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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 computationTue, 24 Nov 2009 13:45:36 -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/24/t1259095580oo7ab03s8tdojwv.htm/, Retrieved Thu, 26 Jun 2025 13:39:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59273, Retrieved Thu, 26 Jun 2025 13:39:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact298

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] [] [2009-11-20 13:13:49] [badc6a9acdc45286bea7f74742e15a21]
-   PD      [Multiple Regression] [] [2009-11-20 13:28:34] [2c5be225250d91402426bbbf07a5e2b3]
-   PD          [Multiple Regression] [4e multiple ] [2009-11-24 20:45:36] [244731fa3e7e6c85774b8c0902c58f85] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2,40	2,00	1,70	1,00	1,20	1,40
2,00	2,00	2,40	1,70	1,00	1,20
2,10	2,00	2,00	2,40	1,70	1,00
2,00	2,00	2,10	2,00	2,40	1,70
1,80	2,00	2,00	2,10	2,00	2,40
2,70	2,00	1,80	2,00	2,10	2,00
2,30	2,00	2,70	1,80	2,00	2,10
1,90	2,00	2,30	2,70	1,80	2,00
2,00	2,00	1,90	2,30	2,70	1,80
2,30	2,00	2,00	1,90	2,30	2,70
2,80	2,00	2,30	2,00	1,90	2,30
2,40	2,00	2,80	2,30	2,00	1,90
2,30	2,00	2,40	2,80	2,30	2,00
2,70	2,00	2,30	2,40	2,80	2,30
2,70	2,00	2,70	2,30	2,40	2,80
2,90	2,00	2,70	2,70	2,30	2,40
3,00	2,00	2,90	2,70	2,70	2,30
2,20	2,00	3,00	2,90	2,70	2,70
2,30	2,00	2,20	3,00	2,90	2,70
2,80	2,21	2,30	2,20	3,00	2,90
2,80	2,25	2,80	2,30	2,20	3,00
2,80	2,25	2,80	2,80	2,30	2,20
2,20	2,45	2,80	2,80	2,80	2,30
2,60	2,50	2,20	2,80	2,80	2,80
2,80	2,50	2,60	2,20	2,80	2,80
2,50	2,64	2,80	2,60	2,20	2,80
2,40	2,75	2,50	2,80	2,60	2,20
2,30	2,93	2,40	2,50	2,80	2,60
1,90	3,00	2,30	2,40	2,50	2,80
1,70	3,17	1,90	2,30	2,40	2,50
2,00	3,25	1,70	1,90	2,30	2,40
2,10	3,39	2,00	1,70	1,90	2,30
1,70	3,50	2,10	2,00	1,70	1,90
1,80	3,50	1,70	2,10	2,00	1,70
1,80	3,65	1,80	1,70	2,10	2,00
1,80	3,75	1,80	1,80	1,70	2,10
1,30	3,75	1,80	1,80	1,80	1,70
1,30	3,90	1,30	1,80	1,80	1,80
1,30	4,00	1,30	1,30	1,80	1,80
1,20	4,00	1,30	1,30	1,30	1,80
1,40	4,00	1,20	1,30	1,30	1,30
2,20	4,00	1,40	1,20	1,30	1,30
2,90	4,00	2,20	1,40	1,20	1,30
3,10	4,00	2,90	2,20	1,40	1,20
3,50	4,00	3,10	2,90	2,20	1,40
3,60	4,00	3,50	3,10	2,90	2,20
4,40	4,00	3,60	3,50	3,10	2,90
4,10	4,00	4,40	3,60	3,50	3,10
5,10	4,00	4,10	4,40	3,60	3,50
5,80	4,00	5,10	4,10	4,40	3,60
5,90	4,18	5,80	5,10	4,10	4,40
5,40	4,25	5,90	5,80	5,10	4,10
5,50	4,25	5,40	5,90	5,80	5,10
4,80	3,97	5,50	5,40	5,90	5,80
3,20	3,42	4,80	5,50	5,40	5,90
2,70	2,75	3,20	4,80	5,50	5,40

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=59273&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=59273&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59273&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
X1[t] = + 0.185036980311549 + 0.073579736810377X2[t] + 1.11584285808511X3[t] -0.256942291868568X4[t] + 0.278431112422916X5[t] -0.293078735356719X6[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
X1[t] =  +  0.185036980311549 +  0.073579736810377X2[t] +  1.11584285808511X3[t] -0.256942291868568X4[t] +  0.278431112422916X5[t] -0.293078735356719X6[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59273&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]X1[t] =  +  0.185036980311549 +  0.073579736810377X2[t] +  1.11584285808511X3[t] -0.256942291868568X4[t] +  0.278431112422916X5[t] -0.293078735356719X6[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59273&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59273&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
X1[t] = + 0.185036980311549 + 0.073579736810377X2[t] + 1.11584285808511X3[t] -0.256942291868568X4[t] + 0.278431112422916X5[t] -0.293078735356719X6[t] + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)0.1850369803115490.2316570.79880.4282110.214106
X20.0735797368103770.072531.01450.3152430.157621
X31.115842858085110.135428.239900
X4-0.2569422918685680.207051-1.2410.2204110.110206
X50.2784311124229160.2111571.31860.1933120.096656
X6-0.2930787353567190.156309-1.8750.066640.03332

\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) & 0.185036980311549 & 0.231657 & 0.7988 & 0.428211 & 0.214106 \tabularnewline
