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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 20 Nov 2009 01:59:37 -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/20/t1258707619uoqspu2f9evyo0q.htm/, Retrieved Tue, 16 Apr 2024 20:45:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57988, Retrieved Tue, 16 Apr 2024 20:45:49 +0000

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Estimated Impact

219

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] [ed603017d2bee8fbd82b6d5ec04e12c3]
-    D              [Multiple Regression] [model 4] [2009-11-20 08:59:37] [87085ce7f5378f281469a8b1f0969170] [Current]
-    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] 

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Dataseries X:

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Boxplots

105.8	93.7	105.9	106	106.1	105.7
105.7	104.5	105.8	105.9	106	106.1
105.6	95.4	105.7	105.8	105.9	106
105.4	86.5	105.6	105.7	105.8	105.9
105.4	102.9	105.4	105.6	105.7	105.8
105.5	101.9	105.4	105.4	105.6	105.7
105.6	103.7	105.5	105.4	105.4	105.6
105.7	100.7	105.6	105.5	105.4	105.4
105.9	94.2	105.7	105.6	105.5	105.4
106.1	93.6	105.9	105.7	105.6	105.5
106	104.7	106.1	105.9	105.7	105.6
105.8	101	106	106.1	105.9	105.7
105.8	97.6	105.8	106	106.1	105.9
105.7	105.8	105.8	105.8	106	106.1
105.5	93.7	105.7	105.8	105.8	106
105.3	91.2	105.5	105.7	105.8	105.8
105.2	106.3	105.3	105.5	105.7	105.8
105.2	103.4	105.2	105.3	105.5	105.7
105	107.4	105.2	105.2	105.3	105.5
105.1	101.2	105	105.2	105.2	105.3
105.1	96.9	105.1	105	105.2	105.2
105.2	96.3	105.1	105.1	105	105.2
104.9	109.8	105.2	105.1	105.1	105
104.8	97.9	104.9	105.2	105.1	105.1
104.5	105.1	104.8	104.9	105.2	105.1
104.5	107.9	104.5	104.8	104.9	105.2
104.4	95	104.5	104.5	104.8	104.9
104.4	95.2	104.4	104.5	104.5	104.8
104.2	105.8	104.4	104.4	104.5	104.5
104.1	110.1	104.2	104.4	104.4	104.5
103.9	112.2	104.1	104.2	104.4	104.4
103.8	102.5	103.9	104.1	104.2	104.4
103.9	103.7	103.8	103.9	104.1	104.2
104.2	102	103.9	103.8	103.9	104.1
104.1	112.3	104.2	103.9	103.8	103.9
103.8	103.3	104.1	104.2	103.9	103.8
103.6	106.9	103.8	104.1	104.2	103.9
103.7	104.6	103.6	103.8	104.1	104.2
103.5	100.7	103.7	103.6	103.8	104.1
103.4	99	103.5	103.7	103.6	103.8
103.1	106.5	103.4	103.5	103.7	103.6
103.1	114.9	103.1	103.4	103.5	103.7
103.1	114.1	103.1	103.1	103.4	103.5
103.2	102.2	103.1	103.1	103.1	103.4
103.3	107	103.2	103.1	103.1	103.1
103.5	107.4	103.3	103.2	103.1	103.1
103.6	107.4	103.5	103.3	103.2	103.1
103.5	110.1	103.6	103.5	103.3	103.2
103.3	105.6	103.5	103.6	103.5	103.3
103.2	110.9	103.3	103.5	103.6	103.5
103.1	101.9	103.2	103.3	103.5	103.6
103.2	93.2	103.1	103.2	103.3	103.5
103	110.5	103.2	103.1	103.2	103.3
103	113.1	103	103.2	103.1	103.2
103.1	101.7	103	103	103.2	103.1
103.4	96.7	103.1	103	103	103.2

