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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 06 Mar 2012 10:49:05 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/06/t1331049050qza4dwgyc4nezsv.htm/, Retrieved Wed, 01 May 2024 15:01:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163541, Retrieved Wed, 01 May 2024 15:01:50 +0000

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Estimated Impact

140

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

-     [Multiple Regression] [15th bird enterin...] [2012-03-06 03:20:16] [74be16979710d4c4e7c6647856088456]
-    D    [Multiple Regression] [Full model with p...] [2012-03-06 15:49:05] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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1217.00 1210.00 31.00 48.00 961.00 2304.00 1488.00 19.00 30.00 10.00
1202.00 1209.00 34.40 38.00 1183.36 1444.00 1307.20 18.30 29.95 10.00
1180.00 1207.00 35.60 37.00 1267.36 1369.00 1317.20 18.90 29.94 10.00
1167.00 1206.00 32.80 48.00 1075.84 2304.00 1574.40 20.60 29.83 10.00
1186.00 1204.00 23.30 81.00 542.89 6561.00 1887.30 20.00 29.85 9.00
1168.00 1201.00 20.00 58.00 400.00 3364.00 1160.00 11.76 29.92 10.00
1142.00 1199.00 16.70 93.00 278.89 8649.00 1553.10 15.60 29.95 6.00
1147.00 1198.00 17.80 86.00 316.84 7396.00 1530.80 15.60 29.94 10.00
1183.00 1196.00 21.20 68.00 449.44 4624.00 1441.60 15.80 29.94 10.00
1149.00 1195.00 23.90 68.00 571.21 4624.00 1625.20 17.80 30.00 10.00
1197.00 1193.00 28.80 68.00 829.44 4624.00 1958.40 16.70 30.03 10.00
1210.00 1191.00 25.60 59.00 655.36 3481.00 1510.40 17.20 29.99 10.00
1206.00 1190.00 29.40 43.00 864.36 1849.00 1264.20 15.60 29.89 10.00
1196.00 1188.00 22.80 59.00 519.84 3481.00 1345.20 14.40 29.98 6.00
1190.00 1187.00 16.10 31.00 259.21 961.00 499.10 -0.60 30.26 10.00
1175.00 1185.00 16.10 49.00 259.21 2401.00 788.90 5.60 30.26 10.00
1186.00 1183.00 20.00 52.00 400.00 2704.00 1040.00 10.08 30.23 10.00
1172.00 1182.00 20.60 75.00 424.36 5625.00 1545.00 16.10 30.16 10.00
1152.00 1185.00 18.30 90.00 334.89 8100.00 1647.00 16.70 30.00 10.00
1154.00 1179.00 21.60 86.00 466.56 7396.00 1857.60 18.30 30.60 8.00
1168.00 1177.00 22.80 87.00 519.84 7569.00 1983.60 20.60 30.00 10.00
1180.00 1175.00 22.80 47.00 519.84 2209.00 1071.60 11.10 30.06 10.00
1169.00 1174.00 17.20 70.00 295.84 4900.00 1204.00 11.70 30.01 10.00
1166.00 1170.00 22.20 61.00 492.84 3721.00 1354.20 14.40 29.86 10.00
1177.00 1169.00 20.60 48.00 424.36 2304.00 988.80 9.40 29.82 10.00
1168.00 1167.00 18.30 67.00 334.89 4489.00 1226.10 12.20 29.83 10.00
1160.00 1166.00 16.70 74.00 278.89 5476.00 1235.80 12.20 29.83 10.00
1147.00 1164.00 22.80 55.00 519.84 3025.00 1254.00 13.30 29.71 10.00
1161.00 1162.00 13.90 47.00 193.21 2209.00 653.30 2.80 29.98 10.00
1143.00 1161.00 10.00 65.00 100.00 4225.00 650.00 3.90 30.18 10.00
1161.00 1159.00 16.10 28.00 259.21 784.00 450.80 -2.20 30.88 10.00
1161.00 1158.00 20.60 30.00 424.36 900.00 618.00 5.00 30.13 10.00
1168.00 1156.00 19.40 67.00 376.36 4489.00 1299.80 13.30 30.24 10.00
1172.00 1155.00 25.60 32.00 655.36 1024.00 819.20 7.80 30.24 10.00

