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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 01:23:13 -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/t12587054728lysygpi6xijj3t.htm/, Retrieved Thu, 28 Mar 2024 08:20:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=57981, Retrieved Thu, 28 Mar 2024 08:20:16 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:06:21] [b98453cac15ba1066b407e146608df68]
-   PD    [Multiple Regression] [] [2009-11-19 16:35:19] [2f674a53c3d7aaa1bcf80e66074d3c9b]
-   P         [Multiple Regression] [] [2009-11-20 08:23:13] [5858ea01c9bd81debbf921a11363ad90] [Current]
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Dataseries X:
56.6	0
56	0
54.8	0
52.7	0
50.9	0
50.6	0
52.1	0
53.3	0
53.9	0
54.3	0
54.2	0
54.2	0
53.5	0
51.4	0
50.5	0
50.3	0
49.8	0
50.7	0
52.8	0
55.3	0
57.3	0
57.5	0
56.8	0
56.4	0
56.3	0
56.4	0
57	0
57.9	0
58.9	0
58.8	0
56.5	1
51.9	1
47.4	1
44.9	1
43.9	1
43.4	1
42.9	1
42.6	1
42.2	1
41.2	1
40.2	1
39.3	1
38.5	1
38.3	1
37.9	1
37.6	1
37.3	1
36	1
34.5	1
33.5	1
32.9	1
32.9	1
32.8	1
31.9	1
30.5	1
29.2	1
28.7	1
28.4	1
28	1
27.4	1
26.9	1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57981&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57981&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57981&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 59.5323076923077 -7.21057692307693X[t] -0.712996794871812M1[t] -0.199326923076930M2[t] -0.373605769230770M3[t] -0.527884615384615M4[t] -0.682163461538468M5[t] -0.616442307692312M6[t] + 0.97139423076923M7[t] + 0.817115384615381M8[t] + 0.582836538461533M9[t] + 0.408557692307688M10[t] + 0.234278846153841M11[t] -0.325721153846153t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  59.5323076923077 -7.21057692307693X[t] -0.712996794871812M1[t] -0.199326923076930M2[t] -0.373605769230770M3[t] -0.527884615384615M4[t] -0.682163461538468M5[t] -0.616442307692312M6[t] +  0.97139423076923M7[t] +  0.817115384615381M8[t] +  0.582836538461533M9[t] +  0.408557692307688M10[t] +  0.234278846153841M11[t] -0.325721153846153t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57981&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  59.5323076923077 -7.21057692307693X[t] -0.712996794871812M1[t] -0.199326923076930M2[t] -0.373605769230770M3[t] -0.527884615384615M4[t] -0.682163461538468M5[t] -0.616442307692312M6[t] +  0.97139423076923M7[t] +  0.817115384615381M8[t] +  0.582836538461533M9[t] +  0.408557692307688M10[t] +  0.234278846153841M11[t] -0.325721153846153t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57981&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57981&T=1

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 59.5323076923077 -7.21057692307693X[t] -0.712996794871812M1[t] -0.199326923076930M2[t] -0.373605769230770M3[t] -0.527884615384615M4[t] -0.682163461538468M5[t] -0.616442307692312M6[t] + 0.97139423076923M7[t] + 0.817115384615381M8[t] + 0.582836538461533M9[t] + 0.408557692307688M10[t] + 0.234278846153841M11[t] -0.325721153846153t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)59.53230769230772.82315321.087200
X-7.210576923076932.725502-2.64560.0110560.005528
M1-0.7129967948718123.168376-0.2250.8229270.411464
M2-0.1993269230769303.327191-0.05990.9524830.476241
M3-0.3736057692307703.321148-0.11250.9109120.455456
M4-0.5278846153846153.316887-0.15920.8742320.437116
M5-0.6821634615384683.314416-0.20580.8378230.418911
M6-0.6164423076923123.313739-0.1860.8532250.426612
M70.971394230769233.3249470.29220.7714550.385728
M80.8171153846153813.3168870.24640.8064840.403242
M90.5828365384615333.3106060.17610.861010.430505
M100.4085576923076883.3061110.12360.9021780.451089
M110.2342788461538413.3034120.07090.9437620.471881
t-0.3257211538461530.07712-4.22350.0001095.5e-05

\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) & 59.5323076923077 & 2.823153 & 21.0872 & 0 & 0 \tabularnewline
X & -7.21057692307693 & 2.725502 & -2.6456 & 0.011056 & 0.005528 \tabularnewline
