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R Software Module

rwasp_multipleregression.wasp

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Multiple Regression

Date of computation

Sat, 09 Jan 2010 07:30:26 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/09/t12630475620xbfs3trsqcaelv.htm/, Retrieved Sun, 28 Apr 2024 19:39:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71769, Retrieved Sun, 28 Apr 2024 19:39:37 +0000

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210

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

F     [Multiple Regression] [Multiple regressi...] [2009-11-14 11:54:22] [d46757a0a8c9b00540ab7e7e0c34bfc4]
-       [Multiple Regression] [Multiple Regressi...] [2009-11-20 23:43:08] [3dd791303389e75e672968b227170a72]
- R PD      [Multiple Regression] [] [2010-01-09 14:30:26] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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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=71769&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=71769&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71769&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
werkl[t] = + 27.862457704015 -0.189544972149105afzetp[t] -0.178728142494257M1[t] -0.558499469364017M2[t] -0.734643384638138M3[t] -0.603597881853048M4[t] -0.260241974005832M5[t] -0.230938975862558M6[t] -0.366886066158616M7[t] -0.666886066158615M8[t] -0.889325572657158M9[t] -0.926689241180551M10[t] -0.164052909703943M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
werkl[t] =  +  27.862457704015 -0.189544972149105afzetp[t] -0.178728142494257M1[t] -0.558499469364017M2[t] -0.734643384638138M3[t] -0.603597881853048M4[t] -0.260241974005832M5[t] -0.230938975862558M6[t] -0.366886066158616M7[t] -0.666886066158615M8[t] -0.889325572657158M9[t] -0.926689241180551M10[t] -0.164052909703943M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71769&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]werkl[t] =  +  27.862457704015 -0.189544972149105afzetp[t] -0.178728142494257M1[t] -0.558499469364017M2[t] -0.734643384638138M3[t] -0.603597881853048M4[t] -0.260241974005832M5[t] -0.230938975862558M6[t] -0.366886066158616M7[t] -0.666886066158615M8[t] -0.889325572657158M9[t] -0.926689241180551M10[t] -0.164052909703943M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71769&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71769&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
werkl[t] = + 27.862457704015 -0.189544972149105afzetp[t] -0.178728142494257M1[t] -0.558499469364017M2[t] -0.734643384638138M3[t] -0.603597881853048M4[t] -0.260241974005832M5[t] -0.230938975862558M6[t] -0.366886066158616M7[t] -0.666886066158615M8[t] -0.889325572657158M9[t] -0.926689241180551M10[t] -0.164052909703943M11[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	27.862457704015	2.113952	13.1803	0	0
afzetp	-0.189544972149105	0.020372	-9.3041	0	0
M1	-0.178728142494257	0.247576	-0.7219	0.473153	0.236576
M2	-0.558499469364017	0.257729	-2.167	0.034215	0.017108
M3	-0.734643384638138	0.25782	-2.8494	0.005993	0.002996
M4	-0.603597881853048	0.258013	-2.3394	0.022661	0.01133
M5	-0.260241974005832	0.257456	-1.0108	0.316161	0.158081
M6	-0.230938975862558	0.257359	-0.8973	0.373124	0.186562
M7	-0.366886066158616	0.25706	-1.4272	0.158695	0.079348
M8	-0.666886066158615	0.25706	-2.5943	0.011895	0.005948
M9	-0.889325572657158	0.256872	-3.4621	0.000994	0.000497
M10	-0.926689241180551	0.256834	-3.6081	0.00063	0.000315
M11	-0.164052909703943	0.256804	-0.6388	0.525367	0.262684

\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) & 27.862457704015 & 2.113952 & 13.1803 & 0 & 0 \tabularnewline
afzetp & -0.189544972149105 & 0.020372 & -9.3041 & 0 & 0 \tabularnewline
M1 & -0.178728142494257 & 0.247576 & -0.7219 & 0.473153 & 0.236576 \tabularnewline
M2 & -0.558499469364017 & 0.257729 & -2.167 & 0.034215 & 0.017108 \tabularnewline
M3 & -0.734643384638138 & 0.25782 & -2.8494 & 0.005993 & 0.002996 \tabularnewline
M4 & -0.603597881853048 & 0.258013 & -2.3394 & 0.022661 & 0.01133 \tabularnewline
M5 & -0.260241974005832 & 0.257456 & -1.0108 & 0.316161 & 0.158081 \tabularnewline
M6 & -0.230938975862558 & 0.257359 & -0.8973 & 0.373124 & 0.186562 \tabularnewline
M7 & -0.366886066158616 & 0.25706 & -1.4272 & 0.158695 & 0.079348 \tabularnewline
M8 & -0.666886066158615 & 0.25706 & -2.5943 & 0.011895 & 0.005948 \tabularnewline
M9 & -0.889325572657158 & 0.256872 & -3.4621 & 0.000994 & 0.000497 \tabularnewline
M10 & -0.926689241180551 & 0.256834 & -3.6081 & 0.00063 & 0.000315 \tabularnewline
M11 & -0.164052909703943 & 0.256804 & -0.6388 & 0.525367 & 0.262684 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71769&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]27.862457704015[/C][C]2.113952[/C][C]13.1803[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]afzetp[/C][C]-0.189544972149105[/C][C]0.020372[/C][C]-9.3041[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-0.178728142494257[/C][C]0.247576[/C][C]-0.7219[/C][C]0.473153[/C][C]0.236576[/C][/ROW]
[ROW][C]M2[/C][C]-0.558499469364017[/C][C]0.257729[/C][C]-2.167[/C][C]0.034215[/C][C]0.017108[/C][/ROW]
[ROW][C]M3[/C][C]-0.734643384638138[/C][C]0.25782[/C][C]-2.8494[/C][C]0.005993[/C][C]0.002996[/C][/ROW]
[ROW][C]M4[/C][C]-0.603597881853048[/C][C]0.258013[/C][C]-2.3394[/C][C]0.022661[/C][C]0.01133[/C][/ROW]
[ROW][C]M5[/C][C]-0.260241974005832[/C][C]0.257456[/C][C]-1.0108[/C][C]0.316161[/C][C]0.158081[/C][/ROW]
[ROW][C]M6[/C][C]-0.230938975862558[/C][C]0.257359[/C][C]-0.8973[/C][C]0.373124[/C][C]0.186562[/C][/ROW]
[ROW][C]M7[/C][C]-0.366886066158616[/C][C]0.25706[/C][C]-1.4272[/C][C]0.158695[/C][C]0.079348[/C][/ROW]
[ROW][C]M8[/C][C]-0.666886066158615[/C][C]0.25706[/C][C]-2.5943[/C][C]0.011895[/C][C]0.005948[/C][/ROW]
[ROW][C]M9[/C][C]-0.889325572657158[/C][C]0.256872[/C][C]-3.4621[/C][C]0.000994[/C][C]0.000497[/C][/ROW]
[ROW][C]M10[/C][C]-0.926689241180551[/C][C]0.256834[/C][C]-3.6081[/C][C]0.00063[/C][C]0.000315[/C][/ROW]
[ROW][C]M11[/C][C]-0.164052909703943[/C][C]0.256804[/C][C]-0.6388[/C][C]0.525367[/C][C]0.262684[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71769&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71769&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)	27.862457704015	2.113952	13.1803	0	0
afzetp	-0.189544972149105	0.020372	-9.3041	0	0
M1	-0.178728142494257	0.247576	-0.7219	0.473153	0.236576
M2	-0.558499469364017	0.257729	-2.167	0.034215	0.017108
M3	-0.734643384638138	0.25782	-2.8494	0.005993	0.002996
M4	-0.603597881853048	0.258013	-2.3394	0.022661	0.01133
M5	-0.260241974005832	0.257456	-1.0108	0.316161	0.158081
M6	-0.230938975862558	0.257359	-0.8973	0.373124	0.186562
M7	-0.366886066158616	0.25706	-1.4272	0.158695	0.079348
M8	-0.666886066158615	0.25706	-2.5943	0.011895	0.005948
M9	-0.889325572657158	0.256872	-3.4621	0.000994	0.000497
M10	-0.926689241180551	0.256834	-3.6081	0.00063	0.000315
M11	-0.164052909703943	0.256804	-0.6388	0.525367	0.262684

