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Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationMon, 05 Nov 2012 06:42:55 -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/Nov/05/t135211581527mhchdq66s8p5a.htm/, Retrieved Sun, 05 Feb 2023 23:01:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=185987, Retrieved Sun, 05 Feb 2023 23:01:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [] [2012-11-05 11:42:55] [e5cf4d544f75f57c12196ef0ffd71d75] [Current]
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Dataseries X:
38	39	13	12	15	11	89	54
37	38	16	14	15	8	76	47
33	31	15	13	15	11	73	45
31	33	16	15	13	11	79	47
39	32	15	10	17	8	90	55
44	39	17	11	17	10	74	44
33	36	15	9	19	11	81	53
35	33	12	11	15	13	72	44
32	33	16	10	13	11	71	42
28	32	10	11	9	20	66	40
40	37	16	8	15	10	77	46
27	30	12	11	15	15	65	40
37	38	14	12	15	12	74	46
32	29	15	12	16	14	82	53
28	22	13	9	11	23	54	33
34	35	15	11	14	14	63	42
30	35	11	10	11	16	54	35
35	34	12	8	15	11	64	40
31	35	8	9	13	12	69	41
32	34	16	8	15	10	54	33
30	34	15	9	16	14	84	51
30	35	17	15	14	12	86	53
31	23	16	11	15	12	77	46
40	31	10	8	16	11	89	55
32	27	18	13	16	12	76	47
36	36	13	12	11	13	60	38
32	31	16	12	12	11	75	46
35	32	13	9	9	19	73	46
38	39	10	7	16	12	85	53
42	37	15	13	13	17	79	47
34	38	16	9	16	9	71	41
35	39	16	6	12	12	72	44
35	34	14	8	9	19	69	43
33	31	10	8	13	18	78	51
36	32	17	15	13	15	54	33
32	37	13	6	14	14	69	43
33	36	15	9	19	11	81	53
34	32	16	11	13	9	84	51
32	35	12	8	12	18	84	50
34	36	13	8	13	16	69	46




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 7 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185987&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185987&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185987&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 time7 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Multiple Linear Regression - Estimated Regression Equation
Connected[t] = + 10.9758440334628 + 0.434969804573434Separate[t] + 0.137588630034852Learning[t] -0.00275390329343048Software[t] + 0.116676408047773Happiness[t] -0.0335936849979727Depression[t] + 0.199184622033619Belonging[t] -0.207011125616048Belonging_Final[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Connected[t] =  +  10.9758440334628 +  0.434969804573434Separate[t] +  0.137588630034852Learning[t] -0.00275390329343048Software[t] +  0.116676408047773Happiness[t] -0.0335936849979727Depression[t] +  0.199184622033619Belonging[t] -0.207011125616048Belonging_Final[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185987&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Connected[t] =  +  10.9758440334628 +  0.434969804573434Separate[t] +  0.137588630034852Learning[t] -0.00275390329343048Software[t] +  0.116676408047773Happiness[t] -0.0335936849979727Depression[t] +  0.199184622033619Belonging[t] -0.207011125616048Belonging_Final[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185987&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185987&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
Connected[t] = + 10.9758440334628 + 0.434969804573434Separate[t] + 0.137588630034852Learning[t] -0.00275390329343048Software[t] + 0.116676408047773Happiness[t] -0.0335936849979727Depression[t] + 0.199184622033619Belonging[t] -0.207011125616048Belonging_Final[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)10.975844033462811.9376580.91940.364750.182375
