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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 11:12:11 -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/20/t1258741320lsijg7sxti2ec1q.htm/, Retrieved Thu, 28 Mar 2024 20:56:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58389, Retrieved Thu, 28 Mar 2024 20:56:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact182
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]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 14:03:14] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [] [2009-11-19 09:42:44] [d181e5359f7da6c8509e4702d1229fb0]
-    D        [Multiple Regression] [multiple regressi...] [2009-11-20 18:12:11] [371dc2189c569d90e2c1567f632c3ec0] [Current]
-    D          [Multiple Regression] [multiple regression] [2009-12-14 19:39:00] [34d27ebe78dc2d31581e8710befe8733]
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Dataseries X:
462	1919
455	1911
461	1870
461	2263
463	1802
462	1863
456	1989
455	2197
456	2409
472	2502
472	2593
471	2598
465	2053
459	2213
465	2238
468	2359
467	2151
463	2474
460	3079
462	2312
461	2565
476	1972
476	2484
471	2202
453	2151
443	1976
442	2012
444	2114
438	1772
427	1957
424	2070
416	1990
406	2182
431	2008
434	1916
418	2397
412	2114
404	1778
409	1641
412	2186
406	1773
398	1785
397	2217
385	2153
390	1895
413	2475
413	1793
401	2308
397	2051
397	1898
409	2142
419	1874
424	1560
428	1808
430	1575
424	1525
433	1997
456	1753
459	1623
446	2251
441	1890




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58389&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58389&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58389&T=0

As an alternative you can also use a QR Code:  

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

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







Multiple Linear Regression - Estimated Regression Equation
wkl[t] = + 356.359058985737 + 0.0361691651132457bvg[t] + 8.56292555607903M1[t] + 4.52298938484529M2[t] + 9.20429259096884M3[t] + 6.34447970174317M4[t] + 17.7168814951074M5[t] + 7.72003391933123M6[t] -2.02485392329182M7[t] -1.57777765723701M8[t] -7.0784462199644M9[t] + 15.7665893416910M10[t] + 19.1439730815084M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
wkl[t] =  +  356.359058985737 +  0.0361691651132457bvg[t] +  8.56292555607903M1[t] +  4.52298938484529M2[t] +  9.20429259096884M3[t] +  6.34447970174317M4[t] +  17.7168814951074M5[t] +  7.72003391933123M6[t] -2.02485392329182M7[t] -1.57777765723701M8[t] -7.0784462199644M9[t] +  15.7665893416910M10[t] +  19.1439730815084M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58389&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]wkl[t] =  +  356.359058985737 +  0.0361691651132457bvg[t] +  8.56292555607903M1[t] +  4.52298938484529M2[t] +  9.20429259096884M3[t] +  6.34447970174317M4[t] +  17.7168814951074M5[t] +  7.72003391933123M6[t] -2.02485392329182M7[t] -1.57777765723701M8[t] -7.0784462199644M9[t] +  15.7665893416910M10[t] +  19.1439730815084M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58389&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58389&T=1

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Estimated Regression Equation
wkl[t] = + 356.359058985737 + 0.0361691651132457bvg[t] + 8.56292555607903M1[t] + 4.52298938484529M2[t] + 9.20429259096884M3[t] + 6.34447970174317M4[t] + 17.7168814951074M5[t] + 7.72003391933123M6[t] -2.02485392329182M7[t] -1.57777765723701M8[t] -7.0784462199644M9[t] + 15.7665893416910M10[t] + 19.1439730815084M11[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)356.35905898573732.2081411.064300
bvg0.03616916511324570.012762.83460.0066950.003348
M18.5629255560790316.3861030.52260.6036760.301838
M24.5229893848452917.3229160.26110.7951330.397567
M39.2042925909688417.2311660.53420.5956930.297846
M46.3444797017431716.7497140.37880.7065210.35326
M517.716881495107417.9432040.98740.3284040.164202
M67.7200339193312317.2424160.44770.6563590.328179
M7-2.0248539232918216.703121-0.12120.9040180.452009
M8-1.5777776572370117.052526-0.09250.9266660.463333
M9-7.078446219964416.667794-0.42470.6729690.336484
M1015.766589341691016.783220.93940.3522160.176108
M1119.143973081508416.9223991.13130.2635580.131779

