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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 20 Nov 2009 07:38:06 -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/Nov/20/t125872809769krb8m4jvy2x38.htm/, Retrieved Tue, 16 Apr 2024 10:10:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58223, Retrieved Tue, 16 Apr 2024 10:10:52 +0000

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Estimated Impact

131

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 14:14:11] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-11-20 14:38:06] [27b6e36591879260e4dc6bb7e89a38fd] [Current]
-    D        [Multiple Regression] [] [2009-12-15 16:17:38] [e149fd9094b67af26551857fa83a9d9d] 

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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	5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58223&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]5 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=58223&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58223&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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
WklBe[t] = + 78.3799061515617 + 14.6195874973145X[t] + 0.898113780807656Y1[t] -20.7234367469645M1[t] -27.0811350164046M2[t] -28.2616920464878M3[t] -11.6422490765710M4[t] -11.2092314050304M5[t] -16.9965909773283M6[t] -21.6360223524573M7[t] -18.3441303358710M8[t] -24.6650706863537M9[t] -12.0177055958290M10[t] + 37.5949348318731M11[t] -0.388490745478934t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
WklBe[t] =  +  78.3799061515617 +  14.6195874973145X[t] +  0.898113780807656Y1[t] -20.7234367469645M1[t] -27.0811350164046M2[t] -28.2616920464878M3[t] -11.6422490765710M4[t] -11.2092314050304M5[t] -16.9965909773283M6[t] -21.6360223524573M7[t] -18.3441303358710M8[t] -24.6650706863537M9[t] -12.0177055958290M10[t] +  37.5949348318731M11[t] -0.388490745478934t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58223&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]WklBe[t] =  +  78.3799061515617 +  14.6195874973145X[t] +  0.898113780807656Y1[t] -20.7234367469645M1[t] -27.0811350164046M2[t] -28.2616920464878M3[t] -11.6422490765710M4[t] -11.2092314050304M5[t] -16.9965909773283M6[t] -21.6360223524573M7[t] -18.3441303358710M8[t] -24.6650706863537M9[t] -12.0177055958290M10[t] +  37.5949348318731M11[t] -0.388490745478934t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58223&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58223&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
WklBe[t] = + 78.3799061515617 + 14.6195874973145X[t] + 0.898113780807656Y1[t] -20.7234367469645M1[t] -27.0811350164046M2[t] -28.2616920464878M3[t] -11.6422490765710M4[t] -11.2092314050304M5[t] -16.9965909773283M6[t] -21.6360223524573M7[t] -18.3441303358710M8[t] -24.6650706863537M9[t] -12.0177055958290M10[t] + 37.5949348318731M11[t] -0.388490745478934t + 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)	78.3799061515617	26.479551	2.96	0.00485	0.002425
X	14.6195874973145	3.288852	4.4452	5.5e-05	2.8e-05
Y1	0.898113780807656	0.039915	22.5009	0	0
M1	-20.7234367469645	3.953963	-5.2412	4e-06	2e-06
M2	-27.0811350164046	4.204585	-6.4409	0	0
M3	-28.2616920464878	4.32882	-6.5287	0	0
M4	-11.6422490765710	4.511667	-2.5805	0.013123	0.006562
M5	-11.2092314050304	4.428655	-2.5311	0.014855	0.007427
M6	-16.9965909773283	4.356003	-3.9019	0.000309	0.000155
M7	-21.6360223524573	4.377076	-4.943	1.1e-05	5e-06
M8	-18.3441303358710	4.473265	-4.1008	0.000166	8.3e-05
M9	-24.6650706863537	4.515308	-5.4625	2e-06	1e-06
M10	-12.0177055958290	4.67794	-2.569	0.013508	0.006754
M11	37.5949348318731	4.590183	8.1903	0	0
t	-0.388490745478934	0.11461	-3.3897	0.001445	0.000722

\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) & 78.3799061515617 & 26.479551 & 2.96 & 0.00485 & 0.002425 \tabularnewline
X & 14.6195874973145 & 3.288852 & 4.4452 & 5.5e-05 & 2.8e-05 \tabularnewline
Y1 & 0.898113780807656 & 0.039915 & 22.5009 & 0 & 0 \tabularnewline