Separate0.4349698045734340.1530552.84190.0077420.003871
Learning0.1375886300348520.2770410.49660.622840.31142
Software-0.002753903293430480.259035-0.01060.9915840.495792
Happiness0.1166764080477730.3454070.33780.7377240.368862
Depression-0.03359368499797270.254622-0.13190.8958610.447931
Belonging0.1991846220336190.2369530.84060.4068040.203402
Belonging_Final-0.2070111256160480.386635-0.53540.5960630.298031

\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) & 10.9758440334628 & 11.937658 & 0.9194 & 0.36475 & 0.182375 \tabularnewline
Separate & 0.434969804573434 & 0.153055 & 2.8419 & 0.007742 & 0.003871 \tabularnewline
Learning & 0.137588630034852 & 0.277041 & 0.4966 & 0.62284 & 0.31142 \tabularnewline
Software & -0.00275390329343048 & 0.259035 & -0.0106 & 0.991584 & 0.495792 \tabularnewline
Happiness & 0.116676408047773 & 0.345407 & 0.3378 & 0.737724 & 0.368862 \tabularnewline
Depression & -0.0335936849979727 & 0.254622 & -0.1319 & 0.895861 & 0.447931 \tabularnewline
Belonging & 0.199184622033619 & 0.236953 & 0.8406 & 0.406804 & 0.203402 \tabularnewline
Belonging_Final & -0.207011125616048 & 0.386635 & -0.5354 & 0.596063 & 0.298031 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185987&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]10.9758440334628[/C][C]11.937658[/C][C]0.9194[/C][C]0.36475[/C][C]0.182375[/C][/ROW]
[ROW][C]Separate[/C][C]0.434969804573434[/C][C]0.153055[/C][C]2.8419[/C][C]0.007742[/C][C]0.003871[/C][/ROW]
[ROW][C]Learning[/C][C]0.137588630034852[/C][C]0.277041[/C][C]0.4966[/C][C]0.62284[/C][C]0.31142[/C][/ROW]
[ROW][C]Software[/C][C]-0.00275390329343048[/C][C]0.259035[/C][C]-0.0106[/C][C]0.991584[/C][C]0.495792[/C][/ROW]
[ROW][C]Happiness[/C][C]0.116676408047773[/C][C]0.345407[/C][C]0.3378[/C][C]0.737724[/C][C]0.368862[/C][/ROW]
[ROW][C]Depression[/C][C]-0.0335936849979727[/C][C]0.254622[/C][C]-0.1319[/C][C]0.895861[/C][C]0.447931[/C][/ROW]
[ROW][C]Belonging[/C][C]0.199184622033619[/C][C]0.236953[/C][C]0.8406[/C][C]0.406804[/C][C]0.203402[/C][/ROW]
[ROW][C]Belonging_Final[/C][C]-0.207011125616048[/C][C]0.386635[/C][C]-0.5354[/C][C]0.596063[/C][C]0.298031[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185987&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185987&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)10.975844033462811.9376580.91940.364750.182375
Separate0.4349698045734340.1530552.84190.0077420.003871
Learning0.1375886300348520.2770410.49660.622840.31142
Software-0.002753903293430480.259035-0.01060.9915840.495792
Happiness0.1166764080477730.3454070.33780.7377240.368862
Depression-0.03359368499797270.254622-0.13190.8958610.447931
Belonging0.1991846220336190.2369530.84060.4068040.203402
Belonging_Final-0.2070111256160480.386635-0.53540.5960630.298031







Multiple Linear Regression - Regression Statistics
Multiple R0.586414070248329
R-squared0.343881461785212
Adjusted R-squared0.200355531550727
F-TEST (value)2.39595354806896
F-TEST (DF numerator)7
F-TEST (DF denominator)32
p-value0.0432899539913394
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.36423019191688
Sum Squared Residuals362.177433094563

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.586414070248329 \tabularnewline
R-squared & 0.343881461785212 \tabularnewline
