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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 computationFri, 20 Nov 2009 10:34:07 -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/20/t1258738577ebfpurlu7043k1o.htm/, Retrieved Thu, 28 Mar 2024 21:05:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58358, Retrieved Thu, 28 Mar 2024 21:05:39 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsShwWs7.3
Estimated Impact156
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]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:06:21] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [Ws7.3 lineaire tr...] [2009-11-20 17:34:07] [51108381f3361ca8af49c4f74052c840] [Current]
-    D        [Multiple Regression] [WS 7 TREND] [2010-11-23 08:46:58] [814f53995537cd15c528d8efbf1cf544]
-               [Multiple Regression] [Lineaire trend] [2011-11-22 08:47:29] [c505444e07acba7694d29053ca5d114e]
- RM            [Multiple Regression] [] [2011-11-22 10:13:16] [74be16979710d4c4e7c6647856088456]
- RM            [Multiple Regression] [] [2013-11-20 15:04:02] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
151,7	105,2
121,3	105,2
133,0	105,6
119,6	105,6
122,2	106,2
117,4	106,3
106,7	106,4
87,5	106,9
81,0	107,2
110,3	107,3
87,0	107,3
55,7	107,4
146,0	107,55
137,5	107,87
138,5	108,37
135,6	108,38
107,3	107,92
99,0	108,03
91,4	108,14
68,4	108,3
82,6	108,64
98,4	108,66
71,3	109,04
47,6	109,03
130,8	109,03
113,6	109,54
125,7	109,75
113,6	109,83
97,1	109,65
104,4	109,82
91,8	109,95
75,1	110,12
89,2	110,15
110,2	110,2
78,4	109,99
68,4	110,14
122,8	110,14
129,7	110,81
159,1	110,97
139,0	110,99
102,2	109,73
113,6	109,81
81,5	110,02
77,4	110,18
87,6	110,21
101,2	110,25
87,2	110,36
64,9	110,51
133,1	110,64
118,0	110,95
135,9	111,18
125,7	111,19
108,0	111,69
128,3	111,7
84,7	111,83
86,4	111,77
92,2	111,73
95,8	112,01
92,3	111,86
54,3	112,04




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=58358&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=58358&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58358&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
Yt[t] = + 247.380841890874 -1.77464261498657Xt[t] + 78.1125743122356M1[t] + 65.7367308094882M2[t] + 80.5308594646116M3[t] + 68.6751867579987M4[t] + 48.8929798102284M5[t] + 54.0815320866646M6[t] + 32.8446193529302M7[t] + 20.7564387499451M8[t] + 28.3924274457508M9[t] + 45.068078292647M10[t] + 25.0159548712641M11[t] + 0.158264129372544t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Yt[t] =  +  247.380841890874 -1.77464261498657Xt[t] +  78.1125743122356M1[t] +  65.7367308094882M2[t] +  80.5308594646116M3[t] +  68.6751867579987M4[t] +  48.8929798102284M5[t] +  54.0815320866646M6[t] +  32.8446193529302M7[t] +  20.7564387499451M8[t] +  28.3924274457508M9[t] +  45.068078292647M10[t] +  25.0159548712641M11[t] +  0.158264129372544t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58358&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Yt[t] =  +  247.380841890874 -1.77464261498657Xt[t] +  78.1125743122356M1[t] +  65.7367308094882M2[t] +  80.5308594646116M3[t] +  68.6751867579987M4[t] +  48.8929798102284M5[t] +  54.0815320866646M6[t] +  32.8446193529302M7[t] +  20.7564387499451M8[t] +  28.3924274457508M9[t] +  45.068078292647M10[t] +  25.0159548712641M11[t] +  0.158264129372544t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58358&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58358&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
Yt[t] = + 247.380841890874 -1.77464261498657Xt[t] + 78.1125743122356M1[t] + 65.7367308094882M2[t] + 80.5308594646116M3[t] + 68.6751867579987M4[t] + 48.8929798102284M5[t] + 54.0815320866646M6[t] + 32.8446193529302M7[t] + 20.7564387499451M8[t] + 28.3924274457508M9[t] + 45.068078292647M10[t] + 25.0159548712641M11[t] + 0.158264129372544t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)247.380841890874262.8639540.94110.3515710.175785
Xt-1.774642614986572.47651-0.71660.477250.238625
