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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Thu, 19 Nov 2009 14:38:11 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/19/t1258666753evqowb8r8vkajna.htm/, Retrieved Fri, 09 May 2025 10:06:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57965, Retrieved Fri, 09 May 2025 10:06:07 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

344

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] [87085ce7f5378f281469a8b1f0969170] [Current]
-   P           [Multiple Regression] [monthly dummies] [2009-11-19 22:00:07] [ed603017d2bee8fbd82b6d5ec04e12c3] 
-   P             [Multiple Regression] [model3] [2009-11-20 08:47:44] [ed603017d2bee8fbd82b6d5ec04e12c3] 
-    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] 
-    D            [Multiple Regression] [W7: Monthly Dummies] [2009-11-21 14:07:55] [03d5b865e91ca35b5a5d21b8d6da5aba] 
-    D            [Multiple Regression] [WS7] [2009-11-21 15:04:45] [9f35ad889e41dd0c9322ca60d75b9f47] 
-    D          [Multiple Regression] [WS7] [2009-11-20 22:38:21] [9f35ad889e41dd0c9322ca60d75b9f47] 
-    D          [Multiple Regression] [W7: Multiple regr...] [2009-11-21 13:40:01] [03d5b865e91ca35b5a5d21b8d6da5aba] 
-    D          [Multiple Regression] [model 1 multiple ...] [2009-12-06 11:43:28] [ed603017d2bee8fbd82b6d5ec04e12c3] 
-   PD          [Multiple Regression] [multiple regressi...] [2009-12-06 12:47:31] [ed603017d2bee8fbd82b6d5ec04e12c3] 
-   PD            [Multiple Regression] [multiple regressi...] [2009-12-08 20:02:18] [ed603017d2bee8fbd82b6d5ec04e12c3] 
-   PD          [Multiple Regression] [multiple regressi...] [2009-12-06 13:06:41] [ed603017d2bee8fbd82b6d5ec04e12c3] 

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Dataseries X:

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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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57965&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57965&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57965&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Werkl[t] = + 143.751260601764 -0.385392472173445Infl[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Werkl[t] =  +  143.751260601764 -0.385392472173445Infl[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57965&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Werkl[t] =  +  143.751260601764 -0.385392472173445Infl[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57965&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57965&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
Werkl[t] = + 143.751260601764 -0.385392472173445Infl[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	143.751260601764	2.15361	66.749	0	0
Infl	-0.385392472173445	0.021134	-18.2352	0	0

\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) & 143.751260601764 & 2.15361 & 66.749 & 0 & 0 \tabularnewline
Infl & -0.385392472173445 & 0.021134 & -18.2352 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57965&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]143.751260601764[/C][C]2.15361[/C][C]66.749[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Infl[/C][C]-0.385392472173445[/C][C]0.021134[/C][C]-18.2352[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57965&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57965&T=2

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	143.751260601764	2.15361	66.749	0	0
Infl	-0.385392472173445	0.021134	-18.2352	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.923941333344126
R-squared	0.853667587461722
Adjusted R-squared	0.851100352154033
F-TEST (value)	332.524091151642
F-TEST (DF numerator)	1
F-TEST (DF denominator)	57
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.406752304805825
Sum Squared Residuals	9.43050393549652

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.923941333344126 \tabularnewline
R-squared & 0.853667587461722 \tabularnewline
Adjusted R-squared & 0.851100352154033 \tabularnewline
F-TEST (value) & 332.524091151642 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 57 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.406752304805825 \tabularnewline
Sum Squared Residuals & 9.43050393549652 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57965&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.923941333344126[/C][/ROW]
[ROW][C]R-squared[/C][C]0.853667587461722[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.851100352154033[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]332.524091151642[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]57[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.406752304805825[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]9.43050393549652[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57965&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57965&T=3

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Regression Statistics
Multiple R	0.923941333344126
R-squared	0.853667587461722
Adjusted R-squared	0.851100352154033
F-TEST (value)	332.524091151642
F-TEST (DF numerator)	1
F-TEST (DF denominator)	57
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.406752304805825
Sum Squared Residuals	9.43050393549652

