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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 computationTue, 30 Nov 2010 21:32:25 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/30/t1291152642ao5wgemsn436i3a.htm/, Retrieved Fri, 01 Nov 2024 00:11:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=103829, Retrieved Fri, 01 Nov 2024 00:11:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact238

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]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
- R PD    [Multiple Regression] [Aantal reizigers ...] [2010-11-26 01:03:33] [97ad38b1c3b35a5feca8b85f7bc7b3ff]
-    D      [Multiple Regression] [Aantal reizigers ...] [2010-11-26 01:44:20] [97ad38b1c3b35a5feca8b85f7bc7b3ff]
-    D        [Multiple Regression] [Aantal reizigers ...] [2010-11-26 01:59:36] [97ad38b1c3b35a5feca8b85f7bc7b3ff]
-   PD            [Multiple Regression] [4 vertragingen - Ws8] [2010-11-30 21:32:25] [8bf9de033bd61652831a8b7489bc3566] [Current]
-   PD              [Multiple Regression] [4 vertragingen - ...] [2010-12-21 19:11:04] [608064602fec1c42028cf50c6f981c88]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
30	35	47	30	37
43	30	35	47	30
82	43	30	35	47
40	82	43	30	35
47	40	82	43	30
19	47	40	82	43
52	19	47	40	82
136	52	19	47	40
80	136	52	19	47
42	80	136	52	19
54	42	80	136	52
66	54	42	80	136
81	66	54	42	80
63	81	66	54	42
137	63	81	66	54
72	137	63	81	66
107	72	137	63	81
58	107	72	137	63
36	58	107	72	137
52	36	58	107	72
79	52	36	58	107
77	79	52	36	58
54	77	79	52	36
84	54	77	79	52
48	84	54	77	79
96	48	84	54	77
83	96	48	84	54
66	83	96	48	84
61	66	83	96	48
53	61	66	83	96
30	53	61	66	83
74	30	53	61	66
69	74	30	53	61
59	69	74	30	53
42	59	69	74	30
65	42	59	69	74
70	65	42	59	69
100	70	65	42	59
63	100	70	65	42
105	63	100	70	65
82	105	63	100	70
81	82	105	63	100
75	81	82	105	63
102	75	81	82	105
121	102	75	81	82
98	121	102	75	81
76	98	121	102	75
77	76	98	121	102
63	77	76	98	121
37	63	77	76	98
35	37	63	77	76
23	35	37	63	77
40	23	35	37	63
29	40	23	35	37
37	29	40	23	35
51	37	29	40	23
20	51	37	29	40
28	20	51	37	29
13	28	20	51	37
22	13	28	20	51
25	22	13	28	20
13	25	22	13	28
16	13	25	22	13
13	16	13	25	22
16	13	16	13	25
17	16	13	16	13
9	17	16	13	16
17	9	17	16	13
25	17	9	17	16
14	25	17	9	17
8	14	25	17	9
7	8	14	25	17
10	7	8	14	25
7	10	7	8	14
10	7	10	7	8
3	10	7	10	7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 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 & 7 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103829&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]7 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=103829&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103829&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 time7 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Ye[t] = + 27.2834214053944 + 0.397125190922649`Ye-1`[t] + 0.241628865980788`Ye-2`[t] -0.0721154477263936`Ye-3`[t] + 0.194553871149098`Ye-4`[t] -8.55123851482719M1[t] -2.43346143954193M2[t] + 8.75387561158733M3[t] -12.7401440949288M4[t] -2.18969425871734M5[t] -16.6086800675589M6[t] -17.5742918715359M7[t] + 23.4944770899369M8[t] + 3.14624069205249M9[t] -11.5904562802941M10[t] -13.6691227830971M11[t] -0.290723078985568t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Ye[t] =  +  27.2834214053944 +  0.397125190922649`Ye-1`[t] +  0.241628865980788`Ye-2`[t] -0.0721154477263936`Ye-3`[t] +  0.194553871149098`Ye-4`[t] -8.55123851482719M1[t] -2.43346143954193M2[t] +  8.75387561158733M3[t] -12.7401440949288M4[t] -2.18969425871734M5[t] -16.6086800675589M6[t] -17.5742918715359M7[t] +  23.4944770899369M8[t] +  3.14624069205249M9[t] -11.5904562802941M10[t] -13.6691227830971M11[t] -0.290723078985568t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103829&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Ye[t] =  +  27.2834214053944 +  0.397125190922649`Ye-1`[t] +  0.241628865980788`Ye-2`[t] -0.0721154477263936`Ye-3`[t] +  0.194553871149098`Ye-4`[t] -8.55123851482719M1[t] -2.43346143954193M2[t] +  8.75387561158733M3[t] -12.7401440949288M4[t] -2.18969425871734M5[t] -16.6086800675589M6[t] -17.5742918715359M7[t] +  23.4944770899369M8[t] +  3.14624069205249M9[t] -11.5904562802941M10[t] -13.6691227830971M11[t] -0.290723078985568t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103829&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103829&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
Ye[t] = + 27.2834214053944 + 0.397125190922649`Ye-1`[t] + 0.241628865980788`Ye-2`[t] -0.0721154477263936`Ye-3`[t] + 0.194553871149098`Ye-4`[t] -8.55123851482719M1[t] -2.43346143954193M2[t] + 8.75387561158733M3[t] -12.7401440949288M4[t] -2.18969425871734M5[t] -16.6086800675589M6[t] -17.5742918715359M7[t] + 23.4944770899369M8[t] + 3.14624069205249M9[t] -11.5904562802941M10[t] -13.6691227830971M11[t] -0.290723078985568t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)27.283421405394413.8269971.97320.0531630.026582
`Ye-1`0.3971251909226490.1263293.14360.0026120.001306
`Ye-2`0.2416288659807880.1357261.78030.0801820.040091
`Ye-3`-0.07211544772639360.134954-0.53440.5950940.297547
`Ye-4`0.1945538711490980.1234481.5760.1203730.060186
