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rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Thu, 19 Nov 2009 03:17:29 -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/19/t1258625893obwjx1i0jm9vrnk.htm/, Retrieved Wed, 24 Apr 2024 04:48:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57679, Retrieved Wed, 24 Apr 2024 04:48:16 +0000

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182

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

-       [Multiple Regression] [Indicator voor he...] [2009-11-19 10:17:29] [41dcf2419e4beff0486cef71832b5d35] [Current]
- R  D    [Multiple Regression] [model 3] [2009-11-20 18:11:14] [fa71ec4c741ffec745cb91dcbd756720] 

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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=57679&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=57679&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57679&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
Y[t] = + 1.82388126251341 + 0.892280450799985X[t] -2.05379470810230M1[t] -1.87816490349226M2[t] -4.25269657265825M3[t] -4.24507385084022M4[t] -0.926679174102201M5[t] + 0.0132594124758251M6[t] -0.357573955866153M7[t] -0.199789760272128M8[t] -1.4204616548381M9[t] -1.07312646661207M10[t] -1.77932810543403M11[t] -0.0187176242900313t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  1.82388126251341 +  0.892280450799985X[t] -2.05379470810230M1[t] -1.87816490349226M2[t] -4.25269657265825M3[t] -4.24507385084022M4[t] -0.926679174102201M5[t] +  0.0132594124758251M6[t] -0.357573955866153M7[t] -0.199789760272128M8[t] -1.4204616548381M9[t] -1.07312646661207M10[t] -1.77932810543403M11[t] -0.0187176242900313t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57679&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  1.82388126251341 +  0.892280450799985X[t] -2.05379470810230M1[t] -1.87816490349226M2[t] -4.25269657265825M3[t] -4.24507385084022M4[t] -0.926679174102201M5[t] +  0.0132594124758251M6[t] -0.357573955866153M7[t] -0.199789760272128M8[t] -1.4204616548381M9[t] -1.07312646661207M10[t] -1.77932810543403M11[t] -0.0187176242900313t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57679&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57679&T=1

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 1.82388126251341 + 0.892280450799985X[t] -2.05379470810230M1[t] -1.87816490349226M2[t] -4.25269657265825M3[t] -4.24507385084022M4[t] -0.926679174102201M5[t] + 0.0132594124758251M6[t] -0.357573955866153M7[t] -0.199789760272128M8[t] -1.4204616548381M9[t] -1.07312646661207M10[t] -1.77932810543403M11[t] -0.0187176242900313t + 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)	1.82388126251341	3.788473	0.4814	0.632494	0.316247
X	0.892280450799985	0.111612	7.9945	0	0
M1	-2.05379470810230	2.848418	-0.721	0.47454	0.23727
M2	-1.87816490349226	2.843325	-0.6606	0.512194	0.256097
M3	-4.25269657265825	2.837918	-1.4985	0.140828	0.070414
M4	-4.24507385084022	2.833833	-1.498	0.140965	0.070483
M5	-0.926679174102201	2.830867	-0.3273	0.74489	0.372445
M6	0.0132594124758251	2.828398	0.0047	0.99628	0.49814
M7	-0.357573955866153	2.826658	-0.1265	0.899887	0.449943
M8	-0.199789760272128	2.825291	-0.0707	0.943931	0.471966
M9	-1.4204616548381	2.823724	-0.503	0.617333	0.308666
M10	-1.07312646661207	2.821957	-0.3803	0.70549	0.352745
M11	-1.77932810543403	2.820984	-0.6307	0.531327	0.265664
t	-0.0187176242900313	0.042106	-0.4445	0.658736	0.329368

\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) & 1.82388126251341 & 3.788473 & 0.4814 & 0.632494 & 0.316247 \tabularnewline
X & 0.892280450799985 & 0.111612 & 7.9945 & 0 & 0 \tabularnewline
M1 & -2.05379470810230 & 2.848418 & -0.721 & 0.47454 & 0.23727 \tabularnewline
M2 & -1.87816490349226 & 2.843325 & -0.6606 & 0.512194 & 0.256097 \tabularnewline
M3 & -4.25269657265825 & 2.837918 & -1.4985 & 0.140828 & 0.070414 \tabularnewline
