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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Mon, 14 Dec 2009 03:56:51 -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/t1260788395ubjavm3t3h6f8s6.htm/, Retrieved Sun, 05 May 2024 12:25:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67515, Retrieved Sun, 05 May 2024 12:25:54 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

174

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 10:56:51] [14869f38c4320b00c96ca15cc00142de] [Current]

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Dataseries X:

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Histogram

Boxplots

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

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=67515&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=67515&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67515&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
Y[t] = -103.597529140216 + 0.456638020998805X[t] + 1.15233154517053`Y(t-1)`[t] -0.132883985021822`Y(t-2)`[t] -0.136717309166669`Y(t-3)`[t] + 0.288076677389240`Y(t-4)`[t] -0.0444267752463386`Y(t-5)`[t] + 2.60941417635306M1[t] + 66.9697686993288M2[t] + 13.9511567062971M3[t] + 0.76530488075559M4[t] -2.58819717511082M5[t] -17.7476852617300M6[t] + 5.99420155049773M7[t] + 3.11341674291098M8[t] -0.771493007730226M9[t] -4.40903117293207M10[t] -2.59469677920587M11[t] -0.457581264982037t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -103.597529140216 +  0.456638020998805X[t] +  1.15233154517053`Y(t-1)`[t] -0.132883985021822`Y(t-2)`[t] -0.136717309166669`Y(t-3)`[t] +  0.288076677389240`Y(t-4)`[t] -0.0444267752463386`Y(t-5)`[t] +  2.60941417635306M1[t] +  66.9697686993288M2[t] +  13.9511567062971M3[t] +  0.76530488075559M4[t] -2.58819717511082M5[t] -17.7476852617300M6[t] +  5.99420155049773M7[t] +  3.11341674291098M8[t] -0.771493007730226M9[t] -4.40903117293207M10[t] -2.59469677920587M11[t] -0.457581264982037t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67515&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -103.597529140216 +  0.456638020998805X[t] +  1.15233154517053`Y(t-1)`[t] -0.132883985021822`Y(t-2)`[t] -0.136717309166669`Y(t-3)`[t] +  0.288076677389240`Y(t-4)`[t] -0.0444267752463386`Y(t-5)`[t] +  2.60941417635306M1[t] +  66.9697686993288M2[t] +  13.9511567062971M3[t] +  0.76530488075559M4[t] -2.58819717511082M5[t] -17.7476852617300M6[t] +  5.99420155049773M7[t] +  3.11341674291098M8[t] -0.771493007730226M9[t] -4.40903117293207M10[t] -2.59469677920587M11[t] -0.457581264982037t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67515&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67515&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] = -103.597529140216 + 0.456638020998805X[t] + 1.15233154517053`Y(t-1)`[t] -0.132883985021822`Y(t-2)`[t] -0.136717309166669`Y(t-3)`[t] + 0.288076677389240`Y(t-4)`[t] -0.0444267752463386`Y(t-5)`[t] + 2.60941417635306M1[t] + 66.9697686993288M2[t] + 13.9511567062971M3[t] + 0.76530488075559M4[t] -2.58819717511082M5[t] -17.7476852617300M6[t] + 5.99420155049773M7[t] + 3.11341674291098M8[t] -0.771493007730226M9[t] -4.40903117293207M10[t] -2.59469677920587M11[t] -0.457581264982037t + 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)	-103.597529140216	42.1143	-2.4599	0.017549	0.008775
X	0.456638020998805	0.253008	1.8048	0.077375	0.038688
`Y(t-1)`	1.15233154517053	0.140525	8.2002	0	0
`Y(t-2)`	-0.132883985021822	0.215596	-0.6164	0.540572	0.270286
`Y(t-3)`	-0.136717309166669	0.245302	-0.5573	0.579884	0.289942
`Y(t-4)`	0.288076677389240	0.258323	1.1152	0.270325	0.135162
`Y(t-5)`	-0.0444267752463386	0.16776	-0.2648	0.792279	0.39614
M1	2.60941417635306	4.094573	0.6373	0.526967	0.263483
M2	66.9697686993288	5.740297	11.6666	0	0
M3	13.9511567062971	9.436584	1.4784	0.14583	0.072915
M4	0.76530488075559	10.061094	0.0761	0.939683	0.469841
M5	-2.58819717511082	9.545484	-0.2711	0.787443	0.393722
M6	-17.7476852617300	9.149096	-1.9398	0.058289	0.029144
M7	5.99420155049773	4.263845	1.4058	0.166218	0.083109
M8	3.11341674291098	4.723967	0.6591	0.513001	0.256501
M9	-0.771493007730226	5.013167	-0.1539	0.878339	0.43917
M10	-4.40903117293207	5.186876	-0.85	0.399525	0.199763
M11	-2.59469677920587	3.527936	-0.7355	0.465631	0.232816
t	-0.457581264982037	0.172888	-2.6467	0.010961	0.00548

