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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 01:47:44 -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/t125870704409d1p8kpu8qhekm.htm/, Retrieved Wed, 19 Nov 2025 22:41:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57985, Retrieved Wed, 19 Nov 2025 22:41:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact526

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]
-    D    [Multiple Regression] [model 1] [2009-11-17 14:36:29] [ed603017d2bee8fbd82b6d5ec04e12c3]
-    D      [Multiple Regression] [multiple regression] [2009-11-19 21:38:11] [ed603017d2bee8fbd82b6d5ec04e12c3]
-   P         [Multiple Regression] [monthly dummies] [2009-11-19 22:00:07] [ed603017d2bee8fbd82b6d5ec04e12c3]
-   P             [Multiple Regression] [model3] [2009-11-20 08:47:44] [87085ce7f5378f281469a8b1f0969170] [Current]
-    D              [Multiple Regression] [model 4] [2009-11-20 08:59:37] [ed603017d2bee8fbd82b6d5ec04e12c3]
-    D                [Multiple Regression] [W7: Model 4] [2009-11-22 13:34:45] [03d5b865e91ca35b5a5d21b8d6da5aba]
-    D                  [Multiple Regression] [review 7] [2009-11-24 21:51:11] [309ee52d0058ff0a6f7eec15e07b2d9f]
-    D                [Multiple Regression] [] [2009-11-22 15:02:10] [9f35ad889e41dd0c9322ca60d75b9f47]
-    D                [Multiple Regression] [Beste model] [2009-12-05 15:17:52] [34b80aeb109c116fd63bf2eb7493a276]
-    D              [Multiple Regression] [Workshop7] [2009-11-20 13:14:04] [34b80aeb109c116fd63bf2eb7493a276]
-    D                [Multiple Regression] [workshop7] [2009-11-20 13:34:45] [34b80aeb109c116fd63bf2eb7493a276]
-   P                   [Multiple Regression] [Workshop 7: verbe...] [2009-11-27 14:49:24] [7c2a5b25a196bd646844b8f5223c9b3e]
-   PD                [Multiple Regression] [Workshop 7] [2009-11-20 16:57:31] [78762f311bef5a0e45c439762ada383c]
-   P                   [Multiple Regression] [verb ws 7] [2009-11-21 09:45:52] [134dc66689e3d457a82860db6471d419]
-    D                [Multiple Regression] [model 3] [2009-12-05 14:58:14] [34b80aeb109c116fd63bf2eb7493a276]
-    D              [Multiple Regression] [W7: Linear Trend] [2009-11-21 14:22:35] [03d5b865e91ca35b5a5d21b8d6da5aba]
-    D              [Multiple Regression] [] [2009-11-22 14:13:11] [9f35ad889e41dd0c9322ca60d75b9f47]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
106.1	97.89
106	98.69
105.9	99.01
105.8	99.18
105.7	98.45
105.6	98.13
105.4	98.29
105.4	99.1
105.5	99.26
105.6	98.85
105.7	98.05
105.9	98.53
106.1	99.34
106	100.14
105.8	100.3
105.8	100.22
105.7	99.9
105.5	99.58
105.3	99.9
105.2	100.78
105.2	100.78
105	100.46
105.1	100.06
105.1	100.28
105.2	100.78
104.9	101.58
104.8	102.06
104.5	102.02
104.5	101.68
104.4	101.32
104.4	101.81
104.2	102.3
104.1	102.12
103.9	102.1
103.8	101.75
103.9	101.5
104.2	102.16
104.1	103.47
103.8	104.05
103.6	104.09
103.7	103.55
103.5	102.77
103.4	102.89
103.1	103.6
103.1	103.76
103.1	103.92
103.2	103.35
103.3	103.32
103.5	104.2
103.6	105.44
103.5	105.81
103.3	106.25
103.2	105.94
103.1	105.82
103.2	105.96
103	106.49
103	106.32
103.1	105.88
103.4	105.07

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57985&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57985&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57985&T=0