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 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=57988&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=57988&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57988&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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Werkl[t] = + 13.181305483574 -0.0167499771012351Infl[t] + 1.01704809359358`Yt-1`[t] + 0.0183717956239474`Yt-2`[t] -0.304695129059736`Yt-3`[t] + 0.159093233761395`Yt-4`[t] + 0.0623924437488247M1[t] + 0.205812380211141M2[t] -0.0775331339962117M3[t] -0.106742976619106M4[t] + 0.0578994848837974M5[t] + 0.227318039355702M6[t] + 0.177074745524402M7[t] + 0.165127828048767M8[t] + 0.204067321450513M9[t] + 0.271447808716314M10[t] + 0.142836066402679M11[t] -0.00332475677410949t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Werkl[t] =  +  13.181305483574 -0.0167499771012351Infl[t] +  1.01704809359358`Yt-1`[t] +  0.0183717956239474`Yt-2`[t] -0.304695129059736`Yt-3`[t] +  0.159093233761395`Yt-4`[t] +  0.0623924437488247M1[t] +  0.205812380211141M2[t] -0.0775331339962117M3[t] -0.106742976619106M4[t] +  0.0578994848837974M5[t] +  0.227318039355702M6[t] +  0.177074745524402M7[t] +  0.165127828048767M8[t] +  0.204067321450513M9[t] +  0.271447808716314M10[t] +  0.142836066402679M11[t] -0.00332475677410949t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57988&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Werkl[t] =  +  13.181305483574 -0.0167499771012351Infl[t] +  1.01704809359358`Yt-1`[t] +  0.0183717956239474`Yt-2`[t] -0.304695129059736`Yt-3`[t] +  0.159093233761395`Yt-4`[t] +  0.0623924437488247M1[t] +  0.205812380211141M2[t] -0.0775331339962117M3[t] -0.106742976619106M4[t] +  0.0578994848837974M5[t] +  0.227318039355702M6[t] +  0.177074745524402M7[t] +  0.165127828048767M8[t] +  0.204067321450513M9[t] +  0.271447808716314M10[t] +  0.142836066402679M11[t] -0.00332475677410949t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57988&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57988&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] = + 13.181305483574 -0.0167499771012351Infl[t] + 1.01704809359358`Yt-1`[t] + 0.0183717956239474`Yt-2`[t] -0.304695129059736`Yt-3`[t] + 0.159093233761395`Yt-4`[t] + 0.0623924437488247M1[t] + 0.205812380211141M2[t] -0.0775331339962117M3[t] -0.106742976619106M4[t] + 0.0578994848837974M5[t] + 0.227318039355702M6[t] + 0.177074745524402M7[t] + 0.165127828048767M8[t] + 0.204067321450513M9[t] + 0.271447808716314M10[t] + 0.142836066402679M11[t] -0.00332475677410949t + 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)	13.181305483574	6.770538	1.9469	0.058971	0.029485
Infl	-0.0167499771012351	0.004804	-3.487	0.00125	0.000625
`Yt-1`	1.01704809359358	0.151537	6.7115	0	0
`Yt-2`	0.0183717956239474	0.220522	0.0833	0.934042	0.467021
`Yt-3`	-0.304695129059736	0.221958	-1.3728	0.177875	0.088938
`Yt-4`	0.159093233761395	0.147438	1.0791	0.287366	0.143683
M1	0.0623924437488247	0.085715	0.7279	0.471132	0.235566
M2	0.205812380211141	0.092299	2.2298	0.031743	0.015871
M3	-0.0775331339962117	0.09766	-0.7939	0.432177	0.216089
M4	-0.106742976619106	0.100624	-1.0608	0.295473	0.147736
M5	0.0578994848837974	0.089024	0.6504	0.519361	0.25968
M6	0.227318039355702	0.089078	2.5519	0.014858	0.007429
M7	0.177074745524402	0.095133	1.8613	0.070444	0.035222
M8	0.165127828048767	0.087082	1.8962	0.065552	0.032776
M9	0.204067321450513	0.090057	2.266	0.029232	0.014616
M10	0.271447808716314	0.087615	3.0982	0.003653	0.001827
M11	0.142836066402679	0.093264	1.5315	0.133925	0.066962
t	-0.00332475677410949	0.003697	-0.8993	0.374174	0.187087

