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rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Fri, 24 Dec 2010 14:12:01 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/24/t1293200023xrjz7gtt2ea45s7.htm/, Retrieved Tue, 30 Apr 2024 01:51:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114984, Retrieved Tue, 30 Apr 2024 01:51:37 +0000

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Estimated Impact

146

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

-       [Multiple Regression] [LKI vertraagd] [2010-12-24 14:12:01] [b6992a7b26e556359948e164e4227eba] [Current]
-         [Multiple Regression] [Finaal model - ve...] [2011-01-26 14:15:00] [49685effa955daf04c1708d99b86c41a] 

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90,09	85,61	87,703	81,71
100,639	85,52	90,09	87,703
83,042	86,51	100,639	90,09
89,956	86,66	83,042	100,639
89,561	87,27	89,956	83,042
105,38	87,62	89,561	89,956
86,554	88,17	105,38	89,561
93,131	87,99	86,554	105,38
92,812	88,83	93,131	86,554
102,195	88,75	92,812	93,131
88,925	88,81	102,195	92,812
94,184	89,43	88,925	102,195
94,196	89,5	94,184	88,925
108,932	89,34	94,196	94,184
91,134	89,75	108,932	94,196
97,149	90,26	91,134	108,932
96,415	90,32	97,149	91,134
112,432	90,76	96,415	97,149
92,47	91,53	112,432	96,415
98,61410515	92,35	92,47	112,432
97,80117197	93,04	98,61410515	92,47
111,8560178	93,35	97,80117197	98,61410515
95,63981455	93,54	111,8560178	97,80117197
104,1120262	95,07	95,63981455	111,8560178
104,0148224	95,39	104,1120262	95,63981455
118,1743476	95,43	104,0148224	104,1120262
102,033431	96,09	118,1743476	104,0148224
109,3138852	96,35	102,033431	118,1743476
108,1523649	96,6	109,3138852	102,033431
121,30381	96,62	108,1523649	109,3138852
103,8725146	97,6	121,30381	108,1523649
112,7185207	97,67	103,8725146	121,30381
109,0381253	98,23	112,7185207	103,8725146
122,4434864	98,29	109,0381253	112,7185207
106,6325686	98,89	122,4434864	109,0381253
113,8153852	99,88	106,6325686	122,4434864
111,1071252	100,42	113,8153852	106,6325686
130,039536	100,81	111,1071252	113,8153852
109,6121057	101,5	130,039536	111,1071252
116,8592117	102,59	109,6121057	130,039536
113,8982545	103,58	116,8592117	109,6121057
128,9375926	103,47	113,8982545	116,8592117
111,8120023	103,77	128,9375926	113,8982545
119,9689463	104,65	111,8120023	128,9375926
117,018539	105,12	119,9689463	111,8120023
132,4743387	104,97	117,018539	119,9689463
116,3369106	105,58	132,4743387	117,018539
124,6405636	106,17	116,3369106	132,4743387
121,025249	106,52	124,6405636	116,3369106
137,2054829	107,87	121,025249	124,6405636
120,0187687	109,63	137,2054829	121,025249
127,0443429	111,54	120,0187687	137,2054829
124,349043	112,47	127,0443429	120,0187687
143,6114438	111,63	124,349043	127,0443429

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	7 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 & 7 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114984&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]7 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=114984&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114984&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	7 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
LKI[t] = -17.2457869176623 + 0.508784678881672CPI[t] + 0.307209058050048LKI_1[t] + 0.380198032535317LKI_2[t] + 2.62067959823466Q1[t] + 15.0228547971945Q2[t] -6.65102587567938Q3[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
LKI[t] =  -17.2457869176623 +  0.508784678881672CPI[t] +  0.307209058050048LKI_1[t] +  0.380198032535317LKI_2[t] +  2.62067959823466Q1[t] +  15.0228547971945Q2[t] -6.65102587567938Q3[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114984&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]LKI[t] =  -17.2457869176623 +  0.508784678881672CPI[t] +  0.307209058050048LKI_1[t] +  0.380198032535317LKI_2[t] +  2.62067959823466Q1[t] +  15.0228547971945Q2[t] -6.65102587567938Q3[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114984&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114984&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
LKI[t] = -17.2457869176623 + 0.508784678881672CPI[t] + 0.307209058050048LKI_1[t] + 0.380198032535317LKI_2[t] + 2.62067959823466Q1[t] + 15.0228547971945Q2[t] -6.65102587567938Q3[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	-17.2457869176623	6.345783	-2.7177	0.009176	0.004588
CPI	0.508784678881672	0.205988	2.47	0.017199	0.008599
LKI_1	0.307209058050048	0.139895	2.196	0.033062	0.016531
LKI_2	0.380198032535317	0.142802	2.6624	0.010588	0.005294
Q1	2.62067959823466	3.214801	0.8152	0.419074	0.209537
Q2	15.0228547971945	2.123296	7.0753	0	0
Q3	-6.65102587567938	3.999931	-1.6628	0.103011	0.051506