Multiple Linear Regression - Regression Statistics
Multiple R	0.811643807977646
R-squared	0.658765671028454
Adjusted R-squared	0.590518805234145
F-TEST (value)	9.65268753899884
F-TEST (DF numerator)	12
F-TEST (DF denominator)	60
p-value	4.30271707152485e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.444709263038103
Sum Squared Residuals	11.8659797179136

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.811643807977646 \tabularnewline
R-squared & 0.658765671028454 \tabularnewline
Adjusted R-squared & 0.590518805234145 \tabularnewline
F-TEST (value) & 9.65268753899884 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 60 \tabularnewline
p-value & 4.30271707152485e-10 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.444709263038103 \tabularnewline
Sum Squared Residuals & 11.8659797179136 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71769&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.811643807977646[/C][/ROW]
[ROW][C]R-squared[/C][C]0.658765671028454[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.590518805234145[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]9.65268753899884[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]60[/C][/ROW]
[ROW][C]p-value[/C][C]4.30271707152485e-10[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.444709263038103[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]11.8659797179136[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71769&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71769&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	0.811643807977646
R-squared	0.658765671028454
Adjusted R-squared	0.590518805234145
F-TEST (value)	9.65268753899884
F-TEST (DF numerator)	12
F-TEST (DF denominator)	60
p-value	4.30271707152485e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.444709263038103
Sum Squared Residuals	11.8659797179136

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	8.4	8.91877731875937	-0.518777318759372
2	8.4	8.6148239807492	-0.214823980749204
3	8.4	8.43868006547508	-0.0386800654750822
4	8.6	8.58868006547508	0.0113199345249173
5	8.9	8.85621798446266	0.0437820155373440
6	8.8	8.79074849653137	0.00925150346862508
7	8.3	8.57898341737568	-0.278983417375678
8	7.5	8.26002892016077	-0.760028920160768
9	7.2	8.01863491644731	-0.818634916447314
10	7.4	7.96231675070901	-0.562316750709013
11	8.8	8.72495308218562	0.0750469178143812
12	9.3	8.87005149467465	0.429948505325351
13	9.3	8.67236885496549	0.627631145034516
14	8.7	8.34946101974046	0.350538980259543
15	8.2	8.19227160168124	0.00772839831875522
16	8.3	8.41808959054089	-0.118089590540886
17	8.5	8.68562750952846	-0.185627509528463
18	8.6	8.75283950210156	-0.152839502101558
19	8.5	8.54107442294586	-0.0410744229458577
20	8.2	8.26002892016077	-0.0600289201607676
21	8.1	7.96177142480258	0.138228575197415
22	7.9	7.86754426463446	0.0324557353655402
23	8.6	8.61122609889616	-0.0112260988961556
24	8.7	8.75632451138519	-0.0563245113851899
25	8.7	8.57759636889093	0.122403631109067
26	8.5	8.235734036451	0.264265963549006
27	8.4	7.96481763510232	0.435182364897681
28	8.5	8.0958631378874	0.40413686211259
29	8.7	8.47712804016444	0.222871959835554
30	8.7	8.4685220438779	0.231477956122100
31	8.6	8.31362045636693	0.286379543633068
32	8.5	7.97571146193711	0.524288538062891
33	8.3	7.65849946936401	0.641500530635986
34	8	7.5832268064108	0.416773193589198
35	8.2	8.3458631378874	-0.145863137887410
36	8.1	8.33932557265716	-0.239325572657158
37	8.1	8.08477944130326	0.015220558696742
38	8	7.74291710886332	0.257082891136680
39	7.9	7.58572769080411	0.314272309195890
40	7.9	7.73572769080411	0.164272309195891
41	8	7.94640211814695	0.0535978818530483
42	8	8.03256860793496	-0.0325686079349559
43	7.9	7.87766702042399	0.0223329795760104
44	8	7.52080352877926	0.479196471220741
45	7.7	7.2604550278509	0.439544972149105
46	7.2	7.18518236489768	0.0148176351023201
47	7.5	7.90990970194447	-0.409909701944466
48	7.3	8.0739626116484	-0.773962611648409
49	7	7.8004619830796	-0.8004619830796
50	7	7.3448726673502	-0.3448726673502
51	7	7.18768324929099	-0.187683249290987
52	7.2	7.28081975764626	-0.0808197576462561
53	7.3	7.62417566549347	-0.324175665493473
54	7.1	7.63452416642184	-0.534524166421837
55	6.8	7.46066808169596	-0.660668081695958
56	6.4	7.17962257891087	-0.77962257891087
57	6.1	6.9192740779825	-0.819274077982507
58	6.5	6.95772839831875	-0.457728398318754
59	7.7	7.70141023258045	-0.00141023258045101
60	7.9	7.80859965063966	0.0914003493603366
61	7.5	7.57300801650068	-0.073008016500676
62	6.9	7.21219118684583	-0.312191186845826
63	6.6	7.13081975764626	-0.530819757646257
64	6.9	7.28081975764626	-0.380819757646256
65	7.7	7.51044868220401	0.189551317795990
66	8	7.52079718313237	0.479202816867626
67	8	7.32798660119158	0.672013398808416
68	7.7	7.10380459005123	0.596195409948773
69	7.3	6.88136508355268	0.418634916447315
70	7.4	6.84400141502929	0.555998584970708
71	8.1	7.6066377465059	0.493362253494101
72	8.3	7.75173615899493	0.548263841005068
73	8.2	7.57300801650068	0.626991983499324