\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) & 356.359058985737 & 32.20814 & 11.0643 & 0 & 0 \tabularnewline
bvg & 0.0361691651132457 & 0.01276 & 2.8346 & 0.006695 & 0.003348 \tabularnewline
M1 & 8.56292555607903 & 16.386103 & 0.5226 & 0.603676 & 0.301838 \tabularnewline
M2 & 4.52298938484529 & 17.322916 & 0.2611 & 0.795133 & 0.397567 \tabularnewline
M3 & 9.20429259096884 & 17.231166 & 0.5342 & 0.595693 & 0.297846 \tabularnewline
M4 & 6.34447970174317 & 16.749714 & 0.3788 & 0.706521 & 0.35326 \tabularnewline
M5 & 17.7168814951074 & 17.943204 & 0.9874 & 0.328404 & 0.164202 \tabularnewline
M6 & 7.72003391933123 & 17.242416 & 0.4477 & 0.656359 & 0.328179 \tabularnewline
M7 & -2.02485392329182 & 16.703121 & -0.1212 & 0.904018 & 0.452009 \tabularnewline
M8 & -1.57777765723701 & 17.052526 & -0.0925 & 0.926666 & 0.463333 \tabularnewline
M9 & -7.0784462199644 & 16.667794 & -0.4247 & 0.672969 & 0.336484 \tabularnewline
M10 & 15.7665893416910 & 16.78322 & 0.9394 & 0.352216 & 0.176108 \tabularnewline
M11 & 19.1439730815084 & 16.922399 & 1.1313 & 0.263558 & 0.131779 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58389&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]356.359058985737[/C][C]32.20814[/C][C]11.0643[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]bvg[/C][C]0.0361691651132457[/C][C]0.01276[/C][C]2.8346[/C][C]0.006695[/C][C]0.003348[/C][/ROW]
[ROW][C]M1[/C][C]8.56292555607903[/C][C]16.386103[/C][C]0.5226[/C][C]0.603676[/C][C]0.301838[/C][/ROW]
[ROW][C]M2[/C][C]4.52298938484529[/C][C]17.322916[/C][C]0.2611[/C][C]0.795133[/C][C]0.397567[/C][/ROW]
[ROW][C]M3[/C][C]9.20429259096884[/C][C]17.231166[/C][C]0.5342[/C][C]0.595693[/C][C]0.297846[/C][/ROW]
[ROW][C]M4[/C][C]6.34447970174317[/C][C]16.749714[/C][C]0.3788[/C][C]0.706521[/C][C]0.35326[/C][/ROW]
[ROW][C]M5[/C][C]17.7168814951074[/C][C]17.943204[/C][C]0.9874[/C][C]0.328404[/C][C]0.164202[/C][/ROW]
[ROW][C]M6[/C][C]7.72003391933123[/C][C]17.242416[/C][C]0.4477[/C][C]0.656359[/C][C]0.328179[/C][/ROW]
[ROW][C]M7[/C][C]-2.02485392329182[/C][C]16.703121[/C][C]-0.1212[/C][C]0.904018[/C][C]0.452009[/C][/ROW]
[ROW][C]M8[/C][C]-1.57777765723701[/C][C]17.052526[/C][C]-0.0925[/C][C]0.926666[/C][C]0.463333[/C][/ROW]
[ROW][C]M9[/C][C]-7.0784462199644[/C][C]16.667794[/C][C]-0.4247[/C][C]0.672969[/C][C]0.336484[/C][/ROW]
[ROW][C]M10[/C][C]15.7665893416910[/C][C]16.78322[/C][C]0.9394[/C][C]0.352216[/C][C]0.176108[/C][/ROW]
[ROW][C]M11[/C][C]19.1439730815084[/C][C]16.922399[/C][C]1.1313[/C][C]0.263558[/C][C]0.131779[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58389&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58389&T=2

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)356.35905898573732.2081411.064300
bvg0.03616916511324570.012762.83460.0066950.003348
M18.5629255560790316.3861030.52260.6036760.301838
M24.5229893848452917.3229160.26110.7951330.397567
M39.2042925909688417.2311660.53420.5956930.297846
M46.3444797017431716.7497140.37880.7065210.35326
M517.716881495107417.9432040.98740.3284040.164202
M67.7200339193312317.2424160.44770.6563590.328179
M7-2.0248539232918216.703121-0.12120.9040180.452009
M8-1.5777776572370117.052526-0.09250.9266660.463333
M9-7.078446219964416.667794-0.42470.6729690.336484
M1015.766589341691016.783220.93940.3522160.176108
M1119.143973081508416.9223991.13130.2635580.131779







Multiple Linear Regression - Regression Statistics
Multiple R0.448758728566603
R-squared0.201384396464714
Adjusted R-squared0.00173049558089289
F-TEST (value)1.00866747693500
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.455970418781994
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation26.1987945445670
Sum Squared Residuals32946.0881082447

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.448758728566603 \tabularnewline
R-squared & 0.201384396464714 \tabularnewline
Adjusted R-squared & 0.00173049558089289 \tabularnewline
F-TEST (value) & 1.00866747693500 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 0.455970418781994 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 26.1987945445670 \tabularnewline
Sum Squared Residuals & 32946.0881082447 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58389&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.448758728566603[/C][/ROW]
[ROW][C]R-squared[/C][C]0.201384396464714[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.00173049558089289[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]1.00866747693500[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]48[/C][/ROW]
[ROW][C]p-value[/C][C]0.455970418781994[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]26.1987945445670[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]32946.0881082447[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58389&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58389&T=3