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & -17.2457869176623 & 6.345783 & -2.7177 & 0.009176 & 0.004588 \tabularnewline
CPI & 0.508784678881672 & 0.205988 & 2.47 & 0.017199 & 0.008599 \tabularnewline
LKI_1 & 0.307209058050048 & 0.139895 & 2.196 & 0.033062 & 0.016531 \tabularnewline
LKI_2 & 0.380198032535317 & 0.142802 & 2.6624 & 0.010588 & 0.005294 \tabularnewline
Q1 & 2.62067959823466 & 3.214801 & 0.8152 & 0.419074 & 0.209537 \tabularnewline
Q2 & 15.0228547971945 & 2.123296 & 7.0753 & 0 & 0 \tabularnewline
Q3 & -6.65102587567938 & 3.999931 & -1.6628 & 0.103011 & 0.051506 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114984&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]-17.2457869176623[/C][C]6.345783[/C][C]-2.7177[/C][C]0.009176[/C][C]0.004588[/C][/ROW]
[ROW][C]CPI[/C][C]0.508784678881672[/C][C]0.205988[/C][C]2.47[/C][C]0.017199[/C][C]0.008599[/C][/ROW]
[ROW][C]LKI_1[/C][C]0.307209058050048[/C][C]0.139895[/C][C]2.196[/C][C]0.033062[/C][C]0.016531[/C][/ROW]
[ROW][C]LKI_2[/C][C]0.380198032535317[/C][C]0.142802[/C][C]2.6624[/C][C]0.010588[/C][C]0.005294[/C][/ROW]
[ROW][C]Q1[/C][C]2.62067959823466[/C][C]3.214801[/C][C]0.8152[/C][C]0.419074[/C][C]0.209537[/C][/ROW]
[ROW][C]Q2[/C][C]15.0228547971945[/C][C]2.123296[/C][C]7.0753[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]Q3[/C][C]-6.65102587567938[/C][C]3.999931[/C][C]-1.6628[/C][C]0.103011[/C][C]0.051506[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114984&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114984&T=2

As an alternative you can also use a QR Code:

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

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	-17.2457869176623	6.345783	-2.7177	0.009176	0.004588
CPI	0.508784678881672	0.205988	2.47	0.017199	0.008599
LKI_1	0.307209058050048	0.139895	2.196	0.033062	0.016531
LKI_2	0.380198032535317	0.142802	2.6624	0.010588	0.005294
Q1	2.62067959823466	3.214801	0.8152	0.419074	0.209537
Q2	15.0228547971945	2.123296	7.0753	0	0
Q3	-6.65102587567938	3.999931	-1.6628	0.103011	0.051506

Multiple Linear Regression - Regression Statistics
Multiple R	0.994087973665726
R-squared	0.98821089938683
Adjusted R-squared	0.98670590781919
F-TEST (value)	656.622216785721
F-TEST (DF numerator)	6
F-TEST (DF denominator)	47
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.61840933480680
Sum Squared Residuals	123.104692424520

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.994087973665726 \tabularnewline
R-squared & 0.98821089938683 \tabularnewline
Adjusted R-squared & 0.98670590781919 \tabularnewline
F-TEST (value) & 656.622216785721 \tabularnewline
F-TEST (DF numerator) & 6 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 1.61840933480680 \tabularnewline
Sum Squared Residuals & 123.104692424520 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114984&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.994087973665726[/C][/ROW]
[ROW][C]R-squared[/C][C]0.98821089938683[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.98670590781919[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]656.622216785721[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]6[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/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]1.61840933480680[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]123.104692424520[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114984&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114984&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	0.994087973665726
R-squared	0.98821089938683
Adjusted R-squared	0.98670590781919
F-TEST (value)	656.622216785721
F-TEST (DF numerator)	6
F-TEST (DF denominator)	47
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.61840933480680
Sum Squared Residuals	123.104692424520

