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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Wed, 09 Dec 2009 08:00:24 -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/09/t1260371301pv334d0lx9pcbal.htm/, Retrieved Mon, 29 Apr 2024 16:07:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64984, Retrieved Mon, 29 Apr 2024 16:07:03 +0000

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Estimated Impact

127

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

-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:06:21] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-12-09 15:00:24] [faa1ded5041cd5a0e2be04844f08502a] [Current]

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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64984&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64984&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64984&T=0

As an alternative you can also use a QR Code:

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

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

Multiple Linear Regression - Estimated Regression Equation
S.[t] = + 17.8743967092323 + 0.28362403777993E.S[t] -1.28301434053189M1[t] -5.00054413482562M2[t] -0.949437394542677M3[t] -1.00592757515550M4[t] -0.554820834872551M5[t] -1.56043890214559M6[t] -4.24968100719855M7[t] -1.74770215357581M8[t] -0.153320220848849M9[t] -0.675314250341956M10[t] -1.44818039317485M11[t] -0.25110674028295t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
S.[t] =  +  17.8743967092323 +  0.28362403777993E.S[t] -1.28301434053189M1[t] -5.00054413482562M2[t] -0.949437394542677M3[t] -1.00592757515550M4[t] -0.554820834872551M5[t] -1.56043890214559M6[t] -4.24968100719855M7[t] -1.74770215357581M8[t] -0.153320220848849M9[t] -0.675314250341956M10[t] -1.44818039317485M11[t] -0.25110674028295t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64984&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]S.[t] =  +  17.8743967092323 +  0.28362403777993E.S[t] -1.28301434053189M1[t] -5.00054413482562M2[t] -0.949437394542677M3[t] -1.00592757515550M4[t] -0.554820834872551M5[t] -1.56043890214559M6[t] -4.24968100719855M7[t] -1.74770215357581M8[t] -0.153320220848849M9[t] -0.675314250341956M10[t] -1.44818039317485M11[t] -0.25110674028295t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64984&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64984&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
S.[t] = + 17.8743967092323 + 0.28362403777993E.S[t] -1.28301434053189M1[t] -5.00054413482562M2[t] -0.949437394542677M3[t] -1.00592757515550M4[t] -0.554820834872551M5[t] -1.56043890214559M6[t] -4.24968100719855M7[t] -1.74770215357581M8[t] -0.153320220848849M9[t] -0.675314250341956M10[t] -1.44818039317485M11[t] -0.25110674028295t + 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)	17.8743967092323	1.836813	9.7312	0	0
E.S	0.28362403777993	0.036843	7.6983	0	0
M1	-1.28301434053189	1.536526	-0.835	0.407937	0.203968
M2	-5.00054413482562	1.614555	-3.0972	0.003292	0.001646
M3	-0.949437394542677	1.612181	-0.5889	0.558738	0.279369
M4	-1.00592757515550	1.606739	-0.6261	0.534299	0.26715
M5	-0.554820834872551	1.60516	-0.3456	0.731149	0.365575
M6	-1.56043890214559	1.603934	-0.9729	0.335592	0.167796
M7	-4.24968100719855	1.604423	-2.6487	0.010967	0.005484
M8	-1.74770215357581	1.601678	-1.0912	0.280761	0.14038
M9	-0.153320220848849	1.600764	-0.0958	0.924103	0.462052
M10	-0.675314250341956	1.60063	-0.4219	0.675018	0.337509
M11	-1.44818039317485	1.600518	-0.9048	0.370176	0.185088
t	-0.25110674028295	0.019249	-13.0454	0	0