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	106.1	106.025191500705	0.0748084992951664
2	106	105.716877522966	0.283122477033612
3	105.9	105.593551931871	0.306448068129123
4	105.8	105.528035211601	0.271964788398600
5	105.7	105.809371716288	-0.109371716288011
6	105.6	105.932697307384	-0.332697307383524
7	105.4	105.871034511836	-0.471034511835758
8	105.4	105.558866609375	-0.158866609375272
9	105.5	105.497203813828	0.00279618617247816
10	105.6	105.655214727419	-0.0552147274186441
11	105.7	105.963528705157	-0.263528705157391
12	105.9	105.778540318514	0.121459681485867
13	106.1	105.466372416054	0.633627583946348
14	106	105.158058438315	0.841941561685108
15	105.8	105.096395642767	0.703604357232855
16	105.8	105.127227040541	0.67277295945898
17	105.7	105.250552631637	0.449447368363486
18	105.5	105.373878222732	0.126121777267978
19	105.3	105.250552631637	0.0494473683634804
20	105.2	104.911407256124	0.288592743876116
21	105.2	104.911407256124	0.288592743876116
22	105	105.034732847219	-0.034732847219392
23	105.1	105.188889836089	-0.0888898360887725
24	105.1	105.104103492211	-0.00410349221061495
25	105.2	104.911407256124	0.288592743876116
26	104.9	104.603093278385	0.296906721614874
27	104.8	104.418104891742	0.381895108258121
28	104.5	104.433520590629	0.0664794093711834
29	104.5	104.564554031168	-0.0645540311677838
30	104.4	104.703295321150	-0.303295321150224
31	104.4	104.514453009785	-0.114453009785232
32	104.2	104.325610698420	-0.125610698420249
33	104.1	104.394981343411	-0.294981343411474
34	103.9	104.402689192855	-0.502689192854936
35	103.8	104.537576558116	-0.737576558115648
36	103.9	104.633924676159	-0.733924676159
37	104.2	104.379565644525	-0.179565644524531
38	104.1	103.874701505977	0.225298494022674
39	103.8	103.651173872117	0.148826127883275
40	103.6	103.635758173230	-0.0357581732297879
41	103.7	103.843870108203	-0.143870108203442
42	103.5	104.144476236499	-0.644476236498733
43	103.4	104.098229139838	-0.698229139837912
44	103.1	103.824600484595	-0.72460048459478
45	103.1	103.762937689047	-0.662937689047024
46	103.1	103.701274893499	-0.601274893499274
47	103.2	103.920948602638	-0.720948602638132
48	103.3	103.932510376803	-0.632510376803342
49	103.5	103.593365001291	-0.0933650012907036
50	103.6	103.115478335796	0.484521664204361
51	103.5	102.972883121091	0.527116878908543
52	103.3	102.803310433335	0.496689566664855
53	103.2	102.922782099709	0.277217900291092
54	103.1	102.969029196370	0.130970803630268
55	103.2	102.915074250265	0.284925749734560
56	103	102.710816240014	0.289183759986483
57	103	102.776332960283	0.223667039716997
58	103.1	102.945905648039	0.154094351960676
59	103.4	103.258073550500	0.141926449500196

