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Author's title

Author*Unverified author*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationTue, 06 Mar 2012 10:35:32 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/06/t133104823638971tjg7jsv8l9.htm/, Retrieved Wed, 01 May 2024 17:46:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163540, Retrieved Wed, 01 May 2024 17:46:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact180
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] [Reduced model ] [2012-03-06 15:35:32] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-    D      [Multiple Regression] [Chimney swift ent...] [2012-03-07 21:49:25] [74be16979710d4c4e7c6647856088456]
-    D        [Multiple Regression] [Chimney swift ent...] [2012-03-08 21:24:40] [74be16979710d4c4e7c6647856088456]
-    D          [Multiple Regression] [TimeIn vs Sunset ...] [2012-03-09 17:37:07] [74be16979710d4c4e7c6647856088456]
-    D          [Multiple Regression] [TimeIn vs Temp Rain] [2012-03-09 17:38:55] [74be16979710d4c4e7c6647856088456]
-    D        [Multiple Regression] [Poster regression...] [2012-04-02 17:00:19] [74be16979710d4c4e7c6647856088456]
-    D          [Multiple Regression] [Including SeasonD...] [2012-04-09 18:04:16] [74be16979710d4c4e7c6647856088456]
- R  D        [Multiple Regression] [Chimney Swift Roo...] [2012-05-08 00:52:59] [74be16979710d4c4e7c6647856088456]
- R  D        [Multiple Regression] [Chimney Swift Roo...] [2012-05-08 01:12:12] [74be16979710d4c4e7c6647856088456]
- R  D        [Multiple Regression] [Fixed 5-7-2012] [2012-05-08 04:26:12] [74be16979710d4c4e7c6647856088456]
- R  D        [Multiple Regression] [Full Model] [2012-06-06 13:44:04] [74be16979710d4c4e7c6647856088456]
- R  D        [Multiple Regression] [Final model] [2012-06-06 13:46:11] [74be16979710d4c4e7c6647856088456]
- R  D        [Multiple Regression] [Final Chimney Swi...] [2012-06-08 15:27:31] [74be16979710d4c4e7c6647856088456]
-    D      [Multiple Regression] [Chimney swift ent...] [2012-03-07 21:54:59] [74be16979710d4c4e7c6647856088456]
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Post a new message
Dataseries X:
1217.00	1210.00	31.00	48.00	961.00	2304.00
1202.00	1209.00	34.40	38.00	1183.36	1444.00
1180.00	1207.00	35.60	37.00	1267.36	1369.00
1167.00	1206.00	32.80	48.00	1075.84	2304.00
1186.00	1204.00	23.30	81.00	542.89	6561.00
1168.00	1201.00	20.00	58.00	400.00	3364.00
1142.00	1199.00	16.70	93.00	278.89	8649.00
1147.00	1198.00	17.80	86.00	316.84	7396.00
1183.00	1196.00	21.20	68.00	449.44	4624.00
1149.00	1195.00	23.90	68.00	571.21	4624.00
1197.00	1193.00	28.80	68.00	829.44	4624.00
1210.00	1191.00	25.60	59.00	655.36	3481.00
1206.00	1190.00	29.40	43.00	864.36	1849.00
1196.00	1188.00	22.80	59.00	519.84	3481.00
1190.00	1187.00	16.10	31.00	259.21	961.00
1175.00	1185.00	16.10	49.00	259.21	2401.00
1186.00	1183.00	20.00	52.00	400.00	2704.00
1172.00	1182.00	20.60	75.00	424.36	5625.00
1152.00	1185.00	18.30	90.00	334.89	8100.00
1154.00	1179.00	21.60	86.00	466.56	7396.00
1168.00	1177.00	22.80	87.00	519.84	7569.00
1180.00	1175.00	22.80	47.00	519.84	2209.00
1169.00	1174.00	17.20	70.00	295.84	4900.00
1166.00	1170.00	22.20	61.00	492.84	3721.00
1177.00	1169.00	20.60	48.00	424.36	2304.00
1168.00	1167.00	18.30	67.00	334.89	4489.00
1160.00	1166.00	16.70	74.00	278.89	5476.00
1147.00	1164.00	22.80	55.00	519.84	3025.00
1161.00	1162.00	13.90	47.00	193.21	2209.00
1143.00	1161.00	10.00	65.00	100.00	4225.00
1161.00	1159.00	16.10	28.00	259.21	784.00
1161.00	1158.00	20.60	30.00	424.36	900.00
1168.00	1156.00	19.40	67.00	376.36	4489.00
1172.00	1155.00	25.60	32.00	655.36	1024.00




