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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Sat, 12 Dec 2009 08:59:20 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/12/t1260633780pvkld0e7lh5j2l4.htm/, Retrieved Mon, 29 Apr 2024 10:24:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67028, Retrieved Mon, 29 Apr 2024 10:24:45 +0000

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Estimated Impact

112

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

-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 14:03:14] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-12-12 15:59:20] [14869f38c4320b00c96ca15cc00142de] [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	8 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 & 8 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67028&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]8 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=67028&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67028&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	8 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 4.05218005035397 + 5.57247979453095X[t] -9.08018148401166M1[t] -17.4122026084505M2[t] -87.6026002969237M3[t] -51.9540472089442M4[t] -56.6728845833714M5[t] -99.4931816097101M6[t] + 91.5516560161159M7[t] + 47.0075301255981M8[t] -37.6725414556083M9[t] -56.6356025629257M10[t] -40.4908145377453M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  4.05218005035397 +  5.57247979453095X[t] -9.08018148401166M1[t] -17.4122026084505M2[t] -87.6026002969237M3[t] -51.9540472089442M4[t] -56.6728845833714M5[t] -99.4931816097101M6[t] +  91.5516560161159M7[t] +  47.0075301255981M8[t] -37.6725414556083M9[t] -56.6356025629257M10[t] -40.4908145377453M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67028&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  4.05218005035397 +  5.57247979453095X[t] -9.08018148401166M1[t] -17.4122026084505M2[t] -87.6026002969237M3[t] -51.9540472089442M4[t] -56.6728845833714M5[t] -99.4931816097101M6[t] +  91.5516560161159M7[t] +  47.0075301255981M8[t] -37.6725414556083M9[t] -56.6356025629257M10[t] -40.4908145377453M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67028&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67028&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] = + 4.05218005035397 + 5.57247979453095X[t] -9.08018148401166M1[t] -17.4122026084505M2[t] -87.6026002969237M3[t] -51.9540472089442M4[t] -56.6728845833714M5[t] -99.4931816097101M6[t] + 91.5516560161159M7[t] + 47.0075301255981M8[t] -37.6725414556083M9[t] -56.6356025629257M10[t] -40.4908145377453M11[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)	4.05218005035397	155.550381	0.0261	0.979305	0.489652
X	5.57247979453095	1.580513	3.5257	0.000824	0.000412
M1	-9.08018148401166	28.606605	-0.3174	0.752049	0.376024
M2	-17.4122026084505	28.586623	-0.6091	0.544794	0.272397
M3	-87.6026002969237	33.900969	-2.5841	0.012259	0.00613
M4	-51.9540472089442	29.223644	-1.7778	0.080589	0.040294
M5	-56.6728845833714	29.159464	-1.9436	0.056724	0.028362
M6	-99.4931816097101	33.986215	-2.9275	0.004848	0.002424
M7	91.5516560161159	35.109688	2.6076	0.011531	0.005765
M8	47.0075301255981	28.884544	1.6274	0.108975	0.054488
M9	-37.6725414556083	34.641859	-1.0875	0.281245	0.140622
M10	-56.6356025629257	35.652986	-1.5885	0.117513	0.058757
M11	-40.4908145377453	30.716634	-1.3182	0.19253	0.096265

\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) & 4.05218005035397 & 155.550381 & 0.0261 & 0.979305 & 0.489652 \tabularnewline
X & 5.57247979453095 & 1.580513 & 3.5257 & 0.000824 & 0.000412 \tabularnewline
M1 & -9.08018148401166 & 28.606605 & -0.3174 & 0.752049 & 0.376024 \tabularnewline
M2 & -17.4122026084505 & 28.586623 & -0.6091 & 0.544794 & 0.272397 \tabularnewline
M3 & -87.6026002969237 & 33.900969 & -2.5841 & 0.012259 & 0.00613 \tabularnewline
M4 & -51.9540472089442 & 29.223644 & -1.7778 & 0.080589 & 0.040294 \tabularnewline
M5 & -56.6728845833714 & 29.159464 & -1.9436 & 0.056724 & 0.028362 \tabularnewline
M6 & -99.4931816097101 & 33.986215 & -2.9275 & 0.004848 & 0.002424 \tabularnewline
M7 & 91.5516560161159 & 35.109688 & 2.6076 & 0.011531 & 0.005765 \tabularnewline
M8 & 47.0075301255981 & 28.884544 & 1.6274 & 0.108975 & 0.054488 \tabularnewline
M9 & -37.6725414556083 & 34.641859 & -1.0875 & 0.281245 & 0.140622 \tabularnewline
M10 & -56.6356025629257 & 35.652986 & -1.5885 & 0.117513 & 0.058757 \tabularnewline
M11 & -40.4908145377453 & 30.716634 & -1.3182 & 0.19253 & 0.096265 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67028&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]4.05218005035397[/C][C]155.550381[/C][C]0.0261[/C][C]0.979305[/C][C]0.489652[/C][/ROW]
[ROW][C]X[/C][C]5.57247979453095[/C][C]1.580513[/C][C]3.5257[/C][C]0.000824[/C][C]0.000412[/C][/ROW]