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	90.09	86.9410862962569	3.14891370374310
2	100.639	102.309305704667	-1.67030570466656
3	83.042	85.2874029209173	-2.24540292091734
4	89.956	90.6194977491373	-0.663497749137338
5	89.561	88.9842346503239	0.576765349676142
6	105.38	104.071826105912	1.30817389408831
7	86.554	87.387338872865	-0.833338872865004
8	93.131	94.1776184561717	-1.04661845617166
9	92.812	92.0885829989522	0.723417001047783
10	102.195	106.852618194068	-4.65761819406831
11	88.925	87.9705240212322	0.954475978767807
12	94.184	94.427730336773	-0.243730336772957
13	94.196	93.6544094070709	0.541590592929128
14	108.932	107.978327019209	0.95367298079056
15	91.134	91.044643120493	0.0893568795069851
16	97.149	98.0900405746677	-0.941040574667734
17	96.415	95.8223451547427	0.59265484525726
18	112.432	110.509785329502	1.92221467049830
19	92.47	93.8691709862734	-1.39917098627343
20	98.61410515	100.894524968959	-2.2804198189589
21	97.80117197	98.1642776258439	-0.363105655843864
22	111.8560178	112.810412328492	-0.954394528491658
23	95.63981455	95.2419010974596	0.397913452540391
24	104.1120262	103.033227738401	1.07879846159948
25	104.0148224	102.254090023632	1.76073237636836
26	118.1743476	117.867872922463	0.306474677537374
27	102.033431	100.842767843264	1.19066315673635
28	109.3138852	108.050865573376	1.26301962662388
29	108.1523649	106.898618083653	1.25374681634693
30	121.30381	121.722153781725	-0.418343781724991
31	103.8725146	104.145517422513	-0.273002822513262
32	112.7185207	110.477259937304	2.24126076269553
33	109.0381253	109.473087941577	-0.434962641576914
34	122.4434864	124.138373532199	-1.69488713219932
35	106.6325686	105.488732932974	1.14383566702581
36	113.8153852	112.882890392147	0.932494807852829
37	111.1071252	111.973660198673	-0.86653499867255
38	130.039536	126.473152158224	3.56638384177639
39	109.6121057	109.936865878669	-0.324760178668566
40	116.8592117	118.065040770793	-1.20582907079335
41	113.8982545	115.649324999157	-1.75107049915740
42	128.9375926	129.841236453877	-0.903643853876615
43	111.8120023	111.814461974203	-0.00245967420316595
44	119.9689463	119.370008658938	0.598937641062172
45	117.018539	118.224588400988	-1.20604940098795
46	132.4743387	132.745308110919	-0.270969410919278
47	116.3369106	115.008208708773	1.32870189122736
48	124.6405636	122.878118096241	1.76244550375922
49	121.025249	122.092411334788	-1.06716233478832
50	137.2054829	137.227820990874	-0.0223380908737981
51	120.0187687	120.045580270364	-0.0268115703639352
52	127.0443429	128.540163697091	-1.49582079709117
53	124.349043	127.257978154342	-2.90893515434170
54	143.6114438	141.075863167870	2.53558063212959

