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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationWed, 09 Dec 2009 08:47:20 -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/Dec/09/t12603739334pcruoo3akts3g8.htm/, Retrieved Mon, 29 Apr 2024 12:21:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65007, Retrieved Mon, 29 Apr 2024 12:21:56 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105

Tree of Dependent Computations

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 14:10:54] [b98453cac15ba1066b407e146608df68]
-    D      [Multiple Regression] [] [2009-12-09 15:47:20] [faa1ded5041cd5a0e2be04844f08502a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
29	38	24	25	22	24
26	42	29	24	25	22
26	35	26	29	24	25
21	25	26	26	29	24
23	24	21	26	26	29
22	22	23	21	26	26
21	27	22	23	21	26
16	17	21	22	23	21
19	30	16	21	22	23
16	30	19	16	21	22
25	34	16	19	16	21
27	37	25	16	19	16
23	36	27	25	16	19
22	33	23	27	25	16
23	33	22	23	27	25
20	33	23	22	23	27
24	37	20	23	22	23
23	40	24	20	23	22
20	35	23	24	20	23
21	37	20	23	24	20
22	43	21	20	23	24
17	42	22	21	20	23
21	33	17	22	21	20
19	39	21	17	22	21
23	40	19	21	17	22
22	37	23	19	21	17
15	44	22	23	19	21
23	42	15	22	23	19
21	43	23	15	22	23
18	40	21	23	15	22
18	30	18	21	23	15
18	30	18	18	21	23
18	31	18	18	18	21
10	18	18	18	18	18
13	24	10	18	18	18
10	22	13	10	18	18
9	26	10	13	10	18
9	28	9	10	13	10
6	23	9	9	10	13
11	17	6	9	9	10
9	12	11	6	9	9
10	9	9	11	6	9
9	19	10	9	11	6
16	21	9	10	9	11
10	18	16	9	10	9
7	18	10	16	9	10
7	15	7	10	16	9
14	24	7	7	10	16
11	18	14	7	7	10
10	19	11	14	7	7
6	30	10	11	14	7
8	33	6	10	11	14
13	35	8	6	10	11
12	36	13	8	6	10
15	47	12	13	8	6
16	46	15	12	13	8
16	43	16	15	12	13

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65007&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]4 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=65007&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65007&T=0

As an alternative you can also use a QR Code:  
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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Multiple Linear Regression - Estimated Regression Equation
S.[t] = + 14.3407345050678 + 0.234013754567813E.S[t] + 0.182528854816488`Y(t-1)`[t] + 0.221610208613917`Y(t-2)`[t] -0.0975425120261347`Y(t-3)`[t] -0.103045667145648`Y(T-4)`[t] -1.6722068286102M1[t] -2.94233377172629M2[t] -4.99006069053998M3[t] -1.85789829104282M4[t] -0.0722188170639816M5[t] -1.61978987381349M6[t] -2.58542682860624M7[t] -0.674084410588761M8[t] -1.53170254156695M9[t] -5.87072081026486M10[t] -0.623269007966605M11[t] -0.208277960241533t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
S.[t] =  +  14.3407345050678 +  0.234013754567813E.S[t] +  0.182528854816488`Y(t-1)`[t] +  0.221610208613917`Y(t-2)`[t] -0.0975425120261347`Y(t-3)`[t] -0.103045667145648`Y(T-4)`[t] -1.6722068286102M1[t] -2.94233377172629M2[t] -4.99006069053998M3[t] -1.85789829104282M4[t] -0.0722188170639816M5[t] -1.61978987381349M6[t] -2.58542682860624M7[t] -0.674084410588761M8[t] -1.53170254156695M9[t] -5.87072081026486M10[t] -0.623269007966605M11[t] -0.208277960241533t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65007&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]S.[t] =  +  14.3407345050678 +  0.234013754567813E.S[t] +  0.182528854816488`Y(t-1)`[t] +  0.221610208613917`Y(t-2)`[t] -0.0975425120261347`Y(t-3)`[t] -0.103045667145648`Y(T-4)`[t] -1.6722068286102M1[t] -2.94233377172629M2[t] -4.99006069053998M3[t] -1.85789829104282M4[t] -0.0722188170639816M5[t] -1.61978987381349M6[t] -2.58542682860624M7[t] -0.674084410588761M8[t] -1.53170254156695M9[t] -5.87072081026486M10[t] -0.623269007966605M11[t] -0.208277960241533t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65007&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65007&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Estimated Regression Equation
S.[t] = + 14.3407345050678 + 0.234013754567813E.S[t] + 0.182528854816488`Y(t-1)`[t] + 0.221610208613917`Y(t-2)`[t] -0.0975425120261347`Y(t-3)`[t] -0.103045667145648`Y(T-4)`[t] -1.6722068286102M1[t] -2.94233377172629M2[t] -4.99006069053998M3[t] -1.85789829104282M4[t] -0.0722188170639816M5[t] -1.61978987381349M6[t] -2.58542682860624M7[t] -0.674084410588761M8[t] -1.53170254156695M9[t] -5.87072081026486M10[t] -0.623269007966605M11[t] -0.208277960241533t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)14.34073450506784.0847623.51080.0011450.000572
E.S0.2340137545678130.0481614.8592e-051e-05
`Y(t-1)`0.1825288548164880.1387191.31580.1959170.097958
`Y(t-2)`0.2216102086139170.140961.57210.1239950.061997
`Y(t-3)`-0.09754251202613470.141112-0.69120.4935070.246753
`Y(T-4)`-0.1030456671456480.134927-0.76370.4496340.224817
M1-1.67220682861021.938508-0.86260.3936170.196809
M2-2.942333771726291.976043-1.4890.1445290.072265
M3-4.990060690539981.857959-2.68580.0105740.005287
M4-1.857898291042821.85734-1.00030.3233310.161666
M5-0.07221881706398161.723861-0.04190.9667970.483399
M6-1.619789873813491.835893-0.88230.3830260.191513
M7-2.585426828606241.92103-1.34590.1861220.093061
M8-0.6740844105887611.832372-0.36790.7149550.357478
M9-1.531702541566951.792892-0.85430.3981450.199073
M10-5.870720810264861.929636-3.04240.0041850.002093
M11-0.6232690079666052.051635-0.30380.7629020.381451
t-0.2082779602415330.056308-3.69890.0006660.000333