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 106.1 & 106.025191500705 & 0.0748084992951664 \tabularnewline
2 & 106 & 105.716877522966 & 0.283122477033612 \tabularnewline
3 & 105.9 & 105.593551931871 & 0.306448068129123 \tabularnewline
4 & 105.8 & 105.528035211601 & 0.271964788398600 \tabularnewline
5 & 105.7 & 105.809371716288 & -0.109371716288011 \tabularnewline
6 & 105.6 & 105.932697307384 & -0.332697307383524 \tabularnewline
7 & 105.4 & 105.871034511836 & -0.471034511835758 \tabularnewline
8 & 105.4 & 105.558866609375 & -0.158866609375272 \tabularnewline
9 & 105.5 & 105.497203813828 & 0.00279618617247816 \tabularnewline
10 & 105.6 & 105.655214727419 & -0.0552147274186441 \tabularnewline
11 & 105.7 & 105.963528705157 & -0.263528705157391 \tabularnewline
12 & 105.9 & 105.778540318514 & 0.121459681485867 \tabularnewline
13 & 106.1 & 105.466372416054 & 0.633627583946348 \tabularnewline
14 & 106 & 105.158058438315 & 0.841941561685108 \tabularnewline
15 & 105.8 & 105.096395642767 & 0.703604357232855 \tabularnewline
16 & 105.8 & 105.127227040541 & 0.67277295945898 \tabularnewline
17 & 105.7 & 105.250552631637 & 0.449447368363486 \tabularnewline
18 & 105.5 & 105.373878222732 & 0.126121777267978 \tabularnewline
19 & 105.3 & 105.250552631637 & 0.0494473683634804 \tabularnewline
20 & 105.2 & 104.911407256124 & 0.288592743876116 \tabularnewline
21 & 105.2 & 104.911407256124 & 0.288592743876116 \tabularnewline
22 & 105 & 105.034732847219 & -0.034732847219392 \tabularnewline
23 & 105.1 & 105.188889836089 & -0.0888898360887725 \tabularnewline
24 & 105.1 & 105.104103492211 & -0.00410349221061495 \tabularnewline
25 & 105.2 & 104.911407256124 & 0.288592743876116 \tabularnewline
26 & 104.9 & 104.603093278385 & 0.296906721614874 \tabularnewline
27 & 104.8 & 104.418104891742 & 0.381895108258121 \tabularnewline
28 & 104.5 & 104.433520590629 & 0.0664794093711834 \tabularnewline
29 & 104.5 & 104.564554031168 & -0.0645540311677838 \tabularnewline
30 & 104.4 & 104.703295321150 & -0.303295321150224 \tabularnewline
31 & 104.4 & 104.514453009785 & -0.114453009785232 \tabularnewline
32 & 104.2 & 104.325610698420 & -0.125610698420249 \tabularnewline
33 & 104.1 & 104.394981343411 & -0.294981343411474 \tabularnewline
34 & 103.9 & 104.402689192855 & -0.502689192854936 \tabularnewline
35 & 103.8 & 104.537576558116 & -0.737576558115648 \tabularnewline
36 & 103.9 & 104.633924676159 & -0.733924676159 \tabularnewline
37 & 104.2 & 104.379565644525 & -0.179565644524531 \tabularnewline
38 & 104.1 & 103.874701505977 & 0.225298494022674 \tabularnewline
39 & 103.8 & 103.651173872117 & 0.148826127883275 \tabularnewline
40 & 103.6 & 103.635758173230 & -0.0357581732297879 \tabularnewline
41 & 103.7 & 103.843870108203 & -0.143870108203442 \tabularnewline
42 & 103.5 & 104.144476236499 & -0.644476236498733 \tabularnewline
43 & 103.4 & 104.098229139838 & -0.698229139837912 \tabularnewline
44 & 103.1 & 103.824600484595 & -0.72460048459478 \tabularnewline
45 & 103.1 & 103.762937689047 & -0.662937689047024 \tabularnewline
46 & 103.1 & 103.701274893499 & -0.601274893499274 \tabularnewline
47 & 103.2 & 103.920948602638 & -0.720948602638132 \tabularnewline
48 & 103.3 & 103.932510376803 & -0.632510376803342 \tabularnewline
49 & 103.5 & 103.593365001291 & -0.0933650012907036 \tabularnewline
50 & 103.6 & 103.115478335796 & 0.484521664204361 \tabularnewline
51 & 103.5 & 102.972883121091 & 0.527116878908543 \tabularnewline
52 & 103.3 & 102.803310433335 & 0.496689566664855 \tabularnewline
53 & 103.2 & 102.922782099709 & 0.277217900291092 \tabularnewline
54 & 103.1 & 102.969029196370 & 0.130970803630268 \tabularnewline
55 & 103.2 & 102.915074250265 & 0.284925749734560 \tabularnewline
56 & 103 & 102.710816240014 & 0.289183759986483 \tabularnewline
57 & 103 & 102.776332960283 & 0.223667039716997 \tabularnewline
58 & 103.1 & 102.945905648039 & 0.154094351960676 \tabularnewline
59 & 103.4 & 103.258073550500 & 0.141926449500196 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57965&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]106.025191500705[/C][C]0.0748084992951664[/C][/ROW]
[ROW][C]2[/C][C]106[/C][C]105.716877522966[/C][C]0.283122477033612[/C][/ROW]
[ROW][C]3[/C][C]105.9[/C][C]105.593551931871[/C][C]0.306448068129123[/C][/ROW]
[ROW][C]4[/C][C]105.8[/C][C]105.528035211601[/C][C]0.271964788398600[/C][/ROW]
[ROW][C]5[/C][C]105.7[/C][C]105.809371716288[/C][C]-0.109371716288011[/C][/ROW]