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 90.09 & 86.9410862962569 & 3.14891370374310 \tabularnewline
2 & 100.639 & 102.309305704667 & -1.67030570466656 \tabularnewline
3 & 83.042 & 85.2874029209173 & -2.24540292091734 \tabularnewline
4 & 89.956 & 90.6194977491373 & -0.663497749137338 \tabularnewline
5 & 89.561 & 88.9842346503239 & 0.576765349676142 \tabularnewline
6 & 105.38 & 104.071826105912 & 1.30817389408831 \tabularnewline
7 & 86.554 & 87.387338872865 & -0.833338872865004 \tabularnewline
8 & 93.131 & 94.1776184561717 & -1.04661845617166 \tabularnewline
9 & 92.812 & 92.0885829989522 & 0.723417001047783 \tabularnewline
10 & 102.195 & 106.852618194068 & -4.65761819406831 \tabularnewline
11 & 88.925 & 87.9705240212322 & 0.954475978767807 \tabularnewline
12 & 94.184 & 94.427730336773 & -0.243730336772957 \tabularnewline
13 & 94.196 & 93.6544094070709 & 0.541590592929128 \tabularnewline
14 & 108.932 & 107.978327019209 & 0.95367298079056 \tabularnewline
15 & 91.134 & 91.044643120493 & 0.0893568795069851 \tabularnewline
16 & 97.149 & 98.0900405746677 & -0.941040574667734 \tabularnewline
17 & 96.415 & 95.8223451547427 & 0.59265484525726 \tabularnewline
18 & 112.432 & 110.509785329502 & 1.92221467049830 \tabularnewline
19 & 92.47 & 93.8691709862734 & -1.39917098627343 \tabularnewline
20 & 98.61410515 & 100.894524968959 & -2.2804198189589 \tabularnewline
21 & 97.80117197 & 98.1642776258439 & -0.363105655843864 \tabularnewline
22 & 111.8560178 & 112.810412328492 & -0.954394528491658 \tabularnewline
23 & 95.63981455 & 95.2419010974596 & 0.397913452540391 \tabularnewline
24 & 104.1120262 & 103.033227738401 & 1.07879846159948 \tabularnewline
25 & 104.0148224 & 102.254090023632 & 1.76073237636836 \tabularnewline
26 & 118.1743476 & 117.867872922463 & 0.306474677537374 \tabularnewline
27 & 102.033431 & 100.842767843264 & 1.19066315673635 \tabularnewline
28 & 109.3138852 & 108.050865573376 & 1.26301962662388 \tabularnewline
29 & 108.1523649 & 106.898618083653 & 1.25374681634693 \tabularnewline
30 & 121.30381 & 121.722153781725 & -0.418343781724991 \tabularnewline
31 & 103.8725146 & 104.145517422513 & -0.273002822513262 \tabularnewline
32 & 112.7185207 & 110.477259937304 & 2.24126076269553 \tabularnewline
33 & 109.0381253 & 109.473087941577 & -0.434962641576914 \tabularnewline
34 & 122.4434864 & 124.138373532199 & -1.69488713219932 \tabularnewline
35 & 106.6325686 & 105.488732932974 & 1.14383566702581 \tabularnewline
36 & 113.8153852 & 112.882890392147 & 0.932494807852829 \tabularnewline
37 & 111.1071252 & 111.973660198673 & -0.86653499867255 \tabularnewline
38 & 130.039536 & 126.473152158224 & 3.56638384177639 \tabularnewline
39 & 109.6121057 & 109.936865878669 & -0.324760178668566 \tabularnewline
40 & 116.8592117 & 118.065040770793 & -1.20582907079335 \tabularnewline
41 & 113.8982545 & 115.649324999157 & -1.75107049915740 \tabularnewline
42 & 128.9375926 & 129.841236453877 & -0.903643853876615 \tabularnewline
43 & 111.8120023 & 111.814461974203 & -0.00245967420316595 \tabularnewline
44 & 119.9689463 & 119.370008658938 & 0.598937641062172 \tabularnewline
45 & 117.018539 & 118.224588400988 & -1.20604940098795 \tabularnewline
46 & 132.4743387 & 132.745308110919 & -0.270969410919278 \tabularnewline
47 & 116.3369106 & 115.008208708773 & 1.32870189122736 \tabularnewline
48 & 124.6405636 & 122.878118096241 & 1.76244550375922 \tabularnewline
49 & 121.025249 & 122.092411334788 & -1.06716233478832 \tabularnewline
50 & 137.2054829 & 137.227820990874 & -0.0223380908737981 \tabularnewline
51 & 120.0187687 & 120.045580270364 & -0.0268115703639352 \tabularnewline
52 & 127.0443429 & 128.540163697091 & -1.49582079709117 \tabularnewline
53 & 124.349043 & 127.257978154342 & -2.90893515434170 \tabularnewline
54 & 143.6114438 & 141.075863167870 & 2.53558063212959 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114984&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]90.09[/C][C]86.9410862962569[/C][C]3.14891370374310[/C][/ROW]
[ROW][C]2[/C][C]100.639[/C][C]102.309305704667[/C][C]-1.67030570466656[/C][/ROW]
[ROW][C]3[/C][C]83.042[/C][C]85.2874029209173[/C][C]-2.24540292091734[/C][/ROW]
[ROW][C]4[/C][C]89.956[/C][C]90.6194977491373[/C][C]-0.663497749137338[/C][/ROW]
[ROW][C]5[/C][C]89.561[/C][C]88.9842346503239[/C][C]0.576765349676142[/C][/ROW]
[ROW][C]6[/C][C]105.38[/C][C]104.071826105912[/C][C]1.30817389408831[/C][/ROW]
[ROW][C]7[/C][C]86.554[/C][C]87.387338872865[/C][C]-0.833338872865004[/C][/ROW]
[ROW][C]8[/C][C]93.131[/C][C]94.1776184561717[/C][C]-1.04661845617166[/C][/ROW]
[ROW][C]9[/C][C]92.812[/C][C]92.0885829989522[/C][C]0.723417001047783[/C][/ROW]
[ROW][C]10[/C][C]102.195[/C][C]106.852618194068[/C][C]-4.65761819406831[/C][/ROW]
[ROW][C]11[/C][C]88.925[/C][C]87.9705240212322[/C][C]0.954475978767807[/C][/ROW]
[ROW][C]12[/C][C]94.184[/C][C]94.427730336773[/C][C]-0.243730336772957[/C][/ROW]
[ROW][C]13[/C][C]94.196[/C][C]93.6544094070709[/C][C]0.541590592929128[/C][/ROW]
[ROW][C]14[/C][C]108.932[/C][C]107.978327019209[/C][C]0.95367298079056[/C][/ROW]
[ROW][C]15[/C][C]91.134[/C][C]91.044643120493[/C][C]0.0893568795069851[/C][/ROW]
[ROW][C]16[/C][C]97.149[/C][C]98.0900405746677[/C][C]-0.941040574667734[/C][/ROW]
[ROW][C]17[/C][C]96.415[/C][C]95.8223451547427[/C][C]0.59265484525726[/C][/ROW]
[ROW][C]18[/C][C]112.432[/C][C]110.509785329502[/C][C]1.92221467049830[/C][/ROW]
[ROW][C]19[/C][C]92.47[/C][C]93.8691709862734[/C][C]-1.39917098627343[/C][/ROW]
[ROW][C]20[/C][C]98.61410515[/C][C]100.894524968959[/C][C]-2.2804198189589[/C][/ROW]
[ROW][C]21[/C][C]97.80117197[/C][C]98.1642776258439[/C][C]-0.363105655843864[/C][/ROW]
