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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 computationMon, 21 Nov 2011 13:28:39 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/21/t132190032196y5zv7ccwriyqc.htm/, Retrieved Fri, 29 Mar 2024 13:56:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=145898, Retrieved Fri, 29 Mar 2024 13:56:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [] [2010-11-17 09:55:05] [b98453cac15ba1066b407e146608df68]
- R PD    [Multiple Regression] [] [2011-11-21 18:28:39] [c092f3a3bdd85c7279ddab6c8c6c9261] [Current]
-    D      [Multiple Regression] [] [2011-11-22 11:12:05] [b4c8fd31b0af00c33711722ddf8d2c4c]
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Dataseries X:
1	1	1	1167	333	70
1	2	2	669	223	44
1	3	3	1053	371	35
1	4	4	1939	873	119
1	5	5	678	186	30
1	6	6	321	111	23
1	7	7	2667	1277	46
1	8	8	345	102	39
1	9	9	1367	580	58
1	10	10	1158	420	51
1	11	11	1385	521	65
1	12	12	1155	358	40
1	13	13	1120	435	41
1	14	14	1703	690	76
1	15	15	1189	393	31
1	16	16	3083	1149	82
1	17	17	1357	486	36
1	18	18	1892	767	62
1	19	19	883	338	28
1	20	20	1627	485	38
1	21	21	1412	465	70
1	22	22	1900	816	76
1	23	23	777	265	33
1	24	24	904	307	40
1	25	25	2115	850	126
1	26	26	1858	704	56
1	27	27	1781	693	63
1	28	28	1286	387	46
1	29	29	1035	406	35
1	30	30	1557	573	108
0	31	0	1527	595	34
0	32	0	1220	394	54
0	33	0	1368	521	35
0	34	0	564	172	23
0	35	0	1990	835	46
0	36	0	1557	669	49
0	37	0	2057	749	56
0	38	0	1111	368	38
0	39	0	686	216	19
0	40	0	2011	772	29
0	41	0	2232	1084	26
0	42	0	1032	445	52
0	43	0	1166	451	54
0	44	0	1020	300	45
0	45	0	1735	836	56
0	46	0	3623	1417	596
0	47	0	918	330	57
0	48	0	1579	477	55
0	49	0	2790	1028	99
0	50	0	1496	646	51
0	51	0	1108	342	21
0	52	0	496	218	20
0	53	0	1750	591	58
0	54	0	744	255	21
0	55	0	1101	434	66
0	56	0	1612	654	47
0	57	0	1805	478	55
0	58	0	2460	753	158
0	59	0	1653	689	46
0	60	0	1234	470	45




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145898&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145898&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145898&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' @ jenkins.wessa.net







Multiple Linear Regression - Estimated Regression Equation
Pageviews[t] = + 61.1133554838062 + 123.682191483255Pop[t] + 4.8328440134903t + 0.084840891490896Pop_t[t] + 2.05542151213013CourseCompView[t] + 0.936910435140116CompendiumView_PR[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Pageviews[t] =  +  61.1133554838062 +  123.682191483255Pop[t] +  4.8328440134903t +  0.084840891490896Pop_t[t] +  2.05542151213013CourseCompView[t] +  0.936910435140116CompendiumView_PR[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145898&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Pageviews[t] =  +  61.1133554838062 +  123.682191483255Pop[t] +  4.8328440134903t +  0.084840891490896Pop_t[t] +  2.05542151213013CourseCompView[t] +  0.936910435140116CompendiumView_PR[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145898&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145898&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
Pageviews[t] = + 61.1133554838062 + 123.682191483255Pop[t] + 4.8328440134903t + 0.084840891490896Pop_t[t] + 2.05542151213013CourseCompView[t] + 0.936910435140116CompendiumView_PR[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)61.1133554838062181.5053050.33670.7376460.368823
Pop123.682191483255187.0089460.66140.5111870.255593
t4.83284401349033.7666071.28310.2049450.102472
Pop_t0.0848408914908965.3373960.01590.9873760.493688
CourseCompView2.055421512130130.09889220.784400
CompendiumView_PR0.9369104351401160.3685062.54250.0139080.006954

\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) & 61.1133554838062 & 181.505305 & 0.3367 & 0.737646 & 0.368823 \tabularnewline
Pop & 123.682191483255 & 187.008946 & 0.6614 & 0.511187 & 0.255593 \tabularnewline
t & 4.8328440134903 & 3.766607 & 1.2831 & 0.204945 & 0.102472 \tabularnewline
Pop_t & 0.084840891490896 & 5.337396 & 0.0159 & 0.987376 & 0.493688 \tabularnewline
CourseCompView & 2.05542151213013 & 0.098892 & 20.7844 & 0 & 0 \tabularnewline
CompendiumView_PR & 0.936910435140116 & 0.368506 & 2.5425 & 0.013908 & 0.006954 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145898&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]61.1133554838062[/C][C]181.505305[/C][C]0.3367[/C][C]0.737646[/C][C]0.368823[/C][/ROW]