\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) & 17.8743967092323 & 1.836813 & 9.7312 & 0 & 0 \tabularnewline
E.S & 0.28362403777993 & 0.036843 & 7.6983 & 0 & 0 \tabularnewline
M1 & -1.28301434053189 & 1.536526 & -0.835 & 0.407937 & 0.203968 \tabularnewline
M2 & -5.00054413482562 & 1.614555 & -3.0972 & 0.003292 & 0.001646 \tabularnewline
M3 & -0.949437394542677 & 1.612181 & -0.5889 & 0.558738 & 0.279369 \tabularnewline
M4 & -1.00592757515550 & 1.606739 & -0.6261 & 0.534299 & 0.26715 \tabularnewline
M5 & -0.554820834872551 & 1.60516 & -0.3456 & 0.731149 & 0.365575 \tabularnewline
M6 & -1.56043890214559 & 1.603934 & -0.9729 & 0.335592 & 0.167796 \tabularnewline
M7 & -4.24968100719855 & 1.604423 & -2.6487 & 0.010967 & 0.005484 \tabularnewline
M8 & -1.74770215357581 & 1.601678 & -1.0912 & 0.280761 & 0.14038 \tabularnewline
M9 & -0.153320220848849 & 1.600764 & -0.0958 & 0.924103 & 0.462052 \tabularnewline
M10 & -0.675314250341956 & 1.60063 & -0.4219 & 0.675018 & 0.337509 \tabularnewline
M11 & -1.44818039317485 & 1.600518 & -0.9048 & 0.370176 & 0.185088 \tabularnewline
t & -0.25110674028295 & 0.019249 & -13.0454 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64984&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]17.8743967092323[/C][C]1.836813[/C][C]9.7312[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]E.S[/C][C]0.28362403777993[/C][C]0.036843[/C][C]7.6983[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-1.28301434053189[/C][C]1.536526[/C][C]-0.835[/C][C]0.407937[/C][C]0.203968[/C][/ROW]
[ROW][C]M2[/C][C]-5.00054413482562[/C][C]1.614555[/C][C]-3.0972[/C][C]0.003292[/C][C]0.001646[/C][/ROW]
[ROW][C]M3[/C][C]-0.949437394542677[/C][C]1.612181[/C][C]-0.5889[/C][C]0.558738[/C][C]0.279369[/C][/ROW]
[ROW][C]M4[/C][C]-1.00592757515550[/C][C]1.606739[/C][C]-0.6261[/C][C]0.534299[/C][C]0.26715[/C][/ROW]
[ROW][C]M5[/C][C]-0.554820834872551[/C][C]1.60516[/C][C]-0.3456[/C][C]0.731149[/C][C]0.365575[/C][/ROW]
[ROW][C]M6[/C][C]-1.56043890214559[/C][C]1.603934[/C][C]-0.9729[/C][C]0.335592[/C][C]0.167796[/C][/ROW]
[ROW][C]M7[/C][C]-4.24968100719855[/C][C]1.604423[/C][C]-2.6487[/C][C]0.010967[/C][C]0.005484[/C][/ROW]
[ROW][C]M8[/C][C]-1.74770215357581[/C][C]1.601678[/C][C]-1.0912[/C][C]0.280761[/C][C]0.14038[/C][/ROW]
[ROW][C]M9[/C][C]-0.153320220848849[/C][C]1.600764[/C][C]-0.0958[/C][C]0.924103[/C][C]0.462052[/C][/ROW]
[ROW][C]M10[/C][C]-0.675314250341956[/C][C]1.60063[/C][C]-0.4219[/C][C]0.675018[/C][C]0.337509[/C][/ROW]
[ROW][C]M11[/C][C]-1.44818039317485[/C][C]1.600518[/C][C]-0.9048[/C][C]0.370176[/C][C]0.185088[/C][/ROW]
[ROW][C]t[/C][C]-0.25110674028295[/C][C]0.019249[/C][C]-13.0454[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64984&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64984&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)	17.8743967092323	1.836813	9.7312	0	0
E.S	0.28362403777993	0.036843	7.6983	0	0
M1	-1.28301434053189	1.536526	-0.835	0.407937	0.203968
M2	-5.00054413482562	1.614555	-3.0972	0.003292	0.001646
M3	-0.949437394542677	1.612181	-0.5889	0.558738	0.279369
M4	-1.00592757515550	1.606739	-0.6261	0.534299	0.26715
M5	-0.554820834872551	1.60516	-0.3456	0.731149	0.365575
M6	-1.56043890214559	1.603934	-0.9729	0.335592	0.167796
M7	-4.24968100719855	1.604423	-2.6487	0.010967	0.005484
M8	-1.74770215357581	1.601678	-1.0912	0.280761	0.14038
M9	-0.153320220848849	1.600764	-0.0958	0.924103	0.462052
M10	-0.675314250341956	1.60063	-0.4219	0.675018	0.337509
M11	-1.44818039317485	1.600518	-0.9048	0.370176	0.185088
t	-0.25110674028295	0.019249	-13.0454	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.932411502373107
R-squared	0.869391209757674
Adjusted R-squared	0.833265374158733
F-TEST (value)	24.0656360010440
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	2.22044604925031e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.52938346360975
Sum Squared Residuals	300.695693181175

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.932411502373107 \tabularnewline
R-squared & 0.869391209757674 \tabularnewline
Adjusted R-squared & 0.833265374158733 \tabularnewline
F-TEST (value) & 24.0656360010440 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 2.22044604925031e-16 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 2.52938346360975 \tabularnewline
Sum Squared Residuals & 300.695693181175 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64984&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.932411502373107[/C][/ROW]
[ROW][C]R-squared[/C][C]0.869391209757674[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.833265374158733[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]24.0656360010440[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]2.22044604925031e-16[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]2.52938346360975[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]300.695693181175[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64984&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64984&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	0.932411502373107
R-squared	0.869391209757674
Adjusted R-squared	0.833265374158733
F-TEST (value)	24.0656360010440
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	2.22044604925031e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.52938346360975
Sum Squared Residuals	300.695693181175