Adjusted R-squared & 0.200355531550727 \tabularnewline
F-TEST (value) & 2.39595354806896 \tabularnewline
F-TEST (DF numerator) & 7 \tabularnewline
F-TEST (DF denominator) & 32 \tabularnewline
p-value & 0.0432899539913394 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 3.36423019191688 \tabularnewline
Sum Squared Residuals & 362.177433094563 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185987&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.586414070248329[/C][/ROW]
[ROW][C]R-squared[/C][C]0.343881461785212[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.200355531550727[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]2.39595354806896[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]7[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]32[/C][/ROW]
[ROW][C]p-value[/C][C]0.0432899539913394[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]3.36423019191688[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]362.177433094563[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185987&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185987&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 R0.586414070248329
R-squared0.343881461785212
Adjusted R-squared0.200355531550727
F-TEST (value)2.39595354806896
F-TEST (DF numerator)7
F-TEST (DF denominator)32
p-value0.0432899539913394
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation3.36423019191688
Sum Squared Residuals362.177433094563







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
13837.6247179262230.375282073776949
23736.55746505303650.442534946963499
33333.0935290244184-0.0935290244183628
43134.6432821218873-3.64328212188729
53935.18692172837263.8130782716274
64437.52711477640566.47288522359442
73335.6834872639909-2.68348726399092
83533.4968496836341.50315031636598
93234.0986302901657-2.09863029016573
102831.4844251459809-3.48442514598091
114036.47802704587743.52197295412263
122731.5585050481466-4.55850504814663
133735.96206274111061.03793725888942
143232.378811264993-0.378811264992972
152826.74443497294851.25556502705148
163433.25064574276920.74935425723078
173031.9422448127937-1.94224481279374
183533.24183609427891.75816390572107
193133.6456629588781-2.64566295887805
203233.2830159583925-1.28301595839245
213035.3743134930398-5.37431349303976
223035.8861186846579-5.88611868465786
233130.31300070197310.686999298026937
244033.65287449513656.34712550486354
253232.0330300341477-0.0330300341477463
263633.32173948119752.67826051880249
273233.0752004520545-1.07520045205452
283532.08851812820932.91148187179065
293836.7190769131171.280923086883
304236.04951840674525.9504815932548
313436.9004609360816-2.90046093608164
323536.3543570085358-1.35435700853583
333532.92309515939822.07690484060184
343331.70470313610171.29529686389829
353632.1300664151413.86993358485899
363234.8472742148992-2.8472742148992
373335.6834872639909-2.68348726399092
383434.4543939081874-0.454393908187432
393235.0052020642351-3.00520206423514
403433.6018994488470.398100551152953

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 38 & 37.624717926223 & 0.375282073776949 \tabularnewline
2 & 37 & 36.5574650530365 & 0.442534946963499 \tabularnewline
3 & 33 & 33.0935290244184 & -0.0935290244183628 \tabularnewline
4 & 31 & 34.6432821218873 & -3.64328212188729 \tabularnewline
5 & 39 & 35.1869217283726 & 3.8130782716274 \tabularnewline
