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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 09:09:48 -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/t12587339308pcyzpci2m9lvz4.htm/, Retrieved Fri, 29 Mar 2024 14:44:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58303, Retrieved Fri, 29 Mar 2024 14:44:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
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]
- R  D      [Multiple Regression] [] [2009-11-20 16:09:48] [c5f9f441970441f2f938cd843072158d] [Current]
-    D        [Multiple Regression] [Model 1] [2009-12-18 15:50:26] [eba9b8a72d680086d9ebbb043233c887]
-   PD        [Multiple Regression] [Model 2] [2009-12-18 16:35:48] [eba9b8a72d680086d9ebbb043233c887]
-   P           [Multiple Regression] [Model 3] [2009-12-19 11:34:37] [eba9b8a72d680086d9ebbb043233c887]
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Dataseries X:
2253	14.9
2218	18.6
1855	19.1
2187	18.8
1852	18.2
1570	18
1851	19
1954	20.7
1828	21.2
2251	20.7
2277	19.6
2085	18.6
2282	18.7
2266	23.8
1878	24.9
2267	24.8
2069	23.8
1746	22.3
2299	21.7
2360	20.7
2214	19.7
2825	18.4
2355	17.4
2333	17
3016	18
2155	23.8
2172	25.5
2150	25.6
2533	23.7
2058	22
2160	21.3
2260	20.7
2498	20.4
2695	20.3
2799	20.4
2946	19.8
2930	19.5
2318	23.1
2540	23.5
2570	23.5
2669	22.9
2450	21.9
2842	21.5
3440	20.5
2678	20.2
2981	19.4
2260	19.2
2844	18.8
2546	18.8
2456	22.6
2295	23.3
2379	23
2479	21.4
2057	19.9
2280	18.8
2351	18.6
2276	18.4
2548	18.6
2311	19.9
2201	19.2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58303&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]6 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=58303&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58303&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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
wngbw[t] = + 2613.94906149101 -12.6101596071860`<25`[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
wngbw[t] =  +  2613.94906149101 -12.6101596071860`<25`[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58303&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]wngbw[t] =  +  2613.94906149101 -12.6101596071860`<25`[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58303&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58303&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
wngbw[t] = + 2613.94906149101 -12.6101596071860`<25`[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)2613.94906149101412.4704586.337300
`<25`-12.610159607186019.859534-0.6350.5279470.263973

\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) & 2613.94906149101 & 412.470458 & 6.3373 & 0 & 0 \tabularnewline
`<25` & -12.6101596071860 & 19.859534 & -0.635 & 0.527947 & 0.263973 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58303&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]2613.94906149101[/C][C]412.470458[/C][C]6.3373[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`<25`[/C][C]-12.6101596071860[/C][C]19.859534[/C][C]-0.635[/C][C]0.527947[/C][C]0.263973[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58303&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58303&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)2613.94906149101412.4704586.337300
`<25`-12.610159607186019.859534-0.6350.5279470.263973







Multiple Linear Regression - Regression Statistics
Multiple R0.0830870362217952
R-squared0.0069034555881219
Adjusted R-squared-0.010218898625876
F-TEST (value)0.403183785467899
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value0.527946632050694
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation351.478594444187
Sum Squared Residuals7165157.73644276

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.0830870362217952 \tabularnewline
R-squared & 0.0069034555881219 \tabularnewline
Adjusted R-squared & -0.010218898625876 \tabularnewline
F-TEST (value) & 0.403183785467899 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 58 \tabularnewline
p-value & 0.527946632050694 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 351.478594444187 \tabularnewline
Sum Squared Residuals & 7165157.73644276 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58303&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.0830870362217952[/C][/ROW]
