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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationThu, 19 Nov 2009 06:56:12 -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/19/t1258639145bvjdlf9nubwk4k2.htm/, Retrieved Fri, 29 Mar 2024 06:07:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57740, Retrieved Fri, 29 Mar 2024 06:07:15 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact148
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]
-    D    [Multiple Regression] [] [2009-11-19 10:20:13] [875a981b2b01315c1c471abd4dd66675]
-   P       [Multiple Regression] [] [2009-11-19 13:31:28] [875a981b2b01315c1c471abd4dd66675]
-   P           [Multiple Regression] [] [2009-11-19 13:56:12] [8551abdd6804649d94d88b1829ac2b1a] [Current]
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Dataseries X:
110.5	55
110.8	48.7
104.2	70.3
88.9	94.8
89.8	58.5
90	62.4
93.9	56.7
91.3	65.1
87.8	114.4
99.7	50.7
73.5	44.5
79.2	72
96.9	61.2
95.2	68.4
95.6	78.7
89.7	64.1
92.8	64.6
88	71.9
101.1	71
92.7	76.4
95.8	117.3
103.8	66.1
81.8	57.3
87.1	75
105.9	63.8
108.1	62.2
102.6	75.4
93.7	58
103.5	62.1
100.6	99.2
113.3	70.7
102.4	73.3
102.1	111.2
106.9	68.9
87.3	57.6
93.1	72.9
109.1	75.9
120.3	79.4
104.9	96.9
92.6	75.2
109.8	60.3
111.4	88.9
117.9	90.5
121.6	79.9
117.8	116.3
124.2	95.2
106.8	81.5
102.7	89.1
116.8	76
113.6	100.5
96.1	83.9
85	75.1
83.2	69.5
84.9	95.1
83	90.1
79.6	78.4
83.2	113.8
83.8	73.6
82.8	56.5
71.4	97.7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
R Framework error message & 
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=57740&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=57740&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57740&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'Gwilym Jenkins' @ 72.249.127.135
R Framework error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.







Multiple Linear Regression - Estimated Regression Equation
prod[t] = + 66.615835719766 + 0.261866270220996`inv `[t] + 24.6859521932016M1[t] + 25.0499411950045M2[t] + 13.7545503461808M3[t] + 5.0785128370699M4[t] + 13.6861755353866M5[t] + 7.51169583306567M6[t] + 16.4218449509768M7[t] + 12.4446259870471M8[t] + 1.82899134082118M9[t] + 19.6463261866882M10[t] + 5.43061782982147M11[t] -0.033778837209496t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
prod[t] =  +  66.615835719766 +  0.261866270220996`inv
`[t] +  24.6859521932016M1[t] +  25.0499411950045M2[t] +  13.7545503461808M3[t] +  5.0785128370699M4[t] +  13.6861755353866M5[t] +  7.51169583306567M6[t] +  16.4218449509768M7[t] +  12.4446259870471M8[t] +  1.82899134082118M9[t] +  19.6463261866882M10[t] +  5.43061782982147M11[t] -0.033778837209496t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57740&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]prod[t] =  +  66.615835719766 +  0.261866270220996`inv
`[t] +  24.6859521932016M1[t] +  25.0499411950045M2[t] +  13.7545503461808M3[t] +  5.0785128370699M4[t] +  13.6861755353866M5[t] +  7.51169583306567M6[t] +  16.4218449509768M7[t] +  12.4446259870471M8[t] +  1.82899134082118M9[t] +  19.6463261866882M10[t] +  5.43061782982147M11[t] -0.033778837209496t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57740&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57740&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
prod[t] = + 66.615835719766 + 0.261866270220996`inv `[t] + 24.6859521932016M1[t] + 25.0499411950045M2[t] + 13.7545503461808M3[t] + 5.0785128370699M4[t] + 13.6861755353866M5[t] + 7.51169583306567M6[t] + 16.4218449509768M7[t] + 12.4446259870471M8[t] + 1.82899134082118M9[t] + 19.6463261866882M10[t] + 5.43061782982147M11[t] -0.033778837209496t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)66.61583571976612.5972725.28813e-062e-06
`inv `0.2618662702209960.1673551.56470.1244990.062249
M124.68595219320167.3683783.35030.001620.00081
M225.04994119500457.2041893.47710.0011180.000559
M313.75455034618087.160311.92090.0609490.030475
M45.07851283706997.1707580.70820.4823790.241189
M513.68617553538667.5771351.80620.0774250.038712
M67.511695833065677.1566781.04960.2993820.149691