[ROW][C]Pop[/C][C]123.682191483255[/C][C]187.008946[/C][C]0.6614[/C][C]0.511187[/C][C]0.255593[/C][/ROW]
[ROW][C]t[/C][C]4.8328440134903[/C][C]3.766607[/C][C]1.2831[/C][C]0.204945[/C][C]0.102472[/C][/ROW]
[ROW][C]Pop_t[/C][C]0.084840891490896[/C][C]5.337396[/C][C]0.0159[/C][C]0.987376[/C][C]0.493688[/C][/ROW]
[ROW][C]CourseCompView[/C][C]2.05542151213013[/C][C]0.098892[/C][C]20.7844[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]CompendiumView_PR[/C][C]0.936910435140116[/C][C]0.368506[/C][C]2.5425[/C][C]0.013908[/C][C]0.006954[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145898&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145898&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)61.1133554838062181.5053050.33670.7376460.368823
Pop123.682191483255187.0089460.66140.5111870.255593
t4.83284401349033.7666071.28310.2049450.102472
Pop_t0.0848408914908965.3373960.01590.9873760.493688
CourseCompView2.055421512130130.09889220.784400
CompendiumView_PR0.9369104351401160.3685062.54250.0139080.006954







Multiple Linear Regression - Regression Statistics
Multiple R0.964910804230803
R-squared0.931052860121335
Adjusted R-squared0.924668865688125
F-TEST (value)145.841740600207
F-TEST (DF numerator)5
F-TEST (DF denominator)54
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation177.502063490688
Sum Squared Residuals1701377.05734642

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.964910804230803 \tabularnewline
R-squared & 0.931052860121335 \tabularnewline
Adjusted R-squared & 0.924668865688125 \tabularnewline
F-TEST (value) & 145.841740600207 \tabularnewline
F-TEST (DF numerator) & 5 \tabularnewline
F-TEST (DF denominator) & 54 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 177.502063490688 \tabularnewline
Sum Squared Residuals & 1701377.05734642 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145898&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.964910804230803[/C][/ROW]
[ROW][C]R-squared[/C][C]0.931052860121335[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.924668865688125[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]145.841740600207[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]5[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]54[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]177.502063490688[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1701377.05734642[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145898&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145898&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 R0.964910804230803
R-squared0.931052860121335
Adjusted R-squared0.924668865688125
F-TEST (value)145.841740600207
F-TEST (DF numerator)5
F-TEST (DF denominator)54
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation177.502063490688
Sum Squared Residuals1701377.05734642







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
11167939.752325871184227.247674128816
2669694.213973128208-25.2139731282076
31053994.90184791218758.0981520878129
419392110.34160845826-171.341608458263
5678619.79968580237558.2003141976252
6321464.002384251616-143.002384251616
726672887.09049230855-220.09049230855
8345470.329527414649-125.329527414649
913671475.53999338549-108.539993385494
1011581145.0318633036712.9681366963265
1113851370.6638670257614.3361329742407
1211551017.12508457503137.874915424973
1311201181.24713634917-61.2471363491679
1417031743.08917207724-40.0891720772359
1511891095.3856982982693.6143017017364
1630832701.98447856577381.015521434232
1713571301.0598209120355.9401790879714
1818921907.91062203922-15.9106220392191
19883999.197523445611-116.197523445611
2016271315.63127498512311.368725014878
2114121309.42166357198102.578336428015
2219002041.41376184548-141.413761845482
23777873.507044855737-96.5070448557369
24904971.310806316164-67.3108063161643
2521152172.89666972986-57.8966697298555
2618581812.1390834040345.8609165959703
2717811801.00550472156-20.0055047215604
2812861161.03672951734124.96327048266
2910351194.70140836625-159.701408366252
3015571611.26894756219-54.2689475621936
3115271465.762274414261.2377255858039
3212201076.19360319233143.806396807667
3313681324.2636809786943.7363190213128
34564600.511492037081-36.5114920370813
3519901989.637738601070.362261398930534
