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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 computationSat, 11 Dec 2010 12:31:50 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/11/t1292070786d3lizvbc72h4atp.htm/, Retrieved Mon, 06 May 2024 13:31:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108093, Retrieved Mon, 06 May 2024 13:31:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [HPC Retail Sales] [2008-03-08 13:40:54] [1c0f2c85e8a48e42648374b3bcceca26]
-  MPD  [Multiple Regression] [W8 - Geboortecijf...] [2010-11-27 10:25:34] [26379b86c25fbf0febe6a7a428e65173]
-    D    [Multiple Regression] [W8 - geboortecijf...] [2010-11-27 18:40:39] [26379b86c25fbf0febe6a7a428e65173]
-           [Multiple Regression] [w8 - geboortecijf...] [2010-11-28 13:07:43] [26379b86c25fbf0febe6a7a428e65173]
-    D          [Multiple Regression] [Meervoudige regre...] [2010-12-11 12:31:50] [bff44ea937c3f909b1dc9a8bfab919e2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
27	41	61	58	59	66	62	46
58	27	41	61	58	59	66	62
70	58	27	41	61	58	59	66
49	70	58	27	41	61	58	59
59	49	70	58	27	41	61	58
44	59	49	70	58	27	41	61
36	44	59	49	70	58	27	41
72	36	44	59	49	70	58	27
45	72	36	44	59	49	70	58
56	45	72	36	44	59	49	70
54	56	45	72	36	44	59	49
53	54	56	45	72	36	44	59
35	53	54	56	45	72	36	44
61	35	53	54	56	45	72	36
52	61	35	53	54	56	45	72
47	52	61	35	53	54	56	45
51	47	52	61	35	53	54	56
52	51	47	52	61	35	53	54
63	52	51	47	52	61	35	53
74	63	52	51	47	52	61	35
45	74	63	52	51	47	52	61
51	45	74	63	52	51	47	52
64	51	45	74	63	52	51	47
36	64	51	45	74	63	52	51
30	36	64	51	45	74	63	52
55	30	36	64	51	45	74	63
64	55	30	36	64	51	45	74
39	64	55	30	36	64	51	45
40	39	64	55	30	36	64	51
63	40	39	64	55	30	36	64
45	63	40	39	64	55	30	36
59	45	63	40	39	64	55	30
55	59	45	63	40	39	64	55
40	55	59	45	63	40	39	64
64	40	55	59	45	63	40	39
27	64	40	55	59	45	63	40
28	27	64	40	55	59	45	63
45	28	27	64	40	55	59	45
57	45	28	27	64	40	55	59
45	57	45	28	27	64	40	55
69	45	57	45	28	27	64	40
60	69	45	57	45	28	27	64
56	60	69	45	57	45	28	27
58	56	60	69	45	57	45	28
50	58	56	60	69	45	57	45
51	50	58	56	60	69	45	57
53	51	50	58	56	60	69	45
37	53	51	50	58	56	60	69
22	37	53	51	50	58	56	60
55	22	37	53	51	50	58	56
70	55	22	37	53	51	50	58
62	70	55	22	37	53	51	50
58	62	70	55	22	37	53	51
39	58	62	70	55	22	37	53
49	39	58	62	70	55	22	37
58	49	39	58	62	70	55	22
47	58	49	39	58	62	70	55
42	47	58	49	39	58	62	70
62	42	47	58	49	39	58	62
39	62	42	47	58	49	39	58
40	39	62	42	47	58	49	39
72	40	39	62	42	47	58	49
70	72	40	39	62	42	47	58
54	70	72	40	39	62	42	47
65	54	70	72	40	39	62	42

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 7 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108093&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108093&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108093&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 time7 seconds
R Server'George Udny Yule' @ 72.249.76.132






Multiple Linear Regression - Estimated Regression Equation
Yt[t] = + 54.1289882375707 + 0.0743007158608039`Yt-1`[t] + 0.0785777695501799`Yt-2`[t] -0.161410948493399`Yt-3`[t] -0.0651190403399635`Yt-4`[t] -0.0877429693266317`Yt-5`[t] -0.116882268075762`Yt-6`[t] -0.0333284658880138`Yt-7`[t] -6.96007335314391M1[t] + 24.4760936488194M2[t] + 25.2621720483599M3[t] + 5.75978078634362M4[t] + 17.1927602981443M5[t] + 11.9528555928096M6[t] + 8.5129331116677M7[t] + 26.9648752251198M8[t] + 10.6154076472889M9[t] + 8.92522966959725M10[t] + 23.8060185192799M11[t] + 0.00905195872685246t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Yt[t] =  +  54.1289882375707 +  0.0743007158608039`Yt-1`[t] +  0.0785777695501799`Yt-2`[t] -0.161410948493399`Yt-3`[t] -0.0651190403399635`Yt-4`[t] -0.0877429693266317`Yt-5`[t] -0.116882268075762`Yt-6`[t] -0.0333284658880138`Yt-7`[t] -6.96007335314391M1[t] +  24.4760936488194M2[t] +  25.2621720483599M3[t] +  5.75978078634362M4[t] +  17.1927602981443M5[t] +  11.9528555928096M6[t] +  8.5129331116677M7[t] +  26.9648752251198M8[t] +  10.6154076472889M9[t] +  8.92522966959725M10[t] +  23.8060185192799M11[t] +  0.00905195872685246t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108093&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Yt[t] =  +  54.1289882375707 +  0.0743007158608039`Yt-1`[t] +  0.0785777695501799`Yt-2`[t] -0.161410948493399`Yt-3`[t] -0.0651190403399635`Yt-4`[t] -0.0877429693266317`Yt-5`[t] -0.116882268075762`Yt-6`[t] -0.0333284658880138`Yt-7`[t] -6.96007335314391M1[t] +  24.4760936488194M2[t] +  25.2621720483599M3[t] +  5.75978078634362M4[t] +  17.1927602981443M5[t] +  11.9528555928096M6[t] +  8.5129331116677M7[t] +  26.9648752251198M8[t] +  10.6154076472889M9[t] +  8.92522966959725M10[t] +  23.8060185192799M11[t] +  0.00905195872685246t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108093&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108093&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
