Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationMon, 19 Nov 2007 02:50:12 -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/2007/Nov/19/t1195465490v9xxcyhhwzvq5is.htm/, Retrieved Fri, 03 May 2024 11:06:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5644, Retrieved Fri, 03 May 2024 11:06:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact234
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [regr anal] [2007-11-19 09:50:12] [079615521100262cd8b5675a0217a3b1] [Current]
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Dataseries X:
106.54	107.89
106.44	107.26
106.57	107.76
106.12	107.32
106.13	107.15
106.26	108.04
105.78	106.52
105.77	106.62
105.2	106.47
105.15	105.46
105.01	106.13
104.75	105.15
104.96	105.39
105.26	104.57
105.13	104.29
104.77	104.09
104.79	104.51
104.4	103.39
103.89	102.71
103.93	102.62
103.48	101.94
103.45	101.65
103.47	101.86
103.5	101.27
103.69	101.21
103.57	102.15
103.47	102.07
102.85	102.8
102.54	103.39
102.39	102.71
102.16	102.65
101.51	101.12
100.83	100.29
100.55	99.79
100.88	100.11
101	99.76
100.51	99.96
100.44	99.98
100.32	100.49
99.98	100.75
100.03	100.84
99.64	100.44
99.11	99.57
98.97	99.22
98.6	99.08
98.31	98.04
98.37	98.73
98.19	98.72
98.51	100.07
98.23	99.02
97.96	98.94
97.77	99
97.49	98.54
97.76	98.42
98.01	97.9
97.73	97.46
97.06	97
96.63	95.97
96.58	96.55
96.66	96.51
96.77	96.76
96.5	96.05
96.53	96.47
96.22	96.38
96.49	97.27
96.34	96.67
96.31	96.59
96.06	96.06
95.9	96.92
95.33	94.96
95.53	95.59
95.42	95.68
95.57	95.35
95.3	95.41
95.31	95.32
95.38	95.8
95.22	95.46
94.62	94.16
93.81	92.49
93.6	91.58
93.2	91.5
93.29	90.83
93.54	91.28
93.23	90.57
93.46	90.93
92.82	90.9
92.85	91.49
92.67	91.38
92.32	90.91
92.06	90.72
91.88	89.53
91.53	89.47
91.19	89.28




Summary of compuational 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 compuational 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=5644&T=0

[TABLE]
[ROW][C]Summary of compuational 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=5644&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5644&T=0

As an alternative you can also use a QR Code:  

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

Summary of compuational 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
y[t] = -9.34493940380609 + 1.09136281362709x[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  -9.34493940380609 +  1.09136281362709x[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5644&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  -9.34493940380609 +  1.09136281362709x[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5644&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5644&T=1

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Estimated Regression Equation
y[t] = -9.34493940380609 + 1.09136281362709x[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-9.344939403806092.376769-3.93180.0001648.2e-05
x1.091362813627090.02393645.59500

\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) & -9.34493940380609 & 2.376769 & -3.9318 & 0.000164 & 8.2e-05 \tabularnewline
x & 1.09136281362709 & 0.023936 & 45.595 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5644&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]-9.34493940380609[/C][C]2.376769[/C][C]-3.9318[/C][C]0.000164[/C][C]8.2e-05[/C][/ROW]
[ROW][C]x[/C][C]1.09136281362709[/C][C]0.023936[/C][C]45.595[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5644&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5644&T=2

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-9.344939403806092.376769-3.93180.0001648.2e-05
x1.091362813627090.02393645.59500







Multiple Linear Regression - Regression Statistics
Multiple R0.978806779791498
R-squared0.958062712165803
Adjusted R-squared0.957601862848944
F-TEST (value)2078.90665585664
F-TEST (DF numerator)1
F-TEST (DF denominator)91
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.02853187503467
Sum Squared Residuals96.2668814345723

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.978806779791498 \tabularnewline
R-squared & 0.958062712165803 \tabularnewline
Adjusted R-squared & 0.957601862848944 \tabularnewline
F-TEST (value) & 2078.90665585664 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 91 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 1.02853187503467 \tabularnewline
Sum Squared Residuals & 96.2668814345723 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5644&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.978806779791498[/C][/ROW]
[ROW][C]R-squared[/C][C]0.958062712165803[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.957601862848944[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]2078.90665585664[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]91[/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]1.02853187503467[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]96.2668814345723[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5644&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5644&T=3