M716.42184495097687.1329972.30220.0258980.012949
M812.44462598704717.1551111.73930.0886770.044338
M91.828991340821189.1511140.19990.8424670.421233
M1019.64632618668827.2785572.69920.009690.004845
M115.430617829821477.9529790.68280.4981320.249066
t-0.0337788372094960.10958-0.30830.7592790.37964

\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) & 66.615835719766 & 12.597272 & 5.2881 & 3e-06 & 2e-06 \tabularnewline
`inv
` & 0.261866270220996 & 0.167355 & 1.5647 & 0.124499 & 0.062249 \tabularnewline
M1 & 24.6859521932016 & 7.368378 & 3.3503 & 0.00162 & 0.00081 \tabularnewline
M2 & 25.0499411950045 & 7.204189 & 3.4771 & 0.001118 & 0.000559 \tabularnewline
M3 & 13.7545503461808 & 7.16031 & 1.9209 & 0.060949 & 0.030475 \tabularnewline
M4 & 5.0785128370699 & 7.170758 & 0.7082 & 0.482379 & 0.241189 \tabularnewline
M5 & 13.6861755353866 & 7.577135 & 1.8062 & 0.077425 & 0.038712 \tabularnewline
M6 & 7.51169583306567 & 7.156678 & 1.0496 & 0.299382 & 0.149691 \tabularnewline
M7 & 16.4218449509768 & 7.132997 & 2.3022 & 0.025898 & 0.012949 \tabularnewline
M8 & 12.4446259870471 & 7.155111 & 1.7393 & 0.088677 & 0.044338 \tabularnewline
M9 & 1.82899134082118 & 9.151114 & 0.1999 & 0.842467 & 0.421233 \tabularnewline
M10 & 19.6463261866882 & 7.278557 & 2.6992 & 0.00969 & 0.004845 \tabularnewline
M11 & 5.43061782982147 & 7.952979 & 0.6828 & 0.498132 & 0.249066 \tabularnewline
t & -0.033778837209496 & 0.10958 & -0.3083 & 0.759279 & 0.37964 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57740&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]66.615835719766[/C][C]12.597272[/C][C]5.2881[/C][C]3e-06[/C][C]2e-06[/C][/ROW]
[ROW][C]`inv
`[/C][C]0.261866270220996[/C][C]0.167355[/C][C]1.5647[/C][C]0.124499[/C][C]0.062249[/C][/ROW]
[ROW][C]M1[/C][C]24.6859521932016[/C][C]7.368378[/C][C]3.3503[/C][C]0.00162[/C][C]0.00081[/C][/ROW]
[ROW][C]M2[/C][C]25.0499411950045[/C][C]7.204189[/C][C]3.4771[/C][C]0.001118[/C][C]0.000559[/C][/ROW]
[ROW][C]M3[/C][C]13.7545503461808[/C][C]7.16031[/C][C]1.9209[/C][C]0.060949[/C][C]0.030475[/C][/ROW]
[ROW][C]M4[/C][C]5.0785128370699[/C][C]7.170758[/C][C]0.7082[/C][C]0.482379[/C][C]0.241189[/C][/ROW]
[ROW][C]M5[/C][C]13.6861755353866[/C][C]7.577135[/C][C]1.8062[/C][C]0.077425[/C][C]0.038712[/C][/ROW]
[ROW][C]M6[/C][C]7.51169583306567[/C][C]7.156678[/C][C]1.0496[/C][C]0.299382[/C][C]0.149691[/C][/ROW]
[ROW][C]M7[/C][C]16.4218449509768[/C][C]7.132997[/C][C]2.3022[/C][C]0.025898[/C][C]0.012949[/C][/ROW]
[ROW][C]M8[/C][C]12.4446259870471[/C][C]7.155111[/C][C]1.7393[/C][C]0.088677[/C][C]0.044338[/C][/ROW]
[ROW][C]M9[/C][C]1.82899134082118[/C][C]9.151114[/C][C]0.1999[/C][C]0.842467[/C][C]0.421233[/C][/ROW]
[ROW][C]M10[/C][C]19.6463261866882[/C][C]7.278557[/C][C]2.6992[/C][C]0.00969[/C][C]0.004845[/C][/ROW]
[ROW][C]M11[/C][C]5.43061782982147[/C][C]7.952979[/C][C]0.6828[/C][C]0.498132[/C][C]0.249066[/C][/ROW]
[ROW][C]t[/C][C]-0.033778837209496[/C][C]0.10958[/C][C]-0.3083[/C][C]0.759279[/C][C]0.37964[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57740&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57740&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)66.61583571976612.5972725.28813e-062e-06
`inv `0.2618662702209960.1673551.56470.1244990.062249
M124.68595219320167.3683783.35030.001620.00081
M225.04994119500457.2041893.47710.0011180.000559
M313.75455034618087.160311.92090.0609490.030475
M45.07851283706997.1707580.70820.4823790.241189
M513.68617553538667.5771351.80620.0774250.038712
M67.511695833065677.1566781.04960.2993820.149691
M716.42184495097687.1329972.30220.0258980.012949
M812.44462598704717.1551111.73930.0886770.044338
M91.828991340821189.1511140.19990.8424670.421233
M1019.64632618668827.2785572.69920.009690.004845
M115.430617829821477.9529790.68280.4981320.249066
t-0.0337788372094960.10958-0.30830.7592790.37964







Multiple Linear Regression - Regression Statistics
Multiple R0.615161986324822
R-squared0.378424269419101
Adjusted R-squared0.202761562950586
F-TEST (value)2.15426641788038
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0.0283017411167295