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 8.4 & 8.91877731875937 & -0.518777318759372 \tabularnewline
2 & 8.4 & 8.6148239807492 & -0.214823980749204 \tabularnewline
3 & 8.4 & 8.43868006547508 & -0.0386800654750822 \tabularnewline
4 & 8.6 & 8.58868006547508 & 0.0113199345249173 \tabularnewline
5 & 8.9 & 8.85621798446266 & 0.0437820155373440 \tabularnewline
6 & 8.8 & 8.79074849653137 & 0.00925150346862508 \tabularnewline
7 & 8.3 & 8.57898341737568 & -0.278983417375678 \tabularnewline
8 & 7.5 & 8.26002892016077 & -0.760028920160768 \tabularnewline
9 & 7.2 & 8.01863491644731 & -0.818634916447314 \tabularnewline
10 & 7.4 & 7.96231675070901 & -0.562316750709013 \tabularnewline
11 & 8.8 & 8.72495308218562 & 0.0750469178143812 \tabularnewline
12 & 9.3 & 8.87005149467465 & 0.429948505325351 \tabularnewline
13 & 9.3 & 8.67236885496549 & 0.627631145034516 \tabularnewline
14 & 8.7 & 8.34946101974046 & 0.350538980259543 \tabularnewline
15 & 8.2 & 8.19227160168124 & 0.00772839831875522 \tabularnewline
16 & 8.3 & 8.41808959054089 & -0.118089590540886 \tabularnewline
17 & 8.5 & 8.68562750952846 & -0.185627509528463 \tabularnewline
18 & 8.6 & 8.75283950210156 & -0.152839502101558 \tabularnewline
19 & 8.5 & 8.54107442294586 & -0.0410744229458577 \tabularnewline
20 & 8.2 & 8.26002892016077 & -0.0600289201607676 \tabularnewline
21 & 8.1 & 7.96177142480258 & 0.138228575197415 \tabularnewline
22 & 7.9 & 7.86754426463446 & 0.0324557353655402 \tabularnewline
23 & 8.6 & 8.61122609889616 & -0.0112260988961556 \tabularnewline
24 & 8.7 & 8.75632451138519 & -0.0563245113851899 \tabularnewline
25 & 8.7 & 8.57759636889093 & 0.122403631109067 \tabularnewline
26 & 8.5 & 8.235734036451 & 0.264265963549006 \tabularnewline
27 & 8.4 & 7.96481763510232 & 0.435182364897681 \tabularnewline
28 & 8.5 & 8.0958631378874 & 0.40413686211259 \tabularnewline
29 & 8.7 & 8.47712804016444 & 0.222871959835554 \tabularnewline
30 & 8.7 & 8.4685220438779 & 0.231477956122100 \tabularnewline
31 & 8.6 & 8.31362045636693 & 0.286379543633068 \tabularnewline
32 & 8.5 & 7.97571146193711 & 0.524288538062891 \tabularnewline
33 & 8.3 & 7.65849946936401 & 0.641500530635986 \tabularnewline
34 & 8 & 7.5832268064108 & 0.416773193589198 \tabularnewline
35 & 8.2 & 8.3458631378874 & -0.145863137887410 \tabularnewline
36 & 8.1 & 8.33932557265716 & -0.239325572657158 \tabularnewline
37 & 8.1 & 8.08477944130326 & 0.015220558696742 \tabularnewline
38 & 8 & 7.74291710886332 & 0.257082891136680 \tabularnewline
39 & 7.9 & 7.58572769080411 & 0.314272309195890 \tabularnewline
40 & 7.9 & 7.73572769080411 & 0.164272309195891 \tabularnewline
41 & 8 & 7.94640211814695 & 0.0535978818530483 \tabularnewline
42 & 8 & 8.03256860793496 & -0.0325686079349559 \tabularnewline
43 & 7.9 & 7.87766702042399 & 0.0223329795760104 \tabularnewline
44 & 8 & 7.52080352877926 & 0.479196471220741 \tabularnewline
45 & 7.7 & 7.2604550278509 & 0.439544972149105 \tabularnewline
46 & 7.2 & 7.18518236489768 & 0.0148176351023201 \tabularnewline
47 & 7.5 & 7.90990970194447 & -0.409909701944466 \tabularnewline
48 & 7.3 & 8.0739626116484 & -0.773962611648409 \tabularnewline
49 & 7 & 7.8004619830796 & -0.8004619830796 \tabularnewline
50 & 7 & 7.3448726673502 & -0.3448726673502 \tabularnewline
51 & 7 & 7.18768324929099 & -0.187683249290987 \tabularnewline
52 & 7.2 & 7.28081975764626 & -0.0808197576462561 \tabularnewline
53 & 7.3 & 7.62417566549347 & -0.324175665493473 \tabularnewline
54 & 7.1 & 7.63452416642184 & -0.534524166421837 \tabularnewline
55 & 6.8 & 7.46066808169596 & -0.660668081695958 \tabularnewline
56 & 6.4 & 7.17962257891087 & -0.77962257891087 \tabularnewline
57 & 6.1 & 6.9192740779825 & -0.819274077982507 \tabularnewline
58 & 6.5 & 6.95772839831875 & -0.457728398318754 \tabularnewline
59 & 7.7 & 7.70141023258045 & -0.00141023258045101 \tabularnewline
60 & 7.9 & 7.80859965063966 & 0.0914003493603366 \tabularnewline
61 & 7.5 & 7.57300801650068 & -0.073008016500676 \tabularnewline
62 & 6.9 & 7.21219118684583 & -0.312191186845826 \tabularnewline
63 & 6.6 & 7.13081975764626 & -0.530819757646257 \tabularnewline
64 & 6.9 & 7.28081975764626 & -0.380819757646256 \tabularnewline
65 & 7.7 & 7.51044868220401 & 0.189551317795990 \tabularnewline
66 & 8 & 7.52079718313237 & 0.479202816867626 \tabularnewline
67 & 8 & 7.32798660119158 & 0.672013398808416 \tabularnewline
68 & 7.7 & 7.10380459005123 & 0.596195409948773 \tabularnewline
69 & 7.3 & 6.88136508355268 & 0.418634916447315 \tabularnewline
70 & 7.4 & 6.84400141502929 & 0.555998584970708 \tabularnewline
71 & 8.1 & 7.6066377465059 & 0.493362253494101 \tabularnewline
