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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 computationTue, 24 Nov 2009 11:17:39 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/24/t12590869326ey6enmylhu51jc.htm/, Retrieved Mon, 22 Jul 2024 19:33:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59205, Retrieved Mon, 22 Jul 2024 19:33:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact186
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-   PD    [Multiple Regression] [] [2009-11-20 13:55:26] [5482608004c1d7bbf873930172393a2d]
-   PD        [Multiple Regression] [Workshop6/module1] [2009-11-24 18:17:39] [f94f05f163a3ee3ab544c4fef41db0eb] [Current]
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Dataseries X:
114.08	136.49
112.95	142.62
135.31	141.71
134.31	149.51
133.03	147.39
140.11	131.96
124.69	136.38
131.68	127.34
150.95	133.85
137.26	125.14
130.51	141.25
143.15	149.32
118.01	120.92
122.56	134.85
147.97	131.93
135.74	134.22
151.62	143.07
154.82	145.37
145.59	134.32
147.12	126.31
175.86	162.21
140.66	124.09
152.69	153.91
154.38	154.34
132.45	138.70
136.44	150.98
153.24	146.39
154.11	178.30
155.93	168.23
142.53	162.52
148.73	158.86
147.73	152.17
166.79	171.01
144.30	171.49
156.07	189.62
161.70	177.46
152.10	179.98
140.45	156.96
155.56	167.89
174.53	194.78
167.16	192.78
159.48	165.06
173.22	196.60
176.13	151.64
180.31	187.02
185.84	210.99
169.43	219.08
195.25	235.68
174.99	241.44
156.42	187.46
182.08	229.57
182.00	208.44
153.28	215.09
136.72	217.00
130.19	171.08
132.04	178.41
143.89	196.34
133.38	172.11
127.98	154.93
150.45	182.26
133.55	181.74




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59205&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59205&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59205&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
InvoerEU[t] = + 90.7172722565875 + 0.390789979219476InvoerAM[t] -18.2713893456953M1[t] -17.3592425044589M2[t] + 0.221347720986538M3[t] -2.20547816051791M4[t] -6.24186513507341M5[t] -8.22411062064349M6[t] -8.5439528631746M7[t] -1.29139665823474M8[t] + 6.37482333788861M9[t] -5.25423247582743M10[t] -10.5025775073663M11[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
InvoerEU[t] =  +  90.7172722565875 +  0.390789979219476InvoerAM[t] -18.2713893456953M1[t] -17.3592425044589M2[t] +  0.221347720986538M3[t] -2.20547816051791M4[t] -6.24186513507341M5[t] -8.22411062064349M6[t] -8.5439528631746M7[t] -1.29139665823474M8[t] +  6.37482333788861M9[t] -5.25423247582743M10[t] -10.5025775073663M11[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59205&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]InvoerEU[t] =  +  90.7172722565875 +  0.390789979219476InvoerAM[t] -18.2713893456953M1[t] -17.3592425044589M2[t] +  0.221347720986538M3[t] -2.20547816051791M4[t] -6.24186513507341M5[t] -8.22411062064349M6[t] -8.5439528631746M7[t] -1.29139665823474M8[t] +  6.37482333788861M9[t] -5.25423247582743M10[t] -10.5025775073663M11[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59205&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59205&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
InvoerEU[t] = + 90.7172722565875 + 0.390789979219476InvoerAM[t] -18.2713893456953M1[t] -17.3592425044589M2[t] + 0.221347720986538M3[t] -2.20547816051791M4[t] -6.24186513507341M5[t] -8.22411062064349M6[t] -8.5439528631746M7[t] -1.29139665823474M8[t] + 6.37482333788861M9[t] -5.25423247582743M10[t] -10.5025775073663M11[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)90.717272256587512.2525277.40400
InvoerAM0.3907899792194760.05956.567900
M1-18.27138934569538.123873-2.24910.0291310.014566
M2-17.35924250445898.577429-2.02380.0485740.024287
M30.2213477209865388.500560.0260.9793340.489667
M4-2.205478160517918.454535-0.26090.7953140.397657
M5-6.241865135073418.453807-0.73830.4638970.231948
M6-8.224110620643498.494714-0.96810.3378250.168913
M7-8.54395286317468.531436-1.00150.3216230.160812
M8-1.291396658234748.665364-0.1490.8821550.441077
M96.374823337888618.4647610.75310.4550670.227533
M10-5.254232475827438.520668-0.61660.5403820.270191
M11-10.50257750736638.458542-1.24170.2203980.110199

\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) & 90.7172722565875 & 12.252527 & 7.404 & 0 & 0 \tabularnewline