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'AstonUniversity' @ aston.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163541&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163541&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163541&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'AstonUniversity' @ aston.wessa.net

Multiple Linear Regression - Estimated Regression Equation
15thbird[t] = + 304.624456116916 + 0.466993831264814Sunset[t] + 5.73065162121162Temp[t] + 1.84042761384214humidity[t] -0.0869866597561731`Temp^2`[t] -0.0181094533450431`Hum^2`[t] + 0.0178458921340469TxH[t] -1.97441632047953Dew[t] + 6.8885131421491pressure[t] -0.867552802961527visibility[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
15thbird[t] =  +  304.624456116916 +  0.466993831264814Sunset[t] +  5.73065162121162Temp[t] +  1.84042761384214humidity[t] -0.0869866597561731`Temp^2`[t] -0.0181094533450431`Hum^2`[t] +  0.0178458921340469TxH[t] -1.97441632047953Dew[t] +  6.8885131421491pressure[t] -0.867552802961527visibility[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163541&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]15thbird[t] =  +  304.624456116916 +  0.466993831264814Sunset[t] +  5.73065162121162Temp[t] +  1.84042761384214humidity[t] -0.0869866597561731`Temp^2`[t] -0.0181094533450431`Hum^2`[t] +  0.0178458921340469TxH[t] -1.97441632047953Dew[t] +  6.8885131421491pressure[t] -0.867552802961527visibility[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163541&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163541&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
15thbird[t] = + 304.624456116916 + 0.466993831264814Sunset[t] + 5.73065162121162Temp[t] + 1.84042761384214humidity[t] -0.0869866597561731`Temp^2`[t] -0.0181094533450431`Hum^2`[t] + 0.0178458921340469TxH[t] -1.97441632047953Dew[t] + 6.8885131421491pressure[t] -0.867552802961527visibility[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)	304.624456116916	642.323159	0.4743	0.639605	0.319803
Sunset	0.466993831264814	0.231019	2.0215	0.05452	0.02726
Temp	5.73065162121162	7.743919	0.74	0.466466	0.233233
humidity	1.84042761384214	2.359548	0.78	0.443021	0.22151
`Temp^2`	-0.0869866597561731	0.092937	-0.936	0.358611	0.179305
`Hum^2`	-0.0181094533450431	0.010173	-1.7801	0.08773	0.043865
TxH	0.0178458921340469	0.050005	0.3569	0.724298	0.362149
Dew	-1.97441632047953	3.094782	-0.638	0.529526	0.264763
pressure	6.8885131421491	15.523502	0.4437	0.6612	0.3306
visibility	-0.867552802961527	2.949533	-0.2941	0.771186	0.385593

