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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 08:46:37 -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/t1258733524yv3zh41laubgqjy.htm/, Retrieved Fri, 29 Mar 2024 13:14:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58297, Retrieved Fri, 29 Mar 2024 13:14:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RMPD  [Multiple Regression] [Seatbelt] [2009-11-12 13:54:52] [b98453cac15ba1066b407e146608df68]
-    D    [Multiple Regression] [Workshop 7] [2009-11-19 16:33:52] [85be98bd9ebcfd4d73e77f8552419c9a]
-   P       [Multiple Regression] [] [2009-11-19 17:52:10] [85be98bd9ebcfd4d73e77f8552419c9a]
-   PD          [Multiple Regression] [2e link] [2009-11-20 15:46:37] [ee8fc1691ecec7724e0ca78f0c288737] [Current]
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Dataseries X:
130	87.1
136.7	110.5
138.1	110.8
139.5	104.2
140.4	88.9
144.6	89.8
151.4	90
147.9	93.9
141.5	91.3
143.8	87.8
143.6	99.7
150.5	73.5
150.1	79.2
154.9	96.9
162.1	95.2
176.7	95.6
186.6	89.7
194.8	92.8
196.3	88
228.8	101.1
267.2	92.7
237.2	95.8
254.7	103.8
258.2	81.8
257.9	87.1
269.6	105.9
266.9	108.1
269.6	102.6
253.9	93.7
258.6	103.5
274.2	100.6
301.5	113.3
304.5	102.4
285.1	102.1
287.7	106.9
265.5	87.3
264.1	93.1
276.1	109.1
258.9	120.3
239.1	104.9
250.1	92.6
276.8	109.8
297.6	111.4
295.4	117.9
283	121.6
275.8	117.8
279.7	124.2
254.6	106.8
234.6	102.7
176.9	116.8
148.1	113.6
122.7	96.1
124.9	85
121.6	83.2
128.4	84.9
144.5	83
151.8	79.6
167.1	83.2
173.8	83.8
203.7	82.8
199.8	71.4




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=58297&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=58297&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58297&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
Y[t] = -118.138386770027 + 3.78371344759034X[t] -19.2118191206132M1[t] -99.749746567234M2[t] -114.917254356113M3[t] -86.954702524727M4[t] -45.2971407566303M5[t] -59.7821994116779M6[t] -46.7920522368219M7[t] -59.1964986084116M8[t] -37.3590286359412M9[t] -44.9661323364949M10[t] -63.3430477153376M11[t] + 0.488172121119932t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  -118.138386770027 +  3.78371344759034X[t] -19.2118191206132M1[t] -99.749746567234M2[t] -114.917254356113M3[t] -86.954702524727M4[t] -45.2971407566303M5[t] -59.7821994116779M6[t] -46.7920522368219M7[t] -59.1964986084116M8[t] -37.3590286359412M9[t] -44.9661323364949M10[t] -63.3430477153376M11[t] +  0.488172121119932t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58297&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  -118.138386770027 +  3.78371344759034X[t] -19.2118191206132M1[t] -99.749746567234M2[t] -114.917254356113M3[t] -86.954702524727M4[t] -45.2971407566303M5[t] -59.7821994116779M6[t] -46.7920522368219M7[t] -59.1964986084116M8[t] -37.3590286359412M9[t] -44.9661323364949M10[t] -63.3430477153376M11[t] +  0.488172121119932t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58297&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58297&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
Y[t] = -118.138386770027 + 3.78371344759034X[t] -19.2118191206132M1[t] -99.749746567234M2[t] -114.917254356113M3[t] -86.954702524727M4[t] -45.2971407566303M5[t] -59.7821994116779M6[t] -46.7920522368219M7[t] -59.1964986084116M8[t] -37.3590286359412M9[t] -44.9661323364949M10[t] -63.3430477153376M11[t] + 0.488172121119932t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-118.13838677002758.247416-2.02820.0482270.024113
X3.783713447590340.624396.059900
M1-19.211819120613229.603294-0.6490.5195130.259756
M2-99.74974656723433.992088-2.93450.0051540.002577
M3-114.91725435611334.398262-3.34080.0016440.000822
M4-86.95470252472732.340004-2.68880.0098920.004946
M5-45.297140756630331.063714-1.45820.1514360.075718
M6-59.782199411677931.533311-1.89580.0641390.032069
M7-46.792052236821931.405516-1.48990.1429230.071462
M8-59.196498608411632.406213-1.82670.0740990.03705
M9-37.359028635941231.67213-1.17960.2441130.122057
M10-44.966132336494931.627685-1.42170.1617060.080853
M11-63.343047715337632.699021-1.93720.058750.029375
t0.4881721211199320.3626471.34610.1847160.092358