Yt[t] = + 54.1289882375707 + 0.0743007158608039`Yt-1`[t] + 0.0785777695501799`Yt-2`[t] -0.161410948493399`Yt-3`[t] -0.0651190403399635`Yt-4`[t] -0.0877429693266317`Yt-5`[t] -0.116882268075762`Yt-6`[t] -0.0333284658880138`Yt-7`[t] -6.96007335314391M1[t] + 24.4760936488194M2[t] + 25.2621720483599M3[t] + 5.75978078634362M4[t] + 17.1927602981443M5[t] + 11.9528555928096M6[t] + 8.5129331116677M7[t] + 26.9648752251198M8[t] + 10.6154076472889M9[t] + 8.92522966959725M10[t] + 23.8060185192799M11[t] + 0.00905195872685246t + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)54.128988237570726.3246132.05620.0455890.022795
`Yt-1`0.07430071586080390.1520330.48870.6274170.313709
`Yt-2`0.07857776955017990.1514060.5190.6063130.303157
`Yt-3`-0.1614109484933990.150009-1.0760.2876590.143829
`Yt-4`-0.06511904033996350.157392-0.41370.6810310.340515
`Yt-5`-0.08774296932663170.157252-0.5580.5796250.289813
`Yt-6`-0.1168822680757620.155699-0.75070.4567440.228372
`Yt-7`-0.03332846588801380.158656-0.21010.8345640.417282
M1-6.960073353143917.519101-0.92570.3595640.179782
M224.47609364881948.1553443.00120.0043750.002187
M325.26217204835996.044894.17910.0001336.7e-05
M45.759780786343627.664770.75150.4562870.228144
M517.19276029814438.9361981.92390.06070.03035
M611.95285559280967.327591.63120.1098260.054913
M78.51293311166777.4618361.14090.2599620.129981
M826.96487522511988.3685653.22220.0023670.001184
M910.61540764728895.9712081.77780.08220.0411
M108.925229669597256.8051171.31150.1963260.098163
M1123.80601851927997.0189943.39170.0014570.000728
t0.009051958726852460.0615580.1470.883750.441875

\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) & 54.1289882375707 & 26.324613 & 2.0562 & 0.045589 & 0.022795 \tabularnewline
`Yt-1` & 0.0743007158608039 & 0.152033 & 0.4887 & 0.627417 & 0.313709 \tabularnewline
`Yt-2` & 0.0785777695501799 & 0.151406 & 0.519 & 0.606313 & 0.303157 \tabularnewline
`Yt-3` & -0.161410948493399 & 0.150009 & -1.076 & 0.287659 & 0.143829 \tabularnewline
`Yt-4` & -0.0651190403399635 & 0.157392 & -0.4137 & 0.681031 & 0.340515 \tabularnewline
`Yt-5` & -0.0877429693266317 & 0.157252 & -0.558 & 0.579625 & 0.289813 \tabularnewline
`Yt-6` & -0.116882268075762 & 0.155699 & -0.7507 & 0.456744 & 0.228372 \tabularnewline
`Yt-7` & -0.0333284658880138 & 0.158656 & -0.2101 & 0.834564 & 0.417282 \tabularnewline
M1 & -6.96007335314391 & 7.519101 & -0.9257 & 0.359564 & 0.179782 \tabularnewline
M2 & 24.4760936488194 & 8.155344 & 3.0012 & 0.004375 & 0.002187 \tabularnewline
M3 & 25.2621720483599 & 6.04489 & 4.1791 & 0.000133 & 6.7e-05 \tabularnewline
M4 & 5.75978078634362 & 7.66477 & 0.7515 & 0.456287 & 0.228144 \tabularnewline
M5 & 17.1927602981443 & 8.936198 & 1.9239 & 0.0607 & 0.03035 \tabularnewline
M6 & 11.9528555928096 & 7.32759 & 1.6312 & 0.109826 & 0.054913 \tabularnewline
M7 & 8.5129331116677 & 7.461836 & 1.1409 & 0.259962 & 0.129981 \tabularnewline
M8 & 26.9648752251198 & 8.368565 & 3.2222 & 0.002367 & 0.001184 \tabularnewline
M9 & 10.6154076472889 & 5.971208 & 1.7778 & 0.0822 & 0.0411 \tabularnewline
M10 & 8.92522966959725 & 6.805117 & 1.3115 & 0.196326 & 0.098163 \tabularnewline
M11 & 23.8060185192799 & 7.018994 & 3.3917 & 0.001457 & 0.000728 \tabularnewline
t & 0.00905195872685246 & 0.061558 & 0.147 & 0.88375 & 0.441875 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108093&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]54.1289882375707[/C][C]26.324613[/C][C]2.0562[/C][C]0.045589[/C][C]0.022795[/C][/ROW]
[ROW][C]`Yt-1`[/C][C]0.0743007158608039[/C][C]0.152033[/C][C]0.4887[/C][C]0.627417[/C][C]0.313709[/C][/ROW]
