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Author's title

Author*Unverified author*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationThu, 18 Jun 2009 07:25:40 -0600
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/Jun/18/t124533192979i1mpdhb5wgqg9.htm/, Retrieved Fri, 10 May 2024 10:13:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42282, Retrieved Fri, 10 May 2024 10:13:53 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact241
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [Enrolment Linear] [2009-06-18 13:25:40] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
101.553223	49.35172089	6.840672934	314.3897134	7.95126257	26	47.49	9.529999733
77.35	0.45	0.78	463.05	12.85	8	33.2	20
43.81	0.61	4.94	142.88	30	4	20	16
102.03	7.03	5.84	286.44	5.92	9	69.3	16.2
86.03	0.36	0.84	567	8.2	39	67	8.1
72.87	0.05	0.16	372.25	8	16	48.57	2.7
65.89	0.73	0.5	200.71	8.1	3	25.65	0.8
69.28	1.07	12.26	767.43	16.91	10	48.73	9.7
32.49	98	60	60.5	56	11	51.4	45
76.64	0.69	1.58	253.28	14.1	49	0.7	35.4
79.78	0.51	9.04	315.59	5.4	5	57.9	29.6
61.32	5.94	5.64	168.97	10.01	11	41.1	16.5
93.89	33.44	120.92	372.26	14.52	13	60.1	47.46
96.87	1.58	24.93	313.43	22.16	46	73.61	12.1
96.81	75.33	187.57	845.24	5.27	93	98.7	91.1
108.89	18.27	12.31	450.23	3.9	14	67.9	44.5
113.99	0.9	60.61	499.9	24.07	32	82.22	18.3
99.07	31.03	12.24	178.64	11.36	9	70.68	11.6
136.86	2.46	6.81	135.72	11.5	56	64.13	19
60.91	5.05	5.61	209.13	16.2	36	21	12.1
89.14	9.8	7.79	441.64	11	11	51.21	11.3
101.38	13.97	229.09	661.38	7.6	72	95	86.1
98.94	7.14	40.3	1014.13	40	26	97.77	3.5
104.32	17.54	10.7	450	2.1	53	89.89	11.44
116.68	46.73	24.1	196.87	10.34	17	48	30.8
100.62	2.84	14.87	1846.99	6.7	32	76.1	11.06
32.76	0.5	0.09	140.19	21	2	22.3	25
69.18	82.41	150.53	713.04	2.6	30	43	56
95.81	0.78	0.67	168.89	7.43	24	64.9	8.3
66.95	4.33	2.97	237	16	9	38.2	29.3
48.95	11.39	7.3	633.43	6	34	60.93	36.3
68.73	1.6	8.49	258.26	2.2	35	68.3	4.2
103.63	0.27	0.32	338.13	12.22	5	53.16	31.6
125.42	0.13	9.29	215.64	10.1	32	66.81	23
99.12	88.73	379.89	1415.42	9.4	93	99.17	87.3
105.75	36.86	262.49	276.53	1.8	43	91	25
74.26	29.96	41.04	340.91	9.6	24	50.2	15.53
80.11	2.65	11.41	205.7	7.34	47	68.5	22




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42282&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42282&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42282&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 time5 seconds
R Server'George Udny Yule' @ 72.249.76.132