\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) & -118.138386770027 & 58.247416 & -2.0282 & 0.048227 & 0.024113 \tabularnewline
X & 3.78371344759034 & 0.62439 & 6.0599 & 0 & 0 \tabularnewline
M1 & -19.2118191206132 & 29.603294 & -0.649 & 0.519513 & 0.259756 \tabularnewline
M2 & -99.749746567234 & 33.992088 & -2.9345 & 0.005154 & 0.002577 \tabularnewline
M3 & -114.917254356113 & 34.398262 & -3.3408 & 0.001644 & 0.000822 \tabularnewline
M4 & -86.954702524727 & 32.340004 & -2.6888 & 0.009892 & 0.004946 \tabularnewline
M5 & -45.2971407566303 & 31.063714 & -1.4582 & 0.151436 & 0.075718 \tabularnewline
M6 & -59.7821994116779 & 31.533311 & -1.8958 & 0.064139 & 0.032069 \tabularnewline
M7 & -46.7920522368219 & 31.405516 & -1.4899 & 0.142923 & 0.071462 \tabularnewline
M8 & -59.1964986084116 & 32.406213 & -1.8267 & 0.074099 & 0.03705 \tabularnewline
M9 & -37.3590286359412 & 31.67213 & -1.1796 & 0.244113 & 0.122057 \tabularnewline
M10 & -44.9661323364949 & 31.627685 & -1.4217 & 0.161706 & 0.080853 \tabularnewline
M11 & -63.3430477153376 & 32.699021 & -1.9372 & 0.05875 & 0.029375 \tabularnewline
t & 0.488172121119932 & 0.362647 & 1.3461 & 0.184716 & 0.092358 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58297&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]-118.138386770027[/C][C]58.247416[/C][C]-2.0282[/C][C]0.048227[/C][C]0.024113[/C][/ROW]
[ROW][C]X[/C][C]3.78371344759034[/C][C]0.62439[/C][C]6.0599[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]-19.2118191206132[/C][C]29.603294[/C][C]-0.649[/C][C]0.519513[/C][C]0.259756[/C][/ROW]
[ROW][C]M2[/C][C]-99.749746567234[/C][C]33.992088[/C][C]-2.9345[/C][C]0.005154[/C][C]0.002577[/C][/ROW]
[ROW][C]M3[/C][C]-114.917254356113[/C][C]34.398262[/C][C]-3.3408[/C][C]0.001644[/C][C]0.000822[/C][/ROW]
[ROW][C]M4[/C][C]-86.954702524727[/C][C]32.340004[/C][C]-2.6888[/C][C]0.009892[/C][C]0.004946[/C][/ROW]
[ROW][C]M5[/C][C]-45.2971407566303[/C][C]31.063714[/C][C]-1.4582[/C][C]0.151436[/C][C]0.075718[/C][/ROW]
[ROW][C]M6[/C][C]-59.7821994116779[/C][C]31.533311[/C][C]-1.8958[/C][C]0.064139[/C][C]0.032069[/C][/ROW]
[ROW][C]M7[/C][C]-46.7920522368219[/C][C]31.405516[/C][C]-1.4899[/C][C]0.142923[/C][C]0.071462[/C][/ROW]
[ROW][C]M8[/C][C]-59.1964986084116[/C][C]32.406213[/C][C]-1.8267[/C][C]0.074099[/C][C]0.03705[/C][/ROW]
[ROW][C]M9[/C][C]-37.3590286359412[/C][C]31.67213[/C][C]-1.1796[/C][C]0.244113[/C][C]0.122057[/C][/ROW]
[ROW][C]M10[/C][C]-44.9661323364949[/C][C]31.627685[/C][C]-1.4217[/C][C]0.161706[/C][C]0.080853[/C][/ROW]
[ROW][C]M11[/C][C]-63.3430477153376[/C][C]32.699021[/C][C]-1.9372[/C][C]0.05875[/C][C]0.029375[/C][/ROW]
[ROW][C]t[/C][C]0.488172121119932[/C][C]0.362647[/C][C]1.3461[/C][C]0.184716[/C][C]0.092358[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58297&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58297&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)-118.13838677002758.247416-2.02820.0482270.024113
X3.783713447590340.624396.059900
M1-19.211819120613229.603294-0.6490.5195130.259756
M2-99.74974656723433.992088-2.93450.0051540.002577
M3-114.91725435611334.398262-3.34080.0016440.000822
M4-86.95470252472732.340004-2.68880.0098920.004946
M5-45.297140756630331.063714-1.45820.1514360.075718
M6-59.782199411677931.533311-1.89580.0641390.032069
M7-46.792052236821931.405516-1.48990.1429230.071462
M8-59.196498608411632.406213-1.82670.0740990.03705
M9-37.359028635941231.67213-1.17960.2441130.122057
M10-44.966132336494931.627685-1.42170.1617060.080853
M11-63.343047715337632.699021-1.93720.058750.029375
t0.4881721211199320.3626471.34610.1847160.092358







Multiple Linear Regression - Regression Statistics
Multiple R0.704334813036706
R-squared0.496087528855452
Adjusted R-squared0.356707483645258
F-TEST (value)3.55924356393571
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value0.000665857165168315
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation48.7928286326505
Sum Squared Residuals111894.785920834

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.704334813036706 \tabularnewline
R-squared & 0.496087528855452 \tabularnewline