\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) & 13.181305483574 & 6.770538 & 1.9469 & 0.058971 & 0.029485 \tabularnewline
Infl & -0.0167499771012351 & 0.004804 & -3.487 & 0.00125 & 0.000625 \tabularnewline
`Yt-1` & 1.01704809359358 & 0.151537 & 6.7115 & 0 & 0 \tabularnewline
`Yt-2` & 0.0183717956239474 & 0.220522 & 0.0833 & 0.934042 & 0.467021 \tabularnewline
`Yt-3` & -0.304695129059736 & 0.221958 & -1.3728 & 0.177875 & 0.088938 \tabularnewline
`Yt-4` & 0.159093233761395 & 0.147438 & 1.0791 & 0.287366 & 0.143683 \tabularnewline
M1 & 0.0623924437488247 & 0.085715 & 0.7279 & 0.471132 & 0.235566 \tabularnewline
M2 & 0.205812380211141 & 0.092299 & 2.2298 & 0.031743 & 0.015871 \tabularnewline
M3 & -0.0775331339962117 & 0.09766 & -0.7939 & 0.432177 & 0.216089 \tabularnewline
M4 & -0.106742976619106 & 0.100624 & -1.0608 & 0.295473 & 0.147736 \tabularnewline
M5 & 0.0578994848837974 & 0.089024 & 0.6504 & 0.519361 & 0.25968 \tabularnewline
M6 & 0.227318039355702 & 0.089078 & 2.5519 & 0.014858 & 0.007429 \tabularnewline
M7 & 0.177074745524402 & 0.095133 & 1.8613 & 0.070444 & 0.035222 \tabularnewline
M8 & 0.165127828048767 & 0.087082 & 1.8962 & 0.065552 & 0.032776 \tabularnewline
M9 & 0.204067321450513 & 0.090057 & 2.266 & 0.029232 & 0.014616 \tabularnewline
M10 & 0.271447808716314 & 0.087615 & 3.0982 & 0.003653 & 0.001827 \tabularnewline
M11 & 0.142836066402679 & 0.093264 & 1.5315 & 0.133925 & 0.066962 \tabularnewline
t & -0.00332475677410949 & 0.003697 & -0.8993 & 0.374174 & 0.187087 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57988&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]13.181305483574[/C][C]6.770538[/C][C]1.9469[/C][C]0.058971[/C][C]0.029485[/C][/ROW]
[ROW][C]Infl[/C][C]-0.0167499771012351[/C][C]0.004804[/C][C]-3.487[/C][C]0.00125[/C][C]0.000625[/C][/ROW]
[ROW][C]`Yt-1`[/C][C]1.01704809359358[/C][C]0.151537[/C][C]6.7115[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Yt-2`[/C][C]0.0183717956239474[/C][C]0.220522[/C][C]0.0833[/C][C]0.934042[/C][C]0.467021[/C][/ROW]
[ROW][C]`Yt-3`[/C][C]-0.304695129059736[/C][C]0.221958[/C][C]-1.3728[/C][C]0.177875[/C][C]0.088938[/C][/ROW]
[ROW][C]`Yt-4`[/C][C]0.159093233761395[/C][C]0.147438[/C][C]1.0791[/C][C]0.287366[/C][C]0.143683[/C][/ROW]
[ROW][C]M1[/C][C]0.0623924437488247[/C][C]0.085715[/C][C]0.7279[/C][C]0.471132[/C][C]0.235566[/C][/ROW]
[ROW][C]M2[/C][C]0.205812380211141[/C][C]0.092299[/C][C]2.2298[/C][C]0.031743[/C][C]0.015871[/C][/ROW]
[ROW][C]M3[/C][C]-0.0775331339962117[/C][C]0.09766[/C][C]-0.7939[/C][C]0.432177[/C][C]0.216089[/C][/ROW]
[ROW][C]M4[/C][C]-0.106742976619106[/C][C]0.100624[/C][C]-1.0608[/C][C]0.295473[/C][C]0.147736[/C][/ROW]
[ROW][C]M5[/C][C]0.0578994848837974[/C][C]0.089024[/C][C]0.6504[/C][C]0.519361[/C][C]0.25968[/C][/ROW]
[ROW][C]M6[/C][C]0.227318039355702[/C][C]0.089078[/C][C]2.5519[/C][C]0.014858[/C][C]0.007429[/C][/ROW]
[ROW][C]M7[/C][C]0.177074745524402[/C][C]0.095133[/C][C]1.8613[/C][C]0.070444[/C][C]0.035222[/C][/ROW]
[ROW][C]M8[/C][C]0.165127828048767[/C][C]0.087082[/C][C]1.8962[/C][C]0.065552[/C][C]0.032776[/C][/ROW]
[ROW][C]M9[/C][C]0.204067321450513[/C][C]0.090057[/C][C]2.266[/C][C]0.029232[/C][C]0.014616[/C][/ROW]
[ROW][C]M10[/C][C]0.271447808716314[/C][C]0.087615[/C][C]3.0982[/C][C]0.003653[/C][C]0.001827[/C][/ROW]
[ROW][C]M11[/C][C]0.142836066402679[/C][C]0.093264[/C][C]1.5315[/C][C]0.133925[/C][C]0.066962[/C][/ROW]
[ROW][C]t[/C][C]-0.00332475677410949[/C][C]0.003697[/C][C]-0.8993[/C][C]0.374174[/C][C]0.187087[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57988&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57988&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)	13.181305483574	6.770538	1.9469	0.058971	0.029485
Infl	-0.0167499771012351	0.004804	-3.487	0.00125	0.000625
`Yt-1`	1.01704809359358	0.151537	6.7115	0	0
`Yt-2`	0.0183717956239474	0.220522	0.0833	0.934042	0.467021
`Yt-3`	-0.304695129059736	0.221958	-1.3728	0.177875	0.088938
`Yt-4`	0.159093233761395	0.147438	1.0791	0.287366	0.143683
M1	0.0623924437488247	0.085715	0.7279	0.471132	0.235566
M2	0.205812380211141	0.092299	2.2298	0.031743	0.015871
M3	-0.0775331339962117	0.09766	-0.7939	0.432177	0.216089
M4	-0.106742976619106	0.100624	-1.0608	0.295473	0.147736
M5	0.0578994848837974	0.089024	0.6504	0.519361	0.25968
M6	0.227318039355702	0.089078	2.5519	0.014858	0.007429
M7	0.177074745524402	0.095133	1.8613	0.070444	0.035222
M8	0.165127828048767	0.087082	1.8962	0.065552	0.032776
M9	0.204067321450513	0.090057	2.266	0.029232	0.014616
M10	0.271447808716314	0.087615	3.0982	0.003653	0.001827
M11	0.142836066402679	0.093264	1.5315	0.133925	0.066962
t	-0.00332475677410949	0.003697	-0.8993	0.374174	0.187087

Multiple Linear Regression - Regression Statistics
Multiple R	0.996509035112443
R-squared	0.993030257060732
Adjusted R-squared	0.989912214166848
F-TEST (value)	318.478703102129
F-TEST (DF numerator)	17
F-TEST (DF denominator)	38
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.102457087339735
Sum Squared Residuals	0.398903280353396