[ROW][C]R-squared[/C][C]0.0069034555881219[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]-0.010218898625876[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]0.403183785467899[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]58[/C][/ROW]
[ROW][C]p-value[/C][C]0.527946632050694[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]351.478594444187[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]7165157.73644276[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58303&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58303&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 R0.0830870362217952
R-squared0.0069034555881219
Adjusted R-squared-0.010218898625876
F-TEST (value)0.403183785467899
F-TEST (DF numerator)1
F-TEST (DF denominator)58
p-value0.527946632050694
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation351.478594444187
Sum Squared Residuals7165157.73644276







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
122532426.05768334395-173.057683343953
222182379.40009279735-161.400092797350
318552373.09501299376-518.095012993757
421872376.87806087591-189.878060875913
518522384.44415664022-532.444156640224
615702386.96618856166-816.966188561661
718512374.35602895448-523.356028954475
819542352.91875762226-398.918757622259
918282346.61367781867-518.613677818666
1022512352.91875762226-101.918757622259
1122772366.78993319016-89.7899331901638
1220852379.40009279735-294.400092797350
1322822378.13907683663-96.1390768366312
1422662313.82726283998-47.8272628399827
1518782299.95608727208-421.956087272078
1622672301.21710323280-34.2171032327968
1720692313.82726283998-244.827262839983
1817462332.74250225076-586.742502250762
1922992340.30859801507-41.3085980150733
2023602352.918757622267.08124237774075
2122142365.52891722945-151.528917229445
2228252381.92212471879443.077875281213
2323552394.53228432597-39.5322843259730
2423332399.57634816885-66.5763481688473
2530162386.96618856166629.033811438339
2621552313.82726283998-158.827262839983
2721722292.38999150777-120.389991507767
2821502291.12897554705-141.128975547048
2925332315.0882788007217.911721199299
3020582336.52555013292-278.525550132917
3121602345.35266185795-185.352661857948
3222602352.91875762226-92.9187576222592
3324982356.70180550442141.298194495585
3426952357.96282146513337.037178534866
3527992356.70180550442442.298194495585
3629462364.26790126873581.732098731273
3729302368.05094915088561.949050849118
3823182322.65437456501-4.6543745650129
3925402317.61031072214222.389689277861
4025702317.61031072214252.389689277861
4126692325.17640648645343.82359351355
4224502337.78656609364112.213433906364
4328422342.83062993651499.16937006349
4434402355.440789543701084.55921045630
4526782359.22383742585318.776162574148
4629812369.3119651116611.688034888399
4722602371.83399703304-111.833997033038
4828442376.87806087591467.121939124087
4925462376.87806087591169.121939124087
5024562328.95945436861127.040545631394
5122952320.13234264358-25.1323426435757
5223792323.9153905257355.0846094742685
5324792344.09164589723134.908354102771
5420572363.00688530801-306.006885308008
5522802376.87806087591-96.8780608759126
5623512379.40009279735-28.4000927973498
5722762381.92212471879-105.922124718787
5825482379.40009279735168.599907202650
5923112363.00688530801-52.006885308008
6022012371.83399703304-170.833997033038

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 2253 & 2426.05768334395 & -173.057683343953 \tabularnewline
2 & 2218 & 2379.40009279735 & -161.400092797350 \tabularnewline
3 & 1855 & 2373.09501299376 & -518.095012993757 \tabularnewline
4 & 2187 & 2376.87806087591 & -189.878060875913 \tabularnewline
5 & 1852 & 2384.44415664022 & -532.444156640224 \tabularnewline
6 & 1570 & 2386.96618856166 & -816.966188561661 \tabularnewline
7 & 1851 & 2374.35602895448 & -523.356028954475 \tabularnewline
8 & 1954 & 2352.91875762226 & -398.918757622259 \tabularnewline
9 & 1828 & 2346.61367781867 & -518.613677818666 \tabularnewline
10 & 2251 & 2352.91875762226 & -101.918757622259 \tabularnewline
11 & 2277 & 2366.78993319016 & -89.7899331901638 \tabularnewline
12 & 2085 & 2379.40009279735 & -294.400092797350 \tabularnewline
13 & 2282 & 2378.13907683663 & -96.1390768366312 \tabularnewline
14 & 2266 & 2313.82726283998 & -47.8272628399827 \tabularnewline
15 & 1878 & 2299.95608727208 & -421.956087272078 \tabularnewline