Adjusted R-squared & 0.356707483645258 \tabularnewline
F-TEST (value) & 3.55924356393571 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 0.000665857165168315 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 48.7928286326505 \tabularnewline
Sum Squared Residuals & 111894.785920834 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58297&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.704334813036706[/C][/ROW]
[ROW][C]R-squared[/C][C]0.496087528855452[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.356707483645258[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]3.55924356393571[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]0.000665857165168315[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]48.7928286326505[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]111894.785920834[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58297&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58297&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 R0.704334813036706
R-squared0.496087528855452
Adjusted R-squared0.356707483645258
F-TEST (value)3.55924356393571
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value0.000665857165168315
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation48.7928286326505
Sum Squared Residuals111894.785920834







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1130192.699407515599-62.6994075155985
2136.7201.188546863712-64.488546863712
3138.1187.64432523023-49.5443252302301
4139.5191.122540428640-51.6225404286396
5140.4175.377458569724-34.9774585697241
6144.6164.785914138628-20.1859141386278
7151.4179.020976124122-27.6209761241217
8147.9181.861184319254-33.9611843192543
9141.5194.349171449110-52.8491714491097
10143.8173.987242803110-30.1872428031097
11143.6201.124689571712-57.5246895717121
12150.5165.822617081303-15.3226170813026
13150.1168.666136733074-18.5661367330744
14154.9155.588109429923-0.688109429922506
15162.1134.4764609012627.6235390987401
16176.7164.44067023280212.2593297671981
17186.6184.2624947812362.33750521876447
18194.8181.99511993483812.8048800651620
19196.3177.31161468238018.9883853176198
20228.8214.96198659534413.8380134046560
21267.2205.50443572917561.6955642708246
22237.2210.11501583727227.0849841627283
23254.7222.49598016027232.2040198397283
24258.2203.08550414974255.1144958502583
25257.9204.41553842247753.4844615775228
26269.6195.49959591167574.1004040883253
27266.9189.14442982861477.7555701713855
28269.6196.78472981937372.8152701806266
29253.9205.25541402503648.6445859749639
30258.6228.33891927749430.2610807225062
31274.2230.84446957545843.3555304245423
32301.5266.98135610938534.5186438906147
33304.5248.06452162424156.4354783757591
34285.1239.8104760105345.28952398947
35287.7240.08355730124147.6164426987591
36265.5229.75399356492835.7460064350723
37264.1232.97588456145831.1241154385416
38276.1213.46554439740362.634455602597
39258.9241.16379934265617.7362006573442
40239.1211.34533620227027.7546637977295
41250.1206.95139468612643.1486053138742
42276.8258.03437945075218.7656205492478
43297.6277.56664026287320.0333597371274
44295.4290.244503421745.15549657825988
45283326.569885271415-43.5698852714146
46275.8305.072842591138-29.2728425911376
47279.7311.399865397993-31.699865397993
48254.6309.394471246379-54.7944712463785
49234.6275.157599111765-40.5575991117649
50176.9248.458203397288-71.5582033972878
51148.1221.670984697240-73.5709846972397
52122.7183.906723316915-61.2067233169146
53124.9184.053237937878-59.1532379378784
54121.6163.245667198288-41.6456671982883
55128.4183.156299355168-54.7562993551677
56144.5164.050969554276-19.5509695542763
57151.8173.511985926059-21.7119859260594
58167.1180.014422757951-12.9144227579510
59173.8164.3959075687829.40409243121765
60203.7224.443413957650-20.7434139576495
61199.8162.58543365562637.2145663443736

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 130 & 192.699407515599 & -62.6994075155985 \tabularnewline
2 & 136.7 & 201.188546863712 & -64.488546863712 \tabularnewline
3 & 138.1 & 187.64432523023 & -49.5443252302301 \tabularnewline
4 & 139.5 & 191.122540428640 & -51.6225404286396 \tabularnewline