\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) & 304.624456116916 & 642.323159 & 0.4743 & 0.639605 & 0.319803 \tabularnewline
Sunset & 0.466993831264814 & 0.231019 & 2.0215 & 0.05452 & 0.02726 \tabularnewline
Temp & 5.73065162121162 & 7.743919 & 0.74 & 0.466466 & 0.233233 \tabularnewline
humidity & 1.84042761384214 & 2.359548 & 0.78 & 0.443021 & 0.22151 \tabularnewline
`Temp^2` & -0.0869866597561731 & 0.092937 & -0.936 & 0.358611 & 0.179305 \tabularnewline
`Hum^2` & -0.0181094533450431 & 0.010173 & -1.7801 & 0.08773 & 0.043865 \tabularnewline
TxH & 0.0178458921340469 & 0.050005 & 0.3569 & 0.724298 & 0.362149 \tabularnewline
Dew & -1.97441632047953 & 3.094782 & -0.638 & 0.529526 & 0.264763 \tabularnewline
pressure & 6.8885131421491 & 15.523502 & 0.4437 & 0.6612 & 0.3306 \tabularnewline
visibility & -0.867552802961527 & 2.949533 & -0.2941 & 0.771186 & 0.385593 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163541&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]304.624456116916[/C][C]642.323159[/C][C]0.4743[/C][C]0.639605[/C][C]0.319803[/C][/ROW]
[ROW][C]Sunset[/C][C]0.466993831264814[/C][C]0.231019[/C][C]2.0215[/C][C]0.05452[/C][C]0.02726[/C][/ROW]
[ROW][C]Temp[/C][C]5.73065162121162[/C][C]7.743919[/C][C]0.74[/C][C]0.466466[/C][C]0.233233[/C][/ROW]
[ROW][C]humidity[/C][C]1.84042761384214[/C][C]2.359548[/C][C]0.78[/C][C]0.443021[/C][C]0.22151[/C][/ROW]
[ROW][C]`Temp^2`[/C][C]-0.0869866597561731[/C][C]0.092937[/C][C]-0.936[/C][C]0.358611[/C][C]0.179305[/C][/ROW]
[ROW][C]`Hum^2`[/C][C]-0.0181094533450431[/C][C]0.010173[/C][C]-1.7801[/C][C]0.08773[/C][C]0.043865[/C][/ROW]
[ROW][C]TxH[/C][C]0.0178458921340469[/C][C]0.050005[/C][C]0.3569[/C][C]0.724298[/C][C]0.362149[/C][/ROW]
[ROW][C]Dew[/C][C]-1.97441632047953[/C][C]3.094782[/C][C]-0.638[/C][C]0.529526[/C][C]0.264763[/C][/ROW]
[ROW][C]pressure[/C][C]6.8885131421491[/C][C]15.523502[/C][C]0.4437[/C][C]0.6612[/C][C]0.3306[/C][/ROW]
[ROW][C]visibility[/C][C]-0.867552802961527[/C][C]2.949533[/C][C]-0.2941[/C][C]0.771186[/C][C]0.385593[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163541&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163541&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)	304.624456116916	642.323159	0.4743	0.639605	0.319803
Sunset	0.466993831264814	0.231019	2.0215	0.05452	0.02726
Temp	5.73065162121162	7.743919	0.74	0.466466	0.233233
humidity	1.84042761384214	2.359548	0.78	0.443021	0.22151
`Temp^2`	-0.0869866597561731	0.092937	-0.936	0.358611	0.179305
`Hum^2`	-0.0181094533450431	0.010173	-1.7801	0.08773	0.043865
TxH	0.0178458921340469	0.050005	0.3569	0.724298	0.362149
Dew	-1.97441632047953	3.094782	-0.638	0.529526	0.264763
pressure	6.8885131421491	15.523502	0.4437	0.6612	0.3306
visibility	-0.867552802961527	2.949533	-0.2941	0.771186	0.385593

Multiple Linear Regression - Regression Statistics
Multiple R	0.758369160691649
R-squared	0.575123783888155
Adjusted R-squared	0.415795202846214
F-TEST (value)	3.6096711596067
F-TEST (DF numerator)	9
F-TEST (DF denominator)	24
p-value	0.0057067064552565
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	14.9232659702473
Sum Squared Residuals	5344.89281324979