[ROW][C]6[/C][C]105.6[/C][C]105.932697307384[/C][C]-0.332697307383524[/C][/ROW]
[ROW][C]7[/C][C]105.4[/C][C]105.871034511836[/C][C]-0.471034511835758[/C][/ROW]
[ROW][C]8[/C][C]105.4[/C][C]105.558866609375[/C][C]-0.158866609375272[/C][/ROW]
[ROW][C]9[/C][C]105.5[/C][C]105.497203813828[/C][C]0.00279618617247816[/C][/ROW]
[ROW][C]10[/C][C]105.6[/C][C]105.655214727419[/C][C]-0.0552147274186441[/C][/ROW]
[ROW][C]11[/C][C]105.7[/C][C]105.963528705157[/C][C]-0.263528705157391[/C][/ROW]
[ROW][C]12[/C][C]105.9[/C][C]105.778540318514[/C][C]0.121459681485867[/C][/ROW]
[ROW][C]13[/C][C]106.1[/C][C]105.466372416054[/C][C]0.633627583946348[/C][/ROW]
[ROW][C]14[/C][C]106[/C][C]105.158058438315[/C][C]0.841941561685108[/C][/ROW]
[ROW][C]15[/C][C]105.8[/C][C]105.096395642767[/C][C]0.703604357232855[/C][/ROW]
[ROW][C]16[/C][C]105.8[/C][C]105.127227040541[/C][C]0.67277295945898[/C][/ROW]
[ROW][C]17[/C][C]105.7[/C][C]105.250552631637[/C][C]0.449447368363486[/C][/ROW]
[ROW][C]18[/C][C]105.5[/C][C]105.373878222732[/C][C]0.126121777267978[/C][/ROW]
[ROW][C]19[/C][C]105.3[/C][C]105.250552631637[/C][C]0.0494473683634804[/C][/ROW]
[ROW][C]20[/C][C]105.2[/C][C]104.911407256124[/C][C]0.288592743876116[/C][/ROW]
[ROW][C]21[/C][C]105.2[/C][C]104.911407256124[/C][C]0.288592743876116[/C][/ROW]
[ROW][C]22[/C][C]105[/C][C]105.034732847219[/C][C]-0.034732847219392[/C][/ROW]
[ROW][C]23[/C][C]105.1[/C][C]105.188889836089[/C][C]-0.0888898360887725[/C][/ROW]
[ROW][C]24[/C][C]105.1[/C][C]105.104103492211[/C][C]-0.00410349221061495[/C][/ROW]
[ROW][C]25[/C][C]105.2[/C][C]104.911407256124[/C][C]0.288592743876116[/C][/ROW]
[ROW][C]26[/C][C]104.9[/C][C]104.603093278385[/C][C]0.296906721614874[/C][/ROW]
[ROW][C]27[/C][C]104.8[/C][C]104.418104891742[/C][C]0.381895108258121[/C][/ROW]
[ROW][C]28[/C][C]104.5[/C][C]104.433520590629[/C][C]0.0664794093711834[/C][/ROW]
[ROW][C]29[/C][C]104.5[/C][C]104.564554031168[/C][C]-0.0645540311677838[/C][/ROW]
[ROW][C]30[/C][C]104.4[/C][C]104.703295321150[/C][C]-0.303295321150224[/C][/ROW]
[ROW][C]31[/C][C]104.4[/C][C]104.514453009785[/C][C]-0.114453009785232[/C][/ROW]
[ROW][C]32[/C][C]104.2[/C][C]104.325610698420[/C][C]-0.125610698420249[/C][/ROW]
[ROW][C]33[/C][C]104.1[/C][C]104.394981343411[/C][C]-0.294981343411474[/C][/ROW]
[ROW][C]34[/C][C]103.9[/C][C]104.402689192855[/C][C]-0.502689192854936[/C][/ROW]
[ROW][C]35[/C][C]103.8[/C][C]104.537576558116[/C][C]-0.737576558115648[/C][/ROW]
[ROW][C]36[/C][C]103.9[/C][C]104.633924676159[/C][C]-0.733924676159[/C][/ROW]
[ROW][C]37[/C][C]104.2[/C][C]104.379565644525[/C][C]-0.179565644524531[/C][/ROW]
[ROW][C]38[/C][C]104.1[/C][C]103.874701505977[/C][C]0.225298494022674[/C][/ROW]
[ROW][C]39[/C][C]103.8[/C][C]103.651173872117[/C][C]0.148826127883275[/C][/ROW]
[ROW][C]40[/C][C]103.6[/C][C]103.635758173230[/C][C]-0.0357581732297879[/C][/ROW]
[ROW][C]41[/C][C]103.7[/C][C]103.843870108203[/C][C]-0.143870108203442[/C][/ROW]
[ROW][C]42[/C][C]103.5[/C][C]104.144476236499[/C][C]-0.644476236498733[/C][/ROW]
[ROW][C]43[/C][C]103.4[/C][C]104.098229139838[/C][C]-0.698229139837912[/C][/ROW]
[ROW][C]44[/C][C]103.1[/C][C]103.824600484595[/C][C]-0.72460048459478[/C][/ROW]
[ROW][C]45[/C][C]103.1[/C][C]103.762937689047[/C][C]-0.662937689047024[/C][/ROW]
[ROW][C]46[/C][C]103.1[/C][C]103.701274893499[/C][C]-0.601274893499274[/C][/ROW]
[ROW][C]47[/C][C]103.2[/C][C]103.920948602638[/C][C]-0.720948602638132[/C][/ROW]
[ROW][C]48[/C][C]103.3[/C][C]103.932510376803[/C][C]-0.632510376803342[/C][/ROW]
[ROW][C]49[/C][C]103.5[/C][C]103.593365001291[/C][C]-0.0933650012907036[/C][/ROW]
[ROW][C]50[/C][C]103.6[/C][C]103.115478335796[/C][C]0.484521664204361[/C][/ROW]
[ROW][C]51[/C][C]103.5[/C][C]102.972883121091[/C][C]0.527116878908543[/C][/ROW]
[ROW][C]52[/C][C]103.3[/C][C]102.803310433335[/C][C]0.496689566664855[/C][/ROW]
[ROW][C]53[/C][C]103.2[/C][C]102.922782099709[/C][C]0.277217900291092[/C][/ROW]
[ROW][C]54[/C][C]103.1[/C][C]102.969029196370[/C][C]0.130970803630268[/C][/ROW]
[ROW][C]55[/C][C]103.2[/C][C]102.915074250265[/C][C]0.284925749734560[/C][/ROW]
[ROW][C]56[/C][C]103[/C][C]102.710816240014[/C][C]0.289183759986483[/C][/ROW]
[ROW][C]57[/C][C]103[/C][C]102.776332960283[/C][C]0.223667039716997[/C][/ROW]
[ROW][C]58[/C][C]103.1[/C][C]102.945905648039[/C][C]0.154094351960676[/C][/ROW]
[ROW][C]59[/C][C]103.4[/C][C]103.258073550500[/C][C]0.141926449500196[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57965&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57965&T=4