X2 & 0.073579736810377 & 0.07253 & 1.0145 & 0.315243 & 0.157621 \tabularnewline
X3 & 1.11584285808511 & 0.13542 & 8.2399 & 0 & 0 \tabularnewline
X4 & -0.256942291868568 & 0.207051 & -1.241 & 0.220411 & 0.110206 \tabularnewline
X5 & 0.278431112422916 & 0.211157 & 1.3186 & 0.193312 & 0.096656 \tabularnewline
X6 & -0.293078735356719 & 0.156309 & -1.875 & 0.06664 & 0.03332 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59273&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]0.185036980311549[/C][C]0.231657[/C][C]0.7988[/C][C]0.428211[/C][C]0.214106[/C][/ROW]
[ROW][C]X2[/C][C]0.073579736810377[/C][C]0.07253[/C][C]1.0145[/C][C]0.315243[/C][C]0.157621[/C][/ROW]
[ROW][C]X3[/C][C]1.11584285808511[/C][C]0.13542[/C][C]8.2399[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X4[/C][C]-0.256942291868568[/C][C]0.207051[/C][C]-1.241[/C][C]0.220411[/C][C]0.110206[/C][/ROW]
[ROW][C]X5[/C][C]0.278431112422916[/C][C]0.211157[/C][C]1.3186[/C][C]0.193312[/C][C]0.096656[/C][/ROW]
[ROW][C]X6[/C][C]-0.293078735356719[/C][C]0.156309[/C][C]-1.875[/C][C]0.06664[/C][C]0.03332[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59273&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59273&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)0.1850369803115490.2316570.79880.4282110.214106
X20.0735797368103770.072531.01450.3152430.157621
X31.115842858085110.135428.239900
X4-0.2569422918685680.207051-1.2410.2204110.110206
X50.2784311124229160.2111571.31860.1933120.096656
X6-0.2930787353567190.156309-1.8750.066640.03332






Multiple Linear Regression - Regression Statistics
Multiple R0.930382067608297
R-squared0.86561079172709
Adjusted R-squared0.8521718708998
F-TEST (value)64.4107367586582
F-TEST (DF numerator)5
F-TEST (DF denominator)50
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.442858093411831
Sum Squared Residuals9.8061645450181

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.930382067608297 \tabularnewline
R-squared & 0.86561079172709 \tabularnewline
Adjusted R-squared & 0.8521718708998 \tabularnewline
F-TEST (value) & 64.4107367586582 \tabularnewline
F-TEST (DF numerator) & 5 \tabularnewline
F-TEST (DF denominator) & 50 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.442858093411831 \tabularnewline
Sum Squared Residuals & 9.8061645450181 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59273&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.930382067608297[/C][/ROW]
[ROW][C]R-squared[/C][C]0.86561079172709[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.8521718708998[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]64.4107367586582[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]5[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]50[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.442858093411831[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]9.8061645450181[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59273&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59273&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 R0.930382067608297
R-squared0.86561079172709
Adjusted R-squared0.8521718708998
F-TEST (value)64.4107367586582
F-TEST (DF numerator)5
F-TEST (DF denominator)50
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.442858093411831
Sum Squared Residuals9.8061645450181






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
12.41.895994126216500.504005873783495
222.50015404715485-0.500154047154846
32.12.12747482538019-0.0274748253801892
422.33158269188247-0.331582691882465
51.81.87777661716823-0.077776617168228
62.71.825376880123040.874623119876957
72.32.82387292599539-0.523872925995388
81.92.11990937113072-0.219909371130724
922.08555289289608-0.0855528928960763
102.31.92477078866180.375229211338199
112.82.239688466074000.560311533926003
122.42.86560181294096-0.465601812940959
132.32.34501498396384-0.0450149839638354
142.72.387499550507190.312500449492806
152.72.601619110280570.0983808897194326
162.92.588230576433540.311769423566464
1732.952079466555400.0479205334446046
182.22.89504379984750-0.695043799847505
192.32.032361506677150.267638493322853
202.82.334178734881640.465821265118362