Multiple Linear Regression - Estimated Regression Equation
Enrol[t] = + 58.7578561581236 -0.0536291396091595Irr[t] -0.0378072341617618Mach[t] -0.00677597264230691Val[t] -0.570464946780196Exp[t] + 0.128149474300660San[t] + 0.633378330948962Lit[t] -0.0426406763956305Road[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Enrol[t] =  +  58.7578561581236 -0.0536291396091595Irr[t] -0.0378072341617618Mach[t] -0.00677597264230691Val[t] -0.570464946780196Exp[t] +  0.128149474300660San[t] +  0.633378330948962Lit[t] -0.0426406763956305Road[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42282&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Enrol[t] =  +  58.7578561581236 -0.0536291396091595Irr[t] -0.0378072341617618Mach[t] -0.00677597264230691Val[t] -0.570464946780196Exp[t] +  0.128149474300660San[t] +  0.633378330948962Lit[t] -0.0426406763956305Road[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42282&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42282&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
Enrol[t] = + 58.7578561581236 -0.0536291396091595Irr[t] -0.0378072341617618Mach[t] -0.00677597264230691Val[t] -0.570464946780196Exp[t] + 0.128149474300660San[t] + 0.633378330948962Lit[t] -0.0426406763956305Road[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)58.757856158123611.650045.04362.1e-051e-05
Irr-0.05362913960915950.170869-0.31390.7557990.3779
Mach-0.03780723416176180.072728-0.51980.6069860.303493
Val-0.006775972642306910.01062-0.6380.52830.26415
Exp-0.5704649467801960.326293-1.74830.0906370.045318
San0.1281494743006600.2099440.61040.5461950.273097
Lit0.6333783309489620.1845933.43120.0017720.000886
Road-0.04264067639563050.238806-0.17860.8594850.429743

\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) & 58.7578561581236 & 11.65004 & 5.0436 & 2.1e-05 & 1e-05 \tabularnewline
Irr & -0.0536291396091595 & 0.170869 & -0.3139 & 0.755799 & 0.3779 \tabularnewline
Mach & -0.0378072341617618 & 0.072728 & -0.5198 & 0.606986 & 0.303493 \tabularnewline
Val & -0.00677597264230691 & 0.01062 & -0.638 & 0.5283 & 0.26415 \tabularnewline
Exp & -0.570464946780196 & 0.326293 & -1.7483 & 0.090637 & 0.045318 \tabularnewline
San & 0.128149474300660 & 0.209944 & 0.6104 & 0.546195 & 0.273097 \tabularnewline
Lit & 0.633378330948962 & 0.184593 & 3.4312 & 0.001772 & 0.000886 \tabularnewline
Road & -0.0426406763956305 & 0.238806 & -0.1786 & 0.859485 & 0.429743 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42282&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]58.7578561581236[/C][C]11.65004[/C][C]5.0436[/C][C]2.1e-05[/C][C]1e-05[/C][/ROW]
[ROW][C]Irr[/C][C]-0.0536291396091595[/C][C]0.170869[/C][C]-0.3139[/C][C]0.755799[/C][C]0.3779[/C][/ROW]
[ROW][C]Mach[/C][C]-0.0378072341617618[/C][C]0.072728[/C][C]-0.5198[/C][C]0.606986[/C][C]0.303493[/C][/ROW]
[ROW][C]Val[/C][C]-0.00677597264230691[/C][C]0.01062[/C][C]-0.638[/C][C]0.5283[/C][C]0.26415[/C][/ROW]
[ROW][C]Exp[/C][C]-0.570464946780196[/C][C]0.326293[/C][C]-1.7483[/C][C]0.090637[/C][C]0.045318[/C][/ROW]
[ROW][C]San[/C][C]0.128149474300660[/C][C]0.209944[/C][C]0.6104[/C][C]0.546195[/C][C]0.273097[/C][/ROW]
[ROW][C]Lit[/C][C]0.633378330948962[/C][C]0.184593[/C][C]3.4312[/C][C]0.001772[/C][C]0.000886[/C][/ROW]
[ROW][C]Road[/C][C]-0.0426406763956305[/C][C]0.238806[/C][C]-0.1786[/C][C]0.859485[/C][C]0.429743[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42282&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42282&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)58.757856158123611.650045.04362.1e-051e-05
Irr-0.05362913960915950.170869-0.31390.7557990.3779
Mach-0.03780723416176180.072728-0.51980.6069860.303493
Val-0.006775972642306910.01062-0.6380.52830.26415
Exp-0.5704649467801960.326293-1.74830.0906370.045318
San0.1281494743006600.2099440.61040.5461950.273097
Lit0.6333783309489620.1845933.43120.0017720.000886
Road-0.04264067639563050.238806-0.17860.8594850.429743







