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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 14 Dec 2009 08:04:18 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/14/t1260803138nvh8wzwoggg7tl1.htm/, Retrieved Sun, 05 May 2024 14:16:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67569, Retrieved Sun, 05 May 2024 14:16:26 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

121

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]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:10:54] [b98453cac15ba1066b407e146608df68]
-   PD      [Multiple Regression] [] [2009-12-14 15:04:18] [14869f38c4320b00c96ca15cc00142de] [Current]
-   P         [Multiple Regression] [] [2009-12-15 11:40:48] [69bbb86d5181c362d5647cae31af3dc7] 
-   PD        [Multiple Regression] [] [2009-12-15 11:51:37] [69bbb86d5181c362d5647cae31af3dc7] 
-   PD        [Multiple Regression] [] [2009-12-15 12:01:39] [69bbb86d5181c362d5647cae31af3dc7] 
-   P           [Multiple Regression] [] [2009-12-15 16:20:27] [69bbb86d5181c362d5647cae31af3dc7] 

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Dataseries X:

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Histogram

Boxplots

101.9	436	443	448	460	467
106.2	431	436	443	448	460
81	484	431	436	443	448
94.7	510	484	431	436	443
101	513	510	484	431	436
109.4	503	513	510	484	431
102.3	471	503	513	510	484
90.7	471	471	503	513	510
96.2	476	471	471	503	513
96.1	475	476	471	471	503
106	470	475	476	471	471
103.1	461	470	475	476	471
102	455	461	470	475	476
104.7	456	455	461	470	475
86	517	456	455	461	470
92.1	525	517	456	455	461
106.9	523	525	517	456	455
112.6	519	523	525	517	456
101.7	509	519	523	525	517
92	512	509	519	523	525
97.4	519	512	509	519	523
97	517	519	512	509	519
105.4	510	517	519	512	509
102.7	509	510	517	519	512
98.1	501	509	510	517	519
104.5	507	501	509	510	517
87.4	569	507	501	509	510
89.9	580	569	507	501	509
109.8	578	580	569	507	501
111.7	565	578	580	569	507
98.6	547	565	578	580	569
96.9	555	547	565	578	580
95.1	562	555	547	565	578
97	561	562	555	547	565
112.7	555	561	562	555	547
102.9	544	555	561	562	555
97.4	537	544	555	561	562
111.4	543	537	544	555	561
87.4	594	543	537	544	555
96.8	611	594	543	537	544
114.1	613	611	594	543	537
110.3	611	613	611	594	543
103.9	594	611	613	611	594
101.6	595	594	611	613	611
94.6	591	595	594	611	613
95.9	589	591	595	594	611
104.7	584	589	591	595	594
102.8	573	584	589	591	595
98.1	567	573	584	589	591
113.9	569	567	573	584	589
80.9	621	569	567	573	584
95.7	629	621	569	567	573
113.2	628	629	621	569	567
105.9	612	628	629	621	569
108.8	595	612	628	629	621
102.3	597	595	612	628	629
99	593	597	595	612	628
100.7	590	593	597	595	612
115.5	580	590	593	597	595
100.7	574	580	590	593	597
109.9	573	574	580	590	593
114.6	573	573	574	580	590
85.4	620	573	573	574	580
100.5	626	620	573	573	574
114.8	620	626	620	573	573
116.5	588	620	626	620	573
112.9	566	588	620	626	620
102	557	566	588	620	626

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67569&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]5 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=67569&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67569&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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Y[t] = -92.3660600861995 + 0.362630771674071X[t] + 1.14703119955930`Y(t-1)`[t] -0.110653706293974`Y(t-2)`[t] -0.103815643244524`Y(t-3)`[t] + 0.183897872205844`Y(t-4)`[t] + 1.43317238272469M1[t] + 6.22529402508988M2[t] + 67.9438754681637M3[t] + 15.8729539109853M4[t] + 2.56701819620161M5[t] -2.37172747838859M6[t] -13.0528345870745M7[t] + 9.09459620655353M8[t] + 6.3060061917542M9[t] + 2.08728280715477M10[t] -2.22348237189695M11[t] -0.410683199025563t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -92.3660600861995 +  0.362630771674071X[t] +  1.14703119955930`Y(t-1)`[t] -0.110653706293974`Y(t-2)`[t] -0.103815643244524`Y(t-3)`[t] +  0.183897872205844`Y(t-4)`[t] +  1.43317238272469M1[t] +  6.22529402508988M2[t] +  67.9438754681637M3[t] +  15.8729539109853M4[t] +  2.56701819620161M5[t] -2.37172747838859M6[t] -13.0528345870745M7[t] +  9.09459620655353M8[t] +  6.3060061917542M9[t] +  2.08728280715477M10[t] -2.22348237189695M11[t] -0.410683199025563t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67569&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -92.3660600861995 +  0.362630771674071X[t] +  1.14703119955930`Y(t-1)`[t] -0.110653706293974`Y(t-2)`[t] -0.103815643244524`Y(t-3)`[t] +  0.183897872205844`Y(t-4)`[t] +  1.43317238272469M1[t] +  6.22529402508988M2[t] +  67.9438754681637M3[t] +  15.8729539109853M4[t] +  2.56701819620161M5[t] -2.37172747838859M6[t] -13.0528345870745M7[t] +  9.09459620655353M8[t] +  6.3060061917542M9[t] +  2.08728280715477M10[t] -2.22348237189695M11[t] -0.410683199025563t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67569&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67569&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
Y[t] = -92.3660600861995 + 0.362630771674071X[t] + 1.14703119955930`Y(t-1)`[t] -0.110653706293974`Y(t-2)`[t] -0.103815643244524`Y(t-3)`[t] + 0.183897872205844`Y(t-4)`[t] + 1.43317238272469M1[t] + 6.22529402508988M2[t] + 67.9438754681637M3[t] + 15.8729539109853M4[t] + 2.56701819620161M5[t] -2.37172747838859M6[t] -13.0528345870745M7[t] + 9.09459620655353M8[t] + 6.3060061917542M9[t] + 2.08728280715477M10[t] -2.22348237189695M11[t] -0.410683199025563t + 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)	-92.3660600861995	40.930368	-2.2567	0.028432	0.014216
X	0.362630771674071	0.240401	1.5084	0.137735	0.068867
`Y(t-1)`	1.14703119955930	0.13991	8.1984	0	0
`Y(t-2)`	-0.110653706293974	0.21447	-0.5159	0.608171	0.304085
`Y(t-3)`	-0.103815643244524	0.236329	-0.4393	0.662349	0.331174
`Y(t-4)`	0.183897872205844	0.169614	1.0842	0.28347	0.141735
M1	1.43317238272469	3.430056	0.4178	0.677862	0.338931
M2	6.22529402508988	4.044369	1.5392	0.130049	0.065024
M3	67.9438754681637	5.705618	11.9082	0	0
M4	15.8729539109853	9.395397	1.6894	0.097362	0.048681
M5	2.56701819620161	9.354512	0.2744	0.784896	0.392448
M6	-2.37172747838859	8.773154	-0.2703	0.788012	0.394006
M7	-13.0528345870745	3.919804	-3.33	0.001637	0.000819
M8	9.09459620655353	4.469141	2.035	0.047172	0.023586
M9	6.3060061917542	4.976633	1.2671	0.210982	0.105491
M10	2.08728280715477	4.960015	0.4208	0.675688	0.337844
M11	-2.22348237189695	3.888194	-0.5719	0.569983	0.284991
t	-0.410683199025563	0.162294	-2.5305	0.014585	0.007292

