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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, 29 Nov 2011 06:55:04 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/29/t1322567847pfblqm4qzrb35l4.htm/, Retrieved Thu, 28 Mar 2024 11:24:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148216, Retrieved Thu, 28 Mar 2024 11:24:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact124
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]
-  M D  [Multiple Regression] [Workshop 8, Multi...] [2010-11-29 10:32:18] [d946de7cca328fbcf207448a112523ab]
-         [Multiple Regression] [Workshop 8, Multi...] [2010-11-29 20:25:47] [3635fb7041b1998c5a1332cf9de22bce]
-    D      [Multiple Regression] [Workshop 8, Multi...] [2010-11-29 20:46:24] [3635fb7041b1998c5a1332cf9de22bce]
-             [Multiple Regression] [Workshop 8 Multip...] [2010-11-30 14:40:24] [a9e130f95bad0a0597234e75c6380c5a]
- R  D            [Multiple Regression] [WS8 Multiple Line...] [2011-11-29 11:55:04] [2934cd91706ad80fc42b61dc996a3109] [Current]
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Dataseries X:
9 700
9 081
9 084
9 743
8 587
9 731
9 563
9 998
9 437
10 038
9 918
9 252
9 737
9 035
9 133
9 487
8 700
9 627
8 947
9 283
8 829
9 947
9 628
9 318
9 605
8 640
9 214
9 567
8 547
9 185
9 470
9 123
9 278
10 170
9 434
9 655
9 429
8 739
9 552
9 687
9 019
9 672
9 206
9 069
9 788
10 312
10 105
9 863
9 656
9 295
9 946
9 701
9 049
10 190
9 706
9 765
9 893
9 994
10 433
10 073
10 112
9 266
9 820
10 097
9 115
10 411
9 678
10 408
10 153
10 368
10 581
10 597
10 680
9 738
9 556




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148216&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148216&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148216&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Multiple Linear Regression - Estimated Regression Equation
y[t] = + 9.27634432548118 -0.000887640787685606V2[t] + 0.0966721877191875M1[t] -0.628484555299927M2[t] -0.289044108511377M3[t] -0.000573106461176947M4[t] -0.865455655625011M5[t] + 0.0750102261750044M6[t] -0.324514531265956M7[t] -0.138949495662991M8[t] -0.208395602658799M9[t] + 0.36598031550785M10[t] + 0.22818586786025M11[t] + 0.011071616426785t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  9.27634432548118 -0.000887640787685606V2[t] +  0.0966721877191875M1[t] -0.628484555299927M2[t] -0.289044108511377M3[t] -0.000573106461176947M4[t] -0.865455655625011M5[t] +  0.0750102261750044M6[t] -0.324514531265956M7[t] -0.138949495662991M8[t] -0.208395602658799M9[t] +  0.36598031550785M10[t] +  0.22818586786025M11[t] +  0.011071616426785t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148216&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  9.27634432548118 -0.000887640787685606V2[t] +  0.0966721877191875M1[t] -0.628484555299927M2[t] -0.289044108511377M3[t] -0.000573106461176947M4[t] -0.865455655625011M5[t] +  0.0750102261750044M6[t] -0.324514531265956M7[t] -0.138949495662991M8[t] -0.208395602658799M9[t] +  0.36598031550785M10[t] +  0.22818586786025M11[t] +  0.011071616426785t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148216&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148216&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] = + 9.27634432548118 -0.000887640787685606V2[t] + 0.0966721877191875M1[t] -0.628484555299927M2[t] -0.289044108511377M3[t] -0.000573106461176947M4[t] -0.865455655625011M5[t] + 0.0750102261750044M6[t] -0.324514531265956M7[t] -0.138949495662991M8[t] -0.208395602658799M9[t] + 0.36598031550785M10[t] + 0.22818586786025M11[t] + 0.011071616426785t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)9.276344325481180.14895662.275800