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	24	25.6998688751552	-1.69986887515521
2	22	22.0148563783584	-0.0148563783583963
3	25	26.3821044539183	-1.38210445391827
4	24	26.0745075330225	-2.07450753302250
5	29	26.8417556085823	2.15824439141765
6	26	26.7195269521461	-0.719526952146089
7	26	21.7938098423507	4.20619015764934
8	21	21.2084415778911	-0.208441577891149
9	23	22.2680927325552	0.731907267444769
10	22	20.9277438872193	1.07225611278068
11	21	21.3218911930031	-0.321891193003126
12	16	19.6827244680957	-3.68272446809572
13	19	21.8357158784200	-2.83571587841997
14	16	17.8670793438433	-1.86707934384330
15	25	22.801575494963	2.19842450503699
16	27	23.344850687407	3.65514931259298
17	23	23.2612266496271	-0.261226649627091
18	22	21.1536297287313	0.846370271268685
19	23	18.2132808833954	4.7867191166046
20	20	20.4641529967352	-0.464152996735191
21	24	22.9419243402989	1.05807565970108
22	23	23.0196956838627	-0.0196956838626574
23	20	20.5776026118472	-0.577602611847163
24	21	22.3419243402989	-1.34192434029892
25	22	22.5095474861637	-0.509547486163658
26	17	18.2572869138071	-1.25728691380705
27	21	19.5046705737877	1.49532942621232
28	19	20.8988178795715	-1.89881787957148
29	23	21.3824419173514	1.61755808264859
30	22	19.2748449964556	2.72515500354436
31	15	18.3198644155792	-3.31986441557923
32	23	20.0034884533592	2.99651154664084
33	21	21.6303876835831	-0.630387683583105
34	18	20.0064148004673	-2.00641480046726
35	18	16.1462015395521	1.85379846044789
36	18	17.343275192444	0.656724807555986
37	18	16.0927781494091	1.90722185059090
38	10	8.43702912369333	1.56297087630667
39	13	13.9387733503729	-0.938773350372907
40	10	13.0639283539173	-3.06392835391727
41	9	14.398424505037	-5.39842450503699
42	9	13.7089477730409	-4.70894777304087
43	6	9.3504787388053	-3.3504787388053
44	11	9.89960662546551	1.10039337453449
45	9	9.82476162900988	-0.824761629009875
46	10	8.20078874589403	1.79921125410597
47	9	10.0130562405775	-1.01305624057748
48	16	11.7773779690292	4.22262203097076
49	10	9.3923847748746	0.607615225125391
50	7	5.42374824029793	1.57625175970207
51	7	8.37287612695814	-1.37287612695814
52	14	10.6178955460817	3.38210445391827
53	11	9.11615131940215	1.88384868059785
54	10	8.1430505496261	1.85694945037390
55	6	8.32256611986941	-2.32256611986941
56	8	11.4243103465490	-3.42431034654899
57	13	13.3348336145529	-0.334833614552865
58	12	12.8453568825567	-0.845356882556735
59	15	14.9412484150201	0.0587515849798848
60	16	15.8546980301321	0.145301969867906
61	16	13.4697048359775	2.53029516402254