212.82.617296360735740.182703639264255
222.82.751131314329130.0488686856708722
232.22.87575494436699-0.675754944366989
242.62.063388848678090.536611151321915
252.82.663891367033270.136108632966732
262.52.62752551760257-0.127525517602565
272.42.53669765903566-0.136697659035659
282.32.45389514175548-0.153895141755482
291.92.23101058591234-0.331010585912336
301.71.88295673648764-0.182956736487639
3121.769916222856260.230083777143744
322.12.084294130375460.0157058696245409
331.72.18843477133064-0.488434771330645
341.81.85854847970796-0.0585484797079644
351.82.02386613342073-0.223866133420735
361.81.86484955941008-0.0648495594100774
371.32.00992416479506-0.709924164795057
381.31.43373182273839-0.133731822738388
391.31.56956094235371-0.26956094235371
401.21.43034538614225-0.230345386142252
411.41.4653004680121-0.0653004680121008
422.21.714163268815980.485836731184022
432.92.527605985668060.372394014331942
443.13.18813624885303-0.0881362488530329
453.53.395574359029050.104425640970954
463.63.75096183430004-0.15096183430004
474.43.6103003110960.789699688903997
484.14.53003706627505-0.430037066275055
495.13.900341992454271.19965800754573
505.85.286704554502610.513295445497391
515.95.506104293907230.393895706092768
525.45.8093342900144-0.409334290014404
535.55.127541675124320.372458324875683
544.85.16968277705279-0.369682777052794
553.24.15390626221353-0.953906262213525
562.72.673501348843050.0264986511569475

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 2.4 & 1.89599412621650 & 0.504005873783495 \tabularnewline
2 & 2 & 2.50015404715485 & -0.500154047154846 \tabularnewline
3 & 2.1 & 2.12747482538019 & -0.0274748253801892 \tabularnewline
4 & 2 & 2.33158269188247 & -0.331582691882465 \tabularnewline
5 & 1.8 & 1.87777661716823 & -0.077776617168228 \tabularnewline
6 & 2.7 & 1.82537688012304 & 0.874623119876957 \tabularnewline
7 & 2.3 & 2.82387292599539 & -0.523872925995388 \tabularnewline
8 & 1.9 & 2.11990937113072 & -0.219909371130724 \tabularnewline
9 & 2 & 2.08555289289608 & -0.0855528928960763 \tabularnewline
10 & 2.3 & 1.9247707886618 & 0.375229211338199 \tabularnewline
11 & 2.8 & 2.23968846607400 & 0.560311533926003 \tabularnewline
12 & 2.4 & 2.86560181294096 & -0.465601812940959 \tabularnewline
13 & 2.3 & 2.34501498396384 & -0.0450149839638354 \tabularnewline
14 & 2.7 & 2.38749955050719 & 0.312500449492806 \tabularnewline
15 & 2.7 & 2.60161911028057 & 0.0983808897194326 \tabularnewline
16 & 2.9 & 2.58823057643354 & 0.311769423566464 \tabularnewline
17 & 3 & 2.95207946655540 & 0.0479205334446046 \tabularnewline
18 & 2.2 & 2.89504379984750 & -0.695043799847505 \tabularnewline
19 & 2.3 & 2.03236150667715 & 0.267638493322853 \tabularnewline
20 & 2.8 & 2.33417873488164 & 0.465821265118362 \tabularnewline
21 & 2.8 & 2.61729636073574 & 0.182703639264255 \tabularnewline
22 & 2.8 & 2.75113131432913 & 0.0488686856708722 \tabularnewline
23 & 2.2 & 2.87575494436699 & -0.675754944366989 \tabularnewline
24 & 2.6 & 2.06338884867809 & 0.536611151321915 \tabularnewline
25 & 2.8 & 2.66389136703327 & 0.136108632966732 \tabularnewline
26 & 2.5 & 2.62752551760257 & -0.127525517602565 \tabularnewline
27 & 2.4 & 2.53669765903566 & -0.136697659035659 \tabularnewline
28 & 2.3 & 2.45389514175548 & -0.153895141755482 \tabularnewline
29 & 1.9 & 2.23101058591234 & -0.331010585912336 \tabularnewline
30 & 1.7 & 1.88295673648764 & -0.182956736487639 \tabularnewline
31 & 2 & 1.76991622285626 & 0.230083777143744 \tabularnewline
32 & 2.1 & 2.08429413037546 & 0.0157058696245409 \tabularnewline
33 & 1.7 & 2.18843477133064 & -0.488434771330645 \tabularnewline
34 & 1.8 & 1.85854847970796 & -0.0585484797079644 \tabularnewline
35 & 1.8 & 2.02386613342073 & -0.223866133420735 \tabularnewline
36 & 1.8 & 1.86484955941008 & -0.0648495594100774 \tabularnewline
37 & 1.3 & 2.00992416479506 & -0.709924164795057 \tabularnewline
38 & 1.3 & 1.43373182273839 & -0.133731822738388 \tabularnewline
39 & 1.3 & 1.56956094235371 & -0.26956094235371 \tabularnewline
40 & 1.2 & 1.43034538614225 & -0.230345386142252 \tabularnewline
41 & 1.4 & 1.4653004680121 & -0.0653004680121008 \tabularnewline