[ROW][C]M1[/C][C]-9.08018148401166[/C][C]28.606605[/C][C]-0.3174[/C][C]0.752049[/C][C]0.376024[/C][/ROW]
[ROW][C]M2[/C][C]-17.4122026084505[/C][C]28.586623[/C][C]-0.6091[/C][C]0.544794[/C][C]0.272397[/C][/ROW]
[ROW][C]M3[/C][C]-87.6026002969237[/C][C]33.900969[/C][C]-2.5841[/C][C]0.012259[/C][C]0.00613[/C][/ROW]
[ROW][C]M4[/C][C]-51.9540472089442[/C][C]29.223644[/C][C]-1.7778[/C][C]0.080589[/C][C]0.040294[/C][/ROW]
[ROW][C]M5[/C][C]-56.6728845833714[/C][C]29.159464[/C][C]-1.9436[/C][C]0.056724[/C][C]0.028362[/C][/ROW]
[ROW][C]M6[/C][C]-99.4931816097101[/C][C]33.986215[/C][C]-2.9275[/C][C]0.004848[/C][C]0.002424[/C][/ROW]
[ROW][C]M7[/C][C]91.5516560161159[/C][C]35.109688[/C][C]2.6076[/C][C]0.011531[/C][C]0.005765[/C][/ROW]
[ROW][C]M8[/C][C]47.0075301255981[/C][C]28.884544[/C][C]1.6274[/C][C]0.108975[/C][C]0.054488[/C][/ROW]
[ROW][C]M9[/C][C]-37.6725414556083[/C][C]34.641859[/C][C]-1.0875[/C][C]0.281245[/C][C]0.140622[/C][/ROW]
[ROW][C]M10[/C][C]-56.6356025629257[/C][C]35.652986[/C][C]-1.5885[/C][C]0.117513[/C][C]0.058757[/C][/ROW]
[ROW][C]M11[/C][C]-40.4908145377453[/C][C]30.716634[/C][C]-1.3182[/C][C]0.19253[/C][C]0.096265[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67028&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67028&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)	4.05218005035397	155.550381	0.0261	0.979305	0.489652
X	5.57247979453095	1.580513	3.5257	0.000824	0.000412
M1	-9.08018148401166	28.606605	-0.3174	0.752049	0.376024
M2	-17.4122026084505	28.586623	-0.6091	0.544794	0.272397
M3	-87.6026002969237	33.900969	-2.5841	0.012259	0.00613
M4	-51.9540472089442	29.223644	-1.7778	0.080589	0.040294
M5	-56.6728845833714	29.159464	-1.9436	0.056724	0.028362
M6	-99.4931816097101	33.986215	-2.9275	0.004848	0.002424
M7	91.5516560161159	35.109688	2.6076	0.011531	0.005765
M8	47.0075301255981	28.884544	1.6274	0.108975	0.054488
M9	-37.6725414556083	34.641859	-1.0875	0.281245	0.140622
M10	-56.6356025629257	35.652986	-1.5885	0.117513	0.058757
M11	-40.4908145377453	30.716634	-1.3182	0.19253	0.096265

Multiple Linear Regression - Regression Statistics
Multiple R	0.576906910484904
R-squared	0.332821583365237
Adjusted R-squared	0.197124278286980
F-TEST (value)	2.45267644168245
F-TEST (DF numerator)	12
F-TEST (DF denominator)	59
p-value	0.0114715642009897
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	49.5074076690988
Sum Squared Residuals	144608.021432746

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.576906910484904 \tabularnewline
R-squared & 0.332821583365237 \tabularnewline
Adjusted R-squared & 0.197124278286980 \tabularnewline
F-TEST (value) & 2.45267644168245 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 59 \tabularnewline
p-value & 0.0114715642009897 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 49.5074076690988 \tabularnewline
Sum Squared Residuals & 144608.021432746 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67028&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.576906910484904[/C][/ROW]
[ROW][C]R-squared[/C][C]0.332821583365237[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.197124278286980[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]2.45267644168245[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]59[/C][/ROW]
[ROW][C]p-value[/C][C]0.0114715642009897[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]49.5074076690988[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]144608.021432746[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67028&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67028&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	0.576906910484904
R-squared	0.332821583365237
Adjusted R-squared	0.197124278286980
F-TEST (value)	2.45267644168245
F-TEST (DF numerator)	12
F-TEST (DF denominator)	59
p-value	0.0114715642009897
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	49.5074076690988
Sum Squared Residuals	144608.021432746

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	467	545.533002266007	-78.5330022660068
2	460	546.674196792265	-86.6741967922649
3	448	531.651349069648	-83.651349069648
4	443	489.285185034194	-46.2851850341943
5	436	515.214986529687	-79.2149865296873
6	431	496.356352619832	-65.3563526198317
7	484	546.974699423478	-62.9746994234775
8	510	578.773546718034	-68.773546718034
9	513	529.200097842372	-16.2000978423725
10	503	557.045867009115	-54.0458670091151
11	471	533.626048493126	-62.6260484931257
12	471	509.476097414312	-38.4760974143121
13	476	531.044554800221	-55.0445548002206
14	475	522.155285696329	-47.1552856963286
15	470	507.132437973712	-37.1324379737118
16	461	526.620799657552	-65.6207996575516
17	455	515.77223450914	-60.7722345091404
18	456	487.997632928035	-31.9976329280352
19	517	574.837098396132	-57.8370983961324
20	525	564.285099252253	-39.2850992522534
21	523	562.077728630105	-39.0777286301051
22	519	574.877802351614	-55.8778023516141