V2-0.0008876407876856060.000123-7.218200
M10.09667218771918750.1636420.59080.5568670.278433
M2-0.6284845552999270.163317-3.84830.0002870.000144
M3-0.2890441085113770.163087-1.77230.0813330.040666
M4-0.0005731064611769470.169939-0.00340.997320.49866
M5-0.8654556556250110.170246-5.08364e-062e-06
M60.07501022617500440.1694310.44270.6595350.329768
M7-0.3245145312659560.170132-1.90740.0611760.030588
M8-0.1389494956629910.169303-0.82070.4150040.207502
M9-0.2083956026587990.169694-1.22810.2241390.112069
M100.365980315507850.1692012.1630.034470.017235
M110.228185867860250.1693161.34770.182740.09137
t0.0110716164267850.0015737.0400

\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) & 9.27634432548118 & 0.148956 & 62.2758 & 0 & 0 \tabularnewline
V2 & -0.000887640787685606 & 0.000123 & -7.2182 & 0 & 0 \tabularnewline
M1 & 0.0966721877191875 & 0.163642 & 0.5908 & 0.556867 & 0.278433 \tabularnewline
M2 & -0.628484555299927 & 0.163317 & -3.8483 & 0.000287 & 0.000144 \tabularnewline
M3 & -0.289044108511377 & 0.163087 & -1.7723 & 0.081333 & 0.040666 \tabularnewline
M4 & -0.000573106461176947 & 0.169939 & -0.0034 & 0.99732 & 0.49866 \tabularnewline
M5 & -0.865455655625011 & 0.170246 & -5.0836 & 4e-06 & 2e-06 \tabularnewline
M6 & 0.0750102261750044 & 0.169431 & 0.4427 & 0.659535 & 0.329768 \tabularnewline
M7 & -0.324514531265956 & 0.170132 & -1.9074 & 0.061176 & 0.030588 \tabularnewline
M8 & -0.138949495662991 & 0.169303 & -0.8207 & 0.415004 & 0.207502 \tabularnewline
M9 & -0.208395602658799 & 0.169694 & -1.2281 & 0.224139 & 0.112069 \tabularnewline
M10 & 0.36598031550785 & 0.169201 & 2.163 & 0.03447 & 0.017235 \tabularnewline
M11 & 0.22818586786025 & 0.169316 & 1.3477 & 0.18274 & 0.09137 \tabularnewline
t & 0.011071616426785 & 0.001573 & 7.04 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148216&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]9.27634432548118[/C][C]0.148956[/C][C]62.2758[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]V2[/C][C]-0.000887640787685606[/C][C]0.000123[/C][C]-7.2182[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]0.0966721877191875[/C][C]0.163642[/C][C]0.5908[/C][C]0.556867[/C][C]0.278433[/C][/ROW]
[ROW][C]M2[/C][C]-0.628484555299927[/C][C]0.163317[/C][C]-3.8483[/C][C]0.000287[/C][C]0.000144[/C][/ROW]
[ROW][C]M3[/C][C]-0.289044108511377[/C][C]0.163087[/C][C]-1.7723[/C][C]0.081333[/C][C]0.040666[/C][/ROW]
[ROW][C]M4[/C][C]-0.000573106461176947[/C][C]0.169939[/C][C]-0.0034[/C][C]0.99732[/C][C]0.49866[/C][/ROW]
[ROW][C]M5[/C][C]-0.865455655625011[/C][C]0.170246[/C][C]-5.0836[/C][C]4e-06[/C][C]2e-06[/C][/ROW]
[ROW][C]M6[/C][C]0.0750102261750044[/C][C]0.169431[/C][C]0.4427[/C][C]0.659535[/C][C]0.329768[/C][/ROW]
[ROW][C]M7[/C][C]-0.324514531265956[/C][C]0.170132[/C][C]-1.9074[/C][C]0.061176[/C][C]0.030588[/C][/ROW]