5 & 140.4 & 175.377458569724 & -34.9774585697241 \tabularnewline
6 & 144.6 & 164.785914138628 & -20.1859141386278 \tabularnewline
7 & 151.4 & 179.020976124122 & -27.6209761241217 \tabularnewline
8 & 147.9 & 181.861184319254 & -33.9611843192543 \tabularnewline
9 & 141.5 & 194.349171449110 & -52.8491714491097 \tabularnewline
10 & 143.8 & 173.987242803110 & -30.1872428031097 \tabularnewline
11 & 143.6 & 201.124689571712 & -57.5246895717121 \tabularnewline
12 & 150.5 & 165.822617081303 & -15.3226170813026 \tabularnewline
13 & 150.1 & 168.666136733074 & -18.5661367330744 \tabularnewline
14 & 154.9 & 155.588109429923 & -0.688109429922506 \tabularnewline
15 & 162.1 & 134.47646090126 & 27.6235390987401 \tabularnewline
16 & 176.7 & 164.440670232802 & 12.2593297671981 \tabularnewline
17 & 186.6 & 184.262494781236 & 2.33750521876447 \tabularnewline
18 & 194.8 & 181.995119934838 & 12.8048800651620 \tabularnewline
19 & 196.3 & 177.311614682380 & 18.9883853176198 \tabularnewline
20 & 228.8 & 214.961986595344 & 13.8380134046560 \tabularnewline
21 & 267.2 & 205.504435729175 & 61.6955642708246 \tabularnewline
22 & 237.2 & 210.115015837272 & 27.0849841627283 \tabularnewline
23 & 254.7 & 222.495980160272 & 32.2040198397283 \tabularnewline
24 & 258.2 & 203.085504149742 & 55.1144958502583 \tabularnewline
25 & 257.9 & 204.415538422477 & 53.4844615775228 \tabularnewline
26 & 269.6 & 195.499595911675 & 74.1004040883253 \tabularnewline
27 & 266.9 & 189.144429828614 & 77.7555701713855 \tabularnewline
28 & 269.6 & 196.784729819373 & 72.8152701806266 \tabularnewline
29 & 253.9 & 205.255414025036 & 48.6445859749639 \tabularnewline
30 & 258.6 & 228.338919277494 & 30.2610807225062 \tabularnewline
31 & 274.2 & 230.844469575458 & 43.3555304245423 \tabularnewline
32 & 301.5 & 266.981356109385 & 34.5186438906147 \tabularnewline
33 & 304.5 & 248.064521624241 & 56.4354783757591 \tabularnewline
34 & 285.1 & 239.81047601053 & 45.28952398947 \tabularnewline
35 & 287.7 & 240.083557301241 & 47.6164426987591 \tabularnewline
36 & 265.5 & 229.753993564928 & 35.7460064350723 \tabularnewline
37 & 264.1 & 232.975884561458 & 31.1241154385416 \tabularnewline
38 & 276.1 & 213.465544397403 & 62.634455602597 \tabularnewline
39 & 258.9 & 241.163799342656 & 17.7362006573442 \tabularnewline
40 & 239.1 & 211.345336202270 & 27.7546637977295 \tabularnewline
41 & 250.1 & 206.951394686126 & 43.1486053138742 \tabularnewline
42 & 276.8 & 258.034379450752 & 18.7656205492478 \tabularnewline
43 & 297.6 & 277.566640262873 & 20.0333597371274 \tabularnewline
44 & 295.4 & 290.24450342174 & 5.15549657825988 \tabularnewline
45 & 283 & 326.569885271415 & -43.5698852714146 \tabularnewline
46 & 275.8 & 305.072842591138 & -29.2728425911376 \tabularnewline
47 & 279.7 & 311.399865397993 & -31.699865397993 \tabularnewline
48 & 254.6 & 309.394471246379 & -54.7944712463785 \tabularnewline
49 & 234.6 & 275.157599111765 & -40.5575991117649 \tabularnewline
50 & 176.9 & 248.458203397288 & -71.5582033972878 \tabularnewline
51 & 148.1 & 221.670984697240 & -73.5709846972397 \tabularnewline
52 & 122.7 & 183.906723316915 & -61.2067233169146 \tabularnewline
53 & 124.9 & 184.053237937878 & -59.1532379378784 \tabularnewline
54 & 121.6 & 163.245667198288 & -41.6456671982883 \tabularnewline
55 & 128.4 & 183.156299355168 & -54.7562993551677 \tabularnewline
56 & 144.5 & 164.050969554276 & -19.5509695542763 \tabularnewline
57 & 151.8 & 173.511985926059 & -21.7119859260594 \tabularnewline
58 & 167.1 & 180.014422757951 & -12.9144227579510 \tabularnewline
59 & 173.8 & 164.395907568782 & 9.40409243121765 \tabularnewline
60 & 203.7 & 224.443413957650 & -20.7434139576495 \tabularnewline
61 & 199.8 & 162.585433655626 & 37.2145663443736 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58297&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]130[/C][C]192.699407515599[/C][C]-62.6994075155985[/C][/ROW]
[ROW][C]2[/C][C]136.7[/C][C]201.188546863712[/C][C]-64.488546863712[/C][/ROW]
[ROW][C]3[/C][C]138.1[/C][C]187.64432523023[/C][C]-49.5443252302301[/C][/ROW]
[ROW][C]4[/C][C]139.5[/C][C]191.122540428640[/C][C]-51.6225404286396[/C][/ROW]
[ROW][C]5[/C][C]140.4[/C][C]175.377458569724[/C][C]-34.9774585697241[/C][/ROW]