M1-8.5512385148271912.080546-0.70790.4818240.240912
M2-2.4334614395419312.239001-0.19880.8430810.42154
M38.7538756115873312.3117750.7110.4798760.239938
M4-12.740144094928812.466598-1.02190.310980.15549
M5-2.1896942587173412.734413-0.1720.8640650.432032
M6-16.608680067558912.472345-1.33160.18810.09405
M7-17.574291871535912.332299-1.42510.1594080.079704
M823.494477089936912.3322751.90510.0616420.030821
M93.1462406920524913.5092360.23290.8166490.408324
M10-11.590456280294113.781157-0.8410.4037230.201862
M11-13.669122783097113.151083-1.03940.3028640.151432
t-0.2907230789855680.13498-2.15380.035350.017675

\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) & 27.2834214053944 & 13.826997 & 1.9732 & 0.053163 & 0.026582 \tabularnewline
`Ye-1` & 0.397125190922649 & 0.126329 & 3.1436 & 0.002612 & 0.001306 \tabularnewline
`Ye-2` & 0.241628865980788 & 0.135726 & 1.7803 & 0.080182 & 0.040091 \tabularnewline
`Ye-3` & -0.0721154477263936 & 0.134954 & -0.5344 & 0.595094 & 0.297547 \tabularnewline
`Ye-4` & 0.194553871149098 & 0.123448 & 1.576 & 0.120373 & 0.060186 \tabularnewline
M1 & -8.55123851482719 & 12.080546 & -0.7079 & 0.481824 & 0.240912 \tabularnewline
M2 & -2.43346143954193 & 12.239001 & -0.1988 & 0.843081 & 0.42154 \tabularnewline
M3 & 8.75387561158733 & 12.311775 & 0.711 & 0.479876 & 0.239938 \tabularnewline
M4 & -12.7401440949288 & 12.466598 & -1.0219 & 0.31098 & 0.15549 \tabularnewline
M5 & -2.18969425871734 & 12.734413 & -0.172 & 0.864065 & 0.432032 \tabularnewline
M6 & -16.6086800675589 & 12.472345 & -1.3316 & 0.1881 & 0.09405 \tabularnewline
M7 & -17.5742918715359 & 12.332299 & -1.4251 & 0.159408 & 0.079704 \tabularnewline
M8 & 23.4944770899369 & 12.332275 & 1.9051 & 0.061642 & 0.030821 \tabularnewline
M9 & 3.14624069205249 & 13.509236 & 0.2329 & 0.816649 & 0.408324 \tabularnewline
M10 & -11.5904562802941 & 13.781157 & -0.841 & 0.403723 & 0.201862 \tabularnewline
M11 & -13.6691227830971 & 13.151083 & -1.0394 & 0.302864 & 0.151432 \tabularnewline
t & -0.290723078985568 & 0.13498 & -2.1538 & 0.03535 & 0.017675 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103829&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]27.2834214053944[/C][C]13.826997[/C][C]1.9732[/C][C]0.053163[/C][C]0.026582[/C][/ROW]
[ROW][C]`Ye-1`[/C][C]0.397125190922649[/C][C]0.126329[/C][C]3.1436[/C][C]0.002612[/C][C]0.001306[/C][/ROW]
[ROW][C]`Ye-2`[/C][C]0.241628865980788[/C][C]0.135726[/C][C]1.7803[/C][C]0.080182[/C][C]0.040091[/C][/ROW]
[ROW][C]`Ye-3`[/C][C]-0.0721154477263936[/C][C]0.134954[/C][C]-0.5344[/C][C]0.595094[/C][C]0.297547[/C][/ROW]
[ROW][C]`Ye-4`[/C][C]0.194553871149098[/C][C]0.123448[/C][C]1.576[/C][C]0.120373[/C][C]0.060186[/C][/ROW]
[ROW][C]M1[/C][C]-8.55123851482719[/C][C]12.080546[/C][C]-0.7079[/C][C]0.481824[/C][C]0.240912[/C][/ROW]
[ROW][C]M2[/C][C]-2.43346143954193[/C][C]12.239001[/C][C]-0.1988[/C][C]0.843081[/C][C]0.42154[/C][/ROW]
[ROW][C]M3[/C][C]8.75387561158733[/C][C]12.311775[/C][C]0.711[/C][C]0.479876[/C][C]0.239938[/C][/ROW]
[ROW][C]M4[/C][C]-12.7401440949288[/C][C]12.466598[/C][C]-1.0219[/C][C]0.31098[/C][C]0.15549[/C][/ROW]
[ROW][C]M5[/C][C]-2.18969425871734[/C][C]12.734413[/C][C]-0.172[/C][C]0.864065[/C][C]0.432032[/C][/ROW]
[ROW][C]M6[/C][C]-16.6086800675589[/C][C]12.472345[/C][C]-1.3316[/C][C]0.1881[/C][C]0.09405[/C][/ROW]
[ROW][C]M7[/C][C]-17.5742918715359[/C][C]12.332299[/C][C]-1.4251[/C][C]0.159408[/C][C]0.079704[/C][/ROW]
[ROW][C]M8[/C][C]23.4944770899369[/C][C]12.332275[/C][C]1.9051[/C][C]0.061642[/C][C]0.030821[/C][/ROW]
[ROW][C]M9[/C][C]3.14624069205249[/C][C]13.509236[/C][C]0.2329[/C][C]0.816649[/C][C]0.408324[/C][/ROW]
[ROW][C]M10[/C][C]-11.5904562802941[/C][C]13.781157[/C][C]-0.841[/C][C]0.403723[/C][C]0.201862[/C][/ROW]
[ROW][C]M11[/C][C]-13.6691227830971[/C][C]13.151083[/C][C]-1.0394[/C][C]0.302864[/C][C]0.151432[/C][/ROW]
[ROW][C]t[/C][C]-0.290723078985568[/C][C]0.13498[/C][C]-2.1538[/C][C]0.03535[/C][C]0.017675[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103829&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103829&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)27.283421405394413.8269971.97320.0531630.026582
`Ye-1`0.3971251909226490.1263293.14360.0026120.001306
`Ye-2`0.2416288659807880.1357261.78030.0801820.040091
`Ye-3`-0.07211544772639360.134954-0.53440.5950940.297547
`Ye-4`0.1945538711490980.1234481.5760.1203730.060186
M1-8.5512385148271912.080546-0.70790.4818240.240912
M2-2.4334614395419312.239001-0.19880.8430810.42154
M38.7538756115873312.3117750.7110.4798760.239938
M4-12.740144094928812.466598-1.02190.310980.15549
M5-2.1896942587173412.734413-0.1720.8640650.432032
M6-16.608680067558912.472345-1.33160.18810.09405
M7-17.574291871535912.332299-1.42510.1594080.079704
M823.494477089936912.3322751.90510.0616420.030821
M93.1462406920524913.5092360.23290.8166490.408324
M10-11.590456280294113.781157-0.8410.4037230.201862
M11-13.669122783097113.151083-1.03940.3028640.151432
t-0.2907230789855680.13498-2.15380.035350.017675






Multiple Linear Regression - Regression Statistics
Multiple R0.819156252095656
R-squared0.671016965347402
Adjusted R-squared0.581801227136528
F-TEST (value)7.52128468366599
F-TEST (DF numerator)16