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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=163540&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=163540&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163540&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Multiple Linear Regression - Estimated Regression Equation
15thbird[t] = + 548.77411711376 + 0.457919900566662Sunset[t] + 5.5127280172675Temp[t] + 1.09183657659764humidity[t] -0.102083596676507`Temp^2`[t] -0.013112777176766`Hum^2`[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
15thbird[t] =  +  548.77411711376 +  0.457919900566662Sunset[t] +  5.5127280172675Temp[t] +  1.09183657659764humidity[t] -0.102083596676507`Temp^2`[t] -0.013112777176766`Hum^2`[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163540&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]15thbird[t] =  +  548.77411711376 +  0.457919900566662Sunset[t] +  5.5127280172675Temp[t] +  1.09183657659764humidity[t] -0.102083596676507`Temp^2`[t] -0.013112777176766`Hum^2`[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163540&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163540&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] = + 548.77411711376 + 0.457919900566662Sunset[t] + 5.5127280172675Temp[t] + 1.09183657659764humidity[t] -0.102083596676507`Temp^2`[t] -0.013112777176766`Hum^2`[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)548.77411711376240.4279482.28250.0302580.015129
Sunset0.4579199005666620.2040892.24370.0329410.016471
Temp5.51272801726752.8025771.9670.0591610.029581
humidity1.091836576597640.875571.2470.2227280.111364
`Temp^2`-0.1020835966765070.060835-1.6780.1044690.052234
`Hum^2`-0.0131127771767660.007202-1.82080.0793370.039669

\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) & 548.77411711376 & 240.427948 & 2.2825 & 0.030258 & 0.015129 \tabularnewline
Sunset & 0.457919900566662 & 0.204089 & 2.2437 & 0.032941 & 0.016471 \tabularnewline
Temp & 5.5127280172675 & 2.802577 & 1.967 & 0.059161 & 0.029581 \tabularnewline
humidity & 1.09183657659764 & 0.87557 & 1.247 & 0.222728 & 0.111364 \tabularnewline
`Temp^2` & -0.102083596676507 & 0.060835 & -1.678 & 0.104469 & 0.052234 \tabularnewline
`Hum^2` & -0.013112777176766 & 0.007202 & -1.8208 & 0.079337 & 0.039669 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163540&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]548.77411711376[/C][C]240.427948[/C][C]2.2825[/C][C]0.030258[/C][C]0.015129[/C][/ROW]
[ROW][C]Sunset[/C][C]0.457919900566662[/C][C]0.204089[/C][C]2.2437[/C][C]0.032941[/C][C]0.016471[/C][/ROW]
[ROW][C]Temp[/C][C]5.5127280172675[/C][C]2.802577[/C][C]1.967[/C][C]0.059161[/C][C]0.029581[/C][/ROW]
[ROW][C]humidity[/C][C]1.09183657659764[/C][C]0.87557[/C][C]1.247[/C][C]0.222728[/C][C]0.111364[/C][/ROW]
[ROW][C]`Temp^2`[/C][C]-0.102083596676507[/C][C]0.060835[/C][C]-1.678[/C][C]0.104469[/C][C]0.052234[/C][/ROW]
[ROW][C]`Hum^2`[/C][C]-0.013112777176766[/C][C]0.007202[/C][C]-1.8208[/C][C]0.079337[/C][C]0.039669[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163540&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163540&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
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)548.77411711376240.4279482.28250.0302580.015129
Sunset0.4579199005666620.2040892.24370.0329410.016471
Temp5.51272801726752.8025771.9670.0591610.029581
humidity1.091836576597640.875571.2470.2227280.111364
`Temp^2`-0.1020835966765070.060835-1.6780.1044690.052234
`Hum^2`-0.0131127771767660.007202-1.82080.0793370.039669







Multiple Linear Regression - Regression Statistics
Multiple R0.737883439021702
R-squared0.544471969582493
Adjusted R-squared0.46312767843651
F-TEST (value)6.69342570833109
F-TEST (DF numerator)5
F-TEST (DF denominator)28
p-value0.00032362923653384
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation14.3059540940118
Sum Squared Residuals5730.48903111925

