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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationMon, 21 Nov 2011 13:32:24 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/21/t1321900418sc4vyc0sbisn7a2.htm/, Retrieved Thu, 28 Mar 2024 14:29:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=145899, Retrieved Thu, 28 Mar 2024 14:29:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [] [2010-11-17 09:55:05] [b98453cac15ba1066b407e146608df68]
- R  D    [Multiple Regression] [] [2011-11-21 18:32:24] [79818163420d1233b8d9d93d595e6c9e] [Current]
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Dataseries X:
1	1	1	1167	333	70
1	2	2	669	223	44
1	3	3	1053	371	35
1	4	4	1939	873	119
1	5	5	678	186	30
1	6	6	321	111	23
1	7	7	2667	1277	46
1	8	8	345	102	39
1	9	9	1367	580	58
1	10	10	1158	420	51
1	11	11	1385	521	65
1	12	12	1155	358	40
1	13	13	1120	435	41
1	14	14	1703	690	76
1	15	15	1189	393	31
1	16	16	3083	1149	82
1	17	17	1357	486	36
1	18	18	1892	767	62
1	19	19	883	338	28
1	20	20	1627	485	38
1	21	21	1412	465	70
1	22	22	1900	816	76
1	23	23	777	265	33
1	24	24	904	307	40
1	25	25	2115	850	126
1	26	26	1858	704	56
1	27	27	1781	693	63
1	28	28	1286	387	46
1	29	29	1035	406	35
1	30	30	1557	573	108
1	31	31	1527	595	34
1	32	32	1220	394	54
1	33	33	1368	521	35
0	34	0	564	172	23
0	35	0	1990	835	46
0	36	0	1557	669	49
0	37	0	2057	749	56
0	38	0	1111	368	38
0	39	0	686	216	19
0	40	0	2011	772	29
0	41	0	2232	1084	26
0	42	0	1032	445	52
0	43	0	1166	451	54
0	44	0	1020	300	45
0	45	0	1735	836	56
0	46	0	3623	1417	596
0	47	0	918	330	57
0	48	0	1579	477	55
0	49	0	2790	1028	99
0	50	0	1496	646	51
0	51	0	1108	342	21
0	52	0	496	218	20
0	53	0	1750	591	58
0	54	0	744	255	21
0	55	0	1101	434	66
0	56	0	1612	654	47
0	57	0	1805	478	55
0	58	0	2460	753	158
0	59	0	1653	689	46
0	60	0	1234	470	45




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145899&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145899&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145899&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Multiple Linear Regression - Estimated Regression Equation
TotalNrPV[t] = -60.577399224116 + 249.166762809405Pop[t] + 7.13109558056245t -2.90055463379471pop_t[t] + 2.06254796783972TotalNrCC[t] + 0.941493590867784TotalNrPRV[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
TotalNrPV[t] =  -60.577399224116 +  249.166762809405Pop[t] +  7.13109558056245t -2.90055463379471pop_t[t] +  2.06254796783972TotalNrCC[t] +  0.941493590867784TotalNrPRV[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145899&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]TotalNrPV[t] =  -60.577399224116 +  249.166762809405Pop[t] +  7.13109558056245t -2.90055463379471pop_t[t] +  2.06254796783972TotalNrCC[t] +  0.941493590867784TotalNrPRV[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145899&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145899&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
TotalNrPV[t] = -60.577399224116 + 249.166762809405Pop[t] + 7.13109558056245t -2.90055463379471pop_t[t] + 2.06254796783972TotalNrCC[t] + 0.941493590867784TotalNrPRV[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-60.577399224116215.741892-0.28080.7799470.389974
Pop249.166762809405218.0093881.14290.2581150.129057
t7.131095580562454.3702561.63170.1085540.054277
pop_t-2.900554633794715.456517-0.53160.59720.2986
TotalNrCC2.062547967839720.09811621.021600
TotalNrPRV0.9414935908677840.3653412.5770.012730.006365

\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) & -60.577399224116 & 215.741892 & -0.2808 & 0.779947 & 0.389974 \tabularnewline
Pop & 249.166762809405 & 218.009388 & 1.1429 & 0.258115 & 0.129057 \tabularnewline
t & 7.13109558056245 & 4.370256 & 1.6317 & 0.108554 & 0.054277 \tabularnewline
pop_t & -2.90055463379471 & 5.456517 & -0.5316 & 0.5972 & 0.2986 \tabularnewline
TotalNrCC & 2.06254796783972 & 0.098116 & 21.0216 & 0 & 0 \tabularnewline
TotalNrPRV & 0.941493590867784 & 0.365341 & 2.577 & 0.01273 & 0.006365 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145899&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]-60.577399224116[/C][C]215.741892[/C][C]-0.2808[/C][C]0.779947[/C][C]0.389974[/C][/ROW]
[ROW][C]Pop[/C][C]249.166762809405[/C][C]218.009388[/C][C]1.1429[/C][C]0.258115[/C][C]0.129057[/C][/ROW]