M1 & -20.7234367469645 & 3.953963 & -5.2412 & 4e-06 & 2e-06 \tabularnewline
M2 & -27.0811350164046 & 4.204585 & -6.4409 & 0 & 0 \tabularnewline
M3 & -28.2616920464878 & 4.32882 & -6.5287 & 0 & 0 \tabularnewline
M4 & -11.6422490765710 & 4.511667 & -2.5805 & 0.013123 & 0.006562 \tabularnewline
M5 & -11.2092314050304 & 4.428655 & -2.5311 & 0.014855 & 0.007427 \tabularnewline
M6 & -16.9965909773283 & 4.356003 & -3.9019 & 0.000309 & 0.000155 \tabularnewline
M7 & -21.6360223524573 & 4.377076 & -4.943 & 1.1e-05 & 5e-06 \tabularnewline
M8 & -18.3441303358710 & 4.473265 & -4.1008 & 0.000166 & 8.3e-05 \tabularnewline
M9 & -24.6650706863537 & 4.515308 & -5.4625 & 2e-06 & 1e-06 \tabularnewline
M10 & -12.0177055958290 & 4.67794 & -2.569 & 0.013508 & 0.006754 \tabularnewline
M11 & 37.5949348318731 & 4.590183 & 8.1903 & 0 & 0 \tabularnewline
t & -0.388490745478934 & 0.11461 & -3.3897 & 0.001445 & 0.000722 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58223&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]78.3799061515617[/C][C]26.479551[/C][C]2.96[/C][C]0.00485[/C][C]0.002425[/C][/ROW]
[ROW][C]X[/C][C]14.6195874973145[/C][C]3.288852[/C][C]4.4452[/C][C]5.5e-05[/C][C]2.8e-05[/C][/ROW]
[ROW][C]Y1[/C][C]0.898113780807656[/C][C]0.039915[/C][C]22.5009[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-20.7234367469645[/C][C]3.953963[/C][C]-5.2412[/C][C]4e-06[/C][C]2e-06[/C][/ROW]
[ROW][C]M2[/C][C]-27.0811350164046[/C][C]4.204585[/C][C]-6.4409[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M3[/C][C]-28.2616920464878[/C][C]4.32882[/C][C]-6.5287[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M4[/C][C]-11.6422490765710[/C][C]4.511667[/C][C]-2.5805[/C][C]0.013123[/C][C]0.006562[/C][/ROW]
[ROW][C]M5[/C][C]-11.2092314050304[/C][C]4.428655[/C][C]-2.5311[/C][C]0.014855[/C][C]0.007427[/C][/ROW]
[ROW][C]M6[/C][C]-16.9965909773283[/C][C]4.356003[/C][C]-3.9019[/C][C]0.000309[/C][C]0.000155[/C][/ROW]
[ROW][C]M7[/C][C]-21.6360223524573[/C][C]4.377076[/C][C]-4.943[/C][C]1.1e-05[/C][C]5e-06[/C][/ROW]
[ROW][C]M8[/C][C]-18.3441303358710[/C][C]4.473265[/C][C]-4.1008[/C][C]0.000166[/C][C]8.3e-05[/C][/ROW]
[ROW][C]M9[/C][C]-24.6650706863537[/C][C]4.515308[/C][C]-5.4625[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M10[/C][C]-12.0177055958290[/C][C]4.67794[/C][C]-2.569[/C][C]0.013508[/C][C]0.006754[/C][/ROW]
[ROW][C]M11[/C][C]37.5949348318731[/C][C]4.590183[/C][C]8.1903[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]t[/C][C]-0.388490745478934[/C][C]0.11461[/C][C]-3.3897[/C][C]0.001445[/C][C]0.000722[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58223&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58223&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)	78.3799061515617	26.479551	2.96	0.00485	0.002425
X	14.6195874973145	3.288852	4.4452	5.5e-05	2.8e-05
Y1	0.898113780807656	0.039915	22.5009	0	0
M1	-20.7234367469645	3.953963	-5.2412	4e-06	2e-06
M2	-27.0811350164046	4.204585	-6.4409	0	0
M3	-28.2616920464878	4.32882	-6.5287	0	0
M4	-11.6422490765710	4.511667	-2.5805	0.013123	0.006562
M5	-11.2092314050304	4.428655	-2.5311	0.014855	0.007427
M6	-16.9965909773283	4.356003	-3.9019	0.000309	0.000155
M7	-21.6360223524573	4.377076	-4.943	1.1e-05	5e-06
M8	-18.3441303358710	4.473265	-4.1008	0.000166	8.3e-05
M9	-24.6650706863537	4.515308	-5.4625	2e-06	1e-06
M10	-12.0177055958290	4.67794	-2.569	0.013508	0.006754
M11	37.5949348318731	4.590183	8.1903	0	0
t	-0.388490745478934	0.11461	-3.3897	0.001445	0.000722

Multiple Linear Regression - Regression Statistics
Multiple R	0.991014050333522
R-squared	0.982108847958452
Adjusted R-squared	0.976663714728416
F-TEST (value)	180.364521209686
F-TEST (DF numerator)	14
F-TEST (DF denominator)	46
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.42361458238997
Sum Squared Residuals	1898.08991794228

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.991014050333522 \tabularnewline
R-squared & 0.982108847958452 \tabularnewline