[ROW][C]M8[/C][C]-0.138949495662991[/C][C]0.169303[/C][C]-0.8207[/C][C]0.415004[/C][C]0.207502[/C][/ROW]
[ROW][C]M9[/C][C]-0.208395602658799[/C][C]0.169694[/C][C]-1.2281[/C][C]0.224139[/C][C]0.112069[/C][/ROW]
[ROW][C]M10[/C][C]0.36598031550785[/C][C]0.169201[/C][C]2.163[/C][C]0.03447[/C][C]0.017235[/C][/ROW]
[ROW][C]M11[/C][C]0.22818586786025[/C][C]0.169316[/C][C]1.3477[/C][C]0.18274[/C][C]0.09137[/C][/ROW]
[ROW][C]t[/C][C]0.011071616426785[/C][C]0.001573[/C][C]7.04[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148216&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148216&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)9.276344325481180.14895662.275800
V2-0.0008876407876856060.000123-7.218200
M10.09667218771918750.1636420.59080.5568670.278433
M2-0.6284845552999270.163317-3.84830.0002870.000144
M3-0.2890441085113770.163087-1.77230.0813330.040666
M4-0.0005731064611769470.169939-0.00340.997320.49866
M5-0.8654556556250110.170246-5.08364e-062e-06
M60.07501022617500440.1694310.44270.6595350.329768
M7-0.3245145312659560.170132-1.90740.0611760.030588
M8-0.1389494956629910.169303-0.82070.4150040.207502
M9-0.2083956026587990.169694-1.22810.2241390.112069
M100.365980315507850.1692012.1630.034470.017235
M110.228185867860250.1693161.34770.182740.09137
t0.0110716164267850.0015737.0400







Multiple Linear Regression - Regression Statistics
Multiple R0.87240276441248
R-squared0.761086583354537
Adjusted R-squared0.71017060931534
F-TEST (value)14.9478940100139
F-TEST (DF numerator)13
F-TEST (DF denominator)61
p-value2.25375273998907e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.293005401753725
Sum Squared Residuals5.23698209286855

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.87240276441248 \tabularnewline
R-squared & 0.761086583354537 \tabularnewline
Adjusted R-squared & 0.71017060931534 \tabularnewline
F-TEST (value) & 14.9478940100139 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 61 \tabularnewline
p-value & 2.25375273998907e-14 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.293005401753725 \tabularnewline
Sum Squared Residuals & 5.23698209286855 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148216&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.87240276441248[/C][/ROW]
[ROW][C]R-squared[/C][C]0.761086583354537[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.71017060931534[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]14.9478940100139[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]61[/C][/ROW]
[ROW][C]p-value[/C][C]2.25375273998907e-14[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.293005401753725[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]5.23698209286855[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148216&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148216&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 R0.87240276441248
R-squared0.761086583354537
Adjusted R-squared0.71017060931534
F-TEST (value)14.9478940100139
F-TEST (DF numerator)13
F-TEST (DF denominator)61
p-value2.25375273998907e-14
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.293005401753725
Sum Squared Residuals5.23698209286855







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