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


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
Werkl[t] = + 91.491378559978 + 0.153267237582525Infl[t] + 0.0739357297362894M1[t] -0.0975590909259045M2[t] -0.235867431137875M3[t] -0.331874013777070M4[t] -0.22297054679554M5[t] -0.224489251969629M6[t] -0.261953247870372M7[t] -0.446548293832267M8[t] -0.365388945862221M9[t] -0.293576150375666M10[t] -0.0235218046077498M11[t] -0.0802397445445542t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Werkl[t] =  +  91.491378559978 +  0.153267237582525Infl[t] +  0.0739357297362894M1[t] -0.0975590909259045M2[t] -0.235867431137875M3[t] -0.331874013777070M4[t] -0.22297054679554M5[t] -0.224489251969629M6[t] -0.261953247870372M7[t] -0.446548293832267M8[t] -0.365388945862221M9[t] -0.293576150375666M10[t] -0.0235218046077498M11[t] -0.0802397445445542t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57985&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Werkl[t] =  +  91.491378559978 +  0.153267237582525Infl[t] +  0.0739357297362894M1[t] -0.0975590909259045M2[t] -0.235867431137875M3[t] -0.331874013777070M4[t] -0.22297054679554M5[t] -0.224489251969629M6[t] -0.261953247870372M7[t] -0.446548293832267M8[t] -0.365388945862221M9[t] -0.293576150375666M10[t] -0.0235218046077498M11[t] -0.0802397445445542t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57985&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57985&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
Werkl[t] = + 91.491378559978 + 0.153267237582525Infl[t] + 0.0739357297362894M1[t] -0.0975590909259045M2[t] -0.235867431137875M3[t] -0.331874013777070M4[t] -0.22297054679554M5[t] -0.224489251969629M6[t] -0.261953247870372M7[t] -0.446548293832267M8[t] -0.365388945862221M9[t] -0.293576150375666M10[t] -0.0235218046077498M11[t] -0.0802397445445542t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)91.49137855997812.2318927.479700
Infl0.1532672375825250.126681.20990.2326450.116322
M10.07393572973628940.2153150.34340.7329090.366454
M2-0.09755909092590450.276681-0.35260.726030.363015
M3-0.2358674311378750.298492-0.79020.4335570.216778
M4-0.3318740137770700.294718-1.12610.2661040.133052
M5-0.222970546795540.243827-0.91450.3653490.182675
M6-0.2244892519696290.211245-1.06270.293590.146795
M7-0.2619532478703720.216299-1.21110.232190.116095
M8-0.4465482938322670.252702-1.76710.0839940.041997
M9-0.3653889458622210.241149-1.51520.1367160.068358
M10-0.2935761503756660.218438-1.3440.1856920.092846
M11-0.02352180460774980.196627-0.11960.9053110.452656
t-0.08023974454455420.018546-4.32668.3e-054.2e-05

\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) & 91.491378559978 & 12.231892 & 7.4797 & 0 & 0 \tabularnewline
Infl & 0.153267237582525 & 0.12668 & 1.2099 & 0.232645 & 0.116322 \tabularnewline
M1 & 0.0739357297362894 & 0.215315 & 0.3434 & 0.732909 & 0.366454 \tabularnewline
M2 & -0.0975590909259045 & 0.276681 & -0.3526 & 0.72603 & 0.363015 \tabularnewline
M3 & -0.235867431137875 & 0.298492 & -0.7902 & 0.433557 & 0.216778 \tabularnewline
M4 & -0.331874013777070 & 0.294718 & -1.1261 & 0.266104 & 0.133052 \tabularnewline
M5 & -0.22297054679554 & 0.243827 & -0.9145 & 0.365349 & 0.182675 \tabularnewline
M6 & -0.224489251969629 & 0.211245 & -1.0627 & 0.29359 & 0.146795 \tabularnewline
M7 & -0.261953247870372 & 0.216299 & -1.2111 & 0.23219 & 0.116095 \tabularnewline
M8 & -0.446548293832267 & 0.252702 & -1.7671 & 0.083994 & 0.041997 \tabularnewline
M9 & -0.365388945862221 & 0.241149 & -1.5152 & 0.136716 & 0.068358 \tabularnewline
M10 & -0.293576150375666 & 0.218438 & -1.344 & 0.185692 & 0.092846 \tabularnewline
M11 & -0.0235218046077498 & 0.196627 & -0.1196 & 0.905311 & 0.452656 \tabularnewline
t & -0.0802397445445542 & 0.018546 & -4.3266 & 8.3e-05 & 4.2e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57985&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]91.491378559978[/C][C]12.231892[/C][C]7.4797[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Infl[/C][C]0.153267237582525[/C][C]0.12668[/C][C]1.2099[/C][C]0.232645[/C][C]0.116322[/C][/ROW]
[ROW][C]M1[/C][C]0.0739357297362894[/C][C]0.215315[/C][C]0.3434[/C][C]0.732909[/C][C]0.366454[/C][/ROW]
[ROW][C]M2[/C][C]-0.0975590909259045[/C][C]0.276681[/C][C]-0.3526[/C][C]0.72603[/C][C]0.363015[/C][/ROW]
[ROW][C]M3[/C][C]-0.235867431137875[/C][C]0.298492[/C][C]-0.7902[/C][C]0.433557[/C][C]0.216778[/C][/ROW]
[ROW][C]M4[/C][C]-0.331874013777070[/C][C]0.294718[/C][C]-1.1261[/C][C]0.266104[/C][C]0.133052[/C][/ROW]
[ROW][C]M5[/C][C]-0.22297054679554[/C][C]0.243827[/C][C]-0.9145[/C][C]0.365349[/C][C]0.182675[/C][/ROW]
[ROW][C]M6[/C][C]-0.224489251969629[/C][C]0.211245[/C][C]-1.0627[/C][C]0.29359[/C][C]0.146795[/C][/ROW]
[ROW][C]M7[/C][C]-0.261953247870372[/C][C]0.216299[/C][C]-1.2111[/C][C]0.23219[/C][C]0.116095[/C][/ROW]
[ROW][C]M8[/C][C]-0.446548293832267[/C][C]0.252702[/C][C]-1.7671[/C][C]0.083994[/C][C]0.041997[/C][/ROW]
[ROW][C]M9[/C][C]-0.365388945862221[/C][C]0.241149[/C][C]-1.5152[/C][C]0.136716[/C][C]0.068358[/C][/ROW]
[ROW][C]M10[/C][C]-0.293576150375666[/C][C]0.218438[/C][C]-1.344[/C][C]0.185692[/C][C]0.092846[/C][/ROW]
[ROW][C]M11[/C][C]-0.0235218046077498[/C][C]0.196627[/C][C]-0.1196[/C][C]0.905311[/C][C]0.452656[/C][/ROW]
[ROW][C]t[/C][C]-0.0802397445445542[/C][C]0.018546[/C][C]-4.3266[/C][C]8.3e-05[/C][C]4.2e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57985&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57985&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)91.49137855997812.2318927.479700
Infl0.1532672375825250.126681.20990.2326450.116322
M10.07393572973628940.2153150.34340.7329090.366454
M2-0.09755909092590450.276681-0.35260.726030.363015
M3-0.2358674311378750.298492-0.79020.4335570.216778
M4-0.3318740137770700.294718-1.12610.2661040.133052
M5-0.222970546795540.243827-0.91450.3653490.182675
M6-0.2244892519696290.211245-1.06270.293590.146795
M7-0.2619532478703720.216299-1.21110.232190.116095
M8-0.4465482938322670.252702-1.76710.0839940.041997
M9-0.3653889458622210.241149-1.51520.1367160.068358
M10-0.2935761503756660.218438-1.3440.1856920.092846
M11-0.02352180460774980.196627-0.11960.9053110.452656
t-0.08023974454455420.018546-4.32668.3e-054.2e-05






