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Author's title

Author*Unverified author*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 07:06:33 -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/t1258726023gf5a21uwupalve5.htm/, Retrieved Fri, 29 Mar 2024 09:08:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58178, Retrieved Fri, 29 Mar 2024 09:08:58 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact192
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 14:14:11] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [] [2009-11-19 15:36:14] [ca7a691f2b8ebdc7b81799394c1aa70d]
-    D        [Multiple Regression] [] [2009-11-20 14:06:33] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
89.1	0	100	88
82.6	0	89.1	100
102.7	0	82.6	89.1
91.8	0	102.7	82.6
94.1	0	91.8	102.7
103.1	0	94.1	91.8
93.2	0	103.1	94.1
91	0	93.2	103.1
94.3	0	91	93.2
99.4	0	94.3	91
115.7	0	99.4	94.3
116.8	0	115.7	99.4
99.8	0	116.8	115.7
96	0	99.8	116.8
115.9	0	96	99.8
109.1	0	115.9	96
117.3	0	109.1	115.9
109.8	0	117.3	109.1
112.8	0	109.8	117.3
110.7	0	112.8	109.8
100	0	110.7	112.8
113.3	0	100	110.7
122.4	0	113.3	100
112.5	0	122.4	113.3
104.2	0	112.5	122.4
92.5	0	104.2	112.5
117.2	0	92.5	104.2
109.3	0	117.2	92.5
106.1	0	109.3	117.2
118.8	0	106.1	109.3
105.3	0	118.8	106.1
106	0	105.3	118.8
102	0	106	105.3
112.9	0	102	106
116.5	0	112.9	102
114.8	0	116.5	112.9
100.5	0	114.8	116.5
85.4	0	100.5	114.8
114.6	0	85.4	100.5
109.9	0	114.6	85.4
100.7	0	109.9	114.6
115.5	0	100.7	109.9
100.7	1	115.5	100.7
99	1	100.7	115.5
102.3	1	99	100.7
108.8	1	102.3	99
105.9	1	108.8	102.3
113.2	1	105.9	108.8
95.7	1	113.2	105.9
80.9	1	95.7	113.2
113.9	1	80.9	95.7
98.1	1	113.9	80.9
102.8	1	98.1	113.9
104.7	1	102.8	98.1
95.9	1	104.7	102.8
94.6	1	95.9	104.7
101.6	1	94.6	95.9
103.9	1	101.6	94.6
110.3	1	103.9	101.6
114.1	1	110.3	103.9




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

\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
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58178&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58178&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58178&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







Multiple Linear Regression - Estimated Regression Equation
TotaleIndustrieleProductie[t] = + 48.7719098176646 -3.92815091693391X[t] + 0.229632225851288Y1[t] + 0.35939013498551Y2[t] -16.6549309698687M1[t] -24.6048091612375M2[t] + 7.98612935353004M3[t] -3.39181676279789M4[t] -9.8962790917531M5[t] -0.591645919035228M6[t] -10.2867511923731M7[t] -11.8673684644641M8[t] -8.68197056383971M9[t] -0.597406321343375M10[t] + 4.17151212199479M11[t] + 0.0603498253718281t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
TotaleIndustrieleProductie[t] =  +  48.7719098176646 -3.92815091693391X[t] +  0.229632225851288Y1[t] +  0.35939013498551Y2[t] -16.6549309698687M1[t] -24.6048091612375M2[t] +  7.98612935353004M3[t] -3.39181676279789M4[t] -9.8962790917531M5[t] -0.591645919035228M6[t] -10.2867511923731M7[t] -11.8673684644641M8[t] -8.68197056383971M9[t] -0.597406321343375M10[t] +  4.17151212199479M11[t] +  0.0603498253718281t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58178&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]TotaleIndustrieleProductie[t] =  +  48.7719098176646 -3.92815091693391X[t] +  0.229632225851288Y1[t] +  0.35939013498551Y2[t] -16.6549309698687M1[t] -24.6048091612375M2[t] +  7.98612935353004M3[t] -3.39181676279789M4[t] -9.8962790917531M5[t] -0.591645919035228M6[t] -10.2867511923731M7[t] -11.8673684644641M8[t] -8.68197056383971M9[t] -0.597406321343375M10[t] +  4.17151212199479M11[t] +  0.0603498253718281t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58178&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58178&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
TotaleIndustrieleProductie[t] = + 48.7719098176646 -3.92815091693391X[t] + 0.229632225851288Y1[t] + 0.35939013498551Y2[t] -16.6549309698687M1[t] -24.6048091612375M2[t] + 7.98612935353004M3[t] -3.39181676279789M4[t] -9.8962790917531M5[t] -0.591645919035228M6[t] -10.2867511923731M7[t] -11.8673684644641M8[t] -8.68197056383971M9[t] -0.597406321343375M10[t] + 4.17151212199479M11[t] + 0.0603498253718281t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)48.771909817664614.3222413.40530.0014210.00071