M4 & -4.24507385084022 & 2.833833 & -1.498 & 0.140965 & 0.070483 \tabularnewline
M5 & -0.926679174102201 & 2.830867 & -0.3273 & 0.74489 & 0.372445 \tabularnewline
M6 & 0.0132594124758251 & 2.828398 & 0.0047 & 0.99628 & 0.49814 \tabularnewline
M7 & -0.357573955866153 & 2.826658 & -0.1265 & 0.899887 & 0.449943 \tabularnewline
M8 & -0.199789760272128 & 2.825291 & -0.0707 & 0.943931 & 0.471966 \tabularnewline
M9 & -1.4204616548381 & 2.823724 & -0.503 & 0.617333 & 0.308666 \tabularnewline
M10 & -1.07312646661207 & 2.821957 & -0.3803 & 0.70549 & 0.352745 \tabularnewline
M11 & -1.77932810543403 & 2.820984 & -0.6307 & 0.531327 & 0.265664 \tabularnewline
t & -0.0187176242900313 & 0.042106 & -0.4445 & 0.658736 & 0.329368 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57679&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]1.82388126251341[/C][C]3.788473[/C][C]0.4814[/C][C]0.632494[/C][C]0.316247[/C][/ROW]
[ROW][C]X[/C][C]0.892280450799985[/C][C]0.111612[/C][C]7.9945[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-2.05379470810230[/C][C]2.848418[/C][C]-0.721[/C][C]0.47454[/C][C]0.23727[/C][/ROW]
[ROW][C]M2[/C][C]-1.87816490349226[/C][C]2.843325[/C][C]-0.6606[/C][C]0.512194[/C][C]0.256097[/C][/ROW]
[ROW][C]M3[/C][C]-4.25269657265825[/C][C]2.837918[/C][C]-1.4985[/C][C]0.140828[/C][C]0.070414[/C][/ROW]
[ROW][C]M4[/C][C]-4.24507385084022[/C][C]2.833833[/C][C]-1.498[/C][C]0.140965[/C][C]0.070483[/C][/ROW]
[ROW][C]M5[/C][C]-0.926679174102201[/C][C]2.830867[/C][C]-0.3273[/C][C]0.74489[/C][C]0.372445[/C][/ROW]
[ROW][C]M6[/C][C]0.0132594124758251[/C][C]2.828398[/C][C]0.0047[/C][C]0.99628[/C][C]0.49814[/C][/ROW]
[ROW][C]M7[/C][C]-0.357573955866153[/C][C]2.826658[/C][C]-0.1265[/C][C]0.899887[/C][C]0.449943[/C][/ROW]
[ROW][C]M8[/C][C]-0.199789760272128[/C][C]2.825291[/C][C]-0.0707[/C][C]0.943931[/C][C]0.471966[/C][/ROW]
[ROW][C]M9[/C][C]-1.4204616548381[/C][C]2.823724[/C][C]-0.503[/C][C]0.617333[/C][C]0.308666[/C][/ROW]
[ROW][C]M10[/C][C]-1.07312646661207[/C][C]2.821957[/C][C]-0.3803[/C][C]0.70549[/C][C]0.352745[/C][/ROW]
[ROW][C]M11[/C][C]-1.77932810543403[/C][C]2.820984[/C][C]-0.6307[/C][C]0.531327[/C][C]0.265664[/C][/ROW]
[ROW][C]t[/C][C]-0.0187176242900313[/C][C]0.042106[/C][C]-0.4445[/C][C]0.658736[/C][C]0.329368[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57679&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57679&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)	1.82388126251341	3.788473	0.4814	0.632494	0.316247
X	0.892280450799985	0.111612	7.9945	0	0
M1	-2.05379470810230	2.848418	-0.721	0.47454	0.23727
M2	-1.87816490349226	2.843325	-0.6606	0.512194	0.256097
M3	-4.25269657265825	2.837918	-1.4985	0.140828	0.070414
M4	-4.24507385084022	2.833833	-1.498	0.140965	0.070483
M5	-0.926679174102201	2.830867	-0.3273	0.74489	0.372445
M6	0.0132594124758251	2.828398	0.0047	0.99628	0.49814
M7	-0.357573955866153	2.826658	-0.1265	0.899887	0.449943
M8	-0.199789760272128	2.825291	-0.0707	0.943931	0.471966
M9	-1.4204616548381	2.823724	-0.503	0.617333	0.308666
M10	-1.07312646661207	2.821957	-0.3803	0.70549	0.352745
M11	-1.77932810543403	2.820984	-0.6307	0.531327	0.265664
t	-0.0187176242900313	0.042106	-0.4445	0.658736	0.329368

Multiple Linear Regression - Regression Statistics
Multiple R	0.839367041031213
R-squared	0.704537029569493
Adjusted R-squared	0.621036624882611
F-TEST (value)	8.43752832350253
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	2.34250538966307e-08
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	4.46003782858767
Sum Squared Residuals	915.029121891917

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.839367041031213 \tabularnewline
R-squared & 0.704537029569493 \tabularnewline
Adjusted R-squared & 0.621036624882611 \tabularnewline
F-TEST (value) & 8.43752832350253 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 2.34250538966307e-08 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 4.46003782858767 \tabularnewline
