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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 06 Mar 2012 10:32:03 -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/t13310480003knk1u2noozte3v.htm/, Retrieved Wed, 01 May 2024 14:32:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163539, Retrieved Wed, 01 May 2024 14:32:59 +0000

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Estimated Impact

132

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] [Model without dew...] [2012-03-06 15:32:03] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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1217.00	1210.00	31.00	19.00	48.00	961.00	2304.00
1202.00	1209.00	34.40	18.30	38.00	1183.36	1444.00
1180.00	1207.00	35.60	18.90	37.00	1267.36	1369.00
1167.00	1206.00	32.80	20.60	48.00	1075.84	2304.00
1186.00	1204.00	23.30	20.00	81.00	542.89	6561.00
1168.00	1201.00	20.00	11.76	58.00	400.00	3364.00
1142.00	1199.00	16.70	15.60	93.00	278.89	8649.00
1147.00	1198.00	17.80	15.60	86.00	316.84	7396.00
1183.00	1196.00	21.20	15.80	68.00	449.44	4624.00
1149.00	1195.00	23.90	17.80	68.00	571.21	4624.00
1197.00	1193.00	28.80	16.70	68.00	829.44	4624.00
1210.00	1191.00	25.60	17.20	59.00	655.36	3481.00
1206.00	1190.00	29.40	15.60	43.00	864.36	1849.00
1196.00	1188.00	22.80	14.40	59.00	519.84	3481.00
1190.00	1187.00	16.10	-0.60	31.00	259.21	961.00
1175.00	1185.00	16.10	5.60	49.00	259.21	2401.00
1186.00	1183.00	20.00	10.08	52.00	400.00	2704.00
1172.00	1182.00	20.60	16.10	75.00	424.36	5625.00
1152.00	1185.00	18.30	16.70	90.00	334.89	8100.00
1154.00	1179.00	21.60	18.30	86.00	466.56	7396.00
1168.00	1177.00	22.80	20.60	87.00	519.84	7569.00
1180.00	1175.00	22.80	11.10	47.00	519.84	2209.00
1169.00	1174.00	17.20	11.70	70.00	295.84	4900.00
1166.00	1170.00	22.20	14.40	61.00	492.84	3721.00
1177.00	1169.00	20.60	9.40	48.00	424.36	2304.00
1168.00	1167.00	18.30	12.20	67.00	334.89	4489.00
1160.00	1166.00	16.70	12.20	74.00	278.89	5476.00
1147.00	1164.00	22.80	13.30	55.00	519.84	3025.00
1161.00	1162.00	13.90	2.80	47.00	193.21	2209.00
1143.00	1161.00	10.00	3.90	65.00	100.00	4225.00
1161.00	1159.00	16.10	-2.20	28.00	259.21	784.00
1161.00	1158.00	20.60	5.00	30.00	424.36	900.00
1168.00	1156.00	19.40	13.30	67.00	376.36	4489.00
1172.00	1155.00	25.60	7.80	32.00	655.36	1024.00

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	'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163539&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163539&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163539&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	'Gertrude Mary Cox' @ cox.wessa.net

Multiple Linear Regression - Estimated Regression Equation
15thbird[t] = + 421.479802505081 + 0.496443514709184Sunset[t] + 8.64553618385391Temp[t] -2.94716695375738Dewpoint[t] + 2.38431188861549humidity[t] -0.115775601570986`Temp^2`[t] -0.0179091849904993`Hum^2`[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
15thbird[t] =  +  421.479802505081 +  0.496443514709184Sunset[t] +  8.64553618385391Temp[t] -2.94716695375738Dewpoint[t] +  2.38431188861549humidity[t] -0.115775601570986`Temp^2`[t] -0.0179091849904993`Hum^2`[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163539&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]15thbird[t] =  +  421.479802505081 +  0.496443514709184Sunset[t] +  8.64553618385391Temp[t] -2.94716695375738Dewpoint[t] +  2.38431188861549humidity[t] -0.115775601570986`Temp^2`[t] -0.0179091849904993`Hum^2`[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163539&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163539&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] = + 421.479802505081 + 0.496443514709184Sunset[t] + 8.64553618385391Temp[t] -2.94716695375738Dewpoint[t] + 2.38431188861549humidity[t] -0.115775601570986`Temp^2`[t] -0.0179091849904993`Hum^2`[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)	421.479802505081	263.78974	1.5978	0.121729	0.060865
Sunset	0.496443514709184	0.205761	2.4127	0.022897	0.011448
Temp	8.64553618385391	3.909339	2.2115	0.035652	0.017826
Dewpoint	-2.94716695375738	2.578644	-1.1429	0.263108	0.131554
humidity	2.38431188861549	1.427296	1.6705	0.106372	0.053186
`Temp^2`	-0.115775601570986	0.06168	-1.877	0.071357	0.035679
`Hum^2`	-0.0179091849904993	0.008301	-2.1574	0.040039	0.02002