M1 & -0.712996794871812 & 3.168376 & -0.225 & 0.822927 & 0.411464 \tabularnewline
M2 & -0.199326923076930 & 3.327191 & -0.0599 & 0.952483 & 0.476241 \tabularnewline
M3 & -0.373605769230770 & 3.321148 & -0.1125 & 0.910912 & 0.455456 \tabularnewline
M4 & -0.527884615384615 & 3.316887 & -0.1592 & 0.874232 & 0.437116 \tabularnewline
M5 & -0.682163461538468 & 3.314416 & -0.2058 & 0.837823 & 0.418911 \tabularnewline
M6 & -0.616442307692312 & 3.313739 & -0.186 & 0.853225 & 0.426612 \tabularnewline
M7 & 0.97139423076923 & 3.324947 & 0.2922 & 0.771455 & 0.385728 \tabularnewline
M8 & 0.817115384615381 & 3.316887 & 0.2464 & 0.806484 & 0.403242 \tabularnewline
M9 & 0.582836538461533 & 3.310606 & 0.1761 & 0.86101 & 0.430505 \tabularnewline
M10 & 0.408557692307688 & 3.306111 & 0.1236 & 0.902178 & 0.451089 \tabularnewline
M11 & 0.234278846153841 & 3.303412 & 0.0709 & 0.943762 & 0.471881 \tabularnewline
t & -0.325721153846153 & 0.07712 & -4.2235 & 0.000109 & 5.5e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57981&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]59.5323076923077[/C][C]2.823153[/C][C]21.0872[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]-7.21057692307693[/C][C]2.725502[/C][C]-2.6456[/C][C]0.011056[/C][C]0.005528[/C][/ROW]
[ROW][C]M1[/C][C]-0.712996794871812[/C][C]3.168376[/C][C]-0.225[/C][C]0.822927[/C][C]0.411464[/C][/ROW]
[ROW][C]M2[/C][C]-0.199326923076930[/C][C]3.327191[/C][C]-0.0599[/C][C]0.952483[/C][C]0.476241[/C][/ROW]
[ROW][C]M3[/C][C]-0.373605769230770[/C][C]3.321148[/C][C]-0.1125[/C][C]0.910912[/C][C]0.455456[/C][/ROW]
[ROW][C]M4[/C][C]-0.527884615384615[/C][C]3.316887[/C][C]-0.1592[/C][C]0.874232[/C][C]0.437116[/C][/ROW]
[ROW][C]M5[/C][C]-0.682163461538468[/C][C]3.314416[/C][C]-0.2058[/C][C]0.837823[/C][C]0.418911[/C][/ROW]
[ROW][C]M6[/C][C]-0.616442307692312[/C][C]3.313739[/C][C]-0.186[/C][C]0.853225[/C][C]0.426612[/C][/ROW]
[ROW][C]M7[/C][C]0.97139423076923[/C][C]3.324947[/C][C]0.2922[/C][C]0.771455[/C][C]0.385728[/C][/ROW]
[ROW][C]M8[/C][C]0.817115384615381[/C][C]3.316887[/C][C]0.2464[/C][C]0.806484[/C][C]0.403242[/C][/ROW]
[ROW][C]M9[/C][C]0.582836538461533[/C][C]3.310606[/C][C]0.1761[/C][C]0.86101[/C][C]0.430505[/C][/ROW]
[ROW][C]M10[/C][C]0.408557692307688[/C][C]3.306111[/C][C]0.1236[/C][C]0.902178[/C][C]0.451089[/C][/ROW]
[ROW][C]M11[/C][C]0.234278846153841[/C][C]3.303412[/C][C]0.0709[/C][C]0.943762[/C][C]0.471881[/C][/ROW]
[ROW][C]t[/C][C]-0.325721153846153[/C][C]0.07712[/C][C]-4.2235[/C][C]0.000109[/C][C]5.5e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57981&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57981&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)59.53230769230772.82315321.087200
X-7.210576923076932.725502-2.64560.0110560.005528
M1-0.7129967948718123.168376-0.2250.8229270.411464
M2-0.1993269230769303.327191-0.05990.9524830.476241
M3-0.3736057692307703.321148-0.11250.9109120.455456
M4-0.5278846153846153.316887-0.15920.8742320.437116
M5-0.6821634615384683.314416-0.20580.8378230.418911
M6-0.6164423076923123.313739-0.1860.8532250.426612
M70.971394230769233.3249470.29220.7714550.385728
M80.8171153846153813.3168870.24640.8064840.403242
M90.5828365384615333.3106060.17610.861010.430505
M100.4085576923076883.3061110.12360.9021780.451089
M110.2342788461538413.3034120.07090.9437620.471881
t-0.3257211538461530.07712-4.22350.0001095.5e-05







Multiple Linear Regression - Regression Statistics
Multiple R0.890912068408306
R-squared0.793724313635566
Adjusted R-squared0.736669336556041
F-TEST (value)13.9115701077095
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value5.62927482405939e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation5.22172889694719
Sum Squared Residuals1281.52327564103

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.890912068408306 \tabularnewline
R-squared & 0.793724313635566 \tabularnewline
Adjusted R-squared & 0.736669336556041 \tabularnewline
F-TEST (value) & 13.9115701077095 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 47 \tabularnewline