X-3.928150916933912.800057-1.40290.1676690.083835
Y10.2296322258512880.1347011.70480.0952930.047646
Y20.359390134985510.1269882.83010.0069860.003493
M1-16.65493096986873.091986-5.38653e-061e-06
M2-24.60480916123753.912985-6.28800
M37.986129353530044.3884981.81980.0755990.037799
M4-3.391816762797893.893557-0.87110.3884080.194204
M5-9.89627909175313.544963-2.79160.0077290.003865
M6-0.5916459190352283.2706-0.18090.8572780.428639
M7-10.28675119237313.035381-3.38890.001490.000745
M8-11.86736846446413.544847-3.34780.0016770.000838
M9-8.681970563839713.393313-2.55860.0140280.007014
M10-0.5974063213433753.411245-0.17510.8617820.430891
M114.171512121994793.1397651.32860.1908280.095414
t0.06034982537182810.073210.82430.4141910.207096

\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) & 48.7719098176646 & 14.322241 & 3.4053 & 0.001421 & 0.00071 \tabularnewline
X & -3.92815091693391 & 2.800057 & -1.4029 & 0.167669 & 0.083835 \tabularnewline
Y1 & 0.229632225851288 & 0.134701 & 1.7048 & 0.095293 & 0.047646 \tabularnewline
Y2 & 0.35939013498551 & 0.126988 & 2.8301 & 0.006986 & 0.003493 \tabularnewline
M1 & -16.6549309698687 & 3.091986 & -5.3865 & 3e-06 & 1e-06 \tabularnewline
M2 & -24.6048091612375 & 3.912985 & -6.288 & 0 & 0 \tabularnewline
M3 & 7.98612935353004 & 4.388498 & 1.8198 & 0.075599 & 0.037799 \tabularnewline
M4 & -3.39181676279789 & 3.893557 & -0.8711 & 0.388408 & 0.194204 \tabularnewline
M5 & -9.8962790917531 & 3.544963 & -2.7916 & 0.007729 & 0.003865 \tabularnewline
M6 & -0.591645919035228 & 3.2706 & -0.1809 & 0.857278 & 0.428639 \tabularnewline
M7 & -10.2867511923731 & 3.035381 & -3.3889 & 0.00149 & 0.000745 \tabularnewline
M8 & -11.8673684644641 & 3.544847 & -3.3478 & 0.001677 & 0.000838 \tabularnewline
M9 & -8.68197056383971 & 3.393313 & -2.5586 & 0.014028 & 0.007014 \tabularnewline
M10 & -0.597406321343375 & 3.411245 & -0.1751 & 0.861782 & 0.430891 \tabularnewline
M11 & 4.17151212199479 & 3.139765 & 1.3286 & 0.190828 & 0.095414 \tabularnewline
t & 0.0603498253718281 & 0.07321 & 0.8243 & 0.414191 & 0.207096 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58178&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]48.7719098176646[/C][C]14.322241[/C][C]3.4053[/C][C]0.001421[/C][C]0.00071[/C][/ROW]
[ROW][C]X[/C][C]-3.92815091693391[/C][C]2.800057[/C][C]-1.4029[/C][C]0.167669[/C][C]0.083835[/C][/ROW]
[ROW][C]Y1[/C][C]0.229632225851288[/C][C]0.134701[/C][C]1.7048[/C][C]0.095293[/C][C]0.047646[/C][/ROW]
[ROW][C]Y2[/C][C]0.35939013498551[/C][C]0.126988[/C][C]2.8301[/C][C]0.006986[/C][C]0.003493[/C][/ROW]
[ROW][C]M1[/C][C]-16.6549309698687[/C][C]3.091986[/C][C]-5.3865[/C][C]3e-06[/C][C]1e-06[/C][/ROW]
[ROW][C]M2[/C][C]-24.6048091612375[/C][C]3.912985[/C][C]-6.288[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M3[/C][C]7.98612935353004[/C][C]4.388498[/C][C]1.8198[/C][C]0.075599[/C][C]0.037799[/C][/ROW]
[ROW][C]M4[/C][C]-3.39181676279789[/C][C]3.893557[/C][C]-0.8711[/C][C]0.388408[/C][C]0.194204[/C][/ROW]
[ROW][C]M5[/C][C]-9.8962790917531[/C][C]3.544963[/C][C]-2.7916[/C][C]0.007729[/C][C]0.003865[/C][/ROW]
[ROW][C]M6[/C][C]-0.591645919035228[/C][C]3.2706[/C][C]-0.1809[/C][C]0.857278[/C][C]0.428639[/C][/ROW]
[ROW][C]M7[/C][C]-10.2867511923731[/C][C]3.035381[/C][C]-3.3889[/C][C]0.00149[/C][C]0.000745[/C][/ROW]
[ROW][C]M8[/C][C]-11.8673684644641[/C][C]3.544847[/C][C]-3.3478[/C][C]0.001677[/C][C]0.000838[/C][/ROW]
[ROW][C]M9[/C][C]-8.68197056383971[/C][C]3.393313[/C][C]-2.5586[/C][C]0.014028[/C][C]0.007014[/C][/ROW]
[ROW][C]M10[/C][C]-0.597406321343375[/C][C]3.411245[/C][C]-0.1751[/C][C]0.861782[/C][C]0.430891[/C][/ROW]
[ROW][C]M11[/C][C]4.17151212199479[/C][C]3.139765[/C][C]1.3286[/C][C]0.190828[/C][C]0.095414[/C][/ROW]
[ROW][C]t[/C][C]0.0603498253718281[/C][C]0.07321[/C][C]0.8243[/C][C]0.414191[/C][C]0.207096[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58178&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58178&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)48.771909817664614.3222413.40530.0014210.00071