[ROW][C]22[/C][C]111.8560178[/C][C]112.810412328492[/C][C]-0.954394528491658[/C][/ROW]
[ROW][C]23[/C][C]95.63981455[/C][C]95.2419010974596[/C][C]0.397913452540391[/C][/ROW]
[ROW][C]24[/C][C]104.1120262[/C][C]103.033227738401[/C][C]1.07879846159948[/C][/ROW]
[ROW][C]25[/C][C]104.0148224[/C][C]102.254090023632[/C][C]1.76073237636836[/C][/ROW]
[ROW][C]26[/C][C]118.1743476[/C][C]117.867872922463[/C][C]0.306474677537374[/C][/ROW]
[ROW][C]27[/C][C]102.033431[/C][C]100.842767843264[/C][C]1.19066315673635[/C][/ROW]
[ROW][C]28[/C][C]109.3138852[/C][C]108.050865573376[/C][C]1.26301962662388[/C][/ROW]
[ROW][C]29[/C][C]108.1523649[/C][C]106.898618083653[/C][C]1.25374681634693[/C][/ROW]
[ROW][C]30[/C][C]121.30381[/C][C]121.722153781725[/C][C]-0.418343781724991[/C][/ROW]
[ROW][C]31[/C][C]103.8725146[/C][C]104.145517422513[/C][C]-0.273002822513262[/C][/ROW]
[ROW][C]32[/C][C]112.7185207[/C][C]110.477259937304[/C][C]2.24126076269553[/C][/ROW]
[ROW][C]33[/C][C]109.0381253[/C][C]109.473087941577[/C][C]-0.434962641576914[/C][/ROW]
[ROW][C]34[/C][C]122.4434864[/C][C]124.138373532199[/C][C]-1.69488713219932[/C][/ROW]
[ROW][C]35[/C][C]106.6325686[/C][C]105.488732932974[/C][C]1.14383566702581[/C][/ROW]
[ROW][C]36[/C][C]113.8153852[/C][C]112.882890392147[/C][C]0.932494807852829[/C][/ROW]
[ROW][C]37[/C][C]111.1071252[/C][C]111.973660198673[/C][C]-0.86653499867255[/C][/ROW]
[ROW][C]38[/C][C]130.039536[/C][C]126.473152158224[/C][C]3.56638384177639[/C][/ROW]
[ROW][C]39[/C][C]109.6121057[/C][C]109.936865878669[/C][C]-0.324760178668566[/C][/ROW]
[ROW][C]40[/C][C]116.8592117[/C][C]118.065040770793[/C][C]-1.20582907079335[/C][/ROW]
[ROW][C]41[/C][C]113.8982545[/C][C]115.649324999157[/C][C]-1.75107049915740[/C][/ROW]
[ROW][C]42[/C][C]128.9375926[/C][C]129.841236453877[/C][C]-0.903643853876615[/C][/ROW]
[ROW][C]43[/C][C]111.8120023[/C][C]111.814461974203[/C][C]-0.00245967420316595[/C][/ROW]
[ROW][C]44[/C][C]119.9689463[/C][C]119.370008658938[/C][C]0.598937641062172[/C][/ROW]
[ROW][C]45[/C][C]117.018539[/C][C]118.224588400988[/C][C]-1.20604940098795[/C][/ROW]
[ROW][C]46[/C][C]132.4743387[/C][C]132.745308110919[/C][C]-0.270969410919278[/C][/ROW]
[ROW][C]47[/C][C]116.3369106[/C][C]115.008208708773[/C][C]1.32870189122736[/C][/ROW]
[ROW][C]48[/C][C]124.6405636[/C][C]122.878118096241[/C][C]1.76244550375922[/C][/ROW]
[ROW][C]49[/C][C]121.025249[/C][C]122.092411334788[/C][C]-1.06716233478832[/C][/ROW]
[ROW][C]50[/C][C]137.2054829[/C][C]137.227820990874[/C][C]-0.0223380908737981[/C][/ROW]
[ROW][C]51[/C][C]120.0187687[/C][C]120.045580270364[/C][C]-0.0268115703639352[/C][/ROW]
[ROW][C]52[/C][C]127.0443429[/C][C]128.540163697091[/C][C]-1.49582079709117[/C][/ROW]
[ROW][C]53[/C][C]124.349043[/C][C]127.257978154342[/C][C]-2.90893515434170[/C][/ROW]
[ROW][C]54[/C][C]143.6114438[/C][C]141.075863167870[/C][C]2.53558063212959[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114984&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114984&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	90.09	86.9410862962569	3.14891370374310
2	100.639	102.309305704667	-1.67030570466656
3	83.042	85.2874029209173	-2.24540292091734
4	89.956	90.6194977491373	-0.663497749137338
5	89.561	88.9842346503239	0.576765349676142
6	105.38	104.071826105912	1.30817389408831
7	86.554	87.387338872865	-0.833338872865004
8	93.131	94.1776184561717	-1.04661845617166
9	92.812	92.0885829989522	0.723417001047783
10	102.195	106.852618194068	-4.65761819406831
11	88.925	87.9705240212322	0.954475978767807
12	94.184	94.427730336773	-0.243730336772957
13	94.196	93.6544094070709	0.541590592929128
14	108.932	107.978327019209	0.95367298079056
15	91.134	91.044643120493	0.0893568795069851
16	97.149	98.0900405746677	-0.941040574667734
17	96.415	95.8223451547427	0.59265484525726
18	112.432	110.509785329502	1.92221467049830
19	92.47	93.8691709862734	-1.39917098627343
20	98.61410515	100.894524968959	-2.2804198189589
21	97.80117197	98.1642776258439	-0.363105655843864
22	111.8560178	112.810412328492	-0.954394528491658
23	95.63981455	95.2419010974596	0.397913452540391
24	104.1120262	103.033227738401	1.07879846159948
25	104.0148224	102.254090023632	1.76073237636836
26	118.1743476	117.867872922463	0.306474677537374
27	102.033431	100.842767843264	1.19066315673635
28	109.3138852	108.050865573376	1.26301962662388
29	108.1523649	106.898618083653	1.25374681634693
30	121.30381	121.722153781725	-0.418343781724991
31	103.8725146	104.145517422513	-0.273002822513262
32	112.7185207	110.477259937304	2.24126076269553
33	109.0381253	109.473087941577	-0.434962641576914
34	122.4434864	124.138373532199	-1.69488713219932
35	106.6325686	105.488732932974	1.14383566702581
36	113.8153852	112.882890392147	0.932494807852829
37	111.1071252	111.973660198673	-0.86653499867255
38	130.039536	126.473152158224	3.56638384177639
39	109.6121057	109.936865878669	-0.324760178668566
40	116.8592117	118.065040770793	-1.20582907079335
41	113.8982545	115.649324999157	-1.75107049915740
42	128.9375926	129.841236453877	-0.903643853876615
43	111.8120023	111.814461974203	-0.00245967420316595
44	119.9689463	119.370008658938	0.598937641062172
45	117.018539	118.224588400988	-1.20604940098795
46	132.4743387	132.745308110919	-0.270969410919278
47	116.3369106	115.008208708773	1.32870189122736
48	124.6405636	122.878118096241	1.76244550375922
49	121.025249	122.092411334788	-1.06716233478832
50	137.2054829	137.227820990874	-0.0223380908737981
51	120.0187687	120.045580270364	-0.0268115703639352
52	127.0443429	128.540163697091	-1.49582079709117
53	124.349043	127.257978154342	-2.90893515434170
54	143.6114438	141.075863167870	2.53558063212959