\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) & -92.3660600861995 & 40.930368 & -2.2567 & 0.028432 & 0.014216 \tabularnewline
X & 0.362630771674071 & 0.240401 & 1.5084 & 0.137735 & 0.068867 \tabularnewline
`Y(t-1)` & 1.14703119955930 & 0.13991 & 8.1984 & 0 & 0 \tabularnewline
`Y(t-2)` & -0.110653706293974 & 0.21447 & -0.5159 & 0.608171 & 0.304085 \tabularnewline
`Y(t-3)` & -0.103815643244524 & 0.236329 & -0.4393 & 0.662349 & 0.331174 \tabularnewline
`Y(t-4)` & 0.183897872205844 & 0.169614 & 1.0842 & 0.28347 & 0.141735 \tabularnewline
M1 & 1.43317238272469 & 3.430056 & 0.4178 & 0.677862 & 0.338931 \tabularnewline
M2 & 6.22529402508988 & 4.044369 & 1.5392 & 0.130049 & 0.065024 \tabularnewline
M3 & 67.9438754681637 & 5.705618 & 11.9082 & 0 & 0 \tabularnewline
M4 & 15.8729539109853 & 9.395397 & 1.6894 & 0.097362 & 0.048681 \tabularnewline
M5 & 2.56701819620161 & 9.354512 & 0.2744 & 0.784896 & 0.392448 \tabularnewline
M6 & -2.37172747838859 & 8.773154 & -0.2703 & 0.788012 & 0.394006 \tabularnewline
M7 & -13.0528345870745 & 3.919804 & -3.33 & 0.001637 & 0.000819 \tabularnewline
M8 & 9.09459620655353 & 4.469141 & 2.035 & 0.047172 & 0.023586 \tabularnewline
M9 & 6.3060061917542 & 4.976633 & 1.2671 & 0.210982 & 0.105491 \tabularnewline
M10 & 2.08728280715477 & 4.960015 & 0.4208 & 0.675688 & 0.337844 \tabularnewline
M11 & -2.22348237189695 & 3.888194 & -0.5719 & 0.569983 & 0.284991 \tabularnewline
t & -0.410683199025563 & 0.162294 & -2.5305 & 0.014585 & 0.007292 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67569&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]-92.3660600861995[/C][C]40.930368[/C][C]-2.2567[/C][C]0.028432[/C][C]0.014216[/C][/ROW]
[ROW][C]X[/C][C]0.362630771674071[/C][C]0.240401[/C][C]1.5084[/C][C]0.137735[/C][C]0.068867[/C][/ROW]
[ROW][C]`Y(t-1)`[/C][C]1.14703119955930[/C][C]0.13991[/C][C]8.1984[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Y(t-2)`[/C][C]-0.110653706293974[/C][C]0.21447[/C][C]-0.5159[/C][C]0.608171[/C][C]0.304085[/C][/ROW]
[ROW][C]`Y(t-3)`[/C][C]-0.103815643244524[/C][C]0.236329[/C][C]-0.4393[/C][C]0.662349[/C][C]0.331174[/C][/ROW]
[ROW][C]`Y(t-4)`[/C][C]0.183897872205844[/C][C]0.169614[/C][C]1.0842[/C][C]0.28347[/C][C]0.141735[/C][/ROW]
[ROW][C]M1[/C][C]1.43317238272469[/C][C]3.430056[/C][C]0.4178[/C][C]0.677862[/C][C]0.338931[/C][/ROW]
[ROW][C]M2[/C][C]6.22529402508988[/C][C]4.044369[/C][C]1.5392[/C][C]0.130049[/C][C]0.065024[/C][/ROW]
[ROW][C]M3[/C][C]67.9438754681637[/C][C]5.705618[/C][C]11.9082[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M4[/C][C]15.8729539109853[/C][C]9.395397[/C][C]1.6894[/C][C]0.097362[/C][C]0.048681[/C][/ROW]
[ROW][C]M5[/C][C]2.56701819620161[/C][C]9.354512[/C][C]0.2744[/C][C]0.784896[/C][C]0.392448[/C][/ROW]
[ROW][C]M6[/C][C]-2.37172747838859[/C][C]8.773154[/C][C]-0.2703[/C][C]0.788012[/C][C]0.394006[/C][/ROW]
[ROW][C]M7[/C][C]-13.0528345870745[/C][C]3.919804[/C][C]-3.33[/C][C]0.001637[/C][C]0.000819[/C][/ROW]
[ROW][C]M8[/C][C]9.09459620655353[/C][C]4.469141[/C][C]2.035[/C][C]0.047172[/C][C]0.023586[/C][/ROW]
[ROW][C]M9[/C][C]6.3060061917542[/C][C]4.976633[/C][C]1.2671[/C][C]0.210982[/C][C]0.105491[/C][/ROW]
[ROW][C]M10[/C][C]2.08728280715477[/C][C]4.960015[/C][C]0.4208[/C][C]0.675688[/C][C]0.337844[/C][/ROW]
[ROW][C]M11[/C][C]-2.22348237189695[/C][C]3.888194[/C][C]-0.5719[/C][C]0.569983[/C][C]0.284991[/C][/ROW]
[ROW][C]t[/C][C]-0.410683199025563[/C][C]0.162294[/C][C]-2.5305[/C][C]0.014585[/C][C]0.007292[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67569&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67569&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)	-92.3660600861995	40.930368	-2.2567	0.028432	0.014216
X	0.362630771674071	0.240401	1.5084	0.137735	0.068867
`Y(t-1)`	1.14703119955930	0.13991	8.1984	0	0
`Y(t-2)`	-0.110653706293974	0.21447	-0.5159	0.608171	0.304085
`Y(t-3)`	-0.103815643244524	0.236329	-0.4393	0.662349	0.331174
`Y(t-4)`	0.183897872205844	0.169614	1.0842	0.28347	0.141735
M1	1.43317238272469	3.430056	0.4178	0.677862	0.338931
M2	6.22529402508988	4.044369	1.5392	0.130049	0.065024
M3	67.9438754681637	5.705618	11.9082	0	0
M4	15.8729539109853	9.395397	1.6894	0.097362	0.048681
M5	2.56701819620161	9.354512	0.2744	0.784896	0.392448
M6	-2.37172747838859	8.773154	-0.2703	0.788012	0.394006
M7	-13.0528345870745	3.919804	-3.33	0.001637	0.000819
M8	9.09459620655353	4.469141	2.035	0.047172	0.023586
M9	6.3060061917542	4.976633	1.2671	0.210982	0.105491
M10	2.08728280715477	4.960015	0.4208	0.675688	0.337844
M11	-2.22348237189695	3.888194	-0.5719	0.569983	0.284991
t	-0.410683199025563	0.162294	-2.5305	0.014585	0.007292