42 & 2.2 & 1.71416326881598 & 0.485836731184022 \tabularnewline
43 & 2.9 & 2.52760598566806 & 0.372394014331942 \tabularnewline
44 & 3.1 & 3.18813624885303 & -0.0881362488530329 \tabularnewline
45 & 3.5 & 3.39557435902905 & 0.104425640970954 \tabularnewline
46 & 3.6 & 3.75096183430004 & -0.15096183430004 \tabularnewline
47 & 4.4 & 3.610300311096 & 0.789699688903997 \tabularnewline
48 & 4.1 & 4.53003706627505 & -0.430037066275055 \tabularnewline
49 & 5.1 & 3.90034199245427 & 1.19965800754573 \tabularnewline
50 & 5.8 & 5.28670455450261 & 0.513295445497391 \tabularnewline
51 & 5.9 & 5.50610429390723 & 0.393895706092768 \tabularnewline
52 & 5.4 & 5.8093342900144 & -0.409334290014404 \tabularnewline
53 & 5.5 & 5.12754167512432 & 0.372458324875683 \tabularnewline
54 & 4.8 & 5.16968277705279 & -0.369682777052794 \tabularnewline
55 & 3.2 & 4.15390626221353 & -0.953906262213525 \tabularnewline
56 & 2.7 & 2.67350134884305 & 0.0264986511569475 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59273&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]2.4[/C][C]1.89599412621650[/C][C]0.504005873783495[/C][/ROW]
[ROW][C]2[/C][C]2[/C][C]2.50015404715485[/C][C]-0.500154047154846[/C][/ROW]
[ROW][C]3[/C][C]2.1[/C][C]2.12747482538019[/C][C]-0.0274748253801892[/C][/ROW]
[ROW][C]4[/C][C]2[/C][C]2.33158269188247[/C][C]-0.331582691882465[/C][/ROW]
[ROW][C]5[/C][C]1.8[/C][C]1.87777661716823[/C][C]-0.077776617168228[/C][/ROW]
[ROW][C]6[/C][C]2.7[/C][C]1.82537688012304[/C][C]0.874623119876957[/C][/ROW]
[ROW][C]7[/C][C]2.3[/C][C]2.82387292599539[/C][C]-0.523872925995388[/C][/ROW]
[ROW][C]8[/C][C]1.9[/C][C]2.11990937113072[/C][C]-0.219909371130724[/C][/ROW]
[ROW][C]9[/C][C]2[/C][C]2.08555289289608[/C][C]-0.0855528928960763[/C][/ROW]
[ROW][C]10[/C][C]2.3[/C][C]1.9247707886618[/C][C]0.375229211338199[/C][/ROW]
[ROW][C]11[/C][C]2.8[/C][C]2.23968846607400[/C][C]0.560311533926003[/C][/ROW]
[ROW][C]12[/C][C]2.4[/C][C]2.86560181294096[/C][C]-0.465601812940959[/C][/ROW]
[ROW][C]13[/C][C]2.3[/C][C]2.34501498396384[/C][C]-0.0450149839638354[/C][/ROW]
[ROW][C]14[/C][C]2.7[/C][C]2.38749955050719[/C][C]0.312500449492806[/C][/ROW]
[ROW][C]15[/C][C]2.7[/C][C]2.60161911028057[/C][C]0.0983808897194326[/C][/ROW]
[ROW][C]16[/C][C]2.9[/C][C]2.58823057643354[/C][C]0.311769423566464[/C][/ROW]
[ROW][C]17[/C][C]3[/C][C]2.95207946655540[/C][C]0.0479205334446046[/C][/ROW]
[ROW][C]18[/C][C]2.2[/C][C]2.89504379984750[/C][C]-0.695043799847505[/C][/ROW]
[ROW][C]19[/C][C]2.3[/C][C]2.03236150667715[/C][C]0.267638493322853[/C][/ROW]
[ROW][C]20[/C][C]2.8[/C][C]2.33417873488164[/C][C]0.465821265118362[/C][/ROW]
[ROW][C]21[/C][C]2.8[/C][C]2.61729636073574[/C][C]0.182703639264255[/C][/ROW]
[ROW][C]22[/C][C]2.8[/C][C]2.75113131432913[/C][C]0.0488686856708722[/C][/ROW]
[ROW][C]23[/C][C]2.2[/C][C]2.87575494436699[/C][C]-0.675754944366989[/C][/ROW]
[ROW][C]24[/C][C]2.6[/C][C]2.06338884867809[/C][C]0.536611151321915[/C][/ROW]
[ROW][C]25[/C][C]2.8[/C][C]2.66389136703327[/C][C]0.136108632966732[/C][/ROW]
[ROW][C]26[/C][C]2.5[/C][C]2.62752551760257[/C][C]-0.127525517602565[/C][/ROW]
[ROW][C]27[/C][C]2.4[/C][C]2.53669765903566[/C][C]-0.136697659035659[/C][/ROW]
[ROW][C]28[/C][C]2.3[/C][C]2.45389514175548[/C][C]-0.153895141755482[/C][/ROW]
[ROW][C]29[/C][C]1.9[/C][C]2.23101058591234[/C][C]-0.331010585912336[/C][/ROW]
[ROW][C]30[/C][C]1.7[/C][C]1.88295673648764[/C][C]-0.182956736487639[/C][/ROW]
[ROW][C]31[/C][C]2[/C][C]1.76991622285626[/C][C]0.230083777143744[/C][/ROW]
[ROW][C]32[/C][C]2.1[/C][C]2.08429413037546[/C][C]0.0157058696245409[/C][/ROW]
[ROW][C]33[/C][C]1.7[/C][C]2.18843477133064[/C][C]-0.488434771330645[/C][/ROW]
[ROW][C]34[/C][C]1.8[/C][C]1.85854847970796[/C][C]-0.0585484797079644[/C][/ROW]
[ROW][C]35[/C][C]1.8[/C][C]2.02386613342073[/C][C]-0.223866133420735[/C][/ROW]
[ROW][C]36[/C][C]1.8[/C][C]1.86484955941008[/C][C]-0.0648495594100774[/C][/ROW]
[ROW][C]37[/C][C]1.3[/C][C]2.00992416479506[/C][C]-0.709924164795057[/C][/ROW]
[ROW][C]38[/C][C]1.3[/C][C]1.43373182273839[/C][C]-0.133731822738388[/C][/ROW]
[ROW][C]39[/C][C]1.3[/C][C]1.56956094235371[/C][C]-0.26956094235371[/C][/ROW]