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.737883439021702 \tabularnewline
R-squared & 0.544471969582493 \tabularnewline
Adjusted R-squared & 0.46312767843651 \tabularnewline
F-TEST (value) & 6.69342570833109 \tabularnewline
F-TEST (DF numerator) & 5 \tabularnewline
F-TEST (DF denominator) & 28 \tabularnewline
p-value & 0.00032362923653384 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 14.3059540940118 \tabularnewline
Sum Squared Residuals & 5730.48903111925 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163540&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.737883439021702[/C][/ROW]
[ROW][C]R-squared[/C][C]0.544471969582493[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.46312767843651[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]6.69342570833109[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]5[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]28[/C][/ROW]
[ROW][C]p-value[/C][C]0.00032362923653384[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]14.3059540940118[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]5730.48903111925[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163540&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163540&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 R0.737883439021702
R-squared0.544471969582493
Adjusted R-squared0.46312767843651
F-TEST (value)6.69342570833109
F-TEST (DF numerator)5
F-TEST (DF denominator)28
p-value0.00032362923653384
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation14.3059540940118
Sum Squared Residuals5730.48903111925







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
112171197.8457459900119.1542540099918
212021193.790415397218.2095846027948
311801190.80644880763-10.8064488076261
411671194.21369657649-27.2136965764929
511861175.5419080462910.458091953708
611681187.37217838909-19.3721783890906
711421149.54093332618-7.54093332617526
811471160.06039551703-13.0603955170338
911831181.047106010541.95289398945705
1011491183.0428321893-34.0428321893003
1111971182.77831250314.2216874969967
1212101187.1538306797322.8461693202749
1312061190.239472666315.7605273336952
1411961184.1788015512811.8211984487237
1511901175.8644260775314.1355739224681
1611751175.71924552061-0.719245520613063
1711861181.233033655974.76696634402964
1811721168.405813279143.59418672086332
1911521150.157143072241.84285692776279
2011541157.02432777748-3.02432777747701
2111681156.1080736911611.8919263088425
2211801181.80325649358-1.80325649358442
2311691163.166543230935.83345676907427
2411661174.42147027175-8.42147027175305
2511771176.520800007670.479199992326284
2611681164.152581985593.84741801440634
2711601155.2915236344.70847636600119
2811471174.80080402389-27.8008040238912
2911611160.130583614980.869416385015417
3011431140.905936083692.09406391631086
3111611162.08812069216-1.08812069216002
3211611170.24096187886-9.24096187886238
3311681160.946057144187.05394285582015
3411721173.4072202145-1.40722021450305