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation11.2201809184622
Sum Squared Residuals5791.05315277902

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.615161986324822 \tabularnewline
R-squared & 0.378424269419101 \tabularnewline
Adjusted R-squared & 0.202761562950586 \tabularnewline
F-TEST (value) & 2.15426641788038 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 0.0283017411167295 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 11.2201809184622 \tabularnewline
Sum Squared Residuals & 5791.05315277902 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57740&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.615161986324822[/C][/ROW]
[ROW][C]R-squared[/C][C]0.378424269419101[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.202761562950586[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]2.15426641788038[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/C][/ROW]
[ROW][C]p-value[/C][C]0.0283017411167295[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]11.2201809184622[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]5791.05315277902[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57740&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57740&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 R0.615161986324822
R-squared0.378424269419101
Adjusted R-squared0.202761562950586
F-TEST (value)2.15426641788038
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0.0283017411167295
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation11.2201809184622
Sum Squared Residuals5791.05315277902







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1110.5105.6706539379134.82934606208667
2110.8104.3511066001146.44889339988596
3104.298.67824835085445.5217516491456
488.996.3841556249483-7.48415562494834
589.895.4522938770334-5.65229387703344
69090.2653137913649-0.265313791364894
793.997.6490463318069-3.74904633180687
891.395.837725200524-4.53772520052403
987.898.0983188389837-10.2983188389837
1099.799.20099343456380.499006565436208
1173.583.3279353651174-9.82793536511739
1279.285.0648611291638-5.86486112916379
1396.9106.888878766769-9.98887876676908
1495.2109.104526076954-13.9045260769537
1595.6100.472578974197-4.87257897419682
1689.787.93951508264991.76048491735015
1792.896.6443320788675-3.84433207886754
188892.3476973119504-4.3476973119504
19101.1100.9883879494530.111612050546823
2092.798.3914680075073-5.69146800750732
2195.898.4523849761106-2.65238497611064
22103.8102.8283879494530.971612050546831
2381.886.2744775774322-4.47447757743218
2487.185.44511389331281.65488610668716
25105.9107.164385022830-1.26438502282974
26108.1107.0756091550701.02439084493039
27102.699.20307423595363.39692576404642
2893.785.93678478778787.76321521221217
29103.595.5843203568017.9156796431989
30100.699.09130044246961.50869955753036
31113.3100.50448202187312.7955179781271
32102.497.17433652330835.22566347669172
33102.196.44965468124865.65034531875138
34106.9103.1562674595583.743732540442
3587.385.94769141198451.35230858801547
3693.184.48984867933488.6101513206652
37109.1109.927620845990-0.82762084598985
38120.3111.1743629563579.12563704364322
39104.9104.4278529991910.472147000808966
4092.690.0355385890752.56446141092498
41109.894.707615023889415.0923849761106
42111.495.988731812679415.4112681873206
43117.9105.28408812573512.6159118742653
44121.698.49730786025323.1026921397471
45117.897.379826612861720.4201733871383
46124.2109.63800431985614.5619956801437
47106.891.800949223752414.9990507762476
48102.788.32673621040114.3732637895990
49116.8109.5484614264987.251538573502
50113.6116.294395211506-2.69439521150585
5196.1100.618245439804-4.51824543980414
528589.604005915539-4.60400591553896
5383.296.7114386634086-13.5114386634086
5484.997.2069566415357-12.3069566415356
5583104.773995571132-21.7739955711323
5679.697.6991624084075-18.0991624084075
5783.296.3198148907953-13.1198148907953
5883.8103.576346836569-19.7763468365688
5982.884.8489464217135-2.04894642171353
6071.490.1734400877876-18.7734400877876

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 110.5 & 105.670653937913 & 4.82934606208667 \tabularnewline
