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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 computationWed, 18 Nov 2009 12:04:16 -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/18/t1258571184ogwv2uk93mys3wp.htm/, Retrieved Fri, 05 Dec 2025 04:07:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57596, Retrieved Fri, 05 Dec 2025 04:07:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact562

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]
-   PD      [Multiple Regression] [] [2009-11-18 19:04:16] [7dd0431c761b876151627bfbf92230c8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
90398	562000
90269	561000
90390	555000
88219	544000
87032	537000
87175	543000
92603	594000
93571	611000
94118	613000
92159	611000
89528	594000
89955	595000
89587	591000
89488	589000
88521	584000
86587	573000
85159	567000
84915	569000
91378	621000
92729	629000
92194	628000
89664	612000
86285	595000
86858	597000
87184	593000
86629	590000
85220	580000
84816	574000
84831	573000
84957	573000
90951	620000
92134	626000
91790	620000
86625	588000
83324	566000
82719	557000
83614	561000
81640	549000
78665	532000
77828	526000
75728	511000
72187	499000
79357	555000
81329	565000
77304	542000
75576	527000
72932	510000
74291	514000
74988	517000
73302	508000
70483	493000
69848	490000
66466	469000
67610	478000
75091	528000
76207	534000
73454	518000
72008	506000
71362	502000
74250	516000

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57596&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]6 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=57596&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57596&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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 25551.4147450011 + 0.113859995860027X[t] -203.055106917519t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  25551.4147450011 +  0.113859995860027X[t] -203.055106917519t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57596&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  25551.4147450011 +  0.113859995860027X[t] -203.055106917519t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57596&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57596&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] = + 25551.4147450011 + 0.113859995860027X[t] -203.055106917519t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)25551.41474500112931.8925368.71500
X0.1138599958600270.00479323.755800
t-203.05510691751911.518337-17.628900

\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) & 25551.4147450011 & 2931.892536 & 8.715 & 0 & 0 \tabularnewline
X & 0.113859995860027 & 0.004793 & 23.7558 & 0 & 0 \tabularnewline
t & -203.055106917519 & 11.518337 & -17.6289 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57596&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]25551.4147450011[/C][C]2931.892536[/C][C]8.715[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]0.113859995860027[/C][C]0.004793[/C][C]23.7558[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]t[/C][C]-203.055106917519[/C][C]11.518337[/C][C]-17.6289[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57596&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57596&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)25551.41474500112931.8925368.71500
X0.1138599958600270.00479323.755800
t-203.05510691751911.518337-17.628900






Multiple Linear Regression - Regression Statistics
Multiple R0.98906748563434
R-squared0.978254491139036
Adjusted R-squared0.977491490828125
F-TEST (value)1282.11545545903
F-TEST (DF numerator)2
F-TEST (DF denominator)57
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1154.56767677021
Sum Squared Residuals75982511.653826

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.98906748563434 \tabularnewline
R-squared & 0.978254491139036 \tabularnewline
Adjusted R-squared & 0.977491490828125 \tabularnewline
F-TEST (value) & 1282.11545545903 \tabularnewline
F-TEST (DF numerator) & 2 \tabularnewline
F-TEST (DF denominator) & 57 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 1154.56767677021 \tabularnewline
Sum Squared Residuals & 75982511.653826 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57596&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.98906748563434[/C][/ROW]