198.762739578247230.237260421752771
298.598104099232290.401895900767712
398.945953240084570.0540467599154335
498.660540579476740.339459420523262
587.945201609618640.0547983903813568
698.768918834418720.231081165581284
798.529589345735720.470410654264278
898.340102255122230.659897744877766
998.779694246444840.220305753555164
10109.719310455324830.280689544675174
1198.811463730940680.188536269059321
1299.18551824410583-0.185518244105827
1398.862756266224280.137243733775719
1498.771794972587250.228205027412754
1599.03531823860939-0.0353182386093922
1699.02063601824567-0.0206360182456725
1787.977757597731590.02224240226841
1898.994092873459440.00590712654056085
1988.32159468038587-0.32159468038587
2099.10762481543886-0.107624815438862
2188.5645984547935-0.564598454793498
2299.04530437644003-0.0453043764400306
2399.20173895649092-0.201738956490925
2499.25979334924-0.259793349239997
2599.1127842473202-0.112784247320201
2688.36763169315888-0.367631693158875
2799.09627873192828-0.0962787319282783
2899.08248415235224-0.0824841523522444
2988.24642603536891-0.246426035368908
3099.5192894987379-0.519289498737897
3198.877858733233320.122141266766676
3299.38250673858998-0.382506738589979
3399.18654792592969-0.186547925929688
34109.867860665593170.132139334406833
3599.50680066642335-0.506800666423352
3699.09351780091137-0.0935178009113682
3799.40186842307429-0.401868423074288
3888.41261465229942-0.412614652299421
3998.929115542811960.0708844571880363
4099.10882665495139-0.108826654951392
4198.847959768388330.152040231611672
4299.21986783225643-0.219867832256427
4399.24505529830375-0.245055298303744
4499.56329873824642-0.563298738246422
4598.866710521331450.133289478668551
46109.874675070863230.125324929136769
47109.931693882693340.0683061173066632
4899.04174791419418-0.0417479141941824
4999.33323336139108-0.333233361391075
5098.939586559153250.0604134408467501
5198.712244469585260.287755530414745
5299.22925908104521-0.229259081045214
5398.954189941879180.0458100581208199
54109.780570089042310.21942991095769
5598.934094301582360.0659056984176386
5699.07836014713866-0.0783601471386608
5798.906367635745880.0936323642541194
5899.40216345078307-0.402163450783068
59109.773407101453880.226592898546122
60109.875843533587230.124156466412769
61109.948969347013470.0510306529865346
6299.09818753911755-0.0981875391175526
6398.956946605955060.0430533940449381
64109.898253513928740.10174648607126
6599.02846504701335-0.0284650470133505
66109.717260872085210.282739127914789
6799.09180764075898-0.0918076407589785
68109.528107305463840.471892694536158
69109.696081215754650.303918784245351
701010.0906859809957-0.0906859809956775
71109.774895661997830.225104338002171
72109.543579157961390.456420842038606
73109.577648776729460.422351223270539
7498.812080484451370.187919515548633
7599.32414317102548-0.324143171025482

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 9 & 8.76273957824723 & 0.237260421752771 \tabularnewline
2 & 9 & 8.59810409923229 & 0.401895900767712 \tabularnewline
3 & 9 & 8.94595324008457 & 0.0540467599154335 \tabularnewline
4 & 9 & 8.66054057947674 & 0.339459420523262 \tabularnewline
5 & 8 & 7.94520160961864 & 0.0547983903813568 \tabularnewline