6 & 44 & 37.5271147764056 & 6.47288522359442 \tabularnewline
7 & 33 & 35.6834872639909 & -2.68348726399092 \tabularnewline
8 & 35 & 33.496849683634 & 1.50315031636598 \tabularnewline
9 & 32 & 34.0986302901657 & -2.09863029016573 \tabularnewline
10 & 28 & 31.4844251459809 & -3.48442514598091 \tabularnewline
11 & 40 & 36.4780270458774 & 3.52197295412263 \tabularnewline
12 & 27 & 31.5585050481466 & -4.55850504814663 \tabularnewline
13 & 37 & 35.9620627411106 & 1.03793725888942 \tabularnewline
14 & 32 & 32.378811264993 & -0.378811264992972 \tabularnewline
15 & 28 & 26.7444349729485 & 1.25556502705148 \tabularnewline
16 & 34 & 33.2506457427692 & 0.74935425723078 \tabularnewline
17 & 30 & 31.9422448127937 & -1.94224481279374 \tabularnewline
18 & 35 & 33.2418360942789 & 1.75816390572107 \tabularnewline
19 & 31 & 33.6456629588781 & -2.64566295887805 \tabularnewline
20 & 32 & 33.2830159583925 & -1.28301595839245 \tabularnewline
21 & 30 & 35.3743134930398 & -5.37431349303976 \tabularnewline
22 & 30 & 35.8861186846579 & -5.88611868465786 \tabularnewline
23 & 31 & 30.3130007019731 & 0.686999298026937 \tabularnewline
24 & 40 & 33.6528744951365 & 6.34712550486354 \tabularnewline
25 & 32 & 32.0330300341477 & -0.0330300341477463 \tabularnewline
26 & 36 & 33.3217394811975 & 2.67826051880249 \tabularnewline
27 & 32 & 33.0752004520545 & -1.07520045205452 \tabularnewline
28 & 35 & 32.0885181282093 & 2.91148187179065 \tabularnewline
29 & 38 & 36.719076913117 & 1.280923086883 \tabularnewline
30 & 42 & 36.0495184067452 & 5.9504815932548 \tabularnewline
31 & 34 & 36.9004609360816 & -2.90046093608164 \tabularnewline
32 & 35 & 36.3543570085358 & -1.35435700853583 \tabularnewline
33 & 35 & 32.9230951593982 & 2.07690484060184 \tabularnewline
34 & 33 & 31.7047031361017 & 1.29529686389829 \tabularnewline
35 & 36 & 32.130066415141 & 3.86993358485899 \tabularnewline
36 & 32 & 34.8472742148992 & -2.8472742148992 \tabularnewline
37 & 33 & 35.6834872639909 & -2.68348726399092 \tabularnewline
38 & 34 & 34.4543939081874 & -0.454393908187432 \tabularnewline
39 & 32 & 35.0052020642351 & -3.00520206423514 \tabularnewline
40 & 34 & 33.601899448847 & 0.398100551152953 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185987&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]38[/C][C]37.624717926223[/C][C]0.375282073776949[/C][/ROW]
[ROW][C]2[/C][C]37[/C][C]36.5574650530365[/C][C]0.442534946963499[/C][/ROW]
[ROW][C]3[/C][C]33[/C][C]33.0935290244184[/C][C]-0.0935290244183628[/C][/ROW]
[ROW][C]4[/C][C]31[/C][C]34.6432821218873[/C][C]-3.64328212188729[/C][/ROW]
[ROW][C]5[/C][C]39[/C][C]35.1869217283726[/C][C]3.8130782716274[/C][/ROW]
[ROW][C]6[/C][C]44[/C][C]37.5271147764056[/C][C]6.47288522359442[/C][/ROW]
[ROW][C]7[/C][C]33[/C][C]35.6834872639909[/C][C]-2.68348726399092[/C][/ROW]
[ROW][C]8[/C][C]35[/C][C]33.496849683634[/C][C]1.50315031636598[/C][/ROW]
[ROW][C]9[/C][C]32[/C][C]34.0986302901657[/C][C]-2.09863029016573[/C][/ROW]
[ROW][C]10[/C][C]28[/C][C]31.4844251459809[/C][C]-3.48442514598091[/C][/ROW]
[ROW][C]11[/C][C]40[/C][C]36.4780270458774[/C][C]3.52197295412263[/C][/ROW]
[ROW][C]12[/C][C]27[/C][C]31.5585050481466[/C][C]-4.55850504814663[/C][/ROW]
[ROW][C]13[/C][C]37[/C][C]35.9620627411106[/C][C]1.03793725888942[/C][/ROW]
[ROW][C]14[/C][C]32[/C][C]32.378811264993[/C][C]-0.378811264992972[/C][/ROW]