\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) & -103.597529140216 & 42.1143 & -2.4599 & 0.017549 & 0.008775 \tabularnewline
X & 0.456638020998805 & 0.253008 & 1.8048 & 0.077375 & 0.038688 \tabularnewline
`Y(t-1)` & 1.15233154517053 & 0.140525 & 8.2002 & 0 & 0 \tabularnewline
`Y(t-2)` & -0.132883985021822 & 0.215596 & -0.6164 & 0.540572 & 0.270286 \tabularnewline
`Y(t-3)` & -0.136717309166669 & 0.245302 & -0.5573 & 0.579884 & 0.289942 \tabularnewline
`Y(t-4)` & 0.288076677389240 & 0.258323 & 1.1152 & 0.270325 & 0.135162 \tabularnewline
`Y(t-5)` & -0.0444267752463386 & 0.16776 & -0.2648 & 0.792279 & 0.39614 \tabularnewline
M1 & 2.60941417635306 & 4.094573 & 0.6373 & 0.526967 & 0.263483 \tabularnewline
M2 & 66.9697686993288 & 5.740297 & 11.6666 & 0 & 0 \tabularnewline
M3 & 13.9511567062971 & 9.436584 & 1.4784 & 0.14583 & 0.072915 \tabularnewline
M4 & 0.76530488075559 & 10.061094 & 0.0761 & 0.939683 & 0.469841 \tabularnewline
M5 & -2.58819717511082 & 9.545484 & -0.2711 & 0.787443 & 0.393722 \tabularnewline
M6 & -17.7476852617300 & 9.149096 & -1.9398 & 0.058289 & 0.029144 \tabularnewline
M7 & 5.99420155049773 & 4.263845 & 1.4058 & 0.166218 & 0.083109 \tabularnewline
M8 & 3.11341674291098 & 4.723967 & 0.6591 & 0.513001 & 0.256501 \tabularnewline
M9 & -0.771493007730226 & 5.013167 & -0.1539 & 0.878339 & 0.43917 \tabularnewline
M10 & -4.40903117293207 & 5.186876 & -0.85 & 0.399525 & 0.199763 \tabularnewline
M11 & -2.59469677920587 & 3.527936 & -0.7355 & 0.465631 & 0.232816 \tabularnewline
t & -0.457581264982037 & 0.172888 & -2.6467 & 0.010961 & 0.00548 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67515&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]-103.597529140216[/C][C]42.1143[/C][C]-2.4599[/C][C]0.017549[/C][C]0.008775[/C][/ROW]
[ROW][C]X[/C][C]0.456638020998805[/C][C]0.253008[/C][C]1.8048[/C][C]0.077375[/C][C]0.038688[/C][/ROW]
[ROW][C]`Y(t-1)`[/C][C]1.15233154517053[/C][C]0.140525[/C][C]8.2002[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`Y(t-2)`[/C][C]-0.132883985021822[/C][C]0.215596[/C][C]-0.6164[/C][C]0.540572[/C][C]0.270286[/C][/ROW]
[ROW][C]`Y(t-3)`[/C][C]-0.136717309166669[/C][C]0.245302[/C][C]-0.5573[/C][C]0.579884[/C][C]0.289942[/C][/ROW]
[ROW][C]`Y(t-4)`[/C][C]0.288076677389240[/C][C]0.258323[/C][C]1.1152[/C][C]0.270325[/C][C]0.135162[/C][/ROW]
[ROW][C]`Y(t-5)`[/C][C]-0.0444267752463386[/C][C]0.16776[/C][C]-0.2648[/C][C]0.792279[/C][C]0.39614[/C][/ROW]
[ROW][C]M1[/C][C]2.60941417635306[/C][C]4.094573[/C][C]0.6373[/C][C]0.526967[/C][C]0.263483[/C][/ROW]
[ROW][C]M2[/C][C]66.9697686993288[/C][C]5.740297[/C][C]11.6666[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M3[/C][C]13.9511567062971[/C][C]9.436584[/C][C]1.4784[/C][C]0.14583[/C][C]0.072915[/C][/ROW]
[ROW][C]M4[/C][C]0.76530488075559[/C][C]10.061094[/C][C]0.0761[/C][C]0.939683[/C][C]0.469841[/C][/ROW]
[ROW][C]M5[/C][C]-2.58819717511082[/C][C]9.545484[/C][C]-0.2711[/C][C]0.787443[/C][C]0.393722[/C][/ROW]
[ROW][C]M6[/C][C]-17.7476852617300[/C][C]9.149096[/C][C]-1.9398[/C][C]0.058289[/C][C]0.029144[/C][/ROW]
[ROW][C]M7[/C][C]5.99420155049773[/C][C]4.263845[/C][C]1.4058[/C][C]0.166218[/C][C]0.083109[/C][/ROW]
[ROW][C]M8[/C][C]3.11341674291098[/C][C]4.723967[/C][C]0.6591[/C][C]0.513001[/C][C]0.256501[/C][/ROW]
[ROW][C]M9[/C][C]-0.771493007730226[/C][C]5.013167[/C][C]-0.1539[/C][C]0.878339[/C][C]0.43917[/C][/ROW]
[ROW][C]M10[/C][C]-4.40903117293207[/C][C]5.186876[/C][C]-0.85[/C][C]0.399525[/C][C]0.199763[/C][/ROW]
[ROW][C]M11[/C][C]-2.59469677920587[/C][C]3.527936[/C][C]-0.7355[/C][C]0.465631[/C][C]0.232816[/C][/ROW]
[ROW][C]t[/C][C]-0.457581264982037[/C][C]0.172888[/C][C]-2.6467[/C][C]0.010961[/C][C]0.00548[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67515&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67515&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)	-103.597529140216	42.1143	-2.4599	0.017549	0.008775
X	0.456638020998805	0.253008	1.8048	0.077375	0.038688
`Y(t-1)`	1.15233154517053	0.140525	8.2002	0	0
`Y(t-2)`	-0.132883985021822	0.215596	-0.6164	0.540572	0.270286
`Y(t-3)`	-0.136717309166669	0.245302	-0.5573	0.579884	0.289942
`Y(t-4)`	0.288076677389240	0.258323	1.1152	0.270325	0.135162
`Y(t-5)`	-0.0444267752463386	0.16776	-0.2648	0.792279	0.39614
M1	2.60941417635306	4.094573	0.6373	0.526967	0.263483
M2	66.9697686993288	5.740297	11.6666	0	0
M3	13.9511567062971	9.436584	1.4784	0.14583	0.072915
M4	0.76530488075559	10.061094	0.0761	0.939683	0.469841
M5	-2.58819717511082	9.545484	-0.2711	0.787443	0.393722
M6	-17.7476852617300	9.149096	-1.9398	0.058289	0.029144
M7	5.99420155049773	4.263845	1.4058	0.166218	0.083109
M8	3.11341674291098	4.723967	0.6591	0.513001	0.256501
M9	-0.771493007730226	5.013167	-0.1539	0.878339	0.43917
M10	-4.40903117293207	5.186876	-0.85	0.399525	0.199763
M11	-2.59469677920587	3.527936	-0.7355	0.465631	0.232816
t	-0.457581264982037	0.172888	-2.6467	0.010961	0.00548