Sum Squared Residuals & 915.029121891917 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57679&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.839367041031213[/C][/ROW]
[ROW][C]R-squared[/C][C]0.704537029569493[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.621036624882611[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]8.43752832350253[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/C][/ROW]
[ROW][C]p-value[/C][C]2.34250538966307e-08[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]4.46003782858767[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]915.029121891917[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57679&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57679&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	0.839367041031213
R-squared	0.704537029569493
Adjusted R-squared	0.621036624882611
F-TEST (value)	8.43752832350253
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	2.34250538966307e-08
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	4.46003782858767
Sum Squared Residuals	915.029121891917

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	23	22.6829765156807	0.31702348431929
2	19	21.9476082452007	-2.94760824520069
3	18	19.1082187263447	-1.10821872634470
4	19	18.5617555533927	0.438244446607296
5	19	22.5752569664807	-3.57525696648068
6	22	21.8011450722487	0.198854927751297
7	23	18.6455246821367	4.35447531786325
8	20	17.6246266674008	2.37537333259924
9	14	16.3852371485448	-2.38523714854476
10	14	19.0337838845607	-5.03378388456072
11	14	16.8812159001687	-2.88121590016875
12	15	17.9280020206728	-2.92800202067276
13	11	14.6062970571605	-3.60629705716045
14	17	15.6554896882804	1.34451031171956
15	16	15.3144854316644	0.68551456833561
16	20	16.1956709799924	3.80432902000764
17	24	21.8152772045203	2.18472279547968
18	23	22.9149542569683	0.0850457430316920
19	20	24.8453324364163	-4.84533243641626
20	21	23.8244344216803	-2.82443442168027
21	19	24.6372899396642	-5.63728993966424
22	23	22.3782941962803	0.621705803719719
23	23	23.3487077896883	-0.348707789688255
24	23	23.1463012790723	-0.146301279072288
25	23	21.2522450368400	1.74775496316004
26	27	22.6583498482799	4.34165015172006
27	26	19.1943640138639	6.80563598613606
28	17	18.4694447507519	-1.46944475075195
29	24	20.6091572171600	3.39084278284004
30	26	21.7980623146880	4.20193768531205
31	24	22.3900198179359	1.60998018206408
32	27	22.4398583441599	4.56014165584008
33	27	20.0405042392639	6.95949576073606
34	26	20.2798937581199	5.72010624188006
35	24	20.0011147204079	3.99888527959207
36	23	22.9216897875919	0.0783102124080875
37	23	19.5999848240796	3.40001517592039
38	24	18.8646165535996	5.13538344640037
39	17	15.8467709445836	1.15322905541638
40	21	16.0141321322716	4.98586786772839
41	19	19.1353530945596	-0.135353094559606
42	22	21.7519069133676	0.24809308663243
43	22	20.1131632896156	1.88683671038442
44	18	21.5906505371196	-3.59065053711955
45	16	18.2990159814236	-2.29901598142359
46	14	19.8768261764796	-5.87682617647957
47	12	17.3673460117676	-5.3673460117676
48	14	18.6818162675116	-4.68181626751161
49	16	17.8584965662393	-1.85849656623926
50	8	15.8739356646393	-7.8739356646393
51	3	10.5361608835433	-7.53616088354334
52	0	7.75899658359138	-7.75899658359138
53	5	6.86495551727944	-1.86495551727944
54	1	5.73393144272747	-4.73393144272747
55	1	4.00595977389549	-3.00595977389549
56	3	3.52043002963949	-0.520430029639488
57	6	2.63795269110348	3.36204730889652
58	7	2.43120198455949	4.56879801544051
59	8	3.40161557796746	4.59838442203254
60	14	6.32219064515144	7.67780935484856

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 23 & 22.6829765156807 & 0.31702348431929 \tabularnewline
2 & 19 & 21.9476082452007 & -2.94760824520069 \tabularnewline
3 & 18 & 19.1082187263447 & -1.10821872634470 \tabularnewline
4 & 19 & 18.5617555533927 & 0.438244446607296 \tabularnewline
5 & 19 & 22.5752569664807 & -3.57525696648068 \tabularnewline