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	106.1	106.025191500705	0.0748084992951664
2	106	105.716877522966	0.283122477033612
3	105.9	105.593551931871	0.306448068129123
4	105.8	105.528035211601	0.271964788398600
5	105.7	105.809371716288	-0.109371716288011
6	105.6	105.932697307384	-0.332697307383524
7	105.4	105.871034511836	-0.471034511835758
8	105.4	105.558866609375	-0.158866609375272
9	105.5	105.497203813828	0.00279618617247816
10	105.6	105.655214727419	-0.0552147274186441
11	105.7	105.963528705157	-0.263528705157391
12	105.9	105.778540318514	0.121459681485867
13	106.1	105.466372416054	0.633627583946348
14	106	105.158058438315	0.841941561685108
15	105.8	105.096395642767	0.703604357232855
16	105.8	105.127227040541	0.67277295945898
17	105.7	105.250552631637	0.449447368363486
18	105.5	105.373878222732	0.126121777267978
19	105.3	105.250552631637	0.0494473683634804
20	105.2	104.911407256124	0.288592743876116
21	105.2	104.911407256124	0.288592743876116
22	105	105.034732847219	-0.034732847219392
23	105.1	105.188889836089	-0.0888898360887725
24	105.1	105.104103492211	-0.00410349221061495
25	105.2	104.911407256124	0.288592743876116
26	104.9	104.603093278385	0.296906721614874
27	104.8	104.418104891742	0.381895108258121
28	104.5	104.433520590629	0.0664794093711834
29	104.5	104.564554031168	-0.0645540311677838
30	104.4	104.703295321150	-0.303295321150224
31	104.4	104.514453009785	-0.114453009785232
32	104.2	104.325610698420	-0.125610698420249
33	104.1	104.394981343411	-0.294981343411474
34	103.9	104.402689192855	-0.502689192854936
35	103.8	104.537576558116	-0.737576558115648
36	103.9	104.633924676159	-0.733924676159
37	104.2	104.379565644525	-0.179565644524531
38	104.1	103.874701505977	0.225298494022674
39	103.8	103.651173872117	0.148826127883275
40	103.6	103.635758173230	-0.0357581732297879
41	103.7	103.843870108203	-0.143870108203442
42	103.5	104.144476236499	-0.644476236498733
43	103.4	104.098229139838	-0.698229139837912
44	103.1	103.824600484595	-0.72460048459478
45	103.1	103.762937689047	-0.662937689047024
46	103.1	103.701274893499	-0.601274893499274
47	103.2	103.920948602638	-0.720948602638132
48	103.3	103.932510376803	-0.632510376803342
49	103.5	103.593365001291	-0.0933650012907036
50	103.6	103.115478335796	0.484521664204361
51	103.5	102.972883121091	0.527116878908543
52	103.3	102.803310433335	0.496689566664855
53	103.2	102.922782099709	0.277217900291092
54	103.1	102.969029196370	0.130970803630268
55	103.2	102.915074250265	0.284925749734560
56	103	102.710816240014	0.289183759986483
57	103	102.776332960283	0.223667039716997
58	103.1	102.945905648039	0.154094351960676
59	103.4	103.258073550500	0.141926449500196