M178.11257431223566.16798612.664200
M265.73673080948826.14548210.696800
M380.53085946461166.17186113.048100
M468.67518675799876.14593311.174100
M548.89297981022846.1222777.986100
M654.08153208666466.1171878.840900
M732.84461935293026.1103945.37522e-061e-06
M820.75643874994516.1063963.39910.0014060.000703
M928.39242744575086.1049484.65072.8e-051.4e-05
M1045.0680782926476.1024177.385300
M1125.01595487126416.0989944.10170.0001668.3e-05
t0.1582641293725440.2649390.59740.5531960.276598

\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) & 247.380841890874 & 262.863954 & 0.9411 & 0.351571 & 0.175785 \tabularnewline
Xt & -1.77464261498657 & 2.47651 & -0.7166 & 0.47725 & 0.238625 \tabularnewline
M1 & 78.1125743122356 & 6.167986 & 12.6642 & 0 & 0 \tabularnewline
M2 & 65.7367308094882 & 6.145482 & 10.6968 & 0 & 0 \tabularnewline
M3 & 80.5308594646116 & 6.171861 & 13.0481 & 0 & 0 \tabularnewline
M4 & 68.6751867579987 & 6.145933 & 11.1741 & 0 & 0 \tabularnewline
M5 & 48.8929798102284 & 6.122277 & 7.9861 & 0 & 0 \tabularnewline
M6 & 54.0815320866646 & 6.117187 & 8.8409 & 0 & 0 \tabularnewline
M7 & 32.8446193529302 & 6.110394 & 5.3752 & 2e-06 & 1e-06 \tabularnewline
M8 & 20.7564387499451 & 6.106396 & 3.3991 & 0.001406 & 0.000703 \tabularnewline
M9 & 28.3924274457508 & 6.104948 & 4.6507 & 2.8e-05 & 1.4e-05 \tabularnewline
M10 & 45.068078292647 & 6.102417 & 7.3853 & 0 & 0 \tabularnewline
M11 & 25.0159548712641 & 6.098994 & 4.1017 & 0.000166 & 8.3e-05 \tabularnewline
t & 0.158264129372544 & 0.264939 & 0.5974 & 0.553196 & 0.276598 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58358&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]247.380841890874[/C][C]262.863954[/C][C]0.9411[/C][C]0.351571[/C][C]0.175785[/C][/ROW]
[ROW][C]Xt[/C][C]-1.77464261498657[/C][C]2.47651[/C][C]-0.7166[/C][C]0.47725[/C][C]0.238625[/C][/ROW]
[ROW][C]M1[/C][C]78.1125743122356[/C][C]6.167986[/C][C]12.6642[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M2[/C][C]65.7367308094882[/C][C]6.145482[/C][C]10.6968[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M3[/C][C]80.5308594646116[/C][C]6.171861[/C][C]13.0481[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M4[/C][C]68.6751867579987[/C][C]6.145933[/C][C]11.1741[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M5[/C][C]48.8929798102284[/C][C]6.122277[/C][C]7.9861[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M6[/C][C]54.0815320866646[/C][C]6.117187[/C][C]8.8409[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M7[/C][C]32.8446193529302[/C][C]6.110394[/C][C]5.3752[/C][C]2e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M8[/C][C]20.7564387499451[/C][C]6.106396[/C][C]3.3991[/C][C]0.001406[/C][C]0.000703[/C][/ROW]
[ROW][C]M9[/C][C]28.3924274457508[/C][C]6.104948[/C][C]4.6507[/C][C]2.8e-05[/C][C]1.4e-05[/C][/ROW]
[ROW][C]M10[/C][C]45.068078292647[/C][C]6.102417[/C][C]7.3853[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M11[/C][C]25.0159548712641[/C][C]6.098994[/C][C]4.1017[/C][C]0.000166[/C][C]8.3e-05[/C][/ROW]
[ROW][C]t[/C][C]0.158264129372544[/C][C]0.264939[/C][C]0.5974[/C][C]0.553196[/C][C]0.276598[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58358&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58358&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)247.380841890874262.8639540.94110.3515710.175785
Xt-1.774642614986572.47651-0.71660.477250.238625
M178.11257431223566.16798612.664200
M265.73673080948826.14548210.696800
M380.53085946461166.17186113.048100
M468.67518675799876.14593311.174100
M548.89297981022846.1222777.986100
M654.08153208666466.1171878.840900
M732.84461935293026.1103945.37522e-061e-06
M820.75643874994516.1063963.39910.0014060.000703
M928.39242744575086.1049484.65072.8e-051.4e-05
M1045.0680782926476.1024177.385300
M1125.01595487126416.0989944.10170.0001668.3e-05
t0.1582641293725440.2649390.59740.5531960.276598







Multiple Linear Regression - Regression Statistics