3615571656.08134290638-99.0813429063788
3720571831.90628093626225.09371906374
3811111036.7591409956574.2408590043507
39686711.366616897698-25.3666168976979
4020111868.38292600694142.617073993059
4122322511.69655049961-279.696550499611
4210321227.47471957559-195.474719575592
4311661246.51391353214-80.5139135321434
441020932.54591529772387.4540847022768
4517352049.3907045995-314.390704599504
4636233754.35508213626-131.355082136261
479181019.95001792378-101.950017923779
4815791325.05600335012253.943996649882
4927902503.65015969347286.349840306525
5014961678.34028518653-182.34028518653
5111081030.2176764582677.7823235417421
52496779.241342532472-283.241342532472
5317501586.34900710582163.650992894175
54744865.894536943408-121.894536943408
5511011280.8088012095-179.808801209496
5616121720.03307962395-108.033079623953
5718051370.60702098366434.392979016339
5824602037.18255565237422.817444347631
5916531805.53445415384-152.534454153838
6012341359.29307657569-125.29307657569

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 1167 & 939.752325871184 & 227.247674128816 \tabularnewline
2 & 669 & 694.213973128208 & -25.2139731282076 \tabularnewline
3 & 1053 & 994.901847912187 & 58.0981520878129 \tabularnewline
4 & 1939 & 2110.34160845826 & -171.341608458263 \tabularnewline
5 & 678 & 619.799685802375 & 58.2003141976252 \tabularnewline
6 & 321 & 464.002384251616 & -143.002384251616 \tabularnewline
7 & 2667 & 2887.09049230855 & -220.09049230855 \tabularnewline
8 & 345 & 470.329527414649 & -125.329527414649 \tabularnewline
9 & 1367 & 1475.53999338549 & -108.539993385494 \tabularnewline
10 & 1158 & 1145.03186330367 & 12.9681366963265 \tabularnewline
11 & 1385 & 1370.66386702576 & 14.3361329742407 \tabularnewline
12 & 1155 & 1017.12508457503 & 137.874915424973 \tabularnewline
13 & 1120 & 1181.24713634917 & -61.2471363491679 \tabularnewline
14 & 1703 & 1743.08917207724 & -40.0891720772359 \tabularnewline
15 & 1189 & 1095.38569829826 & 93.6143017017364 \tabularnewline
16 & 3083 & 2701.98447856577 & 381.015521434232 \tabularnewline
17 & 1357 & 1301.05982091203 & 55.9401790879714 \tabularnewline
18 & 1892 & 1907.91062203922 & -15.9106220392191 \tabularnewline
19 & 883 & 999.197523445611 & -116.197523445611 \tabularnewline
20 & 1627 & 1315.63127498512 & 311.368725014878 \tabularnewline
21 & 1412 & 1309.42166357198 & 102.578336428015 \tabularnewline
22 & 1900 & 2041.41376184548 & -141.413761845482 \tabularnewline
23 & 777 & 873.507044855737 & -96.5070448557369 \tabularnewline
24 & 904 & 971.310806316164 & -67.3108063161643 \tabularnewline
25 & 2115 & 2172.89666972986 & -57.8966697298555 \tabularnewline
26 & 1858 & 1812.13908340403 & 45.8609165959703 \tabularnewline
27 & 1781 & 1801.00550472156 & -20.0055047215604 \tabularnewline
28 & 1286 & 1161.03672951734 & 124.96327048266 \tabularnewline
29 & 1035 & 1194.70140836625 & -159.701408366252 \tabularnewline
30 & 1557 & 1611.26894756219 & -54.2689475621936 \tabularnewline
31 & 1527 & 1465.7622744142 & 61.2377255858039 \tabularnewline
32 & 1220 & 1076.19360319233 & 143.806396807667 \tabularnewline
33 & 1368 & 1324.26368097869 & 43.7363190213128 \tabularnewline
34 & 564 & 600.511492037081 & -36.5114920370813 \tabularnewline
35 & 1990 & 1989.63773860107 & 0.362261398930534 \tabularnewline
36 & 1557 & 1656.08134290638 & -99.0813429063788 \tabularnewline
37 & 2057 & 1831.90628093626 & 225.09371906374 \tabularnewline
38 & 1111 & 1036.75914099565 & 74.2408590043507 \tabularnewline
39 & 686 & 711.366616897698 & -25.3666168976979 \tabularnewline
40 & 2011 & 1868.38292600694 & 142.617073993059 \tabularnewline
41 & 2232 & 2511.69655049961 & -279.696550499611 \tabularnewline
42 & 1032 & 1227.47471957559 & -195.474719575592 \tabularnewline
43 & 1166 & 1246.51391353214 & -80.5139135321434 \tabularnewline
44 & 1020 & 932.545915297723 & 87.4540847022768 \tabularnewline
45 & 1735 & 2049.3907045995 & -314.390704599504 \tabularnewline
46 & 3623 & 3754.35508213626 & -131.355082136261 \tabularnewline
47 & 918 & 1019.95001792378 & -101.950017923779 \tabularnewline
48 & 1579 & 1325.05600335012 & 253.943996649882 \tabularnewline
49 & 2790 & 2503.65015969347 & 286.349840306525 \tabularnewline
50 & 1496 & 1678.34028518653 & -182.34028518653 \tabularnewline
51 & 1108 & 1030.21767645826 & 77.7823235417421 \tabularnewline