[ROW][C]t[/C][C]7.13109558056245[/C][C]4.370256[/C][C]1.6317[/C][C]0.108554[/C][C]0.054277[/C][/ROW]
[ROW][C]pop_t[/C][C]-2.90055463379471[/C][C]5.456517[/C][C]-0.5316[/C][C]0.5972[/C][C]0.2986[/C][/ROW]
[ROW][C]TotalNrCC[/C][C]2.06254796783972[/C][C]0.098116[/C][C]21.0216[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]TotalNrPRV[/C][C]0.941493590867784[/C][C]0.365341[/C][C]2.577[/C][C]0.01273[/C][C]0.006365[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145899&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145899&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
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-60.577399224116215.741892-0.28080.7799470.389974
Pop249.166762809405218.0093881.14290.2581150.129057
t7.131095580562454.3702561.63170.1085540.054277
pop_t-2.900554633794715.456517-0.53160.59720.2986
TotalNrCC2.062547967839720.09811621.021600
TotalNrPRV0.9414935908677840.3653412.5770.012730.006365







Multiple Linear Regression - Regression Statistics
Multiple R0.965497135333629
R-squared0.932184718337444
Adjusted R-squared0.925905525590911
F-TEST (value)148.456140138737
F-TEST (DF numerator)5
F-TEST (DF denominator)54
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation176.03906918437
Sum Squared Residuals1673446.70948217

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.965497135333629 \tabularnewline
R-squared & 0.932184718337444 \tabularnewline
Adjusted R-squared & 0.925905525590911 \tabularnewline
F-TEST (value) & 148.456140138737 \tabularnewline
F-TEST (DF numerator) & 5 \tabularnewline
F-TEST (DF denominator) & 54 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 176.03906918437 \tabularnewline
Sum Squared Residuals & 1673446.70948217 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145899&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.965497135333629[/C][/ROW]
[ROW][C]R-squared[/C][C]0.932184718337444[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.925905525590911[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]148.456140138737[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]5[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]54[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]176.03906918437[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1673446.70948217[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145899&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145899&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 R0.965497135333629
R-squared0.932184718337444
Adjusted R-squared0.925905525590911
F-TEST (value)148.456140138737
F-TEST (DF numerator)5
F-TEST (DF denominator)54
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation176.03906918437
Sum Squared Residuals1673446.70948217







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
11167945.55292918343221.44707081657
2669698.424360305266-29.4243603052656
31053999.43855817450253.5614418254981
419392118.1536406097-179.153640609704
5678621.6207980633556.3792019366498
6321464.569786286064-143.569786286064
726672895.38561032391-228.385610323907
8345469.531833922926-124.531833922926
913671477.54868172357-110.548681723569
1011581145.1810926799112.8189073200929
1113851370.9098886506414.0901113493643
1211551015.40777106783139.592228932166
1311201179.39599912913-59.3959991291282
1417031742.5285475554-39.5285475553975
1511891091.8151304647297.1848695352825
1630832703.34810823257379.651891767428
1713571296.8006413216960.1993586783139
1818921905.08599459398-13.0859945939781
19883992.472675248001-109.472675248001
2016271309.31270337589317.687296624115
2114121302.42007987363109.579920126372
2219002036.25391907734-136.253919077344
23777863.536305337111-86.5363053371106
24904960.984316069221-56.9843160692212
2521152166.14685236759-51.1468523675871
2618581803.3408386490154.6591613509891
2717811791.47380708562-10.4738070856162
2812861148.55927882868137.440721171323
2910351181.62180166485-146.621801664853
3015571599.0268853742-42.0268853742029
3115271578.96295588923-51.9629558892285
3212201187.4512271175732.5487728824321
3313681435.73698175349-67.7369817534924
34564558.2924535733995.70754642660127
3519901954.5472044216635.4527955783443
3615571622.11981811343-65.1198181134278
3720571800.84520625724256.154793742758
3811111005.19864145525105.801358544749
39686680.9340676976885.06593230231228
4020111844.25676930581166.743230694187