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 24 & 25.6998688751552 & -1.69986887515521 \tabularnewline
2 & 22 & 22.0148563783584 & -0.0148563783583963 \tabularnewline
3 & 25 & 26.3821044539183 & -1.38210445391827 \tabularnewline
4 & 24 & 26.0745075330225 & -2.07450753302250 \tabularnewline
5 & 29 & 26.8417556085823 & 2.15824439141765 \tabularnewline
6 & 26 & 26.7195269521461 & -0.719526952146089 \tabularnewline
7 & 26 & 21.7938098423507 & 4.20619015764934 \tabularnewline
8 & 21 & 21.2084415778911 & -0.208441577891149 \tabularnewline
9 & 23 & 22.2680927325552 & 0.731907267444769 \tabularnewline
10 & 22 & 20.9277438872193 & 1.07225611278068 \tabularnewline
11 & 21 & 21.3218911930031 & -0.321891193003126 \tabularnewline
12 & 16 & 19.6827244680957 & -3.68272446809572 \tabularnewline
13 & 19 & 21.8357158784200 & -2.83571587841997 \tabularnewline
14 & 16 & 17.8670793438433 & -1.86707934384330 \tabularnewline
15 & 25 & 22.801575494963 & 2.19842450503699 \tabularnewline
16 & 27 & 23.344850687407 & 3.65514931259298 \tabularnewline
17 & 23 & 23.2612266496271 & -0.261226649627091 \tabularnewline
18 & 22 & 21.1536297287313 & 0.846370271268685 \tabularnewline
19 & 23 & 18.2132808833954 & 4.7867191166046 \tabularnewline
20 & 20 & 20.4641529967352 & -0.464152996735191 \tabularnewline
21 & 24 & 22.9419243402989 & 1.05807565970108 \tabularnewline
22 & 23 & 23.0196956838627 & -0.0196956838626574 \tabularnewline
23 & 20 & 20.5776026118472 & -0.577602611847163 \tabularnewline
24 & 21 & 22.3419243402989 & -1.34192434029892 \tabularnewline
25 & 22 & 22.5095474861637 & -0.509547486163658 \tabularnewline
26 & 17 & 18.2572869138071 & -1.25728691380705 \tabularnewline
27 & 21 & 19.5046705737877 & 1.49532942621232 \tabularnewline
28 & 19 & 20.8988178795715 & -1.89881787957148 \tabularnewline
29 & 23 & 21.3824419173514 & 1.61755808264859 \tabularnewline
30 & 22 & 19.2748449964556 & 2.72515500354436 \tabularnewline
31 & 15 & 18.3198644155792 & -3.31986441557923 \tabularnewline
32 & 23 & 20.0034884533592 & 2.99651154664084 \tabularnewline
33 & 21 & 21.6303876835831 & -0.630387683583105 \tabularnewline
34 & 18 & 20.0064148004673 & -2.00641480046726 \tabularnewline
35 & 18 & 16.1462015395521 & 1.85379846044789 \tabularnewline
36 & 18 & 17.343275192444 & 0.656724807555986 \tabularnewline
37 & 18 & 16.0927781494091 & 1.90722185059090 \tabularnewline
38 & 10 & 8.43702912369333 & 1.56297087630667 \tabularnewline
39 & 13 & 13.9387733503729 & -0.938773350372907 \tabularnewline
40 & 10 & 13.0639283539173 & -3.06392835391727 \tabularnewline
41 & 9 & 14.398424505037 & -5.39842450503699 \tabularnewline
42 & 9 & 13.7089477730409 & -4.70894777304087 \tabularnewline
43 & 6 & 9.3504787388053 & -3.3504787388053 \tabularnewline
44 & 11 & 9.89960662546551 & 1.10039337453449 \tabularnewline
45 & 9 & 9.82476162900988 & -0.824761629009875 \tabularnewline
46 & 10 & 8.20078874589403 & 1.79921125410597 \tabularnewline
47 & 9 & 10.0130562405775 & -1.01305624057748 \tabularnewline
48 & 16 & 11.7773779690292 & 4.22262203097076 \tabularnewline
49 & 10 & 9.3923847748746 & 0.607615225125391 \tabularnewline
50 & 7 & 5.42374824029793 & 1.57625175970207 \tabularnewline
51 & 7 & 8.37287612695814 & -1.37287612695814 \tabularnewline
52 & 14 & 10.6178955460817 & 3.38210445391827 \tabularnewline
53 & 11 & 9.11615131940215 & 1.88384868059785 \tabularnewline
54 & 10 & 8.1430505496261 & 1.85694945037390 \tabularnewline
55 & 6 & 8.32256611986941 & -2.32256611986941 \tabularnewline
56 & 8 & 11.4243103465490 & -3.42431034654899 \tabularnewline
57 & 13 & 13.3348336145529 & -0.334833614552865 \tabularnewline
58 & 12 & 12.8453568825567 & -0.845356882556735 \tabularnewline
59 & 15 & 14.9412484150201 & 0.0587515849798848 \tabularnewline