[ROW][C]15[/C][C]28[/C][C]26.7444349729485[/C][C]1.25556502705148[/C][/ROW]
[ROW][C]16[/C][C]34[/C][C]33.2506457427692[/C][C]0.74935425723078[/C][/ROW]
[ROW][C]17[/C][C]30[/C][C]31.9422448127937[/C][C]-1.94224481279374[/C][/ROW]
[ROW][C]18[/C][C]35[/C][C]33.2418360942789[/C][C]1.75816390572107[/C][/ROW]
[ROW][C]19[/C][C]31[/C][C]33.6456629588781[/C][C]-2.64566295887805[/C][/ROW]
[ROW][C]20[/C][C]32[/C][C]33.2830159583925[/C][C]-1.28301595839245[/C][/ROW]
[ROW][C]21[/C][C]30[/C][C]35.3743134930398[/C][C]-5.37431349303976[/C][/ROW]
[ROW][C]22[/C][C]30[/C][C]35.8861186846579[/C][C]-5.88611868465786[/C][/ROW]
[ROW][C]23[/C][C]31[/C][C]30.3130007019731[/C][C]0.686999298026937[/C][/ROW]
[ROW][C]24[/C][C]40[/C][C]33.6528744951365[/C][C]6.34712550486354[/C][/ROW]
[ROW][C]25[/C][C]32[/C][C]32.0330300341477[/C][C]-0.0330300341477463[/C][/ROW]
[ROW][C]26[/C][C]36[/C][C]33.3217394811975[/C][C]2.67826051880249[/C][/ROW]
[ROW][C]27[/C][C]32[/C][C]33.0752004520545[/C][C]-1.07520045205452[/C][/ROW]
[ROW][C]28[/C][C]35[/C][C]32.0885181282093[/C][C]2.91148187179065[/C][/ROW]
[ROW][C]29[/C][C]38[/C][C]36.719076913117[/C][C]1.280923086883[/C][/ROW]
[ROW][C]30[/C][C]42[/C][C]36.0495184067452[/C][C]5.9504815932548[/C][/ROW]
[ROW][C]31[/C][C]34[/C][C]36.9004609360816[/C][C]-2.90046093608164[/C][/ROW]
[ROW][C]32[/C][C]35[/C][C]36.3543570085358[/C][C]-1.35435700853583[/C][/ROW]
[ROW][C]33[/C][C]35[/C][C]32.9230951593982[/C][C]2.07690484060184[/C][/ROW]
[ROW][C]34[/C][C]33[/C][C]31.7047031361017[/C][C]1.29529686389829[/C][/ROW]
[ROW][C]35[/C][C]36[/C][C]32.130066415141[/C][C]3.86993358485899[/C][/ROW]
[ROW][C]36[/C][C]32[/C][C]34.8472742148992[/C][C]-2.8472742148992[/C][/ROW]
[ROW][C]37[/C][C]33[/C][C]35.6834872639909[/C][C]-2.68348726399092[/C][/ROW]
[ROW][C]38[/C][C]34[/C][C]34.4543939081874[/C][C]-0.454393908187432[/C][/ROW]
[ROW][C]39[/C][C]32[/C][C]35.0052020642351[/C][C]-3.00520206423514[/C][/ROW]
[ROW][C]40[/C][C]34[/C][C]33.601899448847[/C][C]0.398100551152953[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185987&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185987&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
13837.6247179262230.375282073776949
23736.55746505303650.442534946963499
33333.0935290244184-0.0935290244183628
43134.6432821218873-3.64328212188729
53935.18692172837263.8130782716274
64437.52711477640566.47288522359442
73335.6834872639909-2.68348726399092
83533.4968496836341.50315031636598
93234.0986302901657-2.09863029016573
102831.4844251459809-3.48442514598091
114036.47802704587743.52197295412263
122731.5585050481466-4.55850504814663
133735.96206274111061.03793725888942
143232.378811264993-0.378811264992972
152826.74443497294851.25556502705148
163433.25064574276920.74935425723078
173031.9422448127937-1.94224481279374
183533.24183609427891.75816390572107
193133.6456629588781-2.64566295887805
203233.2830159583925-1.28301595839245
213035.3743134930398-5.37431349303976
223035.8861186846579-5.88611868465786
233130.31300070197310.686999298026937
244033.65287449513656.34712550486354
253232.0330300341477-0.0330300341477463
263633.32173948119752.67826051880249
273233.0752004520545-1.07520045205452
283532.08851812820932.91148187179065
293836.7190769131171.280923086883
304236.04951840674525.9504815932548
313436.9004609360816-2.90046093608164