Multiple Linear Regression - Regression Statistics
Multiple R	0.995879165152403
R-squared	0.991775311584647
Adjusted R-squared	0.98869105342889
F-TEST (value)	321.560408208147
F-TEST (DF numerator)	18
F-TEST (DF denominator)	48
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.39725135046519
Sum Squared Residuals	1398.25546272472

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.995879165152403 \tabularnewline
R-squared & 0.991775311584647 \tabularnewline
Adjusted R-squared & 0.98869105342889 \tabularnewline
F-TEST (value) & 321.560408208147 \tabularnewline
F-TEST (DF numerator) & 18 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 5.39725135046519 \tabularnewline
Sum Squared Residuals & 1398.25546272472 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67515&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.995879165152403[/C][/ROW]
[ROW][C]R-squared[/C][C]0.991775311584647[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.98869105342889[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]321.560408208147[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]18[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]48[/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]5.39725135046519[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1398.25546272472[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67515&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67515&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	0.995879165152403
R-squared	0.991775311584647
Adjusted R-squared	0.98869105342889
F-TEST (value)	321.560408208147
F-TEST (DF numerator)	18
F-TEST (DF denominator)	48
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.39725135046519
Sum Squared Residuals	1398.25546272472

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	431	441.116822983256	-10.1168229832557
2	484	486.218502125266	-2.21850212526644
3	510	500.78600065426	9.21399934574013
4	513	511.826339744647	1.17366025535347
5	503	503.477613479077	-0.477613479076982
6	471	484.631994511141	-13.6319945111414
7	471	471.798752016127	-0.798752016126502
8	476	476.300489547179	-0.300489547179060
9	475	479.034899249011	-4.03489924901063
10	470	468.869558832443	1.13044116755710
11	461	464.011358221509	-3.01135822150921
12	455	457.516708627322	-2.51670862732155
13	456	455.356806781775	0.643193218225054
14	517	512.504583673193	4.49541632680735
15	525	530.422970248381	-5.42297024838079
16	523	523.185172747388	-0.185172747387612
17	519	510.824072645417	8.17592735458284
18	509	502.320602726454	6.67939727354561
19	512	510.051754705814	1.94824529418566
20	519	513.580370112286	5.41962988771363
21	517	517.026612681994	-0.0266126819942674
22	510	510.419190042299	-0.419190042299460
23	509	503.093944288661	5.9060557113388
24	501	505.065072290592	-4.06507229059177
25	507	501.123500542677	5.87649945732348
26	569	563.403858910723	5.59614108927686
27	580	582.833161818317	-2.83316181831692
28	578	579.633174772325	-1.63317477232487
29	565	566.530717863766	-1.53071786376572
30	547	546.307451265728	0.692548734271657
31	555	550.488814173832	4.51118582616778
32	562	558.651540891901	3.34845910809889
33	561	560.984679361627	0.0153206383726432
34	555	556.274686832664	-1.2746868326641
35	544	548.522556279	-4.52255627899997
36	537	538.067659439906	-1.06765943990612
37	543	540.229067415193	2.77093258480693
38	594	600.836562447136	-6.83656244713572
39	611	607.67910984444	3.32089015556
40	613	612.399921479967	0.600078520033101
41	611	601.966113747853	9.0338862521472
42	594	592.957285641014	1.04271435898568
43	595	598.225558801828	-3.22555880182787
44	591	595.196418666733	-4.19641866673305
45	589	588.364534263266	0.635465736733481
46	584	581.569534993327	2.43046500667275
47	573	578.152987219608	-5.15298721960834
48	567	565.209378096901	1.79062190309889
49	569	569.40896659631	-0.408966596310248
50	621	621.497012726195	-0.497012726195316
51	629	632.308128837738	-3.30812883773794
52	628	627.451346099964	0.548653900036087
53	612	611.824815730069	0.175184269931155
54	595	593.024971102072	1.97502889792818
55	597	596.008775420746	0.991224579253566
56	593	597.2711807819	-4.27118078190041
57	590	586.589274444101	3.41072555589877
58	580	581.867029299266	-1.86702929926630
59	574	567.219153991221	6.78084600877873
60	573	567.141181545279	5.85881845472055
61	573	571.76483568079	1.23516431921043
62	620	620.539480117487	-0.539480117486715
63	626	626.970628596864	-0.970628596864477
64	620	620.50404515571	-0.504045155710183
65	588	603.376666533818	-15.3766665338185
66	566	562.75769475359	3.24230524641030
67	557	560.426344881653	-3.42634488165263