52 & 496 & 779.241342532472 & -283.241342532472 \tabularnewline
53 & 1750 & 1586.34900710582 & 163.650992894175 \tabularnewline
54 & 744 & 865.894536943408 & -121.894536943408 \tabularnewline
55 & 1101 & 1280.8088012095 & -179.808801209496 \tabularnewline
56 & 1612 & 1720.03307962395 & -108.033079623953 \tabularnewline
57 & 1805 & 1370.60702098366 & 434.392979016339 \tabularnewline
58 & 2460 & 2037.18255565237 & 422.817444347631 \tabularnewline
59 & 1653 & 1805.53445415384 & -152.534454153838 \tabularnewline
60 & 1234 & 1359.29307657569 & -125.29307657569 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145898&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]1167[/C][C]939.752325871184[/C][C]227.247674128816[/C][/ROW]
[ROW][C]2[/C][C]669[/C][C]694.213973128208[/C][C]-25.2139731282076[/C][/ROW]
[ROW][C]3[/C][C]1053[/C][C]994.901847912187[/C][C]58.0981520878129[/C][/ROW]
[ROW][C]4[/C][C]1939[/C][C]2110.34160845826[/C][C]-171.341608458263[/C][/ROW]
[ROW][C]5[/C][C]678[/C][C]619.799685802375[/C][C]58.2003141976252[/C][/ROW]
[ROW][C]6[/C][C]321[/C][C]464.002384251616[/C][C]-143.002384251616[/C][/ROW]
[ROW][C]7[/C][C]2667[/C][C]2887.09049230855[/C][C]-220.09049230855[/C][/ROW]
[ROW][C]8[/C][C]345[/C][C]470.329527414649[/C][C]-125.329527414649[/C][/ROW]
[ROW][C]9[/C][C]1367[/C][C]1475.53999338549[/C][C]-108.539993385494[/C][/ROW]
[ROW][C]10[/C][C]1158[/C][C]1145.03186330367[/C][C]12.9681366963265[/C][/ROW]
[ROW][C]11[/C][C]1385[/C][C]1370.66386702576[/C][C]14.3361329742407[/C][/ROW]
[ROW][C]12[/C][C]1155[/C][C]1017.12508457503[/C][C]137.874915424973[/C][/ROW]
[ROW][C]13[/C][C]1120[/C][C]1181.24713634917[/C][C]-61.2471363491679[/C][/ROW]
[ROW][C]14[/C][C]1703[/C][C]1743.08917207724[/C][C]-40.0891720772359[/C][/ROW]
[ROW][C]15[/C][C]1189[/C][C]1095.38569829826[/C][C]93.6143017017364[/C][/ROW]
[ROW][C]16[/C][C]3083[/C][C]2701.98447856577[/C][C]381.015521434232[/C][/ROW]
[ROW][C]17[/C][C]1357[/C][C]1301.05982091203[/C][C]55.9401790879714[/C][/ROW]
[ROW][C]18[/C][C]1892[/C][C]1907.91062203922[/C][C]-15.9106220392191[/C][/ROW]
[ROW][C]19[/C][C]883[/C][C]999.197523445611[/C][C]-116.197523445611[/C][/ROW]
[ROW][C]20[/C][C]1627[/C][C]1315.63127498512[/C][C]311.368725014878[/C][/ROW]
[ROW][C]21[/C][C]1412[/C][C]1309.42166357198[/C][C]102.578336428015[/C][/ROW]
[ROW][C]22[/C][C]1900[/C][C]2041.41376184548[/C][C]-141.413761845482[/C][/ROW]
[ROW][C]23[/C][C]777[/C][C]873.507044855737[/C][C]-96.5070448557369[/C][/ROW]
[ROW][C]24[/C][C]904[/C][C]971.310806316164[/C][C]-67.3108063161643[/C][/ROW]
[ROW][C]25[/C][C]2115[/C][C]2172.89666972986[/C][C]-57.8966697298555[/C][/ROW]
[ROW][C]26[/C][C]1858[/C][C]1812.13908340403[/C][C]45.8609165959703[/C][/ROW]
[ROW][C]27[/C][C]1781[/C][C]1801.00550472156[/C][C]-20.0055047215604[/C][/ROW]
[ROW][C]28[/C][C]1286[/C][C]1161.03672951734[/C][C]124.96327048266[/C][/ROW]
[ROW][C]29[/C][C]1035[/C][C]1194.70140836625[/C][C]-159.701408366252[/C][/ROW]
[ROW][C]30[/C][C]1557[/C][C]1611.26894756219[/C][C]-54.2689475621936[/C][/ROW]
[ROW][C]31[/C][C]1527[/C][C]1465.7622744142[/C][C]61.2377255858039[/C][/ROW]
[ROW][C]32[/C][C]1220[/C][C]1076.19360319233[/C][C]143.806396807667[/C][/ROW]
[ROW][C]33[/C][C]1368[/C][C]1324.26368097869[/C][C]43.7363190213128[/C][/ROW]
[ROW][C]34[/C][C]564[/C][C]600.511492037081[/C][C]-36.5114920370813[/C][/ROW]
[ROW][C]35[/C][C]1990[/C][C]1989.63773860107[/C][C]0.362261398930534[/C][/ROW]
[ROW][C]36[/C][C]1557[/C][C]1656.08134290638[/C][C]-99.0813429063788[/C][/ROW]
[ROW][C]37[/C][C]2057[/C][C]1831.90628093626[/C][C]225.09371906374[/C][/ROW]
[ROW][C]38[/C][C]1111[/C][C]1036.75914099565[/C][C]74.2408590043507[/C][/ROW]
[ROW][C]39[/C][C]686[/C][C]711.366616897698[/C][C]-25.3666168976979[/C][/ROW]
[ROW][C]40[/C][C]2011[/C][C]1868.38292600694[/C][C]142.617073993059[/C][/ROW]
[ROW][C]41[/C][C]2232[/C][C]2511.69655049961[/C][C]-279.696550499611[/C][/ROW]
[ROW][C]42[/C][C]1032[/C][C]1227.47471957559[/C][C]-195.474719575592[/C][/ROW]
[ROW][C]43[/C][C]1166[/C][C]1246.51391353214[/C][C]-80.5139135321434[/C][/ROW]
[ROW][C]44[/C][C]1020[/C][C]932.545915297723[/C][C]87.4540847022768[/C][/ROW]
[ROW][C]45[/C][C]1735[/C][C]2049.3907045995[/C][C]-314.390704599504[/C][/ROW]
[ROW][C]46[/C][C]3623[/C][C]3754.35508213626[/C][C]-131.355082136261[/C][/ROW]
[ROW][C]47[/C][C]918[/C][C]1019.95001792378[/C][C]-101.950017923779[/C][/ROW]
