 \tabularnewline
27 & 105.74 & 105.825879108859 & -0.0858791088590926 \tabularnewline
28 & 105.95 & 105.824884805968 & 0.125115194032468 \tabularnewline
29 & 106.17 & 106.076132895088 & 0.0938671049122893 \tabularnewline
30 & 106.34 & 106.264783202778 & 0.0752167972220204 \tabularnewline
31 & 106.37 & 106.360007298276 & 0.00999270172379286 \tabularnewline
32 & 106.37 & 106.329077243266 & 0.0409227567341805 \tabularnewline
33 & 106.36 & 106.330716840331 & 0.0292831596691363 \tabularnewline
34 & 106.44 & 106.349649688903 & 0.090350311097268 \tabularnewline
35 & 106.29 & 106.473896647465 & -0.183896647464736 \tabularnewline
36 & 106.23 & 106.271857884708 & -0.0418578847076219 \tabularnewline
37 & 106.23 & 106.246651005248 & -0.0166510052475141 \tabularnewline
38 & 106.23 & 106.298448761885 & -0.0684487618853065 \tabularnewline
39 & 106.23 & 106.265518201909 & -0.0355182019089434 \tabularnewline
40 & 106.34 & 106.251962095134 & 0.0880379048662037 \tabularnewline
41 & 106.44 & 106.384714258579 & 0.0552857414210537 \tabularnewline
42 & 106.44 & 106.454504731863 & -0.0145047318625162 \tabularnewline
43 & 106.48 & 106.409102976189 & 0.0708970238109437 \tabularnewline
44 & 106.5 & 106.435386148578 & 0.064613851422073 \tabularnewline
45 & 106.57 & 106.460450743149 & 0.109549256850864 \tabularnewline
46 & 106.4 & 106.523171028071 & -0.123171028070596 \tabularnewline
47 & 106.37 & 106.297222581807 & 0.0727774181933546 \tabularnewline
48 & 106.25 & 106.362750951892 & -0.112750951892213 \tabularnewline
49 & 106.21 & 106.273155353096 & -0.0631553530956664 \tabularnewline
50 & 106.21 & 106.226905773786 & -0.0169057737860680 \tabularnewline
51 & 106.24 & 106.229316034796 & 0.0106839652035338 \tabularnewline
52 & 106.19 & 106.233514899246 & -0.0435148992462501 \tabularnewline
53 & 106.08 & 106.148854084091 & -0.0688540840912035 \tabularnewline
54 & 106.13 & 106.017191913565 & 0.112808086434877 \tabularnewline
55 & 106.09 & 106.115692286228 & -0.0256922862280168 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60925&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]103.91[/C][C]103.923694876667[/C][C]-0.0136948766666860[/C][/ROW]
[ROW][C]2[/C][C]103.91[/C][C]103.924789755446[/C][C]-0.0147897554456499[/C][/ROW]
[ROW][C]3[/C][C]103.92[/C][C]103.941645341270[/C][C]-0.0216453412702114[/C][/ROW]
[ROW][C]4[/C][C]104.05[/C][C]103.990647458687[/C][C]0.0593525413132544[/C][/ROW]
[ROW][C]5[/C][C]104.23[/C][C]104.172089529124[/C][C]0.0579104708758845[/C][/ROW]
[ROW][C]6[/C][C]104.3[/C][C]104.347101747472[/C][C]-0.0471017474724066[/C][/ROW]
[ROW][C]7[/C][C]104.31[/C][C]104.354053985388[/C][C]-0.0440539853882922[/C][/ROW]
[ROW][C]8[/C][C]104.31[/C][C]104.351380045969[/C][C]-0.0413800459693747[/C][/ROW]
[ROW][C]9[/C][C]104.34[/C][C]104.385306304686[/C][C]-0.0453063046856742[/C][/ROW]
[ROW][C]10[/C][C]104.55[/C][C]104.431121246444[/C][C]0.118878753556377[/C][/ROW]
[ROW][C]11[/C][C]104.65[/C][C]104.694443132558[/C][C]-0.0444431325583265[/C][/ROW]
[ROW][C]12[/C][C]104.73[/C][C]104.73534764295[/C][C]-0.0053476429499675[/C][/ROW]
[ROW][C]13[/C][C]104.75[/C][C]104.773223765681[/C][C]-0.0232237656811312[/C][/ROW]
[ROW][C]14[/C][C]104.75[/C][C]104.810906213889[/C][C]-0.0609062138884949[/C][/ROW]
[ROW][C]15[/C][C]104.76[/C][C]104.828521218190[/C][C]-0.0685212181896317[/C][/ROW]
[ROW][C]16[/C][C]104.94[/C][C]104.860280210625[/C][C]0.0797197893749793[/C][/ROW]