323536.3543570085358-1.35435700853583
333532.92309515939822.07690484060184
343331.70470313610171.29529686389829
353632.1300664151413.86993358485899
363234.8472742148992-2.8472742148992
373335.6834872639909-2.68348726399092
383434.4543939081874-0.454393908187432
393235.0052020642351-3.00520206423514
403433.6018994488470.398100551152953







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
110.4214705114432750.842941022886550.578529488556725
120.5968403172176650.806319365564670.403159682782335
130.459025905230470.9180518104609410.54097409476953
140.5009055641789390.9981888716421220.499094435821061
150.4698762086010660.9397524172021320.530123791398934
160.4260555915120380.8521111830240760.573944408487962
170.3819453239557140.7638906479114270.618054676044286
180.2900067602822320.5800135205644640.709993239717768
190.3817069746367150.763413949273430.618293025363285
200.3545284140450710.7090568280901420.645471585954929
210.5769830371162970.8460339257674060.423016962883703
220.7859039531031340.4281920937937330.214096046896866
230.6901042697260990.6197914605478030.309895730273901
240.9597616570542980.08047668589140340.0402383429457017
250.9382993205423430.1234013589153150.0617006794576574
260.9597718308746990.08045633825060210.040228169125301
270.9540770652897590.09184586942048130.0459229347102407
280.9027686717215160.1944626565569690.0972313282784843
290.7937201408829430.4125597182341150.206279859117058

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
11 & 0.421470511443275 & 0.84294102288655 & 0.578529488556725 \tabularnewline
12 & 0.596840317217665 & 0.80631936556467 & 0.403159682782335 \tabularnewline
13 & 0.45902590523047 & 0.918051810460941 & 0.54097409476953 \tabularnewline
14 & 0.500905564178939 & 0.998188871642122 & 0.499094435821061 \tabularnewline
15 & 0.469876208601066 & 0.939752417202132 & 0.530123791398934 \tabularnewline
16 & 0.426055591512038 & 0.852111183024076 & 0.573944408487962 \tabularnewline
17 & 0.381945323955714 & 0.763890647911427 & 0.618054676044286 \tabularnewline
18 & 0.290006760282232 & 0.580013520564464 & 0.709993239717768 \tabularnewline
19 & 0.381706974636715 & 0.76341394927343 & 0.618293025363285 \tabularnewline
20 & 0.354528414045071 & 0.709056828090142 & 0.645471585954929 \tabularnewline
21 & 0.576983037116297 & 0.846033925767406 & 0.423016962883703 \tabularnewline
22 & 0.785903953103134 & 0.428192093793733 & 0.214096046896866 \tabularnewline
23 & 0.690104269726099 & 0.619791460547803 & 0.309895730273901 \tabularnewline
24 & 0.959761657054298 & 0.0804766858914034 & 0.0402383429457017 \tabularnewline
25 & 0.938299320542343 & 0.123401358915315 & 0.0617006794576574 \tabularnewline
26 & 0.959771830874699 & 0.0804563382506021 & 0.040228169125301 \tabularnewline
27 & 0.954077065289759 & 0.0918458694204813 & 0.0459229347102407 \tabularnewline
28 & 0.902768671721516 & 0.194462656556969 & 0.0972313282784843 \tabularnewline
29 & 0.793720140882943 & 0.412559718234115 & 0.206279859117058 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185987&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]11[/C][C]0.421470511443275[/C][C]0.84294102288655[/C][C]0.578529488556725[/C][/ROW]
[ROW][C]12[/C][C]0.596840317217665[/C][C]0.80631936556467[/C][C]0.403159682782335[/C][/ROW]
[ROW][C]13[/C][C]0.45902590523047[/C][C]0.918051810460941[/C][C]0.54097409476953[/C][/ROW]