4122322492.07835007977-260.078350079766
4210321205.72012757331-173.720127573308
4311661227.10949814264-61.1094981426447
441020914.322408261599105.677591738401
4517352037.3356441038-302.335644103798
4636233751.21364806784-128.213648067842
479181008.89005712889-90.8900571288913
4815791317.33271680016261.667283199843
4927902502.35346065859287.646539341411
5014961676.39954016272-180.399540162724
5111081028.2712457939879.7287542060225
52496778.704899771546-282.704899771546
5317501590.9431438093159.056856190699
54744870.222859333609-126.222859333609
5511011288.91725274653-187.917252746532
5616121731.92052302535-119.920523025345
5718051383.57512499306421.424875006941
5824602054.88075158893405.119248411073
5916531824.56149505056-171.561495050555
6012341379.05309208335-145.053092083351

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1167 & 945.55292918343 & 221.44707081657 \tabularnewline
2 & 669 & 698.424360305266 & -29.4243603052656 \tabularnewline
3 & 1053 & 999.438558174502 & 53.5614418254981 \tabularnewline
4 & 1939 & 2118.1536406097 & -179.153640609704 \tabularnewline
5 & 678 & 621.62079806335 & 56.3792019366498 \tabularnewline
6 & 321 & 464.569786286064 & -143.569786286064 \tabularnewline
7 & 2667 & 2895.38561032391 & -228.385610323907 \tabularnewline
8 & 345 & 469.531833922926 & -124.531833922926 \tabularnewline
9 & 1367 & 1477.54868172357 & -110.548681723569 \tabularnewline
10 & 1158 & 1145.18109267991 & 12.8189073200929 \tabularnewline
11 & 1385 & 1370.90988865064 & 14.0901113493643 \tabularnewline
12 & 1155 & 1015.40777106783 & 139.592228932166 \tabularnewline
13 & 1120 & 1179.39599912913 & -59.3959991291282 \tabularnewline
14 & 1703 & 1742.5285475554 & -39.5285475553975 \tabularnewline
15 & 1189 & 1091.81513046472 & 97.1848695352825 \tabularnewline
16 & 3083 & 2703.34810823257 & 379.651891767428 \tabularnewline
17 & 1357 & 1296.80064132169 & 60.1993586783139 \tabularnewline
18 & 1892 & 1905.08599459398 & -13.0859945939781 \tabularnewline
19 & 883 & 992.472675248001 & -109.472675248001 \tabularnewline
20 & 1627 & 1309.31270337589 & 317.687296624115 \tabularnewline
21 & 1412 & 1302.42007987363 & 109.579920126372 \tabularnewline
22 & 1900 & 2036.25391907734 & -136.253919077344 \tabularnewline
23 & 777 & 863.536305337111 & -86.5363053371106 \tabularnewline
24 & 904 & 960.984316069221 & -56.9843160692212 \tabularnewline
25 & 2115 & 2166.14685236759 & -51.1468523675871 \tabularnewline
26 & 1858 & 1803.34083864901 & 54.6591613509891 \tabularnewline
27 & 1781 & 1791.47380708562 & -10.4738070856162 \tabularnewline
28 & 1286 & 1148.55927882868 & 137.440721171323 \tabularnewline
29 & 1035 & 1181.62180166485 & -146.621801664853 \tabularnewline
30 & 1557 & 1599.0268853742 & -42.0268853742029 \tabularnewline
31 & 1527 & 1578.96295588923 & -51.9629558892285 \tabularnewline
32 & 1220 & 1187.45122711757 & 32.5487728824321 \tabularnewline
33 & 1368 & 1435.73698175349 & -67.7369817534924 \tabularnewline
34 & 564 & 558.292453573399 & 5.70754642660127 \tabularnewline
35 & 1990 & 1954.54720442166 & 35.4527955783443 \tabularnewline
36 & 1557 & 1622.11981811343 & -65.1198181134278 \tabularnewline
37 & 2057 & 1800.84520625724 & 256.154793742758 \tabularnewline
38 & 1111 & 1005.19864145525 & 105.801358544749 \tabularnewline
39 & 686 & 680.934067697688 & 5.06593230231228 \tabularnewline
40 & 2011 & 1844.25676930581 & 166.743230694187 \tabularnewline
41 & 2232 & 2492.07835007977 & -260.078350079766 \tabularnewline
42 & 1032 & 1205.72012757331 & -173.720127573308 \tabularnewline
43 & 1166 & 1227.10949814264 & -61.1094981426447 \tabularnewline
44 & 1020 & 914.322408261599 & 105.677591738401 \tabularnewline
45 & 1735 & 2037.3356441038 & -302.335644103798 \tabularnewline
46 & 3623 & 3751.21364806784 & -128.213648067842 \tabularnewline
47 & 918 & 1008.89005712889 & -90.8900571288913 \tabularnewline
48 & 1579 & 1317.33271680016 & 261.667283199843 \tabularnewline
49 & 2790 & 2502.35346065859 & 287.646539341411 \tabularnewline
50 & 1496 & 1676.39954016272 & -180.399540162724 \tabularnewline
51 & 1108 & 1028.27124579398 & 79.7287542060225 \tabularnewline
52 & 496 & 778.704899771546 & -282.704899771546 \tabularnewline
53 & 1750 & 1590.9431438093 & 159.056856190699 \tabularnewline
54 & 744 & 870.222859333609 & -126.222859333609 \tabularnewline