[ROW][C]6[/C][C]144.6[/C][C]164.785914138628[/C][C]-20.1859141386278[/C][/ROW]
[ROW][C]7[/C][C]151.4[/C][C]179.020976124122[/C][C]-27.6209761241217[/C][/ROW]
[ROW][C]8[/C][C]147.9[/C][C]181.861184319254[/C][C]-33.9611843192543[/C][/ROW]
[ROW][C]9[/C][C]141.5[/C][C]194.349171449110[/C][C]-52.8491714491097[/C][/ROW]
[ROW][C]10[/C][C]143.8[/C][C]173.987242803110[/C][C]-30.1872428031097[/C][/ROW]
[ROW][C]11[/C][C]143.6[/C][C]201.124689571712[/C][C]-57.5246895717121[/C][/ROW]
[ROW][C]12[/C][C]150.5[/C][C]165.822617081303[/C][C]-15.3226170813026[/C][/ROW]
[ROW][C]13[/C][C]150.1[/C][C]168.666136733074[/C][C]-18.5661367330744[/C][/ROW]
[ROW][C]14[/C][C]154.9[/C][C]155.588109429923[/C][C]-0.688109429922506[/C][/ROW]
[ROW][C]15[/C][C]162.1[/C][C]134.47646090126[/C][C]27.6235390987401[/C][/ROW]
[ROW][C]16[/C][C]176.7[/C][C]164.440670232802[/C][C]12.2593297671981[/C][/ROW]
[ROW][C]17[/C][C]186.6[/C][C]184.262494781236[/C][C]2.33750521876447[/C][/ROW]
[ROW][C]18[/C][C]194.8[/C][C]181.995119934838[/C][C]12.8048800651620[/C][/ROW]
[ROW][C]19[/C][C]196.3[/C][C]177.311614682380[/C][C]18.9883853176198[/C][/ROW]
[ROW][C]20[/C][C]228.8[/C][C]214.961986595344[/C][C]13.8380134046560[/C][/ROW]
[ROW][C]21[/C][C]267.2[/C][C]205.504435729175[/C][C]61.6955642708246[/C][/ROW]
[ROW][C]22[/C][C]237.2[/C][C]210.115015837272[/C][C]27.0849841627283[/C][/ROW]
[ROW][C]23[/C][C]254.7[/C][C]222.495980160272[/C][C]32.2040198397283[/C][/ROW]
[ROW][C]24[/C][C]258.2[/C][C]203.085504149742[/C][C]55.1144958502583[/C][/ROW]
[ROW][C]25[/C][C]257.9[/C][C]204.415538422477[/C][C]53.4844615775228[/C][/ROW]
[ROW][C]26[/C][C]269.6[/C][C]195.499595911675[/C][C]74.1004040883253[/C][/ROW]
[ROW][C]27[/C][C]266.9[/C][C]189.144429828614[/C][C]77.7555701713855[/C][/ROW]
[ROW][C]28[/C][C]269.6[/C][C]196.784729819373[/C][C]72.8152701806266[/C][/ROW]
[ROW][C]29[/C][C]253.9[/C][C]205.255414025036[/C][C]48.6445859749639[/C][/ROW]
[ROW][C]30[/C][C]258.6[/C][C]228.338919277494[/C][C]30.2610807225062[/C][/ROW]
[ROW][C]31[/C][C]274.2[/C][C]230.844469575458[/C][C]43.3555304245423[/C][/ROW]
[ROW][C]32[/C][C]301.5[/C][C]266.981356109385[/C][C]34.5186438906147[/C][/ROW]
[ROW][C]33[/C][C]304.5[/C][C]248.064521624241[/C][C]56.4354783757591[/C][/ROW]
[ROW][C]34[/C][C]285.1[/C][C]239.81047601053[/C][C]45.28952398947[/C][/ROW]
[ROW][C]35[/C][C]287.7[/C][C]240.083557301241[/C][C]47.6164426987591[/C][/ROW]
[ROW][C]36[/C][C]265.5[/C][C]229.753993564928[/C][C]35.7460064350723[/C][/ROW]
[ROW][C]37[/C][C]264.1[/C][C]232.975884561458[/C][C]31.1241154385416[/C][/ROW]
[ROW][C]38[/C][C]276.1[/C][C]213.465544397403[/C][C]62.634455602597[/C][/ROW]
[ROW][C]39[/C][C]258.9[/C][C]241.163799342656[/C][C]17.7362006573442[/C][/ROW]
[ROW][C]40[/C][C]239.1[/C][C]211.345336202270[/C][C]27.7546637977295[/C][/ROW]
[ROW][C]41[/C][C]250.1[/C][C]206.951394686126[/C][C]43.1486053138742[/C][/ROW]
[ROW][C]42[/C][C]276.8[/C][C]258.034379450752[/C][C]18.7656205492478[/C][/ROW]
[ROW][C]43[/C][C]297.6[/C][C]277.566640262873[/C][C]20.0333597371274[/C][/ROW]
[ROW][C]44[/C][C]295.4[/C][C]290.24450342174[/C][C]5.15549657825988[/C][/ROW]
[ROW][C]45[/C][C]283[/C][C]326.569885271415[/C][C]-43.5698852714146[/C][/ROW]
[ROW][C]46[/C][C]275.8[/C][C]305.072842591138[/C][C]-29.2728425911376[/C][/ROW]
[ROW][C]47[/C][C]279.7[/C][C]311.399865397993[/C][C]-31.699865397993[/C][/ROW]
[ROW][C]48[/C][C]254.6[/C][C]309.394471246379[/C][C]-54.7944712463785[/C][/ROW]
[ROW][C]49[/C][C]234.6[/C][C]275.157599111765[/C][C]-40.5575991117649[/C][/ROW]
[ROW][C]50[/C][C]176.9[/C][C]248.458203397288[/C][C]-71.5582033972878[/C][/ROW]
[ROW][C]51[/C][C]148.1[/C][C]221.670984697240[/C][C]-73.5709846972397[/C][/ROW]
[ROW][C]52[/C][C]122.7[/C][C]183.906723316915[/C][C]-61.2067233169146[/C][/ROW]
[ROW][C]53[/C][C]124.9[/C][C]184.053237937878[/C][C]-59.1532379378784[/C][/ROW]
[ROW][C]54[/C][C]121.6[/C][C]163.245667198288[/C][C]-41.6456671982883[/C][/ROW]
[ROW][C]55[/C][C]128.4[/C][C]183.156299355168[/C][C]-54.7562993551677[/C][/ROW]
[ROW][C]56[/C][C]144.5[/C][C]164.050969554276[/C][C]-19.5509695542763[/C][/ROW]
[ROW][C]57[/C][C]151.8[/C][C]173.511985926059[/C][C]-21.7119859260594[/C][/ROW]