InvoerAM & 0.390789979219476 & 0.0595 & 6.5679 & 0 & 0 \tabularnewline
M1 & -18.2713893456953 & 8.123873 & -2.2491 & 0.029131 & 0.014566 \tabularnewline
M2 & -17.3592425044589 & 8.577429 & -2.0238 & 0.048574 & 0.024287 \tabularnewline
M3 & 0.221347720986538 & 8.50056 & 0.026 & 0.979334 & 0.489667 \tabularnewline
M4 & -2.20547816051791 & 8.454535 & -0.2609 & 0.795314 & 0.397657 \tabularnewline
M5 & -6.24186513507341 & 8.453807 & -0.7383 & 0.463897 & 0.231948 \tabularnewline
M6 & -8.22411062064349 & 8.494714 & -0.9681 & 0.337825 & 0.168913 \tabularnewline
M7 & -8.5439528631746 & 8.531436 & -1.0015 & 0.321623 & 0.160812 \tabularnewline
M8 & -1.29139665823474 & 8.665364 & -0.149 & 0.882155 & 0.441077 \tabularnewline
M9 & 6.37482333788861 & 8.464761 & 0.7531 & 0.455067 & 0.227533 \tabularnewline
M10 & -5.25423247582743 & 8.520668 & -0.6166 & 0.540382 & 0.270191 \tabularnewline
M11 & -10.5025775073663 & 8.458542 & -1.2417 & 0.220398 & 0.110199 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59205&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]90.7172722565875[/C][C]12.252527[/C][C]7.404[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]InvoerAM[/C][C]0.390789979219476[/C][C]0.0595[/C][C]6.5679[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-18.2713893456953[/C][C]8.123873[/C][C]-2.2491[/C][C]0.029131[/C][C]0.014566[/C][/ROW]
[ROW][C]M2[/C][C]-17.3592425044589[/C][C]8.577429[/C][C]-2.0238[/C][C]0.048574[/C][C]0.024287[/C][/ROW]
[ROW][C]M3[/C][C]0.221347720986538[/C][C]8.50056[/C][C]0.026[/C][C]0.979334[/C][C]0.489667[/C][/ROW]
[ROW][C]M4[/C][C]-2.20547816051791[/C][C]8.454535[/C][C]-0.2609[/C][C]0.795314[/C][C]0.397657[/C][/ROW]
[ROW][C]M5[/C][C]-6.24186513507341[/C][C]8.453807[/C][C]-0.7383[/C][C]0.463897[/C][C]0.231948[/C][/ROW]
[ROW][C]M6[/C][C]-8.22411062064349[/C][C]8.494714[/C][C]-0.9681[/C][C]0.337825[/C][C]0.168913[/C][/ROW]
[ROW][C]M7[/C][C]-8.5439528631746[/C][C]8.531436[/C][C]-1.0015[/C][C]0.321623[/C][C]0.160812[/C][/ROW]
[ROW][C]M8[/C][C]-1.29139665823474[/C][C]8.665364[/C][C]-0.149[/C][C]0.882155[/C][C]0.441077[/C][/ROW]
[ROW][C]M9[/C][C]6.37482333788861[/C][C]8.464761[/C][C]0.7531[/C][C]0.455067[/C][C]0.227533[/C][/ROW]
[ROW][C]M10[/C][C]-5.25423247582743[/C][C]8.520668[/C][C]-0.6166[/C][C]0.540382[/C][C]0.270191[/C][/ROW]
[ROW][C]M11[/C][C]-10.5025775073663[/C][C]8.458542[/C][C]-1.2417[/C][C]0.220398[/C][C]0.110199[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59205&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59205&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)90.717272256587512.2525277.40400
InvoerAM0.3907899792194760.05956.567900
M1-18.27138934569538.123873-2.24910.0291310.014566
M2-17.35924250445898.577429-2.02380.0485740.024287
M30.2213477209865388.500560.0260.9793340.489667
M4-2.205478160517918.454535-0.26090.7953140.397657
M5-6.241865135073418.453807-0.73830.4638970.231948
M6-8.224110620643498.494714-0.96810.3378250.168913
M7-8.54395286317468.531436-1.00150.3216230.160812
M8-1.291396658234748.665364-0.1490.8821550.441077
M96.374823337888618.4647610.75310.4550670.227533
M10-5.254232475827438.520668-0.61660.5403820.270191
M11-10.50257750736638.458542-1.24170.2203980.110199







Multiple Linear Regression - Regression Statistics
Multiple R0.76477950540453
R-squared0.584887691886798
Adjusted R-squared0.481109614858498
F-TEST (value)5.63594651813888
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value6.45611813276936e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation13.3526474338707
Sum Squared Residuals8558.07328767618

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.76477950540453 \tabularnewline
R-squared & 0.584887691886798 \tabularnewline
Adjusted R-squared & 0.481109614858498 \tabularnewline
F-TEST (value) & 5.63594651813888 \tabularnewline
F-TEST (DF numerator) & 12 \tabularnewline
F-TEST (DF denominator) & 48 \tabularnewline
p-value & 6.45611813276936e-06 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 13.3526474338707 \tabularnewline
Sum Squared Residuals & 8558.07328767618 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59205&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.76477950540453[/C][/ROW]