23	509	530.282560616407	-21.2825606164072
24	512	516.720321147202	-4.72032114720225
25	519	537.731530553658	-18.7315305536578
26	517	527.170517511407	-10.1705175114065
27	510	503.788950096993	6.21104990300668
28	509	524.391807739739	-15.3918077397392
29	501	494.03956331047	6.96043668953036
30	507	486.883136969129	20.116863030871
31	569	582.638570108476	-13.6385701084758
32	580	552.025643704285	27.9743562957146
33	578	578.237920034245	-0.237920034244812
34	565	569.862570536536	-4.86257053653626
35	547	513.007873253361	33.9921267466388
36	555	544.025472140404	10.9745278595961
37	562	524.914827026236	37.0851729737635
38	561	527.170517511407	33.8294824885935
39	555	544.468052597069	10.5319474029308
40	544	525.506303698645	18.4936963013546
41	537	490.138827454298	46.8611725457020
42	543	525.333247551393	17.6667524486074
43	594	582.638570108476	11.3614298915242
44	611	590.475754286549	20.5242457134511
45	613	602.199583150728	10.8004168492721
46	611	562.061098824193	48.9389011758071
47	594	542.542016164375	51.4579838356247
48	595	570.216127174699	24.7838728253006
49	591	522.128587128971	68.871412871029
50	589	521.040789737423	67.9592102625775
51	584	499.888214240822	84.1117857591784
52	573	524.949055719192	48.0509442808077
53	567	494.03956331047	72.9604366895303
54	569	539.26444703772	29.7355529622800
55	621	546.417451444025	74.5825485559754
56	629	584.346026512565	44.6539734874351
57	628	597.18435133565	30.8156486643499
58	612	537.542187728257	74.4578122717432
59	595	569.847167157577	25.1528328424231
60	597	574.116863030871	22.8831369691290
61	593	546.647498224907	46.3525017750927
62	590	547.788692751171	42.2113072488290
63	580	560.070996021756	19.9290039782441
64	574	513.246848150677	60.7531518493227
65	573	559.794824885935	13.2051751140651
66	573	543.165182893892	29.8348171061084
67	620	571.493610519414	48.5063894805862
68	626	611.093929526313	14.9060704736866
69	620	606.1003190069	13.8996809931004
70	588	596.610473550285	-8.6104735502848
71	566	592.694334315154	-26.6943343151538
72	557	572.445119092512	-15.4451190925118

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 467 & 545.533002266007 & -78.5330022660068 \tabularnewline
2 & 460 & 546.674196792265 & -86.6741967922649 \tabularnewline
3 & 448 & 531.651349069648 & -83.651349069648 \tabularnewline
4 & 443 & 489.285185034194 & -46.2851850341943 \tabularnewline
5 & 436 & 515.214986529687 & -79.2149865296873 \tabularnewline
6 & 431 & 496.356352619832 & -65.3563526198317 \tabularnewline
7 & 484 & 546.974699423478 & -62.9746994234775 \tabularnewline
8 & 510 & 578.773546718034 & -68.773546718034 \tabularnewline
9 & 513 & 529.200097842372 & -16.2000978423725 \tabularnewline
10 & 503 & 557.045867009115 & -54.0458670091151 \tabularnewline
11 & 471 & 533.626048493126 & -62.6260484931257 \tabularnewline
12 & 471 & 509.476097414312 & -38.4760974143121 \tabularnewline
13 & 476 & 531.044554800221 & -55.0445548002206 \tabularnewline
14 & 475 & 522.155285696329 & -47.1552856963286 \tabularnewline
15 & 470 & 507.132437973712 & -37.1324379737118 \tabularnewline
16 & 461 & 526.620799657552 & -65.6207996575516 \tabularnewline
17 & 455 & 515.77223450914 & -60.7722345091404 \tabularnewline
18 & 456 & 487.997632928035 & -31.9976329280352 \tabularnewline
19 & 517 & 574.837098396132 & -57.8370983961324 \tabularnewline
20 & 525 & 564.285099252253 & -39.2850992522534 \tabularnewline
21 & 523 & 562.077728630105 & -39.0777286301051 \tabularnewline
22 & 519 & 574.877802351614 & -55.8778023516141 \tabularnewline
23 & 509 & 530.282560616407 & -21.2825606164072 \tabularnewline
24 & 512 & 516.720321147202 & -4.72032114720225 \tabularnewline
25 & 519 & 537.731530553658 & -18.7315305536578 \tabularnewline
26 & 517 & 527.170517511407 & -10.1705175114065 \tabularnewline
27 & 510 & 503.788950096993 & 6.21104990300668 \tabularnewline
28 & 509 & 524.391807739739 & -15.3918077397392 \tabularnewline
29 & 501 & 494.03956331047 & 6.96043668953036 \tabularnewline
30 & 507 & 486.883136969129 & 20.116863030871 \tabularnewline
31 & 569 & 582.638570108476 & -13.6385701084758 \tabularnewline
32 & 580 & 552.025643704285 & 27.9743562957146 \tabularnewline
33 & 578 & 578.237920034245 & -0.237920034244812 \tabularnewline
34 & 565 & 569.862570536536 & -4.86257053653626 \tabularnewline
35 & 547 & 513.007873253361 & 33.9921267466388 \tabularnewline
36 & 555 & 544.025472140404 & 10.9745278595961 \tabularnewline
37 & 562 & 524.914827026236 & 37.0851729737635 \tabularnewline
38 & 561 & 527.170517511407 & 33.8294824885935 \tabularnewline
39 & 555 & 544.468052597069 & 10.5319474029308 \tabularnewline
40 & 544 & 525.506303698645 & 18.4936963013546 \tabularnewline
41 & 537 & 490.138827454298 & 46.8611725457020 \tabularnewline
42 & 543 & 525.333247551393 & 17.6667524486074 \tabularnewline
43 & 594 & 582.638570108476 & 11.3614298915242 \tabularnewline