[ROW][C]58[/C][C]167.1[/C][C]180.014422757951[/C][C]-12.9144227579510[/C][/ROW]
[ROW][C]59[/C][C]173.8[/C][C]164.395907568782[/C][C]9.40409243121765[/C][/ROW]
[ROW][C]60[/C][C]203.7[/C][C]224.443413957650[/C][C]-20.7434139576495[/C][/ROW]
[ROW][C]61[/C][C]199.8[/C][C]162.585433655626[/C][C]37.2145663443736[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58297&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58297&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
1130192.699407515599-62.6994075155985
2136.7201.188546863712-64.488546863712
3138.1187.64432523023-49.5443252302301
4139.5191.122540428640-51.6225404286396
5140.4175.377458569724-34.9774585697241
6144.6164.785914138628-20.1859141386278
7151.4179.020976124122-27.6209761241217
8147.9181.861184319254-33.9611843192543
9141.5194.349171449110-52.8491714491097
10143.8173.987242803110-30.1872428031097
11143.6201.124689571712-57.5246895717121
12150.5165.822617081303-15.3226170813026
13150.1168.666136733074-18.5661367330744
14154.9155.588109429923-0.688109429922506
15162.1134.4764609012627.6235390987401
16176.7164.44067023280212.2593297671981
17186.6184.2624947812362.33750521876447
18194.8181.99511993483812.8048800651620
19196.3177.31161468238018.9883853176198
20228.8214.96198659534413.8380134046560
21267.2205.50443572917561.6955642708246
22237.2210.11501583727227.0849841627283
23254.7222.49598016027232.2040198397283
24258.2203.08550414974255.1144958502583
25257.9204.41553842247753.4844615775228
26269.6195.49959591167574.1004040883253
27266.9189.14442982861477.7555701713855
28269.6196.78472981937372.8152701806266
29253.9205.25541402503648.6445859749639
30258.6228.33891927749430.2610807225062
31274.2230.84446957545843.3555304245423
32301.5266.98135610938534.5186438906147
33304.5248.06452162424156.4354783757591
34285.1239.8104760105345.28952398947
35287.7240.08355730124147.6164426987591
36265.5229.75399356492835.7460064350723
37264.1232.97588456145831.1241154385416
38276.1213.46554439740362.634455602597
39258.9241.16379934265617.7362006573442
40239.1211.34533620227027.7546637977295
41250.1206.95139468612643.1486053138742
42276.8258.03437945075218.7656205492478
43297.6277.56664026287320.0333597371274
44295.4290.244503421745.15549657825988
45283326.569885271415-43.5698852714146
46275.8305.072842591138-29.2728425911376
47279.7311.399865397993-31.699865397993
48254.6309.394471246379-54.7944712463785
49234.6275.157599111765-40.5575991117649
50176.9248.458203397288-71.5582033972878
51148.1221.670984697240-73.5709846972397
52122.7183.906723316915-61.2067233169146
53124.9184.053237937878-59.1532379378784
54121.6163.245667198288-41.6456671982883
55128.4183.156299355168-54.7562993551677
56144.5164.050969554276-19.5509695542763
57151.8173.511985926059-21.7119859260594
58167.1180.014422757951-12.9144227579510
59173.8164.3959075687829.40409243121765
60203.7224.443413957650-20.7434139576495
61199.8162.58543365562637.2145663443736







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.006764989778507260.01352997955701450.993235010221493
180.00108217202813390.00216434405626780.998917827971866
190.0001947932209621730.0003895864419243460.999805206779038
200.0004419106069387940.0008838212138775880.999558089393061
210.06345933250414740.1269186650082950.936540667495853
220.04263464556429190.08526929112858380.957365354435708
230.05742757987530630.1148551597506130.942572420124694
240.03873784361131690.07747568722263370.961262156388683
250.03270918834739400.06541837669478810.967290811652606
260.01949713950768550.0389942790153710.980502860492314
270.00999030057779890.01998060115559780.990009699422201
280.004823619926552750.00964723985310550.995176380073447
290.004631347250425110.009262694500850220.995368652749575
300.01403442793760890.02806885587521790.98596557206239
310.01144513865606490.02289027731212980.988554861343935
320.007677684593879590.01535536918775920.99232231540612
330.004406615457375130.008813230914750260.995593384542625
340.002820977214599630.005641954429199270.9971790227854
350.001743460011547280.003486920023094560.998256539988453
360.00558943326991960.01117886653983920.99441056673008