6 & 9 & 8.76891883441872 & 0.231081165581284 \tabularnewline
7 & 9 & 8.52958934573572 & 0.470410654264278 \tabularnewline
8 & 9 & 8.34010225512223 & 0.659897744877766 \tabularnewline
9 & 9 & 8.77969424644484 & 0.220305753555164 \tabularnewline
10 & 10 & 9.71931045532483 & 0.280689544675174 \tabularnewline
11 & 9 & 8.81146373094068 & 0.188536269059321 \tabularnewline
12 & 9 & 9.18551824410583 & -0.185518244105827 \tabularnewline
13 & 9 & 8.86275626622428 & 0.137243733775719 \tabularnewline
14 & 9 & 8.77179497258725 & 0.228205027412754 \tabularnewline
15 & 9 & 9.03531823860939 & -0.0353182386093922 \tabularnewline
16 & 9 & 9.02063601824567 & -0.0206360182456725 \tabularnewline
17 & 8 & 7.97775759773159 & 0.02224240226841 \tabularnewline
18 & 9 & 8.99409287345944 & 0.00590712654056085 \tabularnewline
19 & 8 & 8.32159468038587 & -0.32159468038587 \tabularnewline
20 & 9 & 9.10762481543886 & -0.107624815438862 \tabularnewline
21 & 8 & 8.5645984547935 & -0.564598454793498 \tabularnewline
22 & 9 & 9.04530437644003 & -0.0453043764400306 \tabularnewline
23 & 9 & 9.20173895649092 & -0.201738956490925 \tabularnewline
24 & 9 & 9.25979334924 & -0.259793349239997 \tabularnewline
25 & 9 & 9.1127842473202 & -0.112784247320201 \tabularnewline
26 & 8 & 8.36763169315888 & -0.367631693158875 \tabularnewline
27 & 9 & 9.09627873192828 & -0.0962787319282783 \tabularnewline
28 & 9 & 9.08248415235224 & -0.0824841523522444 \tabularnewline
29 & 8 & 8.24642603536891 & -0.246426035368908 \tabularnewline
30 & 9 & 9.5192894987379 & -0.519289498737897 \tabularnewline
31 & 9 & 8.87785873323332 & 0.122141266766676 \tabularnewline
32 & 9 & 9.38250673858998 & -0.382506738589979 \tabularnewline
33 & 9 & 9.18654792592969 & -0.186547925929688 \tabularnewline
34 & 10 & 9.86786066559317 & 0.132139334406833 \tabularnewline
35 & 9 & 9.50680066642335 & -0.506800666423352 \tabularnewline
36 & 9 & 9.09351780091137 & -0.0935178009113682 \tabularnewline
37 & 9 & 9.40186842307429 & -0.401868423074288 \tabularnewline
38 & 8 & 8.41261465229942 & -0.412614652299421 \tabularnewline
39 & 9 & 8.92911554281196 & 0.0708844571880363 \tabularnewline
40 & 9 & 9.10882665495139 & -0.108826654951392 \tabularnewline
41 & 9 & 8.84795976838833 & 0.152040231611672 \tabularnewline
42 & 9 & 9.21986783225643 & -0.219867832256427 \tabularnewline
43 & 9 & 9.24505529830375 & -0.245055298303744 \tabularnewline
44 & 9 & 9.56329873824642 & -0.563298738246422 \tabularnewline
45 & 9 & 8.86671052133145 & 0.133289478668551 \tabularnewline
46 & 10 & 9.87467507086323 & 0.125324929136769 \tabularnewline
47 & 10 & 9.93169388269334 & 0.0683061173066632 \tabularnewline
48 & 9 & 9.04174791419418 & -0.0417479141941824 \tabularnewline
49 & 9 & 9.33323336139108 & -0.333233361391075 \tabularnewline
50 & 9 & 8.93958655915325 & 0.0604134408467501 \tabularnewline
51 & 9 & 8.71224446958526 & 0.287755530414745 \tabularnewline
52 & 9 & 9.22925908104521 & -0.229259081045214 \tabularnewline
53 & 9 & 8.95418994187918 & 0.0458100581208199 \tabularnewline
54 & 10 & 9.78057008904231 & 0.21942991095769 \tabularnewline
55 & 9 & 8.93409430158236 & 0.0659056984176386 \tabularnewline
56 & 9 & 9.07836014713866 & -0.0783601471386608 \tabularnewline
57 & 9 & 8.90636763574588 & 0.0936323642541194 \tabularnewline