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
10	0.933384986035624	0.133230027928751	0.0666150139643757
11	0.921937795008702	0.156124409982596	0.0780622049912979
12	0.8652175594991	0.269564881001798	0.134782440500899
13	0.80898062662899	0.38203874674202	0.19101937337101
14	0.89955214543752	0.200895709124959	0.100447854562480
15	0.888602584123432	0.222794831753135	0.111397415876568
16	0.847095521581233	0.305808956837533	0.152904478418767
17	0.789026682397122	0.421946635205755	0.210973317602878
18	0.830802905760954	0.338394188478092	0.169197094239046
19	0.812034140704234	0.375931718591532	0.187965859295766
20	0.860568455967124	0.278863088065753	0.139431544032876
21	0.841697032723562	0.316605934552876	0.158302967276438
22	0.837078481417407	0.325843037165186	0.162921518582593
23	0.79618005485147	0.407639890297058	0.203819945148529
24	0.768775960212639	0.462448079574723	0.231224039787361
25	0.735631566160567	0.528736867678866	0.264368433839433
26	0.693519233698767	0.612961532602466	0.306480766301233
27	0.645035118551283	0.709929762897434	0.354964881448717
28	0.601016217143676	0.797967565712648	0.398983782856324
29	0.607052526231926	0.785894947536148	0.392947473768074
30	0.581889595697985	0.83622080860403	0.418110404302015
31	0.495628456069441	0.991256912138883	0.504371543930559
32	0.531717608047371	0.936564783905259	0.468282391952629
33	0.491987577255809	0.983975154511618	0.508012422744191
34	0.631981623668348	0.736036752663304	0.368018376331652
35	0.575913418973918	0.848173162052164	0.424086581026082
36	0.475195813374315	0.95039162674863	0.524804186625685
37	0.440413487552873	0.880826975105745	0.559586512447127
38	0.726716810300376	0.546566379399249	0.273283189699624
39	0.79119097596576	0.417618048068481	0.208809024034240
40	0.729987685219669	0.540024629560663	0.270012314780331
41	0.70402412332244	0.591951753355121	0.295975876677561
42	0.702013328816525	0.595973342366951	0.297986671183475
43	0.554485838748145	0.89102832250371	0.445514161251855
44	0.427818457613053	0.855636915226106	0.572181542386947