[ROW][C]R-squared[/C][C]0.978254491139036[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.977491490828125[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1282.11545545903[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]2[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]57[/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]1154.56767677021[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]75982511.653826[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57596&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57596&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 R0.98906748563434
R-squared0.978254491139036
Adjusted R-squared0.977491490828125
F-TEST (value)1282.11545545903
F-TEST (DF numerator)2
F-TEST (DF denominator)57
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1154.56767677021
Sum Squared Residuals75982511.653826






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
19039889337.67731141871060.32268858134
29026989020.7622086411248.23779135899
39039088134.54712656332255.45287343668
48821986679.03206518551539.96793481449
58703285678.95698724781353.04301275220
68717586159.06185549051015.93814450955
79260391762.8665374343840.133462565718
89357193495.431360137275.5686398627849
99411893520.0962449397597.90375506025
109215993089.3211463022-930.321146302176
118952890950.6461097642-1422.64610976420
128995590861.4509987067-906.450998706712
138958790202.955908349-615.955908349086
148948889772.1808097115-284.180809711513
158852188999.8257234939-478.825723493861
168658787544.310662116-957.31066211605
178515986658.0955800384-1499.09558003837
188491586682.760464841-1767.76046484090
199137892400.4251426448-1022.42514264477
209272993108.2500026075-379.250002607462
219219492791.33489983-597.334899829916
228966490766.519859152-1102.51985915197
238628588627.844822614-2342.844822614
248685888652.5097074165-1794.50970741653
258718487994.0146170589-810.014617058907
268662987449.3795225613-820.379522561307
278522086107.7244570435-887.724457043521
288481685221.5093749658-405.509374965843
298483184904.5942721883-73.5942721882968
308495784701.5391652708255.460834729223
319095189849.90386377451101.09613622549
329213490330.00873201711803.99126798285
339179089443.79364993952346.20635006053
348662585597.2186755011027.78132449890
358332482889.243659663434.756340337006
368271981661.44859000521057.55140999477
378361481913.83346652781700.16653347218
388164080344.458409291295.54159071002
397866578205.783372752459.216627247989
407782877319.5682906743508.431709325668
417572875408.6132458564319.386754143586
427218773839.2381886186-1652.23818861858
437935780012.3428498625-655.342849862546
448132980947.8877015453381.112298454708
457730478126.0526898472-822.052689847161
467557676215.0976450292-639.097645029243
477293274076.4226084913-1144.42260849127
487429174328.8074850139-37.8074850138576
497498874467.3323656764520.667634323583
507330273239.537296018762.4627039813413
517048371328.5822512007-845.582251200741
526984870783.9471567031-935.94715670314
536646668189.832136725-1723.83213672506
546761069011.5169925478-1401.51699254778
557509174501.4616786316589.538321368405
567620774981.56654687421225.43345312577
577345472956.7515061963497.248493803711
587200871387.3764489585620.62355104155
597136270728.8813586008633.118641399175
607425072119.86619372372130.13380627632

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 90398 & 89337.6773114187 & 1060.32268858134 \tabularnewline
2 & 90269 & 89020.762208641 & 1248.23779135899 \tabularnewline
3 & 90390 & 88134.5471265633 & 2255.45287343668 \tabularnewline
4 & 88219 & 86679.0320651855 & 1539.96793481449 \tabularnewline
5 & 87032 & 85678.9569872478 & 1353.04301275220 \tabularnewline
6 & 87175 & 86159.0618554905 & 1015.93814450955 \tabularnewline
7 & 92603 & 91762.8665374343 & 840.133462565718 \tabularnewline
8 & 93571 & 93495.4313601372 & 75.5686398627849 \tabularnewline
9 & 94118 & 93520.0962449397 & 597.90375506025 \tabularnewline
10 & 92159 & 93089.3211463022 & -930.321146302176 \tabularnewline
11 & 89528 & 90950.6461097642 & -1422.64610976420 \tabularnewline
12 & 89955 & 90861.4509987067 & -906.450998706712 \tabularnewline
13 & 89587 & 90202.955908349 & -615.955908349086 \tabularnewline
14 & 89488 & 89772.1808097115 & -284.180809711513 \tabularnewline
15 & 88521 & 88999.8257234939 & -478.825723493861 \tabularnewline