16 & 2267 & 2301.21710323280 & -34.2171032327968 \tabularnewline
17 & 2069 & 2313.82726283998 & -244.827262839983 \tabularnewline
18 & 1746 & 2332.74250225076 & -586.742502250762 \tabularnewline
19 & 2299 & 2340.30859801507 & -41.3085980150733 \tabularnewline
20 & 2360 & 2352.91875762226 & 7.08124237774075 \tabularnewline
21 & 2214 & 2365.52891722945 & -151.528917229445 \tabularnewline
22 & 2825 & 2381.92212471879 & 443.077875281213 \tabularnewline
23 & 2355 & 2394.53228432597 & -39.5322843259730 \tabularnewline
24 & 2333 & 2399.57634816885 & -66.5763481688473 \tabularnewline
25 & 3016 & 2386.96618856166 & 629.033811438339 \tabularnewline
26 & 2155 & 2313.82726283998 & -158.827262839983 \tabularnewline
27 & 2172 & 2292.38999150777 & -120.389991507767 \tabularnewline
28 & 2150 & 2291.12897554705 & -141.128975547048 \tabularnewline
29 & 2533 & 2315.0882788007 & 217.911721199299 \tabularnewline
30 & 2058 & 2336.52555013292 & -278.525550132917 \tabularnewline
31 & 2160 & 2345.35266185795 & -185.352661857948 \tabularnewline
32 & 2260 & 2352.91875762226 & -92.9187576222592 \tabularnewline
33 & 2498 & 2356.70180550442 & 141.298194495585 \tabularnewline
34 & 2695 & 2357.96282146513 & 337.037178534866 \tabularnewline
35 & 2799 & 2356.70180550442 & 442.298194495585 \tabularnewline
36 & 2946 & 2364.26790126873 & 581.732098731273 \tabularnewline
37 & 2930 & 2368.05094915088 & 561.949050849118 \tabularnewline
38 & 2318 & 2322.65437456501 & -4.6543745650129 \tabularnewline
39 & 2540 & 2317.61031072214 & 222.389689277861 \tabularnewline
40 & 2570 & 2317.61031072214 & 252.389689277861 \tabularnewline
41 & 2669 & 2325.17640648645 & 343.82359351355 \tabularnewline
42 & 2450 & 2337.78656609364 & 112.213433906364 \tabularnewline
43 & 2842 & 2342.83062993651 & 499.16937006349 \tabularnewline
44 & 3440 & 2355.44078954370 & 1084.55921045630 \tabularnewline
45 & 2678 & 2359.22383742585 & 318.776162574148 \tabularnewline
46 & 2981 & 2369.3119651116 & 611.688034888399 \tabularnewline
47 & 2260 & 2371.83399703304 & -111.833997033038 \tabularnewline
48 & 2844 & 2376.87806087591 & 467.121939124087 \tabularnewline
49 & 2546 & 2376.87806087591 & 169.121939124087 \tabularnewline
50 & 2456 & 2328.95945436861 & 127.040545631394 \tabularnewline
51 & 2295 & 2320.13234264358 & -25.1323426435757 \tabularnewline
52 & 2379 & 2323.91539052573 & 55.0846094742685 \tabularnewline
53 & 2479 & 2344.09164589723 & 134.908354102771 \tabularnewline
54 & 2057 & 2363.00688530801 & -306.006885308008 \tabularnewline
55 & 2280 & 2376.87806087591 & -96.8780608759126 \tabularnewline
56 & 2351 & 2379.40009279735 & -28.4000927973498 \tabularnewline
57 & 2276 & 2381.92212471879 & -105.922124718787 \tabularnewline
58 & 2548 & 2379.40009279735 & 168.599907202650 \tabularnewline
59 & 2311 & 2363.00688530801 & -52.006885308008 \tabularnewline
60 & 2201 & 2371.83399703304 & -170.833997033038 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58303&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]2253[/C][C]2426.05768334395[/C][C]-173.057683343953[/C][/ROW]
[ROW][C]2[/C][C]2218[/C][C]2379.40009279735[/C][C]-161.400092797350[/C][/ROW]
[ROW][C]3[/C][C]1855[/C][C]2373.09501299376[/C][C]-518.095012993757[/C][/ROW]
[ROW][C]4[/C][C]2187[/C][C]2376.87806087591[/C][C]-189.878060875913[/C][/ROW]
[ROW][C]5[/C][C]1852[/C][C]2384.44415664022[/C][C]-532.444156640224[/C][/ROW]
[ROW][C]6[/C][C]1570[/C][C]2386.96618856166[/C][C]-816.966188561661[/C][/ROW]
[ROW][C]7[/C][C]1851[/C][C]2374.35602895448[/C][C]-523.356028954475[/C][/ROW]
[ROW][C]8[/C][C]1954[/C][C]2352.91875762226[/C][C]-398.918757622259[/C][/ROW]
[ROW][C]9[/C][C]1828[/C][C]2346.61367781867[/C][C]-518.613677818666[/C][/ROW]
[ROW][C]10[/C][C]2251[/C][C]2352.91875762226[/C][C]-101.918757622259[/C][/ROW]
[ROW][C]11[/C][C]2277[/C][C]2366.78993319016[/C][C]-89.7899331901638[/C][/ROW]
[ROW][C]12[/C][C]2085[/C][C]2379.40009279735[/C][C]-294.400092797350[/C][/ROW]
[ROW][C]13[/C][C]2282[/C][C]2378.13907683663[/C][C]-96.1390768366312[/C][/ROW]
[ROW][C]14[/C][C]2266[/C][C]2313.82726283998[/C][C]-47.8272628399827[/C][/ROW]
[ROW][C]15[/C][C]1878[/C][C]2299.95608727208[/C][C]-421.956087272078[/C][/ROW]
[ROW][C]16[/C][C]2267[/C][C]2301.21710323280[/C][C]-34.2171032327968[/C][/ROW]
[ROW][C]17[/C][C]2069[/C][C]2313.82726283998[/C][C]-244.827262839983[/C][/ROW]