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Regression Statistics
Multiple R0.978806779791498
R-squared0.958062712165803
Adjusted R-squared0.957601862848944
F-TEST (value)2078.90665585664
F-TEST (DF numerator)1
F-TEST (DF denominator)91
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.02853187503467
Sum Squared Residuals96.2668814345723







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1107.89106.9288547600240.96114523997586
2107.26106.8197184786610.440281521338944
3107.76106.9615956444330.79840435556744
4107.32106.4704823783000.849517621699604
5107.15106.4813960064370.668603993563355
6108.04106.6232731722081.41672682779182
7106.52106.0994190216670.420580978332819
8106.62106.0885053935310.531494606469105
9106.47105.4664285897631.00357141023653
10105.46105.4118604490820.0481395509178773
11106.13105.2590696551740.870930344825672
12105.15104.9753153236310.174684676368731
13105.39105.2045015144930.185498485507044
14104.57105.531910358581-0.961910358581102
15104.29105.390033192810-1.10003319280956
16104.09104.997142579904-0.90714257990381
17104.51105.018969836176-0.50896983617636
18103.39104.593338338862-1.2033383388618
19102.71104.036743303912-1.32674330391199
20102.62104.080397816457-1.46039781645707
21101.94103.589284550325-1.64928455032488
22101.65103.556543665916-1.90654366591606
23101.86103.578370922189-1.71837092218860
24101.27103.611111806597-2.34111180659742
25101.21103.818470741187-2.60847074118657
26102.15103.687507203551-1.5375072035513
27102.07103.578370922189-1.50837092218861
28102.8102.901725977740-0.101725977739807
29103.39102.5634035055150.82659649448458
30102.71102.3996990834710.310300916528643
31102.65102.1486856363370.501314363662889
32101.12101.439299807480-0.319299807479515
33100.29100.697173094213-0.407173094213087
3499.79100.391591506398-0.601591506397501
35100.11100.751741234894-0.641741234894445
3699.76100.882704772530-1.12270477252969
3799.96100.347936993852-0.387936993852439
3899.98100.271541596899-0.291541596898525
39100.49100.1405780592630.349421940736722
40100.7599.769514702630.980485297369925
41100.8499.82408284331141.01591715668858
42100.4499.39845134599691.04154865400314
4399.5798.82002905477450.749970945225488
4499.2298.66723826086670.552761739133287
4599.0898.26343401982470.816565980175313
4698.0497.94693880387280.0930611961271679
4798.7398.01242057269050.717579427309538
4898.7297.81597526623760.904024733762416
49100.0798.16521136659831.90478863340173
5099.0297.85962977878271.16037022121732
5198.9497.56496181910331.37503818089665
529997.35760288451421.64239711548580
5398.5497.05202129669861.48797870330139
5498.4297.3466892563781.07331074362206
5597.997.61952995978470.28047004021529
5697.4697.31394837196910.146051628030864
579796.5827352868390.41726471316102
5895.9796.1134492769793-0.143449276979326
5996.5596.0588811362980.491118863702023
6096.5196.14619016138810.363809838611866
6196.7696.26624007088710.493759929112887
6296.0595.97157211120780.0784278887921881
6396.4796.00431299561660.465687004383376
6496.3895.66599052339220.714009476607772
6597.2795.96065848307151.30934151692846
6696.6795.79695406102750.873045938972523
6796.5995.76421317661870.825786823381338
6896.0695.49137247321190.568627526788109
6996.9295.31675442303161.60324557696844
7094.9694.6946776192640.265322380735878
7195.5994.91295018198950.677049818010468
7295.6894.79290027249060.88709972750945
7395.3594.95660469453460.393395305465384
7495.4194.66193673485530.748063265144695
7595.3294.67285036299160.647149637008415
7695.894.74924575994551.05075424005453
7795.4694.57462770976510.885372290234858
7894.1693.9198100215890.240189978411106
7992.4993.035806142551-0.545806142550952
8091.5892.8066199516893-1.22661995168925
8191.592.3700748262384-0.870074826238425
8290.8392.4682974794649-1.63829747946487
8391.2892.7411381828716-1.46113818287164
8490.5792.4028157106472-1.83281571064725
8590.9392.6538291577815-1.72382915778145
8690.991.9553569570601-1.05535695706012
8791.4991.988097841469-0.49809784146894
8891.3891.7916525350161-0.411652535016073
8990.9191.4096755502466-0.499675550246581
9090.7291.1259212187036-0.405921218703547
9189.5390.9294759122507-1.39947591225066
9289.4790.5474989274812-1.07749892748119
9389.2890.176435570848-0.896435570847973