6 & 22 & 21.8011450722487 & 0.198854927751297 \tabularnewline
7 & 23 & 18.6455246821367 & 4.35447531786325 \tabularnewline
8 & 20 & 17.6246266674008 & 2.37537333259924 \tabularnewline
9 & 14 & 16.3852371485448 & -2.38523714854476 \tabularnewline
10 & 14 & 19.0337838845607 & -5.03378388456072 \tabularnewline
11 & 14 & 16.8812159001687 & -2.88121590016875 \tabularnewline
12 & 15 & 17.9280020206728 & -2.92800202067276 \tabularnewline
13 & 11 & 14.6062970571605 & -3.60629705716045 \tabularnewline
14 & 17 & 15.6554896882804 & 1.34451031171956 \tabularnewline
15 & 16 & 15.3144854316644 & 0.68551456833561 \tabularnewline
16 & 20 & 16.1956709799924 & 3.80432902000764 \tabularnewline
17 & 24 & 21.8152772045203 & 2.18472279547968 \tabularnewline
18 & 23 & 22.9149542569683 & 0.0850457430316920 \tabularnewline
19 & 20 & 24.8453324364163 & -4.84533243641626 \tabularnewline
20 & 21 & 23.8244344216803 & -2.82443442168027 \tabularnewline
21 & 19 & 24.6372899396642 & -5.63728993966424 \tabularnewline
22 & 23 & 22.3782941962803 & 0.621705803719719 \tabularnewline
23 & 23 & 23.3487077896883 & -0.348707789688255 \tabularnewline
24 & 23 & 23.1463012790723 & -0.146301279072288 \tabularnewline
25 & 23 & 21.2522450368400 & 1.74775496316004 \tabularnewline
26 & 27 & 22.6583498482799 & 4.34165015172006 \tabularnewline
27 & 26 & 19.1943640138639 & 6.80563598613606 \tabularnewline
28 & 17 & 18.4694447507519 & -1.46944475075195 \tabularnewline
29 & 24 & 20.6091572171600 & 3.39084278284004 \tabularnewline
30 & 26 & 21.7980623146880 & 4.20193768531205 \tabularnewline
31 & 24 & 22.3900198179359 & 1.60998018206408 \tabularnewline
32 & 27 & 22.4398583441599 & 4.56014165584008 \tabularnewline
33 & 27 & 20.0405042392639 & 6.95949576073606 \tabularnewline
34 & 26 & 20.2798937581199 & 5.72010624188006 \tabularnewline
35 & 24 & 20.0011147204079 & 3.99888527959207 \tabularnewline
36 & 23 & 22.9216897875919 & 0.0783102124080875 \tabularnewline
37 & 23 & 19.5999848240796 & 3.40001517592039 \tabularnewline
38 & 24 & 18.8646165535996 & 5.13538344640037 \tabularnewline
39 & 17 & 15.8467709445836 & 1.15322905541638 \tabularnewline
40 & 21 & 16.0141321322716 & 4.98586786772839 \tabularnewline
41 & 19 & 19.1353530945596 & -0.135353094559606 \tabularnewline
42 & 22 & 21.7519069133676 & 0.24809308663243 \tabularnewline
43 & 22 & 20.1131632896156 & 1.88683671038442 \tabularnewline
44 & 18 & 21.5906505371196 & -3.59065053711955 \tabularnewline
45 & 16 & 18.2990159814236 & -2.29901598142359 \tabularnewline
46 & 14 & 19.8768261764796 & -5.87682617647957 \tabularnewline
47 & 12 & 17.3673460117676 & -5.3673460117676 \tabularnewline
48 & 14 & 18.6818162675116 & -4.68181626751161 \tabularnewline
49 & 16 & 17.8584965662393 & -1.85849656623926 \tabularnewline
50 & 8 & 15.8739356646393 & -7.8739356646393 \tabularnewline
51 & 3 & 10.5361608835433 & -7.53616088354334 \tabularnewline
52 & 0 & 7.75899658359138 & -7.75899658359138 \tabularnewline
53 & 5 & 6.86495551727944 & -1.86495551727944 \tabularnewline
54 & 1 & 5.73393144272747 & -4.73393144272747 \tabularnewline
55 & 1 & 4.00595977389549 & -3.00595977389549 \tabularnewline
56 & 3 & 3.52043002963949 & -0.520430029639488 \tabularnewline
57 & 6 & 2.63795269110348 & 3.36204730889652 \tabularnewline
58 & 7 & 2.43120198455949 & 4.56879801544051 \tabularnewline
59 & 8 & 3.40161557796746 & 4.59838442203254 \tabularnewline
60 & 14 & 6.32219064515144 & 7.67780935484856 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57679&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]23[/C][C]22.6829765156807[/C][C]0.31702348431929[/C][/ROW]
[ROW][C]2[/C][C]19[/C][C]21.9476082452007[/C][C]-2.94760824520069[/C][/ROW]
[ROW][C]3[/C][C]18[/C][C]19.1082187263447[/C][C]-1.10821872634470[/C][/ROW]
[ROW][C]4[/C][C]19[/C][C]18.5617555533927[/C][C]0.438244446607296[/C][/ROW]
[ROW][C]5[/C][C]19[/C][C]22.5752569664807[/C][C]-3.57525696648068[/C][/ROW]