F-TEST (DF denominator)59
p-value3.64684837883544e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation21.0468770596200
Sum Squared Residuals26135.2910038028

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.819156252095656 \tabularnewline
R-squared & 0.671016965347402 \tabularnewline
Adjusted R-squared & 0.581801227136528 \tabularnewline
F-TEST (value) & 7.52128468366599 \tabularnewline
F-TEST (DF numerator) & 16 \tabularnewline
F-TEST (DF denominator) & 59 \tabularnewline
p-value & 3.64684837883544e-09 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 21.0468770596200 \tabularnewline
Sum Squared Residuals & 26135.2910038028 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103829&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.819156252095656[/C][/ROW]
[ROW][C]R-squared[/C][C]0.671016965347402[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.581801227136528[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]7.52128468366599[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]16[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]59[/C][/ROW]
[ROW][C]p-value[/C][C]3.64684837883544e-09[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]21.0468770596200[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]26135.2910038028[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103829&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103829&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 R0.819156252095656
R-squared0.671016965347402
Adjusted R-squared0.581801227136528
F-TEST (value)7.52128468366599
F-TEST (DF numerator)16
F-TEST (DF denominator)59
p-value3.64684837883544e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation21.0468770596200
Sum Squared Residuals26135.2910038028






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
13048.7324279956963-18.7324279956963
24347.086469936221-4.08646993622098
38266.110368242706515.8896317572935
44060.980613945781-20.9806139457810
54762.0743382813179-15.0743382813179
61939.7127912223652-20.7127912223652
75239.644802834757312.3551971652427
813678.08630104788357.913698952117
980102.160719820264-22.1607198202642
104277.3637956525042-35.3637956525042
115446.7350124596347.26498754036598
126676.0780077967497-10.0780077967497
138166.746465115031614.2535348849684
146373.171510890558-10.1715108905580
1513782.013565496878354.9864345031217
167286.5196819898917-14.5196819898917
1710793.063193546035413.9368064539646
185867.7084772393128-9.70847723931278
193674.5345088777169-38.5345088777169
205279.565943831732-27.5659438317321
217970.30819478685888.69180521314117
227761.922616909805615.0773830901944
235459.8489239987506-5.84892399875062
248464.775931429452619.2240685705474
254867.6874470622396-19.6874470622396
269667.736407720156428.2635922798436
278382.35818921305780.641810786942179
286675.4417767652626-9.4417767652626
296165.3437191668188-4.34371916681884
305354.8167802383049-1.81678023830489
313047.8720617844677-17.8720617844677
327474.636358776985-0.636358776984946
336965.5175980092193.482401990781
345959.2384464349425-0.238446434942508
354244.041841877633-2.04184187763301
366557.17377224544397.8262277545561
377053.106384442697116.8936155573029
3810065.756952211025934.2430477889741
396384.8093951335112-21.8093951335112
4010559.694048061092545.3059519389075
418276.50207071973415.49792928026586
428171.31178251222879.6882174877713
437553.873516483760321.1264835162397
44102101.85710024070.142899759300056
4512186.088124134153934.9118758658461
469885.368200907042512.6317990929575
477675.34144007216090.658559927839122
487778.3083826726402-1.30838267264018
496369.9028900677126-6.90289006771262
503767.5236210706274-30.5236210706274
513560.3598753420447-25.3598753420447
522332.7027017985157-9.70270179851573
534036.86491597750723.13508402249283
542921.09261918917187.90738081082816
553720.051875558152116.9481244418479
565157.788396377094-6.78839637709397
572048.7429062355124-28.7429062355124
582822.07039322485795.92960677514215
591315.9343250260694-2.93432502606939
602230.2482108697931-8.24821086979305
612514.747849417139110.2521505828609
621326.5791014651225-13.5791014651225
631629.8677526473628-13.8677526473628
64137.909477540022235.09052245997777
651619.1517623085866-3.15176230858660
66172.3575495986167014.6424504013833
6793.023234461145685.97676553885432
681740.065899725606-23.065899725606
692521.18245701399183.81754298600822
701412.03654687084731.96345312915268
7185.098456565752062.90154343424794
72714.4156949859207-7.41569498592066
73106.076535899483623.92346410051638
74711.1459367062888-4.14593670628875
751020.4808539244387-10.4808539244387
763-1.248300100565774.24830010056577

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 30 & 48.7324279956963 & -18.7324279956963 \tabularnewline
2 & 43 & 47.086469936221 & -4.08646993622098 \tabularnewline
3 & 82 & 66.1103682427065 & 15.8896317572935 \tabularnewline
4 & 40 & 60.980613945781 & -20.9806139457810 \tabularnewline
5 & 47 & 62.0743382813179 & -15.0743382813179 \tabularnewline
6 & 19 & 39.7127912223652 & -20.7127912223652 \tabularnewline
7 & 52 & 39.6448028347573 & 12.3551971652427 \tabularnewline
8 & 136 & 78.086301047883 & 57.913698952117 \tabularnewline