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 107.89 & 106.928854760024 & 0.96114523997586 \tabularnewline
2 & 107.26 & 106.819718478661 & 0.440281521338944 \tabularnewline
3 & 107.76 & 106.961595644433 & 0.79840435556744 \tabularnewline
4 & 107.32 & 106.470482378300 & 0.849517621699604 \tabularnewline
5 & 107.15 & 106.481396006437 & 0.668603993563355 \tabularnewline
6 & 108.04 & 106.623273172208 & 1.41672682779182 \tabularnewline
7 & 106.52 & 106.099419021667 & 0.420580978332819 \tabularnewline
8 & 106.62 & 106.088505393531 & 0.531494606469105 \tabularnewline
9 & 106.47 & 105.466428589763 & 1.00357141023653 \tabularnewline
10 & 105.46 & 105.411860449082 & 0.0481395509178773 \tabularnewline
11 & 106.13 & 105.259069655174 & 0.870930344825672 \tabularnewline
12 & 105.15 & 104.975315323631 & 0.174684676368731 \tabularnewline
13 & 105.39 & 105.204501514493 & 0.185498485507044 \tabularnewline
14 & 104.57 & 105.531910358581 & -0.961910358581102 \tabularnewline
15 & 104.29 & 105.390033192810 & -1.10003319280956 \tabularnewline
16 & 104.09 & 104.997142579904 & -0.90714257990381 \tabularnewline
17 & 104.51 & 105.018969836176 & -0.50896983617636 \tabularnewline
18 & 103.39 & 104.593338338862 & -1.2033383388618 \tabularnewline
19 & 102.71 & 104.036743303912 & -1.32674330391199 \tabularnewline
20 & 102.62 & 104.080397816457 & -1.46039781645707 \tabularnewline
21 & 101.94 & 103.589284550325 & -1.64928455032488 \tabularnewline
22 & 101.65 & 103.556543665916 & -1.90654366591606 \tabularnewline
23 & 101.86 & 103.578370922189 & -1.71837092218860 \tabularnewline
24 & 101.27 & 103.611111806597 & -2.34111180659742 \tabularnewline
25 & 101.21 & 103.818470741187 & -2.60847074118657 \tabularnewline
26 & 102.15 & 103.687507203551 & -1.5375072035513 \tabularnewline
27 & 102.07 & 103.578370922189 & -1.50837092218861 \tabularnewline
28 & 102.8 & 102.901725977740 & -0.101725977739807 \tabularnewline
29 & 103.39 & 102.563403505515 & 0.82659649448458 \tabularnewline
30 & 102.71 & 102.399699083471 & 0.310300916528643 \tabularnewline
31 & 102.65 & 102.148685636337 & 0.501314363662889 \tabularnewline
32 & 101.12 & 101.439299807480 & -0.319299807479515 \tabularnewline
33 & 100.29 & 100.697173094213 & -0.407173094213087 \tabularnewline
34 & 99.79 & 100.391591506398 & -0.601591506397501 \tabularnewline
35 & 100.11 & 100.751741234894 & -0.641741234894445 \tabularnewline
36 & 99.76 & 100.882704772530 & -1.12270477252969 \tabularnewline
37 & 99.96 & 100.347936993852 & -0.387936993852439 \tabularnewline
38 & 99.98 & 100.271541596899 & -0.291541596898525 \tabularnewline
39 & 100.49 & 100.140578059263 & 0.349421940736722 \tabularnewline
40 & 100.75 & 99.76951470263 & 0.980485297369925 \tabularnewline
41 & 100.84 & 99.8240828433114 & 1.01591715668858 \tabularnewline