Multiple Linear Regression - Regression Statistics
Multiple R	0.996010944770597
R-squared	0.992037802102818
Adjusted R-squared	0.989330654817775
F-TEST (value)	366.451359179527
F-TEST (DF numerator)	17
F-TEST (DF denominator)	50
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.39666594775882
Sum Squared Residuals	1456.20016758498

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.996010944770597 \tabularnewline
R-squared & 0.992037802102818 \tabularnewline
Adjusted R-squared & 0.989330654817775 \tabularnewline
F-TEST (value) & 366.451359179527 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 50 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 5.39666594775882 \tabularnewline
Sum Squared Residuals & 1456.20016758498 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67569&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.996010944770597[/C][/ROW]
[ROW][C]R-squared[/C][C]0.992037802102818[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.989330654817775[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]366.451359179527[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]50[/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]5.39666594775882[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1456.20016758498[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67569&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67569&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	0.996010944770597
R-squared	0.992037802102818
Adjusted R-squared	0.989330654817775
F-TEST (value)	366.451359179527
F-TEST (DF numerator)	17
F-TEST (DF denominator)	50
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.39666594775882
Sum Squared Residuals	1456.20016758498

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	436	442.295576143808	-6.29557614380812
2	431	440.718879653393	-9.71887965339332
3	484	486.240206147269	-2.24020614726883
4	510	499.879785212795	10.1202147872049
5	513	511.637698026276	1.36230197372448
6	503	503.476746416768	-0.476746416767555
7	471	485.055385018247	-14.0553850182473
8	471	471.457052086091	-0.457052086090865
9	476	475.383016766943	0.616983233056703
10	475	477.935624965714	-2.93562496571377
11	470	469.219189585594	0.78081041440638
12	461	463.836779012885	-2.83677901288505
13	455	455.713667087453	-0.713667087452525
14	456	455.523085117619	0.476914882381125
15	517	511.875592796857	5.12440720314337
16	525	530.432098224303	-5.43209822430274
17	523	523.301585367332	-0.301585367332146
18	519	510.691003477078	8.30899652292194
19	509	501.66696543107	7.33303456892982
20	512	510.537311634153	1.46268836584718
21	519	513.891342077552	5.10865792244803
22	517	517.116705406912	-0.116705406912436
23	510	510.222291515929	-0.222291515928921
24	509	503.073060734859	5.92693926514102
25	501	503.549909505286	-2.54990950528584
26	507	501.545502755459	5.45449724454095
27	569	563.236362189392	5.76363781060809
28	580	582.759973771037	-2.75997377103660
29	578	579.922443781353	-1.92244378135339
30	565	566.41757755764	-1.41757755764060
31	547	546.144921960388	0.85507803961171
32	555	550.287641713652	4.71235828634762
33	562	558.585457038347	3.41454296165276
34	561	561.267046907192	-0.267046907191797
35	555	556.176607655119	-1.17660765511894
36	544	548.408565249458	-4.40856524945765
37	537	536.874264980246	0.125735019753701
38	543	539.959502586603	3.0404974133972
39	594	600.259610294342	-6.25961029434169
40	611	607.725236640082	3.27476335991787
41	613	612.228142482842	0.771857517158244
42	611	601.72245549675	9.2775445032501
43	594	593.408383985959	0.591616014041096
44	595	597.951490366801	-2.95149036680107
45	591	595.817372988715	-4.8173729887153
46	589	588.35767809448	0.642321905519389
47	584	581.745853462449	2.25414653755141
48	573	577.954966029115	-4.95496602911459
49	567	564.681055719929	2.31894428007122
50	569	569.278346399407	-0.278346399407539
51	621	621.799896529754	-0.799896529754448
52	629	632.709559424026	-3.70955942402556
53	628	627.450217363976	0.549782636023795
54	612	612.390705302925	-0.39070530292505
55	595	592.840862955161	2.15913704483890
56	597	596.066438062969	0.933561937031172
57	593	597.322811128442	-4.3228111284422
58	590	587.322944625701	2.67705537429862
59	580	581.63605778091	-1.63605778090994
60	574	567.726628973684	6.27337102631626
61	573	565.885526563278	7.11447343672159
62	573	571.974683487518	1.02531651248158
63	620	621.588332042386	-1.58833204238650
64	626	627.493346727758	-1.49334672775785
65	620	620.459912978221	-0.459912978220981
66	588	603.301511748839	-15.3015117488388
67	566	562.883480649174	3.11651935082574
68	557	560.700066136334	-3.70006613633404