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 431 & 441.116822983256 & -10.1168229832557 \tabularnewline
2 & 484 & 486.218502125266 & -2.21850212526644 \tabularnewline
3 & 510 & 500.78600065426 & 9.21399934574013 \tabularnewline
4 & 513 & 511.826339744647 & 1.17366025535347 \tabularnewline
5 & 503 & 503.477613479077 & -0.477613479076982 \tabularnewline
6 & 471 & 484.631994511141 & -13.6319945111414 \tabularnewline
7 & 471 & 471.798752016127 & -0.798752016126502 \tabularnewline
8 & 476 & 476.300489547179 & -0.300489547179060 \tabularnewline
9 & 475 & 479.034899249011 & -4.03489924901063 \tabularnewline
10 & 470 & 468.869558832443 & 1.13044116755710 \tabularnewline
11 & 461 & 464.011358221509 & -3.01135822150921 \tabularnewline
12 & 455 & 457.516708627322 & -2.51670862732155 \tabularnewline
13 & 456 & 455.356806781775 & 0.643193218225054 \tabularnewline
14 & 517 & 512.504583673193 & 4.49541632680735 \tabularnewline
15 & 525 & 530.422970248381 & -5.42297024838079 \tabularnewline
16 & 523 & 523.185172747388 & -0.185172747387612 \tabularnewline
17 & 519 & 510.824072645417 & 8.17592735458284 \tabularnewline
18 & 509 & 502.320602726454 & 6.67939727354561 \tabularnewline
19 & 512 & 510.051754705814 & 1.94824529418566 \tabularnewline
20 & 519 & 513.580370112286 & 5.41962988771363 \tabularnewline
21 & 517 & 517.026612681994 & -0.0266126819942674 \tabularnewline
22 & 510 & 510.419190042299 & -0.419190042299460 \tabularnewline
23 & 509 & 503.093944288661 & 5.9060557113388 \tabularnewline
24 & 501 & 505.065072290592 & -4.06507229059177 \tabularnewline
25 & 507 & 501.123500542677 & 5.87649945732348 \tabularnewline
26 & 569 & 563.403858910723 & 5.59614108927686 \tabularnewline
27 & 580 & 582.833161818317 & -2.83316181831692 \tabularnewline
28 & 578 & 579.633174772325 & -1.63317477232487 \tabularnewline
29 & 565 & 566.530717863766 & -1.53071786376572 \tabularnewline
30 & 547 & 546.307451265728 & 0.692548734271657 \tabularnewline
31 & 555 & 550.488814173832 & 4.51118582616778 \tabularnewline
32 & 562 & 558.651540891901 & 3.34845910809889 \tabularnewline
33 & 561 & 560.984679361627 & 0.0153206383726432 \tabularnewline
34 & 555 & 556.274686832664 & -1.2746868326641 \tabularnewline
35 & 544 & 548.522556279 & -4.52255627899997 \tabularnewline
36 & 537 & 538.067659439906 & -1.06765943990612 \tabularnewline
37 & 543 & 540.229067415193 & 2.77093258480693 \tabularnewline
38 & 594 & 600.836562447136 & -6.83656244713572 \tabularnewline
39 & 611 & 607.67910984444 & 3.32089015556 \tabularnewline
40 & 613 & 612.399921479967 & 0.600078520033101 \tabularnewline
41 & 611 & 601.966113747853 & 9.0338862521472 \tabularnewline
42 & 594 & 592.957285641014 & 1.04271435898568 \tabularnewline
43 & 595 & 598.225558801828 & -3.22555880182787 \tabularnewline
44 & 591 & 595.196418666733 & -4.19641866673305 \tabularnewline
45 & 589 & 588.364534263266 & 0.635465736733481 \tabularnewline
46 & 584 & 581.569534993327 & 2.43046500667275 \tabularnewline
47 & 573 & 578.152987219608 & -5.15298721960834 \tabularnewline
48 & 567 & 565.209378096901 & 1.79062190309889 \tabularnewline
49 & 569 & 569.40896659631 & -0.408966596310248 \tabularnewline
50 & 621 & 621.497012726195 & -0.497012726195316 \tabularnewline
51 & 629 & 632.308128837738 & -3.30812883773794 \tabularnewline
52 & 628 & 627.451346099964 & 0.548653900036087 \tabularnewline
53 & 612 & 611.824815730069 & 0.175184269931155 \tabularnewline
54 & 595 & 593.024971102072 & 1.97502889792818 \tabularnewline
55 & 597 & 596.008775420746 & 0.991224579253566 \tabularnewline
56 & 593 & 597.2711807819 & -4.27118078190041 \tabularnewline
57 & 590 & 586.589274444101 & 3.41072555589877 \tabularnewline
58 & 580 & 581.867029299266 & -1.86702929926630 \tabularnewline
59 & 574 & 567.219153991221 & 6.78084600877873 \tabularnewline
60 & 573 & 567.141181545279 & 5.85881845472055 \tabularnewline
61 & 573 & 571.76483568079 & 1.23516431921043 \tabularnewline
62 & 620 & 620.539480117487 & -0.539480117486715 \tabularnewline
63 & 626 & 626.970628596864 & -0.970628596864477 \tabularnewline
64 & 620 & 620.50404515571 & -0.504045155710183 \tabularnewline
65 & 588 & 603.376666533818 & -15.3766665338185 \tabularnewline