[ROW][C]R-squared[/C][C]0.584887691886798[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.481109614858498[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]5.63594651813888[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]12[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]48[/C][/ROW]
[ROW][C]p-value[/C][C]6.45611813276936e-06[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]13.3526474338707[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]8558.07328767618[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59205&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59205&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 R0.76477950540453
R-squared0.584887691886798
Adjusted R-squared0.481109614858498
F-TEST (value)5.63594651813888
F-TEST (DF numerator)12
F-TEST (DF denominator)48
p-value6.45611813276936e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation13.3526474338707
Sum Squared Residuals8558.07328767618







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1114.08125.784807174559-11.7048071745590
2112.95129.092496588410-16.1424965884104
3135.31146.317467932766-11.0074679327661
4134.31146.938803889174-12.6288038891735
5133.03142.073942158673-9.04394215867274
6140.11134.0618072937466.04819270625387
7124.69135.469256759365-10.7792567593651
8131.68139.189071552161-7.5090715521609
9150.95149.3993343130031.55066568699694
10137.26134.3664977802852.89350221971461
11130.51135.413779313972-4.90377931397221
12143.15149.070031953640-5.92003195363972
13118.01119.700207198111-1.69020719811132
14122.56126.056058449875-3.49605844987504
15147.97142.4955419360005.47445806400042
16135.74140.963625106908-5.22362510690773
17151.62140.38572944844511.2342705515554
18154.82139.30230091507915.5176990849207
19145.59134.66422940217310.9257705978270
20147.12138.7865578735658.33344212643516
21175.86160.48213812366715.3778618763326
22140.66133.9561683021056.70383169789507
23152.69140.36118045089112.3288195491092
24154.38151.0317976493223.34820235067849
25132.45126.6484530286345.80154697136638
26136.44132.3595008146854.08049918531481
27153.24148.1463650355135.09363496448681
28154.11158.189647390902-4.07964739090224
29155.93150.2180053256075.71199467439339
30142.53146.004349058693-3.47434905869334
31148.73144.2542154922194.47578450778104
32147.73148.892386736180-1.16238673618050
33166.79163.9210899407992.86891005920120
34144.3152.479613317108-8.17961331710809
35156.07154.3162906088181.75370939118171
36161.7160.0668619688761.63313803112419
37152.1142.7802633708149.3197366291864
38140.45134.6964248904185.75357510958232
39155.56156.548349588732-0.988349588731937
40174.53164.6298662484399.90013375156078
41167.16159.8118993154457.34810068455523
42159.48146.99695560591112.4830443940892
43173.22159.00262930796214.2173706920380
44176.13148.68526804719427.4447319528058
45180.31170.17763750810310.1323624918974
46185.84167.91581749627717.9241825037226
47169.43165.8289633966243.60103660337595
48195.25182.81865455903412.4313454409663
49174.99166.7982154936438.19178450635741
50156.42146.6155192566129.8044807433883
51182.08180.6522755069891.42772449301077
52182169.96805736457712.0319426354227
53153.28168.530423751831-15.2504237518313
54136.72167.294587126570-30.5745871265704
55130.19149.029669038281-18.8396690382810
56132.04159.146715790900-27.1067157908995
57143.89173.819800114428-29.9298001144281
58133.38152.721903104224-19.3419031042242
59127.98140.759786229695-12.7797862296947
60150.45161.942653869129-11.4926538691293
61133.55143.46805373424-9.91805373423986

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 114.08 & 125.784807174559 & -11.7048071745590 \tabularnewline
2 & 112.95 & 129.092496588410 & -16.1424965884104 \tabularnewline
3 & 135.31 & 146.317467932766 & -11.0074679327661 \tabularnewline
4 & 134.31 & 146.938803889174 & -12.6288038891735 \tabularnewline
5 & 133.03 & 142.073942158673 & -9.04394215867274 \tabularnewline
6 & 140.11 & 134.061807293746 & 6.04819270625387 \tabularnewline
7 & 124.69 & 135.469256759365 & -10.7792567593651 \tabularnewline
8 & 131.68 & 139.189071552161 & -7.5090715521609 \tabularnewline
9 & 150.95 & 149.399334313003 & 1.55066568699694 \tabularnewline
10 & 137.26 & 134.366497780285 & 2.89350221971461 \tabularnewline
11 & 130.51 & 135.413779313972 & -4.90377931397221 \tabularnewline