42 & 100.44 & 99.3984513459969 & 1.04154865400314 \tabularnewline
43 & 99.57 & 98.8200290547745 & 0.749970945225488 \tabularnewline
44 & 99.22 & 98.6672382608667 & 0.552761739133287 \tabularnewline
45 & 99.08 & 98.2634340198247 & 0.816565980175313 \tabularnewline
46 & 98.04 & 97.9469388038728 & 0.0930611961271679 \tabularnewline
47 & 98.73 & 98.0124205726905 & 0.717579427309538 \tabularnewline
48 & 98.72 & 97.8159752662376 & 0.904024733762416 \tabularnewline
49 & 100.07 & 98.1652113665983 & 1.90478863340173 \tabularnewline
50 & 99.02 & 97.8596297787827 & 1.16037022121732 \tabularnewline
51 & 98.94 & 97.5649618191033 & 1.37503818089665 \tabularnewline
52 & 99 & 97.3576028845142 & 1.64239711548580 \tabularnewline
53 & 98.54 & 97.0520212966986 & 1.48797870330139 \tabularnewline
54 & 98.42 & 97.346689256378 & 1.07331074362206 \tabularnewline
55 & 97.9 & 97.6195299597847 & 0.28047004021529 \tabularnewline
56 & 97.46 & 97.3139483719691 & 0.146051628030864 \tabularnewline
57 & 97 & 96.582735286839 & 0.41726471316102 \tabularnewline
58 & 95.97 & 96.1134492769793 & -0.143449276979326 \tabularnewline
59 & 96.55 & 96.058881136298 & 0.491118863702023 \tabularnewline
60 & 96.51 & 96.1461901613881 & 0.363809838611866 \tabularnewline
61 & 96.76 & 96.2662400708871 & 0.493759929112887 \tabularnewline
62 & 96.05 & 95.9715721112078 & 0.0784278887921881 \tabularnewline
63 & 96.47 & 96.0043129956166 & 0.465687004383376 \tabularnewline
64 & 96.38 & 95.6659905233922 & 0.714009476607772 \tabularnewline
65 & 97.27 & 95.9606584830715 & 1.30934151692846 \tabularnewline
66 & 96.67 & 95.7969540610275 & 0.873045938972523 \tabularnewline
67 & 96.59 & 95.7642131766187 & 0.825786823381338 \tabularnewline
68 & 96.06 & 95.4913724732119 & 0.568627526788109 \tabularnewline
69 & 96.92 & 95.3167544230316 & 1.60324557696844 \tabularnewline
70 & 94.96 & 94.694677619264 & 0.265322380735878 \tabularnewline
71 & 95.59 & 94.9129501819895 & 0.677049818010468 \tabularnewline
72 & 95.68 & 94.7929002724906 & 0.88709972750945 \tabularnewline
73 & 95.35 & 94.9566046945346 & 0.393395305465384 \tabularnewline
74 & 95.41 & 94.6619367348553 & 0.748063265144695 \tabularnewline
75 & 95.32 & 94.6728503629916 & 0.647149637008415 \tabularnewline
76 & 95.8 & 94.7492457599455 & 1.05075424005453 \tabularnewline
77 & 95.46 & 94.5746277097651 & 0.885372290234858 \tabularnewline
78 & 94.16 & 93.919810021589 & 0.240189978411106 \tabularnewline
79 & 92.49 & 93.035806142551 & -0.545806142550952 \tabularnewline
80 & 91.58 & 92.8066199516893 & -1.22661995168925 \tabularnewline
81 & 91.5 & 92.3700748262384 & -0.870074826238425 \tabularnewline
82 & 90.83 & 92.4682974794649 & -1.63829747946487 \tabularnewline
83 & 91.28 & 92.7411381828716 & -1.46113818287164 \tabularnewline