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.0657043912428305	0.131408782485661	0.93429560875717
6	0.0889452644193762	0.177890528838752	0.911054735580624
7	0.146880293943616	0.293760587887231	0.853119706056384
8	0.148187746719477	0.296375493438954	0.851812253280523
9	0.0930978776883454	0.186195755376691	0.906902122311655
10	0.0516104980930191	0.103220996186038	0.94838950190698
11	0.0281123004990112	0.0562246009980225	0.971887699500989
12	0.0171703474984610	0.0343406949969221	0.98282965250154
13	0.0292404902431319	0.0584809804862639	0.970759509756868
14	0.0287512808073009	0.0575025616146019	0.9712487191927
15	0.0225811866843572	0.0451623733687144	0.977418813315643
16	0.0190712956310427	0.0381425912620854	0.980928704368957
17	0.0152832464742233	0.0305664929484466	0.984716753525777
18	0.0149056651691330	0.0298113303382660	0.985094334830867
19	0.0257394261855862	0.0514788523711724	0.974260573814414
20	0.0444340514632611	0.0888681029265221	0.955565948536739
21	0.0573603970954792	0.114720794190958	0.94263960290452
22	0.0898840696953125	0.179768139390625	0.910115930304688
23	0.105568827119153	0.211137654238306	0.894431172880847
24	0.11615861273552	0.23231722547104	0.88384138726448
25	0.144949624674705	0.289899249349410	0.855050375325295
26	0.198840540687441	0.397681081374882	0.801159459312559
27	0.302267900601939	0.604535801203878	0.697732099398061
28	0.403034447267361	0.806068894534723	0.596965552732639
29	0.509027696449989	0.981944607100021	0.490972303550011
30	0.627318536595967	0.745362926808065	0.372681463404033
31	0.713853251737293	0.572293496525414	0.286146748262707
32	0.76748647062328	0.465027058753439	0.232513529376720
33	0.81051409478064	0.378971810438721	0.189485905219361
34	0.843316677384611	0.313366645230777	0.156683322615389
35	0.887095563361121	0.225808873277758	0.112904436638879
36	0.90705627451035	0.185887450979298	0.0929437254896492
37	0.943297341635426	0.113405316729147	0.0567026583645735
38	0.987305741602801	0.0253885167943971	0.0126942583971985
39	0.994011958559478	0.0119760828810436	0.00598804144052182
40	0.993655045565876	0.0126899088682481	0.00634495443412403
41	0.996477870532076	0.0070442589358482	0.0035221294679241
42	0.99655303222439	0.00689393555122	0.00344696777561
43	0.995721062587448	0.00855787482510414	0.00427893741255207
44	0.994720803254726	0.0105583934905484	0.00527919674527419
45	0.993357916272452	0.0132841674550970	0.00664208372754852
46	0.992279352634354	0.0154412947312926	0.0077206473656463
47	0.99204320675749	0.0159135864850223	0.00795679324251115
48	0.99552753917083	0.00894492165834016	0.00447246082917008
49	0.993550561497449	0.0128988770051021	0.00644943850255107
50	0.995299009159069	0.00940198168186223	0.00470099084093112
51	0.998682338430718	0.00263532313856470	0.00131766156928235
52	0.999814899465275	0.000370201069450011	0.000185100534725006
53	0.999235784661285	0.00152843067742943	0.000764215338714716
54	0.996915276331129	0.00616944733774284	0.00308472366887142