55 & 1101 & 1288.91725274653 & -187.917252746532 \tabularnewline
56 & 1612 & 1731.92052302535 & -119.920523025345 \tabularnewline
57 & 1805 & 1383.57512499306 & 421.424875006941 \tabularnewline
58 & 2460 & 2054.88075158893 & 405.119248411073 \tabularnewline
59 & 1653 & 1824.56149505056 & -171.561495050555 \tabularnewline
60 & 1234 & 1379.05309208335 & -145.053092083351 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145899&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]1167[/C][C]945.55292918343[/C][C]221.44707081657[/C][/ROW]
[ROW][C]2[/C][C]669[/C][C]698.424360305266[/C][C]-29.4243603052656[/C][/ROW]
[ROW][C]3[/C][C]1053[/C][C]999.438558174502[/C][C]53.5614418254981[/C][/ROW]
[ROW][C]4[/C][C]1939[/C][C]2118.1536406097[/C][C]-179.153640609704[/C][/ROW]
[ROW][C]5[/C][C]678[/C][C]621.62079806335[/C][C]56.3792019366498[/C][/ROW]
[ROW][C]6[/C][C]321[/C][C]464.569786286064[/C][C]-143.569786286064[/C][/ROW]
[ROW][C]7[/C][C]2667[/C][C]2895.38561032391[/C][C]-228.385610323907[/C][/ROW]
[ROW][C]8[/C][C]345[/C][C]469.531833922926[/C][C]-124.531833922926[/C][/ROW]
[ROW][C]9[/C][C]1367[/C][C]1477.54868172357[/C][C]-110.548681723569[/C][/ROW]
[ROW][C]10[/C][C]1158[/C][C]1145.18109267991[/C][C]12.8189073200929[/C][/ROW]
[ROW][C]11[/C][C]1385[/C][C]1370.90988865064[/C][C]14.0901113493643[/C][/ROW]
[ROW][C]12[/C][C]1155[/C][C]1015.40777106783[/C][C]139.592228932166[/C][/ROW]
[ROW][C]13[/C][C]1120[/C][C]1179.39599912913[/C][C]-59.3959991291282[/C][/ROW]
[ROW][C]14[/C][C]1703[/C][C]1742.5285475554[/C][C]-39.5285475553975[/C][/ROW]
[ROW][C]15[/C][C]1189[/C][C]1091.81513046472[/C][C]97.1848695352825[/C][/ROW]
[ROW][C]16[/C][C]3083[/C][C]2703.34810823257[/C][C]379.651891767428[/C][/ROW]
[ROW][C]17[/C][C]1357[/C][C]1296.80064132169[/C][C]60.1993586783139[/C][/ROW]
[ROW][C]18[/C][C]1892[/C][C]1905.08599459398[/C][C]-13.0859945939781[/C][/ROW]
[ROW][C]19[/C][C]883[/C][C]992.472675248001[/C][C]-109.472675248001[/C][/ROW]
[ROW][C]20[/C][C]1627[/C][C]1309.31270337589[/C][C]317.687296624115[/C][/ROW]
[ROW][C]21[/C][C]1412[/C][C]1302.42007987363[/C][C]109.579920126372[/C][/ROW]
[ROW][C]22[/C][C]1900[/C][C]2036.25391907734[/C][C]-136.253919077344[/C][/ROW]
[ROW][C]23[/C][C]777[/C][C]863.536305337111[/C][C]-86.5363053371106[/C][/ROW]
[ROW][C]24[/C][C]904[/C][C]960.984316069221[/C][C]-56.9843160692212[/C][/ROW]
[ROW][C]25[/C][C]2115[/C][C]2166.14685236759[/C][C]-51.1468523675871[/C][/ROW]
[ROW][C]26[/C][C]1858[/C][C]1803.34083864901[/C][C]54.6591613509891[/C][/ROW]
[ROW][C]27[/C][C]1781[/C][C]1791.47380708562[/C][C]-10.4738070856162[/C][/ROW]
[ROW][C]28[/C][C]1286[/C][C]1148.55927882868[/C][C]137.440721171323[/C][/ROW]
[ROW][C]29[/C][C]1035[/C][C]1181.62180166485[/C][C]-146.621801664853[/C][/ROW]
[ROW][C]30[/C][C]1557[/C][C]1599.0268853742[/C][C]-42.0268853742029[/C][/ROW]
[ROW][C]31[/C][C]1527[/C][C]1578.96295588923[/C][C]-51.9629558892285[/C][/ROW]
[ROW][C]32[/C][C]1220[/C][C]1187.45122711757[/C][C]32.5487728824321[/C][/ROW]
[ROW][C]33[/C][C]1368[/C][C]1435.73698175349[/C][C]-67.7369817534924[/C][/ROW]
[ROW][C]34[/C][C]564[/C][C]558.292453573399[/C][C]5.70754642660127[/C][/ROW]
[ROW][C]35[/C][C]1990[/C][C]1954.54720442166[/C][C]35.4527955783443[/C][/ROW]
[ROW][C]36[/C][C]1557[/C][C]1622.11981811343[/C][C]-65.1198181134278[/C][/ROW]
[ROW][C]37[/C][C]2057[/C][C]1800.84520625724[/C][C]256.154793742758[/C][/ROW]
[ROW][C]38[/C][C]1111[/C][C]1005.19864145525[/C][C]105.801358544749[/C][/ROW]
[ROW][C]39[/C][C]686[/C][C]680.934067697688[/C][C]5.06593230231228[/C][/ROW]
[ROW][C]40[/C][C]2011[/C][C]1844.25676930581[/C][C]166.743230694187[/C][/ROW]
[ROW][C]41[/C][C]2232[/C][C]2492.07835007977[/C][C]-260.078350079766[/C][/ROW]
[ROW][C]42[/C][C]1032[/C][C]1205.72012757331[/C][C]-173.720127573308[/C][/ROW]
[ROW][C]43[/C][C]1166[/C][C]1227.10949814264[/C][C]-61.1094981426447[/C][/ROW]
[ROW][C]44[/C][C]1020[/C][C]914.322408261599[/C][C]105.677591738401[/C][/ROW]
[ROW][C]45[/C][C]1735[/C][C]2037.3356441038[/C][C]-302.335644103798[/C][/ROW]
[ROW][C]46[/C][C]3623[/C][C]3751.21364806784[/C][C]-128.213648067842[/C][/ROW]
[ROW][C]47[/C][C]918[/C][C]1008.89005712889[/C][C]-90.8900571288913[/C][/ROW]
[ROW][C]48[/C][C]1579[/C][C]1317.33271680016[/C][C]261.667283199843[/C][/ROW]
[ROW][C]49[/C][C]2790[/C][C]2502.35346065859[/C][C]287.646539341411[/C][/ROW]