[ROW][C]40[/C][C]1.2[/C][C]1.43034538614225[/C][C]-0.230345386142252[/C][/ROW]
[ROW][C]41[/C][C]1.4[/C][C]1.4653004680121[/C][C]-0.0653004680121008[/C][/ROW]
[ROW][C]42[/C][C]2.2[/C][C]1.71416326881598[/C][C]0.485836731184022[/C][/ROW]
[ROW][C]43[/C][C]2.9[/C][C]2.52760598566806[/C][C]0.372394014331942[/C][/ROW]
[ROW][C]44[/C][C]3.1[/C][C]3.18813624885303[/C][C]-0.0881362488530329[/C][/ROW]
[ROW][C]45[/C][C]3.5[/C][C]3.39557435902905[/C][C]0.104425640970954[/C][/ROW]
[ROW][C]46[/C][C]3.6[/C][C]3.75096183430004[/C][C]-0.15096183430004[/C][/ROW]
[ROW][C]47[/C][C]4.4[/C][C]3.610300311096[/C][C]0.789699688903997[/C][/ROW]
[ROW][C]48[/C][C]4.1[/C][C]4.53003706627505[/C][C]-0.430037066275055[/C][/ROW]
[ROW][C]49[/C][C]5.1[/C][C]3.90034199245427[/C][C]1.19965800754573[/C][/ROW]
[ROW][C]50[/C][C]5.8[/C][C]5.28670455450261[/C][C]0.513295445497391[/C][/ROW]
[ROW][C]51[/C][C]5.9[/C][C]5.50610429390723[/C][C]0.393895706092768[/C][/ROW]
[ROW][C]52[/C][C]5.4[/C][C]5.8093342900144[/C][C]-0.409334290014404[/C][/ROW]
[ROW][C]53[/C][C]5.5[/C][C]5.12754167512432[/C][C]0.372458324875683[/C][/ROW]
[ROW][C]54[/C][C]4.8[/C][C]5.16968277705279[/C][C]-0.369682777052794[/C][/ROW]
[ROW][C]55[/C][C]3.2[/C][C]4.15390626221353[/C][C]-0.953906262213525[/C][/ROW]
[ROW][C]56[/C][C]2.7[/C][C]2.67350134884305[/C][C]0.0264986511569475[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59273&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59273&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
12.41.895994126216500.504005873783495
222.50015404715485-0.500154047154846
32.12.12747482538019-0.0274748253801892
422.33158269188247-0.331582691882465
51.81.87777661716823-0.077776617168228
62.71.825376880123040.874623119876957
72.32.82387292599539-0.523872925995388
81.92.11990937113072-0.219909371130724
922.08555289289608-0.0855528928960763
102.31.92477078866180.375229211338199
112.82.239688466074000.560311533926003
122.42.86560181294096-0.465601812940959
132.32.34501498396384-0.0450149839638354
142.72.387499550507190.312500449492806
152.72.601619110280570.0983808897194326
162.92.588230576433540.311769423566464
1732.952079466555400.0479205334446046
182.22.89504379984750-0.695043799847505
192.32.032361506677150.267638493322853
202.82.334178734881640.465821265118362
212.82.617296360735740.182703639264255
222.82.751131314329130.0488686856708722
232.22.87575494436699-0.675754944366989
242.62.063388848678090.536611151321915
252.82.663891367033270.136108632966732
262.52.62752551760257-0.127525517602565
272.42.53669765903566-0.136697659035659
282.32.45389514175548-0.153895141755482
291.92.23101058591234-0.331010585912336
301.71.88295673648764-0.182956736487639
3121.769916222856260.230083777143744
322.12.084294130375460.0157058696245409
331.72.18843477133064-0.488434771330645
341.81.85854847970796-0.0585484797079644
351.82.02386613342073-0.223866133420735
361.81.86484955941008-0.0648495594100774
371.32.00992416479506-0.709924164795057
381.31.43373182273839-0.133731822738388
391.31.56956094235371-0.26956094235371
401.21.43034538614225-0.230345386142252
411.41.4653004680121-0.0653004680121008
422.21.714163268815980.485836731184022
432.92.527605985668060.372394014331942
443.13.18813624885303-0.0881362488530329
453.53.395574359029050.104425640970954
463.63.75096183430004-0.15096183430004
474.43.6103003110960.789699688903997
484.14.53003706627505-0.430037066275055
495.13.900341992454271.19965800754573
505.85.286704554502610.513295445497391
515.95.506104293907230.393895706092768
525.45.8093342900144-0.409334290014404
535.55.127541675124320.372458324875683
544.85.16968277705279-0.369682777052794
553.24.15390626221353-0.953906262213525
562.72.673501348843050.0264986511569475






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
90.4969747686794110.9939495373588230.503025231320589
100.335258125042570.670516250085140.66474187495743
110.4833349297409010.9666698594818020.516665070259099
120.4050261404586230.8100522809172460.594973859541377
130.3130670856387130.6261341712774250.686932914361287
140.2917029573793060.5834059147586120.708297042620694
150.2164662962041520.4329325924083050.783533703795848