Multiple Linear Regression - Regression Statistics
Multiple R0.673547174765554
R-squared0.45366579663466
Adjusted R-squared0.326187815849414
F-TEST (value)3.55877771078695
F-TEST (DF numerator)7
F-TEST (DF denominator)30
p-value0.00666327090111318
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation19.8100601062949
Sum Squared Residuals11773.1544424505

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.673547174765554 \tabularnewline
R-squared & 0.45366579663466 \tabularnewline
Adjusted R-squared & 0.326187815849414 \tabularnewline
F-TEST (value) & 3.55877771078695 \tabularnewline
F-TEST (DF numerator) & 7 \tabularnewline
F-TEST (DF denominator) & 30 \tabularnewline
p-value & 0.00666327090111318 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 19.8100601062949 \tabularnewline
Sum Squared Residuals & 11773.1544424505 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42282&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.673547174765554[/C][/ROW]
[ROW][C]R-squared[/C][C]0.45366579663466[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.326187815849414[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]3.55877771078695[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]7[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]30[/C][/ROW]
[ROW][C]p-value[/C][C]0.00666327090111318[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]19.8100601062949[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]11773.1544424505[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42282&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42282&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 R0.673547174765554
R-squared0.45366579663466
Adjusted R-squared0.326187815849414
F-TEST (value)3.55877771078695
F-TEST (DF numerator)7
F-TEST (DF denominator)30
p-value0.00666327090111318
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation19.8100601062949
Sum Squared Residuals11773.1544424505







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1101.55322382.190983863188419.3622391368116
277.3569.43668755850587.91331244149423
343.8152.954188965516-9.14418896551604
4102.0397.19767161642524.83232838357485
586.0397.2757907318844-11.2457907318844
672.8784.3614974500704-11.4914974500704
765.8969.3155218017974-3.42552180179738
869.2875.1227156020918-5.84271560209179
932.4950.9242430524503-18.4342430524503
1076.6454.114551649364822.5254483506352
1179.7889.2209766934394-9.44097669343944
1261.3278.1086985123142-16.7886985123142
1393.8979.29552672588414.5944732741160
1496.8794.96719401855741.90280598144265
1596.81109.440573528911-12.6305735289109
16108.8994.940056481782613.9499435182174
17113.9994.696518647247219.2934813527528
1899.0794.3659357156564.70406428434405
19136.8697.873229388134238.9867706118658
2060.9165.0147129632899-4.10471296328989
2189.1482.0332261654367.10677383456389
22101.38106.256712774102-4.87671277410237
2398.9492.26904093895716.67095906104285
24104.32116.403990535543-12.0839905355428
25116.6879.375386952766937.3046130472331
26100.6293.53535525750797.0846447424921
2732.7659.1125702690078-26.3525702690078
2869.1871.0242819917336-1.84428199173359
2995.8197.1356694559238-1.32566945592375
3066.9571.77903552601-4.82903552600995
3148.9591.5571006948781-42.6071006948781
3268.73102.911961302673-34.1819613026725
33103.6382.432730766948321.1972692330517
34125.4296.612842372766428.8071576272336
3599.1295.69103385861473.42896614138525
36105.75106.038307159421-0.288307159420816
3774.2682.0220278152853-7.76202781528534
3880.11101.074674195916-20.9646741959155