\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) & 14.3407345050678 & 4.084762 & 3.5108 & 0.001145 & 0.000572 \tabularnewline
E.S & 0.234013754567813 & 0.048161 & 4.859 & 2e-05 & 1e-05 \tabularnewline
`Y(t-1)` & 0.182528854816488 & 0.138719 & 1.3158 & 0.195917 & 0.097958 \tabularnewline
`Y(t-2)` & 0.221610208613917 & 0.14096 & 1.5721 & 0.123995 & 0.061997 \tabularnewline
`Y(t-3)` & -0.0975425120261347 & 0.141112 & -0.6912 & 0.493507 & 0.246753 \tabularnewline
`Y(T-4)` & -0.103045667145648 & 0.134927 & -0.7637 & 0.449634 & 0.224817 \tabularnewline
M1 & -1.6722068286102 & 1.938508 & -0.8626 & 0.393617 & 0.196809 \tabularnewline
M2 & -2.94233377172629 & 1.976043 & -1.489 & 0.144529 & 0.072265 \tabularnewline
M3 & -4.99006069053998 & 1.857959 & -2.6858 & 0.010574 & 0.005287 \tabularnewline
M4 & -1.85789829104282 & 1.85734 & -1.0003 & 0.323331 & 0.161666 \tabularnewline
M5 & -0.0722188170639816 & 1.723861 & -0.0419 & 0.966797 & 0.483399 \tabularnewline
M6 & -1.61978987381349 & 1.835893 & -0.8823 & 0.383026 & 0.191513 \tabularnewline
M7 & -2.58542682860624 & 1.92103 & -1.3459 & 0.186122 & 0.093061 \tabularnewline
M8 & -0.674084410588761 & 1.832372 & -0.3679 & 0.714955 & 0.357478 \tabularnewline
M9 & -1.53170254156695 & 1.792892 & -0.8543 & 0.398145 & 0.199073 \tabularnewline
M10 & -5.87072081026486 & 1.929636 & -3.0424 & 0.004185 & 0.002093 \tabularnewline
M11 & -0.623269007966605 & 2.051635 & -0.3038 & 0.762902 & 0.381451 \tabularnewline
t & -0.208277960241533 & 0.056308 & -3.6989 & 0.000666 & 0.000333 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65007&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]14.3407345050678[/C][C]4.084762[/C][C]3.5108[/C][C]0.001145[/C][C]0.000572[/C][/ROW]
[ROW][C]E.S[/C][C]0.234013754567813[/C][C]0.048161[/C][C]4.859[/C][C]2e-05[/C][C]1e-05[/C][/ROW]
[ROW][C]`Y(t-1)`[/C][C]0.182528854816488[/C][C]0.138719[/C][C]1.3158[/C][C]0.195917[/C][C]0.097958[/C][/ROW]
[ROW][C]`Y(t-2)`[/C][C]0.221610208613917[/C][C]0.14096[/C][C]1.5721[/C][C]0.123995[/C][C]0.061997[/C][/ROW]
[ROW][C]`Y(t-3)`[/C][C]-0.0975425120261347[/C][C]0.141112[/C][C]-0.6912[/C][C]0.493507[/C][C]0.246753[/C][/ROW]
[ROW][C]`Y(T-4)`[/C][C]-0.103045667145648[/C][C]0.134927[/C][C]-0.7637[/C][C]0.449634[/C][C]0.224817[/C][/ROW]
[ROW][C]M1[/C][C]-1.6722068286102[/C][C]1.938508[/C][C]-0.8626[/C][C]0.393617[/C][C]0.196809[/C][/ROW]
[ROW][C]M2[/C][C]-2.94233377172629[/C][C]1.976043[/C][C]-1.489[/C][C]0.144529[/C][C]0.072265[/C][/ROW]
[ROW][C]M3[/C][C]-4.99006069053998[/C][C]1.857959[/C][C]-2.6858[/C][C]0.010574[/C][C]0.005287[/C][/ROW]
[ROW][C]M4[/C][C]-1.85789829104282[/C][C]1.85734[/C][C]-1.0003[/C][C]0.323331[/C][C]0.161666[/C][/ROW]
[ROW][C]M5[/C][C]-0.0722188170639816[/C][C]1.723861[/C][C]-0.0419[/C][C]0.966797[/C][C]0.483399[/C][/ROW]
[ROW][C]M6[/C][C]-1.61978987381349[/C][C]1.835893[/C][C]-0.8823[/C][C]0.383026[/C][C]0.191513[/C][/ROW]
[ROW][C]M7[/C][C]-2.58542682860624[/C][C]1.92103[/C][C]-1.3459[/C][C]0.186122[/C][C]0.093061[/C][/ROW]
[ROW][C]M8[/C][C]-0.674084410588761[/C][C]1.832372[/C][C]-0.3679[/C][C]0.714955[/C][C]0.357478[/C][/ROW]
[ROW][C]M9[/C][C]-1.53170254156695[/C][C]1.792892[/C][C]-0.8543[/C][C]0.398145[/C][C]0.199073[/C][/ROW]
[ROW][C]M10[/C][C]-5.87072081026486[/C][C]1.929636[/C][C]-3.0424[/C][C]0.004185[/C][C]0.002093[/C][/ROW]
[ROW][C]M11[/C][C]-0.623269007966605[/C][C]2.051635[/C][C]-0.3038[/C][C]0.762902[/C][C]0.381451[/C][/ROW]
[ROW][C]t[/C][C]-0.208277960241533[/C][C]0.056308[/C][C]-3.6989[/C][C]0.000666[/C][C]0.000333[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65007&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65007&T=2