[ROW][C]50[/C][C]1496[/C][C]1676.39954016272[/C][C]-180.399540162724[/C][/ROW]
[ROW][C]51[/C][C]1108[/C][C]1028.27124579398[/C][C]79.7287542060225[/C][/ROW]
[ROW][C]52[/C][C]496[/C][C]778.704899771546[/C][C]-282.704899771546[/C][/ROW]
[ROW][C]53[/C][C]1750[/C][C]1590.9431438093[/C][C]159.056856190699[/C][/ROW]
[ROW][C]54[/C][C]744[/C][C]870.222859333609[/C][C]-126.222859333609[/C][/ROW]
[ROW][C]55[/C][C]1101[/C][C]1288.91725274653[/C][C]-187.917252746532[/C][/ROW]
[ROW][C]56[/C][C]1612[/C][C]1731.92052302535[/C][C]-119.920523025345[/C][/ROW]
[ROW][C]57[/C][C]1805[/C][C]1383.57512499306[/C][C]421.424875006941[/C][/ROW]
[ROW][C]58[/C][C]2460[/C][C]2054.88075158893[/C][C]405.119248411073[/C][/ROW]
[ROW][C]59[/C][C]1653[/C][C]1824.56149505056[/C][C]-171.561495050555[/C][/ROW]
[ROW][C]60[/C][C]1234[/C][C]1379.05309208335[/C][C]-145.053092083351[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145899&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145899&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 IndexActualsInterpolationForecastResidualsPrediction Error
11167945.55292918343221.44707081657
2669698.424360305266-29.4243603052656
31053999.43855817450253.5614418254981
419392118.1536406097-179.153640609704
5678621.6207980633556.3792019366498
6321464.569786286064-143.569786286064
726672895.38561032391-228.385610323907
8345469.531833922926-124.531833922926
913671477.54868172357-110.548681723569
1011581145.1810926799112.8189073200929
1113851370.9098886506414.0901113493643
1211551015.40777106783139.592228932166
1311201179.39599912913-59.3959991291282
1417031742.5285475554-39.5285475553975
1511891091.8151304647297.1848695352825
1630832703.34810823257379.651891767428
1713571296.8006413216960.1993586783139
1818921905.08599459398-13.0859945939781
19883992.472675248001-109.472675248001
2016271309.31270337589317.687296624115
2114121302.42007987363109.579920126372
2219002036.25391907734-136.253919077344
23777863.536305337111-86.5363053371106
24904960.984316069221-56.9843160692212
2521152166.14685236759-51.1468523675871
2618581803.3408386490154.6591613509891
2717811791.47380708562-10.4738070856162
2812861148.55927882868137.440721171323
2910351181.62180166485-146.621801664853
3015571599.0268853742-42.0268853742029
3115271578.96295588923-51.9629558892285
3212201187.4512271175732.5487728824321
3313681435.73698175349-67.7369817534924
34564558.2924535733995.70754642660127
3519901954.5472044216635.4527955783443
3615571622.11981811343-65.1198181134278
3720571800.84520625724256.154793742758
3811111005.19864145525105.801358544749
39686680.9340676976885.06593230231228
4020111844.25676930581166.743230694187
4122322492.07835007977-260.078350079766
4210321205.72012757331-173.720127573308
4311661227.10949814264-61.1094981426447
441020914.322408261599105.677591738401
4517352037.3356441038-302.335644103798
4636233751.21364806784-128.213648067842
479181008.89005712889-90.8900571288913
4815791317.33271680016261.667283199843
4927902502.35346065859287.646539341411
5014961676.39954016272-180.399540162724
5111081028.2712457939879.7287542060225
52496778.704899771546-282.704899771546
5317501590.9431438093159.056856190699
54744870.222859333609-126.222859333609
5511011288.91725274653-187.917252746532
5616121731.92052302535-119.920523025345
5718051383.57512499306421.424875006941
5824602054.88075158893405.119248411073
5916531824.56149505056-171.561495050555
6012341379.05309208335-145.053092083351







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
90.4174875482458110.8349750964916220.582512451754189
100.4254932424271690.8509864848543370.574506757572831
110.3680518962715320.7361037925430640.631948103728468
120.3882595169681410.7765190339362820.611740483031859
130.2785821477125760.5571642954251510.721417852287424
140.1941630503845490.3883261007690990.80583694961545
150.15251027038380.30502054076760.8474897296162
160.5126751725835120.9746496548329760.487324827416488
170.4121516399272750.8243032798545510.587848360072724
180.3377051848108320.6754103696216650.662294815189168
190.3210548088327240.6421096176654470.678945191167276
200.4113608498241550.822721699648310.588639150175845
210.3418777104172730.6837554208345460.658122289582727
220.359065348457250.7181306969144990.640934651542751
230.3221476664549110.6442953329098230.677852333545089
240.265794986807050.5315899736141010.73420501319295