X-3.928150916933912.800057-1.40290.1676690.083835
Y10.2296322258512880.1347011.70480.0952930.047646
Y20.359390134985510.1269882.83010.0069860.003493
M1-16.65493096986873.091986-5.38653e-061e-06
M2-24.60480916123753.912985-6.28800
M37.986129353530044.3884981.81980.0755990.037799
M4-3.391816762797893.893557-0.87110.3884080.194204
M5-9.89627909175313.544963-2.79160.0077290.003865
M6-0.5916459190352283.2706-0.18090.8572780.428639
M7-10.28675119237313.035381-3.38890.001490.000745
M8-11.86736846446413.544847-3.34780.0016770.000838
M9-8.681970563839713.393313-2.55860.0140280.007014
M10-0.5974063213433753.411245-0.17510.8617820.430891
M114.171512121994793.1397651.32860.1908280.095414
t0.06034982537182810.073210.82430.4141910.207096







Multiple Linear Regression - Regression Statistics
Multiple R0.904468438807846
R-squared0.818063156799503
Adjusted R-squared0.756039232981151
F-TEST (value)13.1894776472923
F-TEST (DF numerator)15
F-TEST (DF denominator)44
p-value1.17428289314603e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4.75429381103554
Sum Squared Residuals994.545624232637

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.904468438807846 \tabularnewline
R-squared & 0.818063156799503 \tabularnewline
Adjusted R-squared & 0.756039232981151 \tabularnewline
F-TEST (value) & 13.1894776472923 \tabularnewline
F-TEST (DF numerator) & 15 \tabularnewline
F-TEST (DF denominator) & 44 \tabularnewline
p-value & 1.17428289314603e-11 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 4.75429381103554 \tabularnewline
Sum Squared Residuals & 994.545624232637 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58178&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.904468438807846[/C][/ROW]
[ROW][C]R-squared[/C][C]0.818063156799503[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.756039232981151[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]13.1894776472923[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]15[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]44[/C][/ROW]
[ROW][C]p-value[/C][C]1.17428289314603e-11[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]4.75429381103554[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]994.545624232637[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58178&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58178&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 R0.904468438807846
R-squared0.818063156799503
Adjusted R-squared0.756039232981151
F-TEST (value)13.1894776472923
F-TEST (DF numerator)15
F-TEST (DF denominator)44
p-value1.17428289314603e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation4.75429381103554
Sum Squared Residuals994.545624232637







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
189.186.76688313702172.33311686297828
282.680.68704512907171.91295487092829
3102.7107.928371529836-5.22837152983556
491.898.8903471010845-7.09034710108453
594.197.1669850489309-3.06698504893088
6103.1103.142769695136-0.042769695136433
793.296.4013015902987-3.20130159029867
89195.8421863225214-4.84218632252139
994.395.0247808152882-0.72478081528819
1099.4103.136822931497-3.73682293149747
11115.7110.3232029975015.37679700249879
12116.8111.7879356706805.01206432931964
1399.8101.304009174884-1.50400917488376
149689.9060621178996.09393788210103
15115.9115.5751157050500.324884294950293
16109.1107.4615181955891.63848180441069
17117.3106.60777024242910.6922297575712
18109.8115.411884574598-5.61188457459761
19112.8107.0018865396285.79811346037193
20110.7103.4750897580717.22491024192851
21100107.316780214736-7.3167802147365
22113.3112.2499101825261.05008981747369
23122.4116.2878126107136.11218738928652
24112.5119.046192364645-6.54619236464452
25104.2103.4487024125880.751297587411934
2692.590.09526423566892.40473576433112
27117.2117.0769174129680.123082587031616
28109.3107.2263725212092.07362747879137
29106.1107.845101767542-1.74510176754219
30118.8113.6360795765225.16392042347777