[ROW][C]6[/C][C]22[/C][C]21.8011450722487[/C][C]0.198854927751297[/C][/ROW]
[ROW][C]7[/C][C]23[/C][C]18.6455246821367[/C][C]4.35447531786325[/C][/ROW]
[ROW][C]8[/C][C]20[/C][C]17.6246266674008[/C][C]2.37537333259924[/C][/ROW]
[ROW][C]9[/C][C]14[/C][C]16.3852371485448[/C][C]-2.38523714854476[/C][/ROW]
[ROW][C]10[/C][C]14[/C][C]19.0337838845607[/C][C]-5.03378388456072[/C][/ROW]
[ROW][C]11[/C][C]14[/C][C]16.8812159001687[/C][C]-2.88121590016875[/C][/ROW]
[ROW][C]12[/C][C]15[/C][C]17.9280020206728[/C][C]-2.92800202067276[/C][/ROW]
[ROW][C]13[/C][C]11[/C][C]14.6062970571605[/C][C]-3.60629705716045[/C][/ROW]
[ROW][C]14[/C][C]17[/C][C]15.6554896882804[/C][C]1.34451031171956[/C][/ROW]
[ROW][C]15[/C][C]16[/C][C]15.3144854316644[/C][C]0.68551456833561[/C][/ROW]
[ROW][C]16[/C][C]20[/C][C]16.1956709799924[/C][C]3.80432902000764[/C][/ROW]
[ROW][C]17[/C][C]24[/C][C]21.8152772045203[/C][C]2.18472279547968[/C][/ROW]
[ROW][C]18[/C][C]23[/C][C]22.9149542569683[/C][C]0.0850457430316920[/C][/ROW]
[ROW][C]19[/C][C]20[/C][C]24.8453324364163[/C][C]-4.84533243641626[/C][/ROW]
[ROW][C]20[/C][C]21[/C][C]23.8244344216803[/C][C]-2.82443442168027[/C][/ROW]
[ROW][C]21[/C][C]19[/C][C]24.6372899396642[/C][C]-5.63728993966424[/C][/ROW]
[ROW][C]22[/C][C]23[/C][C]22.3782941962803[/C][C]0.621705803719719[/C][/ROW]
[ROW][C]23[/C][C]23[/C][C]23.3487077896883[/C][C]-0.348707789688255[/C][/ROW]
[ROW][C]24[/C][C]23[/C][C]23.1463012790723[/C][C]-0.146301279072288[/C][/ROW]
[ROW][C]25[/C][C]23[/C][C]21.2522450368400[/C][C]1.74775496316004[/C][/ROW]
[ROW][C]26[/C][C]27[/C][C]22.6583498482799[/C][C]4.34165015172006[/C][/ROW]
[ROW][C]27[/C][C]26[/C][C]19.1943640138639[/C][C]6.80563598613606[/C][/ROW]
[ROW][C]28[/C][C]17[/C][C]18.4694447507519[/C][C]-1.46944475075195[/C][/ROW]
[ROW][C]29[/C][C]24[/C][C]20.6091572171600[/C][C]3.39084278284004[/C][/ROW]
[ROW][C]30[/C][C]26[/C][C]21.7980623146880[/C][C]4.20193768531205[/C][/ROW]
[ROW][C]31[/C][C]24[/C][C]22.3900198179359[/C][C]1.60998018206408[/C][/ROW]
[ROW][C]32[/C][C]27[/C][C]22.4398583441599[/C][C]4.56014165584008[/C][/ROW]
[ROW][C]33[/C][C]27[/C][C]20.0405042392639[/C][C]6.95949576073606[/C][/ROW]
[ROW][C]34[/C][C]26[/C][C]20.2798937581199[/C][C]5.72010624188006[/C][/ROW]
[ROW][C]35[/C][C]24[/C][C]20.0011147204079[/C][C]3.99888527959207[/C][/ROW]
[ROW][C]36[/C][C]23[/C][C]22.9216897875919[/C][C]0.0783102124080875[/C][/ROW]
[ROW][C]37[/C][C]23[/C][C]19.5999848240796[/C][C]3.40001517592039[/C][/ROW]
[ROW][C]38[/C][C]24[/C][C]18.8646165535996[/C][C]5.13538344640037[/C][/ROW]
[ROW][C]39[/C][C]17[/C][C]15.8467709445836[/C][C]1.15322905541638[/C][/ROW]
[ROW][C]40[/C][C]21[/C][C]16.0141321322716[/C][C]4.98586786772839[/C][/ROW]
[ROW][C]41[/C][C]19[/C][C]19.1353530945596[/C][C]-0.135353094559606[/C][/ROW]
[ROW][C]42[/C][C]22[/C][C]21.7519069133676[/C][C]0.24809308663243[/C][/ROW]
[ROW][C]43[/C][C]22[/C][C]20.1131632896156[/C][C]1.88683671038442[/C][/ROW]
[ROW][C]44[/C][C]18[/C][C]21.5906505371196[/C][C]-3.59065053711955[/C][/ROW]
[ROW][C]45[/C][C]16[/C][C]18.2990159814236[/C][C]-2.29901598142359[/C][/ROW]
[ROW][C]46[/C][C]14[/C][C]19.8768261764796[/C][C]-5.87682617647957[/C][/ROW]
[ROW][C]47[/C][C]12[/C][C]17.3673460117676[/C][C]-5.3673460117676[/C][/ROW]
[ROW][C]48[/C][C]14[/C][C]18.6818162675116[/C][C]-4.68181626751161[/C][/ROW]
[ROW][C]49[/C][C]16[/C][C]17.8584965662393[/C][C]-1.85849656623926[/C][/ROW]
[ROW][C]50[/C][C]8[/C][C]15.8739356646393[/C][C]-7.8739356646393[/C][/ROW]
[ROW][C]51[/C][C]3[/C][C]10.5361608835433[/C][C]-7.53616088354334[/C][/ROW]
[ROW][C]52[/C][C]0[/C][C]7.75899658359138[/C][C]-7.75899658359138[/C][/ROW]
[ROW][C]53[/C][C]5[/C][C]6.86495551727944[/C][C]-1.86495551727944[/C][/ROW]
[ROW][C]54[/C][C]1[/C][C]5.73393144272747[/C][C]-4.73393144272747[/C][/ROW]
[ROW][C]55[/C][C]1[/C][C]4.00595977389549[/C][C]-3.00595977389549[/C][/ROW]
[ROW][C]56[/C][C]3[/C][C]3.52043002963949[/C][C]-0.520430029639488[/C][/ROW]