Adjusted R-squared & 0.976663714728416 \tabularnewline
F-TEST (value) & 180.364521209686 \tabularnewline
F-TEST (DF numerator) & 14 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 6.42361458238997 \tabularnewline
Sum Squared Residuals & 1898.08991794228 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58223&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.991014050333522[/C][/ROW]
[ROW][C]R-squared[/C][C]0.982108847958452[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.976663714728416[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]180.364521209686[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]14[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/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]6.42361458238997[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1898.08991794228[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58223&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58223&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	0.991014050333522
R-squared	0.982108847958452
Adjusted R-squared	0.976663714728416
F-TEST (value)	180.364521209686
F-TEST (DF numerator)	14
F-TEST (DF denominator)	46
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.42361458238997
Sum Squared Residuals	1898.08991794228

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	613	606.015498732596	6.98450126740352
2	611	601.065537279292	9.934462720708
3	594	597.700261942114	-3.70026194211452
4	595	598.663279892822	-3.66327989282235
5	591	599.605920599692	-8.6059205996916
6	589	589.837615158684	-0.837615158684151
7	584	583.013465476461	0.986534523539002
8	573	581.42629784353	-8.42629784353008
9	567	564.837615158684	2.16238484131586
10	569	571.707806818884	-2.70780681888394
11	621	622.728184062722	-1.72818406272239
12	629	631.446675087369	-2.44667508736856
13	628	617.519657841386	10.4803421586136
14	612	609.87535504566	2.12464495434040
15	595	593.936486777175	1.06351322282496
16	597	594.899504727883	2.10049527211723
17	593	596.74025921556	-3.74025921555972
18	590	586.971953774552	3.02804622544775
19	580	579.249690311521	0.750309688478562
20	574	573.171953774552	0.828046225447751
21	573	561.073839993745	11.9261600062554
22	573	572.434600557983	0.565399442017315
23	620	621.658750240206	-1.65875024020584
24	626	625.886672360814	0.113327639186318
25	620	610.163427553216	9.83657244678383
26	588	598.028555853451	-10.0285558534512
27	566	567.719867092044	-1.71986709204409
28	557	564.192316138714	-7.19231613871355
29	561	556.153819037506	4.84618096249371
30	549	553.57042384296	-4.57042384296006
31	532	537.76513635266	-5.76513635266034
32	526	525.400603350038	0.599396649962425
33	511	513.30248956923	-2.30248956922991
34	499	512.089657202161	-13.0896572021608
35	555	550.536441514692	4.46355848530787
36	565	562.847387662569	2.15261233743114
37	542	550.716597978202	-8.71659797820196
38	527	523.313792004707	3.68620799529316
39	510	508.27303751703	1.72696248297010
40	514	509.236055467738	4.76394453226237
41	517	512.87303751703	4.12696248297012
42	508	509.391528541676	-1.39152854167601
43	493	496.280582393799	-3.28058239379926
44	490	485.712276952792	4.2877230472082
45	469	476.308504514407	-7.30850451440711
46	478	469.706989462492	8.2930105375079
47	528	527.014163171984	0.985836828015844
48	534	533.936426635015	0.063573364985062
49	518	532.832769324732	-14.8327693247320
50	506	511.71675981689	-5.71675981689042
51	502	499.370346671636	2.62965332836356
52	516	512.008843772844	3.99115622715631
53	528	524.626963630213	3.37303636978748
54	533	529.228478682128	3.77152131787247
55	536	528.691125465558	7.30887453444203
56	537	534.288868079088	2.71113192091170
57	524	528.477550763934	-4.47755076393423
58	536	529.06094595848	6.93905404151954
59	587	589.062461010396	-2.06246101039548
60	597	596.882838254234	0.117161745766061
61	581	584.752048569867	-3.75204856986706

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 613 & 606.015498732596 & 6.98450126740352 \tabularnewline