16 & 86587 & 87544.310662116 & -957.31066211605 \tabularnewline
17 & 85159 & 86658.0955800384 & -1499.09558003837 \tabularnewline
18 & 84915 & 86682.760464841 & -1767.76046484090 \tabularnewline
19 & 91378 & 92400.4251426448 & -1022.42514264477 \tabularnewline
20 & 92729 & 93108.2500026075 & -379.250002607462 \tabularnewline
21 & 92194 & 92791.33489983 & -597.334899829916 \tabularnewline
22 & 89664 & 90766.519859152 & -1102.51985915197 \tabularnewline
23 & 86285 & 88627.844822614 & -2342.844822614 \tabularnewline
24 & 86858 & 88652.5097074165 & -1794.50970741653 \tabularnewline
25 & 87184 & 87994.0146170589 & -810.014617058907 \tabularnewline
26 & 86629 & 87449.3795225613 & -820.379522561307 \tabularnewline
27 & 85220 & 86107.7244570435 & -887.724457043521 \tabularnewline
28 & 84816 & 85221.5093749658 & -405.509374965843 \tabularnewline
29 & 84831 & 84904.5942721883 & -73.5942721882968 \tabularnewline
30 & 84957 & 84701.5391652708 & 255.460834729223 \tabularnewline
31 & 90951 & 89849.9038637745 & 1101.09613622549 \tabularnewline
32 & 92134 & 90330.0087320171 & 1803.99126798285 \tabularnewline
33 & 91790 & 89443.7936499395 & 2346.20635006053 \tabularnewline
34 & 86625 & 85597.218675501 & 1027.78132449890 \tabularnewline
35 & 83324 & 82889.243659663 & 434.756340337006 \tabularnewline
36 & 82719 & 81661.4485900052 & 1057.55140999477 \tabularnewline
37 & 83614 & 81913.8334665278 & 1700.16653347218 \tabularnewline
38 & 81640 & 80344.45840929 & 1295.54159071002 \tabularnewline
39 & 78665 & 78205.783372752 & 459.216627247989 \tabularnewline
40 & 77828 & 77319.5682906743 & 508.431709325668 \tabularnewline
41 & 75728 & 75408.6132458564 & 319.386754143586 \tabularnewline
42 & 72187 & 73839.2381886186 & -1652.23818861858 \tabularnewline
43 & 79357 & 80012.3428498625 & -655.342849862546 \tabularnewline
44 & 81329 & 80947.8877015453 & 381.112298454708 \tabularnewline
45 & 77304 & 78126.0526898472 & -822.052689847161 \tabularnewline
46 & 75576 & 76215.0976450292 & -639.097645029243 \tabularnewline
47 & 72932 & 74076.4226084913 & -1144.42260849127 \tabularnewline
48 & 74291 & 74328.8074850139 & -37.8074850138576 \tabularnewline
49 & 74988 & 74467.3323656764 & 520.667634323583 \tabularnewline
50 & 73302 & 73239.5372960187 & 62.4627039813413 \tabularnewline
51 & 70483 & 71328.5822512007 & -845.582251200741 \tabularnewline
52 & 69848 & 70783.9471567031 & -935.94715670314 \tabularnewline
53 & 66466 & 68189.832136725 & -1723.83213672506 \tabularnewline
54 & 67610 & 69011.5169925478 & -1401.51699254778 \tabularnewline
55 & 75091 & 74501.4616786316 & 589.538321368405 \tabularnewline
56 & 76207 & 74981.5665468742 & 1225.43345312577 \tabularnewline
57 & 73454 & 72956.7515061963 & 497.248493803711 \tabularnewline
58 & 72008 & 71387.3764489585 & 620.62355104155 \tabularnewline
59 & 71362 & 70728.8813586008 & 633.118641399175 \tabularnewline
60 & 74250 & 72119.8661937237 & 2130.13380627632 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57596&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]90398[/C][C]89337.6773114187[/C][C]1060.32268858134[/C][/ROW]
[ROW][C]2[/C][C]90269[/C][C]89020.762208641[/C][C]1248.23779135899[/C][/ROW]
[ROW][C]3[/C][C]90390[/C][C]88134.5471265633[/C][C]2255.45287343668[/C][/ROW]
[ROW][C]4[/C][C]88219[/C][C]86679.0320651855[/C][C]1539.96793481449[/C][/ROW]
[ROW][C]5[/C][C]87032[/C][C]85678.9569872478[/C][C]1353.04301275220[/C][/ROW]
[ROW][C]6[/C][C]87175[/C][C]86159.0618554905[/C][C]1015.93814450955[/C][/ROW]
[ROW][C]7[/C][C]92603[/C][C]91762.8665374343[/C][C]840.133462565718[/C][/ROW]
[ROW][C]8[/C][C]93571[/C][C]93495.4313601372[/C][C]75.5686398627849[/C][/ROW]
[ROW][C]9[/C][C]94118[/C][C]93520.0962449397[/C][C]597.90375506025[/C][/ROW]
[ROW][C]10[/C][C]92159[/C][C]93089.3211463022[/C][C]-930.321146302176[/C][/ROW]
[ROW][C]11[/C][C]89528[/C][C]90950.6461097642[/C][C]-1422.64610976420[/C][/ROW]
[ROW][C]12[/C][C]89955[/C][C]90861.4509987067[/C][C]-906.450998706712[/C][/ROW]
[ROW][C]13[/C][C]89587[/C][C]90202.955908349[/C][C]-615.955908349086[/C][/ROW]
[ROW][C]14[/C][C]89488[/C][C]89772.1808097115[/C][C]-284.180809711513[/C][/ROW]
[ROW][C]15[/C][C]88521[/C][C]88999.8257234939[/C][C]-478.825723493861[/C][/ROW]
[ROW][C]16[/C][C]86587[/C][C]87544.310662116[/C][C]-957.31066211605[/C][/ROW]