\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) & 421.479802505081 & 263.78974 & 1.5978 & 0.121729 & 0.060865 \tabularnewline
Sunset & 0.496443514709184 & 0.205761 & 2.4127 & 0.022897 & 0.011448 \tabularnewline
Temp & 8.64553618385391 & 3.909339 & 2.2115 & 0.035652 & 0.017826 \tabularnewline
Dewpoint & -2.94716695375738 & 2.578644 & -1.1429 & 0.263108 & 0.131554 \tabularnewline
humidity & 2.38431188861549 & 1.427296 & 1.6705 & 0.106372 & 0.053186 \tabularnewline
`Temp^2` & -0.115775601570986 & 0.06168 & -1.877 & 0.071357 & 0.035679 \tabularnewline
`Hum^2` & -0.0179091849904993 & 0.008301 & -2.1574 & 0.040039 & 0.02002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163539&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]421.479802505081[/C][C]263.78974[/C][C]1.5978[/C][C]0.121729[/C][C]0.060865[/C][/ROW]
[ROW][C]Sunset[/C][C]0.496443514709184[/C][C]0.205761[/C][C]2.4127[/C][C]0.022897[/C][C]0.011448[/C][/ROW]
[ROW][C]Temp[/C][C]8.64553618385391[/C][C]3.909339[/C][C]2.2115[/C][C]0.035652[/C][C]0.017826[/C][/ROW]
[ROW][C]Dewpoint[/C][C]-2.94716695375738[/C][C]2.578644[/C][C]-1.1429[/C][C]0.263108[/C][C]0.131554[/C][/ROW]
[ROW][C]humidity[/C][C]2.38431188861549[/C][C]1.427296[/C][C]1.6705[/C][C]0.106372[/C][C]0.053186[/C][/ROW]
[ROW][C]`Temp^2`[/C][C]-0.115775601570986[/C][C]0.06168[/C][C]-1.877[/C][C]0.071357[/C][C]0.035679[/C][/ROW]
[ROW][C]`Hum^2`[/C][C]-0.0179091849904993[/C][C]0.008301[/C][C]-2.1574[/C][C]0.040039[/C][C]0.02002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163539&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163539&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)	421.479802505081	263.78974	1.5978	0.121729	0.060865
Sunset	0.496443514709184	0.205761	2.4127	0.022897	0.011448
Temp	8.64553618385391	3.909339	2.2115	0.035652	0.017826
Dewpoint	-2.94716695375738	2.578644	-1.1429	0.263108	0.131554
humidity	2.38431188861549	1.427296	1.6705	0.106372	0.053186
`Temp^2`	-0.115775601570986	0.06168	-1.877	0.071357	0.035679
`Hum^2`	-0.0179091849904993	0.008301	-2.1574	0.040039	0.02002

Multiple Linear Regression - Regression Statistics
Multiple R	0.751992865484892
R-squared	0.565493269740178
Adjusted R-squared	0.468936218571329
F-TEST (value)	5.85657145588778
F-TEST (DF numerator)	6
F-TEST (DF denominator)	27
p-value	0.000517944876300303
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	14.2283539927091
Sum Squared Residuals	5466.04354822972

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.751992865484892 \tabularnewline
R-squared & 0.565493269740178 \tabularnewline
Adjusted R-squared & 0.468936218571329 \tabularnewline
F-TEST (value) & 5.85657145588778 \tabularnewline
F-TEST (DF numerator) & 6 \tabularnewline
F-TEST (DF denominator) & 27 \tabularnewline
p-value & 0.000517944876300303 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 14.2283539927091 \tabularnewline
Sum Squared Residuals & 5466.04354822972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163539&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.751992865484892[/C][/ROW]
[ROW][C]R-squared[/C][C]0.565493269740178[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.468936218571329[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]5.85657145588778[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]6[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]27[/C][/ROW]
[ROW][C]p-value[/C][C]0.000517944876300303[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]14.2283539927091[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]5466.04354822972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163539&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163539&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	0.751992865484892
R-squared	0.565493269740178
Adjusted R-squared	0.468936218571329
F-TEST (value)	5.85657145588778
F-TEST (DF numerator)	6
F-TEST (DF denominator)	27
p-value	0.000517944876300303
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	14.2283539927091
Sum Squared Residuals	5466.04354822972