72 & 8.3 & 7.75173615899493 & 0.548263841005068 \tabularnewline
73 & 8.2 & 7.57300801650068 & 0.626991983499324 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71769&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]8.4[/C][C]8.91877731875937[/C][C]-0.518777318759372[/C][/ROW]
[ROW][C]2[/C][C]8.4[/C][C]8.6148239807492[/C][C]-0.214823980749204[/C][/ROW]
[ROW][C]3[/C][C]8.4[/C][C]8.43868006547508[/C][C]-0.0386800654750822[/C][/ROW]
[ROW][C]4[/C][C]8.6[/C][C]8.58868006547508[/C][C]0.0113199345249173[/C][/ROW]
[ROW][C]5[/C][C]8.9[/C][C]8.85621798446266[/C][C]0.0437820155373440[/C][/ROW]
[ROW][C]6[/C][C]8.8[/C][C]8.79074849653137[/C][C]0.00925150346862508[/C][/ROW]
[ROW][C]7[/C][C]8.3[/C][C]8.57898341737568[/C][C]-0.278983417375678[/C][/ROW]
[ROW][C]8[/C][C]7.5[/C][C]8.26002892016077[/C][C]-0.760028920160768[/C][/ROW]
[ROW][C]9[/C][C]7.2[/C][C]8.01863491644731[/C][C]-0.818634916447314[/C][/ROW]
[ROW][C]10[/C][C]7.4[/C][C]7.96231675070901[/C][C]-0.562316750709013[/C][/ROW]
[ROW][C]11[/C][C]8.8[/C][C]8.72495308218562[/C][C]0.0750469178143812[/C][/ROW]
[ROW][C]12[/C][C]9.3[/C][C]8.87005149467465[/C][C]0.429948505325351[/C][/ROW]
[ROW][C]13[/C][C]9.3[/C][C]8.67236885496549[/C][C]0.627631145034516[/C][/ROW]
[ROW][C]14[/C][C]8.7[/C][C]8.34946101974046[/C][C]0.350538980259543[/C][/ROW]
[ROW][C]15[/C][C]8.2[/C][C]8.19227160168124[/C][C]0.00772839831875522[/C][/ROW]
[ROW][C]16[/C][C]8.3[/C][C]8.41808959054089[/C][C]-0.118089590540886[/C][/ROW]
[ROW][C]17[/C][C]8.5[/C][C]8.68562750952846[/C][C]-0.185627509528463[/C][/ROW]
[ROW][C]18[/C][C]8.6[/C][C]8.75283950210156[/C][C]-0.152839502101558[/C][/ROW]
[ROW][C]19[/C][C]8.5[/C][C]8.54107442294586[/C][C]-0.0410744229458577[/C][/ROW]
[ROW][C]20[/C][C]8.2[/C][C]8.26002892016077[/C][C]-0.0600289201607676[/C][/ROW]
[ROW][C]21[/C][C]8.1[/C][C]7.96177142480258[/C][C]0.138228575197415[/C][/ROW]
[ROW][C]22[/C][C]7.9[/C][C]7.86754426463446[/C][C]0.0324557353655402[/C][/ROW]
[ROW][C]23[/C][C]8.6[/C][C]8.61122609889616[/C][C]-0.0112260988961556[/C][/ROW]
[ROW][C]24[/C][C]8.7[/C][C]8.75632451138519[/C][C]-0.0563245113851899[/C][/ROW]
[ROW][C]25[/C][C]8.7[/C][C]8.57759636889093[/C][C]0.122403631109067[/C][/ROW]
[ROW][C]26[/C][C]8.5[/C][C]8.235734036451[/C][C]0.264265963549006[/C][/ROW]
[ROW][C]27[/C][C]8.4[/C][C]7.96481763510232[/C][C]0.435182364897681[/C][/ROW]
[ROW][C]28[/C][C]8.5[/C][C]8.0958631378874[/C][C]0.40413686211259[/C][/ROW]
[ROW][C]29[/C][C]8.7[/C][C]8.47712804016444[/C][C]0.222871959835554[/C][/ROW]
[ROW][C]30[/C][C]8.7[/C][C]8.4685220438779[/C][C]0.231477956122100[/C][/ROW]
[ROW][C]31[/C][C]8.6[/C][C]8.31362045636693[/C][C]0.286379543633068[/C][/ROW]
[ROW][C]32[/C][C]8.5[/C][C]7.97571146193711[/C][C]0.524288538062891[/C][/ROW]
[ROW][C]33[/C][C]8.3[/C][C]7.65849946936401[/C][C]0.641500530635986[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]7.5832268064108[/C][C]0.416773193589198[/C][/ROW]
[ROW][C]35[/C][C]8.2[/C][C]8.3458631378874[/C][C]-0.145863137887410[/C][/ROW]
[ROW][C]36[/C][C]8.1[/C][C]8.33932557265716[/C][C]-0.239325572657158[/C][/ROW]
[ROW][C]37[/C][C]8.1[/C][C]8.08477944130326[/C][C]0.015220558696742[/C][/ROW]
[ROW][C]38[/C][C]8[/C][C]7.74291710886332[/C][C]0.257082891136680[/C][/ROW]
[ROW][C]39[/C][C]7.9[/C][C]7.58572769080411[/C][C]0.314272309195890[/C][/ROW]
[ROW][C]40[/C][C]7.9[/C][C]7.73572769080411[/C][C]0.164272309195891[/C][/ROW]
[ROW][C]41[/C][C]8[/C][C]7.94640211814695[/C][C]0.0535978818530483[/C][/ROW]
[ROW][C]42[/C][C]8[/C][C]8.03256860793496[/C][C]-0.0325686079349559[/C][/ROW]
[ROW][C]43[/C][C]7.9[/C][C]7.87766702042399[/C][C]0.0223329795760104[/C][/ROW]
[ROW][C]44[/C][C]8[/C][C]7.52080352877926[/C][C]0.479196471220741[/C][/ROW]
[ROW][C]45[/C][C]7.7[/C][C]7.2604550278509[/C][C]0.439544972149105[/C][/ROW]
[ROW][C]46[/C][C]7.2[/C][C]7.18518236489768[/C][C]0.0148176351023201[/C][/ROW]
[ROW][C]47[/C][C]7.5[/C][C]7.90990970194447[/C][C]-0.409909701944466[/C][/ROW]
[ROW][C]48[/C][C]7.3[/C][C]8.0739626116484[/C][C]-0.773962611648409[/C][/ROW]
[ROW][C]49[/C][C]7[/C][C]7.8004619830796[/C][C]-0.8004619830796[/C][/ROW]
[ROW][C]50[/C][C]7[/C][C]7.3448726673502[/C][C]-0.3448726673502[/C][/ROW]
[ROW][C]51[/C][C]7[/C][C]7.18768324929099[/C][C]-0.187683249290987[/C][/ROW]
[ROW][C]52[/C][C]7.2[/C][C]7.28081975764626[/C][C]-0.0808197576462561[/C][/ROW]
[ROW][C]53[/C][C]7.3[/C][C]7.62417566549347[/C][C]-0.324175665493473[/C][/ROW]
[ROW][C]54[/C][C]7.1[/C][C]7.63452416642184[/C][C]-0.534524166421837[/C][/ROW]
[ROW][C]55[/C][C]6.8[/C][C]7.46066808169596[/C][C]-0.660668081695958[/C][/ROW]
[ROW][C]56[/C][C]6.4[/C][C]7.17962257891087[/C][C]-0.77962257891087[/C][/ROW]