[ROW][C]17[/C][C]85159[/C][C]86658.0955800384[/C][C]-1499.09558003837[/C][/ROW]
[ROW][C]18[/C][C]84915[/C][C]86682.760464841[/C][C]-1767.76046484090[/C][/ROW]
[ROW][C]19[/C][C]91378[/C][C]92400.4251426448[/C][C]-1022.42514264477[/C][/ROW]
[ROW][C]20[/C][C]92729[/C][C]93108.2500026075[/C][C]-379.250002607462[/C][/ROW]
[ROW][C]21[/C][C]92194[/C][C]92791.33489983[/C][C]-597.334899829916[/C][/ROW]
[ROW][C]22[/C][C]89664[/C][C]90766.519859152[/C][C]-1102.51985915197[/C][/ROW]
[ROW][C]23[/C][C]86285[/C][C]88627.844822614[/C][C]-2342.844822614[/C][/ROW]
[ROW][C]24[/C][C]86858[/C][C]88652.5097074165[/C][C]-1794.50970741653[/C][/ROW]
[ROW][C]25[/C][C]87184[/C][C]87994.0146170589[/C][C]-810.014617058907[/C][/ROW]
[ROW][C]26[/C][C]86629[/C][C]87449.3795225613[/C][C]-820.379522561307[/C][/ROW]
[ROW][C]27[/C][C]85220[/C][C]86107.7244570435[/C][C]-887.724457043521[/C][/ROW]
[ROW][C]28[/C][C]84816[/C][C]85221.5093749658[/C][C]-405.509374965843[/C][/ROW]
[ROW][C]29[/C][C]84831[/C][C]84904.5942721883[/C][C]-73.5942721882968[/C][/ROW]
[ROW][C]30[/C][C]84957[/C][C]84701.5391652708[/C][C]255.460834729223[/C][/ROW]
[ROW][C]31[/C][C]90951[/C][C]89849.9038637745[/C][C]1101.09613622549[/C][/ROW]
[ROW][C]32[/C][C]92134[/C][C]90330.0087320171[/C][C]1803.99126798285[/C][/ROW]
[ROW][C]33[/C][C]91790[/C][C]89443.7936499395[/C][C]2346.20635006053[/C][/ROW]
[ROW][C]34[/C][C]86625[/C][C]85597.218675501[/C][C]1027.78132449890[/C][/ROW]
[ROW][C]35[/C][C]83324[/C][C]82889.243659663[/C][C]434.756340337006[/C][/ROW]
[ROW][C]36[/C][C]82719[/C][C]81661.4485900052[/C][C]1057.55140999477[/C][/ROW]
[ROW][C]37[/C][C]83614[/C][C]81913.8334665278[/C][C]1700.16653347218[/C][/ROW]
[ROW][C]38[/C][C]81640[/C][C]80344.45840929[/C][C]1295.54159071002[/C][/ROW]
[ROW][C]39[/C][C]78665[/C][C]78205.783372752[/C][C]459.216627247989[/C][/ROW]
[ROW][C]40[/C][C]77828[/C][C]77319.5682906743[/C][C]508.431709325668[/C][/ROW]
[ROW][C]41[/C][C]75728[/C][C]75408.6132458564[/C][C]319.386754143586[/C][/ROW]
[ROW][C]42[/C][C]72187[/C][C]73839.2381886186[/C][C]-1652.23818861858[/C][/ROW]
[ROW][C]43[/C][C]79357[/C][C]80012.3428498625[/C][C]-655.342849862546[/C][/ROW]
[ROW][C]44[/C][C]81329[/C][C]80947.8877015453[/C][C]381.112298454708[/C][/ROW]
[ROW][C]45[/C][C]77304[/C][C]78126.0526898472[/C][C]-822.052689847161[/C][/ROW]
[ROW][C]46[/C][C]75576[/C][C]76215.0976450292[/C][C]-639.097645029243[/C][/ROW]
[ROW][C]47[/C][C]72932[/C][C]74076.4226084913[/C][C]-1144.42260849127[/C][/ROW]
[ROW][C]48[/C][C]74291[/C][C]74328.8074850139[/C][C]-37.8074850138576[/C][/ROW]
[ROW][C]49[/C][C]74988[/C][C]74467.3323656764[/C][C]520.667634323583[/C][/ROW]
[ROW][C]50[/C][C]73302[/C][C]73239.5372960187[/C][C]62.4627039813413[/C][/ROW]
[ROW][C]51[/C][C]70483[/C][C]71328.5822512007[/C][C]-845.582251200741[/C][/ROW]
[ROW][C]52[/C][C]69848[/C][C]70783.9471567031[/C][C]-935.94715670314[/C][/ROW]
[ROW][C]53[/C][C]66466[/C][C]68189.832136725[/C][C]-1723.83213672506[/C][/ROW]
[ROW][C]54[/C][C]67610[/C][C]69011.5169925478[/C][C]-1401.51699254778[/C][/ROW]
[ROW][C]55[/C][C]75091[/C][C]74501.4616786316[/C][C]589.538321368405[/C][/ROW]
[ROW][C]56[/C][C]76207[/C][C]74981.5665468742[/C][C]1225.43345312577[/C][/ROW]
[ROW][C]57[/C][C]73454[/C][C]72956.7515061963[/C][C]497.248493803711[/C][/ROW]
[ROW][C]58[/C][C]72008[/C][C]71387.3764489585[/C][C]620.62355104155[/C][/ROW]
[ROW][C]59[/C][C]71362[/C][C]70728.8813586008[/C][C]633.118641399175[/C][/ROW]
[ROW][C]60[/C][C]74250[/C][C]72119.8661937237[/C][C]2130.13380627632[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57596&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57596&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
19039889337.67731141871060.32268858134
29026989020.7622086411248.23779135899
39039088134.54712656332255.45287343668
48821986679.03206518551539.96793481449
58703285678.95698724781353.04301275220
68717586159.06185549051015.93814450955
79260391762.8665374343840.133462565718
89357193495.431360137275.5686398627849
99411893520.0962449397597.90375506025
109215993089.3211463022-930.321146302176
118952890950.6461097642-1422.64610976420
128995590861.4509987067-906.450998706712
138958790202.955908349-615.955908349086
148948889772.1808097115-284.180809711513
158852188999.8257234939-478.825723493861
168658787544.310662116-957.31066211605
178515986658.0955800384-1499.09558003837