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.758369160691649 \tabularnewline
R-squared & 0.575123783888155 \tabularnewline
Adjusted R-squared & 0.415795202846214 \tabularnewline
F-TEST (value) & 3.6096711596067 \tabularnewline
F-TEST (DF numerator) & 9 \tabularnewline
F-TEST (DF denominator) & 24 \tabularnewline
p-value & 0.0057067064552565 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 14.9232659702473 \tabularnewline
Sum Squared Residuals & 5344.89281324979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163541&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.758369160691649[/C][/ROW]
[ROW][C]R-squared[/C][C]0.575123783888155[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.415795202846214[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]3.6096711596067[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]9[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]24[/C][/ROW]
[ROW][C]p-value[/C][C]0.0057067064552565[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]14.9232659702473[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]5344.89281324979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163541&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163541&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	0.758369160691649
R-squared	0.575123783888155
Adjusted R-squared	0.415795202846214
F-TEST (value)	3.6096711596067
F-TEST (DF numerator)	9
F-TEST (DF denominator)	24
p-value	0.0057067064552565
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	14.9232659702473
Sum Squared Residuals	5344.89281324979

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	1217	1197.38000077787	19.619999222128
2	1202	1192.03585100305	9.96414899694837
3	1180	1189.11447125112	-9.1144712511248
4	1167	1193.04942209804	-26.0494220980432
5	1186	1175.44990522483	10.5500947751667
6	1168	1186.03790066798	-18.0379006679816
7	1142	1148.54455070781	-6.54455070780886
8	1147	1156.95122192872	-9.95122192871726
9	1183	1179.05198947549	3.94801052451337
10	1149	1183.20637340636	-34.2063734063649
11	1197	1196.21477814479	0.785221855208014
12	1210	1186.96289131157	23.037108688434
13	1206	1188.27650394465	17.7234960553487
14	1196	1187.28606780576	8.7139321942416
15	1190	1178.17429842709	11.8257015729127
16	1175	1177.22075335033	-2.22075335032786
17	1186	1181.85263666628	4.1473633337233
18	1172	1168.78115403203	3.2188459679667
19	1152	1147.10331952672	4.8966804732825
20	1154	1163.61381036045	-9.61381036044894
21	1168	1155.46865897729	12.5313410227115
22	1180	1180.87904889734	-0.879048897337968
23	1169	1162.23643460868	6.76356539131823
24	1166	1172.98879434886	-6.98879434885779
25	1177	1174.12079288467	2.87920711533368
26	1168	1161.9633216833	6.0366783166956
27	1160	1152.38060620348	7.61939379651563
28	1147	1172.18861895505	-25.18861895505
29	1161	1160.58942006721	0.410579932792859
30	1143	1141.6469038065	1.35309619349847
31	1161	1169.35054922304	-8.3505492230439
32	1161	1165.48745026891	-4.48745026890688
33	1168	1161.49044422867	6.50955577133139
34	1172	1172.90105573606	-0.901055736057454