31105.3105.767604964914-0.467604964913886
32106105.7115571835180.288442816481648
33102104.266280645306-2.26628064530606
34112.9111.7442389042591.15576109574108
35116.5117.638937894806-1.13893789480592
36114.8118.271804082590-3.47180408258966
37100.5102.580652640093-2.08065264009346
3885.490.7964202149477-5.39642021494772
39114.6114.840983014440-0.240983014439798
40109.9104.8018566800605.09814331993991
41100.7107.772664656553-7.07266465655256
42115.5113.3358975423792.16410245762148
43100.799.8651588782110.834841121789101
4499100.265308486678-1.26530848667826
45102.397.80170743094174.49829256905829
46108.8106.0934446146442.70655538535624
47105.9113.601309796839-7.7013097968393
48113.2111.1602499226532.03975007734658
4995.795.1997526354130.500247364586997
5080.985.9152083024127-5.01520830241273
51113.9108.8786123377075.02138766229344
5298.199.8199055020574-1.71990550205743
53102.8101.6074782845461.19252171545447
54104.7106.373368611365-1.67336861136521
5595.998.8640480269485-2.96404802694849
5694.696.0058582492105-1.40585824921052
57101.695.79045089372755.80954910627246
58103.9105.075583367074-1.17558336707354
59110.3112.94873670014-2.64873670014008
60114.1111.1338179594322.96618204056796

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 89.1 & 86.7668831370217 & 2.33311686297828 \tabularnewline
2 & 82.6 & 80.6870451290717 & 1.91295487092829 \tabularnewline
3 & 102.7 & 107.928371529836 & -5.22837152983556 \tabularnewline
4 & 91.8 & 98.8903471010845 & -7.09034710108453 \tabularnewline
5 & 94.1 & 97.1669850489309 & -3.06698504893088 \tabularnewline
6 & 103.1 & 103.142769695136 & -0.042769695136433 \tabularnewline
7 & 93.2 & 96.4013015902987 & -3.20130159029867 \tabularnewline
8 & 91 & 95.8421863225214 & -4.84218632252139 \tabularnewline
9 & 94.3 & 95.0247808152882 & -0.72478081528819 \tabularnewline
10 & 99.4 & 103.136822931497 & -3.73682293149747 \tabularnewline
11 & 115.7 & 110.323202997501 & 5.37679700249879 \tabularnewline
12 & 116.8 & 111.787935670680 & 5.01206432931964 \tabularnewline
13 & 99.8 & 101.304009174884 & -1.50400917488376 \tabularnewline
14 & 96 & 89.906062117899 & 6.09393788210103 \tabularnewline
15 & 115.9 & 115.575115705050 & 0.324884294950293 \tabularnewline
16 & 109.1 & 107.461518195589 & 1.63848180441069 \tabularnewline
17 & 117.3 & 106.607770242429 & 10.6922297575712 \tabularnewline
18 & 109.8 & 115.411884574598 & -5.61188457459761 \tabularnewline
19 & 112.8 & 107.001886539628 & 5.79811346037193 \tabularnewline
20 & 110.7 & 103.475089758071 & 7.22491024192851 \tabularnewline
21 & 100 & 107.316780214736 & -7.3167802147365 \tabularnewline
22 & 113.3 & 112.249910182526 & 1.05008981747369 \tabularnewline
23 & 122.4 & 116.287812610713 & 6.11218738928652 \tabularnewline
24 & 112.5 & 119.046192364645 & -6.54619236464452 \tabularnewline
25 & 104.2 & 103.448702412588 & 0.751297587411934 \tabularnewline
26 & 92.5 & 90.0952642356689 & 2.40473576433112 \tabularnewline
27 & 117.2 & 117.076917412968 & 0.123082587031616 \tabularnewline
28 & 109.3 & 107.226372521209 & 2.07362747879137 \tabularnewline
29 & 106.1 & 107.845101767542 & -1.74510176754219 \tabularnewline
30 & 118.8 & 113.636079576522 & 5.16392042347777 \tabularnewline
31 & 105.3 & 105.767604964914 & -0.467604964913886 \tabularnewline
32 & 106 & 105.711557183518 & 0.288442816481648 \tabularnewline
33 & 102 & 104.266280645306 & -2.26628064530606 \tabularnewline
34 & 112.9 & 111.744238904259 & 1.15576109574108 \tabularnewline
35 & 116.5 & 117.638937894806 & -1.13893789480592 \tabularnewline
36 & 114.8 & 118.271804082590 & -3.47180408258966 \tabularnewline
37 & 100.5 & 102.580652640093 & -2.08065264009346 \tabularnewline
38 & 85.4 & 90.7964202149477 & -5.39642021494772 \tabularnewline
39 & 114.6 & 114.840983014440 & -0.240983014439798 \tabularnewline
40 & 109.9 & 104.801856680060 & 5.09814331993991 \tabularnewline
41 & 100.7 & 107.772664656553 & -7.07266465655256 \tabularnewline
42 & 115.5 & 113.335897542379 & 2.16410245762148 \tabularnewline
43 & 100.7 & 99.865158878211 & 0.834841121789101 \tabularnewline
44 & 99 & 100.265308486678 & -1.26530848667826 \tabularnewline