188491586682.760464841-1767.76046484090
199137892400.4251426448-1022.42514264477
209272993108.2500026075-379.250002607462
219219492791.33489983-597.334899829916
228966490766.519859152-1102.51985915197
238628588627.844822614-2342.844822614
248685888652.5097074165-1794.50970741653
258718487994.0146170589-810.014617058907
268662987449.3795225613-820.379522561307
278522086107.7244570435-887.724457043521
288481685221.5093749658-405.509374965843
298483184904.5942721883-73.5942721882968
308495784701.5391652708255.460834729223
319095189849.90386377451101.09613622549
329213490330.00873201711803.99126798285
339179089443.79364993952346.20635006053
348662585597.2186755011027.78132449890
358332482889.243659663434.756340337006
368271981661.44859000521057.55140999477
378361481913.83346652781700.16653347218
388164080344.458409291295.54159071002
397866578205.783372752459.216627247989
407782877319.5682906743508.431709325668
417572875408.6132458564319.386754143586
427218773839.2381886186-1652.23818861858
437935780012.3428498625-655.342849862546
448132980947.8877015453381.112298454708
457730478126.0526898472-822.052689847161
467557676215.0976450292-639.097645029243
477293274076.4226084913-1144.42260849127
487429174328.8074850139-37.8074850138576
497498874467.3323656764520.667634323583
507330273239.537296018762.4627039813413
517048371328.5822512007-845.582251200741
526984870783.9471567031-935.94715670314
536646668189.832136725-1723.83213672506
546761069011.5169925478-1401.51699254778
557509174501.4616786316589.538321368405
567620774981.56654687421225.43345312577
577345472956.7515061963497.248493803711
587200871387.3764489585620.62355104155
597136270728.8813586008633.118641399175
607425072119.86619372372130.13380627632






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
60.2534296139236060.5068592278472130.746570386076394
70.1504113636034500.3008227272069010.84958863639655
80.0933480988940580.1866961977881160.906651901105942
90.06341807236141530.1268361447228310.936581927638585
100.1329945839505870.2659891679011740.867005416049413
110.2201489565920690.4402979131841370.779851043407931
120.1467000863125880.2934001726251750.853299913687412
130.1047188499197120.2094376998394250.895281150080288
140.1031762804030560.2063525608061130.896823719596944
150.08260530763973390.1652106152794680.917394692360266
160.05792550372261260.1158510074452250.942074496277387
170.04499663750767660.08999327501535320.955003362492323
180.03126669259918150.0625333851983630.968733307400819
190.04310926565581820.08621853131163650.956890734344182
200.1118407632304100.2236815264608190.88815923676959
210.1452773006977790.2905546013955590.85472269930222
220.1351804369804540.2703608739609070.864819563019546
230.1983722247708160.3967444495416310.801627775229184
240.2561585616283880.5123171232567760.743841438371612
250.3482229752266500.6964459504533010.65177702477335
260.434957562097830.869915124195660.56504243790217
270.4897719992957150.979543998591430.510228000704285
280.5422746513771820.9154506972456360.457725348622818
290.5939327707845870.8121344584308250.406067229215413
300.645039036008920.709921927982160.35496096399108
310.8805465867478920.2389068265042170.119453413252108
320.966276797171180.06744640565764020.0337232028288201
330.9875325845848850.02493483083023050.0124674154151153
340.9844856444380850.03102871112382980.0155143555619149
350.9762564817379230.04748703652415410.0237435182620771
360.9687624931926420.06247501361471570.0312375068073579
370.9756279810307350.04874403793853070.0243720189692653
380.9819009724122180.03619805517556360.0180990275877818
390.983570389141110.03285922171778150.0164296108588908
400.9921857953322060.0156284093355880.007814204667794
410.999710952902440.0005780941951193880.000289047097559694
420.999750040335790.0004999193284180390.000249959664209020
430.9996123870538120.0007752258923757390.000387612946187870
440.9990435851709430.00191282965811430.00095641482905715
450.9993521398462140.001295720307572240.000647860153786121
460.9989545640819010.002090871836197960.00104543591809898
470.9987023711464270.002595257707145340.00129762885357267
480.9966383968853670.006723206229265660.00336160311463283
490.9963350507913840.007329898417231750.00366494920861587
500.9977192511147240.004561497770552810.00228074888527640
510.9967169367654470.00656612646910680.0032830632345534