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Regression Statistics
Multiple R0.448758728566603
R-squared0.201384396464714
Adjusted R-squared0.00173049558089289
F-TEST (value)1.00866747693500
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value0.455970418781994
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation26.1987945445670
Sum Squared Residuals32946.0881082447







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1462434.33061239413427.6693876058664
2455430.00132290199524.9986770980054
3461433.19969033847527.8003096615250
4461444.55435933875516.4456406612451
5463439.25277601491323.7472239850872
6462431.46224751104530.5377524889553
7456426.27467447269129.7253255273094
8455434.244937082320.7550629176995
9456436.41213152358119.5878684764188
10472462.6208994407689.37910055923155
11472469.2896772058912.71032279410877
12471450.32654994994920.6734500500510
13465439.17728051930925.8227194806908
14459440.92441076619518.0755892338053
15465446.50994310014918.4900568998505
16468448.02659918962619.9734008103735
17467451.87581463943615.1241853605644
18463453.5616073952389.43839260476218
19460465.699064446128-5.69906444612843
20462438.40439107032423.5956089296762
21461442.05452128124818.9454787187525
22476443.45124193074832.5487580692518
23476465.34723820854710.6527617914526
24471436.00356056510434.9964394348962
25453442.72185870040710.2781412995928
26443432.35231863435610.6476813656445
27442438.3357117845563.66428821544409
28444439.1651537368814.8348462631187
29438438.167701061515-0.167701061515477
30427434.86214903169-7.86214903168978
31424429.204376846864-5.2043768468635
32416426.757919903859-10.7579199038586
33406428.201731042874-22.2017310428744
34431444.753331874825-13.7533318748251
35434444.803152424224-10.8031524242238
36418443.056547762187-25.0565477621867
37412441.383599591217-29.3835995912172
38404425.190823941933-21.1908239419329
39409424.916951527542-15.9169515275417
40412441.769333625035-29.769333625035
41406438.203870226629-32.2038702266287
42398428.641052632212-30.6410526322115
43397434.521244118511-37.5212441185106
44385432.653493817318-47.6534938173177
45390417.821180655373-27.8211806553729
46413461.644331982711-48.6443319827108
47413440.354345115295-27.3543451152946
48401439.837492067108-38.8374920671078
49397439.104942189083-42.1049421890827
50397429.531123755522-32.5311237555223
51409443.037703249278-34.0377032492779
52419430.484554109702-11.4845541097023
53424430.499838057507-6.49983805750738
54428429.472943429816-1.47294342981616
55430411.30064011580718.6993598841931
56424409.93925812619914.0607418738006
57433421.51043549692411.4895645030760
58456435.53019477094720.4698052290526
59459434.20558704604324.7944129539571
60446437.7758496556538.22415034434721
61441433.281706605857.71829339414989