p-value & 5.62927482405939e-12 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 5.22172889694719 \tabularnewline
Sum Squared Residuals & 1281.52327564103 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57981&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.890912068408306[/C][/ROW]
[ROW][C]R-squared[/C][C]0.793724313635566[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.736669336556041[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]13.9115701077095[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]47[/C][/ROW]
[ROW][C]p-value[/C][C]5.62927482405939e-12[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]5.22172889694719[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1281.52327564103[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57981&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57981&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 R0.890912068408306
R-squared0.793724313635566
Adjusted R-squared0.736669336556041
F-TEST (value)13.9115701077095
F-TEST (DF numerator)13
F-TEST (DF denominator)47
p-value5.62927482405939e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation5.22172889694719
Sum Squared Residuals1281.52327564103







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
156.658.4935897435898-1.8935897435898
25658.6815384615385-2.68153846153848
354.858.1815384615385-3.38153846153846
452.757.7015384615385-5.00153846153845
550.957.2215384615385-6.32153846153846
650.656.9615384615385-6.36153846153846
752.158.2236538461538-6.12365384615384
853.357.7436538461538-4.44365384615384
953.957.1836538461538-3.28365384615384
1054.356.6836538461538-2.38365384615385
1154.256.1836538461538-1.98365384615384
1254.255.6236538461539-1.42365384615385
1353.554.5849358974359-1.08493589743588
1451.454.7728846153846-3.3728846153846
1550.554.2728846153846-3.77288461538461
1650.353.7928846153846-3.49288461538462
1749.853.3128846153846-3.51288461538461
1850.753.0528846153846-2.35288461538461
1952.854.315-1.51500000000000
2055.353.8351.46500000000000
2157.353.2754.025
2257.552.7754.725
2356.852.2754.525
2456.451.7154.68499999999999
2556.350.6762820512825.62371794871796
2656.450.86423076923085.53576923076923
275750.36423076923086.63576923076923
2857.949.88423076923088.01576923076922
2958.949.40423076923089.49576923076923
3058.849.14423076923089.65576923076923
3156.543.195769230769213.3042307692308
3251.942.71576923076929.18423076923077
3347.442.15576923076925.24423076923077
3444.941.65576923076923.24423076923077
3543.941.15576923076922.74423076923077
3643.440.59576923076922.80423076923077
3742.939.55705128205133.34294871794873
3842.639.7452.85500000000000
3942.239.2452.95500000000000
4041.238.7652.435
4140.238.2851.91500000000001
4239.338.0251.27500000000000
4338.539.2871153846154-0.787115384615385
4438.338.8071153846154-0.507115384615387
4537.938.2471153846154-0.347115384615384
4637.637.7471153846154-0.147115384615383
4737.337.24711538461540.0528846153846132
483636.6871153846154-0.68711538461539
4934.535.6483974358974-1.14839743589742
5033.535.8363461538462-2.33634615384615
5132.935.3363461538462-2.43634615384616
5232.934.8563461538462-1.95634615384616
5332.834.3763461538462-1.57634615384616
5431.934.1163461538462-2.21634615384616
5530.535.3784615384615-4.87846153846154
5629.234.8984615384615-5.69846153846154
5728.734.3384615384615-5.63846153846154
5828.433.8384615384615-5.43846153846155
592833.3384615384615-5.33846153846154
6027.432.7784615384615-5.37846153846155
6126.931.7397435897436-4.83974358974358

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 56.6 & 58.4935897435898 & -1.8935897435898 \tabularnewline
2 & 56 & 58.6815384615385 & -2.68153846153848 \tabularnewline
3 & 54.8 & 58.1815384615385 & -3.38153846153846 \tabularnewline
4 & 52.7 & 57.7015384615385 & -5.00153846153845 \tabularnewline
5 & 50.9 & 57.2215384615385 & -6.32153846153846 \tabularnewline
6 & 50.6 & 56.9615384615385 & -6.36153846153846 \tabularnewline
7 & 52.1 & 58.2236538461538 & -6.12365384615384 \tabularnewline