66 & 566 & 562.75769475359 & 3.24230524641030 \tabularnewline
67 & 557 & 560.426344881653 & -3.42634488165263 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67515&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]431[/C][C]441.116822983256[/C][C]-10.1168229832557[/C][/ROW]
[ROW][C]2[/C][C]484[/C][C]486.218502125266[/C][C]-2.21850212526644[/C][/ROW]
[ROW][C]3[/C][C]510[/C][C]500.78600065426[/C][C]9.21399934574013[/C][/ROW]
[ROW][C]4[/C][C]513[/C][C]511.826339744647[/C][C]1.17366025535347[/C][/ROW]
[ROW][C]5[/C][C]503[/C][C]503.477613479077[/C][C]-0.477613479076982[/C][/ROW]
[ROW][C]6[/C][C]471[/C][C]484.631994511141[/C][C]-13.6319945111414[/C][/ROW]
[ROW][C]7[/C][C]471[/C][C]471.798752016127[/C][C]-0.798752016126502[/C][/ROW]
[ROW][C]8[/C][C]476[/C][C]476.300489547179[/C][C]-0.300489547179060[/C][/ROW]
[ROW][C]9[/C][C]475[/C][C]479.034899249011[/C][C]-4.03489924901063[/C][/ROW]
[ROW][C]10[/C][C]470[/C][C]468.869558832443[/C][C]1.13044116755710[/C][/ROW]
[ROW][C]11[/C][C]461[/C][C]464.011358221509[/C][C]-3.01135822150921[/C][/ROW]
[ROW][C]12[/C][C]455[/C][C]457.516708627322[/C][C]-2.51670862732155[/C][/ROW]
[ROW][C]13[/C][C]456[/C][C]455.356806781775[/C][C]0.643193218225054[/C][/ROW]
[ROW][C]14[/C][C]517[/C][C]512.504583673193[/C][C]4.49541632680735[/C][/ROW]
[ROW][C]15[/C][C]525[/C][C]530.422970248381[/C][C]-5.42297024838079[/C][/ROW]
[ROW][C]16[/C][C]523[/C][C]523.185172747388[/C][C]-0.185172747387612[/C][/ROW]
[ROW][C]17[/C][C]519[/C][C]510.824072645417[/C][C]8.17592735458284[/C][/ROW]
[ROW][C]18[/C][C]509[/C][C]502.320602726454[/C][C]6.67939727354561[/C][/ROW]
[ROW][C]19[/C][C]512[/C][C]510.051754705814[/C][C]1.94824529418566[/C][/ROW]
[ROW][C]20[/C][C]519[/C][C]513.580370112286[/C][C]5.41962988771363[/C][/ROW]
[ROW][C]21[/C][C]517[/C][C]517.026612681994[/C][C]-0.0266126819942674[/C][/ROW]
[ROW][C]22[/C][C]510[/C][C]510.419190042299[/C][C]-0.419190042299460[/C][/ROW]
[ROW][C]23[/C][C]509[/C][C]503.093944288661[/C][C]5.9060557113388[/C][/ROW]
[ROW][C]24[/C][C]501[/C][C]505.065072290592[/C][C]-4.06507229059177[/C][/ROW]
[ROW][C]25[/C][C]507[/C][C]501.123500542677[/C][C]5.87649945732348[/C][/ROW]
[ROW][C]26[/C][C]569[/C][C]563.403858910723[/C][C]5.59614108927686[/C][/ROW]
[ROW][C]27[/C][C]580[/C][C]582.833161818317[/C][C]-2.83316181831692[/C][/ROW]
[ROW][C]28[/C][C]578[/C][C]579.633174772325[/C][C]-1.63317477232487[/C][/ROW]
[ROW][C]29[/C][C]565[/C][C]566.530717863766[/C][C]-1.53071786376572[/C][/ROW]
[ROW][C]30[/C][C]547[/C][C]546.307451265728[/C][C]0.692548734271657[/C][/ROW]
[ROW][C]31[/C][C]555[/C][C]550.488814173832[/C][C]4.51118582616778[/C][/ROW]
[ROW][C]32[/C][C]562[/C][C]558.651540891901[/C][C]3.34845910809889[/C][/ROW]
[ROW][C]33[/C][C]561[/C][C]560.984679361627[/C][C]0.0153206383726432[/C][/ROW]
[ROW][C]34[/C][C]555[/C][C]556.274686832664[/C][C]-1.2746868326641[/C][/ROW]
[ROW][C]35[/C][C]544[/C][C]548.522556279[/C][C]-4.52255627899997[/C][/ROW]
[ROW][C]36[/C][C]537[/C][C]538.067659439906[/C][C]-1.06765943990612[/C][/ROW]
[ROW][C]37[/C][C]543[/C][C]540.229067415193[/C][C]2.77093258480693[/C][/ROW]
[ROW][C]38[/C][C]594[/C][C]600.836562447136[/C][C]-6.83656244713572[/C][/ROW]
[ROW][C]39[/C][C]611[/C][C]607.67910984444[/C][C]3.32089015556[/C][/ROW]
[ROW][C]40[/C][C]613[/C][C]612.399921479967[/C][C]0.600078520033101[/C][/ROW]
[ROW][C]41[/C][C]611[/C][C]601.966113747853[/C][C]9.0338862521472[/C][/ROW]
[ROW][C]42[/C][C]594[/C][C]592.957285641014[/C][C]1.04271435898568[/C][/ROW]
[ROW][C]43[/C][C]595[/C][C]598.225558801828[/C][C]-3.22555880182787[/C][/ROW]
[ROW][C]44[/C][C]591[/C][C]595.196418666733[/C][C]-4.19641866673305[/C][/ROW]
[ROW][C]45[/C][C]589[/C][C]588.364534263266[/C][C]0.635465736733481[/C][/ROW]
[ROW][C]46[/C][C]584[/C][C]581.569534993327[/C][C]2.43046500667275[/C][/ROW]
[ROW][C]47[/C][C]573[/C][C]578.152987219608[/C][C]-5.15298721960834[/C][/ROW]
[ROW][C]48[/C][C]567[/C][C]565.209378096901[/C][C]1.79062190309889[/C][/ROW]
[ROW][C]49[/C][C]569[/C][C]569.40896659631[/C][C]-0.408966596310248[/C][/ROW]
[ROW][C]50[/C][C]621[/C][C]621.497012726195[/C][C]-0.497012726195316[/C][/ROW]
[ROW][C]51[/C][C]629[/C][C]632.308128837738[/C][C]-3.30812883773794[/C][/ROW]