9 & 80 & 102.160719820264 & -22.1607198202642 \tabularnewline
10 & 42 & 77.3637956525042 & -35.3637956525042 \tabularnewline
11 & 54 & 46.735012459634 & 7.26498754036598 \tabularnewline
12 & 66 & 76.0780077967497 & -10.0780077967497 \tabularnewline
13 & 81 & 66.7464651150316 & 14.2535348849684 \tabularnewline
14 & 63 & 73.171510890558 & -10.1715108905580 \tabularnewline
15 & 137 & 82.0135654968783 & 54.9864345031217 \tabularnewline
16 & 72 & 86.5196819898917 & -14.5196819898917 \tabularnewline
17 & 107 & 93.0631935460354 & 13.9368064539646 \tabularnewline
18 & 58 & 67.7084772393128 & -9.70847723931278 \tabularnewline
19 & 36 & 74.5345088777169 & -38.5345088777169 \tabularnewline
20 & 52 & 79.565943831732 & -27.5659438317321 \tabularnewline
21 & 79 & 70.3081947868588 & 8.69180521314117 \tabularnewline
22 & 77 & 61.9226169098056 & 15.0773830901944 \tabularnewline
23 & 54 & 59.8489239987506 & -5.84892399875062 \tabularnewline
24 & 84 & 64.7759314294526 & 19.2240685705474 \tabularnewline
25 & 48 & 67.6874470622396 & -19.6874470622396 \tabularnewline
26 & 96 & 67.7364077201564 & 28.2635922798436 \tabularnewline
27 & 83 & 82.3581892130578 & 0.641810786942179 \tabularnewline
28 & 66 & 75.4417767652626 & -9.4417767652626 \tabularnewline
29 & 61 & 65.3437191668188 & -4.34371916681884 \tabularnewline
30 & 53 & 54.8167802383049 & -1.81678023830489 \tabularnewline
31 & 30 & 47.8720617844677 & -17.8720617844677 \tabularnewline
32 & 74 & 74.636358776985 & -0.636358776984946 \tabularnewline
33 & 69 & 65.517598009219 & 3.482401990781 \tabularnewline
34 & 59 & 59.2384464349425 & -0.238446434942508 \tabularnewline
35 & 42 & 44.041841877633 & -2.04184187763301 \tabularnewline
36 & 65 & 57.1737722454439 & 7.8262277545561 \tabularnewline
37 & 70 & 53.1063844426971 & 16.8936155573029 \tabularnewline
38 & 100 & 65.7569522110259 & 34.2430477889741 \tabularnewline
39 & 63 & 84.8093951335112 & -21.8093951335112 \tabularnewline
40 & 105 & 59.6940480610925 & 45.3059519389075 \tabularnewline
41 & 82 & 76.5020707197341 & 5.49792928026586 \tabularnewline
42 & 81 & 71.3117825122287 & 9.6882174877713 \tabularnewline
43 & 75 & 53.8735164837603 & 21.1264835162397 \tabularnewline
44 & 102 & 101.8571002407 & 0.142899759300056 \tabularnewline
45 & 121 & 86.0881241341539 & 34.9118758658461 \tabularnewline
46 & 98 & 85.3682009070425 & 12.6317990929575 \tabularnewline
47 & 76 & 75.3414400721609 & 0.658559927839122 \tabularnewline
48 & 77 & 78.3083826726402 & -1.30838267264018 \tabularnewline
49 & 63 & 69.9028900677126 & -6.90289006771262 \tabularnewline
50 & 37 & 67.5236210706274 & -30.5236210706274 \tabularnewline
51 & 35 & 60.3598753420447 & -25.3598753420447 \tabularnewline
52 & 23 & 32.7027017985157 & -9.70270179851573 \tabularnewline
53 & 40 & 36.8649159775072 & 3.13508402249283 \tabularnewline
54 & 29 & 21.0926191891718 & 7.90738081082816 \tabularnewline
55 & 37 & 20.0518755581521 & 16.9481244418479 \tabularnewline
56 & 51 & 57.788396377094 & -6.78839637709397 \tabularnewline
57 & 20 & 48.7429062355124 & -28.7429062355124 \tabularnewline
58 & 28 & 22.0703932248579 & 5.92960677514215 \tabularnewline
59 & 13 & 15.9343250260694 & -2.93432502606939 \tabularnewline
60 & 22 & 30.2482108697931 & -8.24821086979305 \tabularnewline
61 & 25 & 14.7478494171391 & 10.2521505828609 \tabularnewline
62 & 13 & 26.5791014651225 & -13.5791014651225 \tabularnewline
63 & 16 & 29.8677526473628 & -13.8677526473628 \tabularnewline
64 & 13 & 7.90947754002223 & 5.09052245997777 \tabularnewline
65 & 16 & 19.1517623085866 & -3.15176230858660 \tabularnewline
66 & 17 & 2.35754959861670 & 14.6424504013833 \tabularnewline
67 & 9 & 3.02323446114568 & 5.97676553885432 \tabularnewline
68 & 17 & 40.065899725606 & -23.065899725606 \tabularnewline
69 & 25 & 21.1824570139918 & 3.81754298600822 \tabularnewline
70 & 14 & 12.0365468708473 & 1.96345312915268 \tabularnewline
71 & 8 & 5.09845656575206 & 2.90154343424794 \tabularnewline
72 & 7 & 14.4156949859207 & -7.41569498592066 \tabularnewline
73 & 10 & 6.07653589948362 & 3.92346410051638 \tabularnewline
74 & 7 & 11.1459367062888 & -4.14593670628875 \tabularnewline
75 & 10 & 20.4808539244387 & -10.4808539244387 \tabularnewline
76 & 3 & -1.24830010056577 & 4.24830010056577 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103829&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]30[/C][C]48.7324279956963[/C][C]-18.7324279956963[/C][/ROW]
[ROW][C]2[/C][C]43[/C][C]47.086469936221[/C][C]-4.08646993622098[/C][/ROW]
[ROW][C]3[/C][C]82[/C][C]66.1103682427065[/C][C]15.8896317572935[/C][/ROW]
[ROW][C]4[/C][C]40[/C][C]60.980613945781[/C][C]-20.9806139457810[/C][/ROW]
[ROW][C]5[/C][C]47[/C][C]62.0743382813179[/C][C]-15.0743382813179[/C][/ROW]
[ROW][C]6[/C][C]19[/C][C]39.7127912223652[/C][C]-20.7127912223652[/C][/ROW]
[ROW][C]7[/C][C]52[/C][C]39.6448028347573[/C][C]12.3551971652427[/C][/ROW]
[ROW][C]8[/C][C]136[/C][C]78.086301047883[/C][C]57.913698952117[/C][/ROW]
[ROW][C]9[/C][C]80[/C][C]102.160719820264[/C][C]-22.1607198202642[/C][/ROW]
[ROW][C]10[/C][C]42[/C][C]77.3637956525042[/C][C]-35.3637956525042[/C][/ROW]
[ROW][C]11[/C][C]54[/C][C]46.735012459634[/C][C]7.26498754036598[/C][/ROW]