2 & 611 & 601.065537279292 & 9.934462720708 \tabularnewline
3 & 594 & 597.700261942114 & -3.70026194211452 \tabularnewline
4 & 595 & 598.663279892822 & -3.66327989282235 \tabularnewline
5 & 591 & 599.605920599692 & -8.6059205996916 \tabularnewline
6 & 589 & 589.837615158684 & -0.837615158684151 \tabularnewline
7 & 584 & 583.013465476461 & 0.986534523539002 \tabularnewline
8 & 573 & 581.42629784353 & -8.42629784353008 \tabularnewline
9 & 567 & 564.837615158684 & 2.16238484131586 \tabularnewline
10 & 569 & 571.707806818884 & -2.70780681888394 \tabularnewline
11 & 621 & 622.728184062722 & -1.72818406272239 \tabularnewline
12 & 629 & 631.446675087369 & -2.44667508736856 \tabularnewline
13 & 628 & 617.519657841386 & 10.4803421586136 \tabularnewline
14 & 612 & 609.87535504566 & 2.12464495434040 \tabularnewline
15 & 595 & 593.936486777175 & 1.06351322282496 \tabularnewline
16 & 597 & 594.899504727883 & 2.10049527211723 \tabularnewline
17 & 593 & 596.74025921556 & -3.74025921555972 \tabularnewline
18 & 590 & 586.971953774552 & 3.02804622544775 \tabularnewline
19 & 580 & 579.249690311521 & 0.750309688478562 \tabularnewline
20 & 574 & 573.171953774552 & 0.828046225447751 \tabularnewline
21 & 573 & 561.073839993745 & 11.9261600062554 \tabularnewline
22 & 573 & 572.434600557983 & 0.565399442017315 \tabularnewline
23 & 620 & 621.658750240206 & -1.65875024020584 \tabularnewline
24 & 626 & 625.886672360814 & 0.113327639186318 \tabularnewline
25 & 620 & 610.163427553216 & 9.83657244678383 \tabularnewline
26 & 588 & 598.028555853451 & -10.0285558534512 \tabularnewline
27 & 566 & 567.719867092044 & -1.71986709204409 \tabularnewline
28 & 557 & 564.192316138714 & -7.19231613871355 \tabularnewline
29 & 561 & 556.153819037506 & 4.84618096249371 \tabularnewline
30 & 549 & 553.57042384296 & -4.57042384296006 \tabularnewline
31 & 532 & 537.76513635266 & -5.76513635266034 \tabularnewline
32 & 526 & 525.400603350038 & 0.599396649962425 \tabularnewline
33 & 511 & 513.30248956923 & -2.30248956922991 \tabularnewline
34 & 499 & 512.089657202161 & -13.0896572021608 \tabularnewline
35 & 555 & 550.536441514692 & 4.46355848530787 \tabularnewline
36 & 565 & 562.847387662569 & 2.15261233743114 \tabularnewline
37 & 542 & 550.716597978202 & -8.71659797820196 \tabularnewline
38 & 527 & 523.313792004707 & 3.68620799529316 \tabularnewline
39 & 510 & 508.27303751703 & 1.72696248297010 \tabularnewline
40 & 514 & 509.236055467738 & 4.76394453226237 \tabularnewline
41 & 517 & 512.87303751703 & 4.12696248297012 \tabularnewline
42 & 508 & 509.391528541676 & -1.39152854167601 \tabularnewline
43 & 493 & 496.280582393799 & -3.28058239379926 \tabularnewline
44 & 490 & 485.712276952792 & 4.2877230472082 \tabularnewline
45 & 469 & 476.308504514407 & -7.30850451440711 \tabularnewline
46 & 478 & 469.706989462492 & 8.2930105375079 \tabularnewline
47 & 528 & 527.014163171984 & 0.985836828015844 \tabularnewline
48 & 534 & 533.936426635015 & 0.063573364985062 \tabularnewline
49 & 518 & 532.832769324732 & -14.8327693247320 \tabularnewline
50 & 506 & 511.71675981689 & -5.71675981689042 \tabularnewline
51 & 502 & 499.370346671636 & 2.62965332836356 \tabularnewline
52 & 516 & 512.008843772844 & 3.99115622715631 \tabularnewline
53 & 528 & 524.626963630213 & 3.37303636978748 \tabularnewline
54 & 533 & 529.228478682128 & 3.77152131787247 \tabularnewline
55 & 536 & 528.691125465558 & 7.30887453444203 \tabularnewline
56 & 537 & 534.288868079088 & 2.71113192091170 \tabularnewline
57 & 524 & 528.477550763934 & -4.47755076393423 \tabularnewline
58 & 536 & 529.06094595848 & 6.93905404151954 \tabularnewline
59 & 587 & 589.062461010396 & -2.06246101039548 \tabularnewline
60 & 597 & 596.882838254234 & 0.117161745766061 \tabularnewline
61 & 581 & 584.752048569867 & -3.75204856986706 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58223&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]613[/C][C]606.015498732596[/C][C]6.98450126740352[/C][/ROW]
[ROW][C]2[/C][C]611[/C][C]601.065537279292[/C][C]9.934462720708[/C][/ROW]