2 & 110.8 & 104.351106600114 & 6.44889339988596 \tabularnewline
3 & 104.2 & 98.6782483508544 & 5.5217516491456 \tabularnewline
4 & 88.9 & 96.3841556249483 & -7.48415562494834 \tabularnewline
5 & 89.8 & 95.4522938770334 & -5.65229387703344 \tabularnewline
6 & 90 & 90.2653137913649 & -0.265313791364894 \tabularnewline
7 & 93.9 & 97.6490463318069 & -3.74904633180687 \tabularnewline
8 & 91.3 & 95.837725200524 & -4.53772520052403 \tabularnewline
9 & 87.8 & 98.0983188389837 & -10.2983188389837 \tabularnewline
10 & 99.7 & 99.2009934345638 & 0.499006565436208 \tabularnewline
11 & 73.5 & 83.3279353651174 & -9.82793536511739 \tabularnewline
12 & 79.2 & 85.0648611291638 & -5.86486112916379 \tabularnewline
13 & 96.9 & 106.888878766769 & -9.98887876676908 \tabularnewline
14 & 95.2 & 109.104526076954 & -13.9045260769537 \tabularnewline
15 & 95.6 & 100.472578974197 & -4.87257897419682 \tabularnewline
16 & 89.7 & 87.9395150826499 & 1.76048491735015 \tabularnewline
17 & 92.8 & 96.6443320788675 & -3.84433207886754 \tabularnewline
18 & 88 & 92.3476973119504 & -4.3476973119504 \tabularnewline
19 & 101.1 & 100.988387949453 & 0.111612050546823 \tabularnewline
20 & 92.7 & 98.3914680075073 & -5.69146800750732 \tabularnewline
21 & 95.8 & 98.4523849761106 & -2.65238497611064 \tabularnewline
22 & 103.8 & 102.828387949453 & 0.971612050546831 \tabularnewline
23 & 81.8 & 86.2744775774322 & -4.47447757743218 \tabularnewline
24 & 87.1 & 85.4451138933128 & 1.65488610668716 \tabularnewline
25 & 105.9 & 107.164385022830 & -1.26438502282974 \tabularnewline
26 & 108.1 & 107.075609155070 & 1.02439084493039 \tabularnewline
27 & 102.6 & 99.2030742359536 & 3.39692576404642 \tabularnewline
28 & 93.7 & 85.9367847877878 & 7.76321521221217 \tabularnewline
29 & 103.5 & 95.584320356801 & 7.9156796431989 \tabularnewline
30 & 100.6 & 99.0913004424696 & 1.50869955753036 \tabularnewline
31 & 113.3 & 100.504482021873 & 12.7955179781271 \tabularnewline
32 & 102.4 & 97.1743365233083 & 5.22566347669172 \tabularnewline
33 & 102.1 & 96.4496546812486 & 5.65034531875138 \tabularnewline
34 & 106.9 & 103.156267459558 & 3.743732540442 \tabularnewline
35 & 87.3 & 85.9476914119845 & 1.35230858801547 \tabularnewline
36 & 93.1 & 84.4898486793348 & 8.6101513206652 \tabularnewline
37 & 109.1 & 109.927620845990 & -0.82762084598985 \tabularnewline
38 & 120.3 & 111.174362956357 & 9.12563704364322 \tabularnewline
39 & 104.9 & 104.427852999191 & 0.472147000808966 \tabularnewline
40 & 92.6 & 90.035538589075 & 2.56446141092498 \tabularnewline
41 & 109.8 & 94.7076150238894 & 15.0923849761106 \tabularnewline
42 & 111.4 & 95.9887318126794 & 15.4112681873206 \tabularnewline
43 & 117.9 & 105.284088125735 & 12.6159118742653 \tabularnewline
44 & 121.6 & 98.497307860253 & 23.1026921397471 \tabularnewline
45 & 117.8 & 97.3798266128617 & 20.4201733871383 \tabularnewline
46 & 124.2 & 109.638004319856 & 14.5619956801437 \tabularnewline
47 & 106.8 & 91.8009492237524 & 14.9990507762476 \tabularnewline
48 & 102.7 & 88.326736210401 & 14.3732637895990 \tabularnewline
49 & 116.8 & 109.548461426498 & 7.251538573502 \tabularnewline
50 & 113.6 & 116.294395211506 & -2.69439521150585 \tabularnewline
51 & 96.1 & 100.618245439804 & -4.51824543980414 \tabularnewline
52 & 85 & 89.604005915539 & -4.60400591553896 \tabularnewline
53 & 83.2 & 96.7114386634086 & -13.5114386634086 \tabularnewline
54 & 84.9 & 97.2069566415357 & -12.3069566415356 \tabularnewline
55 & 83 & 104.773995571132 & -21.7739955711323 \tabularnewline
56 & 79.6 & 97.6991624084075 & -18.0991624084075 \tabularnewline
57 & 83.2 & 96.3198148907953 & -13.1198148907953 \tabularnewline
58 & 83.8 & 103.576346836569 & -19.7763468365688 \tabularnewline
59 & 82.8 & 84.8489464217135 & -2.04894642171353 \tabularnewline
60 & 71.4 & 90.1734400877876 & -18.7734400877876 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57740&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]110.5[/C][C]105.670653937913[/C][C]4.82934606208667[/C][/ROW]
[ROW][C]2[/C][C]110.8[/C][C]104.351106600114[/C][C]6.44889339988596[/C][/ROW]