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 462 & 434.330612394134 & 27.6693876058664 \tabularnewline
2 & 455 & 430.001322901995 & 24.9986770980054 \tabularnewline
3 & 461 & 433.199690338475 & 27.8003096615250 \tabularnewline
4 & 461 & 444.554359338755 & 16.4456406612451 \tabularnewline
5 & 463 & 439.252776014913 & 23.7472239850872 \tabularnewline
6 & 462 & 431.462247511045 & 30.5377524889553 \tabularnewline
7 & 456 & 426.274674472691 & 29.7253255273094 \tabularnewline
8 & 455 & 434.2449370823 & 20.7550629176995 \tabularnewline
9 & 456 & 436.412131523581 & 19.5878684764188 \tabularnewline
10 & 472 & 462.620899440768 & 9.37910055923155 \tabularnewline
11 & 472 & 469.289677205891 & 2.71032279410877 \tabularnewline
12 & 471 & 450.326549949949 & 20.6734500500510 \tabularnewline
13 & 465 & 439.177280519309 & 25.8227194806908 \tabularnewline
14 & 459 & 440.924410766195 & 18.0755892338053 \tabularnewline
15 & 465 & 446.509943100149 & 18.4900568998505 \tabularnewline
16 & 468 & 448.026599189626 & 19.9734008103735 \tabularnewline
17 & 467 & 451.875814639436 & 15.1241853605644 \tabularnewline
18 & 463 & 453.561607395238 & 9.43839260476218 \tabularnewline
19 & 460 & 465.699064446128 & -5.69906444612843 \tabularnewline
20 & 462 & 438.404391070324 & 23.5956089296762 \tabularnewline
21 & 461 & 442.054521281248 & 18.9454787187525 \tabularnewline
22 & 476 & 443.451241930748 & 32.5487580692518 \tabularnewline
23 & 476 & 465.347238208547 & 10.6527617914526 \tabularnewline
24 & 471 & 436.003560565104 & 34.9964394348962 \tabularnewline
25 & 453 & 442.721858700407 & 10.2781412995928 \tabularnewline
26 & 443 & 432.352318634356 & 10.6476813656445 \tabularnewline
27 & 442 & 438.335711784556 & 3.66428821544409 \tabularnewline
28 & 444 & 439.165153736881 & 4.8348462631187 \tabularnewline
29 & 438 & 438.167701061515 & -0.167701061515477 \tabularnewline
30 & 427 & 434.86214903169 & -7.86214903168978 \tabularnewline
31 & 424 & 429.204376846864 & -5.2043768468635 \tabularnewline
32 & 416 & 426.757919903859 & -10.7579199038586 \tabularnewline
33 & 406 & 428.201731042874 & -22.2017310428744 \tabularnewline
34 & 431 & 444.753331874825 & -13.7533318748251 \tabularnewline
35 & 434 & 444.803152424224 & -10.8031524242238 \tabularnewline
36 & 418 & 443.056547762187 & -25.0565477621867 \tabularnewline
37 & 412 & 441.383599591217 & -29.3835995912172 \tabularnewline
38 & 404 & 425.190823941933 & -21.1908239419329 \tabularnewline
39 & 409 & 424.916951527542 & -15.9169515275417 \tabularnewline
40 & 412 & 441.769333625035 & -29.769333625035 \tabularnewline
41 & 406 & 438.203870226629 & -32.2038702266287 \tabularnewline
42 & 398 & 428.641052632212 & -30.6410526322115 \tabularnewline
43 & 397 & 434.521244118511 & -37.5212441185106 \tabularnewline
44 & 385 & 432.653493817318 & -47.6534938173177 \tabularnewline
45 & 390 & 417.821180655373 & -27.8211806553729 \tabularnewline
46 & 413 & 461.644331982711 & -48.6443319827108 \tabularnewline
47 & 413 & 440.354345115295 & -27.3543451152946 \tabularnewline
48 & 401 & 439.837492067108 & -38.8374920671078 \tabularnewline
49 & 397 & 439.104942189083 & -42.1049421890827 \tabularnewline
50 & 397 & 429.531123755522 & -32.5311237555223 \tabularnewline
51 & 409 & 443.037703249278 & -34.0377032492779 \tabularnewline
52 & 419 & 430.484554109702 & -11.4845541097023 \tabularnewline
53 & 424 & 430.499838057507 & -6.49983805750738 \tabularnewline
54 & 428 & 429.472943429816 & -1.47294342981616 \tabularnewline
55 & 430 & 411.300640115807 & 18.6993598841931 \tabularnewline
56 & 424 & 409.939258126199 & 14.0607418738006 \tabularnewline
57 & 433 & 421.510435496924 & 11.4895645030760 \tabularnewline
58 & 456 & 435.530194770947 & 20.4698052290526 \tabularnewline
59 & 459 & 434.205587046043 & 24.7944129539571 \tabularnewline
60 & 446 & 437.775849655653 & 8.22415034434721 \tabularnewline
61 & 441 & 433.28170660585 & 7.71829339414989 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58389&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]462[/C][C]434.330612394134[/C][C]27.6693876058664[/C][/ROW]
[ROW][C]2[/C][C]455[/C][C]430.001322901995[/C][C]24.9986770980054[/C][/ROW]
[ROW][C]3[/C][C]461[/C][C]433.199690338475[/C][C]27.8003096615250[/C][/ROW]
[ROW][C]4[/C][C]461[/C][C]444.554359338755[/C][C]16.4456406612451[/C][/ROW]
[ROW][C]5[/C][C]463[/C][C]439.252776014913[/C][C]23.7472239850872[/C][/ROW]
[ROW][C]6[/C][C]462[/C][C]431.462247511045[/C][C]30.5377524889553[/C][/ROW]
[ROW][C]7[/C][C]456[/C][C]426.274674472691[/C][C]29.7253255273094[/C][/ROW]
[ROW][C]8[/C][C]455[/C][C]434.2449370823[/C][C]20.7550629176995[/C][/ROW]
[ROW][C]9[/C][C]456[/C][C]436.412131523581[/C][C]19.5878684764188[/C][/ROW]
[ROW][C]10[/C][C]472[/C][C]462.620899440768[/C][C]9.37910055923155[/C][/ROW]
[ROW][C]11[/C][C]472[/C][C]469.289677205891[/C][C]2.71032279410877[/C][/ROW]
[ROW][C]12[/C][C]471[/C][C]450.326549949949[/C][C]20.6734500500510[/C][/ROW]
[ROW][C]13[/C][C]465[/C][C]439.177280519309[/C][C]25.8227194806908[/C][/ROW]
[ROW][C]14[/C][C]459[/C][C]440.924410766195[/C][C]18.0755892338053[/C][/ROW]
[ROW][C]15[/C][C]465[/C][C]446.509943100149[/C][C]18.4900568998505[/C][/ROW]
[ROW][C]16[/C][C]468[/C][C]448.026599189626[/C][C]19.9734008103735[/C][/ROW]
[ROW][C]17[/C][C]467[/C][C]451.875814639436[/C][C]15.1241853605644[/C][/ROW]
[ROW][C]18[/C][C]463[/C][C]453.561607395238[/C][C]9.43839260476218[/C][/ROW]
[ROW][C]19[/C][C]460[/C][C]465.699064446128[/C][C]-5.69906444612843[/C][/ROW]
[ROW][C]20[/C][C]462[/C][C]438.404391070324[/C][C]23.5956089296762[/C][/ROW]
[ROW][C]21[/C][C]461[/C][C]442.054521281248[/C][C]18.9454787187525[/C][/ROW]
[ROW][C]22[/C][C]476[/C][C]443.451241930748[/C][C]32.5487580692518[/C][/ROW]
[ROW][C]23[/C][C]476[/C][C]465.347238208547[/C][C]10.6527617914526[/C][/ROW]
[ROW][C]24[/C][C]471[/C][C]436.003560565104[/C][C]34.9964394348962[/C][/ROW]
[ROW][C]25[/C][C]453[/C][C]442.721858700407[/C][C]10.2781412995928[/C][/ROW]
[ROW][C]26[/C][C]443[/C][C]432.352318634356[/C][C]10.6476813656445[/C][/ROW]
[ROW][C]27[/C][C]442[/C][C]438.335711784556[/C][C]3.66428821544409[/C][/ROW]
[ROW][C]28[/C][C]444[/C][C]439.165153736881[/C][C]4.8348462631187[/C][/ROW]
[ROW][C]29[/C][C]438[/C][C]438.167701061515[/C][C]-0.167701061515477[/C][/ROW]
[ROW][C]30[/C][C]427[/C][C]434.86214903169[/C][C]-7.86214903168978[/C][/ROW]
[ROW][C]31[/C][C]424[/C][C]429.204376846864[/C][C]-5.2043768468635[/C][/ROW]
[ROW][C]32[/C][C]416[/C][C]426.757919903859[/C][C]-10.7579199038586[/C][/ROW]
[ROW][C]33[/C][C]406[/C][C]428.201731042874[/C][C]-22.2017310428744[/C][/ROW]
[ROW][C]34[/C][C]431[/C][C]444.753331874825[/C][C]-13.7533318748251[/C][/ROW]
[ROW][C]35[/C][C]434[/C][C]444.803152424224[/C][C]-10.8031524242238[/C][/ROW]
[ROW][C]36[/C][C]418[/C][C]443.056547762187[/C][C]-25.0565477621867[/C][/ROW]
[ROW][C]37[/C][C]412[/C][C]441.383599591217[/C][C]-29.3835995912172[/C][/ROW]
[ROW][C]38[/C][C]404[/C][C]425.190823941933[/C][C]-21.1908239419329[/C][/ROW]
[ROW][C]39[/C][C]409[/C][C]424.916951527542[/C][C]-15.9169515275417[/C][/ROW]
[ROW][C]40[/C][C]412[/C][C]441.769333625035[/C][C]-29.769333625035[/C][/ROW]
[ROW][C]41[/C][C]406[/C][C]438.203870226629[/C][C]-32.2038702266287[/C][/ROW]
[ROW][C]42[/C][C]398[/C][C]428.641052632212[/C][C]-30.6410526322115[/C][/ROW]
[ROW][C]43[/C][C]397[/C][C]434.521244118511[/C][C]-37.5212441185106[/C][/ROW]
[ROW][C]44[/C][C]385[/C][C]432.653493817318[/C][C]-47.6534938173177[/C][/ROW]
[ROW][C]45[/C][C]390[/C][C]417.821180655373[/C][C]-27.8211806553729[/C][/ROW]
[ROW][C]46[/C][C]413[/C][C]461.644331982711[/C][C]-48.6443319827108[/C][/ROW]
[ROW][C]47[/C][C]413[/C][C]440.354345115295[/C][C]-27.3543451152946[/C][/ROW]
[ROW][C]48[/C][C]401[/C][C]439.837492067108[/C][C]-38.8374920671078[/C][/ROW]
[ROW][C]49[/C][C]397[/C][C]439.104942189083[/C][C]-42.1049421890827[/C][/ROW]
[ROW][C]50[/C][C]397[/C][C]429.531123755522[/C][C]-32.5311237555223[/C][/ROW]
[ROW][C]51[/C][C]409[/C][C]443.037703249278[/C][C]-34.0377032492779[/C][/ROW]
[ROW][C]52[/C][C]419[/C][C]430.484554109702[/C][C]-11.4845541097023[/C][/ROW]
[ROW][C]53[/C][C]424[/C][C]430.499838057507[/C][C]-6.49983805750738[/C][/ROW]
[ROW][C]54[/C][C]428[/C][C]429.472943429816[/C][C]-1.47294342981616[/C][/ROW]
[ROW][C]55[/C][C]430[/C][C]411.300640115807[/C][C]18.6993598841931[/C][/ROW]
[ROW][C]56[/C][C]424[/C][C]409.939258126199[/C][C]14.0607418738006[/C][/ROW]
[ROW][C]57[/C][C]433[/C][C]421.510435496924[/C][C]11.4895645030760[/C][/ROW]
[ROW][C]58[/C][C]456[/C][C]435.530194770947[/C][C]20.4698052290526[/C][/ROW]
[ROW][C]59[/C][C]459[/C][C]434.205587046043[/C][C]24.7944129539571[/C][/ROW]
[ROW][C]60[/C][C]446[/C][C]437.775849655653[/C][C]8.22415034434721[/C][/ROW]
[ROW][C]61[/C][C]441[/C][C]433.28170660585[/C][C]7.71829339414989[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58389&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58389&T=4