84 & 90.57 & 92.4028157106472 & -1.83281571064725 \tabularnewline
85 & 90.93 & 92.6538291577815 & -1.72382915778145 \tabularnewline
86 & 90.9 & 91.9553569570601 & -1.05535695706012 \tabularnewline
87 & 91.49 & 91.988097841469 & -0.49809784146894 \tabularnewline
88 & 91.38 & 91.7916525350161 & -0.411652535016073 \tabularnewline
89 & 90.91 & 91.4096755502466 & -0.499675550246581 \tabularnewline
90 & 90.72 & 91.1259212187036 & -0.405921218703547 \tabularnewline
91 & 89.53 & 90.9294759122507 & -1.39947591225066 \tabularnewline
92 & 89.47 & 90.5474989274812 & -1.07749892748119 \tabularnewline
93 & 89.28 & 90.176435570848 & -0.896435570847973 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5644&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]107.89[/C][C]106.928854760024[/C][C]0.96114523997586[/C][/ROW]
[ROW][C]2[/C][C]107.26[/C][C]106.819718478661[/C][C]0.440281521338944[/C][/ROW]
[ROW][C]3[/C][C]107.76[/C][C]106.961595644433[/C][C]0.79840435556744[/C][/ROW]
[ROW][C]4[/C][C]107.32[/C][C]106.470482378300[/C][C]0.849517621699604[/C][/ROW]
[ROW][C]5[/C][C]107.15[/C][C]106.481396006437[/C][C]0.668603993563355[/C][/ROW]
[ROW][C]6[/C][C]108.04[/C][C]106.623273172208[/C][C]1.41672682779182[/C][/ROW]
[ROW][C]7[/C][C]106.52[/C][C]106.099419021667[/C][C]0.420580978332819[/C][/ROW]
[ROW][C]8[/C][C]106.62[/C][C]106.088505393531[/C][C]0.531494606469105[/C][/ROW]
[ROW][C]9[/C][C]106.47[/C][C]105.466428589763[/C][C]1.00357141023653[/C][/ROW]
[ROW][C]10[/C][C]105.46[/C][C]105.411860449082[/C][C]0.0481395509178773[/C][/ROW]
[ROW][C]11[/C][C]106.13[/C][C]105.259069655174[/C][C]0.870930344825672[/C][/ROW]
[ROW][C]12[/C][C]105.15[/C][C]104.975315323631[/C][C]0.174684676368731[/C][/ROW]
[ROW][C]13[/C][C]105.39[/C][C]105.204501514493[/C][C]0.185498485507044[/C][/ROW]
[ROW][C]14[/C][C]104.57[/C][C]105.531910358581[/C][C]-0.961910358581102[/C][/ROW]
[ROW][C]15[/C][C]104.29[/C][C]105.390033192810[/C][C]-1.10003319280956[/C][/ROW]
[ROW][C]16[/C][C]104.09[/C][C]104.997142579904[/C][C]-0.90714257990381[/C][/ROW]
[ROW][C]17[/C][C]104.51[/C][C]105.018969836176[/C][C]-0.50896983617636[/C][/ROW]
[ROW][C]18[/C][C]103.39[/C][C]104.593338338862[/C][C]-1.2033383388618[/C][/ROW]
[ROW][C]19[/C][C]102.71[/C][C]104.036743303912[/C][C]-1.32674330391199[/C][/ROW]
[ROW][C]20[/C][C]102.62[/C][C]104.080397816457[/C][C]-1.46039781645707[/C][/ROW]
[ROW][C]21[/C][C]101.94[/C][C]103.589284550325[/C][C]-1.64928455032488[/C][/ROW]
[ROW][C]22[/C][C]101.65[/C][C]103.556543665916[/C][C]-1.90654366591606[/C][/ROW]
[ROW][C]23[/C][C]101.86[/C][C]103.578370922189[/C][C]-1.71837092218860[/C][/ROW]
[ROW][C]24[/C][C]101.27[/C][C]103.611111806597[/C][C]-2.34111180659742[/C][/ROW]
[ROW][C]25[/C][C]101.21[/C][C]103.818470741187[/C][C]-2.60847074118657[/C][/ROW]