520.995175576862940.009648846274118160.00482442313705908
530.9885329989311820.02293400213763510.0114670010688175
540.9920543874277070.01589122514458610.00794561257229305

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
6 & 0.253429613923606 & 0.506859227847213 & 0.746570386076394 \tabularnewline
7 & 0.150411363603450 & 0.300822727206901 & 0.84958863639655 \tabularnewline
8 & 0.093348098894058 & 0.186696197788116 & 0.906651901105942 \tabularnewline
9 & 0.0634180723614153 & 0.126836144722831 & 0.936581927638585 \tabularnewline
10 & 0.132994583950587 & 0.265989167901174 & 0.867005416049413 \tabularnewline
11 & 0.220148956592069 & 0.440297913184137 & 0.779851043407931 \tabularnewline
12 & 0.146700086312588 & 0.293400172625175 & 0.853299913687412 \tabularnewline
13 & 0.104718849919712 & 0.209437699839425 & 0.895281150080288 \tabularnewline
14 & 0.103176280403056 & 0.206352560806113 & 0.896823719596944 \tabularnewline
15 & 0.0826053076397339 & 0.165210615279468 & 0.917394692360266 \tabularnewline
16 & 0.0579255037226126 & 0.115851007445225 & 0.942074496277387 \tabularnewline
17 & 0.0449966375076766 & 0.0899932750153532 & 0.955003362492323 \tabularnewline
18 & 0.0312666925991815 & 0.062533385198363 & 0.968733307400819 \tabularnewline
19 & 0.0431092656558182 & 0.0862185313116365 & 0.956890734344182 \tabularnewline
20 & 0.111840763230410 & 0.223681526460819 & 0.88815923676959 \tabularnewline
21 & 0.145277300697779 & 0.290554601395559 & 0.85472269930222 \tabularnewline
22 & 0.135180436980454 & 0.270360873960907 & 0.864819563019546 \tabularnewline
23 & 0.198372224770816 & 0.396744449541631 & 0.801627775229184 \tabularnewline
24 & 0.256158561628388 & 0.512317123256776 & 0.743841438371612 \tabularnewline
25 & 0.348222975226650 & 0.696445950453301 & 0.65177702477335 \tabularnewline
26 & 0.43495756209783 & 0.86991512419566 & 0.56504243790217 \tabularnewline
27 & 0.489771999295715 & 0.97954399859143 & 0.510228000704285 \tabularnewline
28 & 0.542274651377182 & 0.915450697245636 & 0.457725348622818 \tabularnewline
29 & 0.593932770784587 & 0.812134458430825 & 0.406067229215413 \tabularnewline
30 & 0.64503903600892 & 0.70992192798216 & 0.35496096399108 \tabularnewline
31 & 0.880546586747892 & 0.238906826504217 & 0.119453413252108 \tabularnewline
32 & 0.96627679717118 & 0.0674464056576402 & 0.0337232028288201 \tabularnewline
33 & 0.987532584584885 & 0.0249348308302305 & 0.0124674154151153 \tabularnewline
34 & 0.984485644438085 & 0.0310287111238298 & 0.0155143555619149 \tabularnewline
35 & 0.976256481737923 & 0.0474870365241541 & 0.0237435182620771 \tabularnewline
36 & 0.968762493192642 & 0.0624750136147157 & 0.0312375068073579 \tabularnewline
37 & 0.975627981030735 & 0.0487440379385307 & 0.0243720189692653 \tabularnewline
38 & 0.981900972412218 & 0.0361980551755636 & 0.0180990275877818 \tabularnewline
39 & 0.98357038914111 & 0.0328592217177815 & 0.0164296108588908 \tabularnewline
40 & 0.992185795332206 & 0.015628409335588 & 0.007814204667794 \tabularnewline
41 & 0.99971095290244 & 0.000578094195119388 & 0.000289047097559694 \tabularnewline
42 & 0.99975004033579 & 0.000499919328418039 & 0.000249959664209020 \tabularnewline
43 & 0.999612387053812 & 0.000775225892375739 & 0.000387612946187870 \tabularnewline
44 & 0.999043585170943 & 0.0019128296581143 & 0.00095641482905715 \tabularnewline
45 & 0.999352139846214 & 0.00129572030757224 & 0.000647860153786121 \tabularnewline
46 & 0.998954564081901 & 0.00209087183619796 & 0.00104543591809898 \tabularnewline
47 & 0.998702371146427 & 0.00259525770714534 & 0.00129762885357267 \tabularnewline
48 & 0.996638396885367 & 0.00672320622926566 & 0.00336160311463283 \tabularnewline
49 & 0.996335050791384 & 0.00732989841723175 & 0.00366494920861587 \tabularnewline
50 & 0.997719251114724 & 0.00456149777055281 & 0.00228074888527640 \tabularnewline
51 & 0.996716936765447 & 0.0065661264691068 & 0.0032830632345534 \tabularnewline
52 & 0.99517557686294 & 0.00964884627411816 & 0.00482442313705908 \tabularnewline
53 & 0.988532998931182 & 0.0229340021376351 & 0.0114670010688175 \tabularnewline
54 & 0.992054387427707 & 0.0158912251445861 & 0.00794561257229305 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57596&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]6[/C][C]0.253429613923606[/C][C]0.506859227847213[/C][C]0.746570386076394[/C][/ROW]