As an alternative you can also use a QR Code:  
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)14.34073450506784.0847623.51080.0011450.000572
E.S0.2340137545678130.0481614.8592e-051e-05
`Y(t-1)`0.1825288548164880.1387191.31580.1959170.097958
`Y(t-2)`0.2216102086139170.140961.57210.1239950.061997
`Y(t-3)`-0.09754251202613470.141112-0.69120.4935070.246753
`Y(T-4)`-0.1030456671456480.134927-0.76370.4496340.224817
M1-1.67220682861021.938508-0.86260.3936170.196809
M2-2.942333771726291.976043-1.4890.1445290.072265
M3-4.990060690539981.857959-2.68580.0105740.005287
M4-1.857898291042821.85734-1.00030.3233310.161666
M5-0.07221881706398161.723861-0.04190.9667970.483399
M6-1.619789873813491.835893-0.88230.3830260.191513
M7-2.585426828606241.92103-1.34590.1861220.093061
M8-0.6740844105887611.832372-0.36790.7149550.357478
M9-1.531702541566951.792892-0.85430.3981450.199073
M10-5.870720810264861.929636-3.04240.0041850.002093
M11-0.6232690079666052.051635-0.30380.7629020.381451
t-0.2082779602415330.056308-3.69890.0006660.000333






Multiple Linear Regression - Regression Statistics
Multiple R0.939675191863558
R-squared0.882989466203815
Adjusted R-squared0.831984874549068
F-TEST (value)17.3119603070409
F-TEST (DF numerator)17
F-TEST (DF denominator)39
p-value4.01234601099532e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.52097381474045
Sum Squared Residuals247.857050009673