Multiple R0.943285641139972
R-squared0.889787800780848
Adjusted R-squared0.858640874914566
F-TEST (value)28.5674356628588
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation9.64255873554797
Sum Squared Residuals4277.03119255066

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.943285641139972 \tabularnewline
R-squared & 0.889787800780848 \tabularnewline
Adjusted R-squared & 0.858640874914566 \tabularnewline
F-TEST (value) & 28.5674356628588 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 9.64255873554797 \tabularnewline
Sum Squared Residuals & 4277.03119255066 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58358&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.943285641139972[/C][/ROW]
[ROW][C]R-squared[/C][C]0.889787800780848[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.858640874914566[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]28.5674356628588[/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[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]9.64255873554797[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]4277.03119255066[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58358&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58358&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 R0.943285641139972
R-squared0.889787800780848
Adjusted R-squared0.858640874914566
F-TEST (value)28.5674356628588
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation9.64255873554797
Sum Squared Residuals4277.03119255066







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1151.7138.95927723589512.7407227641054
2121.3126.741697862520-5.44169786251965
3133140.984233601021-7.98423360102095
4119.6129.286825023781-9.68682502378063
5122.2108.59809663639113.6019033636092
6117.4113.7674487807013.63255121929910
7106.792.511335914840514.1886640851595
887.579.69409813373477.80590186626531
98186.9559581744169-5.95595817441691
10110.3103.6124088891876.68759111081307
118783.71854959717663.28145040282337
1255.758.6833945937864-2.98339459378642
13146136.6880366431479.31196335685345
14137.5123.90257163297613.597428367024
15138.5137.9676431099790.532356890021326
16135.6126.2524881065899.3475118934115
17107.3107.444880891084-0.144880891084483
1899112.596486609245-13.5964866092447
1991.491.32262731723430.0773726827656793
2068.479.108768025224-10.7087680252240
2182.686.2996423613068-3.69964236130678
2298.4103.098064485276-4.69806448527572
2371.382.5298409995705-11.2298409995705
2447.657.6898966838288-10.0898966838288
25130.8135.960735125437-5.16073512543691
26113.6122.838088018419-9.23808801841893
27125.7137.417805853768-11.7178058537677
28113.6125.578425867328-11.9784258673285
2997.1106.273918719628-9.17391871962822
30104.4111.319045880889-6.91904588088926
3191.890.00969373657921.79030626342085
3275.177.778088018419-2.67808801841894
3389.285.51910156514763.68089843485243
34110.2102.2642844106677.93571558933307
3578.482.7431000678038-4.34310006780376
3668.457.619212933664310.7807870663358
37122.8135.890051375272-13.0900513752724
38129.7122.4834614498577.21653855014348
39159.1137.15191141595521.9480885840454
40139125.41900998641513.5809900135854
41102.2108.031116862900-5.83111686289982
42113.6113.2359618595100.364038140490366
4381.591.7846383060006-10.2846383060006
4477.479.5707790139903-2.17077901399025
4587.687.3117925607190.288207439281084
46101.2104.074721832388-2.87472183238813
4787.283.98565185272923.21434814727076
4864.958.86176471858976.03823528141027
49133.1136.901899620250-3.8018996202496
50118124.134181036229-6.1341810362289
51135.9138.678406019278-2.77840601927798
52125.7126.963251015888-1.26325101588779
53108106.4519868899971.54801311000334
54128.3111.78105686965616.5189431303445
5584.790.4717047253454-5.77170472534544
5686.478.64826680863217.75173319136786
5792.286.51350533840985.68649466159017
5895.8102.850520382482-7.05052038248228
5992.383.22285748271999.0771425172801
6054.358.0457310701308-3.74573107013079