[ROW][C]48[/C][C]1579[/C][C]1325.05600335012[/C][C]253.943996649882[/C][/ROW]
[ROW][C]49[/C][C]2790[/C][C]2503.65015969347[/C][C]286.349840306525[/C][/ROW]
[ROW][C]50[/C][C]1496[/C][C]1678.34028518653[/C][C]-182.34028518653[/C][/ROW]
[ROW][C]51[/C][C]1108[/C][C]1030.21767645826[/C][C]77.7823235417421[/C][/ROW]
[ROW][C]52[/C][C]496[/C][C]779.241342532472[/C][C]-283.241342532472[/C][/ROW]
[ROW][C]53[/C][C]1750[/C][C]1586.34900710582[/C][C]163.650992894175[/C][/ROW]
[ROW][C]54[/C][C]744[/C][C]865.894536943408[/C][C]-121.894536943408[/C][/ROW]
[ROW][C]55[/C][C]1101[/C][C]1280.8088012095[/C][C]-179.808801209496[/C][/ROW]
[ROW][C]56[/C][C]1612[/C][C]1720.03307962395[/C][C]-108.033079623953[/C][/ROW]
[ROW][C]57[/C][C]1805[/C][C]1370.60702098366[/C][C]434.392979016339[/C][/ROW]
[ROW][C]58[/C][C]2460[/C][C]2037.18255565237[/C][C]422.817444347631[/C][/ROW]
[ROW][C]59[/C][C]1653[/C][C]1805.53445415384[/C][C]-152.534454153838[/C][/ROW]
[ROW][C]60[/C][C]1234[/C][C]1359.29307657569[/C][C]-125.29307657569[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145898&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145898&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
11167939.752325871184227.247674128816
2669694.213973128208-25.2139731282076
31053994.90184791218758.0981520878129
419392110.34160845826-171.341608458263
5678619.79968580237558.2003141976252
6321464.002384251616-143.002384251616
726672887.09049230855-220.09049230855
8345470.329527414649-125.329527414649
913671475.53999338549-108.539993385494
1011581145.0318633036712.9681366963265
1113851370.6638670257614.3361329742407
1211551017.12508457503137.874915424973
1311201181.24713634917-61.2471363491679
1417031743.08917207724-40.0891720772359
1511891095.3856982982693.6143017017364
1630832701.98447856577381.015521434232
1713571301.0598209120355.9401790879714
1818921907.91062203922-15.9106220392191
19883999.197523445611-116.197523445611
2016271315.63127498512311.368725014878
2114121309.42166357198102.578336428015
2219002041.41376184548-141.413761845482
23777873.507044855737-96.5070448557369
24904971.310806316164-67.3108063161643
2521152172.89666972986-57.8966697298555
2618581812.1390834040345.8609165959703
2717811801.00550472156-20.0055047215604
2812861161.03672951734124.96327048266
2910351194.70140836625-159.701408366252
3015571611.26894756219-54.2689475621936
3115271465.762274414261.2377255858039
3212201076.19360319233143.806396807667
3313681324.2636809786943.7363190213128
34564600.511492037081-36.5114920370813
3519901989.637738601070.362261398930534
3615571656.08134290638-99.0813429063788
3720571831.90628093626225.09371906374
3811111036.7591409956574.2408590043507
39686711.366616897698-25.3666168976979
4020111868.38292600694142.617073993059
4122322511.69655049961-279.696550499611
4210321227.47471957559-195.474719575592
4311661246.51391353214-80.5139135321434
441020932.54591529772387.4540847022768
4517352049.3907045995-314.390704599504
4636233754.35508213626-131.355082136261
479181019.95001792378-101.950017923779
4815791325.05600335012253.943996649882
4927902503.65015969347286.349840306525
5014961678.34028518653-182.34028518653
5111081030.2176764582677.7823235417421
52496779.241342532472-283.241342532472
5317501586.34900710582163.650992894175
54744865.894536943408-121.894536943408
5511011280.8088012095-179.808801209496
5616121720.03307962395-108.033079623953
5718051370.60702098366434.392979016339
5824602037.18255565237422.817444347631
5916531805.53445415384-152.534454153838
6012341359.29307657569-125.29307657569







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
90.4078993665441280.8157987330882550.592100633455872
100.4141966377463270.8283932754926540.585803362253673
110.3563867312815370.7127734625630750.643613268718463
120.3746783906666390.7493567813332780.625321609333361
130.2670318861231810.5340637722463620.732968113876819
140.1854531933764170.3709063867528350.814546806623582
150.1449425038128440.2898850076256870.855057496187156
160.4943586694588260.9887173389176510.505641330541174
170.3939899424822880.7879798849645760.606010057517712
180.3206256554424260.6412513108848530.679374344557574
190.3066452898836580.6132905797673160.693354710116342
200.3894599842079130.7789199684158260.610540015792087
210.3224267466757340.6448534933514690.677573253324266
220.3366594898588820.6733189797177650.663340510141118