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1462434.33061239413427.6693876058664
2455430.00132290199524.9986770980054
3461433.19969033847527.8003096615250
4461444.55435933875516.4456406612451
5463439.25277601491323.7472239850872
6462431.46224751104530.5377524889553
7456426.27467447269129.7253255273094
8455434.244937082320.7550629176995
9456436.41213152358119.5878684764188
10472462.6208994407689.37910055923155
11472469.2896772058912.71032279410877
12471450.32654994994920.6734500500510
13465439.17728051930925.8227194806908
14459440.92441076619518.0755892338053
15465446.50994310014918.4900568998505
16468448.02659918962619.9734008103735
17467451.87581463943615.1241853605644
18463453.5616073952389.43839260476218
19460465.699064446128-5.69906444612843
20462438.40439107032423.5956089296762
21461442.05452128124818.9454787187525
22476443.45124193074832.5487580692518
23476465.34723820854710.6527617914526
24471436.00356056510434.9964394348962
25453442.72185870040710.2781412995928
26443432.35231863435610.6476813656445
27442438.3357117845563.66428821544409
28444439.1651537368814.8348462631187
29438438.167701061515-0.167701061515477
30427434.86214903169-7.86214903168978
31424429.204376846864-5.2043768468635
32416426.757919903859-10.7579199038586
33406428.201731042874-22.2017310428744
34431444.753331874825-13.7533318748251
35434444.803152424224-10.8031524242238
36418443.056547762187-25.0565477621867
37412441.383599591217-29.3835995912172
38404425.190823941933-21.1908239419329
39409424.916951527542-15.9169515275417
40412441.769333625035-29.769333625035
41406438.203870226629-32.2038702266287
42398428.641052632212-30.6410526322115
43397434.521244118511-37.5212441185106
44385432.653493817318-47.6534938173177
45390417.821180655373-27.8211806553729
46413461.644331982711-48.6443319827108
47413440.354345115295-27.3543451152946
48401439.837492067108-38.8374920671078
49397439.104942189083-42.1049421890827
50397429.531123755522-32.5311237555223
51409443.037703249278-34.0377032492779
52419430.484554109702-11.4845541097023
53424430.499838057507-6.49983805750738
54428429.472943429816-1.47294342981616
55430411.30064011580718.6993598841931
56424409.93925812619914.0607418738006
57433421.51043549692411.4895645030760
58456435.53019477094720.4698052290526
59459434.20558704604324.7944129539571
60446437.7758496556538.22415034434721
61441433.281706605857.71829339414989