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 151.7 & 138.959277235895 & 12.7407227641054 \tabularnewline
2 & 121.3 & 126.741697862520 & -5.44169786251965 \tabularnewline
3 & 133 & 140.984233601021 & -7.98423360102095 \tabularnewline
4 & 119.6 & 129.286825023781 & -9.68682502378063 \tabularnewline
5 & 122.2 & 108.598096636391 & 13.6019033636092 \tabularnewline
6 & 117.4 & 113.767448780701 & 3.63255121929910 \tabularnewline
7 & 106.7 & 92.5113359148405 & 14.1886640851595 \tabularnewline
8 & 87.5 & 79.6940981337347 & 7.80590186626531 \tabularnewline
9 & 81 & 86.9559581744169 & -5.95595817441691 \tabularnewline
10 & 110.3 & 103.612408889187 & 6.68759111081307 \tabularnewline
11 & 87 & 83.7185495971766 & 3.28145040282337 \tabularnewline
12 & 55.7 & 58.6833945937864 & -2.98339459378642 \tabularnewline
13 & 146 & 136.688036643147 & 9.31196335685345 \tabularnewline
14 & 137.5 & 123.902571632976 & 13.597428367024 \tabularnewline
15 & 138.5 & 137.967643109979 & 0.532356890021326 \tabularnewline
16 & 135.6 & 126.252488106589 & 9.3475118934115 \tabularnewline
17 & 107.3 & 107.444880891084 & -0.144880891084483 \tabularnewline
18 & 99 & 112.596486609245 & -13.5964866092447 \tabularnewline
19 & 91.4 & 91.3226273172343 & 0.0773726827656793 \tabularnewline
20 & 68.4 & 79.108768025224 & -10.7087680252240 \tabularnewline
21 & 82.6 & 86.2996423613068 & -3.69964236130678 \tabularnewline
22 & 98.4 & 103.098064485276 & -4.69806448527572 \tabularnewline
23 & 71.3 & 82.5298409995705 & -11.2298409995705 \tabularnewline
24 & 47.6 & 57.6898966838288 & -10.0898966838288 \tabularnewline
25 & 130.8 & 135.960735125437 & -5.16073512543691 \tabularnewline
26 & 113.6 & 122.838088018419 & -9.23808801841893 \tabularnewline
27 & 125.7 & 137.417805853768 & -11.7178058537677 \tabularnewline
28 & 113.6 & 125.578425867328 & -11.9784258673285 \tabularnewline
29 & 97.1 & 106.273918719628 & -9.17391871962822 \tabularnewline
30 & 104.4 & 111.319045880889 & -6.91904588088926 \tabularnewline
31 & 91.8 & 90.0096937365792 & 1.79030626342085 \tabularnewline
32 & 75.1 & 77.778088018419 & -2.67808801841894 \tabularnewline
33 & 89.2 & 85.5191015651476 & 3.68089843485243 \tabularnewline
34 & 110.2 & 102.264284410667 & 7.93571558933307 \tabularnewline
35 & 78.4 & 82.7431000678038 & -4.34310006780376 \tabularnewline
36 & 68.4 & 57.6192129336643 & 10.7807870663358 \tabularnewline
37 & 122.8 & 135.890051375272 & -13.0900513752724 \tabularnewline
38 & 129.7 & 122.483461449857 & 7.21653855014348 \tabularnewline
39 & 159.1 & 137.151911415955 & 21.9480885840454 \tabularnewline
40 & 139 & 125.419009986415 & 13.5809900135854 \tabularnewline
41 & 102.2 & 108.031116862900 & -5.83111686289982 \tabularnewline
42 & 113.6 & 113.235961859510 & 0.364038140490366 \tabularnewline
43 & 81.5 & 91.7846383060006 & -10.2846383060006 \tabularnewline
44 & 77.4 & 79.5707790139903 & -2.17077901399025 \tabularnewline
45 & 87.6 & 87.311792560719 & 0.288207439281084 \tabularnewline
46 & 101.2 & 104.074721832388 & -2.87472183238813 \tabularnewline
47 & 87.2 & 83.9856518527292 & 3.21434814727076 \tabularnewline
48 & 64.9 & 58.8617647185897 & 6.03823528141027 \tabularnewline
49 & 133.1 & 136.901899620250 & -3.8018996202496 \tabularnewline
50 & 118 & 124.134181036229 & -6.1341810362289 \tabularnewline
51 & 135.9 & 138.678406019278 & -2.77840601927798 \tabularnewline
52 & 125.7 & 126.963251015888 & -1.26325101588779 \tabularnewline
53 & 108 & 106.451986889997 & 1.54801311000334 \tabularnewline
54 & 128.3 & 111.781056869656 & 16.5189431303445 \tabularnewline
55 & 84.7 & 90.4717047253454 & -5.77170472534544 \tabularnewline
56 & 86.4 & 78.6482668086321 & 7.75173319136786 \tabularnewline
57 & 92.2 & 86.5135053384098 & 5.68649466159017 \tabularnewline
58 & 95.8 & 102.850520382482 & -7.05052038248228 \tabularnewline
59 & 92.3 & 83.2228574827199 & 9.0771425172801 \tabularnewline