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	1217	1196.11576020699	20.8842397930099
2	1202	1192.89207402536	9.1079259746357
3	1180	1189.73925669803	-9.73925669802537
4	1167	1191.68081406867	-24.6808140686664
5	1186	1174.4691321419	11.5308678580973
6	1168	1187.69385457497	-19.6938545749663
7	1142	1149.67603356942	-7.67603356941692
8	1147	1160.04602135012	-13.0460213501154
9	1183	1179.23332598532	3.76667401467858
10	1149	1182.0875012562	-33.0875012562041
11	1197	1196.80289158313	0.197108416872642
12	1210	1185.83631345658	24.1636865434237
13	1206	1189.79007352483	16.2099264751651
14	1196	1184.08145859308	11.9185414069215
15	1190	1178.41243528518	11.5875647148206
16	1175	1176.27550075123	-1.27550075122509
17	1186	1181.22330255455	4.77669744545002
18	1172	1167.87838611517	4.12161388482779
19	1152	1149.51257181448	2.48742818551605
20	1154	1158.17535822693	-4.1753582269328
21	1168	1153.89612945805	14.1038705419459
22	1180	1181.52208449379	-1.52208449378772
23	1169	1163.42162955787	5.57837044213443
24	1166	1173.55451423993	-7.55451423992856
25	1177	1176.27062137496	0.729378625042664
26	1168	1163.66973340416	4.33026659583634
27	1160	1154.83768331795	5.162316682051
28	1147	1174.0380386904	-27.0380386903969
29	1161	1160.40031722359	0.599682776414139
30	1143	1140.54853981938	2.45146018062296
31	1161	1165.24447407681	-4.244474076806
32	1161	1166.00415904127	-5.00415904127105
33	1168	1159.67584669832	8.32415330167998
34	1172	1175.2941628214	-3.29416282140373