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 436 & 442.295576143808 & -6.29557614380812 \tabularnewline
2 & 431 & 440.718879653393 & -9.71887965339332 \tabularnewline
3 & 484 & 486.240206147269 & -2.24020614726883 \tabularnewline
4 & 510 & 499.879785212795 & 10.1202147872049 \tabularnewline
5 & 513 & 511.637698026276 & 1.36230197372448 \tabularnewline
6 & 503 & 503.476746416768 & -0.476746416767555 \tabularnewline
7 & 471 & 485.055385018247 & -14.0553850182473 \tabularnewline
8 & 471 & 471.457052086091 & -0.457052086090865 \tabularnewline
9 & 476 & 475.383016766943 & 0.616983233056703 \tabularnewline
10 & 475 & 477.935624965714 & -2.93562496571377 \tabularnewline
11 & 470 & 469.219189585594 & 0.78081041440638 \tabularnewline
12 & 461 & 463.836779012885 & -2.83677901288505 \tabularnewline
13 & 455 & 455.713667087453 & -0.713667087452525 \tabularnewline
14 & 456 & 455.523085117619 & 0.476914882381125 \tabularnewline
15 & 517 & 511.875592796857 & 5.12440720314337 \tabularnewline
16 & 525 & 530.432098224303 & -5.43209822430274 \tabularnewline
17 & 523 & 523.301585367332 & -0.301585367332146 \tabularnewline
18 & 519 & 510.691003477078 & 8.30899652292194 \tabularnewline
19 & 509 & 501.66696543107 & 7.33303456892982 \tabularnewline
20 & 512 & 510.537311634153 & 1.46268836584718 \tabularnewline
21 & 519 & 513.891342077552 & 5.10865792244803 \tabularnewline
22 & 517 & 517.116705406912 & -0.116705406912436 \tabularnewline
23 & 510 & 510.222291515929 & -0.222291515928921 \tabularnewline
24 & 509 & 503.073060734859 & 5.92693926514102 \tabularnewline
25 & 501 & 503.549909505286 & -2.54990950528584 \tabularnewline
26 & 507 & 501.545502755459 & 5.45449724454095 \tabularnewline
27 & 569 & 563.236362189392 & 5.76363781060809 \tabularnewline
28 & 580 & 582.759973771037 & -2.75997377103660 \tabularnewline
29 & 578 & 579.922443781353 & -1.92244378135339 \tabularnewline
30 & 565 & 566.41757755764 & -1.41757755764060 \tabularnewline
31 & 547 & 546.144921960388 & 0.85507803961171 \tabularnewline
32 & 555 & 550.287641713652 & 4.71235828634762 \tabularnewline
33 & 562 & 558.585457038347 & 3.41454296165276 \tabularnewline
34 & 561 & 561.267046907192 & -0.267046907191797 \tabularnewline
35 & 555 & 556.176607655119 & -1.17660765511894 \tabularnewline
36 & 544 & 548.408565249458 & -4.40856524945765 \tabularnewline
37 & 537 & 536.874264980246 & 0.125735019753701 \tabularnewline
38 & 543 & 539.959502586603 & 3.0404974133972 \tabularnewline
39 & 594 & 600.259610294342 & -6.25961029434169 \tabularnewline
40 & 611 & 607.725236640082 & 3.27476335991787 \tabularnewline
41 & 613 & 612.228142482842 & 0.771857517158244 \tabularnewline
42 & 611 & 601.72245549675 & 9.2775445032501 \tabularnewline
43 & 594 & 593.408383985959 & 0.591616014041096 \tabularnewline
44 & 595 & 597.951490366801 & -2.95149036680107 \tabularnewline
45 & 591 & 595.817372988715 & -4.8173729887153 \tabularnewline
46 & 589 & 588.35767809448 & 0.642321905519389 \tabularnewline
47 & 584 & 581.745853462449 & 2.25414653755141 \tabularnewline
48 & 573 & 577.954966029115 & -4.95496602911459 \tabularnewline
49 & 567 & 564.681055719929 & 2.31894428007122 \tabularnewline
50 & 569 & 569.278346399407 & -0.278346399407539 \tabularnewline
51 & 621 & 621.799896529754 & -0.799896529754448 \tabularnewline
52 & 629 & 632.709559424026 & -3.70955942402556 \tabularnewline
53 & 628 & 627.450217363976 & 0.549782636023795 \tabularnewline
54 & 612 & 612.390705302925 & -0.39070530292505 \tabularnewline
55 & 595 & 592.840862955161 & 2.15913704483890 \tabularnewline
56 & 597 & 596.066438062969 & 0.933561937031172 \tabularnewline
57 & 593 & 597.322811128442 & -4.3228111284422 \tabularnewline
58 & 590 & 587.322944625701 & 2.67705537429862 \tabularnewline
59 & 580 & 581.63605778091 & -1.63605778090994 \tabularnewline
60 & 574 & 567.726628973684 & 6.27337102631626 \tabularnewline
61 & 573 & 565.885526563278 & 7.11447343672159 \tabularnewline
62 & 573 & 571.974683487518 & 1.02531651248158 \tabularnewline
63 & 620 & 621.588332042386 & -1.58833204238650 \tabularnewline
64 & 626 & 627.493346727758 & -1.49334672775785 \tabularnewline
65 & 620 & 620.459912978221 & -0.459912978220981 \tabularnewline
66 & 588 & 603.301511748839 & -15.3015117488388 \tabularnewline