[ROW][C]18[/C][C]1746[/C][C]2332.74250225076[/C][C]-586.742502250762[/C][/ROW]
[ROW][C]19[/C][C]2299[/C][C]2340.30859801507[/C][C]-41.3085980150733[/C][/ROW]
[ROW][C]20[/C][C]2360[/C][C]2352.91875762226[/C][C]7.08124237774075[/C][/ROW]
[ROW][C]21[/C][C]2214[/C][C]2365.52891722945[/C][C]-151.528917229445[/C][/ROW]
[ROW][C]22[/C][C]2825[/C][C]2381.92212471879[/C][C]443.077875281213[/C][/ROW]
[ROW][C]23[/C][C]2355[/C][C]2394.53228432597[/C][C]-39.5322843259730[/C][/ROW]
[ROW][C]24[/C][C]2333[/C][C]2399.57634816885[/C][C]-66.5763481688473[/C][/ROW]
[ROW][C]25[/C][C]3016[/C][C]2386.96618856166[/C][C]629.033811438339[/C][/ROW]
[ROW][C]26[/C][C]2155[/C][C]2313.82726283998[/C][C]-158.827262839983[/C][/ROW]
[ROW][C]27[/C][C]2172[/C][C]2292.38999150777[/C][C]-120.389991507767[/C][/ROW]
[ROW][C]28[/C][C]2150[/C][C]2291.12897554705[/C][C]-141.128975547048[/C][/ROW]
[ROW][C]29[/C][C]2533[/C][C]2315.0882788007[/C][C]217.911721199299[/C][/ROW]
[ROW][C]30[/C][C]2058[/C][C]2336.52555013292[/C][C]-278.525550132917[/C][/ROW]
[ROW][C]31[/C][C]2160[/C][C]2345.35266185795[/C][C]-185.352661857948[/C][/ROW]
[ROW][C]32[/C][C]2260[/C][C]2352.91875762226[/C][C]-92.9187576222592[/C][/ROW]
[ROW][C]33[/C][C]2498[/C][C]2356.70180550442[/C][C]141.298194495585[/C][/ROW]
[ROW][C]34[/C][C]2695[/C][C]2357.96282146513[/C][C]337.037178534866[/C][/ROW]
[ROW][C]35[/C][C]2799[/C][C]2356.70180550442[/C][C]442.298194495585[/C][/ROW]
[ROW][C]36[/C][C]2946[/C][C]2364.26790126873[/C][C]581.732098731273[/C][/ROW]
[ROW][C]37[/C][C]2930[/C][C]2368.05094915088[/C][C]561.949050849118[/C][/ROW]
[ROW][C]38[/C][C]2318[/C][C]2322.65437456501[/C][C]-4.6543745650129[/C][/ROW]
[ROW][C]39[/C][C]2540[/C][C]2317.61031072214[/C][C]222.389689277861[/C][/ROW]
[ROW][C]40[/C][C]2570[/C][C]2317.61031072214[/C][C]252.389689277861[/C][/ROW]
[ROW][C]41[/C][C]2669[/C][C]2325.17640648645[/C][C]343.82359351355[/C][/ROW]
[ROW][C]42[/C][C]2450[/C][C]2337.78656609364[/C][C]112.213433906364[/C][/ROW]
[ROW][C]43[/C][C]2842[/C][C]2342.83062993651[/C][C]499.16937006349[/C][/ROW]
[ROW][C]44[/C][C]3440[/C][C]2355.44078954370[/C][C]1084.55921045630[/C][/ROW]
[ROW][C]45[/C][C]2678[/C][C]2359.22383742585[/C][C]318.776162574148[/C][/ROW]
[ROW][C]46[/C][C]2981[/C][C]2369.3119651116[/C][C]611.688034888399[/C][/ROW]
[ROW][C]47[/C][C]2260[/C][C]2371.83399703304[/C][C]-111.833997033038[/C][/ROW]
[ROW][C]48[/C][C]2844[/C][C]2376.87806087591[/C][C]467.121939124087[/C][/ROW]
[ROW][C]49[/C][C]2546[/C][C]2376.87806087591[/C][C]169.121939124087[/C][/ROW]
[ROW][C]50[/C][C]2456[/C][C]2328.95945436861[/C][C]127.040545631394[/C][/ROW]
[ROW][C]51[/C][C]2295[/C][C]2320.13234264358[/C][C]-25.1323426435757[/C][/ROW]
[ROW][C]52[/C][C]2379[/C][C]2323.91539052573[/C][C]55.0846094742685[/C][/ROW]
[ROW][C]53[/C][C]2479[/C][C]2344.09164589723[/C][C]134.908354102771[/C][/ROW]
[ROW][C]54[/C][C]2057[/C][C]2363.00688530801[/C][C]-306.006885308008[/C][/ROW]
[ROW][C]55[/C][C]2280[/C][C]2376.87806087591[/C][C]-96.8780608759126[/C][/ROW]
[ROW][C]56[/C][C]2351[/C][C]2379.40009279735[/C][C]-28.4000927973498[/C][/ROW]
[ROW][C]57[/C][C]2276[/C][C]2381.92212471879[/C][C]-105.922124718787[/C][/ROW]
[ROW][C]58[/C][C]2548[/C][C]2379.40009279735[/C][C]168.599907202650[/C][/ROW]
[ROW][C]59[/C][C]2311[/C][C]2363.00688530801[/C][C]-52.006885308008[/C][/ROW]
[ROW][C]60[/C][C]2201[/C][C]2371.83399703304[/C][C]-170.833997033038[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58303&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58303&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
122532426.05768334395-173.057683343953
222182379.40009279735-161.400092797350
318552373.09501299376-518.095012993757
421872376.87806087591-189.878060875913
518522384.44415664022-532.444156640224
615702386.96618856166-816.966188561661
718512374.35602895448-523.356028954475
819542352.91875762226-398.918757622259
918282346.61367781867-518.613677818666
1022512352.91875762226-101.918757622259
1122772366.78993319016-89.7899331901638
1220852379.40009279735-294.400092797350
1322822378.13907683663-96.1390768366312
1422662313.82726283998-47.8272628399827
1518782299.95608727208-421.956087272078
1622672301.21710323280-34.2171032327968
1720692313.82726283998-244.827262839983
1817462332.74250225076-586.742502250762
1922992340.30859801507-41.3085980150733
2023602352.918757622267.08124237774075
2122142365.52891722945-151.528917229445