Multiple Linear Regression - Regression Statistics
Multiple R0.969649892450111
R-squared0.940220913928512
Adjusted R-squared0.922951400174526
F-TEST (value)54.4439714587521
F-TEST (DF numerator)13
F-TEST (DF denominator)45
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.292594098675783
Sum Squared Residuals3.85250879609523

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.969649892450111 \tabularnewline
R-squared & 0.940220913928512 \tabularnewline
Adjusted R-squared & 0.922951400174526 \tabularnewline
F-TEST (value) & 54.4439714587521 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 45 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.292594098675783 \tabularnewline
Sum Squared Residuals & 3.85250879609523 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57985&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.969649892450111[/C][/ROW]
[ROW][C]R-squared[/C][C]0.940220913928512[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.922951400174526[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]54.4439714587521[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]45[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.292594098675783[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]3.85250879609523[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57985&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57985&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 R0.969649892450111
R-squared0.940220913928512
Adjusted R-squared0.922951400174526
F-TEST (value)54.4439714587521
F-TEST (DF numerator)13
F-TEST (DF denominator)45
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.292594098675783
Sum Squared Residuals3.85250879609523






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1106.1106.488404432123-0.388404432122857
2106106.359283656982-0.359283656982363
3105.9106.189781088252-0.289781088252242
4105.8106.039590191458-0.239590191457530
5105.7105.956368830459-0.256368830459257
6105.6105.825564864714-0.225564864714213
7105.4105.732383882282-0.33238388228211
8105.4105.591695554218-0.191695554217505
9105.5105.617137915656-0.117137915656208
10105.6105.5458713991890.0541286008106235
11105.7105.6130722103470.0869277896532885
12105.9105.6299225444500.270077455550484
13106.1105.7477649920830.352235007916891
14106105.6186442169420.381355783057624
15105.8105.4246188901990.375381109800943
16105.8105.2361111840090.563888815991294
17105.7105.2157293904190.484270609580731
18105.5105.0849254246740.41507457532578
19105.3105.0162672002550.283732799744666
20105.2104.8863075788220.313692421178498
21105.2104.8872271822470.312772817753007
22105104.8297547171630.170245282837413
23105.1104.9582624233530.141737576647053
24105.1104.9352632756840.164736724315702
25105.2105.0055928796670.194407120332713
26104.9104.8764721045270.0235278954734443
27104.8104.7314922938100.0685077061903472
28104.5104.549115277123-0.0491152771225977
29104.5104.525668138782-0.0256681387815173
30104.4104.3887334835330.0112665164668423
31104.4104.3461306895030.0538693104967011
32104.2104.1563968454120.0436031545877104
33104.1104.129728346073-0.0297283460729360
34103.9104.118236052263-0.218236052263273
35103.8104.254407120333-0.454407120332761
36103.9104.159372371000-0.259372371000317
37104.2104.254224732997-0.054224732996521
38104.1104.203270249023-0.10327024902289
39103.8104.073617162064-0.273617162064228
40103.6103.903501524384-0.303501524383782
41103.7103.849400938526-0.149400938526185
42103.5103.648094043493-0.148094043493175
43103.4103.548782371558-0.148782371557775
44103.1103.392767319735-0.292767319734931
45103.1103.418209681174-0.318209681173628
46103.1103.434305490129-0.334305490128832
47103.2103.536757765930-0.336757765930146
48103.3103.475441808866-0.175441808865870
49103.5103.604012963130-0.104012963130227
50103.6103.5423297725260.0576702274741849
51103.5103.3804905656750.11950943432518
52103.3103.2716818230270.0283181769726160
53103.2103.252832701814-0.0528327018137714
54103.1103.152682183585-0.0526821835852335
55103.2103.0564358564010.143564143598519
56103102.8728327018140.127167298186226
57103102.8476968748500.152303125149765
58103.1102.7718323412560.328167658744069
59103.4102.8375004800370.562499519962565