370.07779194745768430.1555838949153690.922208052542316
380.06289419301551780.1257883860310360.937105806984482
390.0949283886252460.1898567772504920.905071611374754
400.1153512863268320.2307025726536650.884648713673168
410.09330423050504370.1866084610100870.906695769494956
420.1131448049576740.2262896099153480.886855195042326
430.4355265680291890.8710531360583790.564473431970811
440.6819693650902760.6360612698194490.318030634909724

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.00676498977850726 & 0.0135299795570145 & 0.993235010221493 \tabularnewline
18 & 0.0010821720281339 & 0.0021643440562678 & 0.998917827971866 \tabularnewline
19 & 0.000194793220962173 & 0.000389586441924346 & 0.999805206779038 \tabularnewline
20 & 0.000441910606938794 & 0.000883821213877588 & 0.999558089393061 \tabularnewline
21 & 0.0634593325041474 & 0.126918665008295 & 0.936540667495853 \tabularnewline
22 & 0.0426346455642919 & 0.0852692911285838 & 0.957365354435708 \tabularnewline
23 & 0.0574275798753063 & 0.114855159750613 & 0.942572420124694 \tabularnewline
24 & 0.0387378436113169 & 0.0774756872226337 & 0.961262156388683 \tabularnewline
25 & 0.0327091883473940 & 0.0654183766947881 & 0.967290811652606 \tabularnewline
26 & 0.0194971395076855 & 0.038994279015371 & 0.980502860492314 \tabularnewline
27 & 0.0099903005777989 & 0.0199806011555978 & 0.990009699422201 \tabularnewline
28 & 0.00482361992655275 & 0.0096472398531055 & 0.995176380073447 \tabularnewline
29 & 0.00463134725042511 & 0.00926269450085022 & 0.995368652749575 \tabularnewline
30 & 0.0140344279376089 & 0.0280688558752179 & 0.98596557206239 \tabularnewline
31 & 0.0114451386560649 & 0.0228902773121298 & 0.988554861343935 \tabularnewline
32 & 0.00767768459387959 & 0.0153553691877592 & 0.99232231540612 \tabularnewline
33 & 0.00440661545737513 & 0.00881323091475026 & 0.995593384542625 \tabularnewline
34 & 0.00282097721459963 & 0.00564195442919927 & 0.9971790227854 \tabularnewline
35 & 0.00174346001154728 & 0.00348692002309456 & 0.998256539988453 \tabularnewline
36 & 0.0055894332699196 & 0.0111788665398392 & 0.99441056673008 \tabularnewline
37 & 0.0777919474576843 & 0.155583894915369 & 0.922208052542316 \tabularnewline
38 & 0.0628941930155178 & 0.125788386031036 & 0.937105806984482 \tabularnewline
39 & 0.094928388625246 & 0.189856777250492 & 0.905071611374754 \tabularnewline
40 & 0.115351286326832 & 0.230702572653665 & 0.884648713673168 \tabularnewline
41 & 0.0933042305050437 & 0.186608461010087 & 0.906695769494956 \tabularnewline
42 & 0.113144804957674 & 0.226289609915348 & 0.886855195042326 \tabularnewline
43 & 0.435526568029189 & 0.871053136058379 & 0.564473431970811 \tabularnewline
44 & 0.681969365090276 & 0.636061269819449 & 0.318030634909724 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58297&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]0.00676498977850726[/C][C]0.0135299795570145[/C][C]0.993235010221493[/C][/ROW]
[ROW][C]18[/C][C]0.0010821720281339[/C][C]0.0021643440562678[/C][C]0.998917827971866[/C][/ROW]
[ROW][C]19[/C][C]0.000194793220962173[/C][C]0.000389586441924346[/C][C]0.999805206779038[/C][/ROW]
[ROW][C]20[/C][C]0.000441910606938794[/C][C]0.000883821213877588[/C][C]0.999558089393061[/C][/ROW]
[ROW][C]21[/C][C]0.0634593325041474[/C][C]0.126918665008295[/C][C]0.936540667495853[/C][/ROW]
[ROW][C]22[/C][C]0.0426346455642919[/C][C]0.0852692911285838[/C][C]0.957365354435708[/C][/ROW]
[ROW][C]23[/C][C]0.0574275798753063[/C][C]0.114855159750613[/C][C]0.942572420124694[/C][/ROW]
[ROW][C]24[/C][C]0.0387378436113169[/C][C]0.0774756872226337[/C][C]0.961262156388683[/C][/ROW]
[ROW][C]25[/C][C]0.0327091883473940[/C][C]0.0654183766947881[/C][C]0.967290811652606[/C][/ROW]
[ROW][C]26[/C][C]0.0194971395076855[/C][C]0.038994279015371[/C][C]0.980502860492314[/C][/ROW]
[ROW][C]27[/C][C]0.0099903005777989[/C][C]0.0199806011555978[/C][C]0.990009699422201[/C][/ROW]
[ROW][C]28[/C][C]0.00482361992655275[/C][C]0.0096472398531055[/C][C]0.995176380073447[/C][/ROW]
[ROW][C]29[/C][C]0.00463134725042511[/C][C]0.00926269450085022[/C][C]0.995368652749575[/C][/ROW]
[ROW][C]30[/C][C]0.0140344279376089[/C][C]0.0280688558752179[/C][C]0.98596557206239[/C][/ROW]