8 & 53.3 & 57.7436538461538 & -4.44365384615384 \tabularnewline
9 & 53.9 & 57.1836538461538 & -3.28365384615384 \tabularnewline
10 & 54.3 & 56.6836538461538 & -2.38365384615385 \tabularnewline
11 & 54.2 & 56.1836538461538 & -1.98365384615384 \tabularnewline
12 & 54.2 & 55.6236538461539 & -1.42365384615385 \tabularnewline
13 & 53.5 & 54.5849358974359 & -1.08493589743588 \tabularnewline
14 & 51.4 & 54.7728846153846 & -3.3728846153846 \tabularnewline
15 & 50.5 & 54.2728846153846 & -3.77288461538461 \tabularnewline
16 & 50.3 & 53.7928846153846 & -3.49288461538462 \tabularnewline
17 & 49.8 & 53.3128846153846 & -3.51288461538461 \tabularnewline
18 & 50.7 & 53.0528846153846 & -2.35288461538461 \tabularnewline
19 & 52.8 & 54.315 & -1.51500000000000 \tabularnewline
20 & 55.3 & 53.835 & 1.46500000000000 \tabularnewline
21 & 57.3 & 53.275 & 4.025 \tabularnewline
22 & 57.5 & 52.775 & 4.725 \tabularnewline
23 & 56.8 & 52.275 & 4.525 \tabularnewline
24 & 56.4 & 51.715 & 4.68499999999999 \tabularnewline
25 & 56.3 & 50.676282051282 & 5.62371794871796 \tabularnewline
26 & 56.4 & 50.8642307692308 & 5.53576923076923 \tabularnewline
27 & 57 & 50.3642307692308 & 6.63576923076923 \tabularnewline
28 & 57.9 & 49.8842307692308 & 8.01576923076922 \tabularnewline
29 & 58.9 & 49.4042307692308 & 9.49576923076923 \tabularnewline
30 & 58.8 & 49.1442307692308 & 9.65576923076923 \tabularnewline
31 & 56.5 & 43.1957692307692 & 13.3042307692308 \tabularnewline
32 & 51.9 & 42.7157692307692 & 9.18423076923077 \tabularnewline
33 & 47.4 & 42.1557692307692 & 5.24423076923077 \tabularnewline
34 & 44.9 & 41.6557692307692 & 3.24423076923077 \tabularnewline
35 & 43.9 & 41.1557692307692 & 2.74423076923077 \tabularnewline
36 & 43.4 & 40.5957692307692 & 2.80423076923077 \tabularnewline
37 & 42.9 & 39.5570512820513 & 3.34294871794873 \tabularnewline
38 & 42.6 & 39.745 & 2.85500000000000 \tabularnewline
39 & 42.2 & 39.245 & 2.95500000000000 \tabularnewline
40 & 41.2 & 38.765 & 2.435 \tabularnewline
41 & 40.2 & 38.285 & 1.91500000000001 \tabularnewline
42 & 39.3 & 38.025 & 1.27500000000000 \tabularnewline
43 & 38.5 & 39.2871153846154 & -0.787115384615385 \tabularnewline
44 & 38.3 & 38.8071153846154 & -0.507115384615387 \tabularnewline
45 & 37.9 & 38.2471153846154 & -0.347115384615384 \tabularnewline
46 & 37.6 & 37.7471153846154 & -0.147115384615383 \tabularnewline
47 & 37.3 & 37.2471153846154 & 0.0528846153846132 \tabularnewline
48 & 36 & 36.6871153846154 & -0.68711538461539 \tabularnewline
49 & 34.5 & 35.6483974358974 & -1.14839743589742 \tabularnewline
50 & 33.5 & 35.8363461538462 & -2.33634615384615 \tabularnewline
51 & 32.9 & 35.3363461538462 & -2.43634615384616 \tabularnewline
52 & 32.9 & 34.8563461538462 & -1.95634615384616 \tabularnewline
53 & 32.8 & 34.3763461538462 & -1.57634615384616 \tabularnewline
54 & 31.9 & 34.1163461538462 & -2.21634615384616 \tabularnewline
55 & 30.5 & 35.3784615384615 & -4.87846153846154 \tabularnewline
56 & 29.2 & 34.8984615384615 & -5.69846153846154 \tabularnewline
57 & 28.7 & 34.3384615384615 & -5.63846153846154 \tabularnewline
58 & 28.4 & 33.8384615384615 & -5.43846153846155 \tabularnewline
59 & 28 & 33.3384615384615 & -5.33846153846154 \tabularnewline
60 & 27.4 & 32.7784615384615 & -5.37846153846155 \tabularnewline
61 & 26.9 & 31.7397435897436 & -4.83974358974358 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57981&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]56.6[/C][C]58.4935897435898[/C][C]-1.8935897435898[/C][/ROW]
[ROW][C]2[/C][C]56[/C][C]58.6815384615385[/C][C]-2.68153846153848[/C][/ROW]
[ROW][C]3[/C][C]54.8[/C][C]58.1815384615385[/C][C]-3.38153846153846[/C][/ROW]
[ROW][C]4[/C][C]52.7[/C][C]57.7015384615385[/C][C]-5.00153846153845[/C][/ROW]
[ROW][C]5[/C][C]50.9[/C][C]57.2215384615385[/C][C]-6.32153846153846[/C][/ROW]
[ROW][C]6[/C][C]50.6[/C][C]56.9615384615385[/C][C]-6.36153846153846[/C][/ROW]
[ROW][C]7[/C][C]52.1[/C][C]58.2236538461538[/C][C]-6.12365384615384[/C][/ROW]
[ROW][C]8[/C][C]53.3[/C][C]57.7436538461538[/C][C]-4.44365384615384[/C][/ROW]