[ROW][C]17[/C][C]105.29[/C][C]105.094013274685[/C][C]0.195986725314739[/C][/ROW]
[ROW][C]18[/C][C]105.38[/C][C]105.460992361427[/C][C]-0.0809923614266413[/C][/ROW]
[ROW][C]19[/C][C]105.43[/C][C]105.415095049229[/C][C]0.0149049507714379[/C][/ROW]
[ROW][C]20[/C][C]105.43[/C][C]105.437550534673[/C][C]-0.00755053467327394[/C][/ROW]
[ROW][C]21[/C][C]105.42[/C][C]105.486978172117[/C][C]-0.0669781721174468[/C][/ROW]
[ROW][C]22[/C][C]105.52[/C][C]105.484468698123[/C][C]0.0355313018768063[/C][/ROW]
[ROW][C]23[/C][C]105.69[/C][C]105.638699907367[/C][C]0.051300092633371[/C][/ROW]
[ROW][C]24[/C][C]105.72[/C][C]105.812012535640[/C][C]-0.0920125356402588[/C][/ROW]
[ROW][C]25[/C][C]105.74[/C][C]105.769985084642[/C][C]-0.02998508464202[/C][/ROW]
[ROW][C]26[/C][C]105.74[/C][C]105.794252462300[/C][C]-0.0542524622996764[/C][/ROW]
[ROW][C]27[/C][C]105.74[/C][C]105.825879108859[/C][C]-0.0858791088590926[/C][/ROW]
[ROW][C]28[/C][C]105.95[/C][C]105.824884805968[/C][C]0.125115194032468[/C][/ROW]
[ROW][C]29[/C][C]106.17[/C][C]106.076132895088[/C][C]0.0938671049122893[/C][/ROW]
[ROW][C]30[/C][C]106.34[/C][C]106.264783202778[/C][C]0.0752167972220204[/C][/ROW]
[ROW][C]31[/C][C]106.37[/C][C]106.360007298276[/C][C]0.00999270172379286[/C][/ROW]
[ROW][C]32[/C][C]106.37[/C][C]106.329077243266[/C][C]0.0409227567341805[/C][/ROW]
[ROW][C]33[/C][C]106.36[/C][C]106.330716840331[/C][C]0.0292831596691363[/C][/ROW]
[ROW][C]34[/C][C]106.44[/C][C]106.349649688903[/C][C]0.090350311097268[/C][/ROW]
[ROW][C]35[/C][C]106.29[/C][C]106.473896647465[/C][C]-0.183896647464736[/C][/ROW]
[ROW][C]36[/C][C]106.23[/C][C]106.271857884708[/C][C]-0.0418578847076219[/C][/ROW]
[ROW][C]37[/C][C]106.23[/C][C]106.246651005248[/C][C]-0.0166510052475141[/C][/ROW]
[ROW][C]38[/C][C]106.23[/C][C]106.298448761885[/C][C]-0.0684487618853065[/C][/ROW]
[ROW][C]39[/C][C]106.23[/C][C]106.265518201909[/C][C]-0.0355182019089434[/C][/ROW]
[ROW][C]40[/C][C]106.34[/C][C]106.251962095134[/C][C]0.0880379048662037[/C][/ROW]
[ROW][C]41[/C][C]106.44[/C][C]106.384714258579[/C][C]0.0552857414210537[/C][/ROW]
[ROW][C]42[/C][C]106.44[/C][C]106.454504731863[/C][C]-0.0145047318625162[/C][/ROW]
[ROW][C]43[/C][C]106.48[/C][C]106.409102976189[/C][C]0.0708970238109437[/C][/ROW]
[ROW][C]44[/C][C]106.5[/C][C]106.435386148578[/C][C]0.064613851422073[/C][/ROW]
[ROW][C]45[/C][C]106.57[/C][C]106.460450743149[/C][C]0.109549256850864[/C][/ROW]
[ROW][C]46[/C][C]106.4[/C][C]106.523171028071[/C][C]-0.123171028070596[/C][/ROW]
[ROW][C]47[/C][C]106.37[/C][C]106.297222581807[/C][C]0.0727774181933546[/C][/ROW]
[ROW][C]48[/C][C]106.25[/C][C]106.362750951892[/C][C]-0.112750951892213[/C][/ROW]
[ROW][C]49[/C][C]106.21[/C][C]106.273155353096[/C][C]-0.0631553530956664[/C][/ROW]
[ROW][C]50[/C][C]106.21[/C][C]106.226905773786[/C][C]-0.0169057737860680[/C][/ROW]
[ROW][C]51[/C][C]106.24[/C][C]106.229316034796[/C][C]0.0106839652035338[/C][/ROW]
[ROW][C]52[/C][C]106.19[/C][C]106.233514899246[/C][C]-0.0435148992462501[/C][/ROW]
[ROW][C]53[/C][C]106.08[/C][C]106.148854084091[/C][C]-0.0688540840912035[/C][/ROW]
[ROW][C]54[/C][C]106.13[/C][C]106.017191913565[/C][C]0.112808086434877[/C][/ROW]
[ROW][C]55[/C][C]106.09[/C][C]106.115692286228[/C][C]-0.0256922862280168[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60925&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60925&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