[ROW][C]3[/C][C]594[/C][C]597.700261942114[/C][C]-3.70026194211452[/C][/ROW]
[ROW][C]4[/C][C]595[/C][C]598.663279892822[/C][C]-3.66327989282235[/C][/ROW]
[ROW][C]5[/C][C]591[/C][C]599.605920599692[/C][C]-8.6059205996916[/C][/ROW]
[ROW][C]6[/C][C]589[/C][C]589.837615158684[/C][C]-0.837615158684151[/C][/ROW]
[ROW][C]7[/C][C]584[/C][C]583.013465476461[/C][C]0.986534523539002[/C][/ROW]
[ROW][C]8[/C][C]573[/C][C]581.42629784353[/C][C]-8.42629784353008[/C][/ROW]
[ROW][C]9[/C][C]567[/C][C]564.837615158684[/C][C]2.16238484131586[/C][/ROW]
[ROW][C]10[/C][C]569[/C][C]571.707806818884[/C][C]-2.70780681888394[/C][/ROW]
[ROW][C]11[/C][C]621[/C][C]622.728184062722[/C][C]-1.72818406272239[/C][/ROW]
[ROW][C]12[/C][C]629[/C][C]631.446675087369[/C][C]-2.44667508736856[/C][/ROW]
[ROW][C]13[/C][C]628[/C][C]617.519657841386[/C][C]10.4803421586136[/C][/ROW]
[ROW][C]14[/C][C]612[/C][C]609.87535504566[/C][C]2.12464495434040[/C][/ROW]
[ROW][C]15[/C][C]595[/C][C]593.936486777175[/C][C]1.06351322282496[/C][/ROW]
[ROW][C]16[/C][C]597[/C][C]594.899504727883[/C][C]2.10049527211723[/C][/ROW]
[ROW][C]17[/C][C]593[/C][C]596.74025921556[/C][C]-3.74025921555972[/C][/ROW]
[ROW][C]18[/C][C]590[/C][C]586.971953774552[/C][C]3.02804622544775[/C][/ROW]
[ROW][C]19[/C][C]580[/C][C]579.249690311521[/C][C]0.750309688478562[/C][/ROW]
[ROW][C]20[/C][C]574[/C][C]573.171953774552[/C][C]0.828046225447751[/C][/ROW]
[ROW][C]21[/C][C]573[/C][C]561.073839993745[/C][C]11.9261600062554[/C][/ROW]
[ROW][C]22[/C][C]573[/C][C]572.434600557983[/C][C]0.565399442017315[/C][/ROW]
[ROW][C]23[/C][C]620[/C][C]621.658750240206[/C][C]-1.65875024020584[/C][/ROW]
[ROW][C]24[/C][C]626[/C][C]625.886672360814[/C][C]0.113327639186318[/C][/ROW]
[ROW][C]25[/C][C]620[/C][C]610.163427553216[/C][C]9.83657244678383[/C][/ROW]
[ROW][C]26[/C][C]588[/C][C]598.028555853451[/C][C]-10.0285558534512[/C][/ROW]
[ROW][C]27[/C][C]566[/C][C]567.719867092044[/C][C]-1.71986709204409[/C][/ROW]
[ROW][C]28[/C][C]557[/C][C]564.192316138714[/C][C]-7.19231613871355[/C][/ROW]
[ROW][C]29[/C][C]561[/C][C]556.153819037506[/C][C]4.84618096249371[/C][/ROW]
[ROW][C]30[/C][C]549[/C][C]553.57042384296[/C][C]-4.57042384296006[/C][/ROW]
[ROW][C]31[/C][C]532[/C][C]537.76513635266[/C][C]-5.76513635266034[/C][/ROW]
[ROW][C]32[/C][C]526[/C][C]525.400603350038[/C][C]0.599396649962425[/C][/ROW]
[ROW][C]33[/C][C]511[/C][C]513.30248956923[/C][C]-2.30248956922991[/C][/ROW]
[ROW][C]34[/C][C]499[/C][C]512.089657202161[/C][C]-13.0896572021608[/C][/ROW]
[ROW][C]35[/C][C]555[/C][C]550.536441514692[/C][C]4.46355848530787[/C][/ROW]
[ROW][C]36[/C][C]565[/C][C]562.847387662569[/C][C]2.15261233743114[/C][/ROW]
[ROW][C]37[/C][C]542[/C][C]550.716597978202[/C][C]-8.71659797820196[/C][/ROW]
[ROW][C]38[/C][C]527[/C][C]523.313792004707[/C][C]3.68620799529316[/C][/ROW]
[ROW][C]39[/C][C]510[/C][C]508.27303751703[/C][C]1.72696248297010[/C][/ROW]
[ROW][C]40[/C][C]514[/C][C]509.236055467738[/C][C]4.76394453226237[/C][/ROW]
[ROW][C]41[/C][C]517[/C][C]512.87303751703[/C][C]4.12696248297012[/C][/ROW]
[ROW][C]42[/C][C]508[/C][C]509.391528541676[/C][C]-1.39152854167601[/C][/ROW]
[ROW][C]43[/C][C]493[/C][C]496.280582393799[/C][C]-3.28058239379926[/C][/ROW]
[ROW][C]44[/C][C]490[/C][C]485.712276952792[/C][C]4.2877230472082[/C][/ROW]
[ROW][C]45[/C][C]469[/C][C]476.308504514407[/C][C]-7.30850451440711[/C][/ROW]
[ROW][C]46[/C][C]478[/C][C]469.706989462492[/C][C]8.2930105375079[/C][/ROW]
[ROW][C]47[/C][C]528[/C][C]527.014163171984[/C][C]0.985836828015844[/C][/ROW]
[ROW][C]48[/C][C]534[/C][C]533.936426635015[/C][C]0.063573364985062[/C][/ROW]
[ROW][C]49[/C][C]518[/C][C]532.832769324732[/C][C]-14.8327693247320[/C][/ROW]
[ROW][C]50[/C][C]506[/C][C]511.71675981689[/C][C]-5.71675981689042[/C][/ROW]
[ROW][C]51[/C][C]502[/C][C]499.370346671636[/C][C]2.62965332836356[/C][/ROW]
[ROW][C]52[/C][C]516[/C][C]512.008843772844[/C][C]3.99115622715631[/C][/ROW]
[ROW][C]53[/C][C]528[/C][C]524.626963630213[/C][C]3.37303636978748[/C][/ROW]