12 & 143.15 & 149.070031953640 & -5.92003195363972 \tabularnewline
13 & 118.01 & 119.700207198111 & -1.69020719811132 \tabularnewline
14 & 122.56 & 126.056058449875 & -3.49605844987504 \tabularnewline
15 & 147.97 & 142.495541936000 & 5.47445806400042 \tabularnewline
16 & 135.74 & 140.963625106908 & -5.22362510690773 \tabularnewline
17 & 151.62 & 140.385729448445 & 11.2342705515554 \tabularnewline
18 & 154.82 & 139.302300915079 & 15.5176990849207 \tabularnewline
19 & 145.59 & 134.664229402173 & 10.9257705978270 \tabularnewline
20 & 147.12 & 138.786557873565 & 8.33344212643516 \tabularnewline
21 & 175.86 & 160.482138123667 & 15.3778618763326 \tabularnewline
22 & 140.66 & 133.956168302105 & 6.70383169789507 \tabularnewline
23 & 152.69 & 140.361180450891 & 12.3288195491092 \tabularnewline
24 & 154.38 & 151.031797649322 & 3.34820235067849 \tabularnewline
25 & 132.45 & 126.648453028634 & 5.80154697136638 \tabularnewline
26 & 136.44 & 132.359500814685 & 4.08049918531481 \tabularnewline
27 & 153.24 & 148.146365035513 & 5.09363496448681 \tabularnewline
28 & 154.11 & 158.189647390902 & -4.07964739090224 \tabularnewline
29 & 155.93 & 150.218005325607 & 5.71199467439339 \tabularnewline
30 & 142.53 & 146.004349058693 & -3.47434905869334 \tabularnewline
31 & 148.73 & 144.254215492219 & 4.47578450778104 \tabularnewline
32 & 147.73 & 148.892386736180 & -1.16238673618050 \tabularnewline
33 & 166.79 & 163.921089940799 & 2.86891005920120 \tabularnewline
34 & 144.3 & 152.479613317108 & -8.17961331710809 \tabularnewline
35 & 156.07 & 154.316290608818 & 1.75370939118171 \tabularnewline
36 & 161.7 & 160.066861968876 & 1.63313803112419 \tabularnewline
37 & 152.1 & 142.780263370814 & 9.3197366291864 \tabularnewline
38 & 140.45 & 134.696424890418 & 5.75357510958232 \tabularnewline
39 & 155.56 & 156.548349588732 & -0.988349588731937 \tabularnewline
40 & 174.53 & 164.629866248439 & 9.90013375156078 \tabularnewline
41 & 167.16 & 159.811899315445 & 7.34810068455523 \tabularnewline
42 & 159.48 & 146.996955605911 & 12.4830443940892 \tabularnewline
43 & 173.22 & 159.002629307962 & 14.2173706920380 \tabularnewline
44 & 176.13 & 148.685268047194 & 27.4447319528058 \tabularnewline
45 & 180.31 & 170.177637508103 & 10.1323624918974 \tabularnewline
46 & 185.84 & 167.915817496277 & 17.9241825037226 \tabularnewline
47 & 169.43 & 165.828963396624 & 3.60103660337595 \tabularnewline
48 & 195.25 & 182.818654559034 & 12.4313454409663 \tabularnewline
49 & 174.99 & 166.798215493643 & 8.19178450635741 \tabularnewline
50 & 156.42 & 146.615519256612 & 9.8044807433883 \tabularnewline
51 & 182.08 & 180.652275506989 & 1.42772449301077 \tabularnewline
52 & 182 & 169.968057364577 & 12.0319426354227 \tabularnewline
53 & 153.28 & 168.530423751831 & -15.2504237518313 \tabularnewline
54 & 136.72 & 167.294587126570 & -30.5745871265704 \tabularnewline
55 & 130.19 & 149.029669038281 & -18.8396690382810 \tabularnewline
56 & 132.04 & 159.146715790900 & -27.1067157908995 \tabularnewline
57 & 143.89 & 173.819800114428 & -29.9298001144281 \tabularnewline
58 & 133.38 & 152.721903104224 & -19.3419031042242 \tabularnewline
59 & 127.98 & 140.759786229695 & -12.7797862296947 \tabularnewline
60 & 150.45 & 161.942653869129 & -11.4926538691293 \tabularnewline
61 & 133.55 & 143.46805373424 & -9.91805373423986 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59205&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]114.08[/C][C]125.784807174559[/C][C]-11.7048071745590[/C][/ROW]
[ROW][C]2[/C][C]112.95[/C][C]129.092496588410[/C][C]-16.1424965884104[/C][/ROW]
[ROW][C]3[/C][C]135.31[/C][C]146.317467932766[/C][C]-11.0074679327661[/C][/ROW]
[ROW][C]4[/C][C]134.31[/C][C]146.938803889174[/C][C]-12.6288038891735[/C][/ROW]
[ROW][C]5[/C][C]133.03[/C][C]142.073942158673[/C][C]-9.04394215867274[/C][/ROW]
[ROW][C]6[/C][C]140.11[/C][C]134.061807293746[/C][C]6.04819270625387[/C][/ROW]
[ROW][C]7[/C][C]124.69[/C][C]135.469256759365[/C][C]-10.7792567593651[/C][/ROW]
[ROW][C]8[/C][C]131.68[/C][C]139.189071552161[/C][C]-7.5090715521609[/C][/ROW]
[ROW][C]9[/C][C]150.95[/C][C]149.399334313003[/C][C]1.55066568699694[/C][/ROW]
[ROW][C]10[/C][C]137.26[/C][C]134.366497780285[/C][C]2.89350221971461[/C][/ROW]