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
5 & 0.0657043912428305 & 0.131408782485661 & 0.93429560875717 \tabularnewline
6 & 0.0889452644193762 & 0.177890528838752 & 0.911054735580624 \tabularnewline
7 & 0.146880293943616 & 0.293760587887231 & 0.853119706056384 \tabularnewline
8 & 0.148187746719477 & 0.296375493438954 & 0.851812253280523 \tabularnewline
9 & 0.0930978776883454 & 0.186195755376691 & 0.906902122311655 \tabularnewline
10 & 0.0516104980930191 & 0.103220996186038 & 0.94838950190698 \tabularnewline
11 & 0.0281123004990112 & 0.0562246009980225 & 0.971887699500989 \tabularnewline
12 & 0.0171703474984610 & 0.0343406949969221 & 0.98282965250154 \tabularnewline
13 & 0.0292404902431319 & 0.0584809804862639 & 0.970759509756868 \tabularnewline
14 & 0.0287512808073009 & 0.0575025616146019 & 0.9712487191927 \tabularnewline
15 & 0.0225811866843572 & 0.0451623733687144 & 0.977418813315643 \tabularnewline
16 & 0.0190712956310427 & 0.0381425912620854 & 0.980928704368957 \tabularnewline
17 & 0.0152832464742233 & 0.0305664929484466 & 0.984716753525777 \tabularnewline
18 & 0.0149056651691330 & 0.0298113303382660 & 0.985094334830867 \tabularnewline
19 & 0.0257394261855862 & 0.0514788523711724 & 0.974260573814414 \tabularnewline
20 & 0.0444340514632611 & 0.0888681029265221 & 0.955565948536739 \tabularnewline
21 & 0.0573603970954792 & 0.114720794190958 & 0.94263960290452 \tabularnewline
22 & 0.0898840696953125 & 0.179768139390625 & 0.910115930304688 \tabularnewline
23 & 0.105568827119153 & 0.211137654238306 & 0.894431172880847 \tabularnewline
24 & 0.11615861273552 & 0.23231722547104 & 0.88384138726448 \tabularnewline
25 & 0.144949624674705 & 0.289899249349410 & 0.855050375325295 \tabularnewline
26 & 0.198840540687441 & 0.397681081374882 & 0.801159459312559 \tabularnewline
27 & 0.302267900601939 & 0.604535801203878 & 0.697732099398061 \tabularnewline
28 & 0.403034447267361 & 0.806068894534723 & 0.596965552732639 \tabularnewline
29 & 0.509027696449989 & 0.981944607100021 & 0.490972303550011 \tabularnewline
30 & 0.627318536595967 & 0.745362926808065 & 0.372681463404033 \tabularnewline
31 & 0.713853251737293 & 0.572293496525414 & 0.286146748262707 \tabularnewline
32 & 0.76748647062328 & 0.465027058753439 & 0.232513529376720 \tabularnewline
33 & 0.81051409478064 & 0.378971810438721 & 0.189485905219361 \tabularnewline
34 & 0.843316677384611 & 0.313366645230777 & 0.156683322615389 \tabularnewline
35 & 0.887095563361121 & 0.225808873277758 & 0.112904436638879 \tabularnewline
36 & 0.90705627451035 & 0.185887450979298 & 0.0929437254896492 \tabularnewline
37 & 0.943297341635426 & 0.113405316729147 & 0.0567026583645735 \tabularnewline
38 & 0.987305741602801 & 0.0253885167943971 & 0.0126942583971985 \tabularnewline
39 & 0.994011958559478 & 0.0119760828810436 & 0.00598804144052182 \tabularnewline
40 & 0.993655045565876 & 0.0126899088682481 & 0.00634495443412403 \tabularnewline
41 & 0.996477870532076 & 0.0070442589358482 & 0.0035221294679241 \tabularnewline
42 & 0.99655303222439 & 0.00689393555122 & 0.00344696777561 \tabularnewline
43 & 0.995721062587448 & 0.00855787482510414 & 0.00427893741255207 \tabularnewline
44 & 0.994720803254726 & 0.0105583934905484 & 0.00527919674527419 \tabularnewline
45 & 0.993357916272452 & 0.0132841674550970 & 0.00664208372754852 \tabularnewline
46 & 0.992279352634354 & 0.0154412947312926 & 0.0077206473656463 \tabularnewline
47 & 0.99204320675749 & 0.0159135864850223 & 0.00795679324251115 \tabularnewline
48 & 0.99552753917083 & 0.00894492165834016 & 0.00447246082917008 \tabularnewline
49 & 0.993550561497449 & 0.0128988770051021 & 0.00644943850255107 \tabularnewline
50 & 0.995299009159069 & 0.00940198168186223 & 0.00470099084093112 \tabularnewline
51 & 0.998682338430718 & 0.00263532313856470 & 0.00131766156928235 \tabularnewline
52 & 0.999814899465275 & 0.000370201069450011 & 0.000185100534725006 \tabularnewline
53 & 0.999235784661285 & 0.00152843067742943 & 0.000764215338714716 \tabularnewline
54 & 0.996915276331129 & 0.00616944733774284 & 0.00308472366887142 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57965&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]5[/C][C]0.0657043912428305[/C][C]0.131408782485661[/C][C]0.93429560875717[/C][/ROW]
[ROW][C]6[/C][C]0.0889452644193762[/C][C]0.177890528838752[/C][C]0.911054735580624[/C][/ROW]
[ROW][C]7[/C][C]0.146880293943616[/C][C]0.293760587887231[/C][C]0.853119706056384[/C][/ROW]
[ROW][C]8[/C][C]0.148187746719477[/C][C]0.296375493438954[/C][C]0.851812253280523[/C][/ROW]
[ROW][C]9[/C][C]0.0930978776883454[/C][C]0.186195755376691[/C][C]0.906902122311655[/C][/ROW]
[ROW][C]10[/C][C]0.0516104980930191[/C][C]0.103220996186038[/C][C]0.94838950190698[/C][/ROW]
[ROW][C]11[/C][C]0.0281123004990112[/C][C]0.0562246009980225[/C][C]0.971887699500989[/C][/ROW]
[ROW][C]12[/C][C]0.0171703474984610[/C][C]0.0343406949969221[/C][C]0.98282965250154[/C][/ROW]
[ROW][C]13[/C][C]0.0292404902431319[/C][C]0.0584809804862639[/C][C]0.970759509756868[/C][/ROW]
[ROW][C]14[/C][C]0.0287512808073009[/C][C]0.0575025616146019[/C][C]0.9712487191927[/C][/ROW]
[ROW][C]15[/C][C]0.0225811866843572[/C][C]0.0451623733687144[/C][C]0.977418813315643[/C][/ROW]
[ROW][C]16[/C][C]0.0190712956310427[/C][C]0.0381425912620854[/C][C]0.980928704368957[/C][/ROW]
[ROW][C]17[/C][C]0.0152832464742233[/C][C]0.0305664929484466[/C][C]0.984716753525777[/C][/ROW]
[ROW][C]18[/C][C]0.0149056651691330[/C][C]0.0298113303382660[/C][C]0.985094334830867[/C][/ROW]
[ROW][C]19[/C][C]0.0257394261855862[/C][C]0.0514788523711724[/C][C]0.974260573814414[/C][/ROW]
[ROW][C]20[/C][C]0.0444340514632611[/C][C]0.0888681029265221[/C][C]0.955565948536739[/C][/ROW]
[ROW][C]21[/C][C]0.0573603970954792[/C][C]0.114720794190958[/C][C]0.94263960290452[/C][/ROW]
[ROW][C]22[/C][C]0.0898840696953125[/C][C]0.179768139390625[/C][C]0.910115930304688[/C][/ROW]
[ROW][C]23[/C][C]0.105568827119153[/C][C]0.211137654238306[/C][C]0.894431172880847[/C][/ROW]
[ROW][C]24[/C][C]0.11615861273552[/C][C]0.23231722547104[/C][C]0.88384138726448[/C][/ROW]
[ROW][C]25[/C][C]0.144949624674705[/C][C]0.289899249349410[/C][C]0.855050375325295[/C][/ROW]
[ROW][C]26[/C][C]0.198840540687441[/C][C]0.397681081374882[/C][C]0.801159459312559[/C][/ROW]
[ROW][C]27[/C][C]0.302267900601939[/C][C]0.604535801203878[/C][C]0.697732099398061[/C][/ROW]
[ROW][C]28[/C][C]0.403034447267361[/C][C]0.806068894534723[/C][C]0.596965552732639[/C][/ROW]
[ROW][C]29[/C][C]0.509027696449989[/C][C]0.981944607100021[/C][C]0.490972303550011[/C][/ROW]
[ROW][C]30[/C][C]0.627318536595967[/C][C]0.745362926808065[/C][C]0.372681463404033[/C][/ROW]
[ROW][C]31[/C][C]0.713853251737293[/C][C]0.572293496525414[/C][C]0.286146748262707[/C][/ROW]
[ROW][C]32[/C][C]0.76748647062328[/C][C]0.465027058753439[/C][C]0.232513529376720[/C][/ROW]
[ROW][C]33[/C][C]0.81051409478064[/C][C]0.378971810438721[/C][C]0.189485905219361[/C][/ROW]
[ROW][C]34[/C][C]0.843316677384611[/C][C]0.313366645230777[/C][C]0.156683322615389[/C][/ROW]
[ROW][C]35[/C][C]0.887095563361121[/C][C]0.225808873277758[/C][C]0.112904436638879[/C][/ROW]
[ROW][C]36[/C][C]0.90705627451035[/C][C]0.185887450979298[/C][C]0.0929437254896492[/C][/ROW]
[ROW][C]37[/C][C]0.943297341635426[/C][C]0.113405316729147[/C][C]0.0567026583645735[/C][/ROW]
[ROW][C]38[/C][C]0.987305741602801[/C][C]0.0253885167943971[/C][C]0.0126942583971985[/C][/ROW]
[ROW][C]39[/C][C]0.994011958559478[/C][C]0.0119760828810436[/C][C]0.00598804144052182[/C][/ROW]
[ROW][C]40[/C][C]0.993655045565876[/C][C]0.0126899088682481[/C][C]0.00634495443412403[/C][/ROW]
[ROW][C]41[/C][C]0.996477870532076[/C][C]0.0070442589358482[/C][C]0.0035221294679241[/C][/ROW]
[ROW][C]42[/C][C]0.99655303222439[/C][C]0.00689393555122[/C][C]0.00344696777561[/C][/ROW]
[ROW][C]43[/C][C]0.995721062587448[/C][C]0.00855787482510414[/C][C]0.00427893741255207[/C][/ROW]
[ROW][C]44[/C][C]0.994720803254726[/C][C]0.0105583934905484[/C][C]0.00527919674527419[/C][/ROW]
[ROW][C]45[/C][C]0.993357916272452[/C][C]0.0132841674550970[/C][C]0.00664208372754852[/C][/ROW]
[ROW][C]46[/C][C]0.992279352634354[/C][C]0.0154412947312926[/C][C]0.0077206473656463[/C][/ROW]
[ROW][C]47[/C][C]0.99204320675749[/C][C]0.0159135864850223[/C][C]0.00795679324251115[/C][/ROW]
[ROW][C]48[/C][C]0.99552753917083[/C][C]0.00894492165834016[/C][C]0.00447246082917008[/C][/ROW]
[ROW][C]49[/C][C]0.993550561497449[/C][C]0.0128988770051021[/C][C]0.00644943850255107[/C][/ROW]
[ROW][C]50[/C][C]0.995299009159069[/C][C]0.00940198168186223[/C][C]0.00470099084093112[/C][/ROW]
[ROW][C]51[/C][C]0.998682338430718[/C][C]0.00263532313856470[/C][C]0.00131766156928235[/C][/ROW]
[ROW][C]52[/C][C]0.999814899465275[/C][C]0.000370201069450011[/C][C]0.000185100534725006[/C][/ROW]
[ROW][C]53[/C][C]0.999235784661285[/C][C]0.00152843067742943[/C][C]0.000764215338714716[/C][/ROW]
[ROW][C]54[/C][C]0.996915276331129[/C][C]0.00616944733774284[/C][C]0.00308472366887142[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57965&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57965&T=5