45 & 102.3 & 97.8017074309417 & 4.49829256905829 \tabularnewline
46 & 108.8 & 106.093444614644 & 2.70655538535624 \tabularnewline
47 & 105.9 & 113.601309796839 & -7.7013097968393 \tabularnewline
48 & 113.2 & 111.160249922653 & 2.03975007734658 \tabularnewline
49 & 95.7 & 95.199752635413 & 0.500247364586997 \tabularnewline
50 & 80.9 & 85.9152083024127 & -5.01520830241273 \tabularnewline
51 & 113.9 & 108.878612337707 & 5.02138766229344 \tabularnewline
52 & 98.1 & 99.8199055020574 & -1.71990550205743 \tabularnewline
53 & 102.8 & 101.607478284546 & 1.19252171545447 \tabularnewline
54 & 104.7 & 106.373368611365 & -1.67336861136521 \tabularnewline
55 & 95.9 & 98.8640480269485 & -2.96404802694849 \tabularnewline
56 & 94.6 & 96.0058582492105 & -1.40585824921052 \tabularnewline
57 & 101.6 & 95.7904508937275 & 5.80954910627246 \tabularnewline
58 & 103.9 & 105.075583367074 & -1.17558336707354 \tabularnewline
59 & 110.3 & 112.94873670014 & -2.64873670014008 \tabularnewline
60 & 114.1 & 111.133817959432 & 2.96618204056796 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58178&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]89.1[/C][C]86.7668831370217[/C][C]2.33311686297828[/C][/ROW]
[ROW][C]2[/C][C]82.6[/C][C]80.6870451290717[/C][C]1.91295487092829[/C][/ROW]
[ROW][C]3[/C][C]102.7[/C][C]107.928371529836[/C][C]-5.22837152983556[/C][/ROW]
[ROW][C]4[/C][C]91.8[/C][C]98.8903471010845[/C][C]-7.09034710108453[/C][/ROW]
[ROW][C]5[/C][C]94.1[/C][C]97.1669850489309[/C][C]-3.06698504893088[/C][/ROW]
[ROW][C]6[/C][C]103.1[/C][C]103.142769695136[/C][C]-0.042769695136433[/C][/ROW]
[ROW][C]7[/C][C]93.2[/C][C]96.4013015902987[/C][C]-3.20130159029867[/C][/ROW]
[ROW][C]8[/C][C]91[/C][C]95.8421863225214[/C][C]-4.84218632252139[/C][/ROW]
[ROW][C]9[/C][C]94.3[/C][C]95.0247808152882[/C][C]-0.72478081528819[/C][/ROW]
[ROW][C]10[/C][C]99.4[/C][C]103.136822931497[/C][C]-3.73682293149747[/C][/ROW]
[ROW][C]11[/C][C]115.7[/C][C]110.323202997501[/C][C]5.37679700249879[/C][/ROW]
[ROW][C]12[/C][C]116.8[/C][C]111.787935670680[/C][C]5.01206432931964[/C][/ROW]
[ROW][C]13[/C][C]99.8[/C][C]101.304009174884[/C][C]-1.50400917488376[/C][/ROW]
[ROW][C]14[/C][C]96[/C][C]89.906062117899[/C][C]6.09393788210103[/C][/ROW]
[ROW][C]15[/C][C]115.9[/C][C]115.575115705050[/C][C]0.324884294950293[/C][/ROW]
[ROW][C]16[/C][C]109.1[/C][C]107.461518195589[/C][C]1.63848180441069[/C][/ROW]
[ROW][C]17[/C][C]117.3[/C][C]106.607770242429[/C][C]10.6922297575712[/C][/ROW]
[ROW][C]18[/C][C]109.8[/C][C]115.411884574598[/C][C]-5.61188457459761[/C][/ROW]
[ROW][C]19[/C][C]112.8[/C][C]107.001886539628[/C][C]5.79811346037193[/C][/ROW]
[ROW][C]20[/C][C]110.7[/C][C]103.475089758071[/C][C]7.22491024192851[/C][/ROW]
[ROW][C]21[/C][C]100[/C][C]107.316780214736[/C][C]-7.3167802147365[/C][/ROW]
[ROW][C]22[/C][C]113.3[/C][C]112.249910182526[/C][C]1.05008981747369[/C][/ROW]
[ROW][C]23[/C][C]122.4[/C][C]116.287812610713[/C][C]6.11218738928652[/C][/ROW]
[ROW][C]24[/C][C]112.5[/C][C]119.046192364645[/C][C]-6.54619236464452[/C][/ROW]
[ROW][C]25[/C][C]104.2[/C][C]103.448702412588[/C][C]0.751297587411934[/C][/ROW]
[ROW][C]26[/C][C]92.5[/C][C]90.0952642356689[/C][C]2.40473576433112[/C][/ROW]
[ROW][C]27[/C][C]117.2[/C][C]117.076917412968[/C][C]0.123082587031616[/C][/ROW]
[ROW][C]28[/C][C]109.3[/C][C]107.226372521209[/C][C]2.07362747879137[/C][/ROW]
[ROW][C]29[/C][C]106.1[/C][C]107.845101767542[/C][C]-1.74510176754219[/C][/ROW]
[ROW][C]30[/C][C]118.8[/C][C]113.636079576522[/C][C]5.16392042347777[/C][/ROW]
[ROW][C]31[/C][C]105.3[/C][C]105.767604964914[/C][C]-0.467604964913886[/C][/ROW]
[ROW][C]32[/C][C]106[/C][C]105.711557183518[/C][C]0.288442816481648[/C][/ROW]
[ROW][C]33[/C][C]102[/C][C]104.266280645306[/C][C]-2.26628064530606[/C][/ROW]
[ROW][C]34[/C][C]112.9[/C][C]111.744238904259[/C][C]1.15576109574108[/C][/ROW]
[ROW][C]35[/C][C]116.5[/C][C]117.638937894806[/C][C]-1.13893789480592[/C][/ROW]
[ROW][C]36[/C][C]114.8[/C][C]118.271804082590[/C][C]-3.47180408258966[/C][/ROW]
[ROW][C]37[/C][C]100.5[/C][C]102.580652640093[/C][C]-2.08065264009346[/C][/ROW]
[ROW][C]38[/C][C]85.4[/C][C]90.7964202149477[/C][C]-5.39642021494772[/C][/ROW]