160.2385704096342580.4771408192685160.761429590365742
170.2100696132225790.4201392264451590.78993038677742
180.2582764156720420.5165528313440840.741723584327958
190.191079720131870.382159440263740.80892027986813
200.1594327534291310.3188655068582630.840567246570869
210.1137352533242800.2274705066485600.88626474667572
220.07828063260400340.1565612652080070.921719367395997
230.1151780837006880.2303561674013760.884821916299312
240.1049468137950480.2098936275900960.895053186204952
250.0799646057514120.1599292115028240.920035394248588
260.05472371466145710.1094474293229140.945276285338543
270.03418510636912040.06837021273824080.96581489363088
280.02336310304115950.0467262060823190.97663689695884
290.02331751881092670.04663503762185340.976682481189073
300.01619361025375990.03238722050751980.98380638974624
310.01258924333200880.02517848666401760.987410756667991
320.008484213946794350.01696842789358870.991515786053206
330.005651321185058160.01130264237011630.994348678814942
340.003188677718801370.006377355437602750.996811322281199
350.001602845289687890.003205690579375790.998397154710312
360.000782291577711320.001564583155422640.999217708422289
370.001298733834412360.002597467668824730.998701266165588
380.0006935433372693810.001387086674538760.99930645666273
390.000402407605562380.000804815211124760.999597592394438
400.0002947663275607810.0005895326551215610.99970523367244
410.0003223672489922520.0006447344979845040.999677632751008
420.0008310851799478030.001662170359895610.999168914820052
430.002352469098759110.004704938197518220.997647530901241
440.003177372310685290.006354744621370590.996822627689315
450.003953030777001170.007906061554002330.996046969222999
460.008983238921819250.01796647784363850.991016761078181
470.008224163356190520.01644832671238100.99177583664381

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
9 & 0.496974768679411 & 0.993949537358823 & 0.503025231320589 \tabularnewline
10 & 0.33525812504257 & 0.67051625008514 & 0.66474187495743 \tabularnewline
11 & 0.483334929740901 & 0.966669859481802 & 0.516665070259099 \tabularnewline
12 & 0.405026140458623 & 0.810052280917246 & 0.594973859541377 \tabularnewline
13 & 0.313067085638713 & 0.626134171277425 & 0.686932914361287 \tabularnewline
14 & 0.291702957379306 & 0.583405914758612 & 0.708297042620694 \tabularnewline
15 & 0.216466296204152 & 0.432932592408305 & 0.783533703795848 \tabularnewline
16 & 0.238570409634258 & 0.477140819268516 & 0.761429590365742 \tabularnewline
17 & 0.210069613222579 & 0.420139226445159 & 0.78993038677742 \tabularnewline
18 & 0.258276415672042 & 0.516552831344084 & 0.741723584327958 \tabularnewline
19 & 0.19107972013187 & 0.38215944026374 & 0.80892027986813 \tabularnewline
20 & 0.159432753429131 & 0.318865506858263 & 0.840567246570869 \tabularnewline
21 & 0.113735253324280 & 0.227470506648560 & 0.88626474667572 \tabularnewline
22 & 0.0782806326040034 & 0.156561265208007 & 0.921719367395997 \tabularnewline
23 & 0.115178083700688 & 0.230356167401376 & 0.884821916299312 \tabularnewline
24 & 0.104946813795048 & 0.209893627590096 & 0.895053186204952 \tabularnewline
25 & 0.079964605751412 & 0.159929211502824 & 0.920035394248588 \tabularnewline
26 & 0.0547237146614571 & 0.109447429322914 & 0.945276285338543 \tabularnewline
27 & 0.0341851063691204 & 0.0683702127382408 & 0.96581489363088 \tabularnewline
28 & 0.0233631030411595 & 0.046726206082319 & 0.97663689695884 \tabularnewline
29 & 0.0233175188109267 & 0.0466350376218534 & 0.976682481189073 \tabularnewline
30 & 0.0161936102537599 & 0.0323872205075198 & 0.98380638974624 \tabularnewline
31 & 0.0125892433320088 & 0.0251784866640176 & 0.987410756667991 \tabularnewline
32 & 0.00848421394679435 & 0.0169684278935887 & 0.991515786053206 \tabularnewline
33 & 0.00565132118505816 & 0.0113026423701163 & 0.994348678814942 \tabularnewline
34 & 0.00318867771880137 & 0.00637735543760275 & 0.996811322281199 \tabularnewline
35 & 0.00160284528968789 & 0.00320569057937579 & 0.998397154710312 \tabularnewline
36 & 0.00078229157771132 & 0.00156458315542264 & 0.999217708422289 \tabularnewline
37 & 0.00129873383441236 & 0.00259746766882473 & 0.998701266165588 \tabularnewline