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 106.1 & 106.488404432123 & -0.388404432122857 \tabularnewline
2 & 106 & 106.359283656982 & -0.359283656982363 \tabularnewline
3 & 105.9 & 106.189781088252 & -0.289781088252242 \tabularnewline
4 & 105.8 & 106.039590191458 & -0.239590191457530 \tabularnewline
5 & 105.7 & 105.956368830459 & -0.256368830459257 \tabularnewline
6 & 105.6 & 105.825564864714 & -0.225564864714213 \tabularnewline
7 & 105.4 & 105.732383882282 & -0.33238388228211 \tabularnewline
8 & 105.4 & 105.591695554218 & -0.191695554217505 \tabularnewline
9 & 105.5 & 105.617137915656 & -0.117137915656208 \tabularnewline
10 & 105.6 & 105.545871399189 & 0.0541286008106235 \tabularnewline
11 & 105.7 & 105.613072210347 & 0.0869277896532885 \tabularnewline
12 & 105.9 & 105.629922544450 & 0.270077455550484 \tabularnewline
13 & 106.1 & 105.747764992083 & 0.352235007916891 \tabularnewline
14 & 106 & 105.618644216942 & 0.381355783057624 \tabularnewline
15 & 105.8 & 105.424618890199 & 0.375381109800943 \tabularnewline
16 & 105.8 & 105.236111184009 & 0.563888815991294 \tabularnewline
17 & 105.7 & 105.215729390419 & 0.484270609580731 \tabularnewline
18 & 105.5 & 105.084925424674 & 0.41507457532578 \tabularnewline
19 & 105.3 & 105.016267200255 & 0.283732799744666 \tabularnewline
20 & 105.2 & 104.886307578822 & 0.313692421178498 \tabularnewline
21 & 105.2 & 104.887227182247 & 0.312772817753007 \tabularnewline
22 & 105 & 104.829754717163 & 0.170245282837413 \tabularnewline
23 & 105.1 & 104.958262423353 & 0.141737576647053 \tabularnewline
24 & 105.1 & 104.935263275684 & 0.164736724315702 \tabularnewline
25 & 105.2 & 105.005592879667 & 0.194407120332713 \tabularnewline
26 & 104.9 & 104.876472104527 & 0.0235278954734443 \tabularnewline
27 & 104.8 & 104.731492293810 & 0.0685077061903472 \tabularnewline
28 & 104.5 & 104.549115277123 & -0.0491152771225977 \tabularnewline
29 & 104.5 & 104.525668138782 & -0.0256681387815173 \tabularnewline
30 & 104.4 & 104.388733483533 & 0.0112665164668423 \tabularnewline
31 & 104.4 & 104.346130689503 & 0.0538693104967011 \tabularnewline
32 & 104.2 & 104.156396845412 & 0.0436031545877104 \tabularnewline
33 & 104.1 & 104.129728346073 & -0.0297283460729360 \tabularnewline
34 & 103.9 & 104.118236052263 & -0.218236052263273 \tabularnewline
35 & 103.8 & 104.254407120333 & -0.454407120332761 \tabularnewline
36 & 103.9 & 104.159372371000 & -0.259372371000317 \tabularnewline
37 & 104.2 & 104.254224732997 & -0.054224732996521 \tabularnewline
38 & 104.1 & 104.203270249023 & -0.10327024902289 \tabularnewline
39 & 103.8 & 104.073617162064 & -0.273617162064228 \tabularnewline
40 & 103.6 & 103.903501524384 & -0.303501524383782 \tabularnewline
41 & 103.7 & 103.849400938526 & -0.149400938526185 \tabularnewline
42 & 103.5 & 103.648094043493 & -0.148094043493175 \tabularnewline
43 & 103.4 & 103.548782371558 & -0.148782371557775 \tabularnewline
44 & 103.1 & 103.392767319735 & -0.292767319734931 \tabularnewline
45 & 103.1 & 103.418209681174 & -0.318209681173628 \tabularnewline
46 & 103.1 & 103.434305490129 & -0.334305490128832 \tabularnewline
47 & 103.2 & 103.536757765930 & -0.336757765930146 \tabularnewline
48 & 103.3 & 103.475441808866 & -0.175441808865870 \tabularnewline
49 & 103.5 & 103.604012963130 & -0.104012963130227 \tabularnewline
50 & 103.6 & 103.542329772526 & 0.0576702274741849 \tabularnewline
51 & 103.5 & 103.380490565675 & 0.11950943432518 \tabularnewline
52 & 103.3 & 103.271681823027 & 0.0283181769726160 \tabularnewline
53 & 103.2 & 103.252832701814 & -0.0528327018137714 \tabularnewline
54 & 103.1 & 103.152682183585 & -0.0526821835852335 \tabularnewline
55 & 103.2 & 103.056435856401 & 0.143564143598519 \tabularnewline
56 & 103 & 102.872832701814 & 0.127167298186226 \tabularnewline