67 & 566 & 562.883480649174 & 3.11651935082574 \tabularnewline
68 & 557 & 560.700066136334 & -3.70006613633404 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67569&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]436[/C][C]442.295576143808[/C][C]-6.29557614380812[/C][/ROW]
[ROW][C]2[/C][C]431[/C][C]440.718879653393[/C][C]-9.71887965339332[/C][/ROW]
[ROW][C]3[/C][C]484[/C][C]486.240206147269[/C][C]-2.24020614726883[/C][/ROW]
[ROW][C]4[/C][C]510[/C][C]499.879785212795[/C][C]10.1202147872049[/C][/ROW]
[ROW][C]5[/C][C]513[/C][C]511.637698026276[/C][C]1.36230197372448[/C][/ROW]
[ROW][C]6[/C][C]503[/C][C]503.476746416768[/C][C]-0.476746416767555[/C][/ROW]
[ROW][C]7[/C][C]471[/C][C]485.055385018247[/C][C]-14.0553850182473[/C][/ROW]
[ROW][C]8[/C][C]471[/C][C]471.457052086091[/C][C]-0.457052086090865[/C][/ROW]
[ROW][C]9[/C][C]476[/C][C]475.383016766943[/C][C]0.616983233056703[/C][/ROW]
[ROW][C]10[/C][C]475[/C][C]477.935624965714[/C][C]-2.93562496571377[/C][/ROW]
[ROW][C]11[/C][C]470[/C][C]469.219189585594[/C][C]0.78081041440638[/C][/ROW]
[ROW][C]12[/C][C]461[/C][C]463.836779012885[/C][C]-2.83677901288505[/C][/ROW]
[ROW][C]13[/C][C]455[/C][C]455.713667087453[/C][C]-0.713667087452525[/C][/ROW]
[ROW][C]14[/C][C]456[/C][C]455.523085117619[/C][C]0.476914882381125[/C][/ROW]
[ROW][C]15[/C][C]517[/C][C]511.875592796857[/C][C]5.12440720314337[/C][/ROW]
[ROW][C]16[/C][C]525[/C][C]530.432098224303[/C][C]-5.43209822430274[/C][/ROW]
[ROW][C]17[/C][C]523[/C][C]523.301585367332[/C][C]-0.301585367332146[/C][/ROW]
[ROW][C]18[/C][C]519[/C][C]510.691003477078[/C][C]8.30899652292194[/C][/ROW]
[ROW][C]19[/C][C]509[/C][C]501.66696543107[/C][C]7.33303456892982[/C][/ROW]
[ROW][C]20[/C][C]512[/C][C]510.537311634153[/C][C]1.46268836584718[/C][/ROW]
[ROW][C]21[/C][C]519[/C][C]513.891342077552[/C][C]5.10865792244803[/C][/ROW]
[ROW][C]22[/C][C]517[/C][C]517.116705406912[/C][C]-0.116705406912436[/C][/ROW]
[ROW][C]23[/C][C]510[/C][C]510.222291515929[/C][C]-0.222291515928921[/C][/ROW]
[ROW][C]24[/C][C]509[/C][C]503.073060734859[/C][C]5.92693926514102[/C][/ROW]
[ROW][C]25[/C][C]501[/C][C]503.549909505286[/C][C]-2.54990950528584[/C][/ROW]
[ROW][C]26[/C][C]507[/C][C]501.545502755459[/C][C]5.45449724454095[/C][/ROW]
[ROW][C]27[/C][C]569[/C][C]563.236362189392[/C][C]5.76363781060809[/C][/ROW]
[ROW][C]28[/C][C]580[/C][C]582.759973771037[/C][C]-2.75997377103660[/C][/ROW]
[ROW][C]29[/C][C]578[/C][C]579.922443781353[/C][C]-1.92244378135339[/C][/ROW]
[ROW][C]30[/C][C]565[/C][C]566.41757755764[/C][C]-1.41757755764060[/C][/ROW]
[ROW][C]31[/C][C]547[/C][C]546.144921960388[/C][C]0.85507803961171[/C][/ROW]
[ROW][C]32[/C][C]555[/C][C]550.287641713652[/C][C]4.71235828634762[/C][/ROW]
[ROW][C]33[/C][C]562[/C][C]558.585457038347[/C][C]3.41454296165276[/C][/ROW]
[ROW][C]34[/C][C]561[/C][C]561.267046907192[/C][C]-0.267046907191797[/C][/ROW]
[ROW][C]35[/C][C]555[/C][C]556.176607655119[/C][C]-1.17660765511894[/C][/ROW]
[ROW][C]36[/C][C]544[/C][C]548.408565249458[/C][C]-4.40856524945765[/C][/ROW]
[ROW][C]37[/C][C]537[/C][C]536.874264980246[/C][C]0.125735019753701[/C][/ROW]
[ROW][C]38[/C][C]543[/C][C]539.959502586603[/C][C]3.0404974133972[/C][/ROW]
[ROW][C]39[/C][C]594[/C][C]600.259610294342[/C][C]-6.25961029434169[/C][/ROW]
[ROW][C]40[/C][C]611[/C][C]607.725236640082[/C][C]3.27476335991787[/C][/ROW]
[ROW][C]41[/C][C]613[/C][C]612.228142482842[/C][C]0.771857517158244[/C][/ROW]
[ROW][C]42[/C][C]611[/C][C]601.72245549675[/C][C]9.2775445032501[/C][/ROW]
[ROW][C]43[/C][C]594[/C][C]593.408383985959[/C][C]0.591616014041096[/C][/ROW]
[ROW][C]44[/C][C]595[/C][C]597.951490366801[/C][C]-2.95149036680107[/C][/ROW]
[ROW][C]45[/C][C]591[/C][C]595.817372988715[/C][C]-4.8173729887153[/C][/ROW]
[ROW][C]46[/C][C]589[/C][C]588.35767809448[/C][C]0.642321905519389[/C][/ROW]
[ROW][C]47[/C][C]584[/C][C]581.745853462449[/C][C]2.25414653755141[/C][/ROW]
[ROW][C]48[/C][C]573[/C][C]577.954966029115[/C][C]-4.95496602911459[/C][/ROW]
[ROW][C]49[/C][C]567[/C][C]564.681055719929[/C][C]2.31894428007122[/C][/ROW]
[ROW][C]50[/C][C]569[/C][C]569.278346399407[/C][C]-0.278346399407539[/C][/ROW]
[ROW][C]51[/C][C]621[/C][C]621.799896529754[/C][C]-0.799896529754448[/C][/ROW]
[ROW][C]52[/C][C]629[/C][C]632.709559424026[/C][C]-3.70955942402556[/C][/ROW]