As an alternative you can also use a QR Code:

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

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
5	0.0657043912428305	0.131408782485661	0.93429560875717
6	0.0889452644193762	0.177890528838752	0.911054735580624
7	0.146880293943616	0.293760587887231	0.853119706056384
8	0.148187746719477	0.296375493438954	0.851812253280523
9	0.0930978776883454	0.186195755376691	0.906902122311655
10	0.0516104980930191	0.103220996186038	0.94838950190698
11	0.0281123004990112	0.0562246009980225	0.971887699500989
12	0.0171703474984610	0.0343406949969221	0.98282965250154
13	0.0292404902431319	0.0584809804862639	0.970759509756868
14	0.0287512808073009	0.0575025616146019	0.9712487191927
15	0.0225811866843572	0.0451623733687144	0.977418813315643
16	0.0190712956310427	0.0381425912620854	0.980928704368957
17	0.0152832464742233	0.0305664929484466	0.984716753525777
18	0.0149056651691330	0.0298113303382660	0.985094334830867
19	0.0257394261855862	0.0514788523711724	0.974260573814414
20	0.0444340514632611	0.0888681029265221	0.955565948536739
21	0.0573603970954792	0.114720794190958	0.94263960290452
22	0.0898840696953125	0.179768139390625	0.910115930304688
23	0.105568827119153	0.211137654238306	0.894431172880847
24	0.11615861273552	0.23231722547104	0.88384138726448
25	0.144949624674705	0.289899249349410	0.855050375325295
26	0.198840540687441	0.397681081374882	0.801159459312559
27	0.302267900601939	0.604535801203878	0.697732099398061
28	0.403034447267361	0.806068894534723	0.596965552732639
29	0.509027696449989	0.981944607100021	0.490972303550011
30	0.627318536595967	0.745362926808065	0.372681463404033
31	0.713853251737293	0.572293496525414	0.286146748262707
32	0.76748647062328	0.465027058753439	0.232513529376720
33	0.81051409478064	0.378971810438721	0.189485905219361
34	0.843316677384611	0.313366645230777	0.156683322615389
35	0.887095563361121	0.225808873277758	0.112904436638879
36	0.90705627451035	0.185887450979298	0.0929437254896492
37	0.943297341635426	0.113405316729147	0.0567026583645735
38	0.987305741602801	0.0253885167943971	0.0126942583971985
39	0.994011958559478	0.0119760828810436	0.00598804144052182
40	0.993655045565876	0.0126899088682481	0.00634495443412403
41	0.996477870532076	0.0070442589358482	0.0035221294679241
42	0.99655303222439	0.00689393555122	0.00344696777561
43	0.995721062587448	0.00855787482510414	0.00427893741255207
44	0.994720803254726	0.0105583934905484	0.00527919674527419
45	0.993357916272452	0.0132841674550970	0.00664208372754852
46	0.992279352634354	0.0154412947312926	0.0077206473656463
47	0.99204320675749	0.0159135864850223	0.00795679324251115
48	0.99552753917083	0.00894492165834016	0.00447246082917008
49	0.993550561497449	0.0128988770051021	0.00644943850255107
50	0.995299009159069	0.00940198168186223	0.00470099084093112
51	0.998682338430718	0.00263532313856470	0.00131766156928235
52	0.999814899465275	0.000370201069450011	0.000185100534725006
53	0.999235784661285	0.00152843067742943	0.000764215338714716
54	0.996915276331129	0.00616944733774284	0.00308472366887142

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	9	0.18	NOK
5% type I error level	22	0.44	NOK
10% type I error level	27	0.54	NOK

\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 & 9 & 0.18 & NOK \tabularnewline
5% type I error level & 22 & 0.44 & NOK \tabularnewline
10% type I error level & 27 & 0.54 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57965&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]9[/C][C]0.18[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]22[/C][C]0.44[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]27[/C][C]0.54[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57965&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57965&T=6

As an alternative you can also use a QR Code:

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	9	0.18	NOK
5% type I error level	22	0.44	NOK
10% type I error level	27	0.54	NOK

Figure 1

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Figure 3

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Figure 4

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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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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code