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 101.553223 & 82.1909838631884 & 19.3622391368116 \tabularnewline
2 & 77.35 & 69.4366875585058 & 7.91331244149423 \tabularnewline
3 & 43.81 & 52.954188965516 & -9.14418896551604 \tabularnewline
4 & 102.03 & 97.1976716164252 & 4.83232838357485 \tabularnewline
5 & 86.03 & 97.2757907318844 & -11.2457907318844 \tabularnewline
6 & 72.87 & 84.3614974500704 & -11.4914974500704 \tabularnewline
7 & 65.89 & 69.3155218017974 & -3.42552180179738 \tabularnewline
8 & 69.28 & 75.1227156020918 & -5.84271560209179 \tabularnewline
9 & 32.49 & 50.9242430524503 & -18.4342430524503 \tabularnewline
10 & 76.64 & 54.1145516493648 & 22.5254483506352 \tabularnewline
11 & 79.78 & 89.2209766934394 & -9.44097669343944 \tabularnewline
12 & 61.32 & 78.1086985123142 & -16.7886985123142 \tabularnewline
13 & 93.89 & 79.295526725884 & 14.5944732741160 \tabularnewline
14 & 96.87 & 94.9671940185574 & 1.90280598144265 \tabularnewline
15 & 96.81 & 109.440573528911 & -12.6305735289109 \tabularnewline
16 & 108.89 & 94.9400564817826 & 13.9499435182174 \tabularnewline
17 & 113.99 & 94.6965186472472 & 19.2934813527528 \tabularnewline
18 & 99.07 & 94.365935715656 & 4.70406428434405 \tabularnewline
19 & 136.86 & 97.8732293881342 & 38.9867706118658 \tabularnewline
20 & 60.91 & 65.0147129632899 & -4.10471296328989 \tabularnewline
21 & 89.14 & 82.033226165436 & 7.10677383456389 \tabularnewline
22 & 101.38 & 106.256712774102 & -4.87671277410237 \tabularnewline
23 & 98.94 & 92.2690409389571 & 6.67095906104285 \tabularnewline
24 & 104.32 & 116.403990535543 & -12.0839905355428 \tabularnewline
25 & 116.68 & 79.3753869527669 & 37.3046130472331 \tabularnewline
26 & 100.62 & 93.5353552575079 & 7.0846447424921 \tabularnewline
27 & 32.76 & 59.1125702690078 & -26.3525702690078 \tabularnewline
28 & 69.18 & 71.0242819917336 & -1.84428199173359 \tabularnewline
29 & 95.81 & 97.1356694559238 & -1.32566945592375 \tabularnewline
30 & 66.95 & 71.77903552601 & -4.82903552600995 \tabularnewline
31 & 48.95 & 91.5571006948781 & -42.6071006948781 \tabularnewline
32 & 68.73 & 102.911961302673 & -34.1819613026725 \tabularnewline
33 & 103.63 & 82.4327307669483 & 21.1972692330517 \tabularnewline
34 & 125.42 & 96.6128423727664 & 28.8071576272336 \tabularnewline
35 & 99.12 & 95.6910338586147 & 3.42896614138525 \tabularnewline
36 & 105.75 & 106.038307159421 & -0.288307159420816 \tabularnewline
37 & 74.26 & 82.0220278152853 & -7.76202781528534 \tabularnewline