44 & 611 & 590.475754286549 & 20.5242457134511 \tabularnewline
45 & 613 & 602.199583150728 & 10.8004168492721 \tabularnewline
46 & 611 & 562.061098824193 & 48.9389011758071 \tabularnewline
47 & 594 & 542.542016164375 & 51.4579838356247 \tabularnewline
48 & 595 & 570.216127174699 & 24.7838728253006 \tabularnewline
49 & 591 & 522.128587128971 & 68.871412871029 \tabularnewline
50 & 589 & 521.040789737423 & 67.9592102625775 \tabularnewline
51 & 584 & 499.888214240822 & 84.1117857591784 \tabularnewline
52 & 573 & 524.949055719192 & 48.0509442808077 \tabularnewline
53 & 567 & 494.03956331047 & 72.9604366895303 \tabularnewline
54 & 569 & 539.26444703772 & 29.7355529622800 \tabularnewline
55 & 621 & 546.417451444025 & 74.5825485559754 \tabularnewline
56 & 629 & 584.346026512565 & 44.6539734874351 \tabularnewline
57 & 628 & 597.18435133565 & 30.8156486643499 \tabularnewline
58 & 612 & 537.542187728257 & 74.4578122717432 \tabularnewline
59 & 595 & 569.847167157577 & 25.1528328424231 \tabularnewline
60 & 597 & 574.116863030871 & 22.8831369691290 \tabularnewline
61 & 593 & 546.647498224907 & 46.3525017750927 \tabularnewline
62 & 590 & 547.788692751171 & 42.2113072488290 \tabularnewline
63 & 580 & 560.070996021756 & 19.9290039782441 \tabularnewline
64 & 574 & 513.246848150677 & 60.7531518493227 \tabularnewline
65 & 573 & 559.794824885935 & 13.2051751140651 \tabularnewline
66 & 573 & 543.165182893892 & 29.8348171061084 \tabularnewline
67 & 620 & 571.493610519414 & 48.5063894805862 \tabularnewline
68 & 626 & 611.093929526313 & 14.9060704736866 \tabularnewline
69 & 620 & 606.1003190069 & 13.8996809931004 \tabularnewline
70 & 588 & 596.610473550285 & -8.6104735502848 \tabularnewline
71 & 566 & 592.694334315154 & -26.6943343151538 \tabularnewline
72 & 557 & 572.445119092512 & -15.4451190925118 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67028&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]467[/C][C]545.533002266007[/C][C]-78.5330022660068[/C][/ROW]
[ROW][C]2[/C][C]460[/C][C]546.674196792265[/C][C]-86.6741967922649[/C][/ROW]
[ROW][C]3[/C][C]448[/C][C]531.651349069648[/C][C]-83.651349069648[/C][/ROW]
[ROW][C]4[/C][C]443[/C][C]489.285185034194[/C][C]-46.2851850341943[/C][/ROW]
[ROW][C]5[/C][C]436[/C][C]515.214986529687[/C][C]-79.2149865296873[/C][/ROW]
[ROW][C]6[/C][C]431[/C][C]496.356352619832[/C][C]-65.3563526198317[/C][/ROW]
[ROW][C]7[/C][C]484[/C][C]546.974699423478[/C][C]-62.9746994234775[/C][/ROW]
[ROW][C]8[/C][C]510[/C][C]578.773546718034[/C][C]-68.773546718034[/C][/ROW]
[ROW][C]9[/C][C]513[/C][C]529.200097842372[/C][C]-16.2000978423725[/C][/ROW]
[ROW][C]10[/C][C]503[/C][C]557.045867009115[/C][C]-54.0458670091151[/C][/ROW]
[ROW][C]11[/C][C]471[/C][C]533.626048493126[/C][C]-62.6260484931257[/C][/ROW]
[ROW][C]12[/C][C]471[/C][C]509.476097414312[/C][C]-38.4760974143121[/C][/ROW]
[ROW][C]13[/C][C]476[/C][C]531.044554800221[/C][C]-55.0445548002206[/C][/ROW]
[ROW][C]14[/C][C]475[/C][C]522.155285696329[/C][C]-47.1552856963286[/C][/ROW]
[ROW][C]15[/C][C]470[/C][C]507.132437973712[/C][C]-37.1324379737118[/C][/ROW]
[ROW][C]16[/C][C]461[/C][C]526.620799657552[/C][C]-65.6207996575516[/C][/ROW]
[ROW][C]17[/C][C]455[/C][C]515.77223450914[/C][C]-60.7722345091404[/C][/ROW]
[ROW][C]18[/C][C]456[/C][C]487.997632928035[/C][C]-31.9976329280352[/C][/ROW]
[ROW][C]19[/C][C]517[/C][C]574.837098396132[/C][C]-57.8370983961324[/C][/ROW]
[ROW][C]20[/C][C]525[/C][C]564.285099252253[/C][C]-39.2850992522534[/C][/ROW]
[ROW][C]21[/C][C]523[/C][C]562.077728630105[/C][C]-39.0777286301051[/C][/ROW]
[ROW][C]22[/C][C]519[/C][C]574.877802351614[/C][C]-55.8778023516141[/C][/ROW]
[ROW][C]23[/C][C]509[/C][C]530.282560616407[/C][C]-21.2825606164072[/C][/ROW]
[ROW][C]24[/C][C]512[/C][C]516.720321147202[/C][C]-4.72032114720225[/C][/ROW]
[ROW][C]25[/C][C]519[/C][C]537.731530553658[/C][C]-18.7315305536578[/C][/ROW]
[ROW][C]26[/C][C]517[/C][C]527.170517511407[/C][C]-10.1705175114065[/C][/ROW]
[ROW][C]27[/C][C]510[/C][C]503.788950096993[/C][C]6.21104990300668[/C][/ROW]
[ROW][C]28[/C][C]509[/C][C]524.391807739739[/C][C]-15.3918077397392[/C][/ROW]
[ROW][C]29[/C][C]501[/C][C]494.03956331047[/C][C]6.96043668953036[/C][/ROW]
[ROW][C]30[/C][C]507[/C][C]486.883136969129[/C][C]20.116863030871[/C][/ROW]
[ROW][C]31[/C][C]569[/C][C]582.638570108476[/C][C]-13.6385701084758[/C][/ROW]
[ROW][C]32[/C][C]580[/C][C]552.025643704285[/C][C]27.9743562957146[/C][/ROW]
[ROW][C]33[/C][C]578[/C][C]578.237920034245[/C][C]-0.237920034244812[/C][/ROW]
[ROW][C]34[/C][C]565[/C][C]569.862570536536[/C][C]-4.86257053653626[/C][/ROW]
[ROW][C]35[/C][C]547[/C][C]513.007873253361[/C][C]33.9921267466388[/C][/ROW]
[ROW][C]36[/C][C]555[/C][C]544.025472140404[/C][C]10.9745278595961[/C][/ROW]
[ROW][C]37[/C][C]562[/C][C]524.914827026236[/C][C]37.0851729737635[/C][/ROW]
[ROW][C]38[/C][C]561[/C][C]527.170517511407[/C][C]33.8294824885935[/C][/ROW]