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.996509035112443 \tabularnewline
R-squared & 0.993030257060732 \tabularnewline
Adjusted R-squared & 0.989912214166848 \tabularnewline
F-TEST (value) & 318.478703102129 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 38 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.102457087339735 \tabularnewline
Sum Squared Residuals & 0.398903280353396 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57988&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.996509035112443[/C][/ROW]
[ROW][C]R-squared[/C][C]0.993030257060732[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.989912214166848[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]318.478703102129[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]38[/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]0.102457087339735[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]0.398903280353396[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57988&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57988&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	0.996509035112443
R-squared	0.993030257060732
Adjusted R-squared	0.989912214166848
F-TEST (value)	318.478703102129
F-TEST (DF numerator)	17
F-TEST (DF denominator)	38
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.102457087339735
Sum Squared Residuals	0.398903280353396

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	105.8	105.811705379203	-0.0117053792030353
2	105.7	105.761465623687	-0.0614656236867831
3	105.6	105.538238344935	0.0617616550653452
4	105.4	105.565796742347	-0.165796742346709
5	105.4	105.261728213864	0.138271786136022
6	105.5	105.455457819068	0.0445421809319375
7	105.6	105.518474321476	0.0815256785244096
8	105.7	105.625175920699	0.074824079300987
9	105.9	105.842737984500	0.057262015499536
10	106.1	106.107530310004	-0.00753031000418853
11	106	105.982192853406	0.0178071465936141
12	105.8	105.754946792834	0.0450532071662002
13	105.8	105.636597224612	0.163402775388063
14	105.7	105.697956392603	0.00204360739653135
15	105.5	105.557285737623	-0.057285737623412
16	105.3	105.329560635946	-0.0295606359461054
17	105.2	105.061339221509	0.138660778491294
18	105.2	105.215658486752	-0.0156584867517507
19	105	105.122373727239	-0.122373727238677
20	105.1	105.006193158452	0.0938068415484304
21	105.1	105.195953923473	-0.0959539234729413
22	105.2	105.332835845600	-0.132835845599708
23	104.9	105.014191305346	-0.114191305346402
24	104.8	104.779987284535	0.0200127154652182
25	104.5	104.580769275428	-0.0807692754280743
26	104.5	104.474330773686	0.0256692263135833
27	104.4	104.380965211401	0.0190347885987440
28	104.4	104.318875022566	0.0811249774335682
29	104.2	104.253077820331	-0.0530778203313235
30	104.1	104.174206610681	-0.0742066106810689
31	103.9	103.964175116303	-0.0641751163027591
32	103.8	103.967070447466	-0.167070447465852
33	103.9	103.875856909242	0.0241430907584613
34	104.2	104.113284933038	0.086715066961893
35	104.1	104.114426143602	-0.0144261436018154
36	103.8	103.976443007382	-0.17644300738184
37	103.6	103.592759953810	0.00724004619013386
38	103.7	103.640656406459	0.059343593540604
39	103.5	103.592840711749	-0.0928407117491103
40	103.4	103.400419689951	-0.000419689951405759
41	103.1	103.268445238279	-0.168445238278550
42	103.1	103.063735969874	0.0362640301264214
43	103.1	103.016707228416	0.083292771584335
44	103.2	103.276259497012	-0.0762594970123955
45	103.3	103.285451182785	0.014548817214944
46	103.5	103.446348911358	0.0536510886420031
47	103.6	103.489189697645	0.110810302354604
48	103.5	103.388622915250	0.111377084750422
49	103.3	103.378168166947	-0.0781681669470875
50	103.2	103.225590803564	-0.0255908035639357
51	103.1	103.030669994292	0.0693300057084329
52	103.2	103.085347909189	0.114652090810652
53	103	103.055409506017	-0.0554095060174416
54	103	102.990941113626	0.00905888637446086
55	103.1	103.078269606567	0.0217303934326917
56	103.4	103.325300976371	0.0746990236288304