2228252381.92212471879443.077875281213
2323552394.53228432597-39.5322843259730
2423332399.57634816885-66.5763481688473
2530162386.96618856166629.033811438339
2621552313.82726283998-158.827262839983
2721722292.38999150777-120.389991507767
2821502291.12897554705-141.128975547048
2925332315.0882788007217.911721199299
3020582336.52555013292-278.525550132917
3121602345.35266185795-185.352661857948
3222602352.91875762226-92.9187576222592
3324982356.70180550442141.298194495585
3426952357.96282146513337.037178534866
3527992356.70180550442442.298194495585
3629462364.26790126873581.732098731273
3729302368.05094915088561.949050849118
3823182322.65437456501-4.6543745650129
3925402317.61031072214222.389689277861
4025702317.61031072214252.389689277861
4126692325.17640648645343.82359351355
4224502337.78656609364112.213433906364
4328422342.83062993651499.16937006349
4434402355.440789543701084.55921045630
4526782359.22383742585318.776162574148
4629812369.3119651116611.688034888399
4722602371.83399703304-111.833997033038
4828442376.87806087591467.121939124087
4925462376.87806087591169.121939124087
5024562328.95945436861127.040545631394
5122952320.13234264358-25.1323426435757
5223792323.9153905257355.0846094742685
5324792344.09164589723134.908354102771
5420572363.00688530801-306.006885308008
5522802376.87806087591-96.8780608759126
5623512379.40009279735-28.4000927973498
5722762381.92212471879-105.922124718787
5825482379.40009279735168.599907202650
5923112363.00688530801-52.006885308008
6022012371.83399703304-170.833997033038







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.2078398188323690.4156796376647380.792160181167631
60.4540129199302950.908025839860590.545987080069705
70.3477092005088320.6954184010176640.652290799491168
80.2631980558672460.5263961117344920.736801944132754
90.1938822353584640.3877644707169280.806117764641536
100.2418999337570920.4837998675141840.758100066242908
110.2456446467693690.4912892935387380.754355353230631
120.1943934087500140.3887868175000270.805606591249986
130.1851818245016440.3703636490032870.814818175498356
140.1623599981250860.3247199962501720.837640001874914
150.1407697663223560.2815395326447130.859230233677644
160.1175680978673650.235136195734730.882431902132635
170.08336471339355470.1667294267871090.916635286606445
180.1347531925790630.2695063851581250.865246807420937
190.1247877941134950.249575588226990.875212205886505
200.1261135649557990.2522271299115990.8738864350442
210.1077616615065900.2155233230131790.89223833849341
220.3420450530229360.6840901060458720.657954946977064
230.3146852432371960.6293704864743930.685314756762804
240.2917870041983780.5835740083967550.708212995801622
250.6075627896197450.7848744207605110.392437210380255
260.5544388018369220.8911223963261560.445561198163078
270.4974473606475170.9948947212950340.502552639352483
280.4482065249784790.8964130499569580.551793475021521
290.4460791223027220.8921582446054430.553920877697278
300.4503720573015800.9007441146031610.54962794269842
310.4311863052059870.8623726104119750.568813694794013
320.3949423034286560.7898846068573110.605057696571344
330.3616966422759360.7233932845518720.638303357724064
340.3850156352656920.7700312705313840.614984364734308
350.4496926754614900.8993853509229810.55030732453851
360.5915037976458910.8169924047082170.408496202354109
370.6969570920749470.6060858158501060.303042907925053
380.6483149496047260.7033701007905480.351685050395274
390.5950652672432690.8098694655134620.404934732756731
400.5399151211855590.9201697576288820.460084878814441
410.5026211678015690.9947576643968630.497378832198431
420.4276588060386590.8553176120773180.572341193961341
430.4589290849842290.9178581699684580.541070915015771
440.9596811299791370.08063774004172520.0403188700208626
450.9540902204078630.09181955918427450.0459097795921372
460.9929867894526450.01402642109471090.00701321054735543
470.9875215293801390.02495694123972270.0124784706198613
480.9985153653432130.002969269313573660.00148463465678683
490.9984466558638190.003106688272362210.00155334413618111
500.9964981933401480.007003613319704630.00350180665985231
510.9908751035295590.01824979294088290.00912489647044144
520.976340455536750.04731908892649970.0236595444632498
530.9851137297078910.02977254058421750.0148862702921087
540.975600194996220.04879961000756170.0243998050037809