[ROW][C]57[/C][C]6.1[/C][C]6.9192740779825[/C][C]-0.819274077982507[/C][/ROW]
[ROW][C]58[/C][C]6.5[/C][C]6.95772839831875[/C][C]-0.457728398318754[/C][/ROW]
[ROW][C]59[/C][C]7.7[/C][C]7.70141023258045[/C][C]-0.00141023258045101[/C][/ROW]
[ROW][C]60[/C][C]7.9[/C][C]7.80859965063966[/C][C]0.0914003493603366[/C][/ROW]
[ROW][C]61[/C][C]7.5[/C][C]7.57300801650068[/C][C]-0.073008016500676[/C][/ROW]
[ROW][C]62[/C][C]6.9[/C][C]7.21219118684583[/C][C]-0.312191186845826[/C][/ROW]
[ROW][C]63[/C][C]6.6[/C][C]7.13081975764626[/C][C]-0.530819757646257[/C][/ROW]
[ROW][C]64[/C][C]6.9[/C][C]7.28081975764626[/C][C]-0.380819757646256[/C][/ROW]
[ROW][C]65[/C][C]7.7[/C][C]7.51044868220401[/C][C]0.189551317795990[/C][/ROW]
[ROW][C]66[/C][C]8[/C][C]7.52079718313237[/C][C]0.479202816867626[/C][/ROW]
[ROW][C]67[/C][C]8[/C][C]7.32798660119158[/C][C]0.672013398808416[/C][/ROW]
[ROW][C]68[/C][C]7.7[/C][C]7.10380459005123[/C][C]0.596195409948773[/C][/ROW]
[ROW][C]69[/C][C]7.3[/C][C]6.88136508355268[/C][C]0.418634916447315[/C][/ROW]
[ROW][C]70[/C][C]7.4[/C][C]6.84400141502929[/C][C]0.555998584970708[/C][/ROW]
[ROW][C]71[/C][C]8.1[/C][C]7.6066377465059[/C][C]0.493362253494101[/C][/ROW]
[ROW][C]72[/C][C]8.3[/C][C]7.75173615899493[/C][C]0.548263841005068[/C][/ROW]
[ROW][C]73[/C][C]8.2[/C][C]7.57300801650068[/C][C]0.626991983499324[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71769&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71769&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	8.4	8.91877731875937	-0.518777318759372
2	8.4	8.6148239807492	-0.214823980749204
3	8.4	8.43868006547508	-0.0386800654750822
4	8.6	8.58868006547508	0.0113199345249173
5	8.9	8.85621798446266	0.0437820155373440
6	8.8	8.79074849653137	0.00925150346862508
7	8.3	8.57898341737568	-0.278983417375678
8	7.5	8.26002892016077	-0.760028920160768
9	7.2	8.01863491644731	-0.818634916447314
10	7.4	7.96231675070901	-0.562316750709013
11	8.8	8.72495308218562	0.0750469178143812
12	9.3	8.87005149467465	0.429948505325351
13	9.3	8.67236885496549	0.627631145034516
14	8.7	8.34946101974046	0.350538980259543
15	8.2	8.19227160168124	0.00772839831875522
16	8.3	8.41808959054089	-0.118089590540886
17	8.5	8.68562750952846	-0.185627509528463
18	8.6	8.75283950210156	-0.152839502101558
19	8.5	8.54107442294586	-0.0410744229458577
20	8.2	8.26002892016077	-0.0600289201607676
21	8.1	7.96177142480258	0.138228575197415
22	7.9	7.86754426463446	0.0324557353655402
23	8.6	8.61122609889616	-0.0112260988961556
24	8.7	8.75632451138519	-0.0563245113851899
25	8.7	8.57759636889093	0.122403631109067
26	8.5	8.235734036451	0.264265963549006
27	8.4	7.96481763510232	0.435182364897681
28	8.5	8.0958631378874	0.40413686211259
29	8.7	8.47712804016444	0.222871959835554
30	8.7	8.4685220438779	0.231477956122100
31	8.6	8.31362045636693	0.286379543633068
32	8.5	7.97571146193711	0.524288538062891
33	8.3	7.65849946936401	0.641500530635986
34	8	7.5832268064108	0.416773193589198
35	8.2	8.3458631378874	-0.145863137887410
36	8.1	8.33932557265716	-0.239325572657158
37	8.1	8.08477944130326	0.015220558696742
38	8	7.74291710886332	0.257082891136680
39	7.9	7.58572769080411	0.314272309195890
40	7.9	7.73572769080411	0.164272309195891
41	8	7.94640211814695	0.0535978818530483
42	8	8.03256860793496	-0.0325686079349559
43	7.9	7.87766702042399	0.0223329795760104
44	8	7.52080352877926	0.479196471220741
45	7.7	7.2604550278509	0.439544972149105
46	7.2	7.18518236489768	0.0148176351023201
47	7.5	7.90990970194447	-0.409909701944466
48	7.3	8.0739626116484	-0.773962611648409
49	7	7.8004619830796	-0.8004619830796
50	7	7.3448726673502	-0.3448726673502
51	7	7.18768324929099	-0.187683249290987
52	7.2	7.28081975764626	-0.0808197576462561
53	7.3	7.62417566549347	-0.324175665493473
54	7.1	7.63452416642184	-0.534524166421837
55	6.8	7.46066808169596	-0.660668081695958
56	6.4	7.17962257891087	-0.77962257891087
57	6.1	6.9192740779825	-0.819274077982507
58	6.5	6.95772839831875	-0.457728398318754
59	7.7	7.70141023258045	-0.00141023258045101
60	7.9	7.80859965063966	0.0914003493603366
61	7.5	7.57300801650068	-0.073008016500676
62	6.9	7.21219118684583	-0.312191186845826
63	6.6	7.13081975764626	-0.530819757646257
64	6.9	7.28081975764626	-0.380819757646256
65	7.7	7.51044868220401	0.189551317795990
66	8	7.52079718313237	0.479202816867626
67	8	7.32798660119158	0.672013398808416
68	7.7	7.10380459005123	0.596195409948773
69	7.3	6.88136508355268	0.418634916447315
70	7.4	6.84400141502929	0.555998584970708
71	8.1	7.6066377465059	0.493362253494101
72	8.3	7.75173615899493	0.548263841005068
73	8.2	7.57300801650068	0.626991983499324