[ROW][C]57[/C][C]6[/C][C]2.63795269110348[/C][C]3.36204730889652[/C][/ROW]
[ROW][C]58[/C][C]7[/C][C]2.43120198455949[/C][C]4.56879801544051[/C][/ROW]
[ROW][C]59[/C][C]8[/C][C]3.40161557796746[/C][C]4.59838442203254[/C][/ROW]
[ROW][C]60[/C][C]14[/C][C]6.32219064515144[/C][C]7.67780935484856[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57679&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57679&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	23	22.6829765156807	0.31702348431929
2	19	21.9476082452007	-2.94760824520069
3	18	19.1082187263447	-1.10821872634470
4	19	18.5617555533927	0.438244446607296
5	19	22.5752569664807	-3.57525696648068
6	22	21.8011450722487	0.198854927751297
7	23	18.6455246821367	4.35447531786325
8	20	17.6246266674008	2.37537333259924
9	14	16.3852371485448	-2.38523714854476
10	14	19.0337838845607	-5.03378388456072
11	14	16.8812159001687	-2.88121590016875
12	15	17.9280020206728	-2.92800202067276
13	11	14.6062970571605	-3.60629705716045
14	17	15.6554896882804	1.34451031171956
15	16	15.3144854316644	0.68551456833561
16	20	16.1956709799924	3.80432902000764
17	24	21.8152772045203	2.18472279547968
18	23	22.9149542569683	0.0850457430316920
19	20	24.8453324364163	-4.84533243641626
20	21	23.8244344216803	-2.82443442168027
21	19	24.6372899396642	-5.63728993966424
22	23	22.3782941962803	0.621705803719719
23	23	23.3487077896883	-0.348707789688255
24	23	23.1463012790723	-0.146301279072288
25	23	21.2522450368400	1.74775496316004
26	27	22.6583498482799	4.34165015172006
27	26	19.1943640138639	6.80563598613606
28	17	18.4694447507519	-1.46944475075195
29	24	20.6091572171600	3.39084278284004
30	26	21.7980623146880	4.20193768531205
31	24	22.3900198179359	1.60998018206408
32	27	22.4398583441599	4.56014165584008
33	27	20.0405042392639	6.95949576073606
34	26	20.2798937581199	5.72010624188006
35	24	20.0011147204079	3.99888527959207
36	23	22.9216897875919	0.0783102124080875
37	23	19.5999848240796	3.40001517592039
38	24	18.8646165535996	5.13538344640037
39	17	15.8467709445836	1.15322905541638
40	21	16.0141321322716	4.98586786772839
41	19	19.1353530945596	-0.135353094559606
42	22	21.7519069133676	0.24809308663243
43	22	20.1131632896156	1.88683671038442
44	18	21.5906505371196	-3.59065053711955
45	16	18.2990159814236	-2.29901598142359
46	14	19.8768261764796	-5.87682617647957
47	12	17.3673460117676	-5.3673460117676
48	14	18.6818162675116	-4.68181626751161
49	16	17.8584965662393	-1.85849656623926
50	8	15.8739356646393	-7.8739356646393
51	3	10.5361608835433	-7.53616088354334
52	0	7.75899658359138	-7.75899658359138
53	5	6.86495551727944	-1.86495551727944
54	1	5.73393144272747	-4.73393144272747
55	1	4.00595977389549	-3.00595977389549
56	3	3.52043002963949	-0.520430029639488
57	6	2.63795269110348	3.36204730889652
58	7	2.43120198455949	4.56879801544051
59	8	3.40161557796746	4.59838442203254
60	14	6.32219064515144	7.67780935484856

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.0798421207445119	0.159684241489024	0.920157879255488
18	0.099958930395833	0.199917860791666	0.900041069604167
19	0.261249254251796	0.522498508503593	0.738750745748204
20	0.172604074043467	0.345208148086935	0.827395925956533
21	0.150444591373305	0.30088918274661	0.849555408626695
22	0.215258235147274	0.430516470294548	0.784741764852726
23	0.204617021896514	0.409234043793027	0.795382978103486
24	0.214509950666125	0.429019901332251	0.785490049333875
25	0.205525511035727	0.411051022071454	0.794474488964273
26	0.177051310424645	0.354102620849291	0.822948689575354
27	0.166853411411175	0.333706822822350	0.833146588588825
28	0.224143107794457	0.448286215588914	0.775856892205543
29	0.163665909016553	0.327331818033105	0.836334090983447
30	0.110603329835750	0.221206659671500	0.88939667016425
31	0.0744694702273713	0.148938940454743	0.925530529772629
32	0.0495831824118534	0.0991663648237067	0.950416817588147
33	0.066296177920931	0.132592355841862	0.933703822079069
34	0.0485431624895558	0.0970863249791116	0.951456837510444