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 105.8 & 105.811705379203 & -0.0117053792030353 \tabularnewline
2 & 105.7 & 105.761465623687 & -0.0614656236867831 \tabularnewline
3 & 105.6 & 105.538238344935 & 0.0617616550653452 \tabularnewline
4 & 105.4 & 105.565796742347 & -0.165796742346709 \tabularnewline
5 & 105.4 & 105.261728213864 & 0.138271786136022 \tabularnewline
6 & 105.5 & 105.455457819068 & 0.0445421809319375 \tabularnewline
7 & 105.6 & 105.518474321476 & 0.0815256785244096 \tabularnewline
8 & 105.7 & 105.625175920699 & 0.074824079300987 \tabularnewline
9 & 105.9 & 105.842737984500 & 0.057262015499536 \tabularnewline
10 & 106.1 & 106.107530310004 & -0.00753031000418853 \tabularnewline
11 & 106 & 105.982192853406 & 0.0178071465936141 \tabularnewline
12 & 105.8 & 105.754946792834 & 0.0450532071662002 \tabularnewline
13 & 105.8 & 105.636597224612 & 0.163402775388063 \tabularnewline
14 & 105.7 & 105.697956392603 & 0.00204360739653135 \tabularnewline
15 & 105.5 & 105.557285737623 & -0.057285737623412 \tabularnewline
16 & 105.3 & 105.329560635946 & -0.0295606359461054 \tabularnewline
17 & 105.2 & 105.061339221509 & 0.138660778491294 \tabularnewline
18 & 105.2 & 105.215658486752 & -0.0156584867517507 \tabularnewline
19 & 105 & 105.122373727239 & -0.122373727238677 \tabularnewline
20 & 105.1 & 105.006193158452 & 0.0938068415484304 \tabularnewline
21 & 105.1 & 105.195953923473 & -0.0959539234729413 \tabularnewline
22 & 105.2 & 105.332835845600 & -0.132835845599708 \tabularnewline
23 & 104.9 & 105.014191305346 & -0.114191305346402 \tabularnewline
24 & 104.8 & 104.779987284535 & 0.0200127154652182 \tabularnewline
25 & 104.5 & 104.580769275428 & -0.0807692754280743 \tabularnewline
26 & 104.5 & 104.474330773686 & 0.0256692263135833 \tabularnewline
27 & 104.4 & 104.380965211401 & 0.0190347885987440 \tabularnewline
28 & 104.4 & 104.318875022566 & 0.0811249774335682 \tabularnewline
29 & 104.2 & 104.253077820331 & -0.0530778203313235 \tabularnewline
30 & 104.1 & 104.174206610681 & -0.0742066106810689 \tabularnewline
31 & 103.9 & 103.964175116303 & -0.0641751163027591 \tabularnewline
32 & 103.8 & 103.967070447466 & -0.167070447465852 \tabularnewline
33 & 103.9 & 103.875856909242 & 0.0241430907584613 \tabularnewline
34 & 104.2 & 104.113284933038 & 0.086715066961893 \tabularnewline
35 & 104.1 & 104.114426143602 & -0.0144261436018154 \tabularnewline
36 & 103.8 & 103.976443007382 & -0.17644300738184 \tabularnewline
37 & 103.6 & 103.592759953810 & 0.00724004619013386 \tabularnewline
38 & 103.7 & 103.640656406459 & 0.059343593540604 \tabularnewline
39 & 103.5 & 103.592840711749 & -0.0928407117491103 \tabularnewline
40 & 103.4 & 103.400419689951 & -0.000419689951405759 \tabularnewline
41 & 103.1 & 103.268445238279 & -0.168445238278550 \tabularnewline
42 & 103.1 & 103.063735969874 & 0.0362640301264214 \tabularnewline
43 & 103.1 & 103.016707228416 & 0.083292771584335 \tabularnewline
44 & 103.2 & 103.276259497012 & -0.0762594970123955 \tabularnewline
45 & 103.3 & 103.285451182785 & 0.014548817214944 \tabularnewline
46 & 103.5 & 103.446348911358 & 0.0536510886420031 \tabularnewline
47 & 103.6 & 103.489189697645 & 0.110810302354604 \tabularnewline
48 & 103.5 & 103.388622915250 & 0.111377084750422 \tabularnewline
49 & 103.3 & 103.378168166947 & -0.0781681669470875 \tabularnewline
50 & 103.2 & 103.225590803564 & -0.0255908035639357 \tabularnewline
51 & 103.1 & 103.030669994292 & 0.0693300057084329 \tabularnewline
52 & 103.2 & 103.085347909189 & 0.114652090810652 \tabularnewline
53 & 103 & 103.055409506017 & -0.0554095060174416 \tabularnewline
54 & 103 & 102.990941113626 & 0.00905888637446086 \tabularnewline