230.3001431805582060.6002863611164130.699856819441794
240.2463325207879660.4926650415759330.753667479212034
250.1979407110708130.3958814221416270.802059288929187
260.1444931476515040.2889862953030070.855506852348496
270.1055196862801780.2110393725603560.894480313719822
280.08536618500140910.1707323700028180.914633814998591
290.07484810980000310.1496962196000060.925151890199997
300.05073660663601910.1014732132720380.949263393363981
310.03302224492714910.06604448985429820.966977755072851
320.02333164532493140.04666329064986270.976668354675069
330.01537708248498130.03075416496996270.984622917515019
340.009242608463594950.01848521692718990.990757391536405
350.005250141464235070.01050028292847010.994749858535765
360.002938437212589850.00587687442517970.99706156278741
370.005335731694161450.01067146338832290.994664268305839
380.003449929158250550.00689985831650110.996550070841749
390.001971319826036520.003942639652073040.998028680173964
400.001985368181098620.003970736362197230.998014631818901
410.003034543888052720.006069087776105450.996965456111947
420.001967351912902440.003934703825804870.998032648087098
430.0009469185359956750.001893837071991350.999053081464004
440.0008883627553065580.001776725510613120.999111637244693
450.002080566056638080.004161132113276160.997919433943362
460.01487116874388120.02974233748776250.985128831256119
470.01236415677093660.02472831354187320.987635843229063
480.02044617980795410.04089235961590810.979553820192046
490.02030837944722670.04061675889445340.979691620552773
500.01739097005032870.03478194010065730.982609029949671
510.01161703022531840.02323406045063670.988382969774682

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
9 & 0.407899366544128 & 0.815798733088255 & 0.592100633455872 \tabularnewline
10 & 0.414196637746327 & 0.828393275492654 & 0.585803362253673 \tabularnewline
11 & 0.356386731281537 & 0.712773462563075 & 0.643613268718463 \tabularnewline
12 & 0.374678390666639 & 0.749356781333278 & 0.625321609333361 \tabularnewline
13 & 0.267031886123181 & 0.534063772246362 & 0.732968113876819 \tabularnewline
14 & 0.185453193376417 & 0.370906386752835 & 0.814546806623582 \tabularnewline
15 & 0.144942503812844 & 0.289885007625687 & 0.855057496187156 \tabularnewline
16 & 0.494358669458826 & 0.988717338917651 & 0.505641330541174 \tabularnewline
17 & 0.393989942482288 & 0.787979884964576 & 0.606010057517712 \tabularnewline
18 & 0.320625655442426 & 0.641251310884853 & 0.679374344557574 \tabularnewline
19 & 0.306645289883658 & 0.613290579767316 & 0.693354710116342 \tabularnewline
20 & 0.389459984207913 & 0.778919968415826 & 0.610540015792087 \tabularnewline
21 & 0.322426746675734 & 0.644853493351469 & 0.677573253324266 \tabularnewline
22 & 0.336659489858882 & 0.673318979717765 & 0.663340510141118 \tabularnewline
23 & 0.300143180558206 & 0.600286361116413 & 0.699856819441794 \tabularnewline
24 & 0.246332520787966 & 0.492665041575933 & 0.753667479212034 \tabularnewline
25 & 0.197940711070813 & 0.395881422141627 & 0.802059288929187 \tabularnewline
26 & 0.144493147651504 & 0.288986295303007 & 0.855506852348496 \tabularnewline
27 & 0.105519686280178 & 0.211039372560356 & 0.894480313719822 \tabularnewline
28 & 0.0853661850014091 & 0.170732370002818 & 0.914633814998591 \tabularnewline
29 & 0.0748481098000031 & 0.149696219600006 & 0.925151890199997 \tabularnewline
30 & 0.0507366066360191 & 0.101473213272038 & 0.949263393363981 \tabularnewline
31 & 0.0330222449271491 & 0.0660444898542982 & 0.966977755072851 \tabularnewline
32 & 0.0233316453249314 & 0.0466632906498627 & 0.976668354675069 \tabularnewline
33 & 0.0153770824849813 & 0.0307541649699627 & 0.984622917515019 \tabularnewline
34 & 0.00924260846359495 & 0.0184852169271899 & 0.990757391536405 \tabularnewline
35 & 0.00525014146423507 & 0.0105002829284701 & 0.994749858535765 \tabularnewline
36 & 0.00293843721258985 & 0.0058768744251797 & 0.99706156278741 \tabularnewline
37 & 0.00533573169416145 & 0.0106714633883229 & 0.994664268305839 \tabularnewline
38 & 0.00344992915825055 & 0.0068998583165011 & 0.996550070841749 \tabularnewline
39 & 0.00197131982603652 & 0.00394263965207304 & 0.998028680173964 \tabularnewline
40 & 0.00198536818109862 & 0.00397073636219723 & 0.998014631818901 \tabularnewline
41 & 0.00303454388805272 & 0.00606908777610545 & 0.996965456111947 \tabularnewline