[ROW][C]39[/C][C]114.6[/C][C]114.840983014440[/C][C]-0.240983014439798[/C][/ROW]
[ROW][C]40[/C][C]109.9[/C][C]104.801856680060[/C][C]5.09814331993991[/C][/ROW]
[ROW][C]41[/C][C]100.7[/C][C]107.772664656553[/C][C]-7.07266465655256[/C][/ROW]
[ROW][C]42[/C][C]115.5[/C][C]113.335897542379[/C][C]2.16410245762148[/C][/ROW]
[ROW][C]43[/C][C]100.7[/C][C]99.865158878211[/C][C]0.834841121789101[/C][/ROW]
[ROW][C]44[/C][C]99[/C][C]100.265308486678[/C][C]-1.26530848667826[/C][/ROW]
[ROW][C]45[/C][C]102.3[/C][C]97.8017074309417[/C][C]4.49829256905829[/C][/ROW]
[ROW][C]46[/C][C]108.8[/C][C]106.093444614644[/C][C]2.70655538535624[/C][/ROW]
[ROW][C]47[/C][C]105.9[/C][C]113.601309796839[/C][C]-7.7013097968393[/C][/ROW]
[ROW][C]48[/C][C]113.2[/C][C]111.160249922653[/C][C]2.03975007734658[/C][/ROW]
[ROW][C]49[/C][C]95.7[/C][C]95.199752635413[/C][C]0.500247364586997[/C][/ROW]
[ROW][C]50[/C][C]80.9[/C][C]85.9152083024127[/C][C]-5.01520830241273[/C][/ROW]
[ROW][C]51[/C][C]113.9[/C][C]108.878612337707[/C][C]5.02138766229344[/C][/ROW]
[ROW][C]52[/C][C]98.1[/C][C]99.8199055020574[/C][C]-1.71990550205743[/C][/ROW]
[ROW][C]53[/C][C]102.8[/C][C]101.607478284546[/C][C]1.19252171545447[/C][/ROW]
[ROW][C]54[/C][C]104.7[/C][C]106.373368611365[/C][C]-1.67336861136521[/C][/ROW]
[ROW][C]55[/C][C]95.9[/C][C]98.8640480269485[/C][C]-2.96404802694849[/C][/ROW]
[ROW][C]56[/C][C]94.6[/C][C]96.0058582492105[/C][C]-1.40585824921052[/C][/ROW]
[ROW][C]57[/C][C]101.6[/C][C]95.7904508937275[/C][C]5.80954910627246[/C][/ROW]
[ROW][C]58[/C][C]103.9[/C][C]105.075583367074[/C][C]-1.17558336707354[/C][/ROW]
[ROW][C]59[/C][C]110.3[/C][C]112.94873670014[/C][C]-2.64873670014008[/C][/ROW]
[ROW][C]60[/C][C]114.1[/C][C]111.133817959432[/C][C]2.96618204056796[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58178&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58178&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
189.186.76688313702172.33311686297828
282.680.68704512907171.91295487092829
3102.7107.928371529836-5.22837152983556
491.898.8903471010845-7.09034710108453
594.197.1669850489309-3.06698504893088
6103.1103.142769695136-0.042769695136433
793.296.4013015902987-3.20130159029867
89195.8421863225214-4.84218632252139
994.395.0247808152882-0.72478081528819
1099.4103.136822931497-3.73682293149747
11115.7110.3232029975015.37679700249879
12116.8111.7879356706805.01206432931964
1399.8101.304009174884-1.50400917488376
149689.9060621178996.09393788210103
15115.9115.5751157050500.324884294950293
16109.1107.4615181955891.63848180441069
17117.3106.60777024242910.6922297575712
18109.8115.411884574598-5.61188457459761
19112.8107.0018865396285.79811346037193
20110.7103.4750897580717.22491024192851
21100107.316780214736-7.3167802147365
22113.3112.2499101825261.05008981747369
23122.4116.2878126107136.11218738928652
24112.5119.046192364645-6.54619236464452
25104.2103.4487024125880.751297587411934
2692.590.09526423566892.40473576433112
27117.2117.0769174129680.123082587031616
28109.3107.2263725212092.07362747879137
29106.1107.845101767542-1.74510176754219
30118.8113.6360795765225.16392042347777
31105.3105.767604964914-0.467604964913886
32106105.7115571835180.288442816481648
33102104.266280645306-2.26628064530606
34112.9111.7442389042591.15576109574108
35116.5117.638937894806-1.13893789480592
36114.8118.271804082590-3.47180408258966
37100.5102.580652640093-2.08065264009346
3885.490.7964202149477-5.39642021494772
39114.6114.840983014440-0.240983014439798
40109.9104.8018566800605.09814331993991
41100.7107.772664656553-7.07266465655256
42115.5113.3358975423792.16410245762148
43100.799.8651588782110.834841121789101
4499100.265308486678-1.26530848667826
45102.397.80170743094174.49829256905829
46108.8106.0934446146442.70655538535624
47105.9113.601309796839-7.7013097968393
48113.2111.1602499226532.03975007734658
4995.795.1997526354130.500247364586997
5080.985.9152083024127-5.01520830241273
51113.9108.8786123377075.02138766229344
5298.199.8199055020574-1.71990550205743
53102.8101.6074782845461.19252171545447
54104.7106.373368611365-1.67336861136521