57 & 103 & 102.847696874850 & 0.152303125149765 \tabularnewline
58 & 103.1 & 102.771832341256 & 0.328167658744069 \tabularnewline
59 & 103.4 & 102.837500480037 & 0.562499519962565 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57985&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]106.1[/C][C]106.488404432123[/C][C]-0.388404432122857[/C][/ROW]
[ROW][C]2[/C][C]106[/C][C]106.359283656982[/C][C]-0.359283656982363[/C][/ROW]
[ROW][C]3[/C][C]105.9[/C][C]106.189781088252[/C][C]-0.289781088252242[/C][/ROW]
[ROW][C]4[/C][C]105.8[/C][C]106.039590191458[/C][C]-0.239590191457530[/C][/ROW]
[ROW][C]5[/C][C]105.7[/C][C]105.956368830459[/C][C]-0.256368830459257[/C][/ROW]
[ROW][C]6[/C][C]105.6[/C][C]105.825564864714[/C][C]-0.225564864714213[/C][/ROW]
[ROW][C]7[/C][C]105.4[/C][C]105.732383882282[/C][C]-0.33238388228211[/C][/ROW]
[ROW][C]8[/C][C]105.4[/C][C]105.591695554218[/C][C]-0.191695554217505[/C][/ROW]
[ROW][C]9[/C][C]105.5[/C][C]105.617137915656[/C][C]-0.117137915656208[/C][/ROW]
[ROW][C]10[/C][C]105.6[/C][C]105.545871399189[/C][C]0.0541286008106235[/C][/ROW]
[ROW][C]11[/C][C]105.7[/C][C]105.613072210347[/C][C]0.0869277896532885[/C][/ROW]
[ROW][C]12[/C][C]105.9[/C][C]105.629922544450[/C][C]0.270077455550484[/C][/ROW]
[ROW][C]13[/C][C]106.1[/C][C]105.747764992083[/C][C]0.352235007916891[/C][/ROW]
[ROW][C]14[/C][C]106[/C][C]105.618644216942[/C][C]0.381355783057624[/C][/ROW]
[ROW][C]15[/C][C]105.8[/C][C]105.424618890199[/C][C]0.375381109800943[/C][/ROW]
[ROW][C]16[/C][C]105.8[/C][C]105.236111184009[/C][C]0.563888815991294[/C][/ROW]
[ROW][C]17[/C][C]105.7[/C][C]105.215729390419[/C][C]0.484270609580731[/C][/ROW]
[ROW][C]18[/C][C]105.5[/C][C]105.084925424674[/C][C]0.41507457532578[/C][/ROW]
[ROW][C]19[/C][C]105.3[/C][C]105.016267200255[/C][C]0.283732799744666[/C][/ROW]
[ROW][C]20[/C][C]105.2[/C][C]104.886307578822[/C][C]0.313692421178498[/C][/ROW]
[ROW][C]21[/C][C]105.2[/C][C]104.887227182247[/C][C]0.312772817753007[/C][/ROW]
[ROW][C]22[/C][C]105[/C][C]104.829754717163[/C][C]0.170245282837413[/C][/ROW]
[ROW][C]23[/C][C]105.1[/C][C]104.958262423353[/C][C]0.141737576647053[/C][/ROW]
[ROW][C]24[/C][C]105.1[/C][C]104.935263275684[/C][C]0.164736724315702[/C][/ROW]
[ROW][C]25[/C][C]105.2[/C][C]105.005592879667[/C][C]0.194407120332713[/C][/ROW]
[ROW][C]26[/C][C]104.9[/C][C]104.876472104527[/C][C]0.0235278954734443[/C][/ROW]
[ROW][C]27[/C][C]104.8[/C][C]104.731492293810[/C][C]0.0685077061903472[/C][/ROW]
[ROW][C]28[/C][C]104.5[/C][C]104.549115277123[/C][C]-0.0491152771225977[/C][/ROW]
[ROW][C]29[/C][C]104.5[/C][C]104.525668138782[/C][C]-0.0256681387815173[/C][/ROW]
[ROW][C]30[/C][C]104.4[/C][C]104.388733483533[/C][C]0.0112665164668423[/C][/ROW]
[ROW][C]31[/C][C]104.4[/C][C]104.346130689503[/C][C]0.0538693104967011[/C][/ROW]
[ROW][C]32[/C][C]104.2[/C][C]104.156396845412[/C][C]0.0436031545877104[/C][/ROW]
[ROW][C]33[/C][C]104.1[/C][C]104.129728346073[/C][C]-0.0297283460729360[/C][/ROW]
[ROW][C]34[/C][C]103.9[/C][C]104.118236052263[/C][C]-0.218236052263273[/C][/ROW]
[ROW][C]35[/C][C]103.8[/C][C]104.254407120333[/C][C]-0.454407120332761[/C][/ROW]
[ROW][C]36[/C][C]103.9[/C][C]104.159372371000[/C][C]-0.259372371000317[/C][/ROW]
[ROW][C]37[/C][C]104.2[/C][C]104.254224732997[/C][C]-0.054224732996521[/C][/ROW]
[ROW][C]38[/C][C]104.1[/C][C]104.203270249023[/C][C]-0.10327024902289[/C][/ROW]
[ROW][C]39[/C][C]103.8[/C][C]104.073617162064[/C][C]-0.273617162064228[/C][/ROW]
[ROW][C]40[/C][C]103.6[/C][C]103.903501524384[/C][C]-0.303501524383782[/C][/ROW]
[ROW][C]41[/C][C]103.7[/C][C]103.849400938526[/C][C]-0.149400938526185[/C][/ROW]
[ROW][C]42[/C][C]103.5[/C][C]103.648094043493[/C][C]-0.148094043493175[/C][/ROW]
[ROW][C]43[/C][C]103.4[/C][C]103.548782371558[/C][C]-0.148782371557775[/C][/ROW]
[ROW][C]44[/C][C]103.1[/C][C]103.392767319735[/C][C]-0.292767319734931[/C][/ROW]