[ROW][C]52[/C][C]628[/C][C]627.451346099964[/C][C]0.548653900036087[/C][/ROW]
[ROW][C]53[/C][C]612[/C][C]611.824815730069[/C][C]0.175184269931155[/C][/ROW]
[ROW][C]54[/C][C]595[/C][C]593.024971102072[/C][C]1.97502889792818[/C][/ROW]
[ROW][C]55[/C][C]597[/C][C]596.008775420746[/C][C]0.991224579253566[/C][/ROW]
[ROW][C]56[/C][C]593[/C][C]597.2711807819[/C][C]-4.27118078190041[/C][/ROW]
[ROW][C]57[/C][C]590[/C][C]586.589274444101[/C][C]3.41072555589877[/C][/ROW]
[ROW][C]58[/C][C]580[/C][C]581.867029299266[/C][C]-1.86702929926630[/C][/ROW]
[ROW][C]59[/C][C]574[/C][C]567.219153991221[/C][C]6.78084600877873[/C][/ROW]
[ROW][C]60[/C][C]573[/C][C]567.141181545279[/C][C]5.85881845472055[/C][/ROW]
[ROW][C]61[/C][C]573[/C][C]571.76483568079[/C][C]1.23516431921043[/C][/ROW]
[ROW][C]62[/C][C]620[/C][C]620.539480117487[/C][C]-0.539480117486715[/C][/ROW]
[ROW][C]63[/C][C]626[/C][C]626.970628596864[/C][C]-0.970628596864477[/C][/ROW]
[ROW][C]64[/C][C]620[/C][C]620.50404515571[/C][C]-0.504045155710183[/C][/ROW]
[ROW][C]65[/C][C]588[/C][C]603.376666533818[/C][C]-15.3766665338185[/C][/ROW]
[ROW][C]66[/C][C]566[/C][C]562.75769475359[/C][C]3.24230524641030[/C][/ROW]
[ROW][C]67[/C][C]557[/C][C]560.426344881653[/C][C]-3.42634488165263[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67515&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67515&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	431	441.116822983256	-10.1168229832557
2	484	486.218502125266	-2.21850212526644
3	510	500.78600065426	9.21399934574013
4	513	511.826339744647	1.17366025535347
5	503	503.477613479077	-0.477613479076982
6	471	484.631994511141	-13.6319945111414
7	471	471.798752016127	-0.798752016126502
8	476	476.300489547179	-0.300489547179060
9	475	479.034899249011	-4.03489924901063
10	470	468.869558832443	1.13044116755710
11	461	464.011358221509	-3.01135822150921
12	455	457.516708627322	-2.51670862732155
13	456	455.356806781775	0.643193218225054
14	517	512.504583673193	4.49541632680735
15	525	530.422970248381	-5.42297024838079
16	523	523.185172747388	-0.185172747387612
17	519	510.824072645417	8.17592735458284
18	509	502.320602726454	6.67939727354561
19	512	510.051754705814	1.94824529418566
20	519	513.580370112286	5.41962988771363
21	517	517.026612681994	-0.0266126819942674
22	510	510.419190042299	-0.419190042299460
23	509	503.093944288661	5.9060557113388
24	501	505.065072290592	-4.06507229059177
25	507	501.123500542677	5.87649945732348
26	569	563.403858910723	5.59614108927686
27	580	582.833161818317	-2.83316181831692
28	578	579.633174772325	-1.63317477232487
29	565	566.530717863766	-1.53071786376572
30	547	546.307451265728	0.692548734271657
31	555	550.488814173832	4.51118582616778
32	562	558.651540891901	3.34845910809889
33	561	560.984679361627	0.0153206383726432
34	555	556.274686832664	-1.2746868326641
35	544	548.522556279	-4.52255627899997
36	537	538.067659439906	-1.06765943990612
37	543	540.229067415193	2.77093258480693
38	594	600.836562447136	-6.83656244713572
39	611	607.67910984444	3.32089015556
40	613	612.399921479967	0.600078520033101
41	611	601.966113747853	9.0338862521472
42	594	592.957285641014	1.04271435898568
43	595	598.225558801828	-3.22555880182787
44	591	595.196418666733	-4.19641866673305
45	589	588.364534263266	0.635465736733481
46	584	581.569534993327	2.43046500667275
47	573	578.152987219608	-5.15298721960834
48	567	565.209378096901	1.79062190309889
49	569	569.40896659631	-0.408966596310248
50	621	621.497012726195	-0.497012726195316
51	629	632.308128837738	-3.30812883773794
52	628	627.451346099964	0.548653900036087
53	612	611.824815730069	0.175184269931155
54	595	593.024971102072	1.97502889792818
55	597	596.008775420746	0.991224579253566
56	593	597.2711807819	-4.27118078190041
57	590	586.589274444101	3.41072555589877
58	580	581.867029299266	-1.86702929926630
59	574	567.219153991221	6.78084600877873
60	573	567.141181545279	5.85881845472055
61	573	571.76483568079	1.23516431921043
62	620	620.539480117487	-0.539480117486715
63	626	626.970628596864	-0.970628596864477
64	620	620.50404515571	-0.504045155710183
65	588	603.376666533818	-15.3766665338185
66	566	562.75769475359	3.24230524641030
67	557	560.426344881653	-3.42634488165263