60 & 54.3 & 58.0457310701308 & -3.74573107013079 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58358&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]151.7[/C][C]138.959277235895[/C][C]12.7407227641054[/C][/ROW]
[ROW][C]2[/C][C]121.3[/C][C]126.741697862520[/C][C]-5.44169786251965[/C][/ROW]
[ROW][C]3[/C][C]133[/C][C]140.984233601021[/C][C]-7.98423360102095[/C][/ROW]
[ROW][C]4[/C][C]119.6[/C][C]129.286825023781[/C][C]-9.68682502378063[/C][/ROW]
[ROW][C]5[/C][C]122.2[/C][C]108.598096636391[/C][C]13.6019033636092[/C][/ROW]
[ROW][C]6[/C][C]117.4[/C][C]113.767448780701[/C][C]3.63255121929910[/C][/ROW]
[ROW][C]7[/C][C]106.7[/C][C]92.5113359148405[/C][C]14.1886640851595[/C][/ROW]
[ROW][C]8[/C][C]87.5[/C][C]79.6940981337347[/C][C]7.80590186626531[/C][/ROW]
[ROW][C]9[/C][C]81[/C][C]86.9559581744169[/C][C]-5.95595817441691[/C][/ROW]
[ROW][C]10[/C][C]110.3[/C][C]103.612408889187[/C][C]6.68759111081307[/C][/ROW]
[ROW][C]11[/C][C]87[/C][C]83.7185495971766[/C][C]3.28145040282337[/C][/ROW]
[ROW][C]12[/C][C]55.7[/C][C]58.6833945937864[/C][C]-2.98339459378642[/C][/ROW]
[ROW][C]13[/C][C]146[/C][C]136.688036643147[/C][C]9.31196335685345[/C][/ROW]
[ROW][C]14[/C][C]137.5[/C][C]123.902571632976[/C][C]13.597428367024[/C][/ROW]
[ROW][C]15[/C][C]138.5[/C][C]137.967643109979[/C][C]0.532356890021326[/C][/ROW]
[ROW][C]16[/C][C]135.6[/C][C]126.252488106589[/C][C]9.3475118934115[/C][/ROW]
[ROW][C]17[/C][C]107.3[/C][C]107.444880891084[/C][C]-0.144880891084483[/C][/ROW]
[ROW][C]18[/C][C]99[/C][C]112.596486609245[/C][C]-13.5964866092447[/C][/ROW]
[ROW][C]19[/C][C]91.4[/C][C]91.3226273172343[/C][C]0.0773726827656793[/C][/ROW]
[ROW][C]20[/C][C]68.4[/C][C]79.108768025224[/C][C]-10.7087680252240[/C][/ROW]
[ROW][C]21[/C][C]82.6[/C][C]86.2996423613068[/C][C]-3.69964236130678[/C][/ROW]
[ROW][C]22[/C][C]98.4[/C][C]103.098064485276[/C][C]-4.69806448527572[/C][/ROW]
[ROW][C]23[/C][C]71.3[/C][C]82.5298409995705[/C][C]-11.2298409995705[/C][/ROW]
[ROW][C]24[/C][C]47.6[/C][C]57.6898966838288[/C][C]-10.0898966838288[/C][/ROW]
[ROW][C]25[/C][C]130.8[/C][C]135.960735125437[/C][C]-5.16073512543691[/C][/ROW]
[ROW][C]26[/C][C]113.6[/C][C]122.838088018419[/C][C]-9.23808801841893[/C][/ROW]
[ROW][C]27[/C][C]125.7[/C][C]137.417805853768[/C][C]-11.7178058537677[/C][/ROW]
[ROW][C]28[/C][C]113.6[/C][C]125.578425867328[/C][C]-11.9784258673285[/C][/ROW]
[ROW][C]29[/C][C]97.1[/C][C]106.273918719628[/C][C]-9.17391871962822[/C][/ROW]
[ROW][C]30[/C][C]104.4[/C][C]111.319045880889[/C][C]-6.91904588088926[/C][/ROW]
[ROW][C]31[/C][C]91.8[/C][C]90.0096937365792[/C][C]1.79030626342085[/C][/ROW]
[ROW][C]32[/C][C]75.1[/C][C]77.778088018419[/C][C]-2.67808801841894[/C][/ROW]
[ROW][C]33[/C][C]89.2[/C][C]85.5191015651476[/C][C]3.68089843485243[/C][/ROW]
[ROW][C]34[/C][C]110.2[/C][C]102.264284410667[/C][C]7.93571558933307[/C][/ROW]
[ROW][C]35[/C][C]78.4[/C][C]82.7431000678038[/C][C]-4.34310006780376[/C][/ROW]
[ROW][C]36[/C][C]68.4[/C][C]57.6192129336643[/C][C]10.7807870663358[/C][/ROW]
[ROW][C]37[/C][C]122.8[/C][C]135.890051375272[/C][C]-13.0900513752724[/C][/ROW]
[ROW][C]38[/C][C]129.7[/C][C]122.483461449857[/C][C]7.21653855014348[/C][/ROW]
[ROW][C]39[/C][C]159.1[/C][C]137.151911415955[/C][C]21.9480885840454[/C][/ROW]
[ROW][C]40[/C][C]139[/C][C]125.419009986415[/C][C]13.5809900135854[/C][/ROW]
[ROW][C]41[/C][C]102.2[/C][C]108.031116862900[/C][C]-5.83111686289982[/C][/ROW]
[ROW][C]42[/C][C]113.6[/C][C]113.235961859510[/C][C]0.364038140490366[/C][/ROW]
[ROW][C]43[/C][C]81.5[/C][C]91.7846383060006[/C][C]-10.2846383060006[/C][/ROW]
[ROW][C]44[/C][C]77.4[/C][C]79.5707790139903[/C][C]-2.17077901399025[/C][/ROW]
[ROW][C]45[/C][C]87.6[/C][C]87.311792560719[/C][C]0.288207439281084[/C][/ROW]
[ROW][C]46[/C][C]101.2[/C][C]104.074721832388[/C][C]-2.87472183238813[/C][/ROW]
[ROW][C]47[/C][C]87.2[/C][C]83.9856518527292[/C][C]3.21434814727076[/C][/ROW]
[ROW][C]48[/C][C]64.9[/C][C]58.8617647185897[/C][C]6.03823528141027[/C][/ROW]
[ROW][C]49[/C][C]133.1[/C][C]136.901899620250[/C][C]-3.8018996202496[/C][/ROW]
[ROW][C]50[/C][C]118[/C][C]124.134181036229[/C][C]-6.1341810362289[/C][/ROW]