[ROW][C]26[/C][C]102.15[/C][C]103.687507203551[/C][C]-1.5375072035513[/C][/ROW]
[ROW][C]27[/C][C]102.07[/C][C]103.578370922189[/C][C]-1.50837092218861[/C][/ROW]
[ROW][C]28[/C][C]102.8[/C][C]102.901725977740[/C][C]-0.101725977739807[/C][/ROW]
[ROW][C]29[/C][C]103.39[/C][C]102.563403505515[/C][C]0.82659649448458[/C][/ROW]
[ROW][C]30[/C][C]102.71[/C][C]102.399699083471[/C][C]0.310300916528643[/C][/ROW]
[ROW][C]31[/C][C]102.65[/C][C]102.148685636337[/C][C]0.501314363662889[/C][/ROW]
[ROW][C]32[/C][C]101.12[/C][C]101.439299807480[/C][C]-0.319299807479515[/C][/ROW]
[ROW][C]33[/C][C]100.29[/C][C]100.697173094213[/C][C]-0.407173094213087[/C][/ROW]
[ROW][C]34[/C][C]99.79[/C][C]100.391591506398[/C][C]-0.601591506397501[/C][/ROW]
[ROW][C]35[/C][C]100.11[/C][C]100.751741234894[/C][C]-0.641741234894445[/C][/ROW]
[ROW][C]36[/C][C]99.76[/C][C]100.882704772530[/C][C]-1.12270477252969[/C][/ROW]
[ROW][C]37[/C][C]99.96[/C][C]100.347936993852[/C][C]-0.387936993852439[/C][/ROW]
[ROW][C]38[/C][C]99.98[/C][C]100.271541596899[/C][C]-0.291541596898525[/C][/ROW]
[ROW][C]39[/C][C]100.49[/C][C]100.140578059263[/C][C]0.349421940736722[/C][/ROW]
[ROW][C]40[/C][C]100.75[/C][C]99.76951470263[/C][C]0.980485297369925[/C][/ROW]
[ROW][C]41[/C][C]100.84[/C][C]99.8240828433114[/C][C]1.01591715668858[/C][/ROW]
[ROW][C]42[/C][C]100.44[/C][C]99.3984513459969[/C][C]1.04154865400314[/C][/ROW]
[ROW][C]43[/C][C]99.57[/C][C]98.8200290547745[/C][C]0.749970945225488[/C][/ROW]
[ROW][C]44[/C][C]99.22[/C][C]98.6672382608667[/C][C]0.552761739133287[/C][/ROW]
[ROW][C]45[/C][C]99.08[/C][C]98.2634340198247[/C][C]0.816565980175313[/C][/ROW]
[ROW][C]46[/C][C]98.04[/C][C]97.9469388038728[/C][C]0.0930611961271679[/C][/ROW]
[ROW][C]47[/C][C]98.73[/C][C]98.0124205726905[/C][C]0.717579427309538[/C][/ROW]
[ROW][C]48[/C][C]98.72[/C][C]97.8159752662376[/C][C]0.904024733762416[/C][/ROW]
[ROW][C]49[/C][C]100.07[/C][C]98.1652113665983[/C][C]1.90478863340173[/C][/ROW]
[ROW][C]50[/C][C]99.02[/C][C]97.8596297787827[/C][C]1.16037022121732[/C][/ROW]
[ROW][C]51[/C][C]98.94[/C][C]97.5649618191033[/C][C]1.37503818089665[/C][/ROW]
[ROW][C]52[/C][C]99[/C][C]97.3576028845142[/C][C]1.64239711548580[/C][/ROW]
[ROW][C]53[/C][C]98.54[/C][C]97.0520212966986[/C][C]1.48797870330139[/C][/ROW]
[ROW][C]54[/C][C]98.42[/C][C]97.346689256378[/C][C]1.07331074362206[/C][/ROW]
[ROW][C]55[/C][C]97.9[/C][C]97.6195299597847[/C][C]0.28047004021529[/C][/ROW]
[ROW][C]56[/C][C]97.46[/C][C]97.3139483719691[/C][C]0.146051628030864[/C][/ROW]
[ROW][C]57[/C][C]97[/C][C]96.582735286839[/C][C]0.41726471316102[/C][/ROW]
[ROW][C]58[/C][C]95.97[/C][C]96.1134492769793[/C][C]-0.143449276979326[/C][/ROW]
[ROW][C]59[/C][C]96.55[/C][C]96.058881136298[/C][C]0.491118863702023[/C][/ROW]
[ROW][C]60[/C][C]96.51[/C][C]96.1461901613881[/C][C]0.363809838611866[/C][/ROW]