42 & 0.00196735191290244 & 0.00393470382580487 & 0.998032648087098 \tabularnewline
43 & 0.000946918535995675 & 0.00189383707199135 & 0.999053081464004 \tabularnewline
44 & 0.000888362755306558 & 0.00177672551061312 & 0.999111637244693 \tabularnewline
45 & 0.00208056605663808 & 0.00416113211327616 & 0.997919433943362 \tabularnewline
46 & 0.0148711687438812 & 0.0297423374877625 & 0.985128831256119 \tabularnewline
47 & 0.0123641567709366 & 0.0247283135418732 & 0.987635843229063 \tabularnewline
48 & 0.0204461798079541 & 0.0408923596159081 & 0.979553820192046 \tabularnewline
49 & 0.0203083794472267 & 0.0406167588944534 & 0.979691620552773 \tabularnewline
50 & 0.0173909700503287 & 0.0347819401006573 & 0.982609029949671 \tabularnewline
51 & 0.0116170302253184 & 0.0232340604506367 & 0.988382969774682 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145898&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]9[/C][C]0.407899366544128[/C][C]0.815798733088255[/C][C]0.592100633455872[/C][/ROW]
[ROW][C]10[/C][C]0.414196637746327[/C][C]0.828393275492654[/C][C]0.585803362253673[/C][/ROW]
[ROW][C]11[/C][C]0.356386731281537[/C][C]0.712773462563075[/C][C]0.643613268718463[/C][/ROW]
[ROW][C]12[/C][C]0.374678390666639[/C][C]0.749356781333278[/C][C]0.625321609333361[/C][/ROW]
[ROW][C]13[/C][C]0.267031886123181[/C][C]0.534063772246362[/C][C]0.732968113876819[/C][/ROW]
[ROW][C]14[/C][C]0.185453193376417[/C][C]0.370906386752835[/C][C]0.814546806623582[/C][/ROW]
[ROW][C]15[/C][C]0.144942503812844[/C][C]0.289885007625687[/C][C]0.855057496187156[/C][/ROW]
[ROW][C]16[/C][C]0.494358669458826[/C][C]0.988717338917651[/C][C]0.505641330541174[/C][/ROW]
[ROW][C]17[/C][C]0.393989942482288[/C][C]0.787979884964576[/C][C]0.606010057517712[/C][/ROW]
[ROW][C]18[/C][C]0.320625655442426[/C][C]0.641251310884853[/C][C]0.679374344557574[/C][/ROW]
[ROW][C]19[/C][C]0.306645289883658[/C][C]0.613290579767316[/C][C]0.693354710116342[/C][/ROW]
[ROW][C]20[/C][C]0.389459984207913[/C][C]0.778919968415826[/C][C]0.610540015792087[/C][/ROW]
[ROW][C]21[/C][C]0.322426746675734[/C][C]0.644853493351469[/C][C]0.677573253324266[/C][/ROW]
[ROW][C]22[/C][C]0.336659489858882[/C][C]0.673318979717765[/C][C]0.663340510141118[/C][/ROW]
[ROW][C]23[/C][C]0.300143180558206[/C][C]0.600286361116413[/C][C]0.699856819441794[/C][/ROW]
[ROW][C]24[/C][C]0.246332520787966[/C][C]0.492665041575933[/C][C]0.753667479212034[/C][/ROW]
[ROW][C]25[/C][C]0.197940711070813[/C][C]0.395881422141627[/C][C]0.802059288929187[/C][/ROW]
[ROW][C]26[/C][C]0.144493147651504[/C][C]0.288986295303007[/C][C]0.855506852348496[/C][/ROW]
[ROW][C]27[/C][C]0.105519686280178[/C][C]0.211039372560356[/C][C]0.894480313719822[/C][/ROW]
[ROW][C]28[/C][C]0.0853661850014091[/C][C]0.170732370002818[/C][C]0.914633814998591[/C][/ROW]
[ROW][C]29[/C][C]0.0748481098000031[/C][C]0.149696219600006[/C][C]0.925151890199997[/C][/ROW]
[ROW][C]30[/C][C]0.0507366066360191[/C][C]0.101473213272038[/C][C]0.949263393363981[/C][/ROW]
[ROW][C]31[/C][C]0.0330222449271491[/C][C]0.0660444898542982[/C][C]0.966977755072851[/C][/ROW]
[ROW][C]32[/C][C]0.0233316453249314[/C][C]0.0466632906498627[/C][C]0.976668354675069[/C][/ROW]
[ROW][C]33[/C][C]0.0153770824849813[/C][C]0.0307541649699627[/C][C]0.984622917515019[/C][/ROW]
[ROW][C]34[/C][C]0.00924260846359495[/C][C]0.0184852169271899[/C][C]0.990757391536405[/C][/ROW]
[ROW][C]35[/C][C]0.00525014146423507[/C][C]0.0105002829284701[/C][C]0.994749858535765[/C][/ROW]
[ROW][C]36[/C][C]0.00293843721258985[/C][C]0.0058768744251797[/C][C]0.99706156278741[/C][/ROW]
[ROW][C]37[/C][C]0.00533573169416145[/C][C]0.0106714633883229[/C][C]0.994664268305839[/C][/ROW]
[ROW][C]38[/C][C]0.00344992915825055[/C][C]0.0068998583165011[/C][C]0.996550070841749[/C][/ROW]
[ROW][C]39[/C][C]0.00197131982603652[/C][C]0.00394263965207304[/C][C]0.998028680173964[/C][/ROW]
[ROW][C]40[/C][C]0.00198536818109862[/C][C]0.00397073636219723[/C][C]0.998014631818901[/C][/ROW]
[ROW][C]41[/C][C]0.00303454388805272[/C][C]0.00606908777610545[/C][C]0.996965456111947[/C][/ROW]
[ROW][C]42[/C][C]0.00196735191290244[/C][C]0.00393470382580487[/C][C]0.998032648087098[/C][/ROW]
[ROW][C]43[/C][C]0.000946918535995675[/C][C]0.00189383707199135[/C][C]0.999053081464004[/C][/ROW]
[ROW][C]44[/C][C]0.000888362755306558[/C][C]0.00177672551061312[/C][C]0.999111637244693[/C][/ROW]