[ROW][C]9[/C][C]53.9[/C][C]57.1836538461538[/C][C]-3.28365384615384[/C][/ROW]
[ROW][C]10[/C][C]54.3[/C][C]56.6836538461538[/C][C]-2.38365384615385[/C][/ROW]
[ROW][C]11[/C][C]54.2[/C][C]56.1836538461538[/C][C]-1.98365384615384[/C][/ROW]
[ROW][C]12[/C][C]54.2[/C][C]55.6236538461539[/C][C]-1.42365384615385[/C][/ROW]
[ROW][C]13[/C][C]53.5[/C][C]54.5849358974359[/C][C]-1.08493589743588[/C][/ROW]
[ROW][C]14[/C][C]51.4[/C][C]54.7728846153846[/C][C]-3.3728846153846[/C][/ROW]
[ROW][C]15[/C][C]50.5[/C][C]54.2728846153846[/C][C]-3.77288461538461[/C][/ROW]
[ROW][C]16[/C][C]50.3[/C][C]53.7928846153846[/C][C]-3.49288461538462[/C][/ROW]
[ROW][C]17[/C][C]49.8[/C][C]53.3128846153846[/C][C]-3.51288461538461[/C][/ROW]
[ROW][C]18[/C][C]50.7[/C][C]53.0528846153846[/C][C]-2.35288461538461[/C][/ROW]
[ROW][C]19[/C][C]52.8[/C][C]54.315[/C][C]-1.51500000000000[/C][/ROW]
[ROW][C]20[/C][C]55.3[/C][C]53.835[/C][C]1.46500000000000[/C][/ROW]
[ROW][C]21[/C][C]57.3[/C][C]53.275[/C][C]4.025[/C][/ROW]
[ROW][C]22[/C][C]57.5[/C][C]52.775[/C][C]4.725[/C][/ROW]
[ROW][C]23[/C][C]56.8[/C][C]52.275[/C][C]4.525[/C][/ROW]
[ROW][C]24[/C][C]56.4[/C][C]51.715[/C][C]4.68499999999999[/C][/ROW]
[ROW][C]25[/C][C]56.3[/C][C]50.676282051282[/C][C]5.62371794871796[/C][/ROW]
[ROW][C]26[/C][C]56.4[/C][C]50.8642307692308[/C][C]5.53576923076923[/C][/ROW]
[ROW][C]27[/C][C]57[/C][C]50.3642307692308[/C][C]6.63576923076923[/C][/ROW]
[ROW][C]28[/C][C]57.9[/C][C]49.8842307692308[/C][C]8.01576923076922[/C][/ROW]
[ROW][C]29[/C][C]58.9[/C][C]49.4042307692308[/C][C]9.49576923076923[/C][/ROW]
[ROW][C]30[/C][C]58.8[/C][C]49.1442307692308[/C][C]9.65576923076923[/C][/ROW]
[ROW][C]31[/C][C]56.5[/C][C]43.1957692307692[/C][C]13.3042307692308[/C][/ROW]
[ROW][C]32[/C][C]51.9[/C][C]42.7157692307692[/C][C]9.18423076923077[/C][/ROW]
[ROW][C]33[/C][C]47.4[/C][C]42.1557692307692[/C][C]5.24423076923077[/C][/ROW]
[ROW][C]34[/C][C]44.9[/C][C]41.6557692307692[/C][C]3.24423076923077[/C][/ROW]
[ROW][C]35[/C][C]43.9[/C][C]41.1557692307692[/C][C]2.74423076923077[/C][/ROW]
[ROW][C]36[/C][C]43.4[/C][C]40.5957692307692[/C][C]2.80423076923077[/C][/ROW]
[ROW][C]37[/C][C]42.9[/C][C]39.5570512820513[/C][C]3.34294871794873[/C][/ROW]
[ROW][C]38[/C][C]42.6[/C][C]39.745[/C][C]2.85500000000000[/C][/ROW]
[ROW][C]39[/C][C]42.2[/C][C]39.245[/C][C]2.95500000000000[/C][/ROW]
[ROW][C]40[/C][C]41.2[/C][C]38.765[/C][C]2.435[/C][/ROW]
[ROW][C]41[/C][C]40.2[/C][C]38.285[/C][C]1.91500000000001[/C][/ROW]
[ROW][C]42[/C][C]39.3[/C][C]38.025[/C][C]1.27500000000000[/C][/ROW]
[ROW][C]43[/C][C]38.5[/C][C]39.2871153846154[/C][C]-0.787115384615385[/C][/ROW]
[ROW][C]44[/C][C]38.3[/C][C]38.8071153846154[/C][C]-0.507115384615387[/C][/ROW]
[ROW][C]45[/C][C]37.9[/C][C]38.2471153846154[/C][C]-0.347115384615384[/C][/ROW]
[ROW][C]46[/C][C]37.6[/C][C]37.7471153846154[/C][C]-0.147115384615383[/C][/ROW]
[ROW][C]47[/C][C]37.3[/C][C]37.2471153846154[/C][C]0.0528846153846132[/C][/ROW]
[ROW][C]48[/C][C]36[/C][C]36.6871153846154[/C][C]-0.68711538461539[/C][/ROW]
[ROW][C]49[/C][C]34.5[/C][C]35.6483974358974[/C][C]-1.14839743589742[/C][/ROW]
[ROW][C]50[/C][C]33.5[/C][C]35.8363461538462[/C][C]-2.33634615384615[/C][/ROW]
[ROW][C]51[/C][C]32.9[/C][C]35.3363461538462[/C][C]-2.43634615384616[/C][/ROW]
[ROW][C]52[/C][C]32.9[/C][C]34.8563461538462[/C][C]-1.95634615384616[/C][/ROW]
[ROW][C]53[/C][C]32.8[/C][C]34.3763461538462[/C][C]-1.57634615384616[/C][/ROW]
[ROW][C]54[/C][C]31.9[/C][C]34.1163461538462[/C][C]-2.21634615384616[/C][/ROW]
[ROW][C]55[/C][C]30.5[/C][C]35.3784615384615[/C][C]-4.87846153846154[/C][/ROW]
[ROW][C]56[/C][C]29.2[/C][C]34.8984615384615[/C][C]-5.69846153846154[/C][/ROW]
[ROW][C]57[/C][C]28.7[/C][C]34.3384615384615[/C][C]-5.63846153846154[/C][/ROW]
[ROW][C]58[/C][C]28.4[/C][C]33.8384615384615[/C][C]-5.43846153846155[/C][/ROW]
[ROW][C]59[/C][C]28[/C][C]33.3384615384615[/C][C]-5.33846153846154[/C][/ROW]
[ROW][C]60[/C][C]27.4[/C][C]32.7784615384615[/C][C]-5.37846153846155[/C][/ROW]