60 & 16 & 15.8546980301321 & 0.145301969867906 \tabularnewline
61 & 16 & 13.4697048359775 & 2.53029516402254 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64984&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]24[/C][C]25.6998688751552[/C][C]-1.69986887515521[/C][/ROW]
[ROW][C]2[/C][C]22[/C][C]22.0148563783584[/C][C]-0.0148563783583963[/C][/ROW]
[ROW][C]3[/C][C]25[/C][C]26.3821044539183[/C][C]-1.38210445391827[/C][/ROW]
[ROW][C]4[/C][C]24[/C][C]26.0745075330225[/C][C]-2.07450753302250[/C][/ROW]
[ROW][C]5[/C][C]29[/C][C]26.8417556085823[/C][C]2.15824439141765[/C][/ROW]
[ROW][C]6[/C][C]26[/C][C]26.7195269521461[/C][C]-0.719526952146089[/C][/ROW]
[ROW][C]7[/C][C]26[/C][C]21.7938098423507[/C][C]4.20619015764934[/C][/ROW]
[ROW][C]8[/C][C]21[/C][C]21.2084415778911[/C][C]-0.208441577891149[/C][/ROW]
[ROW][C]9[/C][C]23[/C][C]22.2680927325552[/C][C]0.731907267444769[/C][/ROW]
[ROW][C]10[/C][C]22[/C][C]20.9277438872193[/C][C]1.07225611278068[/C][/ROW]
[ROW][C]11[/C][C]21[/C][C]21.3218911930031[/C][C]-0.321891193003126[/C][/ROW]
[ROW][C]12[/C][C]16[/C][C]19.6827244680957[/C][C]-3.68272446809572[/C][/ROW]
[ROW][C]13[/C][C]19[/C][C]21.8357158784200[/C][C]-2.83571587841997[/C][/ROW]
[ROW][C]14[/C][C]16[/C][C]17.8670793438433[/C][C]-1.86707934384330[/C][/ROW]
[ROW][C]15[/C][C]25[/C][C]22.801575494963[/C][C]2.19842450503699[/C][/ROW]
[ROW][C]16[/C][C]27[/C][C]23.344850687407[/C][C]3.65514931259298[/C][/ROW]
[ROW][C]17[/C][C]23[/C][C]23.2612266496271[/C][C]-0.261226649627091[/C][/ROW]
[ROW][C]18[/C][C]22[/C][C]21.1536297287313[/C][C]0.846370271268685[/C][/ROW]
[ROW][C]19[/C][C]23[/C][C]18.2132808833954[/C][C]4.7867191166046[/C][/ROW]
[ROW][C]20[/C][C]20[/C][C]20.4641529967352[/C][C]-0.464152996735191[/C][/ROW]
[ROW][C]21[/C][C]24[/C][C]22.9419243402989[/C][C]1.05807565970108[/C][/ROW]
[ROW][C]22[/C][C]23[/C][C]23.0196956838627[/C][C]-0.0196956838626574[/C][/ROW]
[ROW][C]23[/C][C]20[/C][C]20.5776026118472[/C][C]-0.577602611847163[/C][/ROW]
[ROW][C]24[/C][C]21[/C][C]22.3419243402989[/C][C]-1.34192434029892[/C][/ROW]
[ROW][C]25[/C][C]22[/C][C]22.5095474861637[/C][C]-0.509547486163658[/C][/ROW]
[ROW][C]26[/C][C]17[/C][C]18.2572869138071[/C][C]-1.25728691380705[/C][/ROW]
[ROW][C]27[/C][C]21[/C][C]19.5046705737877[/C][C]1.49532942621232[/C][/ROW]
[ROW][C]28[/C][C]19[/C][C]20.8988178795715[/C][C]-1.89881787957148[/C][/ROW]
[ROW][C]29[/C][C]23[/C][C]21.3824419173514[/C][C]1.61755808264859[/C][/ROW]
[ROW][C]30[/C][C]22[/C][C]19.2748449964556[/C][C]2.72515500354436[/C][/ROW]
[ROW][C]31[/C][C]15[/C][C]18.3198644155792[/C][C]-3.31986441557923[/C][/ROW]
[ROW][C]32[/C][C]23[/C][C]20.0034884533592[/C][C]2.99651154664084[/C][/ROW]
[ROW][C]33[/C][C]21[/C][C]21.6303876835831[/C][C]-0.630387683583105[/C][/ROW]
[ROW][C]34[/C][C]18[/C][C]20.0064148004673[/C][C]-2.00641480046726[/C][/ROW]
[ROW][C]35[/C][C]18[/C][C]16.1462015395521[/C][C]1.85379846044789[/C][/ROW]
[ROW][C]36[/C][C]18[/C][C]17.343275192444[/C][C]0.656724807555986[/C][/ROW]
[ROW][C]37[/C][C]18[/C][C]16.0927781494091[/C][C]1.90722185059090[/C][/ROW]
[ROW][C]38[/C][C]10[/C][C]8.43702912369333[/C][C]1.56297087630667[/C][/ROW]
[ROW][C]39[/C][C]13[/C][C]13.9387733503729[/C][C]-0.938773350372907[/C][/ROW]
[ROW][C]40[/C][C]10[/C][C]13.0639283539173[/C][C]-3.06392835391727[/C][/ROW]
[ROW][C]41[/C][C]9[/C][C]14.398424505037[/C][C]-5.39842450503699[/C][/ROW]
[ROW][C]42[/C][C]9[/C][C]13.7089477730409[/C][C]-4.70894777304087[/C][/ROW]
[ROW][C]43[/C][C]6[/C][C]9.3504787388053[/C][C]-3.3504787388053[/C][/ROW]
[ROW][C]44[/C][C]11[/C][C]9.89960662546551[/C][C]1.10039337453449[/C][/ROW]
[ROW][C]45[/C][C]9[/C][C]9.82476162900988[/C][C]-0.824761629009875[/C][/ROW]
[ROW][C]46[/C][C]10[/C][C]8.20078874589403[/C][C]1.79921125410597[/C][/ROW]