[ROW][C]`Yt-2`[/C][C]0.0785777695501799[/C][C]0.151406[/C][C]0.519[/C][C]0.606313[/C][C]0.303157[/C][/ROW]
[ROW][C]`Yt-3`[/C][C]-0.161410948493399[/C][C]0.150009[/C][C]-1.076[/C][C]0.287659[/C][C]0.143829[/C][/ROW]
[ROW][C]`Yt-4`[/C][C]-0.0651190403399635[/C][C]0.157392[/C][C]-0.4137[/C][C]0.681031[/C][C]0.340515[/C][/ROW]
[ROW][C]`Yt-5`[/C][C]-0.0877429693266317[/C][C]0.157252[/C][C]-0.558[/C][C]0.579625[/C][C]0.289813[/C][/ROW]
[ROW][C]`Yt-6`[/C][C]-0.116882268075762[/C][C]0.155699[/C][C]-0.7507[/C][C]0.456744[/C][C]0.228372[/C][/ROW]
[ROW][C]`Yt-7`[/C][C]-0.0333284658880138[/C][C]0.158656[/C][C]-0.2101[/C][C]0.834564[/C][C]0.417282[/C][/ROW]
[ROW][C]M1[/C][C]-6.96007335314391[/C][C]7.519101[/C][C]-0.9257[/C][C]0.359564[/C][C]0.179782[/C][/ROW]
[ROW][C]M2[/C][C]24.4760936488194[/C][C]8.155344[/C][C]3.0012[/C][C]0.004375[/C][C]0.002187[/C][/ROW]
[ROW][C]M3[/C][C]25.2621720483599[/C][C]6.04489[/C][C]4.1791[/C][C]0.000133[/C][C]6.7e-05[/C][/ROW]
[ROW][C]M4[/C][C]5.75978078634362[/C][C]7.66477[/C][C]0.7515[/C][C]0.456287[/C][C]0.228144[/C][/ROW]
[ROW][C]M5[/C][C]17.1927602981443[/C][C]8.936198[/C][C]1.9239[/C][C]0.0607[/C][C]0.03035[/C][/ROW]
[ROW][C]M6[/C][C]11.9528555928096[/C][C]7.32759[/C][C]1.6312[/C][C]0.109826[/C][C]0.054913[/C][/ROW]
[ROW][C]M7[/C][C]8.5129331116677[/C][C]7.461836[/C][C]1.1409[/C][C]0.259962[/C][C]0.129981[/C][/ROW]
[ROW][C]M8[/C][C]26.9648752251198[/C][C]8.368565[/C][C]3.2222[/C][C]0.002367[/C][C]0.001184[/C][/ROW]
[ROW][C]M9[/C][C]10.6154076472889[/C][C]5.971208[/C][C]1.7778[/C][C]0.0822[/C][C]0.0411[/C][/ROW]
[ROW][C]M10[/C][C]8.92522966959725[/C][C]6.805117[/C][C]1.3115[/C][C]0.196326[/C][C]0.098163[/C][/ROW]
[ROW][C]M11[/C][C]23.8060185192799[/C][C]7.018994[/C][C]3.3917[/C][C]0.001457[/C][C]0.000728[/C][/ROW]
[ROW][C]t[/C][C]0.00905195872685246[/C][C]0.061558[/C][C]0.147[/C][C]0.88375[/C][C]0.441875[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108093&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108093&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)54.128988237570726.3246132.05620.0455890.022795
`Yt-1`0.07430071586080390.1520330.48870.6274170.313709
`Yt-2`0.07857776955017990.1514060.5190.6063130.303157
`Yt-3`-0.1614109484933990.150009-1.0760.2876590.143829
`Yt-4`-0.06511904033996350.157392-0.41370.6810310.340515
`Yt-5`-0.08774296932663170.157252-0.5580.5796250.289813
`Yt-6`-0.1168822680757620.155699-0.75070.4567440.228372
`Yt-7`-0.03332846588801380.158656-0.21010.8345640.417282
M1-6.960073353143917.519101-0.92570.3595640.179782
M224.47609364881948.1553443.00120.0043750.002187
M325.26217204835996.044894.17910.0001336.7e-05
M45.759780786343627.664770.75150.4562870.228144
M517.19276029814438.9361981.92390.06070.03035
M611.95285559280967.327591.63120.1098260.054913
M78.51293311166777.4618361.14090.2599620.129981
M826.96487522511988.3685653.22220.0023670.001184
M910.61540764728895.9712081.77780.08220.0411
M108.925229669597256.8051171.31150.1963260.098163
M1123.80601851927997.0189943.39170.0014570.000728
t0.009051958726852460.0615580.1470.883750.441875






Multiple Linear Regression - Regression Statistics
Multiple R0.811379738044797
R-squared0.658337079309643
Adjusted R-squared0.514079401684825
F-TEST (value)4.56361900558133
F-TEST (DF numerator)19
F-TEST (DF denominator)45
p-value1.44195929475677e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation8.58721839245433
Sum Squared Residuals3318.31438738677

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.811379738044797 \tabularnewline
R-squared & 0.658337079309643 \tabularnewline
Adjusted R-squared & 0.514079401684825 \tabularnewline
F-TEST (value) & 4.56361900558133 \tabularnewline
F-TEST (DF numerator) & 19 \tabularnewline
F-TEST (DF denominator) & 45 \tabularnewline
p-value & 1.44195929475677e-05 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 8.58721839245433 \tabularnewline
Sum Squared Residuals & 3318.31438738677 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108093&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.811379738044797[/C][/ROW]
[ROW][C]R-squared[/C][C]0.658337079309643[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.514079401684825[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]4.56361900558133[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]19[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]45[/C][/ROW]