55 & 103.1 & 103.078269606567 & 0.0217303934326917 \tabularnewline
56 & 103.4 & 103.325300976371 & 0.0746990236288304 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57988&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]105.8[/C][C]105.811705379203[/C][C]-0.0117053792030353[/C][/ROW]
[ROW][C]2[/C][C]105.7[/C][C]105.761465623687[/C][C]-0.0614656236867831[/C][/ROW]
[ROW][C]3[/C][C]105.6[/C][C]105.538238344935[/C][C]0.0617616550653452[/C][/ROW]
[ROW][C]4[/C][C]105.4[/C][C]105.565796742347[/C][C]-0.165796742346709[/C][/ROW]
[ROW][C]5[/C][C]105.4[/C][C]105.261728213864[/C][C]0.138271786136022[/C][/ROW]
[ROW][C]6[/C][C]105.5[/C][C]105.455457819068[/C][C]0.0445421809319375[/C][/ROW]
[ROW][C]7[/C][C]105.6[/C][C]105.518474321476[/C][C]0.0815256785244096[/C][/ROW]
[ROW][C]8[/C][C]105.7[/C][C]105.625175920699[/C][C]0.074824079300987[/C][/ROW]
[ROW][C]9[/C][C]105.9[/C][C]105.842737984500[/C][C]0.057262015499536[/C][/ROW]
[ROW][C]10[/C][C]106.1[/C][C]106.107530310004[/C][C]-0.00753031000418853[/C][/ROW]
[ROW][C]11[/C][C]106[/C][C]105.982192853406[/C][C]0.0178071465936141[/C][/ROW]
[ROW][C]12[/C][C]105.8[/C][C]105.754946792834[/C][C]0.0450532071662002[/C][/ROW]
[ROW][C]13[/C][C]105.8[/C][C]105.636597224612[/C][C]0.163402775388063[/C][/ROW]
[ROW][C]14[/C][C]105.7[/C][C]105.697956392603[/C][C]0.00204360739653135[/C][/ROW]
[ROW][C]15[/C][C]105.5[/C][C]105.557285737623[/C][C]-0.057285737623412[/C][/ROW]
[ROW][C]16[/C][C]105.3[/C][C]105.329560635946[/C][C]-0.0295606359461054[/C][/ROW]
[ROW][C]17[/C][C]105.2[/C][C]105.061339221509[/C][C]0.138660778491294[/C][/ROW]
[ROW][C]18[/C][C]105.2[/C][C]105.215658486752[/C][C]-0.0156584867517507[/C][/ROW]
[ROW][C]19[/C][C]105[/C][C]105.122373727239[/C][C]-0.122373727238677[/C][/ROW]
[ROW][C]20[/C][C]105.1[/C][C]105.006193158452[/C][C]0.0938068415484304[/C][/ROW]
[ROW][C]21[/C][C]105.1[/C][C]105.195953923473[/C][C]-0.0959539234729413[/C][/ROW]
[ROW][C]22[/C][C]105.2[/C][C]105.332835845600[/C][C]-0.132835845599708[/C][/ROW]
[ROW][C]23[/C][C]104.9[/C][C]105.014191305346[/C][C]-0.114191305346402[/C][/ROW]
[ROW][C]24[/C][C]104.8[/C][C]104.779987284535[/C][C]0.0200127154652182[/C][/ROW]
[ROW][C]25[/C][C]104.5[/C][C]104.580769275428[/C][C]-0.0807692754280743[/C][/ROW]
[ROW][C]26[/C][C]104.5[/C][C]104.474330773686[/C][C]0.0256692263135833[/C][/ROW]
[ROW][C]27[/C][C]104.4[/C][C]104.380965211401[/C][C]0.0190347885987440[/C][/ROW]
[ROW][C]28[/C][C]104.4[/C][C]104.318875022566[/C][C]0.0811249774335682[/C][/ROW]
[ROW][C]29[/C][C]104.2[/C][C]104.253077820331[/C][C]-0.0530778203313235[/C][/ROW]
[ROW][C]30[/C][C]104.1[/C][C]104.174206610681[/C][C]-0.0742066106810689[/C][/ROW]
[ROW][C]31[/C][C]103.9[/C][C]103.964175116303[/C][C]-0.0641751163027591[/C][/ROW]
[ROW][C]32[/C][C]103.8[/C][C]103.967070447466[/C][C]-0.167070447465852[/C][/ROW]
[ROW][C]33[/C][C]103.9[/C][C]103.875856909242[/C][C]0.0241430907584613[/C][/ROW]
[ROW][C]34[/C][C]104.2[/C][C]104.113284933038[/C][C]0.086715066961893[/C][/ROW]
[ROW][C]35[/C][C]104.1[/C][C]104.114426143602[/C][C]-0.0144261436018154[/C][/ROW]
[ROW][C]36[/C][C]103.8[/C][C]103.976443007382[/C][C]-0.17644300738184[/C][/ROW]
[ROW][C]37[/C][C]103.6[/C][C]103.592759953810[/C][C]0.00724004619013386[/C][/ROW]
[ROW][C]38[/C][C]103.7[/C][C]103.640656406459[/C][C]0.059343593540604[/C][/ROW]
[ROW][C]39[/C][C]103.5[/C][C]103.592840711749[/C][C]-0.0928407117491103[/C][/ROW]
[ROW][C]40[/C][C]103.4[/C][C]103.400419689951[/C][C]-0.000419689951405759[/C][/ROW]
[ROW][C]41[/C][C]103.1[/C][C]103.268445238279[/C][C]-0.168445238278550[/C][/ROW]
[ROW][C]42[/C][C]103.1[/C][C]103.063735969874[/C][C]0.0362640301264214[/C][/ROW]
[ROW][C]43[/C][C]103.1[/C][C]103.016707228416[/C][C]0.083292771584335[/C][/ROW]