38 & 0.000693543337269381 & 0.00138708667453876 & 0.99930645666273 \tabularnewline
39 & 0.00040240760556238 & 0.00080481521112476 & 0.999597592394438 \tabularnewline
40 & 0.000294766327560781 & 0.000589532655121561 & 0.99970523367244 \tabularnewline
41 & 0.000322367248992252 & 0.000644734497984504 & 0.999677632751008 \tabularnewline
42 & 0.000831085179947803 & 0.00166217035989561 & 0.999168914820052 \tabularnewline
43 & 0.00235246909875911 & 0.00470493819751822 & 0.997647530901241 \tabularnewline
44 & 0.00317737231068529 & 0.00635474462137059 & 0.996822627689315 \tabularnewline
45 & 0.00395303077700117 & 0.00790606155400233 & 0.996046969222999 \tabularnewline
46 & 0.00898323892181925 & 0.0179664778436385 & 0.991016761078181 \tabularnewline
47 & 0.00822416335619052 & 0.0164483267123810 & 0.99177583664381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59273&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]9[/C][C]0.496974768679411[/C][C]0.993949537358823[/C][C]0.503025231320589[/C][/ROW]
[ROW][C]10[/C][C]0.33525812504257[/C][C]0.67051625008514[/C][C]0.66474187495743[/C][/ROW]
[ROW][C]11[/C][C]0.483334929740901[/C][C]0.966669859481802[/C][C]0.516665070259099[/C][/ROW]
[ROW][C]12[/C][C]0.405026140458623[/C][C]0.810052280917246[/C][C]0.594973859541377[/C][/ROW]
[ROW][C]13[/C][C]0.313067085638713[/C][C]0.626134171277425[/C][C]0.686932914361287[/C][/ROW]
[ROW][C]14[/C][C]0.291702957379306[/C][C]0.583405914758612[/C][C]0.708297042620694[/C][/ROW]
[ROW][C]15[/C][C]0.216466296204152[/C][C]0.432932592408305[/C][C]0.783533703795848[/C][/ROW]
[ROW][C]16[/C][C]0.238570409634258[/C][C]0.477140819268516[/C][C]0.761429590365742[/C][/ROW]
[ROW][C]17[/C][C]0.210069613222579[/C][C]0.420139226445159[/C][C]0.78993038677742[/C][/ROW]
[ROW][C]18[/C][C]0.258276415672042[/C][C]0.516552831344084[/C][C]0.741723584327958[/C][/ROW]
[ROW][C]19[/C][C]0.19107972013187[/C][C]0.38215944026374[/C][C]0.80892027986813[/C][/ROW]
[ROW][C]20[/C][C]0.159432753429131[/C][C]0.318865506858263[/C][C]0.840567246570869[/C][/ROW]
[ROW][C]21[/C][C]0.113735253324280[/C][C]0.227470506648560[/C][C]0.88626474667572[/C][/ROW]
[ROW][C]22[/C][C]0.0782806326040034[/C][C]0.156561265208007[/C][C]0.921719367395997[/C][/ROW]
[ROW][C]23[/C][C]0.115178083700688[/C][C]0.230356167401376[/C][C]0.884821916299312[/C][/ROW]
[ROW][C]24[/C][C]0.104946813795048[/C][C]0.209893627590096[/C][C]0.895053186204952[/C][/ROW]
[ROW][C]25[/C][C]0.079964605751412[/C][C]0.159929211502824[/C][C]0.920035394248588[/C][/ROW]
[ROW][C]26[/C][C]0.0547237146614571[/C][C]0.109447429322914[/C][C]0.945276285338543[/C][/ROW]
[ROW][C]27[/C][C]0.0341851063691204[/C][C]0.0683702127382408[/C][C]0.96581489363088[/C][/ROW]
[ROW][C]28[/C][C]0.0233631030411595[/C][C]0.046726206082319[/C][C]0.97663689695884[/C][/ROW]
[ROW][C]29[/C][C]0.0233175188109267[/C][C]0.0466350376218534[/C][C]0.976682481189073[/C][/ROW]
[ROW][C]30[/C][C]0.0161936102537599[/C][C]0.0323872205075198[/C][C]0.98380638974624[/C][/ROW]
[ROW][C]31[/C][C]0.0125892433320088[/C][C]0.0251784866640176[/C][C]0.987410756667991[/C][/ROW]
[ROW][C]32[/C][C]0.00848421394679435[/C][C]0.0169684278935887[/C][C]0.991515786053206[/C][/ROW]
[ROW][C]33[/C][C]0.00565132118505816[/C][C]0.0113026423701163[/C][C]0.994348678814942[/C][/ROW]
[ROW][C]34[/C][C]0.00318867771880137[/C][C]0.00637735543760275[/C][C]0.996811322281199[/C][/ROW]
[ROW][C]35[/C][C]0.00160284528968789[/C][C]0.00320569057937579[/C][C]0.998397154710312[/C][/ROW]
[ROW][C]36[/C][C]0.00078229157771132[/C][C]0.00156458315542264[/C][C]0.999217708422289[/C][/ROW]
[ROW][C]37[/C][C]0.00129873383441236[/C][C]0.00259746766882473[/C][C]0.998701266165588[/C][/ROW]
[ROW][C]38[/C][C]0.000693543337269381[/C][C]0.00138708667453876[/C][C]0.99930645666273[/C][/ROW]
[ROW][C]39[/C][C]0.00040240760556238[/C][C]0.00080481521112476[/C][C]0.999597592394438[/C][/ROW]
[ROW][C]40[/C][C]0.000294766327560781[/C][C]0.000589532655121561[/C][C]0.99970523367244[/C][/ROW]
[ROW][C]41[/C][C]0.000322367248992252[/C][C]0.000644734497984504[/C][C]0.999677632751008[/C][/ROW]
[ROW][C]42[/C][C]0.000831085179947803[/C][C]0.00166217035989561[/C][C]0.999168914820052[/C][/ROW]