[ROW][C]45[/C][C]103.1[/C][C]103.418209681174[/C][C]-0.318209681173628[/C][/ROW]
[ROW][C]46[/C][C]103.1[/C][C]103.434305490129[/C][C]-0.334305490128832[/C][/ROW]
[ROW][C]47[/C][C]103.2[/C][C]103.536757765930[/C][C]-0.336757765930146[/C][/ROW]
[ROW][C]48[/C][C]103.3[/C][C]103.475441808866[/C][C]-0.175441808865870[/C][/ROW]
[ROW][C]49[/C][C]103.5[/C][C]103.604012963130[/C][C]-0.104012963130227[/C][/ROW]
[ROW][C]50[/C][C]103.6[/C][C]103.542329772526[/C][C]0.0576702274741849[/C][/ROW]
[ROW][C]51[/C][C]103.5[/C][C]103.380490565675[/C][C]0.11950943432518[/C][/ROW]
[ROW][C]52[/C][C]103.3[/C][C]103.271681823027[/C][C]0.0283181769726160[/C][/ROW]
[ROW][C]53[/C][C]103.2[/C][C]103.252832701814[/C][C]-0.0528327018137714[/C][/ROW]
[ROW][C]54[/C][C]103.1[/C][C]103.152682183585[/C][C]-0.0526821835852335[/C][/ROW]
[ROW][C]55[/C][C]103.2[/C][C]103.056435856401[/C][C]0.143564143598519[/C][/ROW]
[ROW][C]56[/C][C]103[/C][C]102.872832701814[/C][C]0.127167298186226[/C][/ROW]
[ROW][C]57[/C][C]103[/C][C]102.847696874850[/C][C]0.152303125149765[/C][/ROW]
[ROW][C]58[/C][C]103.1[/C][C]102.771832341256[/C][C]0.328167658744069[/C][/ROW]
[ROW][C]59[/C][C]103.4[/C][C]102.837500480037[/C][C]0.562499519962565[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57985&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57985&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
1106.1106.488404432123-0.388404432122857
2106106.359283656982-0.359283656982363
3105.9106.189781088252-0.289781088252242
4105.8106.039590191458-0.239590191457530
5105.7105.956368830459-0.256368830459257
6105.6105.825564864714-0.225564864714213
7105.4105.732383882282-0.33238388228211
8105.4105.591695554218-0.191695554217505
9105.5105.617137915656-0.117137915656208
10105.6105.5458713991890.0541286008106235
11105.7105.6130722103470.0869277896532885
12105.9105.6299225444500.270077455550484
13106.1105.7477649920830.352235007916891
14106105.6186442169420.381355783057624
15105.8105.4246188901990.375381109800943
16105.8105.2361111840090.563888815991294
17105.7105.2157293904190.484270609580731
18105.5105.0849254246740.41507457532578
19105.3105.0162672002550.283732799744666
20105.2104.8863075788220.313692421178498
21105.2104.8872271822470.312772817753007
22105104.8297547171630.170245282837413
23105.1104.9582624233530.141737576647053
24105.1104.9352632756840.164736724315702
25105.2105.0055928796670.194407120332713
26104.9104.8764721045270.0235278954734443
27104.8104.7314922938100.0685077061903472
28104.5104.549115277123-0.0491152771225977
29104.5104.525668138782-0.0256681387815173
30104.4104.3887334835330.0112665164668423
31104.4104.3461306895030.0538693104967011
32104.2104.1563968454120.0436031545877104
33104.1104.129728346073-0.0297283460729360
34103.9104.118236052263-0.218236052263273
35103.8104.254407120333-0.454407120332761
36103.9104.159372371000-0.259372371000317
37104.2104.254224732997-0.054224732996521
38104.1104.203270249023-0.10327024902289
39103.8104.073617162064-0.273617162064228
40103.6103.903501524384-0.303501524383782
41103.7103.849400938526-0.149400938526185
42103.5103.648094043493-0.148094043493175
43103.4103.548782371558-0.148782371557775
44103.1103.392767319735-0.292767319734931
45103.1103.418209681174-0.318209681173628
46103.1103.434305490129-0.334305490128832
47103.2103.536757765930-0.336757765930146
48103.3103.475441808866-0.175441808865870
49103.5103.604012963130-0.104012963130227
50103.6103.5423297725260.0576702274741849
51103.5103.3804905656750.11950943432518
52103.3103.2716818230270.0283181769726160
53103.2103.252832701814-0.0528327018137714
54103.1103.152682183585-0.0526821835852335
55103.2103.0564358564010.143564143598519
56103102.8728327018140.127167298186226
57103102.8476968748500.152303125149765
58103.1102.7718323412560.328167658744069
59103.4102.8375004800370.562499519962565