[ROW][C]47[/C][C]9[/C][C]10.0130562405775[/C][C]-1.01305624057748[/C][/ROW]
[ROW][C]48[/C][C]16[/C][C]11.7773779690292[/C][C]4.22262203097076[/C][/ROW]
[ROW][C]49[/C][C]10[/C][C]9.3923847748746[/C][C]0.607615225125391[/C][/ROW]
[ROW][C]50[/C][C]7[/C][C]5.42374824029793[/C][C]1.57625175970207[/C][/ROW]
[ROW][C]51[/C][C]7[/C][C]8.37287612695814[/C][C]-1.37287612695814[/C][/ROW]
[ROW][C]52[/C][C]14[/C][C]10.6178955460817[/C][C]3.38210445391827[/C][/ROW]
[ROW][C]53[/C][C]11[/C][C]9.11615131940215[/C][C]1.88384868059785[/C][/ROW]
[ROW][C]54[/C][C]10[/C][C]8.1430505496261[/C][C]1.85694945037390[/C][/ROW]
[ROW][C]55[/C][C]6[/C][C]8.32256611986941[/C][C]-2.32256611986941[/C][/ROW]
[ROW][C]56[/C][C]8[/C][C]11.4243103465490[/C][C]-3.42431034654899[/C][/ROW]
[ROW][C]57[/C][C]13[/C][C]13.3348336145529[/C][C]-0.334833614552865[/C][/ROW]
[ROW][C]58[/C][C]12[/C][C]12.8453568825567[/C][C]-0.845356882556735[/C][/ROW]
[ROW][C]59[/C][C]15[/C][C]14.9412484150201[/C][C]0.0587515849798848[/C][/ROW]
[ROW][C]60[/C][C]16[/C][C]15.8546980301321[/C][C]0.145301969867906[/C][/ROW]
[ROW][C]61[/C][C]16[/C][C]13.4697048359775[/C][C]2.53029516402254[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64984&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64984&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	24	25.6998688751552	-1.69986887515521
2	22	22.0148563783584	-0.0148563783583963
3	25	26.3821044539183	-1.38210445391827
4	24	26.0745075330225	-2.07450753302250
5	29	26.8417556085823	2.15824439141765
6	26	26.7195269521461	-0.719526952146089
7	26	21.7938098423507	4.20619015764934
8	21	21.2084415778911	-0.208441577891149
9	23	22.2680927325552	0.731907267444769
10	22	20.9277438872193	1.07225611278068
11	21	21.3218911930031	-0.321891193003126
12	16	19.6827244680957	-3.68272446809572
13	19	21.8357158784200	-2.83571587841997
14	16	17.8670793438433	-1.86707934384330
15	25	22.801575494963	2.19842450503699
16	27	23.344850687407	3.65514931259298
17	23	23.2612266496271	-0.261226649627091
18	22	21.1536297287313	0.846370271268685
19	23	18.2132808833954	4.7867191166046
20	20	20.4641529967352	-0.464152996735191
21	24	22.9419243402989	1.05807565970108
22	23	23.0196956838627	-0.0196956838626574
23	20	20.5776026118472	-0.577602611847163
24	21	22.3419243402989	-1.34192434029892
25	22	22.5095474861637	-0.509547486163658
26	17	18.2572869138071	-1.25728691380705
27	21	19.5046705737877	1.49532942621232
28	19	20.8988178795715	-1.89881787957148
29	23	21.3824419173514	1.61755808264859
30	22	19.2748449964556	2.72515500354436
31	15	18.3198644155792	-3.31986441557923
32	23	20.0034884533592	2.99651154664084
33	21	21.6303876835831	-0.630387683583105
34	18	20.0064148004673	-2.00641480046726
35	18	16.1462015395521	1.85379846044789
36	18	17.343275192444	0.656724807555986
37	18	16.0927781494091	1.90722185059090
38	10	8.43702912369333	1.56297087630667
39	13	13.9387733503729	-0.938773350372907
40	10	13.0639283539173	-3.06392835391727
41	9	14.398424505037	-5.39842450503699
42	9	13.7089477730409	-4.70894777304087
43	6	9.3504787388053	-3.3504787388053
44	11	9.89960662546551	1.10039337453449
45	9	9.82476162900988	-0.824761629009875
46	10	8.20078874589403	1.79921125410597
47	9	10.0130562405775	-1.01305624057748
48	16	11.7773779690292	4.22262203097076
49	10	9.3923847748746	0.607615225125391
50	7	5.42374824029793	1.57625175970207
51	7	8.37287612695814	-1.37287612695814
52	14	10.6178955460817	3.38210445391827
53	11	9.11615131940215	1.88384868059785
54	10	8.1430505496261	1.85694945037390
55	6	8.32256611986941	-2.32256611986941
56	8	11.4243103465490	-3.42431034654899
57	13	13.3348336145529	-0.334833614552865
58	12	12.8453568825567	-0.845356882556735
59	15	14.9412484150201	0.0587515849798848
60	16	15.8546980301321	0.145301969867906
61	16	13.4697048359775	2.53029516402254