[ROW][C]53[/C][C]628[/C][C]627.450217363976[/C][C]0.549782636023795[/C][/ROW]
[ROW][C]54[/C][C]612[/C][C]612.390705302925[/C][C]-0.39070530292505[/C][/ROW]
[ROW][C]55[/C][C]595[/C][C]592.840862955161[/C][C]2.15913704483890[/C][/ROW]
[ROW][C]56[/C][C]597[/C][C]596.066438062969[/C][C]0.933561937031172[/C][/ROW]
[ROW][C]57[/C][C]593[/C][C]597.322811128442[/C][C]-4.3228111284422[/C][/ROW]
[ROW][C]58[/C][C]590[/C][C]587.322944625701[/C][C]2.67705537429862[/C][/ROW]
[ROW][C]59[/C][C]580[/C][C]581.63605778091[/C][C]-1.63605778090994[/C][/ROW]
[ROW][C]60[/C][C]574[/C][C]567.726628973684[/C][C]6.27337102631626[/C][/ROW]
[ROW][C]61[/C][C]573[/C][C]565.885526563278[/C][C]7.11447343672159[/C][/ROW]
[ROW][C]62[/C][C]573[/C][C]571.974683487518[/C][C]1.02531651248158[/C][/ROW]
[ROW][C]63[/C][C]620[/C][C]621.588332042386[/C][C]-1.58833204238650[/C][/ROW]
[ROW][C]64[/C][C]626[/C][C]627.493346727758[/C][C]-1.49334672775785[/C][/ROW]
[ROW][C]65[/C][C]620[/C][C]620.459912978221[/C][C]-0.459912978220981[/C][/ROW]
[ROW][C]66[/C][C]588[/C][C]603.301511748839[/C][C]-15.3015117488388[/C][/ROW]
[ROW][C]67[/C][C]566[/C][C]562.883480649174[/C][C]3.11651935082574[/C][/ROW]
[ROW][C]68[/C][C]557[/C][C]560.700066136334[/C][C]-3.70006613633404[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67569&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67569&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	436	442.295576143808	-6.29557614380812
2	431	440.718879653393	-9.71887965339332
3	484	486.240206147269	-2.24020614726883
4	510	499.879785212795	10.1202147872049
5	513	511.637698026276	1.36230197372448
6	503	503.476746416768	-0.476746416767555
7	471	485.055385018247	-14.0553850182473
8	471	471.457052086091	-0.457052086090865
9	476	475.383016766943	0.616983233056703
10	475	477.935624965714	-2.93562496571377
11	470	469.219189585594	0.78081041440638
12	461	463.836779012885	-2.83677901288505
13	455	455.713667087453	-0.713667087452525
14	456	455.523085117619	0.476914882381125
15	517	511.875592796857	5.12440720314337
16	525	530.432098224303	-5.43209822430274
17	523	523.301585367332	-0.301585367332146
18	519	510.691003477078	8.30899652292194
19	509	501.66696543107	7.33303456892982
20	512	510.537311634153	1.46268836584718
21	519	513.891342077552	5.10865792244803
22	517	517.116705406912	-0.116705406912436
23	510	510.222291515929	-0.222291515928921
24	509	503.073060734859	5.92693926514102
25	501	503.549909505286	-2.54990950528584
26	507	501.545502755459	5.45449724454095
27	569	563.236362189392	5.76363781060809
28	580	582.759973771037	-2.75997377103660
29	578	579.922443781353	-1.92244378135339
30	565	566.41757755764	-1.41757755764060
31	547	546.144921960388	0.85507803961171
32	555	550.287641713652	4.71235828634762
33	562	558.585457038347	3.41454296165276
34	561	561.267046907192	-0.267046907191797
35	555	556.176607655119	-1.17660765511894
36	544	548.408565249458	-4.40856524945765
37	537	536.874264980246	0.125735019753701
38	543	539.959502586603	3.0404974133972
39	594	600.259610294342	-6.25961029434169
40	611	607.725236640082	3.27476335991787
41	613	612.228142482842	0.771857517158244
42	611	601.72245549675	9.2775445032501
43	594	593.408383985959	0.591616014041096
44	595	597.951490366801	-2.95149036680107
45	591	595.817372988715	-4.8173729887153
46	589	588.35767809448	0.642321905519389
47	584	581.745853462449	2.25414653755141
48	573	577.954966029115	-4.95496602911459
49	567	564.681055719929	2.31894428007122
50	569	569.278346399407	-0.278346399407539
51	621	621.799896529754	-0.799896529754448
52	629	632.709559424026	-3.70955942402556
53	628	627.450217363976	0.549782636023795
54	612	612.390705302925	-0.39070530292505
55	595	592.840862955161	2.15913704483890
56	597	596.066438062969	0.933561937031172
57	593	597.322811128442	-4.3228111284422
58	590	587.322944625701	2.67705537429862
59	580	581.63605778091	-1.63605778090994
60	574	567.726628973684	6.27337102631626
61	573	565.885526563278	7.11447343672159
62	573	571.974683487518	1.02531651248158
63	620	621.588332042386	-1.58833204238650
64	626	627.493346727758	-1.49334672775785
65	620	620.459912978221	-0.459912978220981
66	588	603.301511748839	-15.3015117488388
67	566	562.883480649174	3.11651935082574
68	557	560.700066136334	-3.70006613633404