35	0.0289864048615584	0.0579728097231168	0.971013595138442
36	0.031621688380418	0.063243376760836	0.968378311619582
37	0.0253843336806100	0.0507686673612199	0.97461566631939
38	0.0134352880792363	0.0268705761584725	0.986564711920764
39	0.0112652547702724	0.0225305095405448	0.988734745229728
40	0.0311887472986602	0.0623774945973204	0.96881125270134
41	0.0592724764757049	0.11854495295141	0.940727523524295
42	0.141990429827741	0.283980859655481	0.85800957017226
43	0.690535984204343	0.618928031591314	0.309464015795657

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.0798421207445119 & 0.159684241489024 & 0.920157879255488 \tabularnewline
18 & 0.099958930395833 & 0.199917860791666 & 0.900041069604167 \tabularnewline
19 & 0.261249254251796 & 0.522498508503593 & 0.738750745748204 \tabularnewline
20 & 0.172604074043467 & 0.345208148086935 & 0.827395925956533 \tabularnewline
21 & 0.150444591373305 & 0.30088918274661 & 0.849555408626695 \tabularnewline
22 & 0.215258235147274 & 0.430516470294548 & 0.784741764852726 \tabularnewline
23 & 0.204617021896514 & 0.409234043793027 & 0.795382978103486 \tabularnewline
24 & 0.214509950666125 & 0.429019901332251 & 0.785490049333875 \tabularnewline
25 & 0.205525511035727 & 0.411051022071454 & 0.794474488964273 \tabularnewline
26 & 0.177051310424645 & 0.354102620849291 & 0.822948689575354 \tabularnewline
27 & 0.166853411411175 & 0.333706822822350 & 0.833146588588825 \tabularnewline
28 & 0.224143107794457 & 0.448286215588914 & 0.775856892205543 \tabularnewline
29 & 0.163665909016553 & 0.327331818033105 & 0.836334090983447 \tabularnewline
30 & 0.110603329835750 & 0.221206659671500 & 0.88939667016425 \tabularnewline
31 & 0.0744694702273713 & 0.148938940454743 & 0.925530529772629 \tabularnewline
32 & 0.0495831824118534 & 0.0991663648237067 & 0.950416817588147 \tabularnewline
33 & 0.066296177920931 & 0.132592355841862 & 0.933703822079069 \tabularnewline
34 & 0.0485431624895558 & 0.0970863249791116 & 0.951456837510444 \tabularnewline
35 & 0.0289864048615584 & 0.0579728097231168 & 0.971013595138442 \tabularnewline
36 & 0.031621688380418 & 0.063243376760836 & 0.968378311619582 \tabularnewline
37 & 0.0253843336806100 & 0.0507686673612199 & 0.97461566631939 \tabularnewline
38 & 0.0134352880792363 & 0.0268705761584725 & 0.986564711920764 \tabularnewline
39 & 0.0112652547702724 & 0.0225305095405448 & 0.988734745229728 \tabularnewline
40 & 0.0311887472986602 & 0.0623774945973204 & 0.96881125270134 \tabularnewline
41 & 0.0592724764757049 & 0.11854495295141 & 0.940727523524295 \tabularnewline
42 & 0.141990429827741 & 0.283980859655481 & 0.85800957017226 \tabularnewline
43 & 0.690535984204343 & 0.618928031591314 & 0.309464015795657 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57679&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]0.0798421207445119[/C][C]0.159684241489024[/C][C]0.920157879255488[/C][/ROW]
[ROW][C]18[/C][C]0.099958930395833[/C][C]0.199917860791666[/C][C]0.900041069604167[/C][/ROW]
[ROW][C]19[/C][C]0.261249254251796[/C][C]0.522498508503593[/C][C]0.738750745748204[/C][/ROW]
[ROW][C]20[/C][C]0.172604074043467[/C][C]0.345208148086935[/C][C]0.827395925956533[/C][/ROW]
[ROW][C]21[/C][C]0.150444591373305[/C][C]0.30088918274661[/C][C]0.849555408626695[/C][/ROW]
[ROW][C]22[/C][C]0.215258235147274[/C][C]0.430516470294548[/C][C]0.784741764852726[/C][/ROW]
[ROW][C]23[/C][C]0.204617021896514[/C][C]0.409234043793027[/C][C]0.795382978103486[/C][/ROW]
[ROW][C]24[/C][C]0.214509950666125[/C][C]0.429019901332251[/C][C]0.785490049333875[/C][/ROW]
[ROW][C]25[/C][C]0.205525511035727[/C][C]0.411051022071454[/C][C]0.794474488964273[/C][/ROW]
[ROW][C]26[/C][C]0.177051310424645[/C][C]0.354102620849291[/C][C]0.822948689575354[/C][/ROW]
[ROW][C]27[/C][C]0.166853411411175[/C][C]0.333706822822350[/C][C]0.833146588588825[/C][/ROW]
[ROW][C]28[/C][C]0.224143107794457[/C][C]0.448286215588914[/C][C]0.775856892205543[/C][/ROW]