38 & 80.11 & 101.074674195916 & -20.9646741959155 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42282&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]101.553223[/C][C]82.1909838631884[/C][C]19.3622391368116[/C][/ROW]
[ROW][C]2[/C][C]77.35[/C][C]69.4366875585058[/C][C]7.91331244149423[/C][/ROW]
[ROW][C]3[/C][C]43.81[/C][C]52.954188965516[/C][C]-9.14418896551604[/C][/ROW]
[ROW][C]4[/C][C]102.03[/C][C]97.1976716164252[/C][C]4.83232838357485[/C][/ROW]
[ROW][C]5[/C][C]86.03[/C][C]97.2757907318844[/C][C]-11.2457907318844[/C][/ROW]
[ROW][C]6[/C][C]72.87[/C][C]84.3614974500704[/C][C]-11.4914974500704[/C][/ROW]
[ROW][C]7[/C][C]65.89[/C][C]69.3155218017974[/C][C]-3.42552180179738[/C][/ROW]
[ROW][C]8[/C][C]69.28[/C][C]75.1227156020918[/C][C]-5.84271560209179[/C][/ROW]
[ROW][C]9[/C][C]32.49[/C][C]50.9242430524503[/C][C]-18.4342430524503[/C][/ROW]
[ROW][C]10[/C][C]76.64[/C][C]54.1145516493648[/C][C]22.5254483506352[/C][/ROW]
[ROW][C]11[/C][C]79.78[/C][C]89.2209766934394[/C][C]-9.44097669343944[/C][/ROW]
[ROW][C]12[/C][C]61.32[/C][C]78.1086985123142[/C][C]-16.7886985123142[/C][/ROW]
[ROW][C]13[/C][C]93.89[/C][C]79.295526725884[/C][C]14.5944732741160[/C][/ROW]
[ROW][C]14[/C][C]96.87[/C][C]94.9671940185574[/C][C]1.90280598144265[/C][/ROW]
[ROW][C]15[/C][C]96.81[/C][C]109.440573528911[/C][C]-12.6305735289109[/C][/ROW]
[ROW][C]16[/C][C]108.89[/C][C]94.9400564817826[/C][C]13.9499435182174[/C][/ROW]
[ROW][C]17[/C][C]113.99[/C][C]94.6965186472472[/C][C]19.2934813527528[/C][/ROW]
[ROW][C]18[/C][C]99.07[/C][C]94.365935715656[/C][C]4.70406428434405[/C][/ROW]
[ROW][C]19[/C][C]136.86[/C][C]97.8732293881342[/C][C]38.9867706118658[/C][/ROW]
[ROW][C]20[/C][C]60.91[/C][C]65.0147129632899[/C][C]-4.10471296328989[/C][/ROW]
[ROW][C]21[/C][C]89.14[/C][C]82.033226165436[/C][C]7.10677383456389[/C][/ROW]
[ROW][C]22[/C][C]101.38[/C][C]106.256712774102[/C][C]-4.87671277410237[/C][/ROW]
[ROW][C]23[/C][C]98.94[/C][C]92.2690409389571[/C][C]6.67095906104285[/C][/ROW]
[ROW][C]24[/C][C]104.32[/C][C]116.403990535543[/C][C]-12.0839905355428[/C][/ROW]
[ROW][C]25[/C][C]116.68[/C][C]79.3753869527669[/C][C]37.3046130472331[/C][/ROW]
[ROW][C]26[/C][C]100.62[/C][C]93.5353552575079[/C][C]7.0846447424921[/C][/ROW]
[ROW][C]27[/C][C]32.76[/C][C]59.1125702690078[/C][C]-26.3525702690078[/C][/ROW]
[ROW][C]28[/C][C]69.18[/C][C]71.0242819917336[/C][C]-1.84428199173359[/C][/ROW]
[ROW][C]29[/C][C]95.81[/C][C]97.1356694559238[/C][C]-1.32566945592375[/C][/ROW]