[ROW][C]12[/C][C]66[/C][C]76.0780077967497[/C][C]-10.0780077967497[/C][/ROW]
[ROW][C]13[/C][C]81[/C][C]66.7464651150316[/C][C]14.2535348849684[/C][/ROW]
[ROW][C]14[/C][C]63[/C][C]73.171510890558[/C][C]-10.1715108905580[/C][/ROW]
[ROW][C]15[/C][C]137[/C][C]82.0135654968783[/C][C]54.9864345031217[/C][/ROW]
[ROW][C]16[/C][C]72[/C][C]86.5196819898917[/C][C]-14.5196819898917[/C][/ROW]
[ROW][C]17[/C][C]107[/C][C]93.0631935460354[/C][C]13.9368064539646[/C][/ROW]
[ROW][C]18[/C][C]58[/C][C]67.7084772393128[/C][C]-9.70847723931278[/C][/ROW]
[ROW][C]19[/C][C]36[/C][C]74.5345088777169[/C][C]-38.5345088777169[/C][/ROW]
[ROW][C]20[/C][C]52[/C][C]79.565943831732[/C][C]-27.5659438317321[/C][/ROW]
[ROW][C]21[/C][C]79[/C][C]70.3081947868588[/C][C]8.69180521314117[/C][/ROW]
[ROW][C]22[/C][C]77[/C][C]61.9226169098056[/C][C]15.0773830901944[/C][/ROW]
[ROW][C]23[/C][C]54[/C][C]59.8489239987506[/C][C]-5.84892399875062[/C][/ROW]
[ROW][C]24[/C][C]84[/C][C]64.7759314294526[/C][C]19.2240685705474[/C][/ROW]
[ROW][C]25[/C][C]48[/C][C]67.6874470622396[/C][C]-19.6874470622396[/C][/ROW]
[ROW][C]26[/C][C]96[/C][C]67.7364077201564[/C][C]28.2635922798436[/C][/ROW]
[ROW][C]27[/C][C]83[/C][C]82.3581892130578[/C][C]0.641810786942179[/C][/ROW]
[ROW][C]28[/C][C]66[/C][C]75.4417767652626[/C][C]-9.4417767652626[/C][/ROW]
[ROW][C]29[/C][C]61[/C][C]65.3437191668188[/C][C]-4.34371916681884[/C][/ROW]
[ROW][C]30[/C][C]53[/C][C]54.8167802383049[/C][C]-1.81678023830489[/C][/ROW]
[ROW][C]31[/C][C]30[/C][C]47.8720617844677[/C][C]-17.8720617844677[/C][/ROW]
[ROW][C]32[/C][C]74[/C][C]74.636358776985[/C][C]-0.636358776984946[/C][/ROW]
[ROW][C]33[/C][C]69[/C][C]65.517598009219[/C][C]3.482401990781[/C][/ROW]
[ROW][C]34[/C][C]59[/C][C]59.2384464349425[/C][C]-0.238446434942508[/C][/ROW]
[ROW][C]35[/C][C]42[/C][C]44.041841877633[/C][C]-2.04184187763301[/C][/ROW]
[ROW][C]36[/C][C]65[/C][C]57.1737722454439[/C][C]7.8262277545561[/C][/ROW]
[ROW][C]37[/C][C]70[/C][C]53.1063844426971[/C][C]16.8936155573029[/C][/ROW]
[ROW][C]38[/C][C]100[/C][C]65.7569522110259[/C][C]34.2430477889741[/C][/ROW]
[ROW][C]39[/C][C]63[/C][C]84.8093951335112[/C][C]-21.8093951335112[/C][/ROW]
[ROW][C]40[/C][C]105[/C][C]59.6940480610925[/C][C]45.3059519389075[/C][/ROW]
[ROW][C]41[/C][C]82[/C][C]76.5020707197341[/C][C]5.49792928026586[/C][/ROW]
[ROW][C]42[/C][C]81[/C][C]71.3117825122287[/C][C]9.6882174877713[/C][/ROW]
[ROW][C]43[/C][C]75[/C][C]53.8735164837603[/C][C]21.1264835162397[/C][/ROW]
[ROW][C]44[/C][C]102[/C][C]101.8571002407[/C][C]0.142899759300056[/C][/ROW]
[ROW][C]45[/C][C]121[/C][C]86.0881241341539[/C][C]34.9118758658461[/C][/ROW]
[ROW][C]46[/C][C]98[/C][C]85.3682009070425[/C][C]12.6317990929575[/C][/ROW]
[ROW][C]47[/C][C]76[/C][C]75.3414400721609[/C][C]0.658559927839122[/C][/ROW]
[ROW][C]48[/C][C]77[/C][C]78.3083826726402[/C][C]-1.30838267264018[/C][/ROW]
[ROW][C]49[/C][C]63[/C][C]69.9028900677126[/C][C]-6.90289006771262[/C][/ROW]
[ROW][C]50[/C][C]37[/C][C]67.5236210706274[/C][C]-30.5236210706274[/C][/ROW]
[ROW][C]51[/C][C]35[/C][C]60.3598753420447[/C][C]-25.3598753420447[/C][/ROW]
[ROW][C]52[/C][C]23[/C][C]32.7027017985157[/C][C]-9.70270179851573[/C][/ROW]
[ROW][C]53[/C][C]40[/C][C]36.8649159775072[/C][C]3.13508402249283[/C][/ROW]
[ROW][C]54[/C][C]29[/C][C]21.0926191891718[/C][C]7.90738081082816[/C][/ROW]
[ROW][C]55[/C][C]37[/C][C]20.0518755581521[/C][C]16.9481244418479[/C][/ROW]
[ROW][C]56[/C][C]51[/C][C]57.788396377094[/C][C]-6.78839637709397[/C][/ROW]
[ROW][C]57[/C][C]20[/C][C]48.7429062355124[/C][C]-28.7429062355124[/C][/ROW]
[ROW][C]58[/C][C]28[/C][C]22.0703932248579[/C][C]5.92960677514215[/C][/ROW]
[ROW][C]59[/C][C]13[/C][C]15.9343250260694[/C][C]-2.93432502606939[/C][/ROW]
[ROW][C]60[/C][C]22[/C][C]30.2482108697931[/C][C]-8.24821086979305[/C][/ROW]
[ROW][C]61[/C][C]25[/C][C]14.7478494171391[/C][C]10.2521505828609[/C][/ROW]
[ROW][C]62[/C][C]13[/C][C]26.5791014651225[/C][C]-13.5791014651225[/C][/ROW]
[ROW][C]63[/C][C]16[/C][C]29.8677526473628[/C][C]-13.8677526473628[/C][/ROW]
[ROW][C]64[/C][C]13[/C][C]7.90947754002223[/C][C]5.09052245997777[/C][/ROW]
[ROW][C]65[/C][C]16[/C][C]19.1517623085866[/C][C]-3.15176230858660[/C][/ROW]
[ROW][C]66[/C][C]17[/C][C]2.35754959861670[/C][C]14.6424504013833[/C][/ROW]
[ROW][C]67[/C][C]9[/C][C]3.02323446114568[/C][C]5.97676553885432[/C][/ROW]
[ROW][C]68[/C][C]17[/C][C]40.065899725606[/C][C]-23.065899725606[/C][/ROW]
[ROW][C]69[/C][C]25[/C][C]21.1824570139918[/C][C]3.81754298600822[/C][/ROW]
[ROW][C]70[/C][C]14[/C][C]12.0365468708473[/C][C]1.96345312915268[/C][/ROW]
[ROW][C]71[/C][C]8[/C][C]5.09845656575206[/C][C]2.90154343424794[/C][/ROW]
[ROW][C]72[/C][C]7[/C][C]14.4156949859207[/C][C]-7.41569498592066[/C][/ROW]
[ROW][C]73[/C][C]10[/C][C]6.07653589948362[/C][C]3.92346410051638[/C][/ROW]
[ROW][C]74[/C][C]7[/C][C]11.1459367062888[/C][C]-4.14593670628875[/C][/ROW]
[ROW][C]75[/C][C]10[/C][C]20.4808539244387[/C][C]-10.4808539244387[/C][/ROW]
[ROW][C]76[/C][C]3[/C][C]-1.24830010056577[/C][C]4.24830010056577[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103829&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103829&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