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.939675191863558 \tabularnewline
R-squared & 0.882989466203815 \tabularnewline
Adjusted R-squared & 0.831984874549068 \tabularnewline
F-TEST (value) & 17.3119603070409 \tabularnewline
F-TEST (DF numerator) & 17 \tabularnewline
F-TEST (DF denominator) & 39 \tabularnewline
p-value & 4.01234601099532e-13 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 2.52097381474045 \tabularnewline
Sum Squared Residuals & 247.857050009673 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65007&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.939675191863558[/C][/ROW]
[ROW][C]R-squared[/C][C]0.882989466203815[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.831984874549068[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]17.3119603070409[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]17[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]39[/C][/ROW]
[ROW][C]p-value[/C][C]4.01234601099532e-13[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]2.52097381474045[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]247.857050009673[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65007&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65007&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Regression Statistics
Multiple R0.939675191863558
R-squared0.882989466203815
Adjusted R-squared0.831984874549068
F-TEST (value)17.3119603070409
F-TEST (DF numerator)17
F-TEST (DF denominator)39
p-value4.01234601099532e-13
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.52097381474045
Sum Squared Residuals247.857050009673






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
12926.65468884466612.34531115533393
22626.7168368232611-0.716836823261103
32623.17160565144052.8283943485595
42122.7058550261912-1.70585502619122
52322.91399771162840.0860022883715736
62220.25626485350211.74373514649791
72121.0008228338489-0.000822833848893367
81620.2797539941923-4.27975399419228
91921.0132334073926-2.01323340739260
101616.1060608790048-0.106060879004820
112522.78929202800142.21070797199860
122725.10685420658641.89314579341360
132325.3353957849665-2.33539578496654
142222.2993090090691-0.299309009069098
152317.85183841237865.1481615876214
162020.9207202116500-0.920720211650043
172423.61792556843180.382074431568217
182322.63490576368790.365094236312106
192021.1844159243865-1.18441592438648
202122.5052780715671-1.50527807156708
212222.0465225801725-0.0465225801725065
221718.0650248633197-1.06502486331971
232120.51863533820840.481364661791596
241921.7591851103649-2.75918511036494
252321.01876409388871.98123590611126
262219.25027121648952.7497287835105
271519.1191769545178-4.11917695451782
282319.89164297849523.10835702150476
292121.2973774684784-0.297377468478387
301821.0331543983909-3.03315439839085
311816.46927452981161.53072547018839
321816.87822804863291.12177195136712
331816.54506458235071.45493541764933
34109.26472654546660.735273454533395
351314.2477520763983-1.24775207639830
361012.9694205105259-2.96942051052588
37912.9225748975468-3.92257489754676
38911.5965758237533-2.59657582375331
3967.93238249788656-1.93238249788656
40119.311277358748921.68872264125108
41910.0694694150335-1.06946941503350
42108.647200003854031.35279999614597
4399.37415551339281-0.374155513392805
441611.26418552242584.73581447757417
451010.6608887648693-0.660888764869333
4676.564187712208860.435812287791136
4778.44432055739189-1.44432055739189
481410.16454017252283.83545982747721
49119.06857637893191.9314236210681
50109.137007127426990.862992872573009
5167.92499648377652-1.92499648377652
52810.1705044249146-2.17050442491458
531312.10122983642790.898770163572101
541212.4284749805651-0.428474980565132
551514.97133119856020.0286688014397883
561616.0725543631819-0.0725543631819249
571614.73429066521491.26570933478511