[ROW][C]29[/C][C]0.163665909016553[/C][C]0.327331818033105[/C][C]0.836334090983447[/C][/ROW]
[ROW][C]30[/C][C]0.110603329835750[/C][C]0.221206659671500[/C][C]0.88939667016425[/C][/ROW]
[ROW][C]31[/C][C]0.0744694702273713[/C][C]0.148938940454743[/C][C]0.925530529772629[/C][/ROW]
[ROW][C]32[/C][C]0.0495831824118534[/C][C]0.0991663648237067[/C][C]0.950416817588147[/C][/ROW]
[ROW][C]33[/C][C]0.066296177920931[/C][C]0.132592355841862[/C][C]0.933703822079069[/C][/ROW]
[ROW][C]34[/C][C]0.0485431624895558[/C][C]0.0970863249791116[/C][C]0.951456837510444[/C][/ROW]
[ROW][C]35[/C][C]0.0289864048615584[/C][C]0.0579728097231168[/C][C]0.971013595138442[/C][/ROW]
[ROW][C]36[/C][C]0.031621688380418[/C][C]0.063243376760836[/C][C]0.968378311619582[/C][/ROW]
[ROW][C]37[/C][C]0.0253843336806100[/C][C]0.0507686673612199[/C][C]0.97461566631939[/C][/ROW]
[ROW][C]38[/C][C]0.0134352880792363[/C][C]0.0268705761584725[/C][C]0.986564711920764[/C][/ROW]
[ROW][C]39[/C][C]0.0112652547702724[/C][C]0.0225305095405448[/C][C]0.988734745229728[/C][/ROW]
[ROW][C]40[/C][C]0.0311887472986602[/C][C]0.0623774945973204[/C][C]0.96881125270134[/C][/ROW]
[ROW][C]41[/C][C]0.0592724764757049[/C][C]0.11854495295141[/C][C]0.940727523524295[/C][/ROW]
[ROW][C]42[/C][C]0.141990429827741[/C][C]0.283980859655481[/C][C]0.85800957017226[/C][/ROW]
[ROW][C]43[/C][C]0.690535984204343[/C][C]0.618928031591314[/C][C]0.309464015795657[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57679&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57679&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	0.0798421207445119	0.159684241489024	0.920157879255488
18	0.099958930395833	0.199917860791666	0.900041069604167
19	0.261249254251796	0.522498508503593	0.738750745748204
20	0.172604074043467	0.345208148086935	0.827395925956533
21	0.150444591373305	0.30088918274661	0.849555408626695
22	0.215258235147274	0.430516470294548	0.784741764852726
23	0.204617021896514	0.409234043793027	0.795382978103486
24	0.214509950666125	0.429019901332251	0.785490049333875
25	0.205525511035727	0.411051022071454	0.794474488964273
26	0.177051310424645	0.354102620849291	0.822948689575354
27	0.166853411411175	0.333706822822350	0.833146588588825
28	0.224143107794457	0.448286215588914	0.775856892205543
29	0.163665909016553	0.327331818033105	0.836334090983447
30	0.110603329835750	0.221206659671500	0.88939667016425
31	0.0744694702273713	0.148938940454743	0.925530529772629
32	0.0495831824118534	0.0991663648237067	0.950416817588147
33	0.066296177920931	0.132592355841862	0.933703822079069
34	0.0485431624895558	0.0970863249791116	0.951456837510444
35	0.0289864048615584	0.0579728097231168	0.971013595138442
36	0.031621688380418	0.063243376760836	0.968378311619582
37	0.0253843336806100	0.0507686673612199	0.97461566631939
38	0.0134352880792363	0.0268705761584725	0.986564711920764
39	0.0112652547702724	0.0225305095405448	0.988734745229728
40	0.0311887472986602	0.0623774945973204	0.96881125270134
41	0.0592724764757049	0.11854495295141	0.940727523524295
42	0.141990429827741	0.283980859655481	0.85800957017226
43	0.690535984204343	0.618928031591314	0.309464015795657

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	2	0.0740740740740741	NOK
10% type I error level	8	0.296296296296296	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 & 2 & 0.0740740740740741 & NOK \tabularnewline
10% type I error level & 8 & 0.296296296296296 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57679&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]2[/C][C]0.0740740740740741[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]8[/C][C]0.296296296296296[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57679&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57679&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	2	0.0740740740740741	NOK
10% type I error level	8	0.296296296296296	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