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1217 & 1197.84574599001 & 19.1542540099918 \tabularnewline
2 & 1202 & 1193.79041539721 & 8.2095846027948 \tabularnewline
3 & 1180 & 1190.80644880763 & -10.8064488076261 \tabularnewline
4 & 1167 & 1194.21369657649 & -27.2136965764929 \tabularnewline
5 & 1186 & 1175.54190804629 & 10.458091953708 \tabularnewline
6 & 1168 & 1187.37217838909 & -19.3721783890906 \tabularnewline
7 & 1142 & 1149.54093332618 & -7.54093332617526 \tabularnewline
8 & 1147 & 1160.06039551703 & -13.0603955170338 \tabularnewline
9 & 1183 & 1181.04710601054 & 1.95289398945705 \tabularnewline
10 & 1149 & 1183.0428321893 & -34.0428321893003 \tabularnewline
11 & 1197 & 1182.778312503 & 14.2216874969967 \tabularnewline
12 & 1210 & 1187.15383067973 & 22.8461693202749 \tabularnewline
13 & 1206 & 1190.2394726663 & 15.7605273336952 \tabularnewline
14 & 1196 & 1184.17880155128 & 11.8211984487237 \tabularnewline
15 & 1190 & 1175.86442607753 & 14.1355739224681 \tabularnewline
16 & 1175 & 1175.71924552061 & -0.719245520613063 \tabularnewline
17 & 1186 & 1181.23303365597 & 4.76696634402964 \tabularnewline
18 & 1172 & 1168.40581327914 & 3.59418672086332 \tabularnewline
19 & 1152 & 1150.15714307224 & 1.84285692776279 \tabularnewline
20 & 1154 & 1157.02432777748 & -3.02432777747701 \tabularnewline
21 & 1168 & 1156.10807369116 & 11.8919263088425 \tabularnewline
22 & 1180 & 1181.80325649358 & -1.80325649358442 \tabularnewline
23 & 1169 & 1163.16654323093 & 5.83345676907427 \tabularnewline
24 & 1166 & 1174.42147027175 & -8.42147027175305 \tabularnewline
25 & 1177 & 1176.52080000767 & 0.479199992326284 \tabularnewline
26 & 1168 & 1164.15258198559 & 3.84741801440634 \tabularnewline
27 & 1160 & 1155.291523634 & 4.70847636600119 \tabularnewline
28 & 1147 & 1174.80080402389 & -27.8008040238912 \tabularnewline
29 & 1161 & 1160.13058361498 & 0.869416385015417 \tabularnewline
30 & 1143 & 1140.90593608369 & 2.09406391631086 \tabularnewline
31 & 1161 & 1162.08812069216 & -1.08812069216002 \tabularnewline
32 & 1161 & 1170.24096187886 & -9.24096187886238 \tabularnewline
33 & 1168 & 1160.94605714418 & 7.05394285582015 \tabularnewline
34 & 1172 & 1173.4072202145 & -1.40722021450305 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163540&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]1197.84574599001[/C][C]19.1542540099918[/C][/ROW]
[ROW][C]2[/C][C]1202[/C][C]1193.79041539721[/C][C]8.2095846027948[/C][/ROW]
[ROW][C]3[/C][C]1180[/C][C]1190.80644880763[/C][C]-10.8064488076261[/C][/ROW]
[ROW][C]4[/C][C]1167[/C][C]1194.21369657649[/C][C]-27.2136965764929[/C][/ROW]
[ROW][C]5[/C][C]1186[/C][C]1175.54190804629[/C][C]10.458091953708[/C][/ROW]
[ROW][C]6[/C][C]1168[/C][C]1187.37217838909[/C][C]-19.3721783890906[/C][/ROW]
[ROW][C]7[/C][C]1142[/C][C]1149.54093332618[/C][C]-7.54093332617526[/C][/ROW]
[ROW][C]8[/C][C]1147[/C][C]1160.06039551703[/C][C]-13.0603955170338[/C][/ROW]
[ROW][C]9[/C][C]1183[/C][C]1181.04710601054[/C][C]1.95289398945705[/C][/ROW]
[ROW][C]10[/C][C]1149[/C][C]1183.0428321893[/C][C]-34.0428321893003[/C][/ROW]
[ROW][C]11[/C][C]1197[/C][C]1182.778312503[/C][C]14.2216874969967[/C][/ROW]
[ROW][C]12[/C][C]1210[/C][C]1187.15383067973[/C][C]22.8461693202749[/C][/ROW]