550.9288276877240350.1423446245519300.0711723122759651

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
5 & 0.207839818832369 & 0.415679637664738 & 0.792160181167631 \tabularnewline
6 & 0.454012919930295 & 0.90802583986059 & 0.545987080069705 \tabularnewline
7 & 0.347709200508832 & 0.695418401017664 & 0.652290799491168 \tabularnewline
8 & 0.263198055867246 & 0.526396111734492 & 0.736801944132754 \tabularnewline
9 & 0.193882235358464 & 0.387764470716928 & 0.806117764641536 \tabularnewline
10 & 0.241899933757092 & 0.483799867514184 & 0.758100066242908 \tabularnewline
11 & 0.245644646769369 & 0.491289293538738 & 0.754355353230631 \tabularnewline
12 & 0.194393408750014 & 0.388786817500027 & 0.805606591249986 \tabularnewline
13 & 0.185181824501644 & 0.370363649003287 & 0.814818175498356 \tabularnewline
14 & 0.162359998125086 & 0.324719996250172 & 0.837640001874914 \tabularnewline
15 & 0.140769766322356 & 0.281539532644713 & 0.859230233677644 \tabularnewline
16 & 0.117568097867365 & 0.23513619573473 & 0.882431902132635 \tabularnewline
17 & 0.0833647133935547 & 0.166729426787109 & 0.916635286606445 \tabularnewline
18 & 0.134753192579063 & 0.269506385158125 & 0.865246807420937 \tabularnewline
19 & 0.124787794113495 & 0.24957558822699 & 0.875212205886505 \tabularnewline
20 & 0.126113564955799 & 0.252227129911599 & 0.8738864350442 \tabularnewline
21 & 0.107761661506590 & 0.215523323013179 & 0.89223833849341 \tabularnewline
22 & 0.342045053022936 & 0.684090106045872 & 0.657954946977064 \tabularnewline
23 & 0.314685243237196 & 0.629370486474393 & 0.685314756762804 \tabularnewline
24 & 0.291787004198378 & 0.583574008396755 & 0.708212995801622 \tabularnewline
25 & 0.607562789619745 & 0.784874420760511 & 0.392437210380255 \tabularnewline
26 & 0.554438801836922 & 0.891122396326156 & 0.445561198163078 \tabularnewline
27 & 0.497447360647517 & 0.994894721295034 & 0.502552639352483 \tabularnewline
28 & 0.448206524978479 & 0.896413049956958 & 0.551793475021521 \tabularnewline
29 & 0.446079122302722 & 0.892158244605443 & 0.553920877697278 \tabularnewline
30 & 0.450372057301580 & 0.900744114603161 & 0.54962794269842 \tabularnewline
31 & 0.431186305205987 & 0.862372610411975 & 0.568813694794013 \tabularnewline
32 & 0.394942303428656 & 0.789884606857311 & 0.605057696571344 \tabularnewline
33 & 0.361696642275936 & 0.723393284551872 & 0.638303357724064 \tabularnewline
34 & 0.385015635265692 & 0.770031270531384 & 0.614984364734308 \tabularnewline
35 & 0.449692675461490 & 0.899385350922981 & 0.55030732453851 \tabularnewline
36 & 0.591503797645891 & 0.816992404708217 & 0.408496202354109 \tabularnewline
37 & 0.696957092074947 & 0.606085815850106 & 0.303042907925053 \tabularnewline
38 & 0.648314949604726 & 0.703370100790548 & 0.351685050395274 \tabularnewline
39 & 0.595065267243269 & 0.809869465513462 & 0.404934732756731 \tabularnewline
40 & 0.539915121185559 & 0.920169757628882 & 0.460084878814441 \tabularnewline
41 & 0.502621167801569 & 0.994757664396863 & 0.497378832198431 \tabularnewline
42 & 0.427658806038659 & 0.855317612077318 & 0.572341193961341 \tabularnewline
43 & 0.458929084984229 & 0.917858169968458 & 0.541070915015771 \tabularnewline
44 & 0.959681129979137 & 0.0806377400417252 & 0.0403188700208626 \tabularnewline
45 & 0.954090220407863 & 0.0918195591842745 & 0.0459097795921372 \tabularnewline
46 & 0.992986789452645 & 0.0140264210947109 & 0.00701321054735543 \tabularnewline
47 & 0.987521529380139 & 0.0249569412397227 & 0.0124784706198613 \tabularnewline
48 & 0.998515365343213 & 0.00296926931357366 & 0.00148463465678683 \tabularnewline
49 & 0.998446655863819 & 0.00310668827236221 & 0.00155334413618111 \tabularnewline
50 & 0.996498193340148 & 0.00700361331970463 & 0.00350180665985231 \tabularnewline
51 & 0.990875103529559 & 0.0182497929408829 & 0.00912489647044144 \tabularnewline
52 & 0.97634045553675 & 0.0473190889264997 & 0.0236595444632498 \tabularnewline
53 & 0.985113729707891 & 0.0297725405842175 & 0.0148862702921087 \tabularnewline
54 & 0.97560019499622 & 0.0487996100075617 & 0.0243998050037809 \tabularnewline
55 & 0.928827687724035 & 0.142344624551930 & 0.0711723122759651 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58303&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]5[/C][C]0.207839818832369[/C][C]0.415679637664738[/C][C]0.792160181167631[/C][/ROW]