[ROW][C]61[/C][C]26.9[/C][C]31.7397435897436[/C][C]-4.83974358974358[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57981&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57981&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
156.658.4935897435898-1.8935897435898
25658.6815384615385-2.68153846153848
354.858.1815384615385-3.38153846153846
452.757.7015384615385-5.00153846153845
550.957.2215384615385-6.32153846153846
650.656.9615384615385-6.36153846153846
752.158.2236538461538-6.12365384615384
853.357.7436538461538-4.44365384615384
953.957.1836538461538-3.28365384615384
1054.356.6836538461538-2.38365384615385
1154.256.1836538461538-1.98365384615384
1254.255.6236538461539-1.42365384615385
1353.554.5849358974359-1.08493589743588
1451.454.7728846153846-3.3728846153846
1550.554.2728846153846-3.77288461538461
1650.353.7928846153846-3.49288461538462
1749.853.3128846153846-3.51288461538461
1850.753.0528846153846-2.35288461538461
1952.854.315-1.51500000000000
2055.353.8351.46500000000000
2157.353.2754.025
2257.552.7754.725
2356.852.2754.525
2456.451.7154.68499999999999
2556.350.6762820512825.62371794871796
2656.450.86423076923085.53576923076923
275750.36423076923086.63576923076923
2857.949.88423076923088.01576923076922
2958.949.40423076923089.49576923076923
3058.849.14423076923089.65576923076923
3156.543.195769230769213.3042307692308
3251.942.71576923076929.18423076923077
3347.442.15576923076925.24423076923077
3444.941.65576923076923.24423076923077
3543.941.15576923076922.74423076923077
3643.440.59576923076922.80423076923077
3742.939.55705128205133.34294871794873
3842.639.7452.85500000000000
3942.239.2452.95500000000000
4041.238.7652.435
4140.238.2851.91500000000001
4239.338.0251.27500000000000
4338.539.2871153846154-0.787115384615385
4438.338.8071153846154-0.507115384615387
4537.938.2471153846154-0.347115384615384
4637.637.7471153846154-0.147115384615383
4737.337.24711538461540.0528846153846132
483636.6871153846154-0.68711538461539
4934.535.6483974358974-1.14839743589742
5033.535.8363461538462-2.33634615384615
5132.935.3363461538462-2.43634615384616
5232.934.8563461538462-1.95634615384616
5332.834.3763461538462-1.57634615384616
5431.934.1163461538462-2.21634615384616
5530.535.3784615384615-4.87846153846154
5629.234.8984615384615-5.69846153846154
5728.734.3384615384615-5.63846153846154
5828.433.8384615384615-5.43846153846155
592833.3384615384615-5.33846153846154
6027.432.7784615384615-5.37846153846155
6126.931.7397435897436-4.83974358974358







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.04834885593453090.09669771186906180.95165114406547
180.08810755504566060.1762151100913210.91189244495434
190.1812953698327390.3625907396654770.818704630167261
200.3509195079874950.7018390159749910.649080492012505
210.5297344982769830.9405310034460350.470265501723017
220.5957489854594070.8085020290811870.404251014540593
230.6160853706678710.7678292586642580.383914629332129
240.6226652144689010.7546695710621970.377334785531099
250.6108223011666070.7783553976667860.389177698833393
260.6106323124695510.7787353750608990.389367687530449
270.6564473642751270.6871052714497450.343552635724873
280.749478330174480.501043339651040.25052166982552
290.8498647627062420.3002704745875160.150135237293758
300.8680673909729180.2638652180541630.131932609027082
310.9976341033066550.004731793386689610.00236589669334480
320.9999990922621641.81547567208814e-069.0773783604407e-07
330.9999998991035572.01792885263215e-071.00896442631608e-07
340.9999998684529732.63094055117641e-071.31547027558821e-07
350.9999998925623852.14875230803867e-071.07437615401934e-07
360.9999998057743923.88451216032274e-071.94225608016137e-07
370.9999994390892181.12182156397282e-065.60910781986408e-07
380.9999977484903394.50301932283994e-062.25150966141997e-06
390.9999923796494041.52407011921703e-057.62035059608513e-06
400.999957448906518.51021869808447e-054.25510934904223e-05
410.999887809534770.0002243809304606710.000112190465230336
420.9997853194171240.0004293611657525090.000214680582876255