[ROW][C]3[/C][C]104.2[/C][C]98.6782483508544[/C][C]5.5217516491456[/C][/ROW]
[ROW][C]4[/C][C]88.9[/C][C]96.3841556249483[/C][C]-7.48415562494834[/C][/ROW]
[ROW][C]5[/C][C]89.8[/C][C]95.4522938770334[/C][C]-5.65229387703344[/C][/ROW]
[ROW][C]6[/C][C]90[/C][C]90.2653137913649[/C][C]-0.265313791364894[/C][/ROW]
[ROW][C]7[/C][C]93.9[/C][C]97.6490463318069[/C][C]-3.74904633180687[/C][/ROW]
[ROW][C]8[/C][C]91.3[/C][C]95.837725200524[/C][C]-4.53772520052403[/C][/ROW]
[ROW][C]9[/C][C]87.8[/C][C]98.0983188389837[/C][C]-10.2983188389837[/C][/ROW]
[ROW][C]10[/C][C]99.7[/C][C]99.2009934345638[/C][C]0.499006565436208[/C][/ROW]
[ROW][C]11[/C][C]73.5[/C][C]83.3279353651174[/C][C]-9.82793536511739[/C][/ROW]
[ROW][C]12[/C][C]79.2[/C][C]85.0648611291638[/C][C]-5.86486112916379[/C][/ROW]
[ROW][C]13[/C][C]96.9[/C][C]106.888878766769[/C][C]-9.98887876676908[/C][/ROW]
[ROW][C]14[/C][C]95.2[/C][C]109.104526076954[/C][C]-13.9045260769537[/C][/ROW]
[ROW][C]15[/C][C]95.6[/C][C]100.472578974197[/C][C]-4.87257897419682[/C][/ROW]
[ROW][C]16[/C][C]89.7[/C][C]87.9395150826499[/C][C]1.76048491735015[/C][/ROW]
[ROW][C]17[/C][C]92.8[/C][C]96.6443320788675[/C][C]-3.84433207886754[/C][/ROW]
[ROW][C]18[/C][C]88[/C][C]92.3476973119504[/C][C]-4.3476973119504[/C][/ROW]
[ROW][C]19[/C][C]101.1[/C][C]100.988387949453[/C][C]0.111612050546823[/C][/ROW]
[ROW][C]20[/C][C]92.7[/C][C]98.3914680075073[/C][C]-5.69146800750732[/C][/ROW]
[ROW][C]21[/C][C]95.8[/C][C]98.4523849761106[/C][C]-2.65238497611064[/C][/ROW]
[ROW][C]22[/C][C]103.8[/C][C]102.828387949453[/C][C]0.971612050546831[/C][/ROW]
[ROW][C]23[/C][C]81.8[/C][C]86.2744775774322[/C][C]-4.47447757743218[/C][/ROW]
[ROW][C]24[/C][C]87.1[/C][C]85.4451138933128[/C][C]1.65488610668716[/C][/ROW]
[ROW][C]25[/C][C]105.9[/C][C]107.164385022830[/C][C]-1.26438502282974[/C][/ROW]
[ROW][C]26[/C][C]108.1[/C][C]107.075609155070[/C][C]1.02439084493039[/C][/ROW]
[ROW][C]27[/C][C]102.6[/C][C]99.2030742359536[/C][C]3.39692576404642[/C][/ROW]
[ROW][C]28[/C][C]93.7[/C][C]85.9367847877878[/C][C]7.76321521221217[/C][/ROW]
[ROW][C]29[/C][C]103.5[/C][C]95.584320356801[/C][C]7.9156796431989[/C][/ROW]
[ROW][C]30[/C][C]100.6[/C][C]99.0913004424696[/C][C]1.50869955753036[/C][/ROW]
[ROW][C]31[/C][C]113.3[/C][C]100.504482021873[/C][C]12.7955179781271[/C][/ROW]
[ROW][C]32[/C][C]102.4[/C][C]97.1743365233083[/C][C]5.22566347669172[/C][/ROW]
[ROW][C]33[/C][C]102.1[/C][C]96.4496546812486[/C][C]5.65034531875138[/C][/ROW]
[ROW][C]34[/C][C]106.9[/C][C]103.156267459558[/C][C]3.743732540442[/C][/ROW]
[ROW][C]35[/C][C]87.3[/C][C]85.9476914119845[/C][C]1.35230858801547[/C][/ROW]
[ROW][C]36[/C][C]93.1[/C][C]84.4898486793348[/C][C]8.6101513206652[/C][/ROW]
[ROW][C]37[/C][C]109.1[/C][C]109.927620845990[/C][C]-0.82762084598985[/C][/ROW]
[ROW][C]38[/C][C]120.3[/C][C]111.174362956357[/C][C]9.12563704364322[/C][/ROW]
[ROW][C]39[/C][C]104.9[/C][C]104.427852999191[/C][C]0.472147000808966[/C][/ROW]
[ROW][C]40[/C][C]92.6[/C][C]90.035538589075[/C][C]2.56446141092498[/C][/ROW]
[ROW][C]41[/C][C]109.8[/C][C]94.7076150238894[/C][C]15.0923849761106[/C][/ROW]
[ROW][C]42[/C][C]111.4[/C][C]95.9887318126794[/C][C]15.4112681873206[/C][/ROW]
[ROW][C]43[/C][C]117.9[/C][C]105.284088125735[/C][C]12.6159118742653[/C][/ROW]
[ROW][C]44[/C][C]121.6[/C][C]98.497307860253[/C][C]23.1026921397471[/C][/ROW]
[ROW][C]45[/C][C]117.8[/C][C]97.3798266128617[/C][C]20.4201733871383[/C][/ROW]
[ROW][C]46[/C][C]124.2[/C][C]109.638004319856[/C][C]14.5619956801437[/C][/ROW]
[ROW][C]47[/C][C]106.8[/C][C]91.8009492237524[/C][C]14.9990507762476[/C][/ROW]
[ROW][C]48[/C][C]102.7[/C][C]88.326736210401[/C][C]14.3732637895990[/C][/ROW]
[ROW][C]49[/C][C]116.8[/C][C]109.548461426498[/C][C]7.251538573502[/C][/ROW]
[ROW][C]50[/C][C]113.6[/C][C]116.294395211506[/C][C]-2.69439521150585[/C][/ROW]
[ROW][C]51[/C][C]96.1[/C][C]100.618245439804[/C][C]-4.51824543980414[/C][/ROW]
[ROW][C]52[/C][C]85[/C][C]89.604005915539[/C][C]-4.60400591553896[/C][/ROW]
[ROW][C]53[/C][C]83.2[/C][C]96.7114386634086[/C][C]-13.5114386634086[/C][/ROW]
[ROW][C]54[/C][C]84.9[/C][C]97.2069566415357[/C][C]-12.3069566415356[/C][/ROW]