5595.998.8640480269485-2.96404802694849
5694.696.0058582492105-1.40585824921052
57101.695.79045089372755.80954910627246
58103.9105.075583367074-1.17558336707354
59110.3112.94873670014-2.64873670014008
60114.1111.1338179594322.96618204056796







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
190.8857443546620360.2285112906759290.114255645337964
200.8496768909810940.3006462180378110.150323109018906
210.8491034520711770.3017930958576460.150896547928823
220.8432428957364020.3135142085271960.156757104263598
230.9440685990060530.1118628019878950.0559314009939474
240.9982941362682170.003411727463565110.00170586373178255
250.9968477674476840.006304465104631060.00315223255231553
260.9970335437145080.005932912570984070.00296645628549204
270.9933172121019770.01336557579604560.0066827878980228
280.9861818287662040.02763634246759110.0138181712337956
290.982826612706710.03434677458658170.0171733872932908
300.9808189828598550.03836203428029060.0191810171401453
310.9706990077476680.0586019845046640.029300992252332
320.9640073544314020.07198529113719530.0359926455685977
330.9490335046424360.1019329907151280.0509664953575642
340.9113060627241480.1773878745517030.0886939372758516
350.9146890688866840.1706218622266330.0853109311133163
360.8810941838475170.2378116323049670.118905816152483
370.819925314409630.3601493711807390.180074685590370
380.754690517594350.49061896481130.24530948240565
390.7009930854125010.5980138291749980.299006914587499
400.7251935280418640.5496129439162730.274806471958136
410.790978181075250.4180436378494990.209021818924750

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
19 & 0.885744354662036 & 0.228511290675929 & 0.114255645337964 \tabularnewline
20 & 0.849676890981094 & 0.300646218037811 & 0.150323109018906 \tabularnewline
21 & 0.849103452071177 & 0.301793095857646 & 0.150896547928823 \tabularnewline
22 & 0.843242895736402 & 0.313514208527196 & 0.156757104263598 \tabularnewline
23 & 0.944068599006053 & 0.111862801987895 & 0.0559314009939474 \tabularnewline
24 & 0.998294136268217 & 0.00341172746356511 & 0.00170586373178255 \tabularnewline
25 & 0.996847767447684 & 0.00630446510463106 & 0.00315223255231553 \tabularnewline
26 & 0.997033543714508 & 0.00593291257098407 & 0.00296645628549204 \tabularnewline
27 & 0.993317212101977 & 0.0133655757960456 & 0.0066827878980228 \tabularnewline
28 & 0.986181828766204 & 0.0276363424675911 & 0.0138181712337956 \tabularnewline
29 & 0.98282661270671 & 0.0343467745865817 & 0.0171733872932908 \tabularnewline
30 & 0.980818982859855 & 0.0383620342802906 & 0.0191810171401453 \tabularnewline
31 & 0.970699007747668 & 0.058601984504664 & 0.029300992252332 \tabularnewline
32 & 0.964007354431402 & 0.0719852911371953 & 0.0359926455685977 \tabularnewline
33 & 0.949033504642436 & 0.101932990715128 & 0.0509664953575642 \tabularnewline
34 & 0.911306062724148 & 0.177387874551703 & 0.0886939372758516 \tabularnewline
35 & 0.914689068886684 & 0.170621862226633 & 0.0853109311133163 \tabularnewline
36 & 0.881094183847517 & 0.237811632304967 & 0.118905816152483 \tabularnewline
37 & 0.81992531440963 & 0.360149371180739 & 0.180074685590370 \tabularnewline
38 & 0.75469051759435 & 0.4906189648113 & 0.24530948240565 \tabularnewline
39 & 0.700993085412501 & 0.598013829174998 & 0.299006914587499 \tabularnewline
40 & 0.725193528041864 & 0.549612943916273 & 0.274806471958136 \tabularnewline
41 & 0.79097818107525 & 0.418043637849499 & 0.209021818924750 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58178&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]19[/C][C]0.885744354662036[/C][C]0.228511290675929[/C][C]0.114255645337964[/C][/ROW]
[ROW][C]20[/C][C]0.849676890981094[/C][C]0.300646218037811[/C][C]0.150323109018906[/C][/ROW]
[ROW][C]21[/C][C]0.849103452071177[/C][C]0.301793095857646[/C][C]0.150896547928823[/C][/ROW]
[ROW][C]22[/C][C]0.843242895736402[/C][C]0.313514208527196[/C][C]0.156757104263598[/C][/ROW]
[ROW][C]23[/C][C]0.944068599006053[/C][C]0.111862801987895[/C][C]0.0559314009939474[/C][/ROW]
[ROW][C]24[/C][C]0.998294136268217[/C][C]0.00341172746356511[/C][C]0.00170586373178255[/C][/ROW]