430.9993209219712020.001358156057595610.000679078028797807
440.9957803062274280.008439387545143360.00421969377257168

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.0483488559345309 & 0.0966977118690618 & 0.95165114406547 \tabularnewline
18 & 0.0881075550456606 & 0.176215110091321 & 0.91189244495434 \tabularnewline
19 & 0.181295369832739 & 0.362590739665477 & 0.818704630167261 \tabularnewline
20 & 0.350919507987495 & 0.701839015974991 & 0.649080492012505 \tabularnewline
21 & 0.529734498276983 & 0.940531003446035 & 0.470265501723017 \tabularnewline
22 & 0.595748985459407 & 0.808502029081187 & 0.404251014540593 \tabularnewline
23 & 0.616085370667871 & 0.767829258664258 & 0.383914629332129 \tabularnewline
24 & 0.622665214468901 & 0.754669571062197 & 0.377334785531099 \tabularnewline
25 & 0.610822301166607 & 0.778355397666786 & 0.389177698833393 \tabularnewline
26 & 0.610632312469551 & 0.778735375060899 & 0.389367687530449 \tabularnewline
27 & 0.656447364275127 & 0.687105271449745 & 0.343552635724873 \tabularnewline
28 & 0.74947833017448 & 0.50104333965104 & 0.25052166982552 \tabularnewline
29 & 0.849864762706242 & 0.300270474587516 & 0.150135237293758 \tabularnewline
30 & 0.868067390972918 & 0.263865218054163 & 0.131932609027082 \tabularnewline
31 & 0.997634103306655 & 0.00473179338668961 & 0.00236589669334480 \tabularnewline
32 & 0.999999092262164 & 1.81547567208814e-06 & 9.0773783604407e-07 \tabularnewline
33 & 0.999999899103557 & 2.01792885263215e-07 & 1.00896442631608e-07 \tabularnewline
34 & 0.999999868452973 & 2.63094055117641e-07 & 1.31547027558821e-07 \tabularnewline
35 & 0.999999892562385 & 2.14875230803867e-07 & 1.07437615401934e-07 \tabularnewline
36 & 0.999999805774392 & 3.88451216032274e-07 & 1.94225608016137e-07 \tabularnewline
37 & 0.999999439089218 & 1.12182156397282e-06 & 5.60910781986408e-07 \tabularnewline
38 & 0.999997748490339 & 4.50301932283994e-06 & 2.25150966141997e-06 \tabularnewline
39 & 0.999992379649404 & 1.52407011921703e-05 & 7.62035059608513e-06 \tabularnewline
40 & 0.99995744890651 & 8.51021869808447e-05 & 4.25510934904223e-05 \tabularnewline
41 & 0.99988780953477 & 0.000224380930460671 & 0.000112190465230336 \tabularnewline
42 & 0.999785319417124 & 0.000429361165752509 & 0.000214680582876255 \tabularnewline
43 & 0.999320921971202 & 0.00135815605759561 & 0.000679078028797807 \tabularnewline
44 & 0.995780306227428 & 0.00843938754514336 & 0.00421969377257168 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57981&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]17[/C][C]0.0483488559345309[/C][C]0.0966977118690618[/C][C]0.95165114406547[/C][/ROW]
[ROW][C]18[/C][C]0.0881075550456606[/C][C]0.176215110091321[/C][C]0.91189244495434[/C][/ROW]
[ROW][C]19[/C][C]0.181295369832739[/C][C]0.362590739665477[/C][C]0.818704630167261[/C][/ROW]
[ROW][C]20[/C][C]0.350919507987495[/C][C]0.701839015974991[/C][C]0.649080492012505[/C][/ROW]
[ROW][C]21[/C][C]0.529734498276983[/C][C]0.940531003446035[/C][C]0.470265501723017[/C][/ROW]
[ROW][C]22[/C][C]0.595748985459407[/C][C]0.808502029081187[/C][C]0.404251014540593[/C][/ROW]
[ROW][C]23[/C][C]0.616085370667871[/C][C]0.767829258664258[/C][C]0.383914629332129[/C][/ROW]
[ROW][C]24[/C][C]0.622665214468901[/C][C]0.754669571062197[/C][C]0.377334785531099[/C][/ROW]
[ROW][C]25[/C][C]0.610822301166607[/C][C]0.778355397666786[/C][C]0.389177698833393[/C][/ROW]
[ROW][C]26[/C][C]0.610632312469551[/C][C]0.778735375060899[/C][C]0.389367687530449[/C][/ROW]
[ROW][C]27[/C][C]0.656447364275127[/C][C]0.687105271449745[/C][C]0.343552635724873[/C][/ROW]
[ROW][C]28[/C][C]0.74947833017448[/C][C]0.50104333965104[/C][C]0.25052166982552[/C][/ROW]
[ROW][C]29[/C][C]0.849864762706242[/C][C]0.300270474587516[/C][C]0.150135237293758[/C][/ROW]
[ROW][C]30[/C][C]0.868067390972918[/C][C]0.263865218054163[/C][C]0.131932609027082[/C][/ROW]
[ROW][C]31[/C][C]0.997634103306655[/C][C]0.00473179338668961[/C][C]0.00236589669334480[/C][/ROW]
[ROW][C]32[/C][C]0.999999092262164[/C][C]1.81547567208814e-06[/C][C]9.0773783604407e-07[/C][/ROW]