250.2129013445186160.4258026890372330.787098655481383
260.1570862909762660.3141725819525320.842913709023734
270.1127301658295950.225460331659190.887269834170405
280.09444745243665850.1888949048733170.905552547563341
290.08479404485790740.1695880897158150.915205955142093
300.05821178790452320.1164235758090460.941788212095477
310.04008129208435410.08016258416870830.959918707915646
320.0252124871466760.0504249742933520.974787512853324
330.01602286339226880.03204572678453760.983977136607731
340.009325159750462830.01865031950092570.990674840249537
350.005250153861192220.01050030772238440.994749846138808
360.003006425294153950.006012850588307910.996993574705846
370.004003602218994950.00800720443798990.995996397781005
380.002714836852851330.005429673705702670.997285163147149
390.0017851888570050.003570377714010010.998214811142995
400.001652129743927250.003304259487854490.998347870256073
410.003092599308856330.006185198617712660.996907400691144
420.002025962511540470.004051925023080930.99797403748846
430.0009788219693385160.001957643938677030.999021178030661
440.0009053302234476130.001810660446895230.999094669776552
450.00213969161611140.00427938323222280.997860308383889
460.01528478579066940.03056957158133870.984715214209331
470.01274490384243980.02548980768487960.98725509615756
480.02017866994739240.04035733989478490.979821330052608
490.0183973020412860.03679460408257190.981602697958714
500.01657069951530870.03314139903061740.983429300484691
510.01087458682030410.02174917364060830.989125413179696

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
9 & 0.417487548245811 & 0.834975096491622 & 0.582512451754189 \tabularnewline
10 & 0.425493242427169 & 0.850986484854337 & 0.574506757572831 \tabularnewline
11 & 0.368051896271532 & 0.736103792543064 & 0.631948103728468 \tabularnewline
12 & 0.388259516968141 & 0.776519033936282 & 0.611740483031859 \tabularnewline
13 & 0.278582147712576 & 0.557164295425151 & 0.721417852287424 \tabularnewline
14 & 0.194163050384549 & 0.388326100769099 & 0.80583694961545 \tabularnewline
15 & 0.1525102703838 & 0.3050205407676 & 0.8474897296162 \tabularnewline
16 & 0.512675172583512 & 0.974649654832976 & 0.487324827416488 \tabularnewline
17 & 0.412151639927275 & 0.824303279854551 & 0.587848360072724 \tabularnewline
18 & 0.337705184810832 & 0.675410369621665 & 0.662294815189168 \tabularnewline
19 & 0.321054808832724 & 0.642109617665447 & 0.678945191167276 \tabularnewline
20 & 0.411360849824155 & 0.82272169964831 & 0.588639150175845 \tabularnewline
21 & 0.341877710417273 & 0.683755420834546 & 0.658122289582727 \tabularnewline
22 & 0.35906534845725 & 0.718130696914499 & 0.640934651542751 \tabularnewline
23 & 0.322147666454911 & 0.644295332909823 & 0.677852333545089 \tabularnewline
24 & 0.26579498680705 & 0.531589973614101 & 0.73420501319295 \tabularnewline
25 & 0.212901344518616 & 0.425802689037233 & 0.787098655481383 \tabularnewline
26 & 0.157086290976266 & 0.314172581952532 & 0.842913709023734 \tabularnewline
27 & 0.112730165829595 & 0.22546033165919 & 0.887269834170405 \tabularnewline
28 & 0.0944474524366585 & 0.188894904873317 & 0.905552547563341 \tabularnewline
29 & 0.0847940448579074 & 0.169588089715815 & 0.915205955142093 \tabularnewline
30 & 0.0582117879045232 & 0.116423575809046 & 0.941788212095477 \tabularnewline
31 & 0.0400812920843541 & 0.0801625841687083 & 0.959918707915646 \tabularnewline
32 & 0.025212487146676 & 0.050424974293352 & 0.974787512853324 \tabularnewline
33 & 0.0160228633922688 & 0.0320457267845376 & 0.983977136607731 \tabularnewline
34 & 0.00932515975046283 & 0.0186503195009257 & 0.990674840249537 \tabularnewline
35 & 0.00525015386119222 & 0.0105003077223844 & 0.994749846138808 \tabularnewline
36 & 0.00300642529415395 & 0.00601285058830791 & 0.996993574705846 \tabularnewline
37 & 0.00400360221899495 & 0.0080072044379899 & 0.995996397781005 \tabularnewline
38 & 0.00271483685285133 & 0.00542967370570267 & 0.997285163147149 \tabularnewline
39 & 0.001785188857005 & 0.00357037771401001 & 0.998214811142995 \tabularnewline
40 & 0.00165212974392725 & 0.00330425948785449 & 0.998347870256073 \tabularnewline
41 & 0.00309259930885633 & 0.00618519861771266 & 0.996907400691144 \tabularnewline
42 & 0.00202596251154047 & 0.00405192502308093 & 0.99797403748846 \tabularnewline