[ROW][C]39[/C][C]555[/C][C]544.468052597069[/C][C]10.5319474029308[/C][/ROW]
[ROW][C]40[/C][C]544[/C][C]525.506303698645[/C][C]18.4936963013546[/C][/ROW]
[ROW][C]41[/C][C]537[/C][C]490.138827454298[/C][C]46.8611725457020[/C][/ROW]
[ROW][C]42[/C][C]543[/C][C]525.333247551393[/C][C]17.6667524486074[/C][/ROW]
[ROW][C]43[/C][C]594[/C][C]582.638570108476[/C][C]11.3614298915242[/C][/ROW]
[ROW][C]44[/C][C]611[/C][C]590.475754286549[/C][C]20.5242457134511[/C][/ROW]
[ROW][C]45[/C][C]613[/C][C]602.199583150728[/C][C]10.8004168492721[/C][/ROW]
[ROW][C]46[/C][C]611[/C][C]562.061098824193[/C][C]48.9389011758071[/C][/ROW]
[ROW][C]47[/C][C]594[/C][C]542.542016164375[/C][C]51.4579838356247[/C][/ROW]
[ROW][C]48[/C][C]595[/C][C]570.216127174699[/C][C]24.7838728253006[/C][/ROW]
[ROW][C]49[/C][C]591[/C][C]522.128587128971[/C][C]68.871412871029[/C][/ROW]
[ROW][C]50[/C][C]589[/C][C]521.040789737423[/C][C]67.9592102625775[/C][/ROW]
[ROW][C]51[/C][C]584[/C][C]499.888214240822[/C][C]84.1117857591784[/C][/ROW]
[ROW][C]52[/C][C]573[/C][C]524.949055719192[/C][C]48.0509442808077[/C][/ROW]
[ROW][C]53[/C][C]567[/C][C]494.03956331047[/C][C]72.9604366895303[/C][/ROW]
[ROW][C]54[/C][C]569[/C][C]539.26444703772[/C][C]29.7355529622800[/C][/ROW]
[ROW][C]55[/C][C]621[/C][C]546.417451444025[/C][C]74.5825485559754[/C][/ROW]
[ROW][C]56[/C][C]629[/C][C]584.346026512565[/C][C]44.6539734874351[/C][/ROW]
[ROW][C]57[/C][C]628[/C][C]597.18435133565[/C][C]30.8156486643499[/C][/ROW]
[ROW][C]58[/C][C]612[/C][C]537.542187728257[/C][C]74.4578122717432[/C][/ROW]
[ROW][C]59[/C][C]595[/C][C]569.847167157577[/C][C]25.1528328424231[/C][/ROW]
[ROW][C]60[/C][C]597[/C][C]574.116863030871[/C][C]22.8831369691290[/C][/ROW]
[ROW][C]61[/C][C]593[/C][C]546.647498224907[/C][C]46.3525017750927[/C][/ROW]
[ROW][C]62[/C][C]590[/C][C]547.788692751171[/C][C]42.2113072488290[/C][/ROW]
[ROW][C]63[/C][C]580[/C][C]560.070996021756[/C][C]19.9290039782441[/C][/ROW]
[ROW][C]64[/C][C]574[/C][C]513.246848150677[/C][C]60.7531518493227[/C][/ROW]
[ROW][C]65[/C][C]573[/C][C]559.794824885935[/C][C]13.2051751140651[/C][/ROW]
[ROW][C]66[/C][C]573[/C][C]543.165182893892[/C][C]29.8348171061084[/C][/ROW]
[ROW][C]67[/C][C]620[/C][C]571.493610519414[/C][C]48.5063894805862[/C][/ROW]
[ROW][C]68[/C][C]626[/C][C]611.093929526313[/C][C]14.9060704736866[/C][/ROW]
[ROW][C]69[/C][C]620[/C][C]606.1003190069[/C][C]13.8996809931004[/C][/ROW]
[ROW][C]70[/C][C]588[/C][C]596.610473550285[/C][C]-8.6104735502848[/C][/ROW]
[ROW][C]71[/C][C]566[/C][C]592.694334315154[/C][C]-26.6943343151538[/C][/ROW]
[ROW][C]72[/C][C]557[/C][C]572.445119092512[/C][C]-15.4451190925118[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67028&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67028&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	467	545.533002266007	-78.5330022660068
2	460	546.674196792265	-86.6741967922649
3	448	531.651349069648	-83.651349069648
4	443	489.285185034194	-46.2851850341943
5	436	515.214986529687	-79.2149865296873
6	431	496.356352619832	-65.3563526198317
7	484	546.974699423478	-62.9746994234775
8	510	578.773546718034	-68.773546718034
9	513	529.200097842372	-16.2000978423725
10	503	557.045867009115	-54.0458670091151
11	471	533.626048493126	-62.6260484931257
12	471	509.476097414312	-38.4760974143121
13	476	531.044554800221	-55.0445548002206
14	475	522.155285696329	-47.1552856963286
15	470	507.132437973712	-37.1324379737118
16	461	526.620799657552	-65.6207996575516
17	455	515.77223450914	-60.7722345091404
18	456	487.997632928035	-31.9976329280352
19	517	574.837098396132	-57.8370983961324
20	525	564.285099252253	-39.2850992522534
21	523	562.077728630105	-39.0777286301051
22	519	574.877802351614	-55.8778023516141
23	509	530.282560616407	-21.2825606164072
24	512	516.720321147202	-4.72032114720225
25	519	537.731530553658	-18.7315305536578
26	517	527.170517511407	-10.1705175114065
27	510	503.788950096993	6.21104990300668
28	509	524.391807739739	-15.3918077397392
29	501	494.03956331047	6.96043668953036
30	507	486.883136969129	20.116863030871
31	569	582.638570108476	-13.6385701084758
32	580	552.025643704285	27.9743562957146
33	578	578.237920034245	-0.237920034244812
34	565	569.862570536536	-4.86257053653626
35	547	513.007873253361	33.9921267466388
36	555	544.025472140404	10.9745278595961
37	562	524.914827026236	37.0851729737635
38	561	527.170517511407	33.8294824885935
39	555	544.468052597069	10.5319474029308
40	544	525.506303698645	18.4936963013546
41	537	490.138827454298	46.8611725457020
42	543	525.333247551393	17.6667524486074
43	594	582.638570108476	11.3614298915242
44	611	590.475754286549	20.5242457134511
45	613	602.199583150728	10.8004168492721
46	611	562.061098824193	48.9389011758071
47	594	542.542016164375	51.4579838356247
48	595	570.216127174699	24.7838728253006
49	591	522.128587128971	68.871412871029
50	589	521.040789737423	67.9592102625775