[ROW][C]61[/C][C]96.76[/C][C]96.2662400708871[/C][C]0.493759929112887[/C][/ROW]
[ROW][C]62[/C][C]96.05[/C][C]95.9715721112078[/C][C]0.0784278887921881[/C][/ROW]
[ROW][C]63[/C][C]96.47[/C][C]96.0043129956166[/C][C]0.465687004383376[/C][/ROW]
[ROW][C]64[/C][C]96.38[/C][C]95.6659905233922[/C][C]0.714009476607772[/C][/ROW]
[ROW][C]65[/C][C]97.27[/C][C]95.9606584830715[/C][C]1.30934151692846[/C][/ROW]
[ROW][C]66[/C][C]96.67[/C][C]95.7969540610275[/C][C]0.873045938972523[/C][/ROW]
[ROW][C]67[/C][C]96.59[/C][C]95.7642131766187[/C][C]0.825786823381338[/C][/ROW]
[ROW][C]68[/C][C]96.06[/C][C]95.4913724732119[/C][C]0.568627526788109[/C][/ROW]
[ROW][C]69[/C][C]96.92[/C][C]95.3167544230316[/C][C]1.60324557696844[/C][/ROW]
[ROW][C]70[/C][C]94.96[/C][C]94.694677619264[/C][C]0.265322380735878[/C][/ROW]
[ROW][C]71[/C][C]95.59[/C][C]94.9129501819895[/C][C]0.677049818010468[/C][/ROW]
[ROW][C]72[/C][C]95.68[/C][C]94.7929002724906[/C][C]0.88709972750945[/C][/ROW]
[ROW][C]73[/C][C]95.35[/C][C]94.9566046945346[/C][C]0.393395305465384[/C][/ROW]
[ROW][C]74[/C][C]95.41[/C][C]94.6619367348553[/C][C]0.748063265144695[/C][/ROW]
[ROW][C]75[/C][C]95.32[/C][C]94.6728503629916[/C][C]0.647149637008415[/C][/ROW]
[ROW][C]76[/C][C]95.8[/C][C]94.7492457599455[/C][C]1.05075424005453[/C][/ROW]
[ROW][C]77[/C][C]95.46[/C][C]94.5746277097651[/C][C]0.885372290234858[/C][/ROW]
[ROW][C]78[/C][C]94.16[/C][C]93.919810021589[/C][C]0.240189978411106[/C][/ROW]
[ROW][C]79[/C][C]92.49[/C][C]93.035806142551[/C][C]-0.545806142550952[/C][/ROW]
[ROW][C]80[/C][C]91.58[/C][C]92.8066199516893[/C][C]-1.22661995168925[/C][/ROW]
[ROW][C]81[/C][C]91.5[/C][C]92.3700748262384[/C][C]-0.870074826238425[/C][/ROW]
[ROW][C]82[/C][C]90.83[/C][C]92.4682974794649[/C][C]-1.63829747946487[/C][/ROW]
[ROW][C]83[/C][C]91.28[/C][C]92.7411381828716[/C][C]-1.46113818287164[/C][/ROW]
[ROW][C]84[/C][C]90.57[/C][C]92.4028157106472[/C][C]-1.83281571064725[/C][/ROW]
[ROW][C]85[/C][C]90.93[/C][C]92.6538291577815[/C][C]-1.72382915778145[/C][/ROW]
[ROW][C]86[/C][C]90.9[/C][C]91.9553569570601[/C][C]-1.05535695706012[/C][/ROW]
[ROW][C]87[/C][C]91.49[/C][C]91.988097841469[/C][C]-0.49809784146894[/C][/ROW]
[ROW][C]88[/C][C]91.38[/C][C]91.7916525350161[/C][C]-0.411652535016073[/C][/ROW]
[ROW][C]89[/C][C]90.91[/C][C]91.4096755502466[/C][C]-0.499675550246581[/C][/ROW]
[ROW][C]90[/C][C]90.72[/C][C]91.1259212187036[/C][C]-0.405921218703547[/C][/ROW]
[ROW][C]91[/C][C]89.53[/C][C]90.9294759122507[/C][C]-1.39947591225066[/C][/ROW]
[ROW][C]92[/C][C]89.47[/C][C]90.5474989274812[/C][C]-1.07749892748119[/C][/ROW]
[ROW][C]93[/C][C]89.28[/C][C]90.176435570848[/C][C]-0.896435570847973[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5644&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5644&T=4