43 & 0.000978821969338516 & 0.00195764393867703 & 0.999021178030661 \tabularnewline
44 & 0.000905330223447613 & 0.00181066044689523 & 0.999094669776552 \tabularnewline
45 & 0.0021396916161114 & 0.0042793832322228 & 0.997860308383889 \tabularnewline
46 & 0.0152847857906694 & 0.0305695715813387 & 0.984715214209331 \tabularnewline
47 & 0.0127449038424398 & 0.0254898076848796 & 0.98725509615756 \tabularnewline
48 & 0.0201786699473924 & 0.0403573398947849 & 0.979821330052608 \tabularnewline
49 & 0.018397302041286 & 0.0367946040825719 & 0.981602697958714 \tabularnewline
50 & 0.0165706995153087 & 0.0331413990306174 & 0.983429300484691 \tabularnewline
51 & 0.0108745868203041 & 0.0217491736406083 & 0.989125413179696 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145899&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]9[/C][C]0.417487548245811[/C][C]0.834975096491622[/C][C]0.582512451754189[/C][/ROW]
[ROW][C]10[/C][C]0.425493242427169[/C][C]0.850986484854337[/C][C]0.574506757572831[/C][/ROW]
[ROW][C]11[/C][C]0.368051896271532[/C][C]0.736103792543064[/C][C]0.631948103728468[/C][/ROW]
[ROW][C]12[/C][C]0.388259516968141[/C][C]0.776519033936282[/C][C]0.611740483031859[/C][/ROW]
[ROW][C]13[/C][C]0.278582147712576[/C][C]0.557164295425151[/C][C]0.721417852287424[/C][/ROW]
[ROW][C]14[/C][C]0.194163050384549[/C][C]0.388326100769099[/C][C]0.80583694961545[/C][/ROW]
[ROW][C]15[/C][C]0.1525102703838[/C][C]0.3050205407676[/C][C]0.8474897296162[/C][/ROW]
[ROW][C]16[/C][C]0.512675172583512[/C][C]0.974649654832976[/C][C]0.487324827416488[/C][/ROW]
[ROW][C]17[/C][C]0.412151639927275[/C][C]0.824303279854551[/C][C]0.587848360072724[/C][/ROW]
[ROW][C]18[/C][C]0.337705184810832[/C][C]0.675410369621665[/C][C]0.662294815189168[/C][/ROW]
[ROW][C]19[/C][C]0.321054808832724[/C][C]0.642109617665447[/C][C]0.678945191167276[/C][/ROW]
[ROW][C]20[/C][C]0.411360849824155[/C][C]0.82272169964831[/C][C]0.588639150175845[/C][/ROW]
[ROW][C]21[/C][C]0.341877710417273[/C][C]0.683755420834546[/C][C]0.658122289582727[/C][/ROW]
[ROW][C]22[/C][C]0.35906534845725[/C][C]0.718130696914499[/C][C]0.640934651542751[/C][/ROW]
[ROW][C]23[/C][C]0.322147666454911[/C][C]0.644295332909823[/C][C]0.677852333545089[/C][/ROW]
[ROW][C]24[/C][C]0.26579498680705[/C][C]0.531589973614101[/C][C]0.73420501319295[/C][/ROW]
[ROW][C]25[/C][C]0.212901344518616[/C][C]0.425802689037233[/C][C]0.787098655481383[/C][/ROW]
[ROW][C]26[/C][C]0.157086290976266[/C][C]0.314172581952532[/C][C]0.842913709023734[/C][/ROW]
[ROW][C]27[/C][C]0.112730165829595[/C][C]0.22546033165919[/C][C]0.887269834170405[/C][/ROW]
[ROW][C]28[/C][C]0.0944474524366585[/C][C]0.188894904873317[/C][C]0.905552547563341[/C][/ROW]
[ROW][C]29[/C][C]0.0847940448579074[/C][C]0.169588089715815[/C][C]0.915205955142093[/C][/ROW]
[ROW][C]30[/C][C]0.0582117879045232[/C][C]0.116423575809046[/C][C]0.941788212095477[/C][/ROW]
[ROW][C]31[/C][C]0.0400812920843541[/C][C]0.0801625841687083[/C][C]0.959918707915646[/C][/ROW]
[ROW][C]32[/C][C]0.025212487146676[/C][C]0.050424974293352[/C][C]0.974787512853324[/C][/ROW]
[ROW][C]33[/C][C]0.0160228633922688[/C][C]0.0320457267845376[/C][C]0.983977136607731[/C][/ROW]
[ROW][C]34[/C][C]0.00932515975046283[/C][C]0.0186503195009257[/C][C]0.990674840249537[/C][/ROW]
[ROW][C]35[/C][C]0.00525015386119222[/C][C]0.0105003077223844[/C][C]0.994749846138808[/C][/ROW]
[ROW][C]36[/C][C]0.00300642529415395[/C][C]0.00601285058830791[/C][C]0.996993574705846[/C][/ROW]
[ROW][C]37[/C][C]0.00400360221899495[/C][C]0.0080072044379899[/C][C]0.995996397781005[/C][/ROW]
[ROW][C]38[/C][C]0.00271483685285133[/C][C]0.00542967370570267[/C][C]0.997285163147149[/C][/ROW]
[ROW][C]39[/C][C]0.001785188857005[/C][C]0.00357037771401001[/C][C]0.998214811142995[/C][/ROW]
[ROW][C]40[/C][C]0.00165212974392725[/C][C]0.00330425948785449[/C][C]0.998347870256073[/C][/ROW]
[ROW][C]41[/C][C]0.00309259930885633[/C][C]0.00618519861771266[/C][C]0.996907400691144[/C][/ROW]
[ROW][C]42[/C][C]0.00202596251154047[/C][C]0.00405192502308093[/C][C]0.99797403748846[/C][/ROW]
[ROW][C]43[/C][C]0.000978821969338516[/C][C]0.00195764393867703[/C][C]0.999021178030661[/C][/ROW]
[ROW][C]44[/C][C]0.000905330223447613[/C][C]0.00181066044689523[/C][C]0.999094669776552[/C][/ROW]
[ROW][C]45[/C][C]0.0021396916161114[/C][C]0.0042793832322228[/C][C]0.997860308383889[/C][/ROW]