[ROW][C]7[/C][C]0.150411363603450[/C][C]0.300822727206901[/C][C]0.84958863639655[/C][/ROW]
[ROW][C]8[/C][C]0.093348098894058[/C][C]0.186696197788116[/C][C]0.906651901105942[/C][/ROW]
[ROW][C]9[/C][C]0.0634180723614153[/C][C]0.126836144722831[/C][C]0.936581927638585[/C][/ROW]
[ROW][C]10[/C][C]0.132994583950587[/C][C]0.265989167901174[/C][C]0.867005416049413[/C][/ROW]
[ROW][C]11[/C][C]0.220148956592069[/C][C]0.440297913184137[/C][C]0.779851043407931[/C][/ROW]
[ROW][C]12[/C][C]0.146700086312588[/C][C]0.293400172625175[/C][C]0.853299913687412[/C][/ROW]
[ROW][C]13[/C][C]0.104718849919712[/C][C]0.209437699839425[/C][C]0.895281150080288[/C][/ROW]
[ROW][C]14[/C][C]0.103176280403056[/C][C]0.206352560806113[/C][C]0.896823719596944[/C][/ROW]
[ROW][C]15[/C][C]0.0826053076397339[/C][C]0.165210615279468[/C][C]0.917394692360266[/C][/ROW]
[ROW][C]16[/C][C]0.0579255037226126[/C][C]0.115851007445225[/C][C]0.942074496277387[/C][/ROW]
[ROW][C]17[/C][C]0.0449966375076766[/C][C]0.0899932750153532[/C][C]0.955003362492323[/C][/ROW]
[ROW][C]18[/C][C]0.0312666925991815[/C][C]0.062533385198363[/C][C]0.968733307400819[/C][/ROW]
[ROW][C]19[/C][C]0.0431092656558182[/C][C]0.0862185313116365[/C][C]0.956890734344182[/C][/ROW]
[ROW][C]20[/C][C]0.111840763230410[/C][C]0.223681526460819[/C][C]0.88815923676959[/C][/ROW]
[ROW][C]21[/C][C]0.145277300697779[/C][C]0.290554601395559[/C][C]0.85472269930222[/C][/ROW]
[ROW][C]22[/C][C]0.135180436980454[/C][C]0.270360873960907[/C][C]0.864819563019546[/C][/ROW]
[ROW][C]23[/C][C]0.198372224770816[/C][C]0.396744449541631[/C][C]0.801627775229184[/C][/ROW]
[ROW][C]24[/C][C]0.256158561628388[/C][C]0.512317123256776[/C][C]0.743841438371612[/C][/ROW]
[ROW][C]25[/C][C]0.348222975226650[/C][C]0.696445950453301[/C][C]0.65177702477335[/C][/ROW]
[ROW][C]26[/C][C]0.43495756209783[/C][C]0.86991512419566[/C][C]0.56504243790217[/C][/ROW]
[ROW][C]27[/C][C]0.489771999295715[/C][C]0.97954399859143[/C][C]0.510228000704285[/C][/ROW]
[ROW][C]28[/C][C]0.542274651377182[/C][C]0.915450697245636[/C][C]0.457725348622818[/C][/ROW]
[ROW][C]29[/C][C]0.593932770784587[/C][C]0.812134458430825[/C][C]0.406067229215413[/C][/ROW]
[ROW][C]30[/C][C]0.64503903600892[/C][C]0.70992192798216[/C][C]0.35496096399108[/C][/ROW]
[ROW][C]31[/C][C]0.880546586747892[/C][C]0.238906826504217[/C][C]0.119453413252108[/C][/ROW]
[ROW][C]32[/C][C]0.96627679717118[/C][C]0.0674464056576402[/C][C]0.0337232028288201[/C][/ROW]
[ROW][C]33[/C][C]0.987532584584885[/C][C]0.0249348308302305[/C][C]0.0124674154151153[/C][/ROW]
[ROW][C]34[/C][C]0.984485644438085[/C][C]0.0310287111238298[/C][C]0.0155143555619149[/C][/ROW]
[ROW][C]35[/C][C]0.976256481737923[/C][C]0.0474870365241541[/C][C]0.0237435182620771[/C][/ROW]
[ROW][C]36[/C][C]0.968762493192642[/C][C]0.0624750136147157[/C][C]0.0312375068073579[/C][/ROW]
[ROW][C]37[/C][C]0.975627981030735[/C][C]0.0487440379385307[/C][C]0.0243720189692653[/C][/ROW]
[ROW][C]38[/C][C]0.981900972412218[/C][C]0.0361980551755636[/C][C]0.0180990275877818[/C][/ROW]
[ROW][C]39[/C][C]0.98357038914111[/C][C]0.0328592217177815[/C][C]0.0164296108588908[/C][/ROW]
[ROW][C]40[/C][C]0.992185795332206[/C][C]0.015628409335588[/C][C]0.007814204667794[/C][/ROW]
[ROW][C]41[/C][C]0.99971095290244[/C][C]0.000578094195119388[/C][C]0.000289047097559694[/C][/ROW]
[ROW][C]42[/C][C]0.99975004033579[/C][C]0.000499919328418039[/C][C]0.000249959664209020[/C][/ROW]
[ROW][C]43[/C][C]0.999612387053812[/C][C]0.000775225892375739[/C][C]0.000387612946187870[/C][/ROW]
[ROW][C]44[/C][C]0.999043585170943[/C][C]0.0019128296581143[/C][C]0.00095641482905715[/C][/ROW]
[ROW][C]45[/C][C]0.999352139846214[/C][C]0.00129572030757224[/C][C]0.000647860153786121[/C][/ROW]
[ROW][C]46[/C][C]0.998954564081901[/C][C]0.00209087183619796[/C][C]0.00104543591809898[/C][/ROW]
[ROW][C]47[/C][C]0.998702371146427[/C][C]0.00259525770714534[/C][C]0.00129762885357267[/C][/ROW]
[ROW][C]48[/C][C]0.996638396885367[/C][C]0.00672320622926566[/C][C]0.00336160311463283[/C][/ROW]
[ROW][C]49[/C][C]0.996335050791384[/C][C]0.00732989841723175[/C][C]0.00366494920861587[/C][/ROW]
[ROW][C]50[/C][C]0.997719251114724[/C][C]0.00456149777055281[/C][C]0.00228074888527640[/C][/ROW]
[ROW][C]51[/C][C]0.996716936765447[/C][C]0.0065661264691068[/C][C]0.0032830632345534[/C][/ROW]