As an alternative you can also use a QR Code:  

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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1107.89106.9288547600240.96114523997586
2107.26106.8197184786610.440281521338944
3107.76106.9615956444330.79840435556744
4107.32106.4704823783000.849517621699604
5107.15106.4813960064370.668603993563355
6108.04106.6232731722081.41672682779182
7106.52106.0994190216670.420580978332819
8106.62106.0885053935310.531494606469105
9106.47105.4664285897631.00357141023653
10105.46105.4118604490820.0481395509178773
11106.13105.2590696551740.870930344825672
12105.15104.9753153236310.174684676368731
13105.39105.2045015144930.185498485507044
14104.57105.531910358581-0.961910358581102
15104.29105.390033192810-1.10003319280956
16104.09104.997142579904-0.90714257990381
17104.51105.018969836176-0.50896983617636
18103.39104.593338338862-1.2033383388618
19102.71104.036743303912-1.32674330391199
20102.62104.080397816457-1.46039781645707
21101.94103.589284550325-1.64928455032488
22101.65103.556543665916-1.90654366591606
23101.86103.578370922189-1.71837092218860
24101.27103.611111806597-2.34111180659742
25101.21103.818470741187-2.60847074118657
26102.15103.687507203551-1.5375072035513
27102.07103.578370922189-1.50837092218861
28102.8102.901725977740-0.101725977739807
29103.39102.5634035055150.82659649448458
30102.71102.3996990834710.310300916528643
31102.65102.1486856363370.501314363662889
32101.12101.439299807480-0.319299807479515
33100.29100.697173094213-0.407173094213087
3499.79100.391591506398-0.601591506397501
35100.11100.751741234894-0.641741234894445
3699.76100.882704772530-1.12270477252969
3799.96100.347936993852-0.387936993852439
3899.98100.271541596899-0.291541596898525
39100.49100.1405780592630.349421940736722
40100.7599.769514702630.980485297369925
41100.8499.82408284331141.01591715668858
42100.4499.39845134599691.04154865400314
4399.5798.82002905477450.749970945225488
4499.2298.66723826086670.552761739133287
4599.0898.26343401982470.816565980175313
4698.0497.94693880387280.0930611961271679
4798.7398.01242057269050.717579427309538
4898.7297.81597526623760.904024733762416
49100.0798.16521136659831.90478863340173
5099.0297.85962977878271.16037022121732
5198.9497.56496181910331.37503818089665
529997.35760288451421.64239711548580
5398.5497.05202129669861.48797870330139
5498.4297.3466892563781.07331074362206
5597.997.61952995978470.28047004021529
5697.4697.31394837196910.146051628030864
579796.5827352868390.41726471316102
5895.9796.1134492769793-0.143449276979326
5996.5596.0588811362980.491118863702023
6096.5196.14619016138810.363809838611866
6196.7696.26624007088710.493759929112887
6296.0595.97157211120780.0784278887921881
6396.4796.00431299561660.465687004383376
6496.3895.66599052339220.714009476607772
6597.2795.96065848307151.30934151692846
6696.6795.79695406102750.873045938972523
6796.5995.76421317661870.825786823381338
6896.0695.49137247321190.568627526788109
6996.9295.31675442303161.60324557696844
7094.9694.6946776192640.265322380735878
7195.5994.91295018198950.677049818010468
7295.6894.79290027249060.88709972750945
7395.3594.95660469453460.393395305465384
7495.4194.66193673485530.748063265144695
7595.3294.67285036299160.647149637008415
7695.894.74924575994551.05075424005453
7795.4694.57462770976510.885372290234858
7894.1693.9198100215890.240189978411106
7992.4993.035806142551-0.545806142550952
8091.5892.8066199516893-1.22661995168925
8191.592.3700748262384-0.870074826238425
8290.8392.4682974794649-1.63829747946487
8391.2892.7411381828716-1.46113818287164
8490.5792.4028157106472-1.83281571064725
8590.9392.6538291577815-1.72382915778145
8690.991.9553569570601-1.05535695706012
8791.4991.988097841469-0.49809784146894
8891.3891.7916525350161-0.411652535016073
8990.9191.4096755502466-0.499675550246581
9090.7291.1259212187036-0.405921218703547
9189.5390.9294759122507-1.39947591225066
9289.4790.5474989274812-1.07749892748119
9389.2890.176435570848-0.896435570847973



Parameters (Session):
par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
R code (references can be found in the software module):
library(lattice)
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))
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$resid, main='Residual Normal Q-Q Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$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()
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')