[ROW][C]14[/C][C]0.500905564178939[/C][C]0.998188871642122[/C][C]0.499094435821061[/C][/ROW]
[ROW][C]15[/C][C]0.469876208601066[/C][C]0.939752417202132[/C][C]0.530123791398934[/C][/ROW]
[ROW][C]16[/C][C]0.426055591512038[/C][C]0.852111183024076[/C][C]0.573944408487962[/C][/ROW]
[ROW][C]17[/C][C]0.381945323955714[/C][C]0.763890647911427[/C][C]0.618054676044286[/C][/ROW]
[ROW][C]18[/C][C]0.290006760282232[/C][C]0.580013520564464[/C][C]0.709993239717768[/C][/ROW]
[ROW][C]19[/C][C]0.381706974636715[/C][C]0.76341394927343[/C][C]0.618293025363285[/C][/ROW]
[ROW][C]20[/C][C]0.354528414045071[/C][C]0.709056828090142[/C][C]0.645471585954929[/C][/ROW]
[ROW][C]21[/C][C]0.576983037116297[/C][C]0.846033925767406[/C][C]0.423016962883703[/C][/ROW]
[ROW][C]22[/C][C]0.785903953103134[/C][C]0.428192093793733[/C][C]0.214096046896866[/C][/ROW]
[ROW][C]23[/C][C]0.690104269726099[/C][C]0.619791460547803[/C][C]0.309895730273901[/C][/ROW]
[ROW][C]24[/C][C]0.959761657054298[/C][C]0.0804766858914034[/C][C]0.0402383429457017[/C][/ROW]
[ROW][C]25[/C][C]0.938299320542343[/C][C]0.123401358915315[/C][C]0.0617006794576574[/C][/ROW]
[ROW][C]26[/C][C]0.959771830874699[/C][C]0.0804563382506021[/C][C]0.040228169125301[/C][/ROW]
[ROW][C]27[/C][C]0.954077065289759[/C][C]0.0918458694204813[/C][C]0.0459229347102407[/C][/ROW]
[ROW][C]28[/C][C]0.902768671721516[/C][C]0.194462656556969[/C][C]0.0972313282784843[/C][/ROW]
[ROW][C]29[/C][C]0.793720140882943[/C][C]0.412559718234115[/C][C]0.206279859117058[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185987&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185987&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
110.4214705114432750.842941022886550.578529488556725
120.5968403172176650.806319365564670.403159682782335
130.459025905230470.9180518104609410.54097409476953
140.5009055641789390.9981888716421220.499094435821061
150.4698762086010660.9397524172021320.530123791398934
160.4260555915120380.8521111830240760.573944408487962
170.3819453239557140.7638906479114270.618054676044286
180.2900067602822320.5800135205644640.709993239717768
190.3817069746367150.763413949273430.618293025363285
200.3545284140450710.7090568280901420.645471585954929
210.5769830371162970.8460339257674060.423016962883703
220.7859039531031340.4281920937937330.214096046896866
230.6901042697260990.6197914605478030.309895730273901
240.9597616570542980.08047668589140340.0402383429457017
250.9382993205423430.1234013589153150.0617006794576574
260.9597718308746990.08045633825060210.040228169125301
270.9540770652897590.09184586942048130.0459229347102407
280.9027686717215160.1944626565569690.0972313282784843
290.7937201408829430.4125597182341150.206279859117058







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level30.157894736842105NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 3 & 0.157894736842105 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=185987&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]3[/C][C]0.157894736842105[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=185987&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=185987&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 level00OK
5% type I error level00OK
10% type I error level30.157894736842105NOK



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')
}