[ROW][C]51[/C][C]135.9[/C][C]138.678406019278[/C][C]-2.77840601927798[/C][/ROW]
[ROW][C]52[/C][C]125.7[/C][C]126.963251015888[/C][C]-1.26325101588779[/C][/ROW]
[ROW][C]53[/C][C]108[/C][C]106.451986889997[/C][C]1.54801311000334[/C][/ROW]
[ROW][C]54[/C][C]128.3[/C][C]111.781056869656[/C][C]16.5189431303445[/C][/ROW]
[ROW][C]55[/C][C]84.7[/C][C]90.4717047253454[/C][C]-5.77170472534544[/C][/ROW]
[ROW][C]56[/C][C]86.4[/C][C]78.6482668086321[/C][C]7.75173319136786[/C][/ROW]
[ROW][C]57[/C][C]92.2[/C][C]86.5135053384098[/C][C]5.68649466159017[/C][/ROW]
[ROW][C]58[/C][C]95.8[/C][C]102.850520382482[/C][C]-7.05052038248228[/C][/ROW]
[ROW][C]59[/C][C]92.3[/C][C]83.2228574827199[/C][C]9.0771425172801[/C][/ROW]
[ROW][C]60[/C][C]54.3[/C][C]58.0457310701308[/C][C]-3.74573107013079[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58358&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58358&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
1151.7138.95927723589512.7407227641054
2121.3126.741697862520-5.44169786251965
3133140.984233601021-7.98423360102095
4119.6129.286825023781-9.68682502378063
5122.2108.59809663639113.6019033636092
6117.4113.7674487807013.63255121929910
7106.792.511335914840514.1886640851595
887.579.69409813373477.80590186626531
98186.9559581744169-5.95595817441691
10110.3103.6124088891876.68759111081307
118783.71854959717663.28145040282337
1255.758.6833945937864-2.98339459378642
13146136.6880366431479.31196335685345
14137.5123.90257163297613.597428367024
15138.5137.9676431099790.532356890021326
16135.6126.2524881065899.3475118934115
17107.3107.444880891084-0.144880891084483
1899112.596486609245-13.5964866092447
1991.491.32262731723430.0773726827656793
2068.479.108768025224-10.7087680252240
2182.686.2996423613068-3.69964236130678
2298.4103.098064485276-4.69806448527572
2371.382.5298409995705-11.2298409995705
2447.657.6898966838288-10.0898966838288
25130.8135.960735125437-5.16073512543691
26113.6122.838088018419-9.23808801841893
27125.7137.417805853768-11.7178058537677
28113.6125.578425867328-11.9784258673285
2997.1106.273918719628-9.17391871962822
30104.4111.319045880889-6.91904588088926
3191.890.00969373657921.79030626342085
3275.177.778088018419-2.67808801841894
3389.285.51910156514763.68089843485243
34110.2102.2642844106677.93571558933307
3578.482.7431000678038-4.34310006780376
3668.457.619212933664310.7807870663358
37122.8135.890051375272-13.0900513752724
38129.7122.4834614498577.21653855014348
39159.1137.15191141595521.9480885840454
40139125.41900998641513.5809900135854
41102.2108.031116862900-5.83111686289982
42113.6113.2359618595100.364038140490366
4381.591.7846383060006-10.2846383060006
4477.479.5707790139903-2.17077901399025
4587.687.3117925607190.288207439281084
46101.2104.074721832388-2.87472183238813
4787.283.98565185272923.21434814727076
4864.958.86176471858976.03823528141027
49133.1136.901899620250-3.8018996202496
50118124.134181036229-6.1341810362289
51135.9138.678406019278-2.77840601927798
52125.7126.963251015888-1.26325101588779
53108106.4519868899971.54801311000334
54128.3111.78105686965616.5189431303445
5584.790.4717047253454-5.77170472534544
5686.478.64826680863217.75173319136786
5792.286.51350533840985.68649466159017
5895.8102.850520382482-7.05052038248228
5992.383.22285748271999.0771425172801
6054.358.0457310701308-3.74573107013079







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.2164299717598870.4328599435197740.783570028240113
180.1045645069535400.2091290139070790.89543549304646
190.05411409389569810.1082281877913960.945885906104302
200.03342474028230490.06684948056460970.966575259717695
210.2590380101757470.5180760203514930.740961989824253
220.1863191098232300.3726382196464590.81368089017677
230.1432378670822940.2864757341645880.856762132917706
240.1008275521301770.2016551042603530.899172447869823
250.0689300990923510.1378601981847020.931069900907649
260.05660507658169640.1132101531633930.943394923418304