[ROW][C]44[/C][C]103.2[/C][C]103.276259497012[/C][C]-0.0762594970123955[/C][/ROW]
[ROW][C]45[/C][C]103.3[/C][C]103.285451182785[/C][C]0.014548817214944[/C][/ROW]
[ROW][C]46[/C][C]103.5[/C][C]103.446348911358[/C][C]0.0536510886420031[/C][/ROW]
[ROW][C]47[/C][C]103.6[/C][C]103.489189697645[/C][C]0.110810302354604[/C][/ROW]
[ROW][C]48[/C][C]103.5[/C][C]103.388622915250[/C][C]0.111377084750422[/C][/ROW]
[ROW][C]49[/C][C]103.3[/C][C]103.378168166947[/C][C]-0.0781681669470875[/C][/ROW]
[ROW][C]50[/C][C]103.2[/C][C]103.225590803564[/C][C]-0.0255908035639357[/C][/ROW]
[ROW][C]51[/C][C]103.1[/C][C]103.030669994292[/C][C]0.0693300057084329[/C][/ROW]
[ROW][C]52[/C][C]103.2[/C][C]103.085347909189[/C][C]0.114652090810652[/C][/ROW]
[ROW][C]53[/C][C]103[/C][C]103.055409506017[/C][C]-0.0554095060174416[/C][/ROW]
[ROW][C]54[/C][C]103[/C][C]102.990941113626[/C][C]0.00905888637446086[/C][/ROW]
[ROW][C]55[/C][C]103.1[/C][C]103.078269606567[/C][C]0.0217303934326917[/C][/ROW]
[ROW][C]56[/C][C]103.4[/C][C]103.325300976371[/C][C]0.0746990236288304[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57988&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57988&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	105.8	105.811705379203	-0.0117053792030353
2	105.7	105.761465623687	-0.0614656236867831
3	105.6	105.538238344935	0.0617616550653452
4	105.4	105.565796742347	-0.165796742346709
5	105.4	105.261728213864	0.138271786136022
6	105.5	105.455457819068	0.0445421809319375
7	105.6	105.518474321476	0.0815256785244096
8	105.7	105.625175920699	0.074824079300987
9	105.9	105.842737984500	0.057262015499536
10	106.1	106.107530310004	-0.00753031000418853
11	106	105.982192853406	0.0178071465936141
12	105.8	105.754946792834	0.0450532071662002
13	105.8	105.636597224612	0.163402775388063
14	105.7	105.697956392603	0.00204360739653135
15	105.5	105.557285737623	-0.057285737623412
16	105.3	105.329560635946	-0.0295606359461054
17	105.2	105.061339221509	0.138660778491294
18	105.2	105.215658486752	-0.0156584867517507
19	105	105.122373727239	-0.122373727238677
20	105.1	105.006193158452	0.0938068415484304
21	105.1	105.195953923473	-0.0959539234729413
22	105.2	105.332835845600	-0.132835845599708
23	104.9	105.014191305346	-0.114191305346402
24	104.8	104.779987284535	0.0200127154652182
25	104.5	104.580769275428	-0.0807692754280743
26	104.5	104.474330773686	0.0256692263135833
27	104.4	104.380965211401	0.0190347885987440
28	104.4	104.318875022566	0.0811249774335682
29	104.2	104.253077820331	-0.0530778203313235
30	104.1	104.174206610681	-0.0742066106810689
31	103.9	103.964175116303	-0.0641751163027591
32	103.8	103.967070447466	-0.167070447465852
33	103.9	103.875856909242	0.0241430907584613
34	104.2	104.113284933038	0.086715066961893
35	104.1	104.114426143602	-0.0144261436018154
36	103.8	103.976443007382	-0.17644300738184
37	103.6	103.592759953810	0.00724004619013386
38	103.7	103.640656406459	0.059343593540604
39	103.5	103.592840711749	-0.0928407117491103
40	103.4	103.400419689951	-0.000419689951405759
41	103.1	103.268445238279	-0.168445238278550
42	103.1	103.063735969874	0.0362640301264214
43	103.1	103.016707228416	0.083292771584335
44	103.2	103.276259497012	-0.0762594970123955
45	103.3	103.285451182785	0.014548817214944
46	103.5	103.446348911358	0.0536510886420031
47	103.6	103.489189697645	0.110810302354604
48	103.5	103.388622915250	0.111377084750422
49	103.3	103.378168166947	-0.0781681669470875
50	103.2	103.225590803564	-0.0255908035639357
51	103.1	103.030669994292	0.0693300057084329
52	103.2	103.085347909189	0.114652090810652
53	103	103.055409506017	-0.0554095060174416
54	103	102.990941113626	0.00905888637446086
55	103.1	103.078269606567	0.0217303934326917
56	103.4	103.325300976371	0.0746990236288304