[ROW][C]p-value[/C][C]1.44195929475677e-05[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]8.58721839245433[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]3318.31438738677[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108093&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108093&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 R0.811379738044797
R-squared0.658337079309643
Adjusted R-squared0.514079401684825
F-TEST (value)4.56361900558133
F-TEST (DF numerator)19
F-TEST (DF denominator)45
p-value1.44195929475677e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation8.58721839245433
Sum Squared Residuals3318.31438738677






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
12727.2428357162288-0.242835716228843
25855.27059171749922.72940828250075
37061.07442232490198.92557767509808
44948.55768917501650.442310824983464
55956.72780705672682.27219294327316
64450.1002682101377-6.10026821013769
73648.5317551012895-12.5317551012895
87260.763399845698611.2366001543014
94547.645994361605-2.64599436160503
105650.23277825692025.7672217430798
115459.3757049816912-5.3757049816912
125340.430195728420912.5698042715791
133531.50664997196193.49335002803808
146159.57031697905041.42968302094963
155262.1653389304528-10.1653389304528
164746.80648087473820.193519125261784
175154.1001612860111-3.10016128601111
185250.29613869042831.70386130957168
196348.502898156360714.4971018436393
207465.8903894202398.10961057976096
214551.4338651770292-6.43386517702917
225147.15513004545013.84486995454986
236457.33156024271276.66843975728733
243637.7212088739993-1.72120887399933
253028.34705884121631.65294115878368
265555.5494674237535-0.549467423753461
276463.90012292810460.099877071895396
283948.9563064278479-9.95630642784788
294056.3408233183445-16.3408233183445
306349.505043769440213.4949562305598
314550.7517862508023-5.75178625080228
325967.6374485666409-8.63744856664092
335547.45369443528037.54630556471968
344050.5174710112122-10.5174710112122
356461.58912053533272.41087946466728
362736.9884346576492-9.98843465764918
372831.9647181737141-3.96471817371411
384556.9943157283964-11.9943157283964
395764.8575592417146-7.85755924171456
404549.6203607760424-4.62036077604241
416959.2458541457029.75414585429799
426055.24834804561544.75165195438461
435653.81478093872662.18521906127337
445865.1056952866532-7.10569528665319
455047.57315608426572.42684391573433
465145.58330939696195.41669060303809
475358.2409369099814-5.2409369099814
483736.43522816664350.564771833356541
492229.4040915584221-7.40409155842212
505558.6911076130842-3.69110761308419
517063.99249039022326.00750960977677
526251.644056613217310.3559433867827
535860.4573677121149-2.45736771211495
543952.8502012843783-13.8502012843783
554947.39877955282081.60122044717917
565861.6030668807683-3.60306688076827
574747.8932899418198-0.893289941819812
584246.5113112894556-4.51131128945557
596260.4626773302821.53732266971797
603940.4249325732871-1.42493257328708
614033.53464573845676.46535426154332
627259.924200538216312.0757994617837
637067.01006618460292.98993381539714
645450.41510613313773.58489386686232
656555.12798648110069.87201351889938

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 27 & 27.2428357162288 & -0.242835716228843 \tabularnewline
2 & 58 & 55.2705917174992 & 2.72940828250075 \tabularnewline
3 & 70 & 61.0744223249019 & 8.92557767509808 \tabularnewline
4 & 49 & 48.5576891750165 & 0.442310824983464 \tabularnewline
5 & 59 & 56.7278070567268 & 2.27219294327316 \tabularnewline
6 & 44 & 50.1002682101377 & -6.10026821013769 \tabularnewline
7 & 36 & 48.5317551012895 & -12.5317551012895 \tabularnewline
8 & 72 & 60.7633998456986 & 11.2366001543014 \tabularnewline
9 & 45 & 47.645994361605 & -2.64599436160503 \tabularnewline
10 & 56 & 50.2327782569202 & 5.7672217430798 \tabularnewline
11 & 54 & 59.3757049816912 & -5.3757049816912 \tabularnewline
12 & 53 & 40.4301957284209 & 12.5698042715791 \tabularnewline
13 & 35 & 31.5066499719619 & 3.49335002803808 \tabularnewline
14 & 61 & 59.5703169790504 & 1.42968302094963 \tabularnewline
15 & 52 & 62.1653389304528 & -10.1653389304528 \tabularnewline
16 & 47 & 46.8064808747382 & 0.193519125261784 \tabularnewline