270.0607805645067050.121561129013410.939219435493295
280.0651167858638920.1302335717277840.934883214136108
290.04556460938748290.09112921877496590.954435390612517
300.1410479999707870.2820959999415750.858952000029213
310.1170130391814070.2340260783628140.882986960818593
320.2010731275437080.4021462550874160.798926872456292
330.5021992299760080.9956015400479830.497800770023992
340.5846922489362740.8306155021274510.415307751063726
350.7879627071355460.4240745857289080.212037292864454
360.8402349195350310.3195301609299370.159765080464969
370.9577861612557270.08442767748854540.0422138387442727
380.9479514862918780.1040970274162450.0520485137081223
390.968787618373450.06242476325309940.0312123816265497
400.9462245734004440.1075508531991120.0537754265995561
410.8896956244023240.2206087511953530.110304375597676
420.8789289733205360.2421420533589270.121071026679464
430.7875268010254030.4249463979491950.212473198974597

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.216429971759887 & 0.432859943519774 & 0.783570028240113 \tabularnewline
18 & 0.104564506953540 & 0.209129013907079 & 0.89543549304646 \tabularnewline
19 & 0.0541140938956981 & 0.108228187791396 & 0.945885906104302 \tabularnewline
20 & 0.0334247402823049 & 0.0668494805646097 & 0.966575259717695 \tabularnewline
21 & 0.259038010175747 & 0.518076020351493 & 0.740961989824253 \tabularnewline
22 & 0.186319109823230 & 0.372638219646459 & 0.81368089017677 \tabularnewline
23 & 0.143237867082294 & 0.286475734164588 & 0.856762132917706 \tabularnewline
24 & 0.100827552130177 & 0.201655104260353 & 0.899172447869823 \tabularnewline
25 & 0.068930099092351 & 0.137860198184702 & 0.931069900907649 \tabularnewline
26 & 0.0566050765816964 & 0.113210153163393 & 0.943394923418304 \tabularnewline
27 & 0.060780564506705 & 0.12156112901341 & 0.939219435493295 \tabularnewline
28 & 0.065116785863892 & 0.130233571727784 & 0.934883214136108 \tabularnewline
29 & 0.0455646093874829 & 0.0911292187749659 & 0.954435390612517 \tabularnewline
30 & 0.141047999970787 & 0.282095999941575 & 0.858952000029213 \tabularnewline
31 & 0.117013039181407 & 0.234026078362814 & 0.882986960818593 \tabularnewline
32 & 0.201073127543708 & 0.402146255087416 & 0.798926872456292 \tabularnewline
33 & 0.502199229976008 & 0.995601540047983 & 0.497800770023992 \tabularnewline
34 & 0.584692248936274 & 0.830615502127451 & 0.415307751063726 \tabularnewline
35 & 0.787962707135546 & 0.424074585728908 & 0.212037292864454 \tabularnewline
36 & 0.840234919535031 & 0.319530160929937 & 0.159765080464969 \tabularnewline
37 & 0.957786161255727 & 0.0844276774885454 & 0.0422138387442727 \tabularnewline
38 & 0.947951486291878 & 0.104097027416245 & 0.0520485137081223 \tabularnewline
39 & 0.96878761837345 & 0.0624247632530994 & 0.0312123816265497 \tabularnewline
40 & 0.946224573400444 & 0.107550853199112 & 0.0537754265995561 \tabularnewline
41 & 0.889695624402324 & 0.220608751195353 & 0.110304375597676 \tabularnewline
42 & 0.878928973320536 & 0.242142053358927 & 0.121071026679464 \tabularnewline
43 & 0.787526801025403 & 0.424946397949195 & 0.212473198974597 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58358&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]0.216429971759887[/C][C]0.432859943519774[/C][C]0.783570028240113[/C][/ROW]
[ROW][C]18[/C][C]0.104564506953540[/C][C]0.209129013907079[/C][C]0.89543549304646[/C][/ROW]
[ROW][C]19[/C][C]0.0541140938956981[/C][C]0.108228187791396[/C][C]0.945885906104302[/C][/ROW]
[ROW][C]20[/C][C]0.0334247402823049[/C][C]0.0668494805646097[/C][C]0.966575259717695[/C][/ROW]
[ROW][C]21[/C][C]0.259038010175747[/C][C]0.518076020351493[/C][C]0.740961989824253[/C][/ROW]
[ROW][C]22[/C][C]0.186319109823230[/C][C]0.372638219646459[/C][C]0.81368089017677[/C][/ROW]
[ROW][C]23[/C][C]0.143237867082294[/C][C]0.286475734164588[/C][C]0.856762132917706[/C][/ROW]
[ROW][C]24[/C][C]0.100827552130177[/C][C]0.201655104260353[/C][C]0.899172447869823[/C][/ROW]