[ROW][C]55[/C][C]83[/C][C]104.773995571132[/C][C]-21.7739955711323[/C][/ROW]
[ROW][C]56[/C][C]79.6[/C][C]97.6991624084075[/C][C]-18.0991624084075[/C][/ROW]
[ROW][C]57[/C][C]83.2[/C][C]96.3198148907953[/C][C]-13.1198148907953[/C][/ROW]
[ROW][C]58[/C][C]83.8[/C][C]103.576346836569[/C][C]-19.7763468365688[/C][/ROW]
[ROW][C]59[/C][C]82.8[/C][C]84.8489464217135[/C][C]-2.04894642171353[/C][/ROW]
[ROW][C]60[/C][C]71.4[/C][C]90.1734400877876[/C][C]-18.7734400877876[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57740&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57740&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
1110.5105.6706539379134.82934606208667
2110.8104.3511066001146.44889339988596
3104.298.67824835085445.5217516491456
488.996.3841556249483-7.48415562494834
589.895.4522938770334-5.65229387703344
69090.2653137913649-0.265313791364894
793.997.6490463318069-3.74904633180687
891.395.837725200524-4.53772520052403
987.898.0983188389837-10.2983188389837
1099.799.20099343456380.499006565436208
1173.583.3279353651174-9.82793536511739
1279.285.0648611291638-5.86486112916379
1396.9106.888878766769-9.98887876676908
1495.2109.104526076954-13.9045260769537
1595.6100.472578974197-4.87257897419682
1689.787.93951508264991.76048491735015
1792.896.6443320788675-3.84433207886754
188892.3476973119504-4.3476973119504
19101.1100.9883879494530.111612050546823
2092.798.3914680075073-5.69146800750732
2195.898.4523849761106-2.65238497611064
22103.8102.8283879494530.971612050546831
2381.886.2744775774322-4.47447757743218
2487.185.44511389331281.65488610668716
25105.9107.164385022830-1.26438502282974
26108.1107.0756091550701.02439084493039
27102.699.20307423595363.39692576404642
2893.785.93678478778787.76321521221217
29103.595.5843203568017.9156796431989
30100.699.09130044246961.50869955753036
31113.3100.50448202187312.7955179781271
32102.497.17433652330835.22566347669172
33102.196.44965468124865.65034531875138
34106.9103.1562674595583.743732540442
3587.385.94769141198451.35230858801547
3693.184.48984867933488.6101513206652
37109.1109.927620845990-0.82762084598985
38120.3111.1743629563579.12563704364322
39104.9104.4278529991910.472147000808966
4092.690.0355385890752.56446141092498
41109.894.707615023889415.0923849761106
42111.495.988731812679415.4112681873206
43117.9105.28408812573512.6159118742653
44121.698.49730786025323.1026921397471
45117.897.379826612861720.4201733871383
46124.2109.63800431985614.5619956801437
47106.891.800949223752414.9990507762476
48102.788.32673621040114.3732637895990
49116.8109.5484614264987.251538573502
50113.6116.294395211506-2.69439521150585
5196.1100.618245439804-4.51824543980414
528589.604005915539-4.60400591553896
5383.296.7114386634086-13.5114386634086
5484.997.2069566415357-12.3069566415356
5583104.773995571132-21.7739955711323
5679.697.6991624084075-18.0991624084075
5783.296.3198148907953-13.1198148907953
5883.8103.576346836569-19.7763468365688
5982.884.8489464217135-2.04894642171353
6071.490.1734400877876-18.7734400877876







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.09647559493107870.1929511898621570.903524405068921
180.04816272022775330.09632544045550660.951837279772247
190.07078878920085220.1415775784017040.929211210799148
200.0433551545813190.0867103091626380.956644845418681
210.04162817276579580.08325634553159160.958371827234204
220.02556251748869620.05112503497739250.974437482511304
230.02729185337664250.0545837067532850.972708146623358
240.02030291355983610.04060582711967230.979697086440164
250.01164440208814050.0232888041762810.98835559791186
260.006208662601396140.01241732520279230.993791337398604
270.002769519847338030.005539039694676060.997230480152662
280.001127162739688160.002254325479376310.998872837260312
290.001041221732454830.002082443464909670.998958778267545
300.001577158006743030.003154316013486060.998422841993257
310.001686664972507300.003373329945014590.998313335027493
320.001192444906953110.002384889813906220.998807555093047
330.001033790653412270.002067581306824540.998966209346588
340.0005474077200362180.001094815440072440.999452592279964