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1217 & 1197.38000077787 & 19.619999222128 \tabularnewline
2 & 1202 & 1192.03585100305 & 9.96414899694837 \tabularnewline
3 & 1180 & 1189.11447125112 & -9.1144712511248 \tabularnewline
4 & 1167 & 1193.04942209804 & -26.0494220980432 \tabularnewline
5 & 1186 & 1175.44990522483 & 10.5500947751667 \tabularnewline
6 & 1168 & 1186.03790066798 & -18.0379006679816 \tabularnewline
7 & 1142 & 1148.54455070781 & -6.54455070780886 \tabularnewline
8 & 1147 & 1156.95122192872 & -9.95122192871726 \tabularnewline
9 & 1183 & 1179.05198947549 & 3.94801052451337 \tabularnewline
10 & 1149 & 1183.20637340636 & -34.2063734063649 \tabularnewline
11 & 1197 & 1196.21477814479 & 0.785221855208014 \tabularnewline
12 & 1210 & 1186.96289131157 & 23.037108688434 \tabularnewline
13 & 1206 & 1188.27650394465 & 17.7234960553487 \tabularnewline
14 & 1196 & 1187.28606780576 & 8.7139321942416 \tabularnewline
15 & 1190 & 1178.17429842709 & 11.8257015729127 \tabularnewline
16 & 1175 & 1177.22075335033 & -2.22075335032786 \tabularnewline
17 & 1186 & 1181.85263666628 & 4.1473633337233 \tabularnewline
18 & 1172 & 1168.78115403203 & 3.2188459679667 \tabularnewline
19 & 1152 & 1147.10331952672 & 4.8966804732825 \tabularnewline
20 & 1154 & 1163.61381036045 & -9.61381036044894 \tabularnewline
21 & 1168 & 1155.46865897729 & 12.5313410227115 \tabularnewline
22 & 1180 & 1180.87904889734 & -0.879048897337968 \tabularnewline
23 & 1169 & 1162.23643460868 & 6.76356539131823 \tabularnewline
24 & 1166 & 1172.98879434886 & -6.98879434885779 \tabularnewline
25 & 1177 & 1174.12079288467 & 2.87920711533368 \tabularnewline
26 & 1168 & 1161.9633216833 & 6.0366783166956 \tabularnewline
27 & 1160 & 1152.38060620348 & 7.61939379651563 \tabularnewline
28 & 1147 & 1172.18861895505 & -25.18861895505 \tabularnewline
29 & 1161 & 1160.58942006721 & 0.410579932792859 \tabularnewline
30 & 1143 & 1141.6469038065 & 1.35309619349847 \tabularnewline
31 & 1161 & 1169.35054922304 & -8.3505492230439 \tabularnewline
32 & 1161 & 1165.48745026891 & -4.48745026890688 \tabularnewline
33 & 1168 & 1161.49044422867 & 6.50955577133139 \tabularnewline
34 & 1172 & 1172.90105573606 & -0.901055736057454 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163541&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]1217[/C][C]1197.38000077787[/C][C]19.619999222128[/C][/ROW]
[ROW][C]2[/C][C]1202[/C][C]1192.03585100305[/C][C]9.96414899694837[/C][/ROW]
[ROW][C]3[/C][C]1180[/C][C]1189.11447125112[/C][C]-9.1144712511248[/C][/ROW]
[ROW][C]4[/C][C]1167[/C][C]1193.04942209804[/C][C]-26.0494220980432[/C][/ROW]
[ROW][C]5[/C][C]1186[/C][C]1175.44990522483[/C][C]10.5500947751667[/C][/ROW]
[ROW][C]6[/C][C]1168[/C][C]1186.03790066798[/C][C]-18.0379006679816[/C][/ROW]
[ROW][C]7[/C][C]1142[/C][C]1148.54455070781[/C][C]-6.54455070780886[/C][/ROW]
[ROW][C]8[/C][C]1147[/C][C]1156.95122192872[/C][C]-9.95122192871726[/C][/ROW]
[ROW][C]9[/C][C]1183[/C][C]1179.05198947549[/C][C]3.94801052451337[/C][/ROW]
[ROW][C]10[/C][C]1149[/C][C]1183.20637340636[/C][C]-34.2063734063649[/C][/ROW]
[ROW][C]11[/C][C]1197[/C][C]1196.21477814479[/C][C]0.785221855208014[/C][/ROW]
[ROW][C]12[/C][C]1210[/C][C]1186.96289131157[/C][C]23.037108688434[/C][/ROW]