[ROW][C]30[/C][C]66.95[/C][C]71.77903552601[/C][C]-4.82903552600995[/C][/ROW]
[ROW][C]31[/C][C]48.95[/C][C]91.5571006948781[/C][C]-42.6071006948781[/C][/ROW]
[ROW][C]32[/C][C]68.73[/C][C]102.911961302673[/C][C]-34.1819613026725[/C][/ROW]
[ROW][C]33[/C][C]103.63[/C][C]82.4327307669483[/C][C]21.1972692330517[/C][/ROW]
[ROW][C]34[/C][C]125.42[/C][C]96.6128423727664[/C][C]28.8071576272336[/C][/ROW]
[ROW][C]35[/C][C]99.12[/C][C]95.6910338586147[/C][C]3.42896614138525[/C][/ROW]
[ROW][C]36[/C][C]105.75[/C][C]106.038307159421[/C][C]-0.288307159420816[/C][/ROW]
[ROW][C]37[/C][C]74.26[/C][C]82.0220278152853[/C][C]-7.76202781528534[/C][/ROW]
[ROW][C]38[/C][C]80.11[/C][C]101.074674195916[/C][C]-20.9646741959155[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42282&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42282&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
1101.55322382.190983863188419.3622391368116
277.3569.43668755850587.91331244149423
343.8152.954188965516-9.14418896551604
4102.0397.19767161642524.83232838357485
586.0397.2757907318844-11.2457907318844
672.8784.3614974500704-11.4914974500704
765.8969.3155218017974-3.42552180179738
869.2875.1227156020918-5.84271560209179
932.4950.9242430524503-18.4342430524503
1076.6454.114551649364822.5254483506352
1179.7889.2209766934394-9.44097669343944
1261.3278.1086985123142-16.7886985123142
1393.8979.29552672588414.5944732741160
1496.8794.96719401855741.90280598144265
1596.81109.440573528911-12.6305735289109
16108.8994.940056481782613.9499435182174
17113.9994.696518647247219.2934813527528
1899.0794.3659357156564.70406428434405
19136.8697.873229388134238.9867706118658
2060.9165.0147129632899-4.10471296328989
2189.1482.0332261654367.10677383456389
22101.38106.256712774102-4.87671277410237
2398.9492.26904093895716.67095906104285
24104.32116.403990535543-12.0839905355428
25116.6879.375386952766937.3046130472331
26100.6293.53535525750797.0846447424921
2732.7659.1125702690078-26.3525702690078
2869.1871.0242819917336-1.84428199173359
2995.8197.1356694559238-1.32566945592375
3066.9571.77903552601-4.82903552600995
3148.9591.5571006948781-42.6071006948781
3268.73102.911961302673-34.1819613026725
33103.6382.432730766948321.1972692330517
34125.4296.612842372766428.8071576272336
3599.1295.69103385861473.42896614138525
36105.75106.038307159421-0.288307159420816
3774.2682.0220278152853-7.76202781528534
3880.11101.074674195916-20.9646741959155