58 & 9 & 9.40216345078307 & -0.402163450783068 \tabularnewline
59 & 10 & 9.77340710145388 & 0.226592898546122 \tabularnewline
60 & 10 & 9.87584353358723 & 0.124156466412769 \tabularnewline
61 & 10 & 9.94896934701347 & 0.0510306529865346 \tabularnewline
62 & 9 & 9.09818753911755 & -0.0981875391175526 \tabularnewline
63 & 9 & 8.95694660595506 & 0.0430533940449381 \tabularnewline
64 & 10 & 9.89825351392874 & 0.10174648607126 \tabularnewline
65 & 9 & 9.02846504701335 & -0.0284650470133505 \tabularnewline
66 & 10 & 9.71726087208521 & 0.282739127914789 \tabularnewline
67 & 9 & 9.09180764075898 & -0.0918076407589785 \tabularnewline
68 & 10 & 9.52810730546384 & 0.471892694536158 \tabularnewline
69 & 10 & 9.69608121575465 & 0.303918784245351 \tabularnewline
70 & 10 & 10.0906859809957 & -0.0906859809956775 \tabularnewline
71 & 10 & 9.77489566199783 & 0.225104338002171 \tabularnewline
72 & 10 & 9.54357915796139 & 0.456420842038606 \tabularnewline
73 & 10 & 9.57764877672946 & 0.422351223270539 \tabularnewline
74 & 9 & 8.81208048445137 & 0.187919515548633 \tabularnewline
75 & 9 & 9.32414317102548 & -0.324143171025482 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148216&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]9[/C][C]8.76273957824723[/C][C]0.237260421752771[/C][/ROW]
[ROW][C]2[/C][C]9[/C][C]8.59810409923229[/C][C]0.401895900767712[/C][/ROW]
[ROW][C]3[/C][C]9[/C][C]8.94595324008457[/C][C]0.0540467599154335[/C][/ROW]
[ROW][C]4[/C][C]9[/C][C]8.66054057947674[/C][C]0.339459420523262[/C][/ROW]
[ROW][C]5[/C][C]8[/C][C]7.94520160961864[/C][C]0.0547983903813568[/C][/ROW]
[ROW][C]6[/C][C]9[/C][C]8.76891883441872[/C][C]0.231081165581284[/C][/ROW]
[ROW][C]7[/C][C]9[/C][C]8.52958934573572[/C][C]0.470410654264278[/C][/ROW]
[ROW][C]8[/C][C]9[/C][C]8.34010225512223[/C][C]0.659897744877766[/C][/ROW]
[ROW][C]9[/C][C]9[/C][C]8.77969424644484[/C][C]0.220305753555164[/C][/ROW]
[ROW][C]10[/C][C]10[/C][C]9.71931045532483[/C][C]0.280689544675174[/C][/ROW]
[ROW][C]11[/C][C]9[/C][C]8.81146373094068[/C][C]0.188536269059321[/C][/ROW]
[ROW][C]12[/C][C]9[/C][C]9.18551824410583[/C][C]-0.185518244105827[/C][/ROW]
[ROW][C]13[/C][C]9[/C][C]8.86275626622428[/C][C]0.137243733775719[/C][/ROW]
[ROW][C]14[/C][C]9[/C][C]8.77179497258725[/C][C]0.228205027412754[/C][/ROW]
[ROW][C]15[/C][C]9[/C][C]9.03531823860939[/C][C]-0.0353182386093922[/C][/ROW]
[ROW][C]16[/C][C]9[/C][C]9.02063601824567[/C][C]-0.0206360182456725[/C][/ROW]
[ROW][C]17[/C][C]8[/C][C]7.97775759773159[/C][C]0.02224240226841[/C][/ROW]
[ROW][C]18[/C][C]9[/C][C]8.99409287345944[/C][C]0.00590712654056085[/C][/ROW]
[ROW][C]19[/C][C]8[/C][C]8.32159468038587[/C][C]-0.32159468038587[/C][/ROW]
[ROW][C]20[/C][C]9[/C][C]9.10762481543886[/C][C]-0.107624815438862[/C][/ROW]
[ROW][C]21[/C][C]8[/C][C]8.5645984547935[/C][C]-0.564598454793498[/C][/ROW]
[ROW][C]22[/C][C]9[/C][C]9.04530437644003[/C][C]-0.0453043764400306[/C][/ROW]
[ROW][C]23[/C][C]9[/C][C]9.20173895649092[/C][C]-0.201738956490925[/C][/ROW]
[ROW][C]24[/C][C]9[/C][C]9.25979334924[/C][C]-0.259793349239997[/C][/ROW]
[ROW][C]25[/C][C]9[/C][C]9.1127842473202[/C][C]-0.112784247320201[/C][/ROW]
[ROW][C]26[/C][C]8[/C][C]8.36763169315888[/C][C]-0.367631693158875[/C][/ROW]