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.004758269360445020.009516538720890040.995241730639555
180.001893858545558430.003787717091116860.998106141454442
190.0004261113270407180.0008522226540814360.99957388867296
200.0003125930415011810.0006251860830023610.999687406958499
210.001357324265944030.002714648531888060.998642675734056
220.03031725935549050.0606345187109810.96968274064451
230.01779261538061010.03558523076122010.98220738461939
240.05853376922934720.1170675384586940.941466230770653
250.2871854525894960.5743709051789910.712814547410505
260.5406677243480180.9186645513039640.459332275651982
270.5644975456631840.8710049086736310.435502454336816
280.691424960120810.6171500797583790.308575039879190
290.6774482178049850.6451035643900290.322551782195015
300.6751011360586090.6497977278827830.324898863941392
310.6603805551720010.6792388896559980.339619444827999
320.7421458604733450.515708279053310.257854139526655
330.8873186664888980.2253626670222040.112681333511102
340.906934311417040.186131377165920.09306568858296
350.874528897051970.2509422058960580.125471102948029
360.9257428919210380.1485142161579240.0742571080789618
370.9635572144356860.0728855711286280.036442785564314
380.9672718211134230.06545635777315490.0327281788865775
390.955987160928450.08802567814310090.0440128390715504
400.9353366055836560.1293267888326880.0646633944163438
410.9910214550073080.01795708998538310.00897854499269157
420.9935780917273470.01284381654530640.00642190827265319