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
10 & 0.933384986035624 & 0.133230027928751 & 0.0666150139643757 \tabularnewline
11 & 0.921937795008702 & 0.156124409982596 & 0.0780622049912979 \tabularnewline
12 & 0.8652175594991 & 0.269564881001798 & 0.134782440500899 \tabularnewline
13 & 0.80898062662899 & 0.38203874674202 & 0.19101937337101 \tabularnewline
14 & 0.89955214543752 & 0.200895709124959 & 0.100447854562480 \tabularnewline
15 & 0.888602584123432 & 0.222794831753135 & 0.111397415876568 \tabularnewline
16 & 0.847095521581233 & 0.305808956837533 & 0.152904478418767 \tabularnewline
17 & 0.789026682397122 & 0.421946635205755 & 0.210973317602878 \tabularnewline
18 & 0.830802905760954 & 0.338394188478092 & 0.169197094239046 \tabularnewline
19 & 0.812034140704234 & 0.375931718591532 & 0.187965859295766 \tabularnewline
20 & 0.860568455967124 & 0.278863088065753 & 0.139431544032876 \tabularnewline
21 & 0.841697032723562 & 0.316605934552876 & 0.158302967276438 \tabularnewline
22 & 0.837078481417407 & 0.325843037165186 & 0.162921518582593 \tabularnewline
23 & 0.79618005485147 & 0.407639890297058 & 0.203819945148529 \tabularnewline
24 & 0.768775960212639 & 0.462448079574723 & 0.231224039787361 \tabularnewline
25 & 0.735631566160567 & 0.528736867678866 & 0.264368433839433 \tabularnewline
26 & 0.693519233698767 & 0.612961532602466 & 0.306480766301233 \tabularnewline
27 & 0.645035118551283 & 0.709929762897434 & 0.354964881448717 \tabularnewline
28 & 0.601016217143676 & 0.797967565712648 & 0.398983782856324 \tabularnewline
29 & 0.607052526231926 & 0.785894947536148 & 0.392947473768074 \tabularnewline
30 & 0.581889595697985 & 0.83622080860403 & 0.418110404302015 \tabularnewline
31 & 0.495628456069441 & 0.991256912138883 & 0.504371543930559 \tabularnewline
32 & 0.531717608047371 & 0.936564783905259 & 0.468282391952629 \tabularnewline
33 & 0.491987577255809 & 0.983975154511618 & 0.508012422744191 \tabularnewline
34 & 0.631981623668348 & 0.736036752663304 & 0.368018376331652 \tabularnewline
35 & 0.575913418973918 & 0.848173162052164 & 0.424086581026082 \tabularnewline
36 & 0.475195813374315 & 0.95039162674863 & 0.524804186625685 \tabularnewline
37 & 0.440413487552873 & 0.880826975105745 & 0.559586512447127 \tabularnewline
38 & 0.726716810300376 & 0.546566379399249 & 0.273283189699624 \tabularnewline
39 & 0.79119097596576 & 0.417618048068481 & 0.208809024034240 \tabularnewline
40 & 0.729987685219669 & 0.540024629560663 & 0.270012314780331 \tabularnewline
41 & 0.70402412332244 & 0.591951753355121 & 0.295975876677561 \tabularnewline
42 & 0.702013328816525 & 0.595973342366951 & 0.297986671183475 \tabularnewline
43 & 0.554485838748145 & 0.89102832250371 & 0.445514161251855 \tabularnewline
44 & 0.427818457613053 & 0.855636915226106 & 0.572181542386947 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114984&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]10[/C][C]0.933384986035624[/C][C]0.133230027928751[/C][C]0.0666150139643757[/C][/ROW]
[ROW][C]11[/C][C]0.921937795008702[/C][C]0.156124409982596[/C][C]0.0780622049912979[/C][/ROW]
[ROW][C]12[/C][C]0.8652175594991[/C][C]0.269564881001798[/C][C]0.134782440500899[/C][/ROW]
[ROW][C]13[/C][C]0.80898062662899[/C][C]0.38203874674202[/C][C]0.19101937337101[/C][/ROW]
[ROW][C]14[/C][C]0.89955214543752[/C][C]0.200895709124959[/C][C]0.100447854562480[/C][/ROW]
[ROW][C]15[/C][C]0.888602584123432[/C][C]0.222794831753135[/C][C]0.111397415876568[/C][/ROW]
[ROW][C]16[/C][C]0.847095521581233[/C][C]0.305808956837533[/C][C]0.152904478418767[/C][/ROW]
[ROW][C]17[/C][C]0.789026682397122[/C][C]0.421946635205755[/C][C]0.210973317602878[/C][/ROW]
[ROW][C]18[/C][C]0.830802905760954[/C][C]0.338394188478092[/C][C]0.169197094239046[/C][/ROW]
[ROW][C]19[/C][C]0.812034140704234[/C][C]0.375931718591532[/C][C]0.187965859295766[/C][/ROW]
[ROW][C]20[/C][C]0.860568455967124[/C][C]0.278863088065753[/C][C]0.139431544032876[/C][/ROW]
[ROW][C]21[/C][C]0.841697032723562[/C][C]0.316605934552876[/C][C]0.158302967276438[/C][/ROW]
[ROW][C]22[/C][C]0.837078481417407[/C][C]0.325843037165186[/C][C]0.162921518582593[/C][/ROW]
[ROW][C]23[/C][C]0.79618005485147[/C][C]0.407639890297058[/C][C]0.203819945148529[/C][/ROW]
[ROW][C]24[/C][C]0.768775960212639[/C][C]0.462448079574723[/C][C]0.231224039787361[/C][/ROW]
[ROW][C]25[/C][C]0.735631566160567[/C][C]0.528736867678866[/C][C]0.264368433839433[/C][/ROW]
[ROW][C]26[/C][C]0.693519233698767[/C][C]0.612961532602466[/C][C]0.306480766301233[/C][/ROW]