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1217 & 1196.11576020699 & 20.8842397930099 \tabularnewline
2 & 1202 & 1192.89207402536 & 9.1079259746357 \tabularnewline
3 & 1180 & 1189.73925669803 & -9.73925669802537 \tabularnewline
4 & 1167 & 1191.68081406867 & -24.6808140686664 \tabularnewline
5 & 1186 & 1174.4691321419 & 11.5308678580973 \tabularnewline
6 & 1168 & 1187.69385457497 & -19.6938545749663 \tabularnewline
7 & 1142 & 1149.67603356942 & -7.67603356941692 \tabularnewline
8 & 1147 & 1160.04602135012 & -13.0460213501154 \tabularnewline
9 & 1183 & 1179.23332598532 & 3.76667401467858 \tabularnewline
10 & 1149 & 1182.0875012562 & -33.0875012562041 \tabularnewline
11 & 1197 & 1196.80289158313 & 0.197108416872642 \tabularnewline
12 & 1210 & 1185.83631345658 & 24.1636865434237 \tabularnewline
13 & 1206 & 1189.79007352483 & 16.2099264751651 \tabularnewline
14 & 1196 & 1184.08145859308 & 11.9185414069215 \tabularnewline
15 & 1190 & 1178.41243528518 & 11.5875647148206 \tabularnewline
16 & 1175 & 1176.27550075123 & -1.27550075122509 \tabularnewline
17 & 1186 & 1181.22330255455 & 4.77669744545002 \tabularnewline
18 & 1172 & 1167.87838611517 & 4.12161388482779 \tabularnewline
19 & 1152 & 1149.51257181448 & 2.48742818551605 \tabularnewline
20 & 1154 & 1158.17535822693 & -4.1753582269328 \tabularnewline
21 & 1168 & 1153.89612945805 & 14.1038705419459 \tabularnewline
22 & 1180 & 1181.52208449379 & -1.52208449378772 \tabularnewline
23 & 1169 & 1163.42162955787 & 5.57837044213443 \tabularnewline
24 & 1166 & 1173.55451423993 & -7.55451423992856 \tabularnewline
25 & 1177 & 1176.27062137496 & 0.729378625042664 \tabularnewline
26 & 1168 & 1163.66973340416 & 4.33026659583634 \tabularnewline
27 & 1160 & 1154.83768331795 & 5.162316682051 \tabularnewline
28 & 1147 & 1174.0380386904 & -27.0380386903969 \tabularnewline
29 & 1161 & 1160.40031722359 & 0.599682776414139 \tabularnewline
30 & 1143 & 1140.54853981938 & 2.45146018062296 \tabularnewline
31 & 1161 & 1165.24447407681 & -4.244474076806 \tabularnewline
32 & 1161 & 1166.00415904127 & -5.00415904127105 \tabularnewline
33 & 1168 & 1159.67584669832 & 8.32415330167998 \tabularnewline
34 & 1172 & 1175.2941628214 & -3.29416282140373 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163539&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]1196.11576020699[/C][C]20.8842397930099[/C][/ROW]
[ROW][C]2[/C][C]1202[/C][C]1192.89207402536[/C][C]9.1079259746357[/C][/ROW]
[ROW][C]3[/C][C]1180[/C][C]1189.73925669803[/C][C]-9.73925669802537[/C][/ROW]
[ROW][C]4[/C][C]1167[/C][C]1191.68081406867[/C][C]-24.6808140686664[/C][/ROW]
[ROW][C]5[/C][C]1186[/C][C]1174.4691321419[/C][C]11.5308678580973[/C][/ROW]
[ROW][C]6[/C][C]1168[/C][C]1187.69385457497[/C][C]-19.6938545749663[/C][/ROW]
[ROW][C]7[/C][C]1142[/C][C]1149.67603356942[/C][C]-7.67603356941692[/C][/ROW]
[ROW][C]8[/C][C]1147[/C][C]1160.04602135012[/C][C]-13.0460213501154[/C][/ROW]
[ROW][C]9[/C][C]1183[/C][C]1179.23332598532[/C][C]3.76667401467858[/C][/ROW]
[ROW][C]10[/C][C]1149[/C][C]1182.0875012562[/C][C]-33.0875012562041[/C][/ROW]
[ROW][C]11[/C][C]1197[/C][C]1196.80289158313[/C][C]0.197108416872642[/C][/ROW]
[ROW][C]12[/C][C]1210[/C][C]1185.83631345658[/C][C]24.1636865434237[/C][/ROW]