[ROW][C]11[/C][C]130.51[/C][C]135.413779313972[/C][C]-4.90377931397221[/C][/ROW]
[ROW][C]12[/C][C]143.15[/C][C]149.070031953640[/C][C]-5.92003195363972[/C][/ROW]
[ROW][C]13[/C][C]118.01[/C][C]119.700207198111[/C][C]-1.69020719811132[/C][/ROW]
[ROW][C]14[/C][C]122.56[/C][C]126.056058449875[/C][C]-3.49605844987504[/C][/ROW]
[ROW][C]15[/C][C]147.97[/C][C]142.495541936000[/C][C]5.47445806400042[/C][/ROW]
[ROW][C]16[/C][C]135.74[/C][C]140.963625106908[/C][C]-5.22362510690773[/C][/ROW]
[ROW][C]17[/C][C]151.62[/C][C]140.385729448445[/C][C]11.2342705515554[/C][/ROW]
[ROW][C]18[/C][C]154.82[/C][C]139.302300915079[/C][C]15.5176990849207[/C][/ROW]
[ROW][C]19[/C][C]145.59[/C][C]134.664229402173[/C][C]10.9257705978270[/C][/ROW]
[ROW][C]20[/C][C]147.12[/C][C]138.786557873565[/C][C]8.33344212643516[/C][/ROW]
[ROW][C]21[/C][C]175.86[/C][C]160.482138123667[/C][C]15.3778618763326[/C][/ROW]
[ROW][C]22[/C][C]140.66[/C][C]133.956168302105[/C][C]6.70383169789507[/C][/ROW]
[ROW][C]23[/C][C]152.69[/C][C]140.361180450891[/C][C]12.3288195491092[/C][/ROW]
[ROW][C]24[/C][C]154.38[/C][C]151.031797649322[/C][C]3.34820235067849[/C][/ROW]
[ROW][C]25[/C][C]132.45[/C][C]126.648453028634[/C][C]5.80154697136638[/C][/ROW]
[ROW][C]26[/C][C]136.44[/C][C]132.359500814685[/C][C]4.08049918531481[/C][/ROW]
[ROW][C]27[/C][C]153.24[/C][C]148.146365035513[/C][C]5.09363496448681[/C][/ROW]
[ROW][C]28[/C][C]154.11[/C][C]158.189647390902[/C][C]-4.07964739090224[/C][/ROW]
[ROW][C]29[/C][C]155.93[/C][C]150.218005325607[/C][C]5.71199467439339[/C][/ROW]
[ROW][C]30[/C][C]142.53[/C][C]146.004349058693[/C][C]-3.47434905869334[/C][/ROW]
[ROW][C]31[/C][C]148.73[/C][C]144.254215492219[/C][C]4.47578450778104[/C][/ROW]
[ROW][C]32[/C][C]147.73[/C][C]148.892386736180[/C][C]-1.16238673618050[/C][/ROW]
[ROW][C]33[/C][C]166.79[/C][C]163.921089940799[/C][C]2.86891005920120[/C][/ROW]
[ROW][C]34[/C][C]144.3[/C][C]152.479613317108[/C][C]-8.17961331710809[/C][/ROW]
[ROW][C]35[/C][C]156.07[/C][C]154.316290608818[/C][C]1.75370939118171[/C][/ROW]
[ROW][C]36[/C][C]161.7[/C][C]160.066861968876[/C][C]1.63313803112419[/C][/ROW]
[ROW][C]37[/C][C]152.1[/C][C]142.780263370814[/C][C]9.3197366291864[/C][/ROW]
[ROW][C]38[/C][C]140.45[/C][C]134.696424890418[/C][C]5.75357510958232[/C][/ROW]
[ROW][C]39[/C][C]155.56[/C][C]156.548349588732[/C][C]-0.988349588731937[/C][/ROW]
[ROW][C]40[/C][C]174.53[/C][C]164.629866248439[/C][C]9.90013375156078[/C][/ROW]
[ROW][C]41[/C][C]167.16[/C][C]159.811899315445[/C][C]7.34810068455523[/C][/ROW]
[ROW][C]42[/C][C]159.48[/C][C]146.996955605911[/C][C]12.4830443940892[/C][/ROW]
[ROW][C]43[/C][C]173.22[/C][C]159.002629307962[/C][C]14.2173706920380[/C][/ROW]
[ROW][C]44[/C][C]176.13[/C][C]148.685268047194[/C][C]27.4447319528058[/C][/ROW]
[ROW][C]45[/C][C]180.31[/C][C]170.177637508103[/C][C]10.1323624918974[/C][/ROW]
[ROW][C]46[/C][C]185.84[/C][C]167.915817496277[/C][C]17.9241825037226[/C][/ROW]
[ROW][C]47[/C][C]169.43[/C][C]165.828963396624[/C][C]3.60103660337595[/C][/ROW]
[ROW][C]48[/C][C]195.25[/C][C]182.818654559034[/C][C]12.4313454409663[/C][/ROW]
[ROW][C]49[/C][C]174.99[/C][C]166.798215493643[/C][C]8.19178450635741[/C][/ROW]
[ROW][C]50[/C][C]156.42[/C][C]146.615519256612[/C][C]9.8044807433883[/C][/ROW]
[ROW][C]51[/C][C]182.08[/C][C]180.652275506989[/C][C]1.42772449301077[/C][/ROW]
[ROW][C]52[/C][C]182[/C][C]169.968057364577[/C][C]12.0319426354227[/C][/ROW]
[ROW][C]53[/C][C]153.28[/C][C]168.530423751831[/C][C]-15.2504237518313[/C][/ROW]
[ROW][C]54[/C][C]136.72[/C][C]167.294587126570[/C][C]-30.5745871265704[/C][/ROW]
[ROW][C]55[/C][C]130.19[/C][C]149.029669038281[/C][C]-18.8396690382810[/C][/ROW]
[ROW][C]56[/C][C]132.04[/C][C]159.146715790900[/C][C]-27.1067157908995[/C][/ROW]
[ROW][C]57[/C][C]143.89[/C][C]173.819800114428[/C][C]-29.9298001144281[/C][/ROW]
[ROW][C]58[/C][C]133.38[/C][C]152.721903104224[/C][C]-19.3419031042242[/C][/ROW]
[ROW][C]59[/C][C]127.98[/C][C]140.759786229695[/C][C]-12.7797862296947[/C][/ROW]
[ROW][C]60[/C][C]150.45[/C][C]161.942653869129[/C][C]-11.4926538691293[/C][/ROW]
[ROW][C]61[/C][C]133.55[/C][C]143.46805373424[/C][C]-9.91805373423986[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59205&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59205&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