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.747515140273827	0.504969719452346	0.252484859726173
22	0.724596359982256	0.550807280035488	0.275403640017744
23	0.675975286593944	0.648049426812112	0.324024713406056
24	0.759624611212188	0.480750777575625	0.240375388787812
25	0.74028073563245	0.519438528735099	0.259719264367549
26	0.791306721315375	0.417386557369249	0.208693278684625
27	0.742245505581885	0.515508988836231	0.257754494418115
28	0.732950625853426	0.534098748293149	0.267049374146574
29	0.966131009154233	0.067737981691533	0.0338689908457665
30	0.949839455727235	0.100321088545529	0.0501605442727646
31	0.937656429036802	0.124687141926397	0.0623435709631984
32	0.934563929953443	0.130872140093114	0.0654360700465571
33	0.884327938712213	0.231344122575574	0.115672061287787
34	0.819234270766169	0.361531458467662	0.180765729233831
35	0.771134674933003	0.457730650133994	0.228865325066997

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.747515140273827 & 0.504969719452346 & 0.252484859726173 \tabularnewline
22 & 0.724596359982256 & 0.550807280035488 & 0.275403640017744 \tabularnewline
23 & 0.675975286593944 & 0.648049426812112 & 0.324024713406056 \tabularnewline
24 & 0.759624611212188 & 0.480750777575625 & 0.240375388787812 \tabularnewline
25 & 0.74028073563245 & 0.519438528735099 & 0.259719264367549 \tabularnewline
26 & 0.791306721315375 & 0.417386557369249 & 0.208693278684625 \tabularnewline
27 & 0.742245505581885 & 0.515508988836231 & 0.257754494418115 \tabularnewline
28 & 0.732950625853426 & 0.534098748293149 & 0.267049374146574 \tabularnewline
29 & 0.966131009154233 & 0.067737981691533 & 0.0338689908457665 \tabularnewline
30 & 0.949839455727235 & 0.100321088545529 & 0.0501605442727646 \tabularnewline
31 & 0.937656429036802 & 0.124687141926397 & 0.0623435709631984 \tabularnewline
32 & 0.934563929953443 & 0.130872140093114 & 0.0654360700465571 \tabularnewline
33 & 0.884327938712213 & 0.231344122575574 & 0.115672061287787 \tabularnewline
34 & 0.819234270766169 & 0.361531458467662 & 0.180765729233831 \tabularnewline
35 & 0.771134674933003 & 0.457730650133994 & 0.228865325066997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57988&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]21[/C][C]0.747515140273827[/C][C]0.504969719452346[/C][C]0.252484859726173[/C][/ROW]
[ROW][C]22[/C][C]0.724596359982256[/C][C]0.550807280035488[/C][C]0.275403640017744[/C][/ROW]
[ROW][C]23[/C][C]0.675975286593944[/C][C]0.648049426812112[/C][C]0.324024713406056[/C][/ROW]
[ROW][C]24[/C][C]0.759624611212188[/C][C]0.480750777575625[/C][C]0.240375388787812[/C][/ROW]
[ROW][C]25[/C][C]0.74028073563245[/C][C]0.519438528735099[/C][C]0.259719264367549[/C][/ROW]
[ROW][C]26[/C][C]0.791306721315375[/C][C]0.417386557369249[/C][C]0.208693278684625[/C][/ROW]
[ROW][C]27[/C][C]0.742245505581885[/C][C]0.515508988836231[/C][C]0.257754494418115[/C][/ROW]
[ROW][C]28[/C][C]0.732950625853426[/C][C]0.534098748293149[/C][C]0.267049374146574[/C][/ROW]
[ROW][C]29[/C][C]0.966131009154233[/C][C]0.067737981691533[/C][C]0.0338689908457665[/C][/ROW]
[ROW][C]30[/C][C]0.949839455727235[/C][C]0.100321088545529[/C][C]0.0501605442727646[/C][/ROW]
[ROW][C]31[/C][C]0.937656429036802[/C][C]0.124687141926397[/C][C]0.0623435709631984[/C][/ROW]
[ROW][C]32[/C][C]0.934563929953443[/C][C]0.130872140093114[/C][C]0.0654360700465571[/C][/ROW]
[ROW][C]33[/C][C]0.884327938712213[/C][C]0.231344122575574[/C][C]0.115672061287787[/C][/ROW]
[ROW][C]34[/C][C]0.819234270766169[/C][C]0.361531458467662[/C][C]0.180765729233831[/C][/ROW]
[ROW][C]35[/C][C]0.771134674933003[/C][C]0.457730650133994[/C][C]0.228865325066997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57988&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57988&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
21	0.747515140273827	0.504969719452346	0.252484859726173
22	0.724596359982256	0.550807280035488	0.275403640017744
23	0.675975286593944	0.648049426812112	0.324024713406056
24	0.759624611212188	0.480750777575625	0.240375388787812
25	0.74028073563245	0.519438528735099	0.259719264367549
26	0.791306721315375	0.417386557369249	0.208693278684625
27	0.742245505581885	0.515508988836231	0.257754494418115
28	0.732950625853426	0.534098748293149	0.267049374146574
29	0.966131009154233	0.067737981691533	0.0338689908457665
30	0.949839455727235	0.100321088545529	0.0501605442727646
31	0.937656429036802	0.124687141926397	0.0623435709631984
32	0.934563929953443	0.130872140093114	0.0654360700465571
33	0.884327938712213	0.231344122575574	0.115672061287787
34	0.819234270766169	0.361531458467662	0.180765729233831
35	0.771134674933003	0.457730650133994	0.228865325066997

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	1	0.0666666666666667	OK

\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 & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 1 & 0.0666666666666667 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57988&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]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]1[/C][C]0.0666666666666667[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57988&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57988&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	0	0	OK
5% type I error level	0	0	OK
10% type I error level	1	0.0666666666666667	OK

Figure 1

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Postscript link

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Figure 2

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Figure 3

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Figure 4

PNG link

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PDF link

Figure 5

PNG link

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Figure 6

PNG link

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Figure 7

PNG link

Postscript link

PDF link

Figure 8

PNG link

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PDF link

Figure 9

PNG link

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PDF link

Figure 10

PNG link

Postscript link

PDF link

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')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code