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 29 & 26.6546888446661 & 2.34531115533393 \tabularnewline
2 & 26 & 26.7168368232611 & -0.716836823261103 \tabularnewline
3 & 26 & 23.1716056514405 & 2.8283943485595 \tabularnewline
4 & 21 & 22.7058550261912 & -1.70585502619122 \tabularnewline
5 & 23 & 22.9139977116284 & 0.0860022883715736 \tabularnewline
6 & 22 & 20.2562648535021 & 1.74373514649791 \tabularnewline
7 & 21 & 21.0008228338489 & -0.000822833848893367 \tabularnewline
8 & 16 & 20.2797539941923 & -4.27975399419228 \tabularnewline
9 & 19 & 21.0132334073926 & -2.01323340739260 \tabularnewline
10 & 16 & 16.1060608790048 & -0.106060879004820 \tabularnewline
11 & 25 & 22.7892920280014 & 2.21070797199860 \tabularnewline
12 & 27 & 25.1068542065864 & 1.89314579341360 \tabularnewline
13 & 23 & 25.3353957849665 & -2.33539578496654 \tabularnewline
14 & 22 & 22.2993090090691 & -0.299309009069098 \tabularnewline
15 & 23 & 17.8518384123786 & 5.1481615876214 \tabularnewline
16 & 20 & 20.9207202116500 & -0.920720211650043 \tabularnewline
17 & 24 & 23.6179255684318 & 0.382074431568217 \tabularnewline
18 & 23 & 22.6349057636879 & 0.365094236312106 \tabularnewline
19 & 20 & 21.1844159243865 & -1.18441592438648 \tabularnewline
20 & 21 & 22.5052780715671 & -1.50527807156708 \tabularnewline
21 & 22 & 22.0465225801725 & -0.0465225801725065 \tabularnewline
22 & 17 & 18.0650248633197 & -1.06502486331971 \tabularnewline
23 & 21 & 20.5186353382084 & 0.481364661791596 \tabularnewline
24 & 19 & 21.7591851103649 & -2.75918511036494 \tabularnewline
25 & 23 & 21.0187640938887 & 1.98123590611126 \tabularnewline
26 & 22 & 19.2502712164895 & 2.7497287835105 \tabularnewline
27 & 15 & 19.1191769545178 & -4.11917695451782 \tabularnewline
28 & 23 & 19.8916429784952 & 3.10835702150476 \tabularnewline
29 & 21 & 21.2973774684784 & -0.297377468478387 \tabularnewline
30 & 18 & 21.0331543983909 & -3.03315439839085 \tabularnewline
31 & 18 & 16.4692745298116 & 1.53072547018839 \tabularnewline
32 & 18 & 16.8782280486329 & 1.12177195136712 \tabularnewline
33 & 18 & 16.5450645823507 & 1.45493541764933 \tabularnewline
34 & 10 & 9.2647265454666 & 0.735273454533395 \tabularnewline
35 & 13 & 14.2477520763983 & -1.24775207639830 \tabularnewline
36 & 10 & 12.9694205105259 & -2.96942051052588 \tabularnewline
37 & 9 & 12.9225748975468 & -3.92257489754676 \tabularnewline
38 & 9 & 11.5965758237533 & -2.59657582375331 \tabularnewline
39 & 6 & 7.93238249788656 & -1.93238249788656 \tabularnewline
40 & 11 & 9.31127735874892 & 1.68872264125108 \tabularnewline
41 & 9 & 10.0694694150335 & -1.06946941503350 \tabularnewline
42 & 10 & 8.64720000385403 & 1.35279999614597 \tabularnewline
43 & 9 & 9.37415551339281 & -0.374155513392805 \tabularnewline
44 & 16 & 11.2641855224258 & 4.73581447757417 \tabularnewline
45 & 10 & 10.6608887648693 & -0.660888764869333 \tabularnewline
46 & 7 & 6.56418771220886 & 0.435812287791136 \tabularnewline
47 & 7 & 8.44432055739189 & -1.44432055739189 \tabularnewline
48 & 14 & 10.1645401725228 & 3.83545982747721 \tabularnewline
49 & 11 & 9.0685763789319 & 1.9314236210681 \tabularnewline
50 & 10 & 9.13700712742699 & 0.862992872573009 \tabularnewline
51 & 6 & 7.92499648377652 & -1.92499648377652 \tabularnewline
52 & 8 & 10.1705044249146 & -2.17050442491458 \tabularnewline
53 & 13 & 12.1012298364279 & 0.898770163572101 \tabularnewline
54 & 12 & 12.4284749805651 & -0.428474980565132 \tabularnewline
55 & 15 & 14.9713311985602 & 0.0286688014397883 \tabularnewline
56 & 16 & 16.0725543631819 & -0.0725543631819249 \tabularnewline
57 & 16 & 14.7342906652149 & 1.26570933478511 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65007&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]29[/C][C]26.6546888446661[/C][C]2.34531115533393[/C][/ROW]
[ROW][C]2[/C][C]26[/C][C]26.7168368232611[/C][C]-0.716836823261103[/C][/ROW]
[ROW][C]3[/C][C]26[/C][C]23.1716056514405[/C][C]2.8283943485595[/C][/ROW]
[ROW][C]4[/C][C]21[/C][C]22.7058550261912[/C][C]-1.70585502619122[/C][/ROW]
[ROW][C]5[/C][C]23[/C][C]22.9139977116284[/C][C]0.0860022883715736[/C][/ROW]