[ROW][C]13[/C][C]1206[/C][C]1190.2394726663[/C][C]15.7605273336952[/C][/ROW]
[ROW][C]14[/C][C]1196[/C][C]1184.17880155128[/C][C]11.8211984487237[/C][/ROW]
[ROW][C]15[/C][C]1190[/C][C]1175.86442607753[/C][C]14.1355739224681[/C][/ROW]
[ROW][C]16[/C][C]1175[/C][C]1175.71924552061[/C][C]-0.719245520613063[/C][/ROW]
[ROW][C]17[/C][C]1186[/C][C]1181.23303365597[/C][C]4.76696634402964[/C][/ROW]
[ROW][C]18[/C][C]1172[/C][C]1168.40581327914[/C][C]3.59418672086332[/C][/ROW]
[ROW][C]19[/C][C]1152[/C][C]1150.15714307224[/C][C]1.84285692776279[/C][/ROW]
[ROW][C]20[/C][C]1154[/C][C]1157.02432777748[/C][C]-3.02432777747701[/C][/ROW]
[ROW][C]21[/C][C]1168[/C][C]1156.10807369116[/C][C]11.8919263088425[/C][/ROW]
[ROW][C]22[/C][C]1180[/C][C]1181.80325649358[/C][C]-1.80325649358442[/C][/ROW]
[ROW][C]23[/C][C]1169[/C][C]1163.16654323093[/C][C]5.83345676907427[/C][/ROW]
[ROW][C]24[/C][C]1166[/C][C]1174.42147027175[/C][C]-8.42147027175305[/C][/ROW]
[ROW][C]25[/C][C]1177[/C][C]1176.52080000767[/C][C]0.479199992326284[/C][/ROW]
[ROW][C]26[/C][C]1168[/C][C]1164.15258198559[/C][C]3.84741801440634[/C][/ROW]
[ROW][C]27[/C][C]1160[/C][C]1155.291523634[/C][C]4.70847636600119[/C][/ROW]
[ROW][C]28[/C][C]1147[/C][C]1174.80080402389[/C][C]-27.8008040238912[/C][/ROW]
[ROW][C]29[/C][C]1161[/C][C]1160.13058361498[/C][C]0.869416385015417[/C][/ROW]
[ROW][C]30[/C][C]1143[/C][C]1140.90593608369[/C][C]2.09406391631086[/C][/ROW]
[ROW][C]31[/C][C]1161[/C][C]1162.08812069216[/C][C]-1.08812069216002[/C][/ROW]
[ROW][C]32[/C][C]1161[/C][C]1170.24096187886[/C][C]-9.24096187886238[/C][/ROW]
[ROW][C]33[/C][C]1168[/C][C]1160.94605714418[/C][C]7.05394285582015[/C][/ROW]
[ROW][C]34[/C][C]1172[/C][C]1173.4072202145[/C][C]-1.40722021450305[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163540&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163540&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 IndexActualsInterpolationForecastResidualsPrediction Error
112171197.8457459900119.1542540099918
212021193.790415397218.2095846027948
311801190.80644880763-10.8064488076261
411671194.21369657649-27.2136965764929
511861175.5419080462910.458091953708
611681187.37217838909-19.3721783890906
711421149.54093332618-7.54093332617526
811471160.06039551703-13.0603955170338
911831181.047106010541.95289398945705
1011491183.0428321893-34.0428321893003
1111971182.77831250314.2216874969967
1212101187.1538306797322.8461693202749
1312061190.239472666315.7605273336952
1411961184.1788015512811.8211984487237
1511901175.8644260775314.1355739224681
1611751175.71924552061-0.719245520613063
1711861181.233033655974.76696634402964
1811721168.405813279143.59418672086332
1911521150.157143072241.84285692776279
2011541157.02432777748-3.02432777747701
2111681156.1080736911611.8919263088425
2211801181.80325649358-1.80325649358442
2311691163.166543230935.83345676907427
2411661174.42147027175-8.42147027175305
2511771176.520800007670.479199992326284
2611681164.152581985593.84741801440634
2711601155.2915236344.70847636600119
2811471174.80080402389-27.8008040238912
2911611160.130583614980.869416385015417
3011431140.905936083692.09406391631086
3111611162.08812069216-1.08812069216002
3211611170.24096187886-9.24096187886238
3311681160.946057144187.05394285582015
3411721173.4072202145-1.40722021450305