[ROW][C]25[/C][C]0.068930099092351[/C][C]0.137860198184702[/C][C]0.931069900907649[/C][/ROW]
[ROW][C]26[/C][C]0.0566050765816964[/C][C]0.113210153163393[/C][C]0.943394923418304[/C][/ROW]
[ROW][C]27[/C][C]0.060780564506705[/C][C]0.12156112901341[/C][C]0.939219435493295[/C][/ROW]
[ROW][C]28[/C][C]0.065116785863892[/C][C]0.130233571727784[/C][C]0.934883214136108[/C][/ROW]
[ROW][C]29[/C][C]0.0455646093874829[/C][C]0.0911292187749659[/C][C]0.954435390612517[/C][/ROW]
[ROW][C]30[/C][C]0.141047999970787[/C][C]0.282095999941575[/C][C]0.858952000029213[/C][/ROW]
[ROW][C]31[/C][C]0.117013039181407[/C][C]0.234026078362814[/C][C]0.882986960818593[/C][/ROW]
[ROW][C]32[/C][C]0.201073127543708[/C][C]0.402146255087416[/C][C]0.798926872456292[/C][/ROW]
[ROW][C]33[/C][C]0.502199229976008[/C][C]0.995601540047983[/C][C]0.497800770023992[/C][/ROW]
[ROW][C]34[/C][C]0.584692248936274[/C][C]0.830615502127451[/C][C]0.415307751063726[/C][/ROW]
[ROW][C]35[/C][C]0.787962707135546[/C][C]0.424074585728908[/C][C]0.212037292864454[/C][/ROW]
[ROW][C]36[/C][C]0.840234919535031[/C][C]0.319530160929937[/C][C]0.159765080464969[/C][/ROW]
[ROW][C]37[/C][C]0.957786161255727[/C][C]0.0844276774885454[/C][C]0.0422138387442727[/C][/ROW]
[ROW][C]38[/C][C]0.947951486291878[/C][C]0.104097027416245[/C][C]0.0520485137081223[/C][/ROW]
[ROW][C]39[/C][C]0.96878761837345[/C][C]0.0624247632530994[/C][C]0.0312123816265497[/C][/ROW]
[ROW][C]40[/C][C]0.946224573400444[/C][C]0.107550853199112[/C][C]0.0537754265995561[/C][/ROW]
[ROW][C]41[/C][C]0.889695624402324[/C][C]0.220608751195353[/C][C]0.110304375597676[/C][/ROW]
[ROW][C]42[/C][C]0.878928973320536[/C][C]0.242142053358927[/C][C]0.121071026679464[/C][/ROW]
[ROW][C]43[/C][C]0.787526801025403[/C][C]0.424946397949195[/C][C]0.212473198974597[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58358&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58358&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
170.2164299717598870.4328599435197740.783570028240113
180.1045645069535400.2091290139070790.89543549304646
190.05411409389569810.1082281877913960.945885906104302
200.03342474028230490.06684948056460970.966575259717695
210.2590380101757470.5180760203514930.740961989824253
220.1863191098232300.3726382196464590.81368089017677
230.1432378670822940.2864757341645880.856762132917706
240.1008275521301770.2016551042603530.899172447869823
250.0689300990923510.1378601981847020.931069900907649
260.05660507658169640.1132101531633930.943394923418304
270.0607805645067050.121561129013410.939219435493295
280.0651167858638920.1302335717277840.934883214136108
290.04556460938748290.09112921877496590.954435390612517
300.1410479999707870.2820959999415750.858952000029213
310.1170130391814070.2340260783628140.882986960818593
320.2010731275437080.4021462550874160.798926872456292
330.5021992299760080.9956015400479830.497800770023992
340.5846922489362740.8306155021274510.415307751063726
350.7879627071355460.4240745857289080.212037292864454
360.8402349195350310.3195301609299370.159765080464969
370.9577861612557270.08442767748854540.0422138387442727
380.9479514862918780.1040970274162450.0520485137081223
390.968787618373450.06242476325309940.0312123816265497
400.9462245734004440.1075508531991120.0537754265995561
410.8896956244023240.2206087511953530.110304375597676
420.8789289733205360.2421420533589270.121071026679464
430.7875268010254030.4249463979491950.212473198974597







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level40.148148148148148NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 4 & 0.148148148148148 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58358&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]4[/C][C]0.148148148148148[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58358&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58358&T=6

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level40.148148148148148NOK



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')
}