[ROW][C]25[/C][C]0.996847767447684[/C][C]0.00630446510463106[/C][C]0.00315223255231553[/C][/ROW]
[ROW][C]26[/C][C]0.997033543714508[/C][C]0.00593291257098407[/C][C]0.00296645628549204[/C][/ROW]
[ROW][C]27[/C][C]0.993317212101977[/C][C]0.0133655757960456[/C][C]0.0066827878980228[/C][/ROW]
[ROW][C]28[/C][C]0.986181828766204[/C][C]0.0276363424675911[/C][C]0.0138181712337956[/C][/ROW]
[ROW][C]29[/C][C]0.98282661270671[/C][C]0.0343467745865817[/C][C]0.0171733872932908[/C][/ROW]
[ROW][C]30[/C][C]0.980818982859855[/C][C]0.0383620342802906[/C][C]0.0191810171401453[/C][/ROW]
[ROW][C]31[/C][C]0.970699007747668[/C][C]0.058601984504664[/C][C]0.029300992252332[/C][/ROW]
[ROW][C]32[/C][C]0.964007354431402[/C][C]0.0719852911371953[/C][C]0.0359926455685977[/C][/ROW]
[ROW][C]33[/C][C]0.949033504642436[/C][C]0.101932990715128[/C][C]0.0509664953575642[/C][/ROW]
[ROW][C]34[/C][C]0.911306062724148[/C][C]0.177387874551703[/C][C]0.0886939372758516[/C][/ROW]
[ROW][C]35[/C][C]0.914689068886684[/C][C]0.170621862226633[/C][C]0.0853109311133163[/C][/ROW]
[ROW][C]36[/C][C]0.881094183847517[/C][C]0.237811632304967[/C][C]0.118905816152483[/C][/ROW]
[ROW][C]37[/C][C]0.81992531440963[/C][C]0.360149371180739[/C][C]0.180074685590370[/C][/ROW]
[ROW][C]38[/C][C]0.75469051759435[/C][C]0.4906189648113[/C][C]0.24530948240565[/C][/ROW]
[ROW][C]39[/C][C]0.700993085412501[/C][C]0.598013829174998[/C][C]0.299006914587499[/C][/ROW]
[ROW][C]40[/C][C]0.725193528041864[/C][C]0.549612943916273[/C][C]0.274806471958136[/C][/ROW]
[ROW][C]41[/C][C]0.79097818107525[/C][C]0.418043637849499[/C][C]0.209021818924750[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58178&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58178&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
190.8857443546620360.2285112906759290.114255645337964
200.8496768909810940.3006462180378110.150323109018906
210.8491034520711770.3017930958576460.150896547928823
220.8432428957364020.3135142085271960.156757104263598
230.9440685990060530.1118628019878950.0559314009939474
240.9982941362682170.003411727463565110.00170586373178255
250.9968477674476840.006304465104631060.00315223255231553
260.9970335437145080.005932912570984070.00296645628549204
270.9933172121019770.01336557579604560.0066827878980228
280.9861818287662040.02763634246759110.0138181712337956
290.982826612706710.03434677458658170.0171733872932908
300.9808189828598550.03836203428029060.0191810171401453
310.9706990077476680.0586019845046640.029300992252332
320.9640073544314020.07198529113719530.0359926455685977
330.9490335046424360.1019329907151280.0509664953575642
340.9113060627241480.1773878745517030.0886939372758516
350.9146890688866840.1706218622266330.0853109311133163
360.8810941838475170.2378116323049670.118905816152483
370.819925314409630.3601493711807390.180074685590370
380.754690517594350.49061896481130.24530948240565
390.7009930854125010.5980138291749980.299006914587499
400.7251935280418640.5496129439162730.274806471958136
410.790978181075250.4180436378494990.209021818924750







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level30.130434782608696NOK
5% type I error level70.304347826086957NOK
10% type I error level90.391304347826087NOK

\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 & 3 & 0.130434782608696 & NOK \tabularnewline
5% type I error level & 7 & 0.304347826086957 & NOK \tabularnewline
10% type I error level & 9 & 0.391304347826087 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58178&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]3[/C][C]0.130434782608696[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]7[/C][C]0.304347826086957[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]9[/C][C]0.391304347826087[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58178&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58178&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 level30.130434782608696NOK
5% type I error level70.304347826086957NOK
10% type I error level90.391304347826087NOK



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')
}