13048.7324279956963-18.7324279956963
24347.086469936221-4.08646993622098
38266.110368242706515.8896317572935
44060.980613945781-20.9806139457810
54762.0743382813179-15.0743382813179
61939.7127912223652-20.7127912223652
75239.644802834757312.3551971652427
813678.08630104788357.913698952117
980102.160719820264-22.1607198202642
104277.3637956525042-35.3637956525042
115446.7350124596347.26498754036598
126676.0780077967497-10.0780077967497
138166.746465115031614.2535348849684
146373.171510890558-10.1715108905580
1513782.013565496878354.9864345031217
167286.5196819898917-14.5196819898917
1710793.063193546035413.9368064539646
185867.7084772393128-9.70847723931278
193674.5345088777169-38.5345088777169
205279.565943831732-27.5659438317321
217970.30819478685888.69180521314117
227761.922616909805615.0773830901944
235459.8489239987506-5.84892399875062
248464.775931429452619.2240685705474
254867.6874470622396-19.6874470622396
269667.736407720156428.2635922798436
278382.35818921305780.641810786942179
286675.4417767652626-9.4417767652626
296165.3437191668188-4.34371916681884
305354.8167802383049-1.81678023830489
313047.8720617844677-17.8720617844677
327474.636358776985-0.636358776984946
336965.5175980092193.482401990781
345959.2384464349425-0.238446434942508
354244.041841877633-2.04184187763301
366557.17377224544397.8262277545561
377053.106384442697116.8936155573029
3810065.756952211025934.2430477889741
396384.8093951335112-21.8093951335112
4010559.694048061092545.3059519389075
418276.50207071973415.49792928026586
428171.31178251222879.6882174877713
437553.873516483760321.1264835162397
44102101.85710024070.142899759300056
4512186.088124134153934.9118758658461
469885.368200907042512.6317990929575
477675.34144007216090.658559927839122
487778.3083826726402-1.30838267264018
496369.9028900677126-6.90289006771262
503767.5236210706274-30.5236210706274
513560.3598753420447-25.3598753420447
522332.7027017985157-9.70270179851573
534036.86491597750723.13508402249283
542921.09261918917187.90738081082816
553720.051875558152116.9481244418479
565157.788396377094-6.78839637709397
572048.7429062355124-28.7429062355124
582822.07039322485795.92960677514215
591315.9343250260694-2.93432502606939
602230.2482108697931-8.24821086979305
612514.747849417139110.2521505828609
621326.5791014651225-13.5791014651225
631629.8677526473628-13.8677526473628
64137.909477540022235.09052245997777
651619.1517623085866-3.15176230858660
66172.3575495986167014.6424504013833
6793.023234461145685.97676553885432
681740.065899725606-23.065899725606
692521.18245701399183.81754298600822
701412.03654687084731.96345312915268
7185.098456565752062.90154343424794
72714.4156949859207-7.41569498592066
73106.076535899483623.92346410051638
74711.1459367062888-4.14593670628875
751020.4808539244387-10.4808539244387
763-1.248300100565774.24830010056577






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
200.9960993359498880.007801328100224420.00390066405011221
210.9970242451121290.005951509775743120.00297575488787156
220.9970102011530750.005979597693850760.00298979884692538
230.9979756372390230.004048725521953010.00202436276097650
240.9968933571068950.006213285786209330.00310664289310467
250.9982856764959040.003428647008192550.00171432350409628
260.9986465605704660.002706878859067150.00135343942953357
270.998982453013920.002035093972159230.00101754698607962
280.9989892078349040.002021584330192320.00101079216509616
290.9986225365877340.002754926824532280.00137746341226614
300.997338229585380.005323540829239340.00266177041461967
310.9975491775564210.004901644887157570.00245082244357879
320.9965721550529060.006855689894188420.00342784494709421
330.9934910441877450.01301791162450980.00650895581225492
340.9915274954249260.01694500915014760.00847250457507381
350.9905749882830610.01885002343387740.0094250117169387
360.983202765050020.03359446989995920.0167972349499796
370.974683728557730.05063254288453920.0253162714422696
380.9874621199120820.02507576017583660.0125378800879183
390.9939527481103820.01209450377923580.00604725188961791
400.9986172675233350.002765464953329050.00138273247666452
410.9977994679420490.004401064115902380.00220053205795119
420.9956442403476780.008711519304644180.00435575965232209
430.994291487467910.01141702506418210.00570851253209106
440.9954019063971390.009196187205721680.00459809360286084
450.9998960498716610.0002079002566770330.000103950128338516
460.9998622975113020.0002754049773966680.000137702488698334
470.999621620478160.0007567590436804630.000378379521840231
480.9994282302215770.001143539556845850.000571769778422925
490.9992980531144720.001403893771056240.000701946885528119
500.9988152802292450.002369439541509340.00118471977075467
510.997588637071420.004822725857160410.00241136292858021
520.9936886582170020.01262268356599610.00631134178299806
530.9869473354762860.02610532904742770.0130526645237139
540.9645164715433720.07096705691325580.0354835284566279
550.9486501591083470.1026996817833050.0513498408916527
560.9953250504571160.009349899085768990.00467494954288449

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
20 & 0.996099335949888 & 0.00780132810022442 & 0.00390066405011221 \tabularnewline