17 & 51 & 54.1001612860111 & -3.10016128601111 \tabularnewline
18 & 52 & 50.2961386904283 & 1.70386130957168 \tabularnewline
19 & 63 & 48.5028981563607 & 14.4971018436393 \tabularnewline
20 & 74 & 65.890389420239 & 8.10961057976096 \tabularnewline
21 & 45 & 51.4338651770292 & -6.43386517702917 \tabularnewline
22 & 51 & 47.1551300454501 & 3.84486995454986 \tabularnewline
23 & 64 & 57.3315602427127 & 6.66843975728733 \tabularnewline
24 & 36 & 37.7212088739993 & -1.72120887399933 \tabularnewline
25 & 30 & 28.3470588412163 & 1.65294115878368 \tabularnewline
26 & 55 & 55.5494674237535 & -0.549467423753461 \tabularnewline
27 & 64 & 63.9001229281046 & 0.099877071895396 \tabularnewline
28 & 39 & 48.9563064278479 & -9.95630642784788 \tabularnewline
29 & 40 & 56.3408233183445 & -16.3408233183445 \tabularnewline
30 & 63 & 49.5050437694402 & 13.4949562305598 \tabularnewline
31 & 45 & 50.7517862508023 & -5.75178625080228 \tabularnewline
32 & 59 & 67.6374485666409 & -8.63744856664092 \tabularnewline
33 & 55 & 47.4536944352803 & 7.54630556471968 \tabularnewline
34 & 40 & 50.5174710112122 & -10.5174710112122 \tabularnewline
35 & 64 & 61.5891205353327 & 2.41087946466728 \tabularnewline
36 & 27 & 36.9884346576492 & -9.98843465764918 \tabularnewline
37 & 28 & 31.9647181737141 & -3.96471817371411 \tabularnewline
38 & 45 & 56.9943157283964 & -11.9943157283964 \tabularnewline
39 & 57 & 64.8575592417146 & -7.85755924171456 \tabularnewline
40 & 45 & 49.6203607760424 & -4.62036077604241 \tabularnewline
41 & 69 & 59.245854145702 & 9.75414585429799 \tabularnewline
42 & 60 & 55.2483480456154 & 4.75165195438461 \tabularnewline
43 & 56 & 53.8147809387266 & 2.18521906127337 \tabularnewline
44 & 58 & 65.1056952866532 & -7.10569528665319 \tabularnewline
45 & 50 & 47.5731560842657 & 2.42684391573433 \tabularnewline
46 & 51 & 45.5833093969619 & 5.41669060303809 \tabularnewline
47 & 53 & 58.2409369099814 & -5.2409369099814 \tabularnewline
48 & 37 & 36.4352281666435 & 0.564771833356541 \tabularnewline
49 & 22 & 29.4040915584221 & -7.40409155842212 \tabularnewline
50 & 55 & 58.6911076130842 & -3.69110761308419 \tabularnewline
51 & 70 & 63.9924903902232 & 6.00750960977677 \tabularnewline
52 & 62 & 51.6440566132173 & 10.3559433867827 \tabularnewline
53 & 58 & 60.4573677121149 & -2.45736771211495 \tabularnewline
54 & 39 & 52.8502012843783 & -13.8502012843783 \tabularnewline
55 & 49 & 47.3987795528208 & 1.60122044717917 \tabularnewline
56 & 58 & 61.6030668807683 & -3.60306688076827 \tabularnewline
57 & 47 & 47.8932899418198 & -0.893289941819812 \tabularnewline
58 & 42 & 46.5113112894556 & -4.51131128945557 \tabularnewline
59 & 62 & 60.462677330282 & 1.53732266971797 \tabularnewline
60 & 39 & 40.4249325732871 & -1.42493257328708 \tabularnewline
61 & 40 & 33.5346457384567 & 6.46535426154332 \tabularnewline
62 & 72 & 59.9242005382163 & 12.0757994617837 \tabularnewline
63 & 70 & 67.0100661846029 & 2.98993381539714 \tabularnewline
64 & 54 & 50.4151061331377 & 3.58489386686232 \tabularnewline
65 & 65 & 55.1279864811006 & 9.87201351889938 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108093&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]27[/C][C]27.2428357162288[/C][C]-0.242835716228843[/C][/ROW]
[ROW][C]2[/C][C]58[/C][C]55.2705917174992[/C][C]2.72940828250075[/C][/ROW]
[ROW][C]3[/C][C]70[/C][C]61.0744223249019[/C][C]8.92557767509808[/C][/ROW]
[ROW][C]4[/C][C]49[/C][C]48.5576891750165[/C][C]0.442310824983464[/C][/ROW]
[ROW][C]5[/C][C]59[/C][C]56.7278070567268[/C][C]2.27219294327316[/C][/ROW]
[ROW][C]6[/C][C]44[/C][C]50.1002682101377[/C][C]-6.10026821013769[/C][/ROW]
[ROW][C]7[/C][C]36[/C][C]48.5317551012895[/C][C]-12.5317551012895[/C][/ROW]
[ROW][C]8[/C][C]72[/C][C]60.7633998456986[/C][C]11.2366001543014[/C][/ROW]
[ROW][C]9[/C][C]45[/C][C]47.645994361605[/C][C]-2.64599436160503[/C][/ROW]
[ROW][C]10[/C][C]56[/C][C]50.2327782569202[/C][C]5.7672217430798[/C][/ROW]
[ROW][C]11[/C][C]54[/C][C]59.3757049816912[/C][C]-5.3757049816912[/C][/ROW]
[ROW][C]12[/C][C]53[/C][C]40.4301957284209[/C][C]12.5698042715791[/C][/ROW]
[ROW][C]13[/C][C]35[/C][C]31.5066499719619[/C][C]3.49335002803808[/C][/ROW]
[ROW][C]14[/C][C]61[/C][C]59.5703169790504[/C][C]1.42968302094963[/C][/ROW]
[ROW][C]15[/C][C]52[/C][C]62.1653389304528[/C][C]-10.1653389304528[/C][/ROW]