[ROW][C]27[/C][C]0.645035118551283[/C][C]0.709929762897434[/C][C]0.354964881448717[/C][/ROW]
[ROW][C]28[/C][C]0.601016217143676[/C][C]0.797967565712648[/C][C]0.398983782856324[/C][/ROW]
[ROW][C]29[/C][C]0.607052526231926[/C][C]0.785894947536148[/C][C]0.392947473768074[/C][/ROW]
[ROW][C]30[/C][C]0.581889595697985[/C][C]0.83622080860403[/C][C]0.418110404302015[/C][/ROW]
[ROW][C]31[/C][C]0.495628456069441[/C][C]0.991256912138883[/C][C]0.504371543930559[/C][/ROW]
[ROW][C]32[/C][C]0.531717608047371[/C][C]0.936564783905259[/C][C]0.468282391952629[/C][/ROW]
[ROW][C]33[/C][C]0.491987577255809[/C][C]0.983975154511618[/C][C]0.508012422744191[/C][/ROW]
[ROW][C]34[/C][C]0.631981623668348[/C][C]0.736036752663304[/C][C]0.368018376331652[/C][/ROW]
[ROW][C]35[/C][C]0.575913418973918[/C][C]0.848173162052164[/C][C]0.424086581026082[/C][/ROW]
[ROW][C]36[/C][C]0.475195813374315[/C][C]0.95039162674863[/C][C]0.524804186625685[/C][/ROW]
[ROW][C]37[/C][C]0.440413487552873[/C][C]0.880826975105745[/C][C]0.559586512447127[/C][/ROW]
[ROW][C]38[/C][C]0.726716810300376[/C][C]0.546566379399249[/C][C]0.273283189699624[/C][/ROW]
[ROW][C]39[/C][C]0.79119097596576[/C][C]0.417618048068481[/C][C]0.208809024034240[/C][/ROW]
[ROW][C]40[/C][C]0.729987685219669[/C][C]0.540024629560663[/C][C]0.270012314780331[/C][/ROW]
[ROW][C]41[/C][C]0.70402412332244[/C][C]0.591951753355121[/C][C]0.295975876677561[/C][/ROW]
[ROW][C]42[/C][C]0.702013328816525[/C][C]0.595973342366951[/C][C]0.297986671183475[/C][/ROW]
[ROW][C]43[/C][C]0.554485838748145[/C][C]0.89102832250371[/C][C]0.445514161251855[/C][/ROW]
[ROW][C]44[/C][C]0.427818457613053[/C][C]0.855636915226106[/C][C]0.572181542386947[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114984&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114984&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
10	0.933384986035624	0.133230027928751	0.0666150139643757
11	0.921937795008702	0.156124409982596	0.0780622049912979
12	0.8652175594991	0.269564881001798	0.134782440500899
13	0.80898062662899	0.38203874674202	0.19101937337101
14	0.89955214543752	0.200895709124959	0.100447854562480
15	0.888602584123432	0.222794831753135	0.111397415876568
16	0.847095521581233	0.305808956837533	0.152904478418767
17	0.789026682397122	0.421946635205755	0.210973317602878
18	0.830802905760954	0.338394188478092	0.169197094239046
19	0.812034140704234	0.375931718591532	0.187965859295766
20	0.860568455967124	0.278863088065753	0.139431544032876
21	0.841697032723562	0.316605934552876	0.158302967276438
22	0.837078481417407	0.325843037165186	0.162921518582593
23	0.79618005485147	0.407639890297058	0.203819945148529
24	0.768775960212639	0.462448079574723	0.231224039787361
25	0.735631566160567	0.528736867678866	0.264368433839433
26	0.693519233698767	0.612961532602466	0.306480766301233
27	0.645035118551283	0.709929762897434	0.354964881448717
28	0.601016217143676	0.797967565712648	0.398983782856324
29	0.607052526231926	0.785894947536148	0.392947473768074
30	0.581889595697985	0.83622080860403	0.418110404302015
31	0.495628456069441	0.991256912138883	0.504371543930559
32	0.531717608047371	0.936564783905259	0.468282391952629
33	0.491987577255809	0.983975154511618	0.508012422744191
34	0.631981623668348	0.736036752663304	0.368018376331652
35	0.575913418973918	0.848173162052164	0.424086581026082
36	0.475195813374315	0.95039162674863	0.524804186625685
37	0.440413487552873	0.880826975105745	0.559586512447127
38	0.726716810300376	0.546566379399249	0.273283189699624
39	0.79119097596576	0.417618048068481	0.208809024034240
40	0.729987685219669	0.540024629560663	0.270012314780331
41	0.70402412332244	0.591951753355121	0.295975876677561
42	0.702013328816525	0.595973342366951	0.297986671183475
43	0.554485838748145	0.89102832250371	0.445514161251855
44	0.427818457613053	0.855636915226106	0.572181542386947

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

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114984&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114984&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114984&T=6

As an alternative you can also use a QR Code:

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

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

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 Quarterly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Quarterly Dummies ; par3 = No Linear Trend ;

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code