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
21	0.95892248465378	0.0821550306924388	0.0410775153462194
22	0.96228136152731	0.0754372769453798	0.0377186384726899
23	0.928001956836039	0.143996086327923	0.0719980431639614
24	0.900706140343339	0.198587719313323	0.0992938596566614
25	0.870298752791565	0.259402494416869	0.129701247208435
26	0.8263292515386	0.347341496922799	0.173670748461399
27	0.807994731864986	0.384010536270029	0.192005268135014
28	0.798164107725607	0.403671784548785	0.201835892274393
29	0.771914047873933	0.456171904252134	0.228085952126067
30	0.757501189768281	0.484997620463438	0.242498810231719
31	0.696912596813477	0.606174806373046	0.303087403186523
32	0.615181836920694	0.769636326158612	0.384818163079306
33	0.56428753184188	0.87142493631624	0.43571246815812
34	0.493731894464299	0.987463788928598	0.506268105535701
35	0.409335992290908	0.818671984581815	0.590664007709092
36	0.370718822481043	0.741437644962086	0.629281177518957
37	0.39594667414585	0.7918933482917	0.60405332585415
38	0.300049913927194	0.600099827854388	0.699950086072806
39	0.379760108044419	0.759520216088838	0.620239891955581
40	0.282876353745788	0.565752707491576	0.717123646254212
41	0.213517943990979	0.427035887981958	0.786482056009021
42	0.684346671617592	0.631306656764816	0.315653328382408
43	0.579738478971633	0.840523042056733	0.420261521028367
44	0.495093142471813	0.990186284943626	0.504906857528187
45	0.420603296942968	0.841206593885936	0.579396703057032
46	0.284537259739542	0.569074519479084	0.715462740260458
47	0.165659659573057	0.331319319146114	0.834340340426943