[ROW][C]31[/C][C]0.0114451386560649[/C][C]0.0228902773121298[/C][C]0.988554861343935[/C][/ROW]
[ROW][C]32[/C][C]0.00767768459387959[/C][C]0.0153553691877592[/C][C]0.99232231540612[/C][/ROW]
[ROW][C]33[/C][C]0.00440661545737513[/C][C]0.00881323091475026[/C][C]0.995593384542625[/C][/ROW]
[ROW][C]34[/C][C]0.00282097721459963[/C][C]0.00564195442919927[/C][C]0.9971790227854[/C][/ROW]
[ROW][C]35[/C][C]0.00174346001154728[/C][C]0.00348692002309456[/C][C]0.998256539988453[/C][/ROW]
[ROW][C]36[/C][C]0.0055894332699196[/C][C]0.0111788665398392[/C][C]0.99441056673008[/C][/ROW]
[ROW][C]37[/C][C]0.0777919474576843[/C][C]0.155583894915369[/C][C]0.922208052542316[/C][/ROW]
[ROW][C]38[/C][C]0.0628941930155178[/C][C]0.125788386031036[/C][C]0.937105806984482[/C][/ROW]
[ROW][C]39[/C][C]0.094928388625246[/C][C]0.189856777250492[/C][C]0.905071611374754[/C][/ROW]
[ROW][C]40[/C][C]0.115351286326832[/C][C]0.230702572653665[/C][C]0.884648713673168[/C][/ROW]
[ROW][C]41[/C][C]0.0933042305050437[/C][C]0.186608461010087[/C][C]0.906695769494956[/C][/ROW]
[ROW][C]42[/C][C]0.113144804957674[/C][C]0.226289609915348[/C][C]0.886855195042326[/C][/ROW]
[ROW][C]43[/C][C]0.435526568029189[/C][C]0.871053136058379[/C][C]0.564473431970811[/C][/ROW]
[ROW][C]44[/C][C]0.681969365090276[/C][C]0.636061269819449[/C][C]0.318030634909724[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58297&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58297&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
170.006764989778507260.01352997955701450.993235010221493
180.00108217202813390.00216434405626780.998917827971866
190.0001947932209621730.0003895864419243460.999805206779038
200.0004419106069387940.0008838212138775880.999558089393061
210.06345933250414740.1269186650082950.936540667495853
220.04263464556429190.08526929112858380.957365354435708
230.05742757987530630.1148551597506130.942572420124694
240.03873784361131690.07747568722263370.961262156388683
250.03270918834739400.06541837669478810.967290811652606
260.01949713950768550.0389942790153710.980502860492314
270.00999030057779890.01998060115559780.990009699422201
280.004823619926552750.00964723985310550.995176380073447
290.004631347250425110.009262694500850220.995368652749575
300.01403442793760890.02806885587521790.98596557206239
310.01144513865606490.02289027731212980.988554861343935
320.007677684593879590.01535536918775920.99232231540612
330.004406615457375130.008813230914750260.995593384542625
340.002820977214599630.005641954429199270.9971790227854
350.001743460011547280.003486920023094560.998256539988453
360.00558943326991960.01117886653983920.99441056673008
370.07779194745768430.1555838949153690.922208052542316
380.06289419301551780.1257883860310360.937105806984482
390.0949283886252460.1898567772504920.905071611374754
400.1153512863268320.2307025726536650.884648713673168
410.09330423050504370.1866084610100870.906695769494956
420.1131448049576740.2262896099153480.886855195042326
430.4355265680291890.8710531360583790.564473431970811
440.6819693650902760.6360612698194490.318030634909724







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level80.285714285714286NOK
5% type I error level150.535714285714286NOK
10% type I error level180.642857142857143NOK

\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 & 8 & 0.285714285714286 & NOK \tabularnewline
5% type I error level & 15 & 0.535714285714286 & NOK \tabularnewline
10% type I error level & 18 & 0.642857142857143 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58297&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]8[/C][C]0.285714285714286[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]15[/C][C]0.535714285714286[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]18[/C][C]0.642857142857143[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58297&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58297&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 level80.285714285714286NOK
5% type I error level150.535714285714286NOK
10% type I error level180.642857142857143NOK



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')
}