[ROW][C]13[/C][C]1206[/C][C]1189.79007352483[/C][C]16.2099264751651[/C][/ROW]
[ROW][C]14[/C][C]1196[/C][C]1184.08145859308[/C][C]11.9185414069215[/C][/ROW]
[ROW][C]15[/C][C]1190[/C][C]1178.41243528518[/C][C]11.5875647148206[/C][/ROW]
[ROW][C]16[/C][C]1175[/C][C]1176.27550075123[/C][C]-1.27550075122509[/C][/ROW]
[ROW][C]17[/C][C]1186[/C][C]1181.22330255455[/C][C]4.77669744545002[/C][/ROW]
[ROW][C]18[/C][C]1172[/C][C]1167.87838611517[/C][C]4.12161388482779[/C][/ROW]
[ROW][C]19[/C][C]1152[/C][C]1149.51257181448[/C][C]2.48742818551605[/C][/ROW]
[ROW][C]20[/C][C]1154[/C][C]1158.17535822693[/C][C]-4.1753582269328[/C][/ROW]
[ROW][C]21[/C][C]1168[/C][C]1153.89612945805[/C][C]14.1038705419459[/C][/ROW]
[ROW][C]22[/C][C]1180[/C][C]1181.52208449379[/C][C]-1.52208449378772[/C][/ROW]
[ROW][C]23[/C][C]1169[/C][C]1163.42162955787[/C][C]5.57837044213443[/C][/ROW]
[ROW][C]24[/C][C]1166[/C][C]1173.55451423993[/C][C]-7.55451423992856[/C][/ROW]
[ROW][C]25[/C][C]1177[/C][C]1176.27062137496[/C][C]0.729378625042664[/C][/ROW]
[ROW][C]26[/C][C]1168[/C][C]1163.66973340416[/C][C]4.33026659583634[/C][/ROW]
[ROW][C]27[/C][C]1160[/C][C]1154.83768331795[/C][C]5.162316682051[/C][/ROW]
[ROW][C]28[/C][C]1147[/C][C]1174.0380386904[/C][C]-27.0380386903969[/C][/ROW]
[ROW][C]29[/C][C]1161[/C][C]1160.40031722359[/C][C]0.599682776414139[/C][/ROW]
[ROW][C]30[/C][C]1143[/C][C]1140.54853981938[/C][C]2.45146018062296[/C][/ROW]
[ROW][C]31[/C][C]1161[/C][C]1165.24447407681[/C][C]-4.244474076806[/C][/ROW]
[ROW][C]32[/C][C]1161[/C][C]1166.00415904127[/C][C]-5.00415904127105[/C][/ROW]
[ROW][C]33[/C][C]1168[/C][C]1159.67584669832[/C][C]8.32415330167998[/C][/ROW]
[ROW][C]34[/C][C]1172[/C][C]1175.2941628214[/C][C]-3.29416282140373[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163539&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163539&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	1196.11576020699	20.8842397930099
2	1202	1192.89207402536	9.1079259746357
3	1180	1189.73925669803	-9.73925669802537
4	1167	1191.68081406867	-24.6808140686664
5	1186	1174.4691321419	11.5308678580973
6	1168	1187.69385457497	-19.6938545749663
7	1142	1149.67603356942	-7.67603356941692
8	1147	1160.04602135012	-13.0460213501154
9	1183	1179.23332598532	3.76667401467858
10	1149	1182.0875012562	-33.0875012562041
11	1197	1196.80289158313	0.197108416872642
12	1210	1185.83631345658	24.1636865434237
13	1206	1189.79007352483	16.2099264751651
14	1196	1184.08145859308	11.9185414069215
15	1190	1178.41243528518	11.5875647148206
16	1175	1176.27550075123	-1.27550075122509
17	1186	1181.22330255455	4.77669744545002
18	1172	1167.87838611517	4.12161388482779
19	1152	1149.51257181448	2.48742818551605
20	1154	1158.17535822693	-4.1753582269328
21	1168	1153.89612945805	14.1038705419459
22	1180	1181.52208449379	-1.52208449378772
23	1169	1163.42162955787	5.57837044213443
24	1166	1173.55451423993	-7.55451423992856
25	1177	1176.27062137496	0.729378625042664
26	1168	1163.66973340416	4.33026659583634
27	1160	1154.83768331795	5.162316682051
28	1147	1174.0380386904	-27.0380386903969
29	1161	1160.40031722359	0.599682776414139
30	1143	1140.54853981938	2.45146018062296
31	1161	1165.24447407681	-4.244474076806
32	1161	1166.00415904127	-5.00415904127105
33	1168	1159.67584669832	8.32415330167998
34	1172	1175.2941628214	-3.29416282140373