1114.08125.784807174559-11.7048071745590
2112.95129.092496588410-16.1424965884104
3135.31146.317467932766-11.0074679327661
4134.31146.938803889174-12.6288038891735
5133.03142.073942158673-9.04394215867274
6140.11134.0618072937466.04819270625387
7124.69135.469256759365-10.7792567593651
8131.68139.189071552161-7.5090715521609
9150.95149.3993343130031.55066568699694
10137.26134.3664977802852.89350221971461
11130.51135.413779313972-4.90377931397221
12143.15149.070031953640-5.92003195363972
13118.01119.700207198111-1.69020719811132
14122.56126.056058449875-3.49605844987504
15147.97142.4955419360005.47445806400042
16135.74140.963625106908-5.22362510690773
17151.62140.38572944844511.2342705515554
18154.82139.30230091507915.5176990849207
19145.59134.66422940217310.9257705978270
20147.12138.7865578735658.33344212643516
21175.86160.48213812366715.3778618763326
22140.66133.9561683021056.70383169789507
23152.69140.36118045089112.3288195491092
24154.38151.0317976493223.34820235067849
25132.45126.6484530286345.80154697136638
26136.44132.3595008146854.08049918531481
27153.24148.1463650355135.09363496448681
28154.11158.189647390902-4.07964739090224
29155.93150.2180053256075.71199467439339
30142.53146.004349058693-3.47434905869334
31148.73144.2542154922194.47578450778104
32147.73148.892386736180-1.16238673618050
33166.79163.9210899407992.86891005920120
34144.3152.479613317108-8.17961331710809
35156.07154.3162906088181.75370939118171
36161.7160.0668619688761.63313803112419
37152.1142.7802633708149.3197366291864
38140.45134.6964248904185.75357510958232
39155.56156.548349588732-0.988349588731937
40174.53164.6298662484399.90013375156078
41167.16159.8118993154457.34810068455523
42159.48146.99695560591112.4830443940892
43173.22159.00262930796214.2173706920380
44176.13148.68526804719427.4447319528058
45180.31170.17763750810310.1323624918974
46185.84167.91581749627717.9241825037226
47169.43165.8289633966243.60103660337595
48195.25182.81865455903412.4313454409663
49174.99166.7982154936438.19178450635741
50156.42146.6155192566129.8044807433883
51182.08180.6522755069891.42772449301077
52182169.96805736457712.0319426354227
53153.28168.530423751831-15.2504237518313
54136.72167.294587126570-30.5745871265704
55130.19149.029669038281-18.8396690382810
56132.04159.146715790900-27.1067157908995
57143.89173.819800114428-29.9298001144281
58133.38152.721903104224-19.3419031042242
59127.98140.759786229695-12.7797862296947
60150.45161.942653869129-11.4926538691293
61133.55143.46805373424-9.91805373423986







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.04863387348192880.09726774696385770.951366126518071
170.08550241210522660.1710048242104530.914497587894773
180.1363817609510640.2727635219021280.863618239048936
190.1682842636523920.3365685273047830.831715736347608
200.1419975514457170.2839951028914340.858002448554283
210.1940633974479000.3881267948957990.8059366025521
220.1256860604270970.2513721208541950.874313939572903
230.1215595088662860.2431190177325710.878440491133714
240.08183329588462130.1636665917692430.918166704115379
250.06108482678758190.1221696535751640.938915173212418
260.04505131586943780.09010263173887570.954948684130562
270.02688590249358850.05377180498717690.973114097506412
280.01646082458890390.03292164917780770.983539175411096
290.008891208051132040.01778241610226410.991108791948868
300.009224899193330840.01844979838666170.990775100806669
310.00476335779179520.00952671558359040.995236642208205
320.002321913869338620.004643827738677240.997678086130661
330.001363067508554670.002726135017109330.998636932491445
340.0009578224074018180.001915644814803640.999042177592598
350.0004151666292405520.0008303332584811040.99958483337076
360.0001714719686652960.0003429439373305920.999828528031335
370.0001145674883032610.0002291349766065210.999885432511697
385.84924889815724e-050.0001169849779631450.999941507511018
392.02215353975267e-054.04430707950534e-050.999979778464603
401.30628728061160e-052.61257456122319e-050.999986937127194
416.76569317837849e-061.35313863567570e-050.999993234306822
423.98026062621464e-057.96052125242928e-050.999960197393738
433.30720316337286e-056.61440632674571e-050.999966927968366
440.01591328586085170.03182657172170330.984086714139148
450.3316432114509140.6632864229018280.668356788549086