[ROW][C]6[/C][C]22[/C][C]20.2562648535021[/C][C]1.74373514649791[/C][/ROW]
[ROW][C]7[/C][C]21[/C][C]21.0008228338489[/C][C]-0.000822833848893367[/C][/ROW]
[ROW][C]8[/C][C]16[/C][C]20.2797539941923[/C][C]-4.27975399419228[/C][/ROW]
[ROW][C]9[/C][C]19[/C][C]21.0132334073926[/C][C]-2.01323340739260[/C][/ROW]
[ROW][C]10[/C][C]16[/C][C]16.1060608790048[/C][C]-0.106060879004820[/C][/ROW]
[ROW][C]11[/C][C]25[/C][C]22.7892920280014[/C][C]2.21070797199860[/C][/ROW]
[ROW][C]12[/C][C]27[/C][C]25.1068542065864[/C][C]1.89314579341360[/C][/ROW]
[ROW][C]13[/C][C]23[/C][C]25.3353957849665[/C][C]-2.33539578496654[/C][/ROW]
[ROW][C]14[/C][C]22[/C][C]22.2993090090691[/C][C]-0.299309009069098[/C][/ROW]
[ROW][C]15[/C][C]23[/C][C]17.8518384123786[/C][C]5.1481615876214[/C][/ROW]
[ROW][C]16[/C][C]20[/C][C]20.9207202116500[/C][C]-0.920720211650043[/C][/ROW]
[ROW][C]17[/C][C]24[/C][C]23.6179255684318[/C][C]0.382074431568217[/C][/ROW]
[ROW][C]18[/C][C]23[/C][C]22.6349057636879[/C][C]0.365094236312106[/C][/ROW]
[ROW][C]19[/C][C]20[/C][C]21.1844159243865[/C][C]-1.18441592438648[/C][/ROW]
[ROW][C]20[/C][C]21[/C][C]22.5052780715671[/C][C]-1.50527807156708[/C][/ROW]
[ROW][C]21[/C][C]22[/C][C]22.0465225801725[/C][C]-0.0465225801725065[/C][/ROW]
[ROW][C]22[/C][C]17[/C][C]18.0650248633197[/C][C]-1.06502486331971[/C][/ROW]
[ROW][C]23[/C][C]21[/C][C]20.5186353382084[/C][C]0.481364661791596[/C][/ROW]
[ROW][C]24[/C][C]19[/C][C]21.7591851103649[/C][C]-2.75918511036494[/C][/ROW]
[ROW][C]25[/C][C]23[/C][C]21.0187640938887[/C][C]1.98123590611126[/C][/ROW]
[ROW][C]26[/C][C]22[/C][C]19.2502712164895[/C][C]2.7497287835105[/C][/ROW]
[ROW][C]27[/C][C]15[/C][C]19.1191769545178[/C][C]-4.11917695451782[/C][/ROW]
[ROW][C]28[/C][C]23[/C][C]19.8916429784952[/C][C]3.10835702150476[/C][/ROW]
[ROW][C]29[/C][C]21[/C][C]21.2973774684784[/C][C]-0.297377468478387[/C][/ROW]
[ROW][C]30[/C][C]18[/C][C]21.0331543983909[/C][C]-3.03315439839085[/C][/ROW]
[ROW][C]31[/C][C]18[/C][C]16.4692745298116[/C][C]1.53072547018839[/C][/ROW]
[ROW][C]32[/C][C]18[/C][C]16.8782280486329[/C][C]1.12177195136712[/C][/ROW]
[ROW][C]33[/C][C]18[/C][C]16.5450645823507[/C][C]1.45493541764933[/C][/ROW]
[ROW][C]34[/C][C]10[/C][C]9.2647265454666[/C][C]0.735273454533395[/C][/ROW]
[ROW][C]35[/C][C]13[/C][C]14.2477520763983[/C][C]-1.24775207639830[/C][/ROW]
[ROW][C]36[/C][C]10[/C][C]12.9694205105259[/C][C]-2.96942051052588[/C][/ROW]
[ROW][C]37[/C][C]9[/C][C]12.9225748975468[/C][C]-3.92257489754676[/C][/ROW]
[ROW][C]38[/C][C]9[/C][C]11.5965758237533[/C][C]-2.59657582375331[/C][/ROW]
[ROW][C]39[/C][C]6[/C][C]7.93238249788656[/C][C]-1.93238249788656[/C][/ROW]
[ROW][C]40[/C][C]11[/C][C]9.31127735874892[/C][C]1.68872264125108[/C][/ROW]
[ROW][C]41[/C][C]9[/C][C]10.0694694150335[/C][C]-1.06946941503350[/C][/ROW]
[ROW][C]42[/C][C]10[/C][C]8.64720000385403[/C][C]1.35279999614597[/C][/ROW]
[ROW][C]43[/C][C]9[/C][C]9.37415551339281[/C][C]-0.374155513392805[/C][/ROW]
[ROW][C]44[/C][C]16[/C][C]11.2641855224258[/C][C]4.73581447757417[/C][/ROW]
[ROW][C]45[/C][C]10[/C][C]10.6608887648693[/C][C]-0.660888764869333[/C][/ROW]
[ROW][C]46[/C][C]7[/C][C]6.56418771220886[/C][C]0.435812287791136[/C][/ROW]
[ROW][C]47[/C][C]7[/C][C]8.44432055739189[/C][C]-1.44432055739189[/C][/ROW]
[ROW][C]48[/C][C]14[/C][C]10.1645401725228[/C][C]3.83545982747721[/C][/ROW]
[ROW][C]49[/C][C]11[/C][C]9.0685763789319[/C][C]1.9314236210681[/C][/ROW]
[ROW][C]50[/C][C]10[/C][C]9.13700712742699[/C][C]0.862992872573009[/C][/ROW]
[ROW][C]51[/C][C]6[/C][C]7.92499648377652[/C][C]-1.92499648377652[/C][/ROW]
[ROW][C]52[/C][C]8[/C][C]10.1705044249146[/C][C]-2.17050442491458[/C][/ROW]
[ROW][C]53[/C][C]13[/C][C]12.1012298364279[/C][C]0.898770163572101[/C][/ROW]
[ROW][C]54[/C][C]12[/C][C]12.4284749805651[/C][C]-0.428474980565132[/C][/ROW]
[ROW][C]55[/C][C]15[/C][C]14.9713311985602[/C][C]0.0286688014397883[/C][/ROW]
[ROW][C]56[/C][C]16[/C][C]16.0725543631819[/C][C]-0.0725543631819249[/C][/ROW]
[ROW][C]57[/C][C]16[/C][C]14.7342906652149[/C][C]1.26570933478511[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65007&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65007&T=4