51	584	499.888214240822	84.1117857591784
52	573	524.949055719192	48.0509442808077
53	567	494.03956331047	72.9604366895303
54	569	539.26444703772	29.7355529622800
55	621	546.417451444025	74.5825485559754
56	629	584.346026512565	44.6539734874351
57	628	597.18435133565	30.8156486643499
58	612	537.542187728257	74.4578122717432
59	595	569.847167157577	25.1528328424231
60	597	574.116863030871	22.8831369691290
61	593	546.647498224907	46.3525017750927
62	590	547.788692751171	42.2113072488290
63	580	560.070996021756	19.9290039782441
64	574	513.246848150677	60.7531518493227
65	573	559.794824885935	13.2051751140651
66	573	543.165182893892	29.8348171061084
67	620	571.493610519414	48.5063894805862
68	626	611.093929526313	14.9060704736866
69	620	606.1003190069	13.8996809931004
70	588	596.610473550285	-8.6104735502848
71	566	592.694334315154	-26.6943343151538
72	557	572.445119092512	-15.4451190925118

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
16	0.0569342615136426	0.113868523027285	0.943065738486357
17	0.0346614726223942	0.0693229452447884	0.965338527377606
18	0.0264580663791672	0.0529161327583345	0.973541933620833
19	0.0411693298481614	0.0823386596963229	0.958830670151839
20	0.0293289545694815	0.0586579091389629	0.970671045430519
21	0.0184169995391228	0.0368339990782456	0.981583000460877
22	0.0165099816106934	0.0330199632213868	0.983490018389307
23	0.034640907403994	0.069281814807988	0.965359092596006
24	0.0580653379073016	0.116130675814603	0.941934662092698
25	0.175983794857455	0.35196758971491	0.824016205142545
26	0.371993296082033	0.743986592164066	0.628006703917967
27	0.561949424290689	0.876101151418623	0.438050575709311
28	0.77680012196335	0.446399756073299	0.223199878036650
29	0.896303401415752	0.207393197168495	0.103696598584248
30	0.958729914902964	0.0825401701940721	0.0412700850970360
31	0.989425659453904	0.0211486810921925	0.0105743405460962
32	0.995121498854478	0.0097570022910443	0.00487850114552215
33	0.998110823031489	0.00377835393702244	0.00188917696851122
34	0.99923066312496	0.00153867375008027	0.000769336875040134
35	0.999685574280316	0.000628851439367929	0.000314425719683965
36	0.999824452838195	0.000351094323610872	0.000175547161805436
37	0.999942057065093	0.000115885869814312	5.79429349071562e-05
38	0.999977118704606	4.57625907873837e-05	2.28812953936918e-05
39	0.99998626916426	2.74616714800909e-05	1.37308357400455e-05
40	0.999992521672983	1.49566540343420e-05	7.47832701717102e-06
41	0.99999861372127	2.77255746140348e-06	1.38627873070174e-06
42	0.999999482156504	1.03568699207632e-06	5.17843496038158e-07
43	0.999999549779121	9.00441757919387e-07	4.50220878959693e-07
44	0.9999993459582	1.30808359924549e-06	6.54041799622746e-07
45	0.999998213196842	3.57360631575212e-06	1.78680315787606e-06
46	0.999996701002714	6.59799457287187e-06	3.29899728643594e-06
47	0.999991327648296	1.73447034075732e-05	8.67235170378658e-06
48	0.999983579453233	3.28410935345649e-05	1.64205467672825e-05
49	0.999960629350277	7.874129944706e-05	3.937064972353e-05
50	0.999893830246037	0.000212339507926434	0.000106169753963217
51	0.99972266762987	0.000554664740260523	0.000277332370130261
52	0.99907240532355	0.00185518935290029	0.000927594676450144
53	0.99848304858233	0.00303390283534185	0.00151695141767092
54	0.994419327177858	0.0111613456442834	0.00558067282214171
55	0.98333069523584	0.0333386095283207	0.0166693047641604
56	0.947107758468507	0.105784483062987	0.0528922415314934

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.0569342615136426 & 0.113868523027285 & 0.943065738486357 \tabularnewline
17 & 0.0346614726223942 & 0.0693229452447884 & 0.965338527377606 \tabularnewline
18 & 0.0264580663791672 & 0.0529161327583345 & 0.973541933620833 \tabularnewline
19 & 0.0411693298481614 & 0.0823386596963229 & 0.958830670151839 \tabularnewline
20 & 0.0293289545694815 & 0.0586579091389629 & 0.970671045430519 \tabularnewline
21 & 0.0184169995391228 & 0.0368339990782456 & 0.981583000460877 \tabularnewline
22 & 0.0165099816106934 & 0.0330199632213868 & 0.983490018389307 \tabularnewline
23 & 0.034640907403994 & 0.069281814807988 & 0.965359092596006 \tabularnewline
24 & 0.0580653379073016 & 0.116130675814603 & 0.941934662092698 \tabularnewline
25 & 0.175983794857455 & 0.35196758971491 & 0.824016205142545 \tabularnewline
26 & 0.371993296082033 & 0.743986592164066 & 0.628006703917967 \tabularnewline
27 & 0.561949424290689 & 0.876101151418623 & 0.438050575709311 \tabularnewline
28 & 0.77680012196335 & 0.446399756073299 & 0.223199878036650 \tabularnewline
29 & 0.896303401415752 & 0.207393197168495 & 0.103696598584248 \tabularnewline
30 & 0.958729914902964 & 0.0825401701940721 & 0.0412700850970360 \tabularnewline
31 & 0.989425659453904 & 0.0211486810921925 & 0.0105743405460962 \tabularnewline
32 & 0.995121498854478 & 0.0097570022910443 & 0.00487850114552215 \tabularnewline