[ROW][C]6[/C][C]0.454012919930295[/C][C]0.90802583986059[/C][C]0.545987080069705[/C][/ROW]
[ROW][C]7[/C][C]0.347709200508832[/C][C]0.695418401017664[/C][C]0.652290799491168[/C][/ROW]
[ROW][C]8[/C][C]0.263198055867246[/C][C]0.526396111734492[/C][C]0.736801944132754[/C][/ROW]
[ROW][C]9[/C][C]0.193882235358464[/C][C]0.387764470716928[/C][C]0.806117764641536[/C][/ROW]
[ROW][C]10[/C][C]0.241899933757092[/C][C]0.483799867514184[/C][C]0.758100066242908[/C][/ROW]
[ROW][C]11[/C][C]0.245644646769369[/C][C]0.491289293538738[/C][C]0.754355353230631[/C][/ROW]
[ROW][C]12[/C][C]0.194393408750014[/C][C]0.388786817500027[/C][C]0.805606591249986[/C][/ROW]
[ROW][C]13[/C][C]0.185181824501644[/C][C]0.370363649003287[/C][C]0.814818175498356[/C][/ROW]
[ROW][C]14[/C][C]0.162359998125086[/C][C]0.324719996250172[/C][C]0.837640001874914[/C][/ROW]
[ROW][C]15[/C][C]0.140769766322356[/C][C]0.281539532644713[/C][C]0.859230233677644[/C][/ROW]
[ROW][C]16[/C][C]0.117568097867365[/C][C]0.23513619573473[/C][C]0.882431902132635[/C][/ROW]
[ROW][C]17[/C][C]0.0833647133935547[/C][C]0.166729426787109[/C][C]0.916635286606445[/C][/ROW]
[ROW][C]18[/C][C]0.134753192579063[/C][C]0.269506385158125[/C][C]0.865246807420937[/C][/ROW]
[ROW][C]19[/C][C]0.124787794113495[/C][C]0.24957558822699[/C][C]0.875212205886505[/C][/ROW]
[ROW][C]20[/C][C]0.126113564955799[/C][C]0.252227129911599[/C][C]0.8738864350442[/C][/ROW]
[ROW][C]21[/C][C]0.107761661506590[/C][C]0.215523323013179[/C][C]0.89223833849341[/C][/ROW]
[ROW][C]22[/C][C]0.342045053022936[/C][C]0.684090106045872[/C][C]0.657954946977064[/C][/ROW]
[ROW][C]23[/C][C]0.314685243237196[/C][C]0.629370486474393[/C][C]0.685314756762804[/C][/ROW]
[ROW][C]24[/C][C]0.291787004198378[/C][C]0.583574008396755[/C][C]0.708212995801622[/C][/ROW]
[ROW][C]25[/C][C]0.607562789619745[/C][C]0.784874420760511[/C][C]0.392437210380255[/C][/ROW]
[ROW][C]26[/C][C]0.554438801836922[/C][C]0.891122396326156[/C][C]0.445561198163078[/C][/ROW]
[ROW][C]27[/C][C]0.497447360647517[/C][C]0.994894721295034[/C][C]0.502552639352483[/C][/ROW]
[ROW][C]28[/C][C]0.448206524978479[/C][C]0.896413049956958[/C][C]0.551793475021521[/C][/ROW]
[ROW][C]29[/C][C]0.446079122302722[/C][C]0.892158244605443[/C][C]0.553920877697278[/C][/ROW]
[ROW][C]30[/C][C]0.450372057301580[/C][C]0.900744114603161[/C][C]0.54962794269842[/C][/ROW]
[ROW][C]31[/C][C]0.431186305205987[/C][C]0.862372610411975[/C][C]0.568813694794013[/C][/ROW]
[ROW][C]32[/C][C]0.394942303428656[/C][C]0.789884606857311[/C][C]0.605057696571344[/C][/ROW]
[ROW][C]33[/C][C]0.361696642275936[/C][C]0.723393284551872[/C][C]0.638303357724064[/C][/ROW]
[ROW][C]34[/C][C]0.385015635265692[/C][C]0.770031270531384[/C][C]0.614984364734308[/C][/ROW]
[ROW][C]35[/C][C]0.449692675461490[/C][C]0.899385350922981[/C][C]0.55030732453851[/C][/ROW]
[ROW][C]36[/C][C]0.591503797645891[/C][C]0.816992404708217[/C][C]0.408496202354109[/C][/ROW]
[ROW][C]37[/C][C]0.696957092074947[/C][C]0.606085815850106[/C][C]0.303042907925053[/C][/ROW]
[ROW][C]38[/C][C]0.648314949604726[/C][C]0.703370100790548[/C][C]0.351685050395274[/C][/ROW]
[ROW][C]39[/C][C]0.595065267243269[/C][C]0.809869465513462[/C][C]0.404934732756731[/C][/ROW]
[ROW][C]40[/C][C]0.539915121185559[/C][C]0.920169757628882[/C][C]0.460084878814441[/C][/ROW]
[ROW][C]41[/C][C]0.502621167801569[/C][C]0.994757664396863[/C][C]0.497378832198431[/C][/ROW]
[ROW][C]42[/C][C]0.427658806038659[/C][C]0.855317612077318[/C][C]0.572341193961341[/C][/ROW]
[ROW][C]43[/C][C]0.458929084984229[/C][C]0.917858169968458[/C][C]0.541070915015771[/C][/ROW]
[ROW][C]44[/C][C]0.959681129979137[/C][C]0.0806377400417252[/C][C]0.0403188700208626[/C][/ROW]
[ROW][C]45[/C][C]0.954090220407863[/C][C]0.0918195591842745[/C][C]0.0459097795921372[/C][/ROW]
[ROW][C]46[/C][C]0.992986789452645[/C][C]0.0140264210947109[/C][C]0.00701321054735543[/C][/ROW]
[ROW][C]47[/C][C]0.987521529380139[/C][C]0.0249569412397227[/C][C]0.0124784706198613[/C][/ROW]
[ROW][C]48[/C][C]0.998515365343213[/C][C]0.00296926931357366[/C][C]0.00148463465678683[/C][/ROW]
[ROW][C]49[/C][C]0.998446655863819[/C][C]0.00310668827236221[/C][C]0.00155334413618111[/C][/ROW]
[ROW][C]50[/C][C]0.996498193340148[/C][C]0.00700361331970463[/C][C]0.00350180665985231[/C][/ROW]
[ROW][C]51[/C][C]0.990875103529559[/C][C]0.0182497929408829[/C][C]0.00912489647044144[/C][/ROW]