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
10	0.881281126974023	0.237437746051955	0.118718873025977
11	0.975815177296495	0.0483696454070097	0.0241848227035049
12	0.991096834454874	0.0178063310902511	0.00890316554512557
13	0.990774888013364	0.0184502239732729	0.00922511198663643
14	0.989336109333945	0.0213277813321103	0.0106638906660551
15	0.983281857734567	0.0334362845308665	0.0167181422654332
16	0.979290529164562	0.0414189416708749	0.0207094708354374
17	0.963393475786014	0.0732130484279712	0.0366065242139856
18	0.931481728002504	0.137036543994993	0.0685182719974963
19	0.887349384874944	0.225301230250113	0.112650615125056
20	0.899506554932162	0.200986890135676	0.100493445067838
21	0.81743127170226	0.365137456595479	0.18256872829774
22	0.776347804053658	0.447304391892684	0.223652195946342
23	0.667559622724874	0.664880754550252	0.332440377275126
24	0.505138409406678	0.989723181186644	0.494861590593322

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
10 & 0.881281126974023 & 0.237437746051955 & 0.118718873025977 \tabularnewline
11 & 0.975815177296495 & 0.0483696454070097 & 0.0241848227035049 \tabularnewline
12 & 0.991096834454874 & 0.0178063310902511 & 0.00890316554512557 \tabularnewline
13 & 0.990774888013364 & 0.0184502239732729 & 0.00922511198663643 \tabularnewline
14 & 0.989336109333945 & 0.0213277813321103 & 0.0106638906660551 \tabularnewline
15 & 0.983281857734567 & 0.0334362845308665 & 0.0167181422654332 \tabularnewline
16 & 0.979290529164562 & 0.0414189416708749 & 0.0207094708354374 \tabularnewline
17 & 0.963393475786014 & 0.0732130484279712 & 0.0366065242139856 \tabularnewline
18 & 0.931481728002504 & 0.137036543994993 & 0.0685182719974963 \tabularnewline
19 & 0.887349384874944 & 0.225301230250113 & 0.112650615125056 \tabularnewline
20 & 0.899506554932162 & 0.200986890135676 & 0.100493445067838 \tabularnewline
21 & 0.81743127170226 & 0.365137456595479 & 0.18256872829774 \tabularnewline
22 & 0.776347804053658 & 0.447304391892684 & 0.223652195946342 \tabularnewline
23 & 0.667559622724874 & 0.664880754550252 & 0.332440377275126 \tabularnewline
24 & 0.505138409406678 & 0.989723181186644 & 0.494861590593322 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163539&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]0.881281126974023[/C][C]0.237437746051955[/C][C]0.118718873025977[/C][/ROW]
[ROW][C]11[/C][C]0.975815177296495[/C][C]0.0483696454070097[/C][C]0.0241848227035049[/C][/ROW]
[ROW][C]12[/C][C]0.991096834454874[/C][C]0.0178063310902511[/C][C]0.00890316554512557[/C][/ROW]
[ROW][C]13[/C][C]0.990774888013364[/C][C]0.0184502239732729[/C][C]0.00922511198663643[/C][/ROW]
[ROW][C]14[/C][C]0.989336109333945[/C][C]0.0213277813321103[/C][C]0.0106638906660551[/C][/ROW]
[ROW][C]15[/C][C]0.983281857734567[/C][C]0.0334362845308665[/C][C]0.0167181422654332[/C][/ROW]
[ROW][C]16[/C][C]0.979290529164562[/C][C]0.0414189416708749[/C][C]0.0207094708354374[/C][/ROW]
[ROW][C]17[/C][C]0.963393475786014[/C][C]0.0732130484279712[/C][C]0.0366065242139856[/C][/ROW]
[ROW][C]18[/C][C]0.931481728002504[/C][C]0.137036543994993[/C][C]0.0685182719974963[/C][/ROW]
[ROW][C]19[/C][C]0.887349384874944[/C][C]0.225301230250113[/C][C]0.112650615125056[/C][/ROW]
[ROW][C]20[/C][C]0.899506554932162[/C][C]0.200986890135676[/C][C]0.100493445067838[/C][/ROW]
[ROW][C]21[/C][C]0.81743127170226[/C][C]0.365137456595479[/C][C]0.18256872829774[/C][/ROW]
[ROW][C]22[/C][C]0.776347804053658[/C][C]0.447304391892684[/C][C]0.223652195946342[/C][/ROW]
[ROW][C]23[/C][C]0.667559622724874[/C][C]0.664880754550252[/C][C]0.332440377275126[/C][/ROW]
[ROW][C]24[/C][C]0.505138409406678[/C][C]0.989723181186644[/C][C]0.494861590593322[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163539&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163539&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	0.881281126974023	0.237437746051955	0.118718873025977
11	0.975815177296495	0.0483696454070097	0.0241848227035049
12	0.991096834454874	0.0178063310902511	0.00890316554512557
13	0.990774888013364	0.0184502239732729	0.00922511198663643
14	0.989336109333945	0.0213277813321103	0.0106638906660551
15	0.983281857734567	0.0334362845308665	0.0167181422654332
16	0.979290529164562	0.0414189416708749	0.0207094708354374
17	0.963393475786014	0.0732130484279712	0.0366065242139856
18	0.931481728002504	0.137036543994993	0.0685182719974963
19	0.887349384874944	0.225301230250113	0.112650615125056
20	0.899506554932162	0.200986890135676	0.100493445067838
21	0.81743127170226	0.365137456595479	0.18256872829774
22	0.776347804053658	0.447304391892684	0.223652195946342
23	0.667559622724874	0.664880754550252	0.332440377275126
24	0.505138409406678	0.989723181186644	0.494861590593322

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	6	0.4	NOK
10% type I error level	7	0.466666666666667	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 & 6 & 0.4 & NOK \tabularnewline
10% type I error level & 7 & 0.466666666666667 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163539&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]6[/C][C]0.4[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]7[/C][C]0.466666666666667[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163539&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163539&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	6	0.4	NOK
10% type I error level	7	0.466666666666667	NOK

Figure 1

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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 = 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