[ROW][C]13[/C][C]1206[/C][C]1188.27650394465[/C][C]17.7234960553487[/C][/ROW]
[ROW][C]14[/C][C]1196[/C][C]1187.28606780576[/C][C]8.7139321942416[/C][/ROW]
[ROW][C]15[/C][C]1190[/C][C]1178.17429842709[/C][C]11.8257015729127[/C][/ROW]
[ROW][C]16[/C][C]1175[/C][C]1177.22075335033[/C][C]-2.22075335032786[/C][/ROW]
[ROW][C]17[/C][C]1186[/C][C]1181.85263666628[/C][C]4.1473633337233[/C][/ROW]
[ROW][C]18[/C][C]1172[/C][C]1168.78115403203[/C][C]3.2188459679667[/C][/ROW]
[ROW][C]19[/C][C]1152[/C][C]1147.10331952672[/C][C]4.8966804732825[/C][/ROW]
[ROW][C]20[/C][C]1154[/C][C]1163.61381036045[/C][C]-9.61381036044894[/C][/ROW]
[ROW][C]21[/C][C]1168[/C][C]1155.46865897729[/C][C]12.5313410227115[/C][/ROW]
[ROW][C]22[/C][C]1180[/C][C]1180.87904889734[/C][C]-0.879048897337968[/C][/ROW]
[ROW][C]23[/C][C]1169[/C][C]1162.23643460868[/C][C]6.76356539131823[/C][/ROW]
[ROW][C]24[/C][C]1166[/C][C]1172.98879434886[/C][C]-6.98879434885779[/C][/ROW]
[ROW][C]25[/C][C]1177[/C][C]1174.12079288467[/C][C]2.87920711533368[/C][/ROW]
[ROW][C]26[/C][C]1168[/C][C]1161.9633216833[/C][C]6.0366783166956[/C][/ROW]
[ROW][C]27[/C][C]1160[/C][C]1152.38060620348[/C][C]7.61939379651563[/C][/ROW]
[ROW][C]28[/C][C]1147[/C][C]1172.18861895505[/C][C]-25.18861895505[/C][/ROW]
[ROW][C]29[/C][C]1161[/C][C]1160.58942006721[/C][C]0.410579932792859[/C][/ROW]
[ROW][C]30[/C][C]1143[/C][C]1141.6469038065[/C][C]1.35309619349847[/C][/ROW]
[ROW][C]31[/C][C]1161[/C][C]1169.35054922304[/C][C]-8.3505492230439[/C][/ROW]
[ROW][C]32[/C][C]1161[/C][C]1165.48745026891[/C][C]-4.48745026890688[/C][/ROW]
[ROW][C]33[/C][C]1168[/C][C]1161.49044422867[/C][C]6.50955577133139[/C][/ROW]
[ROW][C]34[/C][C]1172[/C][C]1172.90105573606[/C][C]-0.901055736057454[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163541&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163541&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	1217	1197.38000077787	19.619999222128
2	1202	1192.03585100305	9.96414899694837
3	1180	1189.11447125112	-9.1144712511248
4	1167	1193.04942209804	-26.0494220980432
5	1186	1175.44990522483	10.5500947751667
6	1168	1186.03790066798	-18.0379006679816
7	1142	1148.54455070781	-6.54455070780886
8	1147	1156.95122192872	-9.95122192871726
9	1183	1179.05198947549	3.94801052451337
10	1149	1183.20637340636	-34.2063734063649
11	1197	1196.21477814479	0.785221855208014
12	1210	1186.96289131157	23.037108688434
13	1206	1188.27650394465	17.7234960553487
14	1196	1187.28606780576	8.7139321942416
15	1190	1178.17429842709	11.8257015729127
16	1175	1177.22075335033	-2.22075335032786
17	1186	1181.85263666628	4.1473633337233
18	1172	1168.78115403203	3.2188459679667
19	1152	1147.10331952672	4.8966804732825
20	1154	1163.61381036045	-9.61381036044894
21	1168	1155.46865897729	12.5313410227115
22	1180	1180.87904889734	-0.879048897337968
23	1169	1162.23643460868	6.76356539131823
24	1166	1172.98879434886	-6.98879434885779
25	1177	1174.12079288467	2.87920711533368
26	1168	1161.9633216833	6.0366783166956
27	1160	1152.38060620348	7.61939379651563
28	1147	1172.18861895505	-25.18861895505
29	1161	1160.58942006721	0.410579932792859
30	1143	1141.6469038065	1.35309619349847
31	1161	1169.35054922304	-8.3505492230439
32	1161	1165.48745026891	-4.48745026890688
33	1168	1161.49044422867	6.50955577133139
34	1172	1172.90105573606	-0.901055736057454