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.455070840551577	0.910141681103154	0.544929159448423
17	0.407600087532378	0.815200175064756	0.592399912467622
18	0.285990130023005	0.57198026004601	0.714009869976995
19	0.187834774270815	0.375669548541630	0.812165225729185
20	0.238518006125678	0.477036012251356	0.761481993874322
21	0.333649669404469	0.667299338808938	0.666350330595531
22	0.280598059746178	0.561196119492357	0.719401940253822
23	0.21367804341037	0.42735608682074	0.78632195658963
24	0.219912812593181	0.439825625186362	0.780087187406819
25	0.162045409423105	0.32409081884621	0.837954590576895
26	0.110119988153509	0.220239976307018	0.889880011846491
27	0.073895203418545	0.14779040683709	0.926104796581455
28	0.047569423942351	0.095138847884702	0.952430576057649
29	0.0284577423503733	0.0569154847007466	0.971542257649627
30	0.0163731757960353	0.0327463515920705	0.983626824203965
31	0.00954880911841636	0.0190976182368327	0.990451190881584
32	0.0107471582575501	0.0214943165151002	0.98925284174245
33	0.0114717928680272	0.0229435857360545	0.988528207131973
34	0.00727577892695357	0.0145515578539071	0.992724221073046
35	0.00900158258446219	0.0180031651689244	0.990998417415538
36	0.0229023211939820	0.0458046423879640	0.977097678806018
37	0.0238662328888059	0.0477324657776117	0.976133767111194
38	0.0205485971019279	0.0410971942038559	0.979451402898072
39	0.0184585063846128	0.0369170127692255	0.981541493615387
40	0.0154600038102840	0.0309200076205679	0.984539996189716
41	0.0114097046905800	0.0228194093811601	0.98859029530942
42	0.00826681199603015	0.0165336239920603	0.99173318800397
43	0.0059650225422706	0.0119300450845412	0.99403497745773
44	0.0117502531708912	0.0235005063417825	0.988249746829109
45	0.0746545595400973	0.149309119080195	0.925345440459903
46	0.160198427677807	0.320396855355615	0.839801572322193
47	0.198597880299571	0.397195760599142	0.801402119700429
48	0.296482073356868	0.592964146713737	0.703517926643132
49	0.363679356816687	0.727358713633374	0.636320643183313
50	0.522944172065068	0.954111655869865	0.477055827934932
51	0.629651513457192	0.740696973085616	0.370348486542808
52	0.550661878165937	0.898676243668126	0.449338121834063
53	0.550801336602287	0.898397326795426	0.449198663397713
54	0.451564363430038	0.903128726860076	0.548435636569962
55	0.346067125246831	0.692134250493663	0.653932874753169
56	0.374453597684712	0.748907195369425	0.625546402315288
57	0.649561992855417	0.700876014289166	0.350438007144583