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
12926.65468884466612.34531115533393
22626.7168368232611-0.716836823261103
32623.17160565144052.8283943485595
42122.7058550261912-1.70585502619122
52322.91399771162840.0860022883715736
62220.25626485350211.74373514649791
72121.0008228338489-0.000822833848893367
81620.2797539941923-4.27975399419228
91921.0132334073926-2.01323340739260
101616.1060608790048-0.106060879004820
112522.78929202800142.21070797199860
122725.10685420658641.89314579341360
132325.3353957849665-2.33539578496654
142222.2993090090691-0.299309009069098
152317.85183841237865.1481615876214
162020.9207202116500-0.920720211650043
172423.61792556843180.382074431568217
182322.63490576368790.365094236312106
192021.1844159243865-1.18441592438648
202122.5052780715671-1.50527807156708
212222.0465225801725-0.0465225801725065
221718.0650248633197-1.06502486331971
232120.51863533820840.481364661791596
241921.7591851103649-2.75918511036494
252321.01876409388871.98123590611126
262219.25027121648952.7497287835105
271519.1191769545178-4.11917695451782
282319.89164297849523.10835702150476
292121.2973774684784-0.297377468478387
301821.0331543983909-3.03315439839085
311816.46927452981161.53072547018839
321816.87822804863291.12177195136712
331816.54506458235071.45493541764933
34109.26472654546660.735273454533395
351314.2477520763983-1.24775207639830
361012.9694205105259-2.96942051052588
37912.9225748975468-3.92257489754676
38911.5965758237533-2.59657582375331
3967.93238249788656-1.93238249788656
40119.311277358748921.68872264125108
41910.0694694150335-1.06946941503350
42108.647200003854031.35279999614597
4399.37415551339281-0.374155513392805
441611.26418552242584.73581447757417
451010.6608887648693-0.660888764869333
4676.564187712208860.435812287791136
4778.44432055739189-1.44432055739189
481410.16454017252283.83545982747721
49119.06857637893191.9314236210681
50109.137007127426990.862992872573009
5167.92499648377652-1.92499648377652
52810.1705044249146-2.17050442491458
531312.10122983642790.898770163572101
541212.4284749805651-0.428474980565132
551514.97133119856020.0286688014397883
561616.0725543631819-0.0725543631819249
571614.73429066521491.26570933478511