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.286903576026991	0.573807152053982	0.713096423973009
18	0.503946114457648	0.992107771084704	0.496053885542352
19	0.481022028168762	0.962044056337524	0.518977971831238
20	0.407119981781704	0.814239963563409	0.592880018218296
21	0.29738267450978	0.59476534901956	0.70261732549022
22	0.211446468865883	0.422892937731767	0.788553531134117
23	0.135191231941780	0.270382463883561	0.86480876805822
24	0.113535555728901	0.227071111457801	0.8864644442711
25	0.0748331285526746	0.149666257105349	0.925166871447325
26	0.0535676066650276	0.107135213330055	0.946432393334972
27	0.0338629269635512	0.0677258539271023	0.96613707303645
28	0.0447431544289080	0.0894863088578161	0.955256845571092
29	0.0329532666490065	0.065906533298013	0.967046733350994
30	0.0426618963298799	0.0853237926597598	0.95733810367012
31	0.265821046595439	0.531642093190877	0.734178953404561
32	0.418951292056361	0.837902584112722	0.581048707943639
33	0.389341857138154	0.778683714276309	0.610658142861846
34	0.330675589541358	0.661351179082716	0.669324410458642
35	0.374631726757619	0.749263453515238	0.625368273242381
36	0.319671087180859	0.639342174361718	0.680328912819141
37	0.357930355464067	0.715860710928133	0.642069644535933
38	0.310593790623056	0.621187581246111	0.689406209376944
39	0.536143295009435	0.92771340998113	0.463856704990565
40	0.54729007875488	0.90541984249024	0.45270992124512
41	0.594615516954635	0.81076896609073	0.405384483045365
42	0.651191348414926	0.697617303170148	0.348808651585074
43	0.701200338895713	0.597599322208574	0.298799661104287
44	0.57559147041526	0.848817059169479	0.424408529584739