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.001113839015199940.002227678030399880.9988861609848
179.2964761969175e-050.000185929523938350.999907035238031
182.85027988114868e-055.70055976229736e-050.999971497201188
193.55272712958011e-067.10545425916021e-060.99999644727287
202.04131820005764e-064.08263640011528e-060.9999979586818
216.05032366324585e-071.21006473264917e-060.999999394967634
223.57327540352414e-077.14655080704828e-070.99999964267246
231.77416735414836e-073.54833470829673e-070.999999822583265
245.33112449775572e-081.06622489955114e-070.999999946688755
255.02709000663388e-071.00541800132678e-060.999999497291
267.04174380946219e-061.40834876189244e-050.99999295825619
270.0002316283794512590.0004632567589025180.999768371620549
280.001237818907010270.002475637814020530.99876218109299
290.008152555949832330.01630511189966470.991847444050168
300.04675737601500950.0935147520300190.95324262398499
310.08048430163636680.1609686032727340.919515698363633
320.1830498112875100.3660996225750190.81695018871249
330.3228721191721260.6457442383442530.677127880827874
340.3672621723662260.7345243447324530.632737827633774
350.3146489114096050.6292978228192090.685351088590395
360.4269733300486940.8539466600973870.573026669951306
370.4943092315346860.9886184630693720.505690768465314
380.4706092963675440.9412185927350880.529390703632456
390.478897195462080.957794390924160.52110280453792
400.4586529073539710.9173058147079410.541347092646029
410.4122199529822720.8244399059645430.587780047017728
420.4197504903268610.8395009806537220.580249509673139
430.3443111636536810.6886223273073630.655688836346319
440.2892289834785210.5784579669570410.71077101652148
450.3838589902993590.7677179805987180.616141009700641