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.07422619205875460.1484523841175090.925773807941245
220.02726686892672980.05453373785345960.97273313107327
230.02689872347286170.05379744694572340.973101276527138
240.1849565058982140.3699130117964270.815043494101786
250.1450646455256470.2901292910512940.854935354474353
260.1685353436661310.3370706873322620.831464656333869
270.5168388139785420.9663223720429170.483161186021458
280.6052951423527720.7894097152944560.394704857647228
290.5628107726456090.8743784547087820.437189227354391
300.4485904888941840.8971809777883680.551409511105816
310.4239529201525330.8479058403050660.576047079847467
320.3942130326582690.7884260653165370.605786967341731
330.4404222900029270.8808445800058540.559577709997073
340.5138977764096350.972204447180730.486102223590365
350.6436308629228170.7127382741543670.356369137077183
360.5792349226109780.8415301547780440.420765077389022

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
21 & 0.0742261920587546 & 0.148452384117509 & 0.925773807941245 \tabularnewline
22 & 0.0272668689267298 & 0.0545337378534596 & 0.97273313107327 \tabularnewline
23 & 0.0268987234728617 & 0.0537974469457234 & 0.973101276527138 \tabularnewline
24 & 0.184956505898214 & 0.369913011796427 & 0.815043494101786 \tabularnewline
25 & 0.145064645525647 & 0.290129291051294 & 0.854935354474353 \tabularnewline
26 & 0.168535343666131 & 0.337070687332262 & 0.831464656333869 \tabularnewline
27 & 0.516838813978542 & 0.966322372042917 & 0.483161186021458 \tabularnewline
28 & 0.605295142352772 & 0.789409715294456 & 0.394704857647228 \tabularnewline
29 & 0.562810772645609 & 0.874378454708782 & 0.437189227354391 \tabularnewline
30 & 0.448590488894184 & 0.897180977788368 & 0.551409511105816 \tabularnewline
31 & 0.423952920152533 & 0.847905840305066 & 0.576047079847467 \tabularnewline
32 & 0.394213032658269 & 0.788426065316537 & 0.605786967341731 \tabularnewline
33 & 0.440422290002927 & 0.880844580005854 & 0.559577709997073 \tabularnewline
34 & 0.513897776409635 & 0.97220444718073 & 0.486102223590365 \tabularnewline
35 & 0.643630862922817 & 0.712738274154367 & 0.356369137077183 \tabularnewline
36 & 0.579234922610978 & 0.841530154778044 & 0.420765077389022 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65007&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]21[/C][C]0.0742261920587546[/C][C]0.148452384117509[/C][C]0.925773807941245[/C][/ROW]
[ROW][C]22[/C][C]0.0272668689267298[/C][C]0.0545337378534596[/C][C]0.97273313107327[/C][/ROW]
[ROW][C]23[/C][C]0.0268987234728617[/C][C]0.0537974469457234[/C][C]0.973101276527138[/C][/ROW]
[ROW][C]24[/C][C]0.184956505898214[/C][C]0.369913011796427[/C][C]0.815043494101786[/C][/ROW]
[ROW][C]25[/C][C]0.145064645525647[/C][C]0.290129291051294[/C][C]0.854935354474353[/C][/ROW]
[ROW][C]26[/C][C]0.168535343666131[/C][C]0.337070687332262[/C][C]0.831464656333869[/C][/ROW]
[ROW][C]27[/C][C]0.516838813978542[/C][C]0.966322372042917[/C][C]0.483161186021458[/C][/ROW]
[ROW][C]28[/C][C]0.605295142352772[/C][C]0.789409715294456[/C][C]0.394704857647228[/C][/ROW]
[ROW][C]29[/C][C]0.562810772645609[/C][C]0.874378454708782[/C][C]0.437189227354391[/C][/ROW]
[ROW][C]30[/C][C]0.448590488894184[/C][C]0.897180977788368[/C][C]0.551409511105816[/C][/ROW]
[ROW][C]31[/C][C]0.423952920152533[/C][C]0.847905840305066[/C][C]0.576047079847467[/C][/ROW]
[ROW][C]32[/C][C]0.394213032658269[/C][C]0.788426065316537[/C][C]0.605786967341731[/C][/ROW]
[ROW][C]33[/C][C]0.440422290002927[/C][C]0.880844580005854[/C][C]0.559577709997073[/C][/ROW]
[ROW][C]34[/C][C]0.513897776409635[/C][C]0.97220444718073[/C][C]0.486102223590365[/C][/ROW]
[ROW][C]35[/C][C]0.643630862922817[/C][C]0.712738274154367[/C][C]0.356369137077183[/C][/ROW]
[ROW][C]36[/C][C]0.579234922610978[/C][C]0.841530154778044[/C][C]0.420765077389022[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65007&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65007&T=5

As an alternative you can also use a QR Code:  
QR Code


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
210.07422619205875460.1484523841175090.925773807941245
220.02726686892672980.05453373785345960.97273313107327
230.02689872347286170.05379744694572340.973101276527138
240.1849565058982140.3699130117964270.815043494101786
250.1450646455256470.2901292910512940.854935354474353
260.1685353436661310.3370706873322620.831464656333869
270.5168388139785420.9663223720429170.483161186021458
280.6052951423527720.7894097152944560.394704857647228
290.5628107726456090.8743784547087820.437189227354391
300.4485904888941840.8971809777883680.551409511105816
310.4239529201525330.8479058403050660.576047079847467
320.3942130326582690.7884260653165370.605786967341731
330.4404222900029270.8808445800058540.559577709997073
340.5138977764096350.972204447180730.486102223590365
350.6436308629228170.7127382741543670.356369137077183
360.5792349226109780.8415301547780440.420765077389022






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 level20.125NOK

\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 & 2 & 0.125 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65007&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]2[/C][C]0.125[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65007&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65007&T=6

As an alternative you can also use a QR Code:  
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 level20.125NOK


Figures (Output of Computation)

Figure 1
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Figure 10
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Input Parameters & R Code

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')
}