[ROW][C]43[/C][C]0.00235246909875911[/C][C]0.00470493819751822[/C][C]0.997647530901241[/C][/ROW]
[ROW][C]44[/C][C]0.00317737231068529[/C][C]0.00635474462137059[/C][C]0.996822627689315[/C][/ROW]
[ROW][C]45[/C][C]0.00395303077700117[/C][C]0.00790606155400233[/C][C]0.996046969222999[/C][/ROW]
[ROW][C]46[/C][C]0.00898323892181925[/C][C]0.0179664778436385[/C][C]0.991016761078181[/C][/ROW]
[ROW][C]47[/C][C]0.00822416335619052[/C][C]0.0164483267123810[/C][C]0.99177583664381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59273&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59273&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
90.4969747686794110.9939495373588230.503025231320589
100.335258125042570.670516250085140.66474187495743
110.4833349297409010.9666698594818020.516665070259099
120.4050261404586230.8100522809172460.594973859541377
130.3130670856387130.6261341712774250.686932914361287
140.2917029573793060.5834059147586120.708297042620694
150.2164662962041520.4329325924083050.783533703795848
160.2385704096342580.4771408192685160.761429590365742
170.2100696132225790.4201392264451590.78993038677742
180.2582764156720420.5165528313440840.741723584327958
190.191079720131870.382159440263740.80892027986813
200.1594327534291310.3188655068582630.840567246570869
210.1137352533242800.2274705066485600.88626474667572
220.07828063260400340.1565612652080070.921719367395997
230.1151780837006880.2303561674013760.884821916299312
240.1049468137950480.2098936275900960.895053186204952
250.0799646057514120.1599292115028240.920035394248588
260.05472371466145710.1094474293229140.945276285338543
270.03418510636912040.06837021273824080.96581489363088
280.02336310304115950.0467262060823190.97663689695884
290.02331751881092670.04663503762185340.976682481189073
300.01619361025375990.03238722050751980.98380638974624
310.01258924333200880.02517848666401760.987410756667991
320.008484213946794350.01696842789358870.991515786053206
330.005651321185058160.01130264237011630.994348678814942
340.003188677718801370.006377355437602750.996811322281199
350.001602845289687890.003205690579375790.998397154710312
360.000782291577711320.001564583155422640.999217708422289
370.001298733834412360.002597467668824730.998701266165588
380.0006935433372693810.001387086674538760.99930645666273
390.000402407605562380.000804815211124760.999597592394438
400.0002947663275607810.0005895326551215610.99970523367244
410.0003223672489922520.0006447344979845040.999677632751008
420.0008310851799478030.001662170359895610.999168914820052
430.002352469098759110.004704938197518220.997647530901241
440.003177372310685290.006354744621370590.996822627689315
450.003953030777001170.007906061554002330.996046969222999
460.008983238921819250.01796647784363850.991016761078181
470.008224163356190520.01644832671238100.99177583664381






Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level120.307692307692308NOK
5% type I error level200.512820512820513NOK
10% type I error level210.538461538461538NOK

\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 & 12 & 0.307692307692308 & NOK \tabularnewline
5% type I error level & 20 & 0.512820512820513 & NOK \tabularnewline
10% type I error level & 21 & 0.538461538461538 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59273&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]12[/C][C]0.307692307692308[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]20[/C][C]0.512820512820513[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]21[/C][C]0.538461538461538[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59273&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59273&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 level120.307692307692308NOK
5% type I error level200.512820512820513NOK
10% type I error level210.538461538461538NOK


Figures (Output of Computation)

Figure 1
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Figure 9
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Figure 10
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Input Parameters & R Code

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')
}