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.00111383901519994 & 0.00222767803039988 & 0.9988861609848 \tabularnewline
17 & 9.2964761969175e-05 & 0.00018592952393835 & 0.999907035238031 \tabularnewline
18 & 2.85027988114868e-05 & 5.70055976229736e-05 & 0.999971497201188 \tabularnewline
19 & 3.55272712958011e-06 & 7.10545425916021e-06 & 0.99999644727287 \tabularnewline
20 & 2.04131820005764e-06 & 4.08263640011528e-06 & 0.9999979586818 \tabularnewline
21 & 6.05032366324585e-07 & 1.21006473264917e-06 & 0.999999394967634 \tabularnewline
22 & 3.57327540352414e-07 & 7.14655080704828e-07 & 0.99999964267246 \tabularnewline
23 & 1.77416735414836e-07 & 3.54833470829673e-07 & 0.999999822583265 \tabularnewline
24 & 5.33112449775572e-08 & 1.06622489955114e-07 & 0.999999946688755 \tabularnewline
25 & 5.02709000663388e-07 & 1.00541800132678e-06 & 0.999999497291 \tabularnewline
26 & 7.04174380946219e-06 & 1.40834876189244e-05 & 0.99999295825619 \tabularnewline
27 & 0.000231628379451259 & 0.000463256758902518 & 0.999768371620549 \tabularnewline
28 & 0.00123781890701027 & 0.00247563781402053 & 0.99876218109299 \tabularnewline
29 & 0.00815255594983233 & 0.0163051118996647 & 0.991847444050168 \tabularnewline
30 & 0.0467573760150095 & 0.093514752030019 & 0.95324262398499 \tabularnewline
31 & 0.0804843016363668 & 0.160968603272734 & 0.919515698363633 \tabularnewline
32 & 0.183049811287510 & 0.366099622575019 & 0.81695018871249 \tabularnewline
33 & 0.322872119172126 & 0.645744238344253 & 0.677127880827874 \tabularnewline
34 & 0.367262172366226 & 0.734524344732453 & 0.632737827633774 \tabularnewline
35 & 0.314648911409605 & 0.629297822819209 & 0.685351088590395 \tabularnewline
36 & 0.426973330048694 & 0.853946660097387 & 0.573026669951306 \tabularnewline
37 & 0.494309231534686 & 0.988618463069372 & 0.505690768465314 \tabularnewline
38 & 0.470609296367544 & 0.941218592735088 & 0.529390703632456 \tabularnewline
39 & 0.47889719546208 & 0.95779439092416 & 0.52110280453792 \tabularnewline
40 & 0.458652907353971 & 0.917305814707941 & 0.541347092646029 \tabularnewline
41 & 0.412219952982272 & 0.824439905964543 & 0.587780047017728 \tabularnewline
42 & 0.419750490326861 & 0.839500980653722 & 0.580249509673139 \tabularnewline
43 & 0.344311163653681 & 0.688622327307363 & 0.655688836346319 \tabularnewline
44 & 0.289228983478521 & 0.578457966957041 & 0.71077101652148 \tabularnewline
45 & 0.383858990299359 & 0.767717980598718 & 0.616141009700641 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58389&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]16[/C][C]0.00111383901519994[/C][C]0.00222767803039988[/C][C]0.9988861609848[/C][/ROW]
[ROW][C]17[/C][C]9.2964761969175e-05[/C][C]0.00018592952393835[/C][C]0.999907035238031[/C][/ROW]
[ROW][C]18[/C][C]2.85027988114868e-05[/C][C]5.70055976229736e-05[/C][C]0.999971497201188[/C][/ROW]
[ROW][C]19[/C][C]3.55272712958011e-06[/C][C]7.10545425916021e-06[/C][C]0.99999644727287[/C][/ROW]
[ROW][C]20[/C][C]2.04131820005764e-06[/C][C]4.08263640011528e-06[/C][C]0.9999979586818[/C][/ROW]
[ROW][C]21[/C][C]6.05032366324585e-07[/C][C]1.21006473264917e-06[/C][C]0.999999394967634[/C][/ROW]
[ROW][C]22[/C][C]3.57327540352414e-07[/C][C]7.14655080704828e-07[/C][C]0.99999964267246[/C][/ROW]
[ROW][C]23[/C][C]1.77416735414836e-07[/C][C]3.54833470829673e-07[/C][C]0.999999822583265[/C][/ROW]
[ROW][C]24[/C][C]5.33112449775572e-08[/C][C]1.06622489955114e-07[/C][C]0.999999946688755[/C][/ROW]
[ROW][C]25[/C][C]5.02709000663388e-07[/C][C]1.00541800132678e-06[/C][C]0.999999497291[/C][/ROW]
[ROW][C]26[/C][C]7.04174380946219e-06[/C][C]1.40834876189244e-05[/C][C]0.99999295825619[/C][/ROW]
[ROW][C]27[/C][C]0.000231628379451259[/C][C]0.000463256758902518[/C][C]0.999768371620549[/C][/ROW]
[ROW][C]28[/C][C]0.00123781890701027[/C][C]0.00247563781402053[/C][C]0.99876218109299[/C][/ROW]
[ROW][C]29[/C][C]0.00815255594983233[/C][C]0.0163051118996647[/C][C]0.991847444050168[/C][/ROW]
[ROW][C]30[/C][C]0.0467573760150095[/C][C]0.093514752030019[/C][C]0.95324262398499[/C][/ROW]
[ROW][C]31[/C][C]0.0804843016363668[/C][C]0.160968603272734[/C][C]0.919515698363633[/C][/ROW]
[ROW][C]32[/C][C]0.183049811287510[/C][C]0.366099622575019[/C][C]0.81695018871249[/C][/ROW]
[ROW][C]33[/C][C]0.322872119172126[/C][C]0.645744238344253[/C][C]0.677127880827874[/C][/ROW]
[ROW][C]34[/C][C]0.367262172366226[/C][C]0.734524344732453[/C][C]0.632737827633774[/C][/ROW]
[ROW][C]35[/C][C]0.314648911409605[/C][C]0.629297822819209[/C][C]0.685351088590395[/C][/ROW]
[ROW][C]36[/C][C]0.426973330048694[/C][C]0.853946660097387[/C][C]0.573026669951306[/C][/ROW]
[ROW][C]37[/C][C]0.494309231534686[/C][C]0.988618463069372[/C][C]0.505690768465314[/C][/ROW]
[ROW][C]38[/C][C]0.470609296367544[/C][C]0.941218592735088[/C][C]0.529390703632456[/C][/ROW]
[ROW][C]39[/C][C]0.47889719546208[/C][C]0.95779439092416[/C][C]0.52110280453792[/C][/ROW]
[ROW][C]40[/C][C]0.458652907353971[/C][C]0.917305814707941[/C][C]0.541347092646029[/C][/ROW]
[ROW][C]41[/C][C]0.412219952982272[/C][C]0.824439905964543[/C][C]0.587780047017728[/C][/ROW]
[ROW][C]42[/C][C]0.419750490326861[/C][C]0.839500980653722[/C][C]0.580249509673139[/C][/ROW]
[ROW][C]43[/C][C]0.344311163653681[/C][C]0.688622327307363[/C][C]0.655688836346319[/C][/ROW]
[ROW][C]44[/C][C]0.289228983478521[/C][C]0.578457966957041[/C][C]0.71077101652148[/C][/ROW]
[ROW][C]45[/C][C]0.383858990299359[/C][C]0.767717980598718[/C][C]0.616141009700641[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58389&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58389&T=5