[ROW][C]45[/C][C]0.00208056605663808[/C][C]0.00416113211327616[/C][C]0.997919433943362[/C][/ROW]
[ROW][C]46[/C][C]0.0148711687438812[/C][C]0.0297423374877625[/C][C]0.985128831256119[/C][/ROW]
[ROW][C]47[/C][C]0.0123641567709366[/C][C]0.0247283135418732[/C][C]0.987635843229063[/C][/ROW]
[ROW][C]48[/C][C]0.0204461798079541[/C][C]0.0408923596159081[/C][C]0.979553820192046[/C][/ROW]
[ROW][C]49[/C][C]0.0203083794472267[/C][C]0.0406167588944534[/C][C]0.979691620552773[/C][/ROW]
[ROW][C]50[/C][C]0.0173909700503287[/C][C]0.0347819401006573[/C][C]0.982609029949671[/C][/ROW]
[ROW][C]51[/C][C]0.0116170302253184[/C][C]0.0232340604506367[/C][C]0.988382969774682[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145898&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145898&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
90.4078993665441280.8157987330882550.592100633455872
100.4141966377463270.8283932754926540.585803362253673
110.3563867312815370.7127734625630750.643613268718463
120.3746783906666390.7493567813332780.625321609333361
130.2670318861231810.5340637722463620.732968113876819
140.1854531933764170.3709063867528350.814546806623582
150.1449425038128440.2898850076256870.855057496187156
160.4943586694588260.9887173389176510.505641330541174
170.3939899424822880.7879798849645760.606010057517712
180.3206256554424260.6412513108848530.679374344557574
190.3066452898836580.6132905797673160.693354710116342
200.3894599842079130.7789199684158260.610540015792087
210.3224267466757340.6448534933514690.677573253324266
220.3366594898588820.6733189797177650.663340510141118
230.3001431805582060.6002863611164130.699856819441794
240.2463325207879660.4926650415759330.753667479212034
250.1979407110708130.3958814221416270.802059288929187
260.1444931476515040.2889862953030070.855506852348496
270.1055196862801780.2110393725603560.894480313719822
280.08536618500140910.1707323700028180.914633814998591
290.07484810980000310.1496962196000060.925151890199997
300.05073660663601910.1014732132720380.949263393363981
310.03302224492714910.06604448985429820.966977755072851
320.02333164532493140.04666329064986270.976668354675069
330.01537708248498130.03075416496996270.984622917515019
340.009242608463594950.01848521692718990.990757391536405
350.005250141464235070.01050028292847010.994749858535765
360.002938437212589850.00587687442517970.99706156278741
370.005335731694161450.01067146338832290.994664268305839
380.003449929158250550.00689985831650110.996550070841749
390.001971319826036520.003942639652073040.998028680173964
400.001985368181098620.003970736362197230.998014631818901
410.003034543888052720.006069087776105450.996965456111947
420.001967351912902440.003934703825804870.998032648087098
430.0009469185359956750.001893837071991350.999053081464004
440.0008883627553065580.001776725510613120.999111637244693
450.002080566056638080.004161132113276160.997919433943362
460.01487116874388120.02974233748776250.985128831256119
470.01236415677093660.02472831354187320.987635843229063
480.02044617980795410.04089235961590810.979553820192046
490.02030837944722670.04061675889445340.979691620552773
500.01739097005032870.03478194010065730.982609029949671
510.01161703022531840.02323406045063670.988382969774682







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level90.209302325581395NOK
5% type I error level200.465116279069767NOK
10% type I error level210.488372093023256NOK

\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 & 9 & 0.209302325581395 & NOK \tabularnewline
5% type I error level & 20 & 0.465116279069767 & NOK \tabularnewline
10% type I error level & 21 & 0.488372093023256 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145898&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]9[/C][C]0.209302325581395[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]20[/C][C]0.465116279069767[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]21[/C][C]0.488372093023256[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145898&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145898&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 level90.209302325581395NOK
5% type I error level200.465116279069767NOK
10% type I error level210.488372093023256NOK



Parameters (Session):
par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 4 ; 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')
}