[ROW][C]16[/C][C]47[/C][C]46.8064808747382[/C][C]0.193519125261784[/C][/ROW]
[ROW][C]17[/C][C]51[/C][C]54.1001612860111[/C][C]-3.10016128601111[/C][/ROW]
[ROW][C]18[/C][C]52[/C][C]50.2961386904283[/C][C]1.70386130957168[/C][/ROW]
[ROW][C]19[/C][C]63[/C][C]48.5028981563607[/C][C]14.4971018436393[/C][/ROW]
[ROW][C]20[/C][C]74[/C][C]65.890389420239[/C][C]8.10961057976096[/C][/ROW]
[ROW][C]21[/C][C]45[/C][C]51.4338651770292[/C][C]-6.43386517702917[/C][/ROW]
[ROW][C]22[/C][C]51[/C][C]47.1551300454501[/C][C]3.84486995454986[/C][/ROW]
[ROW][C]23[/C][C]64[/C][C]57.3315602427127[/C][C]6.66843975728733[/C][/ROW]
[ROW][C]24[/C][C]36[/C][C]37.7212088739993[/C][C]-1.72120887399933[/C][/ROW]
[ROW][C]25[/C][C]30[/C][C]28.3470588412163[/C][C]1.65294115878368[/C][/ROW]
[ROW][C]26[/C][C]55[/C][C]55.5494674237535[/C][C]-0.549467423753461[/C][/ROW]
[ROW][C]27[/C][C]64[/C][C]63.9001229281046[/C][C]0.099877071895396[/C][/ROW]
[ROW][C]28[/C][C]39[/C][C]48.9563064278479[/C][C]-9.95630642784788[/C][/ROW]
[ROW][C]29[/C][C]40[/C][C]56.3408233183445[/C][C]-16.3408233183445[/C][/ROW]
[ROW][C]30[/C][C]63[/C][C]49.5050437694402[/C][C]13.4949562305598[/C][/ROW]
[ROW][C]31[/C][C]45[/C][C]50.7517862508023[/C][C]-5.75178625080228[/C][/ROW]
[ROW][C]32[/C][C]59[/C][C]67.6374485666409[/C][C]-8.63744856664092[/C][/ROW]
[ROW][C]33[/C][C]55[/C][C]47.4536944352803[/C][C]7.54630556471968[/C][/ROW]
[ROW][C]34[/C][C]40[/C][C]50.5174710112122[/C][C]-10.5174710112122[/C][/ROW]
[ROW][C]35[/C][C]64[/C][C]61.5891205353327[/C][C]2.41087946466728[/C][/ROW]
[ROW][C]36[/C][C]27[/C][C]36.9884346576492[/C][C]-9.98843465764918[/C][/ROW]
[ROW][C]37[/C][C]28[/C][C]31.9647181737141[/C][C]-3.96471817371411[/C][/ROW]
[ROW][C]38[/C][C]45[/C][C]56.9943157283964[/C][C]-11.9943157283964[/C][/ROW]
[ROW][C]39[/C][C]57[/C][C]64.8575592417146[/C][C]-7.85755924171456[/C][/ROW]
[ROW][C]40[/C][C]45[/C][C]49.6203607760424[/C][C]-4.62036077604241[/C][/ROW]
[ROW][C]41[/C][C]69[/C][C]59.245854145702[/C][C]9.75414585429799[/C][/ROW]
[ROW][C]42[/C][C]60[/C][C]55.2483480456154[/C][C]4.75165195438461[/C][/ROW]
[ROW][C]43[/C][C]56[/C][C]53.8147809387266[/C][C]2.18521906127337[/C][/ROW]
[ROW][C]44[/C][C]58[/C][C]65.1056952866532[/C][C]-7.10569528665319[/C][/ROW]
[ROW][C]45[/C][C]50[/C][C]47.5731560842657[/C][C]2.42684391573433[/C][/ROW]
[ROW][C]46[/C][C]51[/C][C]45.5833093969619[/C][C]5.41669060303809[/C][/ROW]
[ROW][C]47[/C][C]53[/C][C]58.2409369099814[/C][C]-5.2409369099814[/C][/ROW]
[ROW][C]48[/C][C]37[/C][C]36.4352281666435[/C][C]0.564771833356541[/C][/ROW]
[ROW][C]49[/C][C]22[/C][C]29.4040915584221[/C][C]-7.40409155842212[/C][/ROW]
[ROW][C]50[/C][C]55[/C][C]58.6911076130842[/C][C]-3.69110761308419[/C][/ROW]
[ROW][C]51[/C][C]70[/C][C]63.9924903902232[/C][C]6.00750960977677[/C][/ROW]
[ROW][C]52[/C][C]62[/C][C]51.6440566132173[/C][C]10.3559433867827[/C][/ROW]
[ROW][C]53[/C][C]58[/C][C]60.4573677121149[/C][C]-2.45736771211495[/C][/ROW]
[ROW][C]54[/C][C]39[/C][C]52.8502012843783[/C][C]-13.8502012843783[/C][/ROW]
[ROW][C]55[/C][C]49[/C][C]47.3987795528208[/C][C]1.60122044717917[/C][/ROW]
[ROW][C]56[/C][C]58[/C][C]61.6030668807683[/C][C]-3.60306688076827[/C][/ROW]
[ROW][C]57[/C][C]47[/C][C]47.8932899418198[/C][C]-0.893289941819812[/C][/ROW]
[ROW][C]58[/C][C]42[/C][C]46.5113112894556[/C][C]-4.51131128945557[/C][/ROW]
[ROW][C]59[/C][C]62[/C][C]60.462677330282[/C][C]1.53732266971797[/C][/ROW]
[ROW][C]60[/C][C]39[/C][C]40.4249325732871[/C][C]-1.42493257328708[/C][/ROW]
[ROW][C]61[/C][C]40[/C][C]33.5346457384567[/C][C]6.46535426154332[/C][/ROW]
[ROW][C]62[/C][C]72[/C][C]59.9242005382163[/C][C]12.0757994617837[/C][/ROW]
[ROW][C]63[/C][C]70[/C][C]67.0100661846029[/C][C]2.98993381539714[/C][/ROW]
[ROW][C]64[/C][C]54[/C][C]50.4151061331377[/C][C]3.58489386686232[/C][/ROW]
[ROW][C]65[/C][C]65[/C][C]55.1279864811006[/C][C]9.87201351889938[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108093&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108093&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
12727.2428357162288-0.242835716228843
25855.27059171749922.72940828250075
37061.07442232490198.92557767509808
44948.55768917501650.442310824983464
55956.72780705672682.27219294327316
64450.1002682101377-6.10026821013769