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.95892248465378 & 0.0821550306924388 & 0.0410775153462194 \tabularnewline
22 & 0.96228136152731 & 0.0754372769453798 & 0.0377186384726899 \tabularnewline
23 & 0.928001956836039 & 0.143996086327923 & 0.0719980431639614 \tabularnewline
24 & 0.900706140343339 & 0.198587719313323 & 0.0992938596566614 \tabularnewline
25 & 0.870298752791565 & 0.259402494416869 & 0.129701247208435 \tabularnewline
26 & 0.8263292515386 & 0.347341496922799 & 0.173670748461399 \tabularnewline
27 & 0.807994731864986 & 0.384010536270029 & 0.192005268135014 \tabularnewline
28 & 0.798164107725607 & 0.403671784548785 & 0.201835892274393 \tabularnewline
29 & 0.771914047873933 & 0.456171904252134 & 0.228085952126067 \tabularnewline
30 & 0.757501189768281 & 0.484997620463438 & 0.242498810231719 \tabularnewline
31 & 0.696912596813477 & 0.606174806373046 & 0.303087403186523 \tabularnewline
32 & 0.615181836920694 & 0.769636326158612 & 0.384818163079306 \tabularnewline
33 & 0.56428753184188 & 0.87142493631624 & 0.43571246815812 \tabularnewline
34 & 0.493731894464299 & 0.987463788928598 & 0.506268105535701 \tabularnewline
35 & 0.409335992290908 & 0.818671984581815 & 0.590664007709092 \tabularnewline
36 & 0.370718822481043 & 0.741437644962086 & 0.629281177518957 \tabularnewline
37 & 0.39594667414585 & 0.7918933482917 & 0.60405332585415 \tabularnewline
38 & 0.300049913927194 & 0.600099827854388 & 0.699950086072806 \tabularnewline
39 & 0.379760108044419 & 0.759520216088838 & 0.620239891955581 \tabularnewline
40 & 0.282876353745788 & 0.565752707491576 & 0.717123646254212 \tabularnewline
41 & 0.213517943990979 & 0.427035887981958 & 0.786482056009021 \tabularnewline
42 & 0.684346671617592 & 0.631306656764816 & 0.315653328382408 \tabularnewline
43 & 0.579738478971633 & 0.840523042056733 & 0.420261521028367 \tabularnewline
44 & 0.495093142471813 & 0.990186284943626 & 0.504906857528187 \tabularnewline
45 & 0.420603296942968 & 0.841206593885936 & 0.579396703057032 \tabularnewline
46 & 0.284537259739542 & 0.569074519479084 & 0.715462740260458 \tabularnewline
47 & 0.165659659573057 & 0.331319319146114 & 0.834340340426943 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67569&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]0.95892248465378[/C][C]0.0821550306924388[/C][C]0.0410775153462194[/C][/ROW]
[ROW][C]22[/C][C]0.96228136152731[/C][C]0.0754372769453798[/C][C]0.0377186384726899[/C][/ROW]
[ROW][C]23[/C][C]0.928001956836039[/C][C]0.143996086327923[/C][C]0.0719980431639614[/C][/ROW]
[ROW][C]24[/C][C]0.900706140343339[/C][C]0.198587719313323[/C][C]0.0992938596566614[/C][/ROW]
[ROW][C]25[/C][C]0.870298752791565[/C][C]0.259402494416869[/C][C]0.129701247208435[/C][/ROW]
[ROW][C]26[/C][C]0.8263292515386[/C][C]0.347341496922799[/C][C]0.173670748461399[/C][/ROW]
[ROW][C]27[/C][C]0.807994731864986[/C][C]0.384010536270029[/C][C]0.192005268135014[/C][/ROW]
[ROW][C]28[/C][C]0.798164107725607[/C][C]0.403671784548785[/C][C]0.201835892274393[/C][/ROW]
[ROW][C]29[/C][C]0.771914047873933[/C][C]0.456171904252134[/C][C]0.228085952126067[/C][/ROW]
[ROW][C]30[/C][C]0.757501189768281[/C][C]0.484997620463438[/C][C]0.242498810231719[/C][/ROW]
[ROW][C]31[/C][C]0.696912596813477[/C][C]0.606174806373046[/C][C]0.303087403186523[/C][/ROW]
[ROW][C]32[/C][C]0.615181836920694[/C][C]0.769636326158612[/C][C]0.384818163079306[/C][/ROW]
[ROW][C]33[/C][C]0.56428753184188[/C][C]0.87142493631624[/C][C]0.43571246815812[/C][/ROW]
[ROW][C]34[/C][C]0.493731894464299[/C][C]0.987463788928598[/C][C]0.506268105535701[/C][/ROW]
[ROW][C]35[/C][C]0.409335992290908[/C][C]0.818671984581815[/C][C]0.590664007709092[/C][/ROW]
[ROW][C]36[/C][C]0.370718822481043[/C][C]0.741437644962086[/C][C]0.629281177518957[/C][/ROW]
[ROW][C]37[/C][C]0.39594667414585[/C][C]0.7918933482917[/C][C]0.60405332585415[/C][/ROW]
[ROW][C]38[/C][C]0.300049913927194[/C][C]0.600099827854388[/C][C]0.699950086072806[/C][/ROW]
[ROW][C]39[/C][C]0.379760108044419[/C][C]0.759520216088838[/C][C]0.620239891955581[/C][/ROW]
[ROW][C]40[/C][C]0.282876353745788[/C][C]0.565752707491576[/C][C]0.717123646254212[/C][/ROW]
[ROW][C]41[/C][C]0.213517943990979[/C][C]0.427035887981958[/C][C]0.786482056009021[/C][/ROW]
[ROW][C]42[/C][C]0.684346671617592[/C][C]0.631306656764816[/C][C]0.315653328382408[/C][/ROW]
[ROW][C]43[/C][C]0.579738478971633[/C][C]0.840523042056733[/C][C]0.420261521028367[/C][/ROW]
[ROW][C]44[/C][C]0.495093142471813[/C][C]0.990186284943626[/C][C]0.504906857528187[/C][/ROW]
[ROW][C]45[/C][C]0.420603296942968[/C][C]0.841206593885936[/C][C]0.579396703057032[/C][/ROW]
[ROW][C]46[/C][C]0.284537259739542[/C][C]0.569074519479084[/C][C]0.715462740260458[/C][/ROW]
[ROW][C]47[/C][C]0.165659659573057[/C][C]0.331319319146114[/C][C]0.834340340426943[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67569&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67569&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	0.95892248465378	0.0821550306924388	0.0410775153462194
22	0.96228136152731	0.0754372769453798	0.0377186384726899
23	0.928001956836039	0.143996086327923	0.0719980431639614
24	0.900706140343339	0.198587719313323	0.0992938596566614
25	0.870298752791565	0.259402494416869	0.129701247208435
26	0.8263292515386	0.347341496922799	0.173670748461399
27	0.807994731864986	0.384010536270029	0.192005268135014
28	0.798164107725607	0.403671784548785	0.201835892274393
29	0.771914047873933	0.456171904252134	0.228085952126067
30	0.757501189768281	0.484997620463438	0.242498810231719
31	0.696912596813477	0.606174806373046	0.303087403186523
32	0.615181836920694	0.769636326158612	0.384818163079306
33	0.56428753184188	0.87142493631624	0.43571246815812
34	0.493731894464299	0.987463788928598	0.506268105535701
35	0.409335992290908	0.818671984581815	0.590664007709092
36	0.370718822481043	0.741437644962086	0.629281177518957
37	0.39594667414585	0.7918933482917	0.60405332585415
38	0.300049913927194	0.600099827854388	0.699950086072806
39	0.379760108044419	0.759520216088838	0.620239891955581
40	0.282876353745788	0.565752707491576	0.717123646254212
41	0.213517943990979	0.427035887981958	0.786482056009021
42	0.684346671617592	0.631306656764816	0.315653328382408
43	0.579738478971633	0.840523042056733	0.420261521028367
44	0.495093142471813	0.990186284943626	0.504906857528187
45	0.420603296942968	0.841206593885936	0.579396703057032
46	0.284537259739542	0.569074519479084	0.715462740260458
47	0.165659659573057	0.331319319146114	0.834340340426943

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	2	0.0740740740740741	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 & 2 & 0.0740740740740741 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67569&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]2[/C][C]0.0740740740740741[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67569&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67569&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	2	0.0740740740740741	OK

Figure 1

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Figure 2

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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 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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