[ROW][C]54[/C][C]533[/C][C]529.228478682128[/C][C]3.77152131787247[/C][/ROW]
[ROW][C]55[/C][C]536[/C][C]528.691125465558[/C][C]7.30887453444203[/C][/ROW]
[ROW][C]56[/C][C]537[/C][C]534.288868079088[/C][C]2.71113192091170[/C][/ROW]
[ROW][C]57[/C][C]524[/C][C]528.477550763934[/C][C]-4.47755076393423[/C][/ROW]
[ROW][C]58[/C][C]536[/C][C]529.06094595848[/C][C]6.93905404151954[/C][/ROW]
[ROW][C]59[/C][C]587[/C][C]589.062461010396[/C][C]-2.06246101039548[/C][/ROW]
[ROW][C]60[/C][C]597[/C][C]596.882838254234[/C][C]0.117161745766061[/C][/ROW]
[ROW][C]61[/C][C]581[/C][C]584.752048569867[/C][C]-3.75204856986706[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58223&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58223&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	613	606.015498732596	6.98450126740352
2	611	601.065537279292	9.934462720708
3	594	597.700261942114	-3.70026194211452
4	595	598.663279892822	-3.66327989282235
5	591	599.605920599692	-8.6059205996916
6	589	589.837615158684	-0.837615158684151
7	584	583.013465476461	0.986534523539002
8	573	581.42629784353	-8.42629784353008
9	567	564.837615158684	2.16238484131586
10	569	571.707806818884	-2.70780681888394
11	621	622.728184062722	-1.72818406272239
12	629	631.446675087369	-2.44667508736856
13	628	617.519657841386	10.4803421586136
14	612	609.87535504566	2.12464495434040
15	595	593.936486777175	1.06351322282496
16	597	594.899504727883	2.10049527211723
17	593	596.74025921556	-3.74025921555972
18	590	586.971953774552	3.02804622544775
19	580	579.249690311521	0.750309688478562
20	574	573.171953774552	0.828046225447751
21	573	561.073839993745	11.9261600062554
22	573	572.434600557983	0.565399442017315
23	620	621.658750240206	-1.65875024020584
24	626	625.886672360814	0.113327639186318
25	620	610.163427553216	9.83657244678383
26	588	598.028555853451	-10.0285558534512
27	566	567.719867092044	-1.71986709204409
28	557	564.192316138714	-7.19231613871355
29	561	556.153819037506	4.84618096249371
30	549	553.57042384296	-4.57042384296006
31	532	537.76513635266	-5.76513635266034
32	526	525.400603350038	0.599396649962425
33	511	513.30248956923	-2.30248956922991
34	499	512.089657202161	-13.0896572021608
35	555	550.536441514692	4.46355848530787
36	565	562.847387662569	2.15261233743114
37	542	550.716597978202	-8.71659797820196
38	527	523.313792004707	3.68620799529316
39	510	508.27303751703	1.72696248297010
40	514	509.236055467738	4.76394453226237
41	517	512.87303751703	4.12696248297012
42	508	509.391528541676	-1.39152854167601
43	493	496.280582393799	-3.28058239379926
44	490	485.712276952792	4.2877230472082
45	469	476.308504514407	-7.30850451440711
46	478	469.706989462492	8.2930105375079
47	528	527.014163171984	0.985836828015844
48	534	533.936426635015	0.063573364985062
49	518	532.832769324732	-14.8327693247320
50	506	511.71675981689	-5.71675981689042
51	502	499.370346671636	2.62965332836356
52	516	512.008843772844	3.99115622715631
53	528	524.626963630213	3.37303636978748
54	533	529.228478682128	3.77152131787247
55	536	528.691125465558	7.30887453444203
56	537	534.288868079088	2.71113192091170
57	524	528.477550763934	-4.47755076393423
58	536	529.06094595848	6.93905404151954
59	587	589.062461010396	-2.06246101039548
60	597	596.882838254234	0.117161745766061
61	581	584.752048569867	-3.75204856986706

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
18	0.184311703662680	0.368623407325359	0.81568829633732
19	0.112462404175104	0.224924808350208	0.887537595824896
20	0.0590282321957096	0.118056464391419	0.94097176780429
21	0.0665574323850992	0.133114864770198	0.9334425676149
22	0.0307951655398725	0.0615903310797449	0.969204834460128
23	0.0173572421928665	0.0347144843857331	0.982642757807134
24	0.00890413147933768	0.0178082629586754	0.991095868520662
25	0.0397428852502019	0.0794857705004039	0.960257114749798
26	0.663342193988467	0.673315612023067	0.336657806011533
27	0.567097597544108	0.865804804911784	0.432902402455892
28	0.566784307602038	0.866431384795925	0.433215692397962