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.00475826936044502 & 0.00951653872089004 & 0.995241730639555 \tabularnewline
18 & 0.00189385854555843 & 0.00378771709111686 & 0.998106141454442 \tabularnewline
19 & 0.000426111327040718 & 0.000852222654081436 & 0.99957388867296 \tabularnewline
20 & 0.000312593041501181 & 0.000625186083002361 & 0.999687406958499 \tabularnewline
21 & 0.00135732426594403 & 0.00271464853188806 & 0.998642675734056 \tabularnewline
22 & 0.0303172593554905 & 0.060634518710981 & 0.96968274064451 \tabularnewline
23 & 0.0177926153806101 & 0.0355852307612201 & 0.98220738461939 \tabularnewline
24 & 0.0585337692293472 & 0.117067538458694 & 0.941466230770653 \tabularnewline
25 & 0.287185452589496 & 0.574370905178991 & 0.712814547410505 \tabularnewline
26 & 0.540667724348018 & 0.918664551303964 & 0.459332275651982 \tabularnewline
27 & 0.564497545663184 & 0.871004908673631 & 0.435502454336816 \tabularnewline
28 & 0.69142496012081 & 0.617150079758379 & 0.308575039879190 \tabularnewline
29 & 0.677448217804985 & 0.645103564390029 & 0.322551782195015 \tabularnewline
30 & 0.675101136058609 & 0.649797727882783 & 0.324898863941392 \tabularnewline
31 & 0.660380555172001 & 0.679238889655998 & 0.339619444827999 \tabularnewline
32 & 0.742145860473345 & 0.51570827905331 & 0.257854139526655 \tabularnewline
33 & 0.887318666488898 & 0.225362667022204 & 0.112681333511102 \tabularnewline
34 & 0.90693431141704 & 0.18613137716592 & 0.09306568858296 \tabularnewline
35 & 0.87452889705197 & 0.250942205896058 & 0.125471102948029 \tabularnewline
36 & 0.925742891921038 & 0.148514216157924 & 0.0742571080789618 \tabularnewline
37 & 0.963557214435686 & 0.072885571128628 & 0.036442785564314 \tabularnewline
38 & 0.967271821113423 & 0.0654563577731549 & 0.0327281788865775 \tabularnewline
39 & 0.95598716092845 & 0.0880256781431009 & 0.0440128390715504 \tabularnewline
40 & 0.935336605583656 & 0.129326788832688 & 0.0646633944163438 \tabularnewline
41 & 0.991021455007308 & 0.0179570899853831 & 0.00897854499269157 \tabularnewline
42 & 0.993578091727347 & 0.0128438165453064 & 0.00642190827265319 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57985&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]17[/C][C]0.00475826936044502[/C][C]0.00951653872089004[/C][C]0.995241730639555[/C][/ROW]
[ROW][C]18[/C][C]0.00189385854555843[/C][C]0.00378771709111686[/C][C]0.998106141454442[/C][/ROW]
[ROW][C]19[/C][C]0.000426111327040718[/C][C]0.000852222654081436[/C][C]0.99957388867296[/C][/ROW]
[ROW][C]20[/C][C]0.000312593041501181[/C][C]0.000625186083002361[/C][C]0.999687406958499[/C][/ROW]
[ROW][C]21[/C][C]0.00135732426594403[/C][C]0.00271464853188806[/C][C]0.998642675734056[/C][/ROW]
[ROW][C]22[/C][C]0.0303172593554905[/C][C]0.060634518710981[/C][C]0.96968274064451[/C][/ROW]
[ROW][C]23[/C][C]0.0177926153806101[/C][C]0.0355852307612201[/C][C]0.98220738461939[/C][/ROW]
[ROW][C]24[/C][C]0.0585337692293472[/C][C]0.117067538458694[/C][C]0.941466230770653[/C][/ROW]
[ROW][C]25[/C][C]0.287185452589496[/C][C]0.574370905178991[/C][C]0.712814547410505[/C][/ROW]
[ROW][C]26[/C][C]0.540667724348018[/C][C]0.918664551303964[/C][C]0.459332275651982[/C][/ROW]
[ROW][C]27[/C][C]0.564497545663184[/C][C]0.871004908673631[/C][C]0.435502454336816[/C][/ROW]
[ROW][C]28[/C][C]0.69142496012081[/C][C]0.617150079758379[/C][C]0.308575039879190[/C][/ROW]
[ROW][C]29[/C][C]0.677448217804985[/C][C]0.645103564390029[/C][C]0.322551782195015[/C][/ROW]
[ROW][C]30[/C][C]0.675101136058609[/C][C]0.649797727882783[/C][C]0.324898863941392[/C][/ROW]
[ROW][C]31[/C][C]0.660380555172001[/C][C]0.679238889655998[/C][C]0.339619444827999[/C][/ROW]
[ROW][C]32[/C][C]0.742145860473345[/C][C]0.51570827905331[/C][C]0.257854139526655[/C][/ROW]
[ROW][C]33[/C][C]0.887318666488898[/C][C]0.225362667022204[/C][C]0.112681333511102[/C][/ROW]
[ROW][C]34[/C][C]0.90693431141704[/C][C]0.18613137716592[/C][C]0.09306568858296[/C][/ROW]
[ROW][C]35[/C][C]0.87452889705197[/C][C]0.250942205896058[/C][C]0.125471102948029[/C][/ROW]
[ROW][C]36[/C][C]0.925742891921038[/C][C]0.148514216157924[/C][C]0.0742571080789618[/C][/ROW]
[ROW][C]37[/C][C]0.963557214435686[/C][C]0.072885571128628[/C][C]0.036442785564314[/C][/ROW]
[ROW][C]38[/C][C]0.967271821113423[/C][C]0.0654563577731549[/C][C]0.0327281788865775[/C][/ROW]
[ROW][C]39[/C][C]0.95598716092845[/C][C]0.0880256781431009[/C][C]0.0440128390715504[/C][/ROW]
[ROW][C]40[/C][C]0.935336605583656[/C][C]0.129326788832688[/C][C]0.0646633944163438[/C][/ROW]
[ROW][C]41[/C][C]0.991021455007308[/C][C]0.0179570899853831[/C][C]0.00897854499269157[/C][/ROW]
[ROW][C]42[/C][C]0.993578091727347[/C][C]0.0128438165453064[/C][C]0.00642190827265319[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57985&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57985&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
170.004758269360445020.009516538720890040.995241730639555
180.001893858545558430.003787717091116860.998106141454442
190.0004261113270407180.0008522226540814360.99957388867296
200.0003125930415011810.0006251860830023610.999687406958499
210.001357324265944030.002714648531888060.998642675734056
220.03031725935549050.0606345187109810.96968274064451
230.01779261538061010.03558523076122010.98220738461939
240.05853376922934720.1170675384586940.941466230770653
250.2871854525894960.5743709051789910.712814547410505
260.5406677243480180.9186645513039640.459332275651982
270.5644975456631840.8710049086736310.435502454336816
280.691424960120810.6171500797583790.308575039879190
290.6774482178049850.6451035643900290.322551782195015
300.6751011360586090.6497977278827830.324898863941392
310.6603805551720010.6792388896559980.339619444827999
320.7421458604733450.515708279053310.257854139526655
330.8873186664888980.2253626670222040.112681333511102
340.906934311417040.186131377165920.09306568858296
350.874528897051970.2509422058960580.125471102948029
360.9257428919210380.1485142161579240.0742571080789618
370.9635572144356860.0728855711286280.036442785564314
380.9672718211134230.06545635777315490.0327281788865775
390.955987160928450.08802567814310090.0440128390715504
400.9353366055836560.1293267888326880.0646633944163438
410.9910214550073080.01795708998538310.00897854499269157
420.9935780917273470.01284381654530640.00642190827265319






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level50.192307692307692NOK
5% type I error level80.307692307692308NOK
10% type I error level120.461538461538462NOK

\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 & 5 & 0.192307692307692 & NOK \tabularnewline
5% type I error level & 8 & 0.307692307692308 & NOK \tabularnewline
10% type I error level & 12 & 0.461538461538462 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57985&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]5[/C][C]0.192307692307692[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]8[/C][C]0.307692307692308[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]12[/C][C]0.461538461538462[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57985&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57985&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 level50.192307692307692NOK
5% type I error level80.307692307692308NOK
10% type I error level120.461538461538462NOK


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

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