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
22	0.945301696466527	0.109396607066946	0.0546983035334728
23	0.956371062638483	0.0872578747230338	0.0436289373615169
24	0.927267176650401	0.145465646699198	0.072732823349599
25	0.902887334753056	0.194225330493888	0.097112665246944
26	0.880663608179335	0.238672783641329	0.119336391820665
27	0.861203841146589	0.277592317706822	0.138796158853411
28	0.833442320305853	0.333115359388293	0.166557679694147
29	0.809159597422938	0.381680805154124	0.190840402577062
30	0.741986873356598	0.516026253286804	0.258013126643402
31	0.657522689955267	0.684954620089466	0.342477310044733
32	0.597794387766836	0.804411224466328	0.402205612233164
33	0.533268714942308	0.933462570115384	0.466731285057692
34	0.451812766068561	0.903625532137122	0.548187233931439
35	0.405685566085889	0.811371132171777	0.594314433914111
36	0.418256357205204	0.836512714410408	0.581743642794796
37	0.315662939189519	0.631325878379038	0.68433706081048
38	0.39241196249685	0.7848239249937	0.60758803750315
39	0.288906748316459	0.577813496632917	0.711093251683541
40	0.20884992618528	0.41769985237056	0.79115007381472
41	0.637717457485602	0.724565085028796	0.362282542514398
42	0.521713239301276	0.956573521397448	0.478286760698724
43	0.444948705538771	0.889897411077541	0.555051294461229
44	0.346447843028887	0.692895686057774	0.653552156971113
45	0.224277307459137	0.448554614918274	0.775722692540863