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.455070840551577 & 0.910141681103154 & 0.544929159448423 \tabularnewline
17 & 0.407600087532378 & 0.815200175064756 & 0.592399912467622 \tabularnewline
18 & 0.285990130023005 & 0.57198026004601 & 0.714009869976995 \tabularnewline
19 & 0.187834774270815 & 0.375669548541630 & 0.812165225729185 \tabularnewline
20 & 0.238518006125678 & 0.477036012251356 & 0.761481993874322 \tabularnewline
21 & 0.333649669404469 & 0.667299338808938 & 0.666350330595531 \tabularnewline
22 & 0.280598059746178 & 0.561196119492357 & 0.719401940253822 \tabularnewline
23 & 0.21367804341037 & 0.42735608682074 & 0.78632195658963 \tabularnewline
24 & 0.219912812593181 & 0.439825625186362 & 0.780087187406819 \tabularnewline
25 & 0.162045409423105 & 0.32409081884621 & 0.837954590576895 \tabularnewline
26 & 0.110119988153509 & 0.220239976307018 & 0.889880011846491 \tabularnewline
27 & 0.073895203418545 & 0.14779040683709 & 0.926104796581455 \tabularnewline
28 & 0.047569423942351 & 0.095138847884702 & 0.952430576057649 \tabularnewline
29 & 0.0284577423503733 & 0.0569154847007466 & 0.971542257649627 \tabularnewline
30 & 0.0163731757960353 & 0.0327463515920705 & 0.983626824203965 \tabularnewline
31 & 0.00954880911841636 & 0.0190976182368327 & 0.990451190881584 \tabularnewline
32 & 0.0107471582575501 & 0.0214943165151002 & 0.98925284174245 \tabularnewline
33 & 0.0114717928680272 & 0.0229435857360545 & 0.988528207131973 \tabularnewline
34 & 0.00727577892695357 & 0.0145515578539071 & 0.992724221073046 \tabularnewline
35 & 0.00900158258446219 & 0.0180031651689244 & 0.990998417415538 \tabularnewline
36 & 0.0229023211939820 & 0.0458046423879640 & 0.977097678806018 \tabularnewline
37 & 0.0238662328888059 & 0.0477324657776117 & 0.976133767111194 \tabularnewline
38 & 0.0205485971019279 & 0.0410971942038559 & 0.979451402898072 \tabularnewline
39 & 0.0184585063846128 & 0.0369170127692255 & 0.981541493615387 \tabularnewline
40 & 0.0154600038102840 & 0.0309200076205679 & 0.984539996189716 \tabularnewline
41 & 0.0114097046905800 & 0.0228194093811601 & 0.98859029530942 \tabularnewline
42 & 0.00826681199603015 & 0.0165336239920603 & 0.99173318800397 \tabularnewline
43 & 0.0059650225422706 & 0.0119300450845412 & 0.99403497745773 \tabularnewline
44 & 0.0117502531708912 & 0.0235005063417825 & 0.988249746829109 \tabularnewline
45 & 0.0746545595400973 & 0.149309119080195 & 0.925345440459903 \tabularnewline
46 & 0.160198427677807 & 0.320396855355615 & 0.839801572322193 \tabularnewline
47 & 0.198597880299571 & 0.397195760599142 & 0.801402119700429 \tabularnewline
48 & 0.296482073356868 & 0.592964146713737 & 0.703517926643132 \tabularnewline
49 & 0.363679356816687 & 0.727358713633374 & 0.636320643183313 \tabularnewline
50 & 0.522944172065068 & 0.954111655869865 & 0.477055827934932 \tabularnewline
51 & 0.629651513457192 & 0.740696973085616 & 0.370348486542808 \tabularnewline
52 & 0.550661878165937 & 0.898676243668126 & 0.449338121834063 \tabularnewline
53 & 0.550801336602287 & 0.898397326795426 & 0.449198663397713 \tabularnewline
54 & 0.451564363430038 & 0.903128726860076 & 0.548435636569962 \tabularnewline
55 & 0.346067125246831 & 0.692134250493663 & 0.653932874753169 \tabularnewline
56 & 0.374453597684712 & 0.748907195369425 & 0.625546402315288 \tabularnewline
57 & 0.649561992855417 & 0.700876014289166 & 0.350438007144583 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71769&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]16[/C][C]0.455070840551577[/C][C]0.910141681103154[/C][C]0.544929159448423[/C][/ROW]
[ROW][C]17[/C][C]0.407600087532378[/C][C]0.815200175064756[/C][C]0.592399912467622[/C][/ROW]
[ROW][C]18[/C][C]0.285990130023005[/C][C]0.57198026004601[/C][C]0.714009869976995[/C][/ROW]
[ROW][C]19[/C][C]0.187834774270815[/C][C]0.375669548541630[/C][C]0.812165225729185[/C][/ROW]
[ROW][C]20[/C][C]0.238518006125678[/C][C]0.477036012251356[/C][C]0.761481993874322[/C][/ROW]
[ROW][C]21[/C][C]0.333649669404469[/C][C]0.667299338808938[/C][C]0.666350330595531[/C][/ROW]
[ROW][C]22[/C][C]0.280598059746178[/C][C]0.561196119492357[/C][C]0.719401940253822[/C][/ROW]
[ROW][C]23[/C][C]0.21367804341037[/C][C]0.42735608682074[/C][C]0.78632195658963[/C][/ROW]
[ROW][C]24[/C][C]0.219912812593181[/C][C]0.439825625186362[/C][C]0.780087187406819[/C][/ROW]
[ROW][C]25[/C][C]0.162045409423105[/C][C]0.32409081884621[/C][C]0.837954590576895[/C][/ROW]
[ROW][C]26[/C][C]0.110119988153509[/C][C]0.220239976307018[/C][C]0.889880011846491[/C][/ROW]
[ROW][C]27[/C][C]0.073895203418545[/C][C]0.14779040683709[/C][C]0.926104796581455[/C][/ROW]
[ROW][C]28[/C][C]0.047569423942351[/C][C]0.095138847884702[/C][C]0.952430576057649[/C][/ROW]
[ROW][C]29[/C][C]0.0284577423503733[/C][C]0.0569154847007466[/C][C]0.971542257649627[/C][/ROW]
[ROW][C]30[/C][C]0.0163731757960353[/C][C]0.0327463515920705[/C][C]0.983626824203965[/C][/ROW]
[ROW][C]31[/C][C]0.00954880911841636[/C][C]0.0190976182368327[/C][C]0.990451190881584[/C][/ROW]
[ROW][C]32[/C][C]0.0107471582575501[/C][C]0.0214943165151002[/C][C]0.98925284174245[/C][/ROW]
[ROW][C]33[/C][C]0.0114717928680272[/C][C]0.0229435857360545[/C][C]0.988528207131973[/C][/ROW]
[ROW][C]34[/C][C]0.00727577892695357[/C][C]0.0145515578539071[/C][C]0.992724221073046[/C][/ROW]
[ROW][C]35[/C][C]0.00900158258446219[/C][C]0.0180031651689244[/C][C]0.990998417415538[/C][/ROW]
[ROW][C]36[/C][C]0.0229023211939820[/C][C]0.0458046423879640[/C][C]0.977097678806018[/C][/ROW]