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
110.1025445426925060.2050890853850120.897455457307494
120.07279172811113420.1455834562222680.927208271888866
130.07046959426009960.1409391885201990.9295304057399
140.06463812594842030.1292762518968410.93536187405158
150.1435619014779790.2871238029559580.856438098522021
160.1113620046013920.2227240092027830.888637995398608
170.1484504876786250.2969009753572490.851549512321375
180.0898333475830560.1796666951661120.910166652416944
190.2088887321673720.4177774643347450.791111267832628
200.2602265960977270.5204531921954530.739773403902273
210.1840464088821690.3680928177643380.815953591117831
220.1181359590727720.2362719181455450.881864040927228
230.3632990609941330.7265981219882650.636700939005867
240.49976944444620.99953888889240.5002305555538
250.5342482678377910.9315034643244180.465751732162209
260.7976674709887610.4046650580224780.202332529011239
270.6837382611184270.6325234777631460.316261738881573

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
11 & 0.102544542692506 & 0.205089085385012 & 0.897455457307494 \tabularnewline
12 & 0.0727917281111342 & 0.145583456222268 & 0.927208271888866 \tabularnewline
13 & 0.0704695942600996 & 0.140939188520199 & 0.9295304057399 \tabularnewline
14 & 0.0646381259484203 & 0.129276251896841 & 0.93536187405158 \tabularnewline
15 & 0.143561901477979 & 0.287123802955958 & 0.856438098522021 \tabularnewline
16 & 0.111362004601392 & 0.222724009202783 & 0.888637995398608 \tabularnewline
17 & 0.148450487678625 & 0.296900975357249 & 0.851549512321375 \tabularnewline
18 & 0.089833347583056 & 0.179666695166112 & 0.910166652416944 \tabularnewline
19 & 0.208888732167372 & 0.417777464334745 & 0.791111267832628 \tabularnewline
20 & 0.260226596097727 & 0.520453192195453 & 0.739773403902273 \tabularnewline
21 & 0.184046408882169 & 0.368092817764338 & 0.815953591117831 \tabularnewline
22 & 0.118135959072772 & 0.236271918145545 & 0.881864040927228 \tabularnewline
23 & 0.363299060994133 & 0.726598121988265 & 0.636700939005867 \tabularnewline
24 & 0.4997694444462 & 0.9995388888924 & 0.5002305555538 \tabularnewline
25 & 0.534248267837791 & 0.931503464324418 & 0.465751732162209 \tabularnewline
26 & 0.797667470988761 & 0.404665058022478 & 0.202332529011239 \tabularnewline
27 & 0.683738261118427 & 0.632523477763146 & 0.316261738881573 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42282&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]11[/C][C]0.102544542692506[/C][C]0.205089085385012[/C][C]0.897455457307494[/C][/ROW]
[ROW][C]12[/C][C]0.0727917281111342[/C][C]0.145583456222268[/C][C]0.927208271888866[/C][/ROW]
[ROW][C]13[/C][C]0.0704695942600996[/C][C]0.140939188520199[/C][C]0.9295304057399[/C][/ROW]
[ROW][C]14[/C][C]0.0646381259484203[/C][C]0.129276251896841[/C][C]0.93536187405158[/C][/ROW]
[ROW][C]15[/C][C]0.143561901477979[/C][C]0.287123802955958[/C][C]0.856438098522021[/C][/ROW]
[ROW][C]16[/C][C]0.111362004601392[/C][C]0.222724009202783[/C][C]0.888637995398608[/C][/ROW]
[ROW][C]17[/C][C]0.148450487678625[/C][C]0.296900975357249[/C][C]0.851549512321375[/C][/ROW]
[ROW][C]18[/C][C]0.089833347583056[/C][C]0.179666695166112[/C][C]0.910166652416944[/C][/ROW]
[ROW][C]19[/C][C]0.208888732167372[/C][C]0.417777464334745[/C][C]0.791111267832628[/C][/ROW]
[ROW][C]20[/C][C]0.260226596097727[/C][C]0.520453192195453[/C][C]0.739773403902273[/C][/ROW]
[ROW][C]21[/C][C]0.184046408882169[/C][C]0.368092817764338[/C][C]0.815953591117831[/C][/ROW]
[ROW][C]22[/C][C]0.118135959072772[/C][C]0.236271918145545[/C][C]0.881864040927228[/C][/ROW]
[ROW][C]23[/C][C]0.363299060994133[/C][C]0.726598121988265[/C][C]0.636700939005867[/C][/ROW]
[ROW][C]24[/C][C]0.4997694444462[/C][C]0.9995388888924[/C][C]0.5002305555538[/C][/ROW]
[ROW][C]25[/C][C]0.534248267837791[/C][C]0.931503464324418[/C][C]0.465751732162209[/C][/ROW]
[ROW][C]26[/C][C]0.797667470988761[/C][C]0.404665058022478[/C][C]0.202332529011239[/C][/ROW]
[ROW][C]27[/C][C]0.683738261118427[/C][C]0.632523477763146[/C][C]0.316261738881573[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42282&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42282&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
110.1025445426925060.2050890853850120.897455457307494
120.07279172811113420.1455834562222680.927208271888866
130.07046959426009960.1409391885201990.9295304057399
140.06463812594842030.1292762518968410.93536187405158
150.1435619014779790.2871238029559580.856438098522021
160.1113620046013920.2227240092027830.888637995398608
170.1484504876786250.2969009753572490.851549512321375
180.0898333475830560.1796666951661120.910166652416944
190.2088887321673720.4177774643347450.791111267832628
200.2602265960977270.5204531921954530.739773403902273
210.1840464088821690.3680928177643380.815953591117831
220.1181359590727720.2362719181455450.881864040927228
230.3632990609941330.7265981219882650.636700939005867
240.49976944444620.99953888889240.5002305555538
250.5342482678377910.9315034643244180.465751732162209
260.7976674709887610.4046650580224780.202332529011239
270.6837382611184270.6325234777631460.316261738881573







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

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42282&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42282&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42282&T=6

As an alternative you can also use a QR Code:  

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

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



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')
}