[ROW][C]52[/C][C]0.99517557686294[/C][C]0.00964884627411816[/C][C]0.00482442313705908[/C][/ROW]
[ROW][C]53[/C][C]0.988532998931182[/C][C]0.0229340021376351[/C][C]0.0114670010688175[/C][/ROW]
[ROW][C]54[/C][C]0.992054387427707[/C][C]0.0158912251445861[/C][C]0.00794561257229305[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57596&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57596&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
60.2534296139236060.5068592278472130.746570386076394
70.1504113636034500.3008227272069010.84958863639655
80.0933480988940580.1866961977881160.906651901105942
90.06341807236141530.1268361447228310.936581927638585
100.1329945839505870.2659891679011740.867005416049413
110.2201489565920690.4402979131841370.779851043407931
120.1467000863125880.2934001726251750.853299913687412
130.1047188499197120.2094376998394250.895281150080288
140.1031762804030560.2063525608061130.896823719596944
150.08260530763973390.1652106152794680.917394692360266
160.05792550372261260.1158510074452250.942074496277387
170.04499663750767660.08999327501535320.955003362492323
180.03126669259918150.0625333851983630.968733307400819
190.04310926565581820.08621853131163650.956890734344182
200.1118407632304100.2236815264608190.88815923676959
210.1452773006977790.2905546013955590.85472269930222
220.1351804369804540.2703608739609070.864819563019546
230.1983722247708160.3967444495416310.801627775229184
240.2561585616283880.5123171232567760.743841438371612
250.3482229752266500.6964459504533010.65177702477335
260.434957562097830.869915124195660.56504243790217
270.4897719992957150.979543998591430.510228000704285
280.5422746513771820.9154506972456360.457725348622818
290.5939327707845870.8121344584308250.406067229215413
300.645039036008920.709921927982160.35496096399108
310.8805465867478920.2389068265042170.119453413252108
320.966276797171180.06744640565764020.0337232028288201
330.9875325845848850.02493483083023050.0124674154151153
340.9844856444380850.03102871112382980.0155143555619149
350.9762564817379230.04748703652415410.0237435182620771
360.9687624931926420.06247501361471570.0312375068073579
370.9756279810307350.04874403793853070.0243720189692653
380.9819009724122180.03619805517556360.0180990275877818
390.983570389141110.03285922171778150.0164296108588908
400.9921857953322060.0156284093355880.007814204667794
410.999710952902440.0005780941951193880.000289047097559694
420.999750040335790.0004999193284180390.000249959664209020
430.9996123870538120.0007752258923757390.000387612946187870
440.9990435851709430.00191282965811430.00095641482905715
450.9993521398462140.001295720307572240.000647860153786121
460.9989545640819010.002090871836197960.00104543591809898
470.9987023711464270.002595257707145340.00129762885357267
480.9966383968853670.006723206229265660.00336160311463283
490.9963350507913840.007329898417231750.00366494920861587
500.9977192511147240.004561497770552810.00228074888527640
510.9967169367654470.00656612646910680.0032830632345534
520.995175576862940.009648846274118160.00482442313705908
530.9885329989311820.02293400213763510.0114670010688175
540.9920543874277070.01589122514458610.00794561257229305






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level120.244897959183673NOK
5% type I error level210.428571428571429NOK
10% type I error level260.530612244897959NOK

\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 & 12 & 0.244897959183673 & NOK \tabularnewline
5% type I error level & 21 & 0.428571428571429 & NOK \tabularnewline
10% type I error level & 26 & 0.530612244897959 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57596&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]12[/C][C]0.244897959183673[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]21[/C][C]0.428571428571429[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]26[/C][C]0.530612244897959[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57596&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57596&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 level120.244897959183673NOK
5% type I error level210.428571428571429NOK
10% type I error level260.530612244897959NOK


Figures (Output of Computation)

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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 2 ; 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')
}