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
90.5289642217574030.9420715564851950.471035778242597
100.9745896417676140.05082071646477230.0254103582323862
110.9959291643171190.008141671365761860.00407083568288093
120.9960677649434440.007864470113112060.00393223505655603
130.9946837149835580.01063257003288320.00531628501644162
140.993345567661190.01330886467761980.0066544323388099
150.9892336880631740.02153262387365290.0107663119368264
160.9851906721541180.02961865569176350.0148093278458818
170.9742520283338120.05149594333237530.0257479716661877
180.9508111687669090.09837766246618150.0491888312330908
190.9204556982185560.1590886035628880.0795443017814438
200.9236107470704690.1527785058590630.0763892529295315
210.8607632007004140.2784735985991730.139236799299586
220.8311130300350720.3377739399298550.168886969964928
230.7467550324736760.5064899350526470.253244967526324
240.6218231745584180.7563536508831640.378176825441582
250.6372080685415880.7255838629168240.362791931458412

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
9 & 0.528964221757403 & 0.942071556485195 & 0.471035778242597 \tabularnewline
10 & 0.974589641767614 & 0.0508207164647723 & 0.0254103582323862 \tabularnewline
11 & 0.995929164317119 & 0.00814167136576186 & 0.00407083568288093 \tabularnewline
12 & 0.996067764943444 & 0.00786447011311206 & 0.00393223505655603 \tabularnewline
13 & 0.994683714983558 & 0.0106325700328832 & 0.00531628501644162 \tabularnewline
14 & 0.99334556766119 & 0.0133088646776198 & 0.0066544323388099 \tabularnewline
15 & 0.989233688063174 & 0.0215326238736529 & 0.0107663119368264 \tabularnewline
16 & 0.985190672154118 & 0.0296186556917635 & 0.0148093278458818 \tabularnewline
17 & 0.974252028333812 & 0.0514959433323753 & 0.0257479716661877 \tabularnewline
18 & 0.950811168766909 & 0.0983776624661815 & 0.0491888312330908 \tabularnewline
19 & 0.920455698218556 & 0.159088603562888 & 0.0795443017814438 \tabularnewline
20 & 0.923610747070469 & 0.152778505859063 & 0.0763892529295315 \tabularnewline
21 & 0.860763200700414 & 0.278473598599173 & 0.139236799299586 \tabularnewline
22 & 0.831113030035072 & 0.337773939929855 & 0.168886969964928 \tabularnewline
23 & 0.746755032473676 & 0.506489935052647 & 0.253244967526324 \tabularnewline
24 & 0.621823174558418 & 0.756353650883164 & 0.378176825441582 \tabularnewline
25 & 0.637208068541588 & 0.725583862916824 & 0.362791931458412 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163540&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]9[/C][C]0.528964221757403[/C][C]0.942071556485195[/C][C]0.471035778242597[/C][/ROW]
[ROW][C]10[/C][C]0.974589641767614[/C][C]0.0508207164647723[/C][C]0.0254103582323862[/C][/ROW]
[ROW][C]11[/C][C]0.995929164317119[/C][C]0.00814167136576186[/C][C]0.00407083568288093[/C][/ROW]
[ROW][C]12[/C][C]0.996067764943444[/C][C]0.00786447011311206[/C][C]0.00393223505655603[/C][/ROW]
[ROW][C]13[/C][C]0.994683714983558[/C][C]0.0106325700328832[/C][C]0.00531628501644162[/C][/ROW]
[ROW][C]14[/C][C]0.99334556766119[/C][C]0.0133088646776198[/C][C]0.0066544323388099[/C][/ROW]
[ROW][C]15[/C][C]0.989233688063174[/C][C]0.0215326238736529[/C][C]0.0107663119368264[/C][/ROW]
[ROW][C]16[/C][C]0.985190672154118[/C][C]0.0296186556917635[/C][C]0.0148093278458818[/C][/ROW]
[ROW][C]17[/C][C]0.974252028333812[/C][C]0.0514959433323753[/C][C]0.0257479716661877[/C][/ROW]
[ROW][C]18[/C][C]0.950811168766909[/C][C]0.0983776624661815[/C][C]0.0491888312330908[/C][/ROW]
[ROW][C]19[/C][C]0.920455698218556[/C][C]0.159088603562888[/C][C]0.0795443017814438[/C][/ROW]
[ROW][C]20[/C][C]0.923610747070469[/C][C]0.152778505859063[/C][C]0.0763892529295315[/C][/ROW]
[ROW][C]21[/C][C]0.860763200700414[/C][C]0.278473598599173[/C][C]0.139236799299586[/C][/ROW]
[ROW][C]22[/C][C]0.831113030035072[/C][C]0.337773939929855[/C][C]0.168886969964928[/C][/ROW]
[ROW][C]23[/C][C]0.746755032473676[/C][C]0.506489935052647[/C][C]0.253244967526324[/C][/ROW]
[ROW][C]24[/C][C]0.621823174558418[/C][C]0.756353650883164[/C][C]0.378176825441582[/C][/ROW]
[ROW][C]25[/C][C]0.637208068541588[/C][C]0.725583862916824[/C][C]0.362791931458412[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163540&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163540&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-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
90.5289642217574030.9420715564851950.471035778242597
100.9745896417676140.05082071646477230.0254103582323862
110.9959291643171190.008141671365761860.00407083568288093
120.9960677649434440.007864470113112060.00393223505655603
130.9946837149835580.01063257003288320.00531628501644162
140.993345567661190.01330886467761980.0066544323388099
150.9892336880631740.02153262387365290.0107663119368264
160.9851906721541180.02961865569176350.0148093278458818
170.9742520283338120.05149594333237530.0257479716661877
180.9508111687669090.09837766246618150.0491888312330908
190.9204556982185560.1590886035628880.0795443017814438
200.9236107470704690.1527785058590630.0763892529295315
210.8607632007004140.2784735985991730.139236799299586
220.8311130300350720.3377739399298550.168886969964928
230.7467550324736760.5064899350526470.253244967526324
240.6218231745584180.7563536508831640.378176825441582
250.6372080685415880.7255838629168240.362791931458412







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level20.117647058823529NOK
5% type I error level60.352941176470588NOK
10% type I error level90.529411764705882NOK

\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 & 2 & 0.117647058823529 & NOK \tabularnewline
5% type I error level & 6 & 0.352941176470588 & NOK \tabularnewline
10% type I error level & 9 & 0.529411764705882 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163540&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]2[/C][C]0.117647058823529[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]6[/C][C]0.352941176470588[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]9[/C][C]0.529411764705882[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163540&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163540&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 testsOK/NOK
1% type I error level20.117647058823529NOK
5% type I error level60.352941176470588NOK
10% type I error level90.529411764705882NOK



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')
}