21 & 0.997024245112129 & 0.00595150977574312 & 0.00297575488787156 \tabularnewline
22 & 0.997010201153075 & 0.00597959769385076 & 0.00298979884692538 \tabularnewline
23 & 0.997975637239023 & 0.00404872552195301 & 0.00202436276097650 \tabularnewline
24 & 0.996893357106895 & 0.00621328578620933 & 0.00310664289310467 \tabularnewline
25 & 0.998285676495904 & 0.00342864700819255 & 0.00171432350409628 \tabularnewline
26 & 0.998646560570466 & 0.00270687885906715 & 0.00135343942953357 \tabularnewline
27 & 0.99898245301392 & 0.00203509397215923 & 0.00101754698607962 \tabularnewline
28 & 0.998989207834904 & 0.00202158433019232 & 0.00101079216509616 \tabularnewline
29 & 0.998622536587734 & 0.00275492682453228 & 0.00137746341226614 \tabularnewline
30 & 0.99733822958538 & 0.00532354082923934 & 0.00266177041461967 \tabularnewline
31 & 0.997549177556421 & 0.00490164488715757 & 0.00245082244357879 \tabularnewline
32 & 0.996572155052906 & 0.00685568989418842 & 0.00342784494709421 \tabularnewline
33 & 0.993491044187745 & 0.0130179116245098 & 0.00650895581225492 \tabularnewline
34 & 0.991527495424926 & 0.0169450091501476 & 0.00847250457507381 \tabularnewline
35 & 0.990574988283061 & 0.0188500234338774 & 0.0094250117169387 \tabularnewline
36 & 0.98320276505002 & 0.0335944698999592 & 0.0167972349499796 \tabularnewline
37 & 0.97468372855773 & 0.0506325428845392 & 0.0253162714422696 \tabularnewline
38 & 0.987462119912082 & 0.0250757601758366 & 0.0125378800879183 \tabularnewline
39 & 0.993952748110382 & 0.0120945037792358 & 0.00604725188961791 \tabularnewline
40 & 0.998617267523335 & 0.00276546495332905 & 0.00138273247666452 \tabularnewline
41 & 0.997799467942049 & 0.00440106411590238 & 0.00220053205795119 \tabularnewline
42 & 0.995644240347678 & 0.00871151930464418 & 0.00435575965232209 \tabularnewline
43 & 0.99429148746791 & 0.0114170250641821 & 0.00570851253209106 \tabularnewline
44 & 0.995401906397139 & 0.00919618720572168 & 0.00459809360286084 \tabularnewline
45 & 0.999896049871661 & 0.000207900256677033 & 0.000103950128338516 \tabularnewline
46 & 0.999862297511302 & 0.000275404977396668 & 0.000137702488698334 \tabularnewline
47 & 0.99962162047816 & 0.000756759043680463 & 0.000378379521840231 \tabularnewline
48 & 0.999428230221577 & 0.00114353955684585 & 0.000571769778422925 \tabularnewline
49 & 0.999298053114472 & 0.00140389377105624 & 0.000701946885528119 \tabularnewline
50 & 0.998815280229245 & 0.00236943954150934 & 0.00118471977075467 \tabularnewline
51 & 0.99758863707142 & 0.00482272585716041 & 0.00241136292858021 \tabularnewline
52 & 0.993688658217002 & 0.0126226835659961 & 0.00631134178299806 \tabularnewline
53 & 0.986947335476286 & 0.0261053290474277 & 0.0130526645237139 \tabularnewline
54 & 0.964516471543372 & 0.0709670569132558 & 0.0354835284566279 \tabularnewline
55 & 0.948650159108347 & 0.102699681783305 & 0.0513498408916527 \tabularnewline
56 & 0.995325050457116 & 0.00934989908576899 & 0.00467494954288449 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103829&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]20[/C][C]0.996099335949888[/C][C]0.00780132810022442[/C][C]0.00390066405011221[/C][/ROW]
[ROW][C]21[/C][C]0.997024245112129[/C][C]0.00595150977574312[/C][C]0.00297575488787156[/C][/ROW]
[ROW][C]22[/C][C]0.997010201153075[/C][C]0.00597959769385076[/C][C]0.00298979884692538[/C][/ROW]
[ROW][C]23[/C][C]0.997975637239023[/C][C]0.00404872552195301[/C][C]0.00202436276097650[/C][/ROW]
[ROW][C]24[/C][C]0.996893357106895[/C][C]0.00621328578620933[/C][C]0.00310664289310467[/C][/ROW]
[ROW][C]25[/C][C]0.998285676495904[/C][C]0.00342864700819255[/C][C]0.00171432350409628[/C][/ROW]
[ROW][C]26[/C][C]0.998646560570466[/C][C]0.00270687885906715[/C][C]0.00135343942953357[/C][/ROW]
[ROW][C]27[/C][C]0.99898245301392[/C][C]0.00203509397215923[/C][C]0.00101754698607962[/C][/ROW]
[ROW][C]28[/C][C]0.998989207834904[/C][C]0.00202158433019232[/C][C]0.00101079216509616[/C][/ROW]
[ROW][C]29[/C][C]0.998622536587734[/C][C]0.00275492682453228[/C][C]0.00137746341226614[/C][/ROW]
[ROW][C]30[/C][C]0.99733822958538[/C][C]0.00532354082923934[/C][C]0.00266177041461967[/C][/ROW]
[ROW][C]31[/C][C]0.997549177556421[/C][C]0.00490164488715757[/C][C]0.00245082244357879[/C][/ROW]
[ROW][C]32[/C][C]0.996572155052906[/C][C]0.00685568989418842[/C][C]0.00342784494709421[/C][/ROW]
[ROW][C]33[/C][C]0.993491044187745[/C][C]0.0130179116245098[/C][C]0.00650895581225492[/C][/ROW]
[ROW][C]34[/C][C]0.991527495424926[/C][C]0.0169450091501476[/C][C]0.00847250457507381[/C][/ROW]
[ROW][C]35[/C][C]0.990574988283061[/C][C]0.0188500234338774[/C][C]0.0094250117169387[/C][/ROW]
[ROW][C]36[/C][C]0.98320276505002[/C][C]0.0335944698999592[/C][C]0.0167972349499796[/C][/ROW]
[ROW][C]37[/C][C]0.97468372855773[/C][C]0.0506325428845392[/C][C]0.0253162714422696[/C][/ROW]
[ROW][C]38[/C][C]0.987462119912082[/C][C]0.0250757601758366[/C][C]0.0125378800879183[/C][/ROW]
[ROW][C]39[/C][C]0.993952748110382[/C][C]0.0120945037792358[/C][C]0.00604725188961791[/C][/ROW]
[ROW][C]40[/C][C]0.998617267523335[/C][C]0.00276546495332905[/C][C]0.00138273247666452[/C][/ROW]
[ROW][C]41[/C][C]0.997799467942049[/C][C]0.00440106411590238[/C][C]0.00220053205795119[/C][/ROW]