[ROW][C]52[/C][C]0.97634045553675[/C][C]0.0473190889264997[/C][C]0.0236595444632498[/C][/ROW]
[ROW][C]53[/C][C]0.985113729707891[/C][C]0.0297725405842175[/C][C]0.0148862702921087[/C][/ROW]
[ROW][C]54[/C][C]0.97560019499622[/C][C]0.0487996100075617[/C][C]0.0243998050037809[/C][/ROW]
[ROW][C]55[/C][C]0.928827687724035[/C][C]0.142344624551930[/C][C]0.0711723122759651[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58303&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58303&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
50.2078398188323690.4156796376647380.792160181167631
60.4540129199302950.908025839860590.545987080069705
70.3477092005088320.6954184010176640.652290799491168
80.2631980558672460.5263961117344920.736801944132754
90.1938822353584640.3877644707169280.806117764641536
100.2418999337570920.4837998675141840.758100066242908
110.2456446467693690.4912892935387380.754355353230631
120.1943934087500140.3887868175000270.805606591249986
130.1851818245016440.3703636490032870.814818175498356
140.1623599981250860.3247199962501720.837640001874914
150.1407697663223560.2815395326447130.859230233677644
160.1175680978673650.235136195734730.882431902132635
170.08336471339355470.1667294267871090.916635286606445
180.1347531925790630.2695063851581250.865246807420937
190.1247877941134950.249575588226990.875212205886505
200.1261135649557990.2522271299115990.8738864350442
210.1077616615065900.2155233230131790.89223833849341
220.3420450530229360.6840901060458720.657954946977064
230.3146852432371960.6293704864743930.685314756762804
240.2917870041983780.5835740083967550.708212995801622
250.6075627896197450.7848744207605110.392437210380255
260.5544388018369220.8911223963261560.445561198163078
270.4974473606475170.9948947212950340.502552639352483
280.4482065249784790.8964130499569580.551793475021521
290.4460791223027220.8921582446054430.553920877697278
300.4503720573015800.9007441146031610.54962794269842
310.4311863052059870.8623726104119750.568813694794013
320.3949423034286560.7898846068573110.605057696571344
330.3616966422759360.7233932845518720.638303357724064
340.3850156352656920.7700312705313840.614984364734308
350.4496926754614900.8993853509229810.55030732453851
360.5915037976458910.8169924047082170.408496202354109
370.6969570920749470.6060858158501060.303042907925053
380.6483149496047260.7033701007905480.351685050395274
390.5950652672432690.8098694655134620.404934732756731
400.5399151211855590.9201697576288820.460084878814441
410.5026211678015690.9947576643968630.497378832198431
420.4276588060386590.8553176120773180.572341193961341
430.4589290849842290.9178581699684580.541070915015771
440.9596811299791370.08063774004172520.0403188700208626
450.9540902204078630.09181955918427450.0459097795921372
460.9929867894526450.01402642109471090.00701321054735543
470.9875215293801390.02495694123972270.0124784706198613
480.9985153653432130.002969269313573660.00148463465678683
490.9984466558638190.003106688272362210.00155334413618111
500.9964981933401480.007003613319704630.00350180665985231
510.9908751035295590.01824979294088290.00912489647044144
520.976340455536750.04731908892649970.0236595444632498
530.9851137297078910.02977254058421750.0148862702921087
540.975600194996220.04879961000756170.0243998050037809
550.9288276877240350.1423446245519300.0711723122759651







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level30.0588235294117647NOK
5% type I error level90.176470588235294NOK
10% type I error level110.215686274509804NOK

\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 & 0.0588235294117647 & NOK \tabularnewline
5% type I error level & 9 & 0.176470588235294 & NOK \tabularnewline
10% type I error level & 11 & 0.215686274509804 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58303&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]0.0588235294117647[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]9[/C][C]0.176470588235294[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]11[/C][C]0.215686274509804[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58303&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58303&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 level30.0588235294117647NOK
5% type I error level90.176470588235294NOK
10% type I error level110.215686274509804NOK



Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}