73648.5317551012895-12.5317551012895
87260.763399845698611.2366001543014
94547.645994361605-2.64599436160503
105650.23277825692025.7672217430798
115459.3757049816912-5.3757049816912
125340.430195728420912.5698042715791
133531.50664997196193.49335002803808
146159.57031697905041.42968302094963
155262.1653389304528-10.1653389304528
164746.80648087473820.193519125261784
175154.1001612860111-3.10016128601111
185250.29613869042831.70386130957168
196348.502898156360714.4971018436393
207465.8903894202398.10961057976096
214551.4338651770292-6.43386517702917
225147.15513004545013.84486995454986
236457.33156024271276.66843975728733
243637.7212088739993-1.72120887399933
253028.34705884121631.65294115878368
265555.5494674237535-0.549467423753461
276463.90012292810460.099877071895396
283948.9563064278479-9.95630642784788
294056.3408233183445-16.3408233183445
306349.505043769440213.4949562305598
314550.7517862508023-5.75178625080228
325967.6374485666409-8.63744856664092
335547.45369443528037.54630556471968
344050.5174710112122-10.5174710112122
356461.58912053533272.41087946466728
362736.9884346576492-9.98843465764918
372831.9647181737141-3.96471817371411
384556.9943157283964-11.9943157283964
395764.8575592417146-7.85755924171456
404549.6203607760424-4.62036077604241
416959.2458541457029.75414585429799
426055.24834804561544.75165195438461
435653.81478093872662.18521906127337
445865.1056952866532-7.10569528665319
455047.57315608426572.42684391573433
465145.58330939696195.41669060303809
475358.2409369099814-5.2409369099814
483736.43522816664350.564771833356541
492229.4040915584221-7.40409155842212
505558.6911076130842-3.69110761308419
517063.99249039022326.00750960977677
526251.644056613217310.3559433867827
535860.4573677121149-2.45736771211495
543952.8502012843783-13.8502012843783
554947.39877955282081.60122044717917
565861.6030668807683-3.60306688076827
574747.8932899418198-0.893289941819812
584246.5113112894556-4.51131128945557
596260.4626773302821.53732266971797
603940.4249325732871-1.42493257328708
614033.53464573845676.46535426154332
627259.924200538216312.0757994617837
637067.01006618460292.98993381539714
645450.41510613313773.58489386686232
656555.12798648110069.87201351889938






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
230.8131028602240240.3737942795519520.186897139775976
240.7988528936905740.4022942126188530.201147106309426
250.744742951499270.5105140970014590.255257048500729
260.7136425668847370.5727148662305260.286357433115263
270.6291329646869150.7417340706261710.370867035313085
280.5570687597499140.8858624805001730.442931240250087
290.6519184114670330.6961631770659340.348081588532967
300.8025951114636430.3948097770727140.197404888536357
310.7288003788458950.542399242308210.271199621154105
320.6938310825930610.6123378348138770.306168917406939
330.6940490566948410.6119018866103180.305950943305159
340.7172001868498110.5655996263003780.282799813150189
350.655220326605360.689559346789280.34477967339464
360.6144364482641730.7711271034716550.385563551735827
370.5199978642542130.9600042714915750.480002135745787
380.5730792775180220.8538414449639550.426920722481978
390.4599656862045210.9199313724090420.540034313795479
400.4263145861673010.8526291723346030.573685413832699
410.3967590341228930.7935180682457860.603240965877107
420.5020000066333690.9959999867332620.497999993366631

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
23 & 0.813102860224024 & 0.373794279551952 & 0.186897139775976 \tabularnewline
24 & 0.798852893690574 & 0.402294212618853 & 0.201147106309426 \tabularnewline
25 & 0.74474295149927 & 0.510514097001459 & 0.255257048500729 \tabularnewline
26 & 0.713642566884737 & 0.572714866230526 & 0.286357433115263 \tabularnewline
27 & 0.629132964686915 & 0.741734070626171 & 0.370867035313085 \tabularnewline
28 & 0.557068759749914 & 0.885862480500173 & 0.442931240250087 \tabularnewline
29 & 0.651918411467033 & 0.696163177065934 & 0.348081588532967 \tabularnewline
30 & 0.802595111463643 & 0.394809777072714 & 0.197404888536357 \tabularnewline
31 & 0.728800378845895 & 0.54239924230821 & 0.271199621154105 \tabularnewline
32 & 0.693831082593061 & 0.612337834813877 & 0.306168917406939 \tabularnewline
33 & 0.694049056694841 & 0.611901886610318 & 0.305950943305159 \tabularnewline