1103.91103.923694876667-0.0136948766666860
2103.91103.924789755446-0.0147897554456499
3103.92103.941645341270-0.0216453412702114
4104.05103.9906474586870.0593525413132544
5104.23104.1720895291240.0579104708758845
6104.3104.347101747472-0.0471017474724066
7104.31104.354053985388-0.0440539853882922
8104.31104.351380045969-0.0413800459693747
9104.34104.385306304686-0.0453063046856742
10104.55104.4311212464440.118878753556377
11104.65104.694443132558-0.0444431325583265
12104.73104.73534764295-0.0053476429499675
13104.75104.773223765681-0.0232237656811312
14104.75104.810906213889-0.0609062138884949
15104.76104.828521218190-0.0685212181896317
16104.94104.8602802106250.0797197893749793
17105.29105.0940132746850.195986725314739
18105.38105.460992361427-0.0809923614266413
19105.43105.4150950492290.0149049507714379
20105.43105.437550534673-0.00755053467327394
21105.42105.486978172117-0.0669781721174468
22105.52105.4844686981230.0355313018768063
23105.69105.6386999073670.051300092633371
24105.72105.812012535640-0.0920125356402588
25105.74105.769985084642-0.02998508464202
26105.74105.794252462300-0.0542524622996764
27105.74105.825879108859-0.0858791088590926
28105.95105.8248848059680.125115194032468
29106.17106.0761328950880.0938671049122893
30106.34106.2647832027780.0752167972220204
31106.37106.3600072982760.00999270172379286
32106.37106.3290772432660.0409227567341805
33106.36106.3307168403310.0292831596691363
34106.44106.3496496889030.090350311097268
35106.29106.473896647465-0.183896647464736
36106.23106.271857884708-0.0418578847076219
37106.23106.246651005248-0.0166510052475141
38106.23106.298448761885-0.0684487618853065
39106.23106.265518201909-0.0355182019089434
40106.34106.2519620951340.0880379048662037
41106.44106.3847142585790.0552857414210537
42106.44106.454504731863-0.0145047318625162
43106.48106.4091029761890.0708970238109437
44106.5106.4353861485780.064613851422073
45106.57106.4604507431490.109549256850864
46106.4106.523171028071-0.123171028070596
47106.37106.2972225818070.0727774181933546
48106.25106.362750951892-0.112750951892213
49106.21106.273155353096-0.0631553530956664
50106.21106.226905773786-0.0169057737860680
51106.24106.2293160347960.0106839652035338
52106.19106.233514899246-0.0435148992462501
53106.08106.148854084091-0.0688540840912035
54106.13106.0171919135650.112808086434877
55106.09106.115692286228-0.0256922862280168






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
110.0712659508708450.142531901741690.928734049129155
120.02188948580322150.04377897160644310.978110514196779
130.008146702633663010.01629340526732600.991853297366337
140.004933087346571630.009866174693143270.995066912653428
150.002166677968401620.004333355936803230.997833322031598
160.0006359126312422970.001271825262484590.999364087368758
170.1066322338161740.2132644676323490.893367766183826
180.09383319155733140.1876663831146630.906166808442669
190.2384143541982040.4768287083964090.761585645801796
200.1979306141627670.3958612283255340.802069385837233
210.160205197927140.320410395854280.83979480207286
220.1501414248717280.3002828497434560.849858575128272
230.1081637035510910.2163274071021820.891836296448909
240.167181947389080.334363894778160.83281805261092
250.1517987722854620.3035975445709240.848201227714538
260.1737674082817900.3475348165635800.82623259171821