29	0.627546103508796	0.744907792982408	0.372453896491204
30	0.587205140439537	0.825589719120926	0.412794859560463
31	0.550303074322729	0.899393851354543	0.449696925677271
32	0.471488502244588	0.942977004489176	0.528511497755412
33	0.498841453065955	0.99768290613191	0.501158546934045
34	0.93063954398019	0.138720912039621	0.0693604560198104
35	0.94409004578764	0.111819908424721	0.0559099542123607
36	0.93986246051344	0.120275078973122	0.0601375394865612
37	0.953888264595582	0.0922234708088362	0.0461117354044181
38	0.982939448518759	0.0341211029624829	0.0170605514812415
39	0.96637143545757	0.0672571290848587	0.0336285645424294
40	0.95903041019747	0.081939179605061	0.0409695898025305
41	0.9805407502295	0.0389184995410022	0.0194592497705011
42	0.980583891790982	0.0388322164180356	0.0194161082090178
43	0.9710323120147	0.0579353759706005	0.0289676879853002

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
18 & 0.184311703662680 & 0.368623407325359 & 0.81568829633732 \tabularnewline
19 & 0.112462404175104 & 0.224924808350208 & 0.887537595824896 \tabularnewline
20 & 0.0590282321957096 & 0.118056464391419 & 0.94097176780429 \tabularnewline
21 & 0.0665574323850992 & 0.133114864770198 & 0.9334425676149 \tabularnewline
22 & 0.0307951655398725 & 0.0615903310797449 & 0.969204834460128 \tabularnewline
23 & 0.0173572421928665 & 0.0347144843857331 & 0.982642757807134 \tabularnewline
24 & 0.00890413147933768 & 0.0178082629586754 & 0.991095868520662 \tabularnewline
25 & 0.0397428852502019 & 0.0794857705004039 & 0.960257114749798 \tabularnewline
26 & 0.663342193988467 & 0.673315612023067 & 0.336657806011533 \tabularnewline
27 & 0.567097597544108 & 0.865804804911784 & 0.432902402455892 \tabularnewline
28 & 0.566784307602038 & 0.866431384795925 & 0.433215692397962 \tabularnewline
29 & 0.627546103508796 & 0.744907792982408 & 0.372453896491204 \tabularnewline
30 & 0.587205140439537 & 0.825589719120926 & 0.412794859560463 \tabularnewline
31 & 0.550303074322729 & 0.899393851354543 & 0.449696925677271 \tabularnewline
32 & 0.471488502244588 & 0.942977004489176 & 0.528511497755412 \tabularnewline
33 & 0.498841453065955 & 0.99768290613191 & 0.501158546934045 \tabularnewline
34 & 0.93063954398019 & 0.138720912039621 & 0.0693604560198104 \tabularnewline
35 & 0.94409004578764 & 0.111819908424721 & 0.0559099542123607 \tabularnewline
36 & 0.93986246051344 & 0.120275078973122 & 0.0601375394865612 \tabularnewline
37 & 0.953888264595582 & 0.0922234708088362 & 0.0461117354044181 \tabularnewline
38 & 0.982939448518759 & 0.0341211029624829 & 0.0170605514812415 \tabularnewline
39 & 0.96637143545757 & 0.0672571290848587 & 0.0336285645424294 \tabularnewline
40 & 0.95903041019747 & 0.081939179605061 & 0.0409695898025305 \tabularnewline
41 & 0.9805407502295 & 0.0389184995410022 & 0.0194592497705011 \tabularnewline
42 & 0.980583891790982 & 0.0388322164180356 & 0.0194161082090178 \tabularnewline
43 & 0.9710323120147 & 0.0579353759706005 & 0.0289676879853002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58223&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]18[/C][C]0.184311703662680[/C][C]0.368623407325359[/C][C]0.81568829633732[/C][/ROW]
[ROW][C]19[/C][C]0.112462404175104[/C][C]0.224924808350208[/C][C]0.887537595824896[/C][/ROW]
[ROW][C]20[/C][C]0.0590282321957096[/C][C]0.118056464391419[/C][C]0.94097176780429[/C][/ROW]
[ROW][C]21[/C][C]0.0665574323850992[/C][C]0.133114864770198[/C][C]0.9334425676149[/C][/ROW]
[ROW][C]22[/C][C]0.0307951655398725[/C][C]0.0615903310797449[/C][C]0.969204834460128[/C][/ROW]
[ROW][C]23[/C][C]0.0173572421928665[/C][C]0.0347144843857331[/C][C]0.982642757807134[/C][/ROW]
[ROW][C]24[/C][C]0.00890413147933768[/C][C]0.0178082629586754[/C][C]0.991095868520662[/C][/ROW]
[ROW][C]25[/C][C]0.0397428852502019[/C][C]0.0794857705004039[/C][C]0.960257114749798[/C][/ROW]
[ROW][C]26[/C][C]0.663342193988467[/C][C]0.673315612023067[/C][C]0.336657806011533[/C][/ROW]
[ROW][C]27[/C][C]0.567097597544108[/C][C]0.865804804911784[/C][C]0.432902402455892[/C][/ROW]