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.286903576026991 & 0.573807152053982 & 0.713096423973009 \tabularnewline
18 & 0.503946114457648 & 0.992107771084704 & 0.496053885542352 \tabularnewline
19 & 0.481022028168762 & 0.962044056337524 & 0.518977971831238 \tabularnewline
20 & 0.407119981781704 & 0.814239963563409 & 0.592880018218296 \tabularnewline
21 & 0.29738267450978 & 0.59476534901956 & 0.70261732549022 \tabularnewline
22 & 0.211446468865883 & 0.422892937731767 & 0.788553531134117 \tabularnewline
23 & 0.135191231941780 & 0.270382463883561 & 0.86480876805822 \tabularnewline
24 & 0.113535555728901 & 0.227071111457801 & 0.8864644442711 \tabularnewline
25 & 0.0748331285526746 & 0.149666257105349 & 0.925166871447325 \tabularnewline
26 & 0.0535676066650276 & 0.107135213330055 & 0.946432393334972 \tabularnewline
27 & 0.0338629269635512 & 0.0677258539271023 & 0.96613707303645 \tabularnewline
28 & 0.0447431544289080 & 0.0894863088578161 & 0.955256845571092 \tabularnewline
29 & 0.0329532666490065 & 0.065906533298013 & 0.967046733350994 \tabularnewline
30 & 0.0426618963298799 & 0.0853237926597598 & 0.95733810367012 \tabularnewline
31 & 0.265821046595439 & 0.531642093190877 & 0.734178953404561 \tabularnewline
32 & 0.418951292056361 & 0.837902584112722 & 0.581048707943639 \tabularnewline
33 & 0.389341857138154 & 0.778683714276309 & 0.610658142861846 \tabularnewline
34 & 0.330675589541358 & 0.661351179082716 & 0.669324410458642 \tabularnewline
35 & 0.374631726757619 & 0.749263453515238 & 0.625368273242381 \tabularnewline
36 & 0.319671087180859 & 0.639342174361718 & 0.680328912819141 \tabularnewline
37 & 0.357930355464067 & 0.715860710928133 & 0.642069644535933 \tabularnewline
38 & 0.310593790623056 & 0.621187581246111 & 0.689406209376944 \tabularnewline
39 & 0.536143295009435 & 0.92771340998113 & 0.463856704990565 \tabularnewline
40 & 0.54729007875488 & 0.90541984249024 & 0.45270992124512 \tabularnewline
41 & 0.594615516954635 & 0.81076896609073 & 0.405384483045365 \tabularnewline
42 & 0.651191348414926 & 0.697617303170148 & 0.348808651585074 \tabularnewline
43 & 0.701200338895713 & 0.597599322208574 & 0.298799661104287 \tabularnewline
44 & 0.57559147041526 & 0.848817059169479 & 0.424408529584739 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64984&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]17[/C][C]0.286903576026991[/C][C]0.573807152053982[/C][C]0.713096423973009[/C][/ROW]
[ROW][C]18[/C][C]0.503946114457648[/C][C]0.992107771084704[/C][C]0.496053885542352[/C][/ROW]
[ROW][C]19[/C][C]0.481022028168762[/C][C]0.962044056337524[/C][C]0.518977971831238[/C][/ROW]
[ROW][C]20[/C][C]0.407119981781704[/C][C]0.814239963563409[/C][C]0.592880018218296[/C][/ROW]
[ROW][C]21[/C][C]0.29738267450978[/C][C]0.59476534901956[/C][C]0.70261732549022[/C][/ROW]
[ROW][C]22[/C][C]0.211446468865883[/C][C]0.422892937731767[/C][C]0.788553531134117[/C][/ROW]
[ROW][C]23[/C][C]0.135191231941780[/C][C]0.270382463883561[/C][C]0.86480876805822[/C][/ROW]
[ROW][C]24[/C][C]0.113535555728901[/C][C]0.227071111457801[/C][C]0.8864644442711[/C][/ROW]
[ROW][C]25[/C][C]0.0748331285526746[/C][C]0.149666257105349[/C][C]0.925166871447325[/C][/ROW]
[ROW][C]26[/C][C]0.0535676066650276[/C][C]0.107135213330055[/C][C]0.946432393334972[/C][/ROW]
[ROW][C]27[/C][C]0.0338629269635512[/C][C]0.0677258539271023[/C][C]0.96613707303645[/C][/ROW]
[ROW][C]28[/C][C]0.0447431544289080[/C][C]0.0894863088578161[/C][C]0.955256845571092[/C][/ROW]
[ROW][C]29[/C][C]0.0329532666490065[/C][C]0.065906533298013[/C][C]0.967046733350994[/C][/ROW]
[ROW][C]30[/C][C]0.0426618963298799[/C][C]0.0853237926597598[/C][C]0.95733810367012[/C][/ROW]
[ROW][C]31[/C][C]0.265821046595439[/C][C]0.531642093190877[/C][C]0.734178953404561[/C][/ROW]
[ROW][C]32[/C][C]0.418951292056361[/C][C]0.837902584112722[/C][C]0.581048707943639[/C][/ROW]
[ROW][C]33[/C][C]0.389341857138154[/C][C]0.778683714276309[/C][C]0.610658142861846[/C][/ROW]
[ROW][C]34[/C][C]0.330675589541358[/C][C]0.661351179082716[/C][C]0.669324410458642[/C][/ROW]
[ROW][C]35[/C][C]0.374631726757619[/C][C]0.749263453515238[/C][C]0.625368273242381[/C][/ROW]
[ROW][C]36[/C][C]0.319671087180859[/C][C]0.639342174361718[/C][C]0.680328912819141[/C][/ROW]
[ROW][C]37[/C][C]0.357930355464067[/C][C]0.715860710928133[/C][C]0.642069644535933[/C][/ROW]
[ROW][C]38[/C][C]0.310593790623056[/C][C]0.621187581246111[/C][C]0.689406209376944[/C][/ROW]
[ROW][C]39[/C][C]0.536143295009435[/C][C]0.92771340998113[/C][C]0.463856704990565[/C][/ROW]
[ROW][C]40[/C][C]0.54729007875488[/C][C]0.90541984249024[/C][C]0.45270992124512[/C][/ROW]
[ROW][C]41[/C][C]0.594615516954635[/C][C]0.81076896609073[/C][C]0.405384483045365[/C][/ROW]
[ROW][C]42[/C][C]0.651191348414926[/C][C]0.697617303170148[/C][C]0.348808651585074[/C][/ROW]
[ROW][C]43[/C][C]0.701200338895713[/C][C]0.597599322208574[/C][C]0.298799661104287[/C][/ROW]
[ROW][C]44[/C][C]0.57559147041526[/C][C]0.848817059169479[/C][C]0.424408529584739[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64984&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64984&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
17	0.286903576026991	0.573807152053982	0.713096423973009
18	0.503946114457648	0.992107771084704	0.496053885542352
19	0.481022028168762	0.962044056337524	0.518977971831238
20	0.407119981781704	0.814239963563409	0.592880018218296
21	0.29738267450978	0.59476534901956	0.70261732549022
22	0.211446468865883	0.422892937731767	0.788553531134117
23	0.135191231941780	0.270382463883561	0.86480876805822
24	0.113535555728901	0.227071111457801	0.8864644442711
25	0.0748331285526746	0.149666257105349	0.925166871447325
26	0.0535676066650276	0.107135213330055	0.946432393334972
27	0.0338629269635512	0.0677258539271023	0.96613707303645
28	0.0447431544289080	0.0894863088578161	0.955256845571092
29	0.0329532666490065	0.065906533298013	0.967046733350994
30	0.0426618963298799	0.0853237926597598	0.95733810367012
31	0.265821046595439	0.531642093190877	0.734178953404561
32	0.418951292056361	0.837902584112722	0.581048707943639
33	0.389341857138154	0.778683714276309	0.610658142861846
34	0.330675589541358	0.661351179082716	0.669324410458642
35	0.374631726757619	0.749263453515238	0.625368273242381
36	0.319671087180859	0.639342174361718	0.680328912819141
37	0.357930355464067	0.715860710928133	0.642069644535933
38	0.310593790623056	0.621187581246111	0.689406209376944
39	0.536143295009435	0.92771340998113	0.463856704990565
40	0.54729007875488	0.90541984249024	0.45270992124512
41	0.594615516954635	0.81076896609073	0.405384483045365
42	0.651191348414926	0.697617303170148	0.348808651585074
43	0.701200338895713	0.597599322208574	0.298799661104287
44	0.57559147041526	0.848817059169479	0.424408529584739

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	4	0.142857142857143	NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 4 & 0.142857142857143 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64984&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]4[/C][C]0.142857142857143[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64984&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64984&T=6

As an alternative you can also use a QR Code:

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

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	4	0.142857142857143	NOK

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code