270.3392357502991630.6784715005983270.660764249700837
280.2942318666309030.5884637332618060.705768133369097
290.2386372800982020.4772745601964030.761362719901798
300.2002142962650970.4004285925301950.799785703734903
310.1474724255028570.2949448510057150.852527574497143
320.1330162569708950.2660325139417910.866983743029105
330.1244495980435780.2488991960871570.875550401956422
340.09205296964975020.1841059392995000.90794703035025
350.5563518781808090.8872962436383820.443648121819191
360.6270494475853810.7459011048292380.372950552414619
370.5922743211040150.815451357791970.407725678895985
380.6481576408118140.7036847183763710.351842359188186
390.6864296927557430.6271406144885140.313570307244257
400.6961571432462080.6076857135075830.303842856753792
410.648754313294390.7024913734112190.351245686705610
420.8513944709047420.2972110581905160.148605529095258
430.7558498711469040.4883002577061910.244150128853096
440.9557873353160.08842532936800120.0442126646840006

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
11 & 0.071265950870845 & 0.14253190174169 & 0.928734049129155 \tabularnewline
12 & 0.0218894858032215 & 0.0437789716064431 & 0.978110514196779 \tabularnewline
13 & 0.00814670263366301 & 0.0162934052673260 & 0.991853297366337 \tabularnewline
14 & 0.00493308734657163 & 0.00986617469314327 & 0.995066912653428 \tabularnewline
15 & 0.00216667796840162 & 0.00433335593680323 & 0.997833322031598 \tabularnewline
16 & 0.000635912631242297 & 0.00127182526248459 & 0.999364087368758 \tabularnewline
17 & 0.106632233816174 & 0.213264467632349 & 0.893367766183826 \tabularnewline
18 & 0.0938331915573314 & 0.187666383114663 & 0.906166808442669 \tabularnewline
19 & 0.238414354198204 & 0.476828708396409 & 0.761585645801796 \tabularnewline
20 & 0.197930614162767 & 0.395861228325534 & 0.802069385837233 \tabularnewline
21 & 0.16020519792714 & 0.32041039585428 & 0.83979480207286 \tabularnewline
22 & 0.150141424871728 & 0.300282849743456 & 0.849858575128272 \tabularnewline
23 & 0.108163703551091 & 0.216327407102182 & 0.891836296448909 \tabularnewline
24 & 0.16718194738908 & 0.33436389477816 & 0.83281805261092 \tabularnewline
25 & 0.151798772285462 & 0.303597544570924 & 0.848201227714538 \tabularnewline
26 & 0.173767408281790 & 0.347534816563580 & 0.82623259171821 \tabularnewline
27 & 0.339235750299163 & 0.678471500598327 & 0.660764249700837 \tabularnewline
28 & 0.294231866630903 & 0.588463733261806 & 0.705768133369097 \tabularnewline
29 & 0.238637280098202 & 0.477274560196403 & 0.761362719901798 \tabularnewline
30 & 0.200214296265097 & 0.400428592530195 & 0.799785703734903 \tabularnewline
31 & 0.147472425502857 & 0.294944851005715 & 0.852527574497143 \tabularnewline
32 & 0.133016256970895 & 0.266032513941791 & 0.866983743029105 \tabularnewline
33 & 0.124449598043578 & 0.248899196087157 & 0.875550401956422 \tabularnewline
34 & 0.0920529696497502 & 0.184105939299500 & 0.90794703035025 \tabularnewline
35 & 0.556351878180809 & 0.887296243638382 & 0.443648121819191 \tabularnewline
36 & 0.627049447585381 & 0.745901104829238 & 0.372950552414619 \tabularnewline
37 & 0.592274321104015 & 0.81545135779197 & 0.407725678895985 \tabularnewline
38 & 0.648157640811814 & 0.703684718376371 & 0.351842359188186 \tabularnewline
39 & 0.686429692755743 & 0.627140614488514 & 0.313570307244257 \tabularnewline