[ROW][C]28[/C][C]0.566784307602038[/C][C]0.866431384795925[/C][C]0.433215692397962[/C][/ROW]
[ROW][C]29[/C][C]0.627546103508796[/C][C]0.744907792982408[/C][C]0.372453896491204[/C][/ROW]
[ROW][C]30[/C][C]0.587205140439537[/C][C]0.825589719120926[/C][C]0.412794859560463[/C][/ROW]
[ROW][C]31[/C][C]0.550303074322729[/C][C]0.899393851354543[/C][C]0.449696925677271[/C][/ROW]
[ROW][C]32[/C][C]0.471488502244588[/C][C]0.942977004489176[/C][C]0.528511497755412[/C][/ROW]
[ROW][C]33[/C][C]0.498841453065955[/C][C]0.99768290613191[/C][C]0.501158546934045[/C][/ROW]
[ROW][C]34[/C][C]0.93063954398019[/C][C]0.138720912039621[/C][C]0.0693604560198104[/C][/ROW]
[ROW][C]35[/C][C]0.94409004578764[/C][C]0.111819908424721[/C][C]0.0559099542123607[/C][/ROW]
[ROW][C]36[/C][C]0.93986246051344[/C][C]0.120275078973122[/C][C]0.0601375394865612[/C][/ROW]
[ROW][C]37[/C][C]0.953888264595582[/C][C]0.0922234708088362[/C][C]0.0461117354044181[/C][/ROW]
[ROW][C]38[/C][C]0.982939448518759[/C][C]0.0341211029624829[/C][C]0.0170605514812415[/C][/ROW]
[ROW][C]39[/C][C]0.96637143545757[/C][C]0.0672571290848587[/C][C]0.0336285645424294[/C][/ROW]
[ROW][C]40[/C][C]0.95903041019747[/C][C]0.081939179605061[/C][C]0.0409695898025305[/C][/ROW]
[ROW][C]41[/C][C]0.9805407502295[/C][C]0.0389184995410022[/C][C]0.0194592497705011[/C][/ROW]
[ROW][C]42[/C][C]0.980583891790982[/C][C]0.0388322164180356[/C][C]0.0194161082090178[/C][/ROW]
[ROW][C]43[/C][C]0.9710323120147[/C][C]0.0579353759706005[/C][C]0.0289676879853002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58223&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58223&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
18	0.184311703662680	0.368623407325359	0.81568829633732
19	0.112462404175104	0.224924808350208	0.887537595824896
20	0.0590282321957096	0.118056464391419	0.94097176780429
21	0.0665574323850992	0.133114864770198	0.9334425676149
22	0.0307951655398725	0.0615903310797449	0.969204834460128
23	0.0173572421928665	0.0347144843857331	0.982642757807134
24	0.00890413147933768	0.0178082629586754	0.991095868520662
25	0.0397428852502019	0.0794857705004039	0.960257114749798
26	0.663342193988467	0.673315612023067	0.336657806011533
27	0.567097597544108	0.865804804911784	0.432902402455892
28	0.566784307602038	0.866431384795925	0.433215692397962
29	0.627546103508796	0.744907792982408	0.372453896491204
30	0.587205140439537	0.825589719120926	0.412794859560463
31	0.550303074322729	0.899393851354543	0.449696925677271
32	0.471488502244588	0.942977004489176	0.528511497755412
33	0.498841453065955	0.99768290613191	0.501158546934045
34	0.93063954398019	0.138720912039621	0.0693604560198104
35	0.94409004578764	0.111819908424721	0.0559099542123607
36	0.93986246051344	0.120275078973122	0.0601375394865612
37	0.953888264595582	0.0922234708088362	0.0461117354044181
38	0.982939448518759	0.0341211029624829	0.0170605514812415
39	0.96637143545757	0.0672571290848587	0.0336285645424294
40	0.95903041019747	0.081939179605061	0.0409695898025305
41	0.9805407502295	0.0389184995410022	0.0194592497705011
42	0.980583891790982	0.0388322164180356	0.0194161082090178
43	0.9710323120147	0.0579353759706005	0.0289676879853002

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	5	0.192307692307692	NOK
10% type I error level	11	0.423076923076923	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 & 5 & 0.192307692307692 & NOK \tabularnewline
10% type I error level & 11 & 0.423076923076923 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58223&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]5[/C][C]0.192307692307692[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]11[/C][C]0.423076923076923[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58223&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58223&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	5	0.192307692307692	NOK
10% type I error level	11	0.423076923076923	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