33 & 0.998110823031489 & 0.00377835393702244 & 0.00188917696851122 \tabularnewline
34 & 0.99923066312496 & 0.00153867375008027 & 0.000769336875040134 \tabularnewline
35 & 0.999685574280316 & 0.000628851439367929 & 0.000314425719683965 \tabularnewline
36 & 0.999824452838195 & 0.000351094323610872 & 0.000175547161805436 \tabularnewline
37 & 0.999942057065093 & 0.000115885869814312 & 5.79429349071562e-05 \tabularnewline
38 & 0.999977118704606 & 4.57625907873837e-05 & 2.28812953936918e-05 \tabularnewline
39 & 0.99998626916426 & 2.74616714800909e-05 & 1.37308357400455e-05 \tabularnewline
40 & 0.999992521672983 & 1.49566540343420e-05 & 7.47832701717102e-06 \tabularnewline
41 & 0.99999861372127 & 2.77255746140348e-06 & 1.38627873070174e-06 \tabularnewline
42 & 0.999999482156504 & 1.03568699207632e-06 & 5.17843496038158e-07 \tabularnewline
43 & 0.999999549779121 & 9.00441757919387e-07 & 4.50220878959693e-07 \tabularnewline
44 & 0.9999993459582 & 1.30808359924549e-06 & 6.54041799622746e-07 \tabularnewline
45 & 0.999998213196842 & 3.57360631575212e-06 & 1.78680315787606e-06 \tabularnewline
46 & 0.999996701002714 & 6.59799457287187e-06 & 3.29899728643594e-06 \tabularnewline
47 & 0.999991327648296 & 1.73447034075732e-05 & 8.67235170378658e-06 \tabularnewline
48 & 0.999983579453233 & 3.28410935345649e-05 & 1.64205467672825e-05 \tabularnewline
49 & 0.999960629350277 & 7.874129944706e-05 & 3.937064972353e-05 \tabularnewline
50 & 0.999893830246037 & 0.000212339507926434 & 0.000106169753963217 \tabularnewline
51 & 0.99972266762987 & 0.000554664740260523 & 0.000277332370130261 \tabularnewline
52 & 0.99907240532355 & 0.00185518935290029 & 0.000927594676450144 \tabularnewline
53 & 0.99848304858233 & 0.00303390283534185 & 0.00151695141767092 \tabularnewline
54 & 0.994419327177858 & 0.0111613456442834 & 0.00558067282214171 \tabularnewline
55 & 0.98333069523584 & 0.0333386095283207 & 0.0166693047641604 \tabularnewline
56 & 0.947107758468507 & 0.105784483062987 & 0.0528922415314934 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67028&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]0.0569342615136426[/C][C]0.113868523027285[/C][C]0.943065738486357[/C][/ROW]
[ROW][C]17[/C][C]0.0346614726223942[/C][C]0.0693229452447884[/C][C]0.965338527377606[/C][/ROW]
[ROW][C]18[/C][C]0.0264580663791672[/C][C]0.0529161327583345[/C][C]0.973541933620833[/C][/ROW]
[ROW][C]19[/C][C]0.0411693298481614[/C][C]0.0823386596963229[/C][C]0.958830670151839[/C][/ROW]
[ROW][C]20[/C][C]0.0293289545694815[/C][C]0.0586579091389629[/C][C]0.970671045430519[/C][/ROW]
[ROW][C]21[/C][C]0.0184169995391228[/C][C]0.0368339990782456[/C][C]0.981583000460877[/C][/ROW]
[ROW][C]22[/C][C]0.0165099816106934[/C][C]0.0330199632213868[/C][C]0.983490018389307[/C][/ROW]
[ROW][C]23[/C][C]0.034640907403994[/C][C]0.069281814807988[/C][C]0.965359092596006[/C][/ROW]
[ROW][C]24[/C][C]0.0580653379073016[/C][C]0.116130675814603[/C][C]0.941934662092698[/C][/ROW]
[ROW][C]25[/C][C]0.175983794857455[/C][C]0.35196758971491[/C][C]0.824016205142545[/C][/ROW]
[ROW][C]26[/C][C]0.371993296082033[/C][C]0.743986592164066[/C][C]0.628006703917967[/C][/ROW]
[ROW][C]27[/C][C]0.561949424290689[/C][C]0.876101151418623[/C][C]0.438050575709311[/C][/ROW]
[ROW][C]28[/C][C]0.77680012196335[/C][C]0.446399756073299[/C][C]0.223199878036650[/C][/ROW]
[ROW][C]29[/C][C]0.896303401415752[/C][C]0.207393197168495[/C][C]0.103696598584248[/C][/ROW]
[ROW][C]30[/C][C]0.958729914902964[/C][C]0.0825401701940721[/C][C]0.0412700850970360[/C][/ROW]
[ROW][C]31[/C][C]0.989425659453904[/C][C]0.0211486810921925[/C][C]0.0105743405460962[/C][/ROW]
[ROW][C]32[/C][C]0.995121498854478[/C][C]0.0097570022910443[/C][C]0.00487850114552215[/C][/ROW]
[ROW][C]33[/C][C]0.998110823031489[/C][C]0.00377835393702244[/C][C]0.00188917696851122[/C][/ROW]
[ROW][C]34[/C][C]0.99923066312496[/C][C]0.00153867375008027[/C][C]0.000769336875040134[/C][/ROW]
[ROW][C]35[/C][C]0.999685574280316[/C][C]0.000628851439367929[/C][C]0.000314425719683965[/C][/ROW]
[ROW][C]36[/C][C]0.999824452838195[/C][C]0.000351094323610872[/C][C]0.000175547161805436[/C][/ROW]
[ROW][C]37[/C][C]0.999942057065093[/C][C]0.000115885869814312[/C][C]5.79429349071562e-05[/C][/ROW]
[ROW][C]38[/C][C]0.999977118704606[/C][C]4.57625907873837e-05[/C][C]2.28812953936918e-05[/C][/ROW]
[ROW][C]39[/C][C]0.99998626916426[/C][C]2.74616714800909e-05[/C][C]1.37308357400455e-05[/C][/ROW]
[ROW][C]40[/C][C]0.999992521672983[/C][C]1.49566540343420e-05[/C][C]7.47832701717102e-06[/C][/ROW]
[ROW][C]41[/C][C]0.99999861372127[/C][C]2.77255746140348e-06[/C][C]1.38627873070174e-06[/C][/ROW]
[ROW][C]42[/C][C]0.999999482156504[/C][C]1.03568699207632e-06[/C][C]5.17843496038158e-07[/C][/ROW]
[ROW][C]43[/C][C]0.999999549779121[/C][C]9.00441757919387e-07[/C][C]4.50220878959693e-07[/C][/ROW]
[ROW][C]44[/C][C]0.9999993459582[/C][C]1.30808359924549e-06[/C][C]6.54041799622746e-07[/C][/ROW]