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
16 & 0.0486338734819288 & 0.0972677469638577 & 0.951366126518071 \tabularnewline
17 & 0.0855024121052266 & 0.171004824210453 & 0.914497587894773 \tabularnewline
18 & 0.136381760951064 & 0.272763521902128 & 0.863618239048936 \tabularnewline
19 & 0.168284263652392 & 0.336568527304783 & 0.831715736347608 \tabularnewline
20 & 0.141997551445717 & 0.283995102891434 & 0.858002448554283 \tabularnewline
21 & 0.194063397447900 & 0.388126794895799 & 0.8059366025521 \tabularnewline
22 & 0.125686060427097 & 0.251372120854195 & 0.874313939572903 \tabularnewline
23 & 0.121559508866286 & 0.243119017732571 & 0.878440491133714 \tabularnewline
24 & 0.0818332958846213 & 0.163666591769243 & 0.918166704115379 \tabularnewline
25 & 0.0610848267875819 & 0.122169653575164 & 0.938915173212418 \tabularnewline
26 & 0.0450513158694378 & 0.0901026317388757 & 0.954948684130562 \tabularnewline
27 & 0.0268859024935885 & 0.0537718049871769 & 0.973114097506412 \tabularnewline
28 & 0.0164608245889039 & 0.0329216491778077 & 0.983539175411096 \tabularnewline
29 & 0.00889120805113204 & 0.0177824161022641 & 0.991108791948868 \tabularnewline
30 & 0.00922489919333084 & 0.0184497983866617 & 0.990775100806669 \tabularnewline
31 & 0.0047633577917952 & 0.0095267155835904 & 0.995236642208205 \tabularnewline
32 & 0.00232191386933862 & 0.00464382773867724 & 0.997678086130661 \tabularnewline
33 & 0.00136306750855467 & 0.00272613501710933 & 0.998636932491445 \tabularnewline
34 & 0.000957822407401818 & 0.00191564481480364 & 0.999042177592598 \tabularnewline
35 & 0.000415166629240552 & 0.000830333258481104 & 0.99958483337076 \tabularnewline
36 & 0.000171471968665296 & 0.000342943937330592 & 0.999828528031335 \tabularnewline
37 & 0.000114567488303261 & 0.000229134976606521 & 0.999885432511697 \tabularnewline
38 & 5.84924889815724e-05 & 0.000116984977963145 & 0.999941507511018 \tabularnewline
39 & 2.02215353975267e-05 & 4.04430707950534e-05 & 0.999979778464603 \tabularnewline
40 & 1.30628728061160e-05 & 2.61257456122319e-05 & 0.999986937127194 \tabularnewline
41 & 6.76569317837849e-06 & 1.35313863567570e-05 & 0.999993234306822 \tabularnewline
42 & 3.98026062621464e-05 & 7.96052125242928e-05 & 0.999960197393738 \tabularnewline
43 & 3.30720316337286e-05 & 6.61440632674571e-05 & 0.999966927968366 \tabularnewline
44 & 0.0159132858608517 & 0.0318265717217033 & 0.984086714139148 \tabularnewline
45 & 0.331643211450914 & 0.663286422901828 & 0.668356788549086 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59205&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]16[/C][C]0.0486338734819288[/C][C]0.0972677469638577[/C][C]0.951366126518071[/C][/ROW]
[ROW][C]17[/C][C]0.0855024121052266[/C][C]0.171004824210453[/C][C]0.914497587894773[/C][/ROW]
[ROW][C]18[/C][C]0.136381760951064[/C][C]0.272763521902128[/C][C]0.863618239048936[/C][/ROW]
[ROW][C]19[/C][C]0.168284263652392[/C][C]0.336568527304783[/C][C]0.831715736347608[/C][/ROW]
[ROW][C]20[/C][C]0.141997551445717[/C][C]0.283995102891434[/C][C]0.858002448554283[/C][/ROW]
[ROW][C]21[/C][C]0.194063397447900[/C][C]0.388126794895799[/C][C]0.8059366025521[/C][/ROW]
[ROW][C]22[/C][C]0.125686060427097[/C][C]0.251372120854195[/C][C]0.874313939572903[/C][/ROW]
[ROW][C]23[/C][C]0.121559508866286[/C][C]0.243119017732571[/C][C]0.878440491133714[/C][/ROW]
[ROW][C]24[/C][C]0.0818332958846213[/C][C]0.163666591769243[/C][C]0.918166704115379[/C][/ROW]
[ROW][C]25[/C][C]0.0610848267875819[/C][C]0.122169653575164[/C][C]0.938915173212418[/C][/ROW]
[ROW][C]26[/C][C]0.0450513158694378[/C][C]0.0901026317388757[/C][C]0.954948684130562[/C][/ROW]
[ROW][C]27[/C][C]0.0268859024935885[/C][C]0.0537718049871769[/C][C]0.973114097506412[/C][/ROW]
[ROW][C]28[/C][C]0.0164608245889039[/C][C]0.0329216491778077[/C][C]0.983539175411096[/C][/ROW]
[ROW][C]29[/C][C]0.00889120805113204[/C][C]0.0177824161022641[/C][C]0.991108791948868[/C][/ROW]
[ROW][C]30[/C][C]0.00922489919333084[/C][C]0.0184497983866617[/C][C]0.990775100806669[/C][/ROW]
[ROW][C]31[/C][C]0.0047633577917952[/C][C]0.0095267155835904[/C][C]0.995236642208205[/C][/ROW]
[ROW][C]32[/C][C]0.00232191386933862[/C][C]0.00464382773867724[/C][C]0.997678086130661[/C][/ROW]