34 & 0.717200186849811 & 0.565599626300378 & 0.282799813150189 \tabularnewline
35 & 0.65522032660536 & 0.68955934678928 & 0.34477967339464 \tabularnewline
36 & 0.614436448264173 & 0.771127103471655 & 0.385563551735827 \tabularnewline
37 & 0.519997864254213 & 0.960004271491575 & 0.480002135745787 \tabularnewline
38 & 0.573079277518022 & 0.853841444963955 & 0.426920722481978 \tabularnewline
39 & 0.459965686204521 & 0.919931372409042 & 0.540034313795479 \tabularnewline
40 & 0.426314586167301 & 0.852629172334603 & 0.573685413832699 \tabularnewline
41 & 0.396759034122893 & 0.793518068245786 & 0.603240965877107 \tabularnewline
42 & 0.502000006633369 & 0.995999986733262 & 0.497999993366631 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108093&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]23[/C][C]0.813102860224024[/C][C]0.373794279551952[/C][C]0.186897139775976[/C][/ROW]
[ROW][C]24[/C][C]0.798852893690574[/C][C]0.402294212618853[/C][C]0.201147106309426[/C][/ROW]
[ROW][C]25[/C][C]0.74474295149927[/C][C]0.510514097001459[/C][C]0.255257048500729[/C][/ROW]
[ROW][C]26[/C][C]0.713642566884737[/C][C]0.572714866230526[/C][C]0.286357433115263[/C][/ROW]
[ROW][C]27[/C][C]0.629132964686915[/C][C]0.741734070626171[/C][C]0.370867035313085[/C][/ROW]
[ROW][C]28[/C][C]0.557068759749914[/C][C]0.885862480500173[/C][C]0.442931240250087[/C][/ROW]
[ROW][C]29[/C][C]0.651918411467033[/C][C]0.696163177065934[/C][C]0.348081588532967[/C][/ROW]
[ROW][C]30[/C][C]0.802595111463643[/C][C]0.394809777072714[/C][C]0.197404888536357[/C][/ROW]
[ROW][C]31[/C][C]0.728800378845895[/C][C]0.54239924230821[/C][C]0.271199621154105[/C][/ROW]
[ROW][C]32[/C][C]0.693831082593061[/C][C]0.612337834813877[/C][C]0.306168917406939[/C][/ROW]
[ROW][C]33[/C][C]0.694049056694841[/C][C]0.611901886610318[/C][C]0.305950943305159[/C][/ROW]
[ROW][C]34[/C][C]0.717200186849811[/C][C]0.565599626300378[/C][C]0.282799813150189[/C][/ROW]
[ROW][C]35[/C][C]0.65522032660536[/C][C]0.68955934678928[/C][C]0.34477967339464[/C][/ROW]
[ROW][C]36[/C][C]0.614436448264173[/C][C]0.771127103471655[/C][C]0.385563551735827[/C][/ROW]
[ROW][C]37[/C][C]0.519997864254213[/C][C]0.960004271491575[/C][C]0.480002135745787[/C][/ROW]
[ROW][C]38[/C][C]0.573079277518022[/C][C]0.853841444963955[/C][C]0.426920722481978[/C][/ROW]
[ROW][C]39[/C][C]0.459965686204521[/C][C]0.919931372409042[/C][C]0.540034313795479[/C][/ROW]
[ROW][C]40[/C][C]0.426314586167301[/C][C]0.852629172334603[/C][C]0.573685413832699[/C][/ROW]
[ROW][C]41[/C][C]0.396759034122893[/C][C]0.793518068245786[/C][C]0.603240965877107[/C][/ROW]
[ROW][C]42[/C][C]0.502000006633369[/C][C]0.995999986733262[/C][C]0.497999993366631[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108093&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108093&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
230.8131028602240240.3737942795519520.186897139775976
240.7988528936905740.4022942126188530.201147106309426
250.744742951499270.5105140970014590.255257048500729
260.7136425668847370.5727148662305260.286357433115263
270.6291329646869150.7417340706261710.370867035313085
280.5570687597499140.8858624805001730.442931240250087
290.6519184114670330.6961631770659340.348081588532967
300.8025951114636430.3948097770727140.197404888536357
310.7288003788458950.542399242308210.271199621154105
320.6938310825930610.6123378348138770.306168917406939
330.6940490566948410.6119018866103180.305950943305159
340.7172001868498110.5655996263003780.282799813150189
350.655220326605360.689559346789280.34477967339464
360.6144364482641730.7711271034716550.385563551735827
370.5199978642542130.9600042714915750.480002135745787
380.5730792775180220.8538414449639550.426920722481978
390.4599656862045210.9199313724090420.540034313795479
400.4263145861673010.8526291723346030.573685413832699
410.3967590341228930.7935180682457860.603240965877107
420.5020000066333690.9959999867332620.497999993366631






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

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108093&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108093&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108093&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 level00OK


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')
}