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
13	0.990931322302527	0.0181373553949462	0.00906867769747309
14	0.987378179813676	0.0252436403726476	0.0126218201863238
15	0.98356353888317	0.0328729222336602	0.0164364611168301
16	0.971326068506158	0.0573478629876838	0.0286739314938419
17	0.941233273825312	0.117533452349376	0.0587667261746882
18	0.875830630931036	0.248338738137927	0.124169369068964
19	0.864156622328427	0.271686755343146	0.135843377671573
20	0.794162553707591	0.411674892584817	0.205837446292409
21	0.846921555690243	0.306156888619515	0.153078444309757

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
13 & 0.990931322302527 & 0.0181373553949462 & 0.00906867769747309 \tabularnewline
14 & 0.987378179813676 & 0.0252436403726476 & 0.0126218201863238 \tabularnewline
15 & 0.98356353888317 & 0.0328729222336602 & 0.0164364611168301 \tabularnewline
16 & 0.971326068506158 & 0.0573478629876838 & 0.0286739314938419 \tabularnewline
17 & 0.941233273825312 & 0.117533452349376 & 0.0587667261746882 \tabularnewline
18 & 0.875830630931036 & 0.248338738137927 & 0.124169369068964 \tabularnewline
19 & 0.864156622328427 & 0.271686755343146 & 0.135843377671573 \tabularnewline
20 & 0.794162553707591 & 0.411674892584817 & 0.205837446292409 \tabularnewline
21 & 0.846921555690243 & 0.306156888619515 & 0.153078444309757 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163541&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]13[/C][C]0.990931322302527[/C][C]0.0181373553949462[/C][C]0.00906867769747309[/C][/ROW]
[ROW][C]14[/C][C]0.987378179813676[/C][C]0.0252436403726476[/C][C]0.0126218201863238[/C][/ROW]
[ROW][C]15[/C][C]0.98356353888317[/C][C]0.0328729222336602[/C][C]0.0164364611168301[/C][/ROW]
[ROW][C]16[/C][C]0.971326068506158[/C][C]0.0573478629876838[/C][C]0.0286739314938419[/C][/ROW]
[ROW][C]17[/C][C]0.941233273825312[/C][C]0.117533452349376[/C][C]0.0587667261746882[/C][/ROW]
[ROW][C]18[/C][C]0.875830630931036[/C][C]0.248338738137927[/C][C]0.124169369068964[/C][/ROW]
[ROW][C]19[/C][C]0.864156622328427[/C][C]0.271686755343146[/C][C]0.135843377671573[/C][/ROW]
[ROW][C]20[/C][C]0.794162553707591[/C][C]0.411674892584817[/C][C]0.205837446292409[/C][/ROW]
[ROW][C]21[/C][C]0.846921555690243[/C][C]0.306156888619515[/C][C]0.153078444309757[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163541&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163541&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
13	0.990931322302527	0.0181373553949462	0.00906867769747309
14	0.987378179813676	0.0252436403726476	0.0126218201863238
15	0.98356353888317	0.0328729222336602	0.0164364611168301
16	0.971326068506158	0.0573478629876838	0.0286739314938419
17	0.941233273825312	0.117533452349376	0.0587667261746882
18	0.875830630931036	0.248338738137927	0.124169369068964
19	0.864156622328427	0.271686755343146	0.135843377671573
20	0.794162553707591	0.411674892584817	0.205837446292409
21	0.846921555690243	0.306156888619515	0.153078444309757

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	3	0.333333333333333	NOK
10% type I error level	4	0.444444444444444	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 & 3 & 0.333333333333333 & NOK \tabularnewline
10% type I error level & 4 & 0.444444444444444 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163541&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]3[/C][C]0.333333333333333[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]4[/C][C]0.444444444444444[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163541&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163541&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	3	0.333333333333333	NOK
10% type I error level	4	0.444444444444444	NOK

Figure 1

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Figure 3

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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 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code