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
22 & 0.945301696466527 & 0.109396607066946 & 0.0546983035334728 \tabularnewline
23 & 0.956371062638483 & 0.0872578747230338 & 0.0436289373615169 \tabularnewline
24 & 0.927267176650401 & 0.145465646699198 & 0.072732823349599 \tabularnewline
25 & 0.902887334753056 & 0.194225330493888 & 0.097112665246944 \tabularnewline
26 & 0.880663608179335 & 0.238672783641329 & 0.119336391820665 \tabularnewline
27 & 0.861203841146589 & 0.277592317706822 & 0.138796158853411 \tabularnewline
28 & 0.833442320305853 & 0.333115359388293 & 0.166557679694147 \tabularnewline
29 & 0.809159597422938 & 0.381680805154124 & 0.190840402577062 \tabularnewline
30 & 0.741986873356598 & 0.516026253286804 & 0.258013126643402 \tabularnewline
31 & 0.657522689955267 & 0.684954620089466 & 0.342477310044733 \tabularnewline
32 & 0.597794387766836 & 0.804411224466328 & 0.402205612233164 \tabularnewline
33 & 0.533268714942308 & 0.933462570115384 & 0.466731285057692 \tabularnewline
34 & 0.451812766068561 & 0.903625532137122 & 0.548187233931439 \tabularnewline
35 & 0.405685566085889 & 0.811371132171777 & 0.594314433914111 \tabularnewline
36 & 0.418256357205204 & 0.836512714410408 & 0.581743642794796 \tabularnewline
37 & 0.315662939189519 & 0.631325878379038 & 0.68433706081048 \tabularnewline
38 & 0.39241196249685 & 0.7848239249937 & 0.60758803750315 \tabularnewline
39 & 0.288906748316459 & 0.577813496632917 & 0.711093251683541 \tabularnewline
40 & 0.20884992618528 & 0.41769985237056 & 0.79115007381472 \tabularnewline
41 & 0.637717457485602 & 0.724565085028796 & 0.362282542514398 \tabularnewline
42 & 0.521713239301276 & 0.956573521397448 & 0.478286760698724 \tabularnewline
43 & 0.444948705538771 & 0.889897411077541 & 0.555051294461229 \tabularnewline
44 & 0.346447843028887 & 0.692895686057774 & 0.653552156971113 \tabularnewline
45 & 0.224277307459137 & 0.448554614918274 & 0.775722692540863 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67515&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]22[/C][C]0.945301696466527[/C][C]0.109396607066946[/C][C]0.0546983035334728[/C][/ROW]
[ROW][C]23[/C][C]0.956371062638483[/C][C]0.0872578747230338[/C][C]0.0436289373615169[/C][/ROW]
[ROW][C]24[/C][C]0.927267176650401[/C][C]0.145465646699198[/C][C]0.072732823349599[/C][/ROW]
[ROW][C]25[/C][C]0.902887334753056[/C][C]0.194225330493888[/C][C]0.097112665246944[/C][/ROW]
[ROW][C]26[/C][C]0.880663608179335[/C][C]0.238672783641329[/C][C]0.119336391820665[/C][/ROW]
[ROW][C]27[/C][C]0.861203841146589[/C][C]0.277592317706822[/C][C]0.138796158853411[/C][/ROW]
[ROW][C]28[/C][C]0.833442320305853[/C][C]0.333115359388293[/C][C]0.166557679694147[/C][/ROW]
[ROW][C]29[/C][C]0.809159597422938[/C][C]0.381680805154124[/C][C]0.190840402577062[/C][/ROW]
[ROW][C]30[/C][C]0.741986873356598[/C][C]0.516026253286804[/C][C]0.258013126643402[/C][/ROW]
[ROW][C]31[/C][C]0.657522689955267[/C][C]0.684954620089466[/C][C]0.342477310044733[/C][/ROW]
[ROW][C]32[/C][C]0.597794387766836[/C][C]0.804411224466328[/C][C]0.402205612233164[/C][/ROW]
[ROW][C]33[/C][C]0.533268714942308[/C][C]0.933462570115384[/C][C]0.466731285057692[/C][/ROW]
[ROW][C]34[/C][C]0.451812766068561[/C][C]0.903625532137122[/C][C]0.548187233931439[/C][/ROW]
[ROW][C]35[/C][C]0.405685566085889[/C][C]0.811371132171777[/C][C]0.594314433914111[/C][/ROW]
[ROW][C]36[/C][C]0.418256357205204[/C][C]0.836512714410408[/C][C]0.581743642794796[/C][/ROW]
[ROW][C]37[/C][C]0.315662939189519[/C][C]0.631325878379038[/C][C]0.68433706081048[/C][/ROW]
[ROW][C]38[/C][C]0.39241196249685[/C][C]0.7848239249937[/C][C]0.60758803750315[/C][/ROW]
[ROW][C]39[/C][C]0.288906748316459[/C][C]0.577813496632917[/C][C]0.711093251683541[/C][/ROW]
[ROW][C]40[/C][C]0.20884992618528[/C][C]0.41769985237056[/C][C]0.79115007381472[/C][/ROW]
[ROW][C]41[/C][C]0.637717457485602[/C][C]0.724565085028796[/C][C]0.362282542514398[/C][/ROW]
[ROW][C]42[/C][C]0.521713239301276[/C][C]0.956573521397448[/C][C]0.478286760698724[/C][/ROW]
[ROW][C]43[/C][C]0.444948705538771[/C][C]0.889897411077541[/C][C]0.555051294461229[/C][/ROW]
[ROW][C]44[/C][C]0.346447843028887[/C][C]0.692895686057774[/C][C]0.653552156971113[/C][/ROW]
[ROW][C]45[/C][C]0.224277307459137[/C][C]0.448554614918274[/C][C]0.775722692540863[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67515&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67515&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
22	0.945301696466527	0.109396607066946	0.0546983035334728
23	0.956371062638483	0.0872578747230338	0.0436289373615169
24	0.927267176650401	0.145465646699198	0.072732823349599
25	0.902887334753056	0.194225330493888	0.097112665246944
26	0.880663608179335	0.238672783641329	0.119336391820665
27	0.861203841146589	0.277592317706822	0.138796158853411
28	0.833442320305853	0.333115359388293	0.166557679694147
29	0.809159597422938	0.381680805154124	0.190840402577062
30	0.741986873356598	0.516026253286804	0.258013126643402
31	0.657522689955267	0.684954620089466	0.342477310044733
32	0.597794387766836	0.804411224466328	0.402205612233164
33	0.533268714942308	0.933462570115384	0.466731285057692
34	0.451812766068561	0.903625532137122	0.548187233931439
35	0.405685566085889	0.811371132171777	0.594314433914111
36	0.418256357205204	0.836512714410408	0.581743642794796
37	0.315662939189519	0.631325878379038	0.68433706081048
38	0.39241196249685	0.7848239249937	0.60758803750315
39	0.288906748316459	0.577813496632917	0.711093251683541
40	0.20884992618528	0.41769985237056	0.79115007381472
41	0.637717457485602	0.724565085028796	0.362282542514398
42	0.521713239301276	0.956573521397448	0.478286760698724
43	0.444948705538771	0.889897411077541	0.555051294461229
44	0.346447843028887	0.692895686057774	0.653552156971113
45	0.224277307459137	0.448554614918274	0.775722692540863

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	0.0416666666666667	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 & 0.0416666666666667 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67515&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]0.0416666666666667[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67515&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67515&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	0.0416666666666667	OK

Figure 1

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Parameters (Session):

par1 = 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