[ROW][C]45[/C][C]0.999998213196842[/C][C]3.57360631575212e-06[/C][C]1.78680315787606e-06[/C][/ROW]
[ROW][C]46[/C][C]0.999996701002714[/C][C]6.59799457287187e-06[/C][C]3.29899728643594e-06[/C][/ROW]
[ROW][C]47[/C][C]0.999991327648296[/C][C]1.73447034075732e-05[/C][C]8.67235170378658e-06[/C][/ROW]
[ROW][C]48[/C][C]0.999983579453233[/C][C]3.28410935345649e-05[/C][C]1.64205467672825e-05[/C][/ROW]
[ROW][C]49[/C][C]0.999960629350277[/C][C]7.874129944706e-05[/C][C]3.937064972353e-05[/C][/ROW]
[ROW][C]50[/C][C]0.999893830246037[/C][C]0.000212339507926434[/C][C]0.000106169753963217[/C][/ROW]
[ROW][C]51[/C][C]0.99972266762987[/C][C]0.000554664740260523[/C][C]0.000277332370130261[/C][/ROW]
[ROW][C]52[/C][C]0.99907240532355[/C][C]0.00185518935290029[/C][C]0.000927594676450144[/C][/ROW]
[ROW][C]53[/C][C]0.99848304858233[/C][C]0.00303390283534185[/C][C]0.00151695141767092[/C][/ROW]
[ROW][C]54[/C][C]0.994419327177858[/C][C]0.0111613456442834[/C][C]0.00558067282214171[/C][/ROW]
[ROW][C]55[/C][C]0.98333069523584[/C][C]0.0333386095283207[/C][C]0.0166693047641604[/C][/ROW]
[ROW][C]56[/C][C]0.947107758468507[/C][C]0.105784483062987[/C][C]0.0528922415314934[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67028&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67028&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	0.0569342615136426	0.113868523027285	0.943065738486357
17	0.0346614726223942	0.0693229452447884	0.965338527377606
18	0.0264580663791672	0.0529161327583345	0.973541933620833
19	0.0411693298481614	0.0823386596963229	0.958830670151839
20	0.0293289545694815	0.0586579091389629	0.970671045430519
21	0.0184169995391228	0.0368339990782456	0.981583000460877
22	0.0165099816106934	0.0330199632213868	0.983490018389307
23	0.034640907403994	0.069281814807988	0.965359092596006
24	0.0580653379073016	0.116130675814603	0.941934662092698
25	0.175983794857455	0.35196758971491	0.824016205142545
26	0.371993296082033	0.743986592164066	0.628006703917967
27	0.561949424290689	0.876101151418623	0.438050575709311
28	0.77680012196335	0.446399756073299	0.223199878036650
29	0.896303401415752	0.207393197168495	0.103696598584248
30	0.958729914902964	0.0825401701940721	0.0412700850970360
31	0.989425659453904	0.0211486810921925	0.0105743405460962
32	0.995121498854478	0.0097570022910443	0.00487850114552215
33	0.998110823031489	0.00377835393702244	0.00188917696851122
34	0.99923066312496	0.00153867375008027	0.000769336875040134
35	0.999685574280316	0.000628851439367929	0.000314425719683965
36	0.999824452838195	0.000351094323610872	0.000175547161805436
37	0.999942057065093	0.000115885869814312	5.79429349071562e-05
38	0.999977118704606	4.57625907873837e-05	2.28812953936918e-05
39	0.99998626916426	2.74616714800909e-05	1.37308357400455e-05
40	0.999992521672983	1.49566540343420e-05	7.47832701717102e-06
41	0.99999861372127	2.77255746140348e-06	1.38627873070174e-06
42	0.999999482156504	1.03568699207632e-06	5.17843496038158e-07
43	0.999999549779121	9.00441757919387e-07	4.50220878959693e-07
44	0.9999993459582	1.30808359924549e-06	6.54041799622746e-07
45	0.999998213196842	3.57360631575212e-06	1.78680315787606e-06
46	0.999996701002714	6.59799457287187e-06	3.29899728643594e-06
47	0.999991327648296	1.73447034075732e-05	8.67235170378658e-06
48	0.999983579453233	3.28410935345649e-05	1.64205467672825e-05
49	0.999960629350277	7.874129944706e-05	3.937064972353e-05
50	0.999893830246037	0.000212339507926434	0.000106169753963217
51	0.99972266762987	0.000554664740260523	0.000277332370130261
52	0.99907240532355	0.00185518935290029	0.000927594676450144
53	0.99848304858233	0.00303390283534185	0.00151695141767092
54	0.994419327177858	0.0111613456442834	0.00558067282214171
55	0.98333069523584	0.0333386095283207	0.0166693047641604
56	0.947107758468507	0.105784483062987	0.0528922415314934

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	22	0.536585365853659	NOK
5% type I error level	27	0.658536585365854	NOK
10% type I error level	33	0.804878048780488	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 & 22 & 0.536585365853659 & NOK \tabularnewline
5% type I error level & 27 & 0.658536585365854 & NOK \tabularnewline
10% type I error level & 33 & 0.804878048780488 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67028&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]22[/C][C]0.536585365853659[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]27[/C][C]0.658536585365854[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]33[/C][C]0.804878048780488[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67028&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67028&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	22	0.536585365853659	NOK
5% type I error level	27	0.658536585365854	NOK
10% type I error level	33	0.804878048780488	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