[ROW][C]33[/C][C]0.00136306750855467[/C][C]0.00272613501710933[/C][C]0.998636932491445[/C][/ROW]
[ROW][C]34[/C][C]0.000957822407401818[/C][C]0.00191564481480364[/C][C]0.999042177592598[/C][/ROW]
[ROW][C]35[/C][C]0.000415166629240552[/C][C]0.000830333258481104[/C][C]0.99958483337076[/C][/ROW]
[ROW][C]36[/C][C]0.000171471968665296[/C][C]0.000342943937330592[/C][C]0.999828528031335[/C][/ROW]
[ROW][C]37[/C][C]0.000114567488303261[/C][C]0.000229134976606521[/C][C]0.999885432511697[/C][/ROW]
[ROW][C]38[/C][C]5.84924889815724e-05[/C][C]0.000116984977963145[/C][C]0.999941507511018[/C][/ROW]
[ROW][C]39[/C][C]2.02215353975267e-05[/C][C]4.04430707950534e-05[/C][C]0.999979778464603[/C][/ROW]
[ROW][C]40[/C][C]1.30628728061160e-05[/C][C]2.61257456122319e-05[/C][C]0.999986937127194[/C][/ROW]
[ROW][C]41[/C][C]6.76569317837849e-06[/C][C]1.35313863567570e-05[/C][C]0.999993234306822[/C][/ROW]
[ROW][C]42[/C][C]3.98026062621464e-05[/C][C]7.96052125242928e-05[/C][C]0.999960197393738[/C][/ROW]
[ROW][C]43[/C][C]3.30720316337286e-05[/C][C]6.61440632674571e-05[/C][C]0.999966927968366[/C][/ROW]
[ROW][C]44[/C][C]0.0159132858608517[/C][C]0.0318265717217033[/C][C]0.984086714139148[/C][/ROW]
[ROW][C]45[/C][C]0.331643211450914[/C][C]0.663286422901828[/C][C]0.668356788549086[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59205&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59205&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
160.04863387348192880.09726774696385770.951366126518071
170.08550241210522660.1710048242104530.914497587894773
180.1363817609510640.2727635219021280.863618239048936
190.1682842636523920.3365685273047830.831715736347608
200.1419975514457170.2839951028914340.858002448554283
210.1940633974479000.3881267948957990.8059366025521
220.1256860604270970.2513721208541950.874313939572903
230.1215595088662860.2431190177325710.878440491133714
240.08183329588462130.1636665917692430.918166704115379
250.06108482678758190.1221696535751640.938915173212418
260.04505131586943780.09010263173887570.954948684130562
270.02688590249358850.05377180498717690.973114097506412
280.01646082458890390.03292164917780770.983539175411096
290.008891208051132040.01778241610226410.991108791948868
300.009224899193330840.01844979838666170.990775100806669
310.00476335779179520.00952671558359040.995236642208205
320.002321913869338620.004643827738677240.997678086130661
330.001363067508554670.002726135017109330.998636932491445
340.0009578224074018180.001915644814803640.999042177592598
350.0004151666292405520.0008303332584811040.99958483337076
360.0001714719686652960.0003429439373305920.999828528031335
370.0001145674883032610.0002291349766065210.999885432511697
385.84924889815724e-050.0001169849779631450.999941507511018
392.02215353975267e-054.04430707950534e-050.999979778464603
401.30628728061160e-052.61257456122319e-050.999986937127194
416.76569317837849e-061.35313863567570e-050.999993234306822
423.98026062621464e-057.96052125242928e-050.999960197393738
433.30720316337286e-056.61440632674571e-050.999966927968366
440.01591328586085170.03182657172170330.984086714139148
450.3316432114509140.6632864229018280.668356788549086







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level130.433333333333333NOK
5% type I error level170.566666666666667NOK
10% type I error level200.666666666666667NOK

\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 & 13 & 0.433333333333333 & NOK \tabularnewline
5% type I error level & 17 & 0.566666666666667 & NOK \tabularnewline
10% type I error level & 20 & 0.666666666666667 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59205&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]13[/C][C]0.433333333333333[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]17[/C][C]0.566666666666667[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]20[/C][C]0.666666666666667[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59205&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59205&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 level130.433333333333333NOK
5% type I error level170.566666666666667NOK
10% type I error level200.666666666666667NOK



Parameters (Session):
Parameters (R input):
par1 = 1 ; par2 = Include Monthly 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')
}