40 & 0.696157143246208 & 0.607685713507583 & 0.303842856753792 \tabularnewline
41 & 0.64875431329439 & 0.702491373411219 & 0.351245686705610 \tabularnewline
42 & 0.851394470904742 & 0.297211058190516 & 0.148605529095258 \tabularnewline
43 & 0.755849871146904 & 0.488300257706191 & 0.244150128853096 \tabularnewline
44 & 0.955787335316 & 0.0884253293680012 & 0.0442126646840006 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60925&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]11[/C][C]0.071265950870845[/C][C]0.14253190174169[/C][C]0.928734049129155[/C][/ROW]
[ROW][C]12[/C][C]0.0218894858032215[/C][C]0.0437789716064431[/C][C]0.978110514196779[/C][/ROW]
[ROW][C]13[/C][C]0.00814670263366301[/C][C]0.0162934052673260[/C][C]0.991853297366337[/C][/ROW]
[ROW][C]14[/C][C]0.00493308734657163[/C][C]0.00986617469314327[/C][C]0.995066912653428[/C][/ROW]
[ROW][C]15[/C][C]0.00216667796840162[/C][C]0.00433335593680323[/C][C]0.997833322031598[/C][/ROW]
[ROW][C]16[/C][C]0.000635912631242297[/C][C]0.00127182526248459[/C][C]0.999364087368758[/C][/ROW]
[ROW][C]17[/C][C]0.106632233816174[/C][C]0.213264467632349[/C][C]0.893367766183826[/C][/ROW]
[ROW][C]18[/C][C]0.0938331915573314[/C][C]0.187666383114663[/C][C]0.906166808442669[/C][/ROW]
[ROW][C]19[/C][C]0.238414354198204[/C][C]0.476828708396409[/C][C]0.761585645801796[/C][/ROW]
[ROW][C]20[/C][C]0.197930614162767[/C][C]0.395861228325534[/C][C]0.802069385837233[/C][/ROW]
[ROW][C]21[/C][C]0.16020519792714[/C][C]0.32041039585428[/C][C]0.83979480207286[/C][/ROW]
[ROW][C]22[/C][C]0.150141424871728[/C][C]0.300282849743456[/C][C]0.849858575128272[/C][/ROW]
[ROW][C]23[/C][C]0.108163703551091[/C][C]0.216327407102182[/C][C]0.891836296448909[/C][/ROW]
[ROW][C]24[/C][C]0.16718194738908[/C][C]0.33436389477816[/C][C]0.83281805261092[/C][/ROW]
[ROW][C]25[/C][C]0.151798772285462[/C][C]0.303597544570924[/C][C]0.848201227714538[/C][/ROW]
[ROW][C]26[/C][C]0.173767408281790[/C][C]0.347534816563580[/C][C]0.82623259171821[/C][/ROW]
[ROW][C]27[/C][C]0.339235750299163[/C][C]0.678471500598327[/C][C]0.660764249700837[/C][/ROW]
[ROW][C]28[/C][C]0.294231866630903[/C][C]0.588463733261806[/C][C]0.705768133369097[/C][/ROW]
[ROW][C]29[/C][C]0.238637280098202[/C][C]0.477274560196403[/C][C]0.761362719901798[/C][/ROW]
[ROW][C]30[/C][C]0.200214296265097[/C][C]0.400428592530195[/C][C]0.799785703734903[/C][/ROW]
[ROW][C]31[/C][C]0.147472425502857[/C][C]0.294944851005715[/C][C]0.852527574497143[/C][/ROW]
[ROW][C]32[/C][C]0.133016256970895[/C][C]0.266032513941791[/C][C]0.866983743029105[/C][/ROW]
[ROW][C]33[/C][C]0.124449598043578[/C][C]0.248899196087157[/C][C]0.875550401956422[/C][/ROW]
[ROW][C]34[/C][C]0.0920529696497502[/C][C]0.184105939299500[/C][C]0.90794703035025[/C][/ROW]
[ROW][C]35[/C][C]0.556351878180809[/C][C]0.887296243638382[/C][C]0.443648121819191[/C][/ROW]
[ROW][C]36[/C][C]0.627049447585381[/C][C]0.745901104829238[/C][C]0.372950552414619[/C][/ROW]
[ROW][C]37[/C][C]0.592274321104015[/C][C]0.81545135779197[/C][C]0.407725678895985[/C][/ROW]
[ROW][C]38[/C][C]0.648157640811814[/C][C]0.703684718376371[/C][C]0.351842359188186[/C][/ROW]
[ROW][C]39[/C][C]0.686429692755743[/C][C]0.627140614488514[/C][C]0.313570307244257[/C][/ROW]
[ROW][C]40[/C][C]0.696157143246208[/C][C]0.607685713507583[/C][C]0.303842856753792[/C][/ROW]
[ROW][C]41[/C][C]0.64875431329439[/C][C]0.702491373411219[/C][C]0.351245686705610[/C][/ROW]