[ROW][C]42[/C][C]0.995644240347678[/C][C]0.00871151930464418[/C][C]0.00435575965232209[/C][/ROW]
[ROW][C]43[/C][C]0.99429148746791[/C][C]0.0114170250641821[/C][C]0.00570851253209106[/C][/ROW]
[ROW][C]44[/C][C]0.995401906397139[/C][C]0.00919618720572168[/C][C]0.00459809360286084[/C][/ROW]
[ROW][C]45[/C][C]0.999896049871661[/C][C]0.000207900256677033[/C][C]0.000103950128338516[/C][/ROW]
[ROW][C]46[/C][C]0.999862297511302[/C][C]0.000275404977396668[/C][C]0.000137702488698334[/C][/ROW]
[ROW][C]47[/C][C]0.99962162047816[/C][C]0.000756759043680463[/C][C]0.000378379521840231[/C][/ROW]
[ROW][C]48[/C][C]0.999428230221577[/C][C]0.00114353955684585[/C][C]0.000571769778422925[/C][/ROW]
[ROW][C]49[/C][C]0.999298053114472[/C][C]0.00140389377105624[/C][C]0.000701946885528119[/C][/ROW]
[ROW][C]50[/C][C]0.998815280229245[/C][C]0.00236943954150934[/C][C]0.00118471977075467[/C][/ROW]
[ROW][C]51[/C][C]0.99758863707142[/C][C]0.00482272585716041[/C][C]0.00241136292858021[/C][/ROW]
[ROW][C]52[/C][C]0.993688658217002[/C][C]0.0126226835659961[/C][C]0.00631134178299806[/C][/ROW]
[ROW][C]53[/C][C]0.986947335476286[/C][C]0.0261053290474277[/C][C]0.0130526645237139[/C][/ROW]
[ROW][C]54[/C][C]0.964516471543372[/C][C]0.0709670569132558[/C][C]0.0354835284566279[/C][/ROW]
[ROW][C]55[/C][C]0.948650159108347[/C][C]0.102699681783305[/C][C]0.0513498408916527[/C][/ROW]
[ROW][C]56[/C][C]0.995325050457116[/C][C]0.00934989908576899[/C][C]0.00467494954288449[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103829&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103829&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
200.9960993359498880.007801328100224420.00390066405011221
210.9970242451121290.005951509775743120.00297575488787156
220.9970102011530750.005979597693850760.00298979884692538
230.9979756372390230.004048725521953010.00202436276097650
240.9968933571068950.006213285786209330.00310664289310467
250.9982856764959040.003428647008192550.00171432350409628
260.9986465605704660.002706878859067150.00135343942953357
270.998982453013920.002035093972159230.00101754698607962
280.9989892078349040.002021584330192320.00101079216509616
290.9986225365877340.002754926824532280.00137746341226614
300.997338229585380.005323540829239340.00266177041461967
310.9975491775564210.004901644887157570.00245082244357879
320.9965721550529060.006855689894188420.00342784494709421
330.9934910441877450.01301791162450980.00650895581225492
340.9915274954249260.01694500915014760.00847250457507381
350.9905749882830610.01885002343387740.0094250117169387
360.983202765050020.03359446989995920.0167972349499796
370.974683728557730.05063254288453920.0253162714422696
380.9874621199120820.02507576017583660.0125378800879183
390.9939527481103820.01209450377923580.00604725188961791
400.9986172675233350.002765464953329050.00138273247666452
410.9977994679420490.004401064115902380.00220053205795119
420.9956442403476780.008711519304644180.00435575965232209
430.994291487467910.01141702506418210.00570851253209106
440.9954019063971390.009196187205721680.00459809360286084
450.9998960498716610.0002079002566770330.000103950128338516
460.9998622975113020.0002754049773966680.000137702488698334
470.999621620478160.0007567590436804630.000378379521840231
480.9994282302215770.001143539556845850.000571769778422925
490.9992980531144720.001403893771056240.000701946885528119
500.9988152802292450.002369439541509340.00118471977075467
510.997588637071420.004822725857160410.00241136292858021
520.9936886582170020.01262268356599610.00631134178299806
530.9869473354762860.02610532904742770.0130526645237139
540.9645164715433720.07096705691325580.0354835284566279
550.9486501591083470.1026996817833050.0513498408916527
560.9953250504571160.009349899085768990.00467494954288449






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level250.675675675675676NOK
5% type I error level340.918918918918919NOK
10% type I error level360.972972972972973NOK

\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 & 25 & 0.675675675675676 & NOK \tabularnewline
5% type I error level & 34 & 0.918918918918919 & NOK \tabularnewline
10% type I error level & 36 & 0.972972972972973 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103829&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]25[/C][C]0.675675675675676[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]34[/C][C]0.918918918918919[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]36[/C][C]0.972972972972973[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103829&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103829&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 level250.675675675675676NOK
5% type I error level340.918918918918919NOK
10% type I error level360.972972972972973NOK


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 5
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Figure 6
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Figure 7
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Figure 8
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Figure 9
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 2 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}