As an alternative you can also use a QR Code:  

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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.001113839015199940.002227678030399880.9988861609848
179.2964761969175e-050.000185929523938350.999907035238031
182.85027988114868e-055.70055976229736e-050.999971497201188
193.55272712958011e-067.10545425916021e-060.99999644727287
202.04131820005764e-064.08263640011528e-060.9999979586818
216.05032366324585e-071.21006473264917e-060.999999394967634
223.57327540352414e-077.14655080704828e-070.99999964267246
231.77416735414836e-073.54833470829673e-070.999999822583265
245.33112449775572e-081.06622489955114e-070.999999946688755
255.02709000663388e-071.00541800132678e-060.999999497291
267.04174380946219e-061.40834876189244e-050.99999295825619
270.0002316283794512590.0004632567589025180.999768371620549
280.001237818907010270.002475637814020530.99876218109299
290.008152555949832330.01630511189966470.991847444050168
300.04675737601500950.0935147520300190.95324262398499
310.08048430163636680.1609686032727340.919515698363633
320.1830498112875100.3660996225750190.81695018871249
330.3228721191721260.6457442383442530.677127880827874
340.3672621723662260.7345243447324530.632737827633774
350.3146489114096050.6292978228192090.685351088590395
360.4269733300486940.8539466600973870.573026669951306
370.4943092315346860.9886184630693720.505690768465314
380.4706092963675440.9412185927350880.529390703632456
390.478897195462080.957794390924160.52110280453792
400.4586529073539710.9173058147079410.541347092646029
410.4122199529822720.8244399059645430.587780047017728
420.4197504903268610.8395009806537220.580249509673139
430.3443111636536810.6886223273073630.655688836346319
440.2892289834785210.5784579669570410.71077101652148
450.3838589902993590.7677179805987180.616141009700641







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level130.433333333333333NOK
5% type I error level140.466666666666667NOK
10% type I error level150.5NOK

\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 & 13 & 0.433333333333333 & NOK \tabularnewline
5% type I error level & 14 & 0.466666666666667 & NOK \tabularnewline
10% type I error level & 15 & 0.5 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58389&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]13[/C][C]0.433333333333333[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]14[/C][C]0.466666666666667[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]15[/C][C]0.5[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58389&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58389&T=6

As an alternative you can also use a QR Code:  

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level130.433333333333333NOK
5% type I error level140.466666666666667NOK
10% type I error level150.5NOK



Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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')
}