[ROW][C]46[/C][C]0.0152847857906694[/C][C]0.0305695715813387[/C][C]0.984715214209331[/C][/ROW]
[ROW][C]47[/C][C]0.0127449038424398[/C][C]0.0254898076848796[/C][C]0.98725509615756[/C][/ROW]
[ROW][C]48[/C][C]0.0201786699473924[/C][C]0.0403573398947849[/C][C]0.979821330052608[/C][/ROW]
[ROW][C]49[/C][C]0.018397302041286[/C][C]0.0367946040825719[/C][C]0.981602697958714[/C][/ROW]
[ROW][C]50[/C][C]0.0165706995153087[/C][C]0.0331413990306174[/C][C]0.983429300484691[/C][/ROW]
[ROW][C]51[/C][C]0.0108745868203041[/C][C]0.0217491736406083[/C][C]0.989125413179696[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145899&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145899&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-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
90.4174875482458110.8349750964916220.582512451754189
100.4254932424271690.8509864848543370.574506757572831
110.3680518962715320.7361037925430640.631948103728468
120.3882595169681410.7765190339362820.611740483031859
130.2785821477125760.5571642954251510.721417852287424
140.1941630503845490.3883261007690990.80583694961545
150.15251027038380.30502054076760.8474897296162
160.5126751725835120.9746496548329760.487324827416488
170.4121516399272750.8243032798545510.587848360072724
180.3377051848108320.6754103696216650.662294815189168
190.3210548088327240.6421096176654470.678945191167276
200.4113608498241550.822721699648310.588639150175845
210.3418777104172730.6837554208345460.658122289582727
220.359065348457250.7181306969144990.640934651542751
230.3221476664549110.6442953329098230.677852333545089
240.265794986807050.5315899736141010.73420501319295
250.2129013445186160.4258026890372330.787098655481383
260.1570862909762660.3141725819525320.842913709023734
270.1127301658295950.225460331659190.887269834170405
280.09444745243665850.1888949048733170.905552547563341
290.08479404485790740.1695880897158150.915205955142093
300.05821178790452320.1164235758090460.941788212095477
310.04008129208435410.08016258416870830.959918707915646
320.0252124871466760.0504249742933520.974787512853324
330.01602286339226880.03204572678453760.983977136607731
340.009325159750462830.01865031950092570.990674840249537
350.005250153861192220.01050030772238440.994749846138808
360.003006425294153950.006012850588307910.996993574705846
370.004003602218994950.00800720443798990.995996397781005
380.002714836852851330.005429673705702670.997285163147149
390.0017851888570050.003570377714010010.998214811142995
400.001652129743927250.003304259487854490.998347870256073
410.003092599308856330.006185198617712660.996907400691144
420.002025962511540470.004051925023080930.99797403748846
430.0009788219693385160.001957643938677030.999021178030661
440.0009053302234476130.001810660446895230.999094669776552
450.00213969161611140.00427938323222280.997860308383889
460.01528478579066940.03056957158133870.984715214209331
470.01274490384243980.02548980768487960.98725509615756
480.02017866994739240.04035733989478490.979821330052608
490.0183973020412860.03679460408257190.981602697958714
500.01657069951530870.03314139903061740.983429300484691
510.01087458682030410.02174917364060830.989125413179696







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level100.232558139534884NOK
5% type I error level190.441860465116279NOK
10% type I error level210.488372093023256NOK

\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 & 10 & 0.232558139534884 & NOK \tabularnewline
5% type I error level & 19 & 0.441860465116279 & NOK \tabularnewline
10% type I error level & 21 & 0.488372093023256 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145899&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]10[/C][C]0.232558139534884[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]19[/C][C]0.441860465116279[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]21[/C][C]0.488372093023256[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145899&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145899&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 testsOK/NOK
1% type I error level100.232558139534884NOK
5% type I error level190.441860465116279NOK
10% type I error level210.488372093023256NOK



Parameters (Session):
par1 = 8 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 4 ; par2 = Do not include Seasonal 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')
}