[ROW][C]33[/C][C]0.999999899103557[/C][C]2.01792885263215e-07[/C][C]1.00896442631608e-07[/C][/ROW]
[ROW][C]34[/C][C]0.999999868452973[/C][C]2.63094055117641e-07[/C][C]1.31547027558821e-07[/C][/ROW]
[ROW][C]35[/C][C]0.999999892562385[/C][C]2.14875230803867e-07[/C][C]1.07437615401934e-07[/C][/ROW]
[ROW][C]36[/C][C]0.999999805774392[/C][C]3.88451216032274e-07[/C][C]1.94225608016137e-07[/C][/ROW]
[ROW][C]37[/C][C]0.999999439089218[/C][C]1.12182156397282e-06[/C][C]5.60910781986408e-07[/C][/ROW]
[ROW][C]38[/C][C]0.999997748490339[/C][C]4.50301932283994e-06[/C][C]2.25150966141997e-06[/C][/ROW]
[ROW][C]39[/C][C]0.999992379649404[/C][C]1.52407011921703e-05[/C][C]7.62035059608513e-06[/C][/ROW]
[ROW][C]40[/C][C]0.99995744890651[/C][C]8.51021869808447e-05[/C][C]4.25510934904223e-05[/C][/ROW]
[ROW][C]41[/C][C]0.99988780953477[/C][C]0.000224380930460671[/C][C]0.000112190465230336[/C][/ROW]
[ROW][C]42[/C][C]0.999785319417124[/C][C]0.000429361165752509[/C][C]0.000214680582876255[/C][/ROW]
[ROW][C]43[/C][C]0.999320921971202[/C][C]0.00135815605759561[/C][C]0.000679078028797807[/C][/ROW]
[ROW][C]44[/C][C]0.995780306227428[/C][C]0.00843938754514336[/C][C]0.00421969377257168[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57981&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57981&T=5

As an alternative you can also use a QR Code:  

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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.04834885593453090.09669771186906180.95165114406547
180.08810755504566060.1762151100913210.91189244495434
190.1812953698327390.3625907396654770.818704630167261
200.3509195079874950.7018390159749910.649080492012505
210.5297344982769830.9405310034460350.470265501723017
220.5957489854594070.8085020290811870.404251014540593
230.6160853706678710.7678292586642580.383914629332129
240.6226652144689010.7546695710621970.377334785531099
250.6108223011666070.7783553976667860.389177698833393
260.6106323124695510.7787353750608990.389367687530449
270.6564473642751270.6871052714497450.343552635724873
280.749478330174480.501043339651040.25052166982552
290.8498647627062420.3002704745875160.150135237293758
300.8680673909729180.2638652180541630.131932609027082
310.9976341033066550.004731793386689610.00236589669334480
320.9999990922621641.81547567208814e-069.0773783604407e-07
330.9999998991035572.01792885263215e-071.00896442631608e-07
340.9999998684529732.63094055117641e-071.31547027558821e-07
350.9999998925623852.14875230803867e-071.07437615401934e-07
360.9999998057743923.88451216032274e-071.94225608016137e-07
370.9999994390892181.12182156397282e-065.60910781986408e-07
380.9999977484903394.50301932283994e-062.25150966141997e-06
390.9999923796494041.52407011921703e-057.62035059608513e-06
400.999957448906518.51021869808447e-054.25510934904223e-05
410.999887809534770.0002243809304606710.000112190465230336
420.9997853194171240.0004293611657525090.000214680582876255
430.9993209219712020.001358156057595610.000679078028797807
440.9957803062274280.008439387545143360.00421969377257168







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level140.5NOK
5% type I error level140.5NOK
10% type I error level150.535714285714286NOK

\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 & 14 & 0.5 & NOK \tabularnewline
5% type I error level & 14 & 0.5 & NOK \tabularnewline
10% type I error level & 15 & 0.535714285714286 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=57981&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]14[/C][C]0.5[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]14[/C][C]0.5[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]15[/C][C]0.535714285714286[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=57981&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=57981&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 level140.5NOK
5% type I error level140.5NOK
10% type I error level150.535714285714286NOK



Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}