350.001808341235987070.003616682471974130.998191658764013
360.002127026911957100.004254053823914210.997872973088043
370.01622805867774880.03245611735549750.983771941322251
380.02994308912590820.05988617825181640.970056910874092
390.08237946009764720.1647589201952940.917620539902353
400.5266375782412390.9467248435175220.473362421758761
410.4779728608412210.9559457216824420.522027139158779
420.519785035745130.960429928509740.48021496425487
430.3640932815551670.7281865631103350.635906718444833

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.0964755949310787 & 0.192951189862157 & 0.903524405068921 \tabularnewline
18 & 0.0481627202277533 & 0.0963254404555066 & 0.951837279772247 \tabularnewline
19 & 0.0707887892008522 & 0.141577578401704 & 0.929211210799148 \tabularnewline
20 & 0.043355154581319 & 0.086710309162638 & 0.956644845418681 \tabularnewline
21 & 0.0416281727657958 & 0.0832563455315916 & 0.958371827234204 \tabularnewline
22 & 0.0255625174886962 & 0.0511250349773925 & 0.974437482511304 \tabularnewline
23 & 0.0272918533766425 & 0.054583706753285 & 0.972708146623358 \tabularnewline
24 & 0.0203029135598361 & 0.0406058271196723 & 0.979697086440164 \tabularnewline
25 & 0.0116444020881405 & 0.023288804176281 & 0.98835559791186 \tabularnewline
26 & 0.00620866260139614 & 0.0124173252027923 & 0.993791337398604 \tabularnewline
27 & 0.00276951984733803 & 0.00553903969467606 & 0.997230480152662 \tabularnewline
28 & 0.00112716273968816 & 0.00225432547937631 & 0.998872837260312 \tabularnewline
29 & 0.00104122173245483 & 0.00208244346490967 & 0.998958778267545 \tabularnewline
30 & 0.00157715800674303 & 0.00315431601348606 & 0.998422841993257 \tabularnewline
31 & 0.00168666497250730 & 0.00337332994501459 & 0.998313335027493 \tabularnewline
32 & 0.00119244490695311 & 0.00238488981390622 & 0.998807555093047 \tabularnewline
33 & 0.00103379065341227 & 0.00206758130682454 & 0.998966209346588 \tabularnewline
34 & 0.000547407720036218 & 0.00109481544007244 & 0.999452592279964 \tabularnewline
35 & 0.00180834123598707 & 0.00361668247197413 & 0.998191658764013 \tabularnewline
36 & 0.00212702691195710 & 0.00425405382391421 & 0.997872973088043 \tabularnewline
37 & 0.0162280586777488 & 0.0324561173554975 & 0.983771941322251 \tabularnewline
38 & 0.0299430891259082 & 0.0598861782518164 & 0.970056910874092 \tabularnewline
39 & 0.0823794600976472 & 0.164758920195294 & 0.917620539902353 \tabularnewline
40 & 0.526637578241239 & 0.946724843517522 & 0.473362421758761 \tabularnewline
41 & 0.477972860841221 & 0.955945721682442 & 0.522027139158779 \tabularnewline
42 & 0.51978503574513 & 0.96042992850974 & 0.48021496425487 \tabularnewline
43 & 0.364093281555167 & 0.728186563110335 & 0.635906718444833 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57740&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]17[/C][C]0.0964755949310787[/C][C]0.192951189862157[/C][C]0.903524405068921[/C][/ROW]
[ROW][C]18[/C][C]0.0481627202277533[/C][C]0.0963254404555066[/C][C]0.951837279772247[/C][/ROW]
[ROW][C]19[/C][C]0.0707887892008522[/C][C]0.141577578401704[/C][C]0.929211210799148[/C][/ROW]
[ROW][C]20[/C][C]0.043355154581319[/C][C]0.086710309162638[/C][C]0.956644845418681[/C][/ROW]
[ROW][C]21[/C][C]0.0416281727657958[/C][C]0.0832563455315916[/C][C]0.958371827234204[/C][/ROW]
[ROW][C]22[/C][C]0.0255625174886962[/C][C]0.0511250349773925[/C][C]0.974437482511304[/C][/ROW]
[ROW][C]23[/C][C]0.0272918533766425[/C][C]0.054583706753285[/C][C]0.972708146623358[/C][/ROW]
[ROW][C]24[/C][C]0.0203029135598361[/C][C]0.0406058271196723[/C][C]0.979697086440164[/C][/ROW]
[ROW][C]25[/C][C]0.0116444020881405[/C][C]0.023288804176281[/C][C]0.98835559791186[/C][/ROW]
[ROW][C]26[/C][C]0.00620866260139614[/C][C]0.0124173252027923[/C][C]0.993791337398604[/C][/ROW]
[ROW][C]27[/C][C]0.00276951984733803[/C][C]0.00553903969467606[/C][C]0.997230480152662[/C][/ROW]
[ROW][C]28[/C][C]0.00112716273968816[/C][C]0.00225432547937631[/C][C]0.998872837260312[/C][/ROW]
[ROW][C]29[/C][C]0.00104122173245483[/C][C]0.00208244346490967[/C][C]0.998958778267545[/C][/ROW]