[ROW][C]37[/C][C]0.0238662328888059[/C][C]0.0477324657776117[/C][C]0.976133767111194[/C][/ROW]
[ROW][C]38[/C][C]0.0205485971019279[/C][C]0.0410971942038559[/C][C]0.979451402898072[/C][/ROW]
[ROW][C]39[/C][C]0.0184585063846128[/C][C]0.0369170127692255[/C][C]0.981541493615387[/C][/ROW]
[ROW][C]40[/C][C]0.0154600038102840[/C][C]0.0309200076205679[/C][C]0.984539996189716[/C][/ROW]
[ROW][C]41[/C][C]0.0114097046905800[/C][C]0.0228194093811601[/C][C]0.98859029530942[/C][/ROW]
[ROW][C]42[/C][C]0.00826681199603015[/C][C]0.0165336239920603[/C][C]0.99173318800397[/C][/ROW]
[ROW][C]43[/C][C]0.0059650225422706[/C][C]0.0119300450845412[/C][C]0.99403497745773[/C][/ROW]
[ROW][C]44[/C][C]0.0117502531708912[/C][C]0.0235005063417825[/C][C]0.988249746829109[/C][/ROW]
[ROW][C]45[/C][C]0.0746545595400973[/C][C]0.149309119080195[/C][C]0.925345440459903[/C][/ROW]
[ROW][C]46[/C][C]0.160198427677807[/C][C]0.320396855355615[/C][C]0.839801572322193[/C][/ROW]
[ROW][C]47[/C][C]0.198597880299571[/C][C]0.397195760599142[/C][C]0.801402119700429[/C][/ROW]
[ROW][C]48[/C][C]0.296482073356868[/C][C]0.592964146713737[/C][C]0.703517926643132[/C][/ROW]
[ROW][C]49[/C][C]0.363679356816687[/C][C]0.727358713633374[/C][C]0.636320643183313[/C][/ROW]
[ROW][C]50[/C][C]0.522944172065068[/C][C]0.954111655869865[/C][C]0.477055827934932[/C][/ROW]
[ROW][C]51[/C][C]0.629651513457192[/C][C]0.740696973085616[/C][C]0.370348486542808[/C][/ROW]
[ROW][C]52[/C][C]0.550661878165937[/C][C]0.898676243668126[/C][C]0.449338121834063[/C][/ROW]
[ROW][C]53[/C][C]0.550801336602287[/C][C]0.898397326795426[/C][C]0.449198663397713[/C][/ROW]
[ROW][C]54[/C][C]0.451564363430038[/C][C]0.903128726860076[/C][C]0.548435636569962[/C][/ROW]
[ROW][C]55[/C][C]0.346067125246831[/C][C]0.692134250493663[/C][C]0.653932874753169[/C][/ROW]
[ROW][C]56[/C][C]0.374453597684712[/C][C]0.748907195369425[/C][C]0.625546402315288[/C][/ROW]
[ROW][C]57[/C][C]0.649561992855417[/C][C]0.700876014289166[/C][C]0.350438007144583[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71769&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71769&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
16	0.455070840551577	0.910141681103154	0.544929159448423
17	0.407600087532378	0.815200175064756	0.592399912467622
18	0.285990130023005	0.57198026004601	0.714009869976995
19	0.187834774270815	0.375669548541630	0.812165225729185
20	0.238518006125678	0.477036012251356	0.761481993874322
21	0.333649669404469	0.667299338808938	0.666350330595531
22	0.280598059746178	0.561196119492357	0.719401940253822
23	0.21367804341037	0.42735608682074	0.78632195658963
24	0.219912812593181	0.439825625186362	0.780087187406819
25	0.162045409423105	0.32409081884621	0.837954590576895
26	0.110119988153509	0.220239976307018	0.889880011846491
27	0.073895203418545	0.14779040683709	0.926104796581455
28	0.047569423942351	0.095138847884702	0.952430576057649
29	0.0284577423503733	0.0569154847007466	0.971542257649627
30	0.0163731757960353	0.0327463515920705	0.983626824203965
31	0.00954880911841636	0.0190976182368327	0.990451190881584
32	0.0107471582575501	0.0214943165151002	0.98925284174245
33	0.0114717928680272	0.0229435857360545	0.988528207131973
34	0.00727577892695357	0.0145515578539071	0.992724221073046
35	0.00900158258446219	0.0180031651689244	0.990998417415538
36	0.0229023211939820	0.0458046423879640	0.977097678806018
37	0.0238662328888059	0.0477324657776117	0.976133767111194
38	0.0205485971019279	0.0410971942038559	0.979451402898072
39	0.0184585063846128	0.0369170127692255	0.981541493615387
40	0.0154600038102840	0.0309200076205679	0.984539996189716
41	0.0114097046905800	0.0228194093811601	0.98859029530942
42	0.00826681199603015	0.0165336239920603	0.99173318800397
43	0.0059650225422706	0.0119300450845412	0.99403497745773
44	0.0117502531708912	0.0235005063417825	0.988249746829109
45	0.0746545595400973	0.149309119080195	0.925345440459903
46	0.160198427677807	0.320396855355615	0.839801572322193
47	0.198597880299571	0.397195760599142	0.801402119700429
48	0.296482073356868	0.592964146713737	0.703517926643132
49	0.363679356816687	0.727358713633374	0.636320643183313
50	0.522944172065068	0.954111655869865	0.477055827934932
51	0.629651513457192	0.740696973085616	0.370348486542808
52	0.550661878165937	0.898676243668126	0.449338121834063
53	0.550801336602287	0.898397326795426	0.449198663397713
54	0.451564363430038	0.903128726860076	0.548435636569962
55	0.346067125246831	0.692134250493663	0.653932874753169
56	0.374453597684712	0.748907195369425	0.625546402315288
57	0.649561992855417	0.700876014289166	0.350438007144583

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	15	0.357142857142857	NOK
10% type I error level	17	0.404761904761905	NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 15 & 0.357142857142857 & NOK \tabularnewline
10% type I error level & 17 & 0.404761904761905 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71769&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]15[/C][C]0.357142857142857[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]17[/C][C]0.404761904761905[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71769&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71769&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	15	0.357142857142857	NOK
10% type I error level	17	0.404761904761905	NOK

Figure 1

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code