[ROW][C]42[/C][C]0.851394470904742[/C][C]0.297211058190516[/C][C]0.148605529095258[/C][/ROW]
[ROW][C]43[/C][C]0.755849871146904[/C][C]0.488300257706191[/C][C]0.244150128853096[/C][/ROW]
[ROW][C]44[/C][C]0.955787335316[/C][C]0.0884253293680012[/C][C]0.0442126646840006[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60925&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60925&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
110.0712659508708450.142531901741690.928734049129155
120.02188948580322150.04377897160644310.978110514196779
130.008146702633663010.01629340526732600.991853297366337
140.004933087346571630.009866174693143270.995066912653428
150.002166677968401620.004333355936803230.997833322031598
160.0006359126312422970.001271825262484590.999364087368758
170.1066322338161740.2132644676323490.893367766183826
180.09383319155733140.1876663831146630.906166808442669
190.2384143541982040.4768287083964090.761585645801796
200.1979306141627670.3958612283255340.802069385837233
210.160205197927140.320410395854280.83979480207286
220.1501414248717280.3002828497434560.849858575128272
230.1081637035510910.2163274071021820.891836296448909
240.167181947389080.334363894778160.83281805261092
250.1517987722854620.3035975445709240.848201227714538
260.1737674082817900.3475348165635800.82623259171821
270.3392357502991630.6784715005983270.660764249700837
280.2942318666309030.5884637332618060.705768133369097
290.2386372800982020.4772745601964030.761362719901798
300.2002142962650970.4004285925301950.799785703734903
310.1474724255028570.2949448510057150.852527574497143
320.1330162569708950.2660325139417910.866983743029105
330.1244495980435780.2488991960871570.875550401956422
340.09205296964975020.1841059392995000.90794703035025
350.5563518781808090.8872962436383820.443648121819191
360.6270494475853810.7459011048292380.372950552414619
370.5922743211040150.815451357791970.407725678895985
380.6481576408118140.7036847183763710.351842359188186
390.6864296927557430.6271406144885140.313570307244257
400.6961571432462080.6076857135075830.303842856753792
410.648754313294390.7024913734112190.351245686705610
420.8513944709047420.2972110581905160.148605529095258
430.7558498711469040.4883002577061910.244150128853096
440.9557873353160.08842532936800120.0442126646840006






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level30.088235294117647NOK
5% type I error level50.147058823529412NOK
10% type I error level60.176470588235294NOK

\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 & 3 & 0.088235294117647 & NOK \tabularnewline
5% type I error level & 5 & 0.147058823529412 & NOK \tabularnewline
10% type I error level & 6 & 0.176470588235294 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60925&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]3[/C][C]0.088235294117647[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]5[/C][C]0.147058823529412[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]6[/C][C]0.176470588235294[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60925&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60925&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 level30.088235294117647NOK
5% type I error level50.147058823529412NOK
10% type I error level60.176470588235294NOK


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal 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')
}