[ROW][C]30[/C][C]0.00157715800674303[/C][C]0.00315431601348606[/C][C]0.998422841993257[/C][/ROW]
[ROW][C]31[/C][C]0.00168666497250730[/C][C]0.00337332994501459[/C][C]0.998313335027493[/C][/ROW]
[ROW][C]32[/C][C]0.00119244490695311[/C][C]0.00238488981390622[/C][C]0.998807555093047[/C][/ROW]
[ROW][C]33[/C][C]0.00103379065341227[/C][C]0.00206758130682454[/C][C]0.998966209346588[/C][/ROW]
[ROW][C]34[/C][C]0.000547407720036218[/C][C]0.00109481544007244[/C][C]0.999452592279964[/C][/ROW]
[ROW][C]35[/C][C]0.00180834123598707[/C][C]0.00361668247197413[/C][C]0.998191658764013[/C][/ROW]
[ROW][C]36[/C][C]0.00212702691195710[/C][C]0.00425405382391421[/C][C]0.997872973088043[/C][/ROW]
[ROW][C]37[/C][C]0.0162280586777488[/C][C]0.0324561173554975[/C][C]0.983771941322251[/C][/ROW]
[ROW][C]38[/C][C]0.0299430891259082[/C][C]0.0598861782518164[/C][C]0.970056910874092[/C][/ROW]
[ROW][C]39[/C][C]0.0823794600976472[/C][C]0.164758920195294[/C][C]0.917620539902353[/C][/ROW]
[ROW][C]40[/C][C]0.526637578241239[/C][C]0.946724843517522[/C][C]0.473362421758761[/C][/ROW]
[ROW][C]41[/C][C]0.477972860841221[/C][C]0.955945721682442[/C][C]0.522027139158779[/C][/ROW]
[ROW][C]42[/C][C]0.51978503574513[/C][C]0.96042992850974[/C][C]0.48021496425487[/C][/ROW]
[ROW][C]43[/C][C]0.364093281555167[/C][C]0.728186563110335[/C][C]0.635906718444833[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57740&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57740&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
170.09647559493107870.1929511898621570.903524405068921
180.04816272022775330.09632544045550660.951837279772247
190.07078878920085220.1415775784017040.929211210799148
200.0433551545813190.0867103091626380.956644845418681
210.04162817276579580.08325634553159160.958371827234204
220.02556251748869620.05112503497739250.974437482511304
230.02729185337664250.0545837067532850.972708146623358
240.02030291355983610.04060582711967230.979697086440164
250.01164440208814050.0232888041762810.98835559791186
260.006208662601396140.01241732520279230.993791337398604
270.002769519847338030.005539039694676060.997230480152662
280.001127162739688160.002254325479376310.998872837260312
290.001041221732454830.002082443464909670.998958778267545
300.001577158006743030.003154316013486060.998422841993257
310.001686664972507300.003373329945014590.998313335027493
320.001192444906953110.002384889813906220.998807555093047
330.001033790653412270.002067581306824540.998966209346588
340.0005474077200362180.001094815440072440.999452592279964
350.001808341235987070.003616682471974130.998191658764013
360.002127026911957100.004254053823914210.997872973088043
370.01622805867774880.03245611735549750.983771941322251
380.02994308912590820.05988617825181640.970056910874092
390.08237946009764720.1647589201952940.917620539902353
400.5266375782412390.9467248435175220.473362421758761
410.4779728608412210.9559457216824420.522027139158779
420.519785035745130.960429928509740.48021496425487
430.3640932815551670.7281865631103350.635906718444833







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level100.370370370370370NOK
5% type I error level140.518518518518518NOK
10% type I error level200.740740740740741NOK

\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 & 10 & 0.370370370370370 & NOK \tabularnewline
5% type I error level & 14 & 0.518518518518518 & NOK \tabularnewline
10% type I error level & 20 & 0.740740740740741 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57740&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]10[/C][C]0.370370370370370[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]14[/C][C]0.518518518518518[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]20[/C][C]0.740740740740741[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57740&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57740&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 level100.370370370370370NOK
5% type I error level140.518518518518518NOK
10% type I error level200.740740740740741NOK



Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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')
}