[ROW][C]27[/C][C]9[/C][C]9.09627873192828[/C][C]-0.0962787319282783[/C][/ROW]
[ROW][C]28[/C][C]9[/C][C]9.08248415235224[/C][C]-0.0824841523522444[/C][/ROW]
[ROW][C]29[/C][C]8[/C][C]8.24642603536891[/C][C]-0.246426035368908[/C][/ROW]
[ROW][C]30[/C][C]9[/C][C]9.5192894987379[/C][C]-0.519289498737897[/C][/ROW]
[ROW][C]31[/C][C]9[/C][C]8.87785873323332[/C][C]0.122141266766676[/C][/ROW]
[ROW][C]32[/C][C]9[/C][C]9.38250673858998[/C][C]-0.382506738589979[/C][/ROW]
[ROW][C]33[/C][C]9[/C][C]9.18654792592969[/C][C]-0.186547925929688[/C][/ROW]
[ROW][C]34[/C][C]10[/C][C]9.86786066559317[/C][C]0.132139334406833[/C][/ROW]
[ROW][C]35[/C][C]9[/C][C]9.50680066642335[/C][C]-0.506800666423352[/C][/ROW]
[ROW][C]36[/C][C]9[/C][C]9.09351780091137[/C][C]-0.0935178009113682[/C][/ROW]
[ROW][C]37[/C][C]9[/C][C]9.40186842307429[/C][C]-0.401868423074288[/C][/ROW]
[ROW][C]38[/C][C]8[/C][C]8.41261465229942[/C][C]-0.412614652299421[/C][/ROW]
[ROW][C]39[/C][C]9[/C][C]8.92911554281196[/C][C]0.0708844571880363[/C][/ROW]
[ROW][C]40[/C][C]9[/C][C]9.10882665495139[/C][C]-0.108826654951392[/C][/ROW]
[ROW][C]41[/C][C]9[/C][C]8.84795976838833[/C][C]0.152040231611672[/C][/ROW]
[ROW][C]42[/C][C]9[/C][C]9.21986783225643[/C][C]-0.219867832256427[/C][/ROW]
[ROW][C]43[/C][C]9[/C][C]9.24505529830375[/C][C]-0.245055298303744[/C][/ROW]
[ROW][C]44[/C][C]9[/C][C]9.56329873824642[/C][C]-0.563298738246422[/C][/ROW]
[ROW][C]45[/C][C]9[/C][C]8.86671052133145[/C][C]0.133289478668551[/C][/ROW]
[ROW][C]46[/C][C]10[/C][C]9.87467507086323[/C][C]0.125324929136769[/C][/ROW]
[ROW][C]47[/C][C]10[/C][C]9.93169388269334[/C][C]0.0683061173066632[/C][/ROW]
[ROW][C]48[/C][C]9[/C][C]9.04174791419418[/C][C]-0.0417479141941824[/C][/ROW]
[ROW][C]49[/C][C]9[/C][C]9.33323336139108[/C][C]-0.333233361391075[/C][/ROW]
[ROW][C]50[/C][C]9[/C][C]8.93958655915325[/C][C]0.0604134408467501[/C][/ROW]
[ROW][C]51[/C][C]9[/C][C]8.71224446958526[/C][C]0.287755530414745[/C][/ROW]
[ROW][C]52[/C][C]9[/C][C]9.22925908104521[/C][C]-0.229259081045214[/C][/ROW]
[ROW][C]53[/C][C]9[/C][C]8.95418994187918[/C][C]0.0458100581208199[/C][/ROW]
[ROW][C]54[/C][C]10[/C][C]9.78057008904231[/C][C]0.21942991095769[/C][/ROW]
[ROW][C]55[/C][C]9[/C][C]8.93409430158236[/C][C]0.0659056984176386[/C][/ROW]
[ROW][C]56[/C][C]9[/C][C]9.07836014713866[/C][C]-0.0783601471386608[/C][/ROW]
[ROW][C]57[/C][C]9[/C][C]8.90636763574588[/C][C]0.0936323642541194[/C][/ROW]
[ROW][C]58[/C][C]9[/C][C]9.40216345078307[/C][C]-0.402163450783068[/C][/ROW]
[ROW][C]59[/C][C]10[/C][C]9.77340710145388[/C][C]0.226592898546122[/C][/ROW]
[ROW][C]60[/C][C]10[/C][C]9.87584353358723[/C][C]0.124156466412769[/C][/ROW]
[ROW][C]61[/C][C]10[/C][C]9.94896934701347[/C][C]0.0510306529865346[/C][/ROW]
[ROW][C]62[/C][C]9[/C][C]9.09818753911755[/C][C]-0.0981875391175526[/C][/ROW]
[ROW][C]63[/C][C]9[/C][C]8.95694660595506[/C][C]0.0430533940449381[/C][/ROW]
[ROW][C]64[/C][C]10[/C][C]9.89825351392874[/C][C]0.10174648607126[/C][/ROW]
[ROW][C]65[/C][C]9[/C][C]9.02846504701335[/C][C]-0.0284650470133505[/C][/ROW]
[ROW][C]66[/C][C]10[/C][C]9.71726087208521[/C][C]0.282739127914789[/C][/ROW]
[ROW][C]67[/C][C]9[/C][C]9.09180764075898[/C][C]-0.0918076407589785[/C][/ROW]
[ROW][C]68[/C][C]10[/C][C]9.52810730546384[/C][C]0.471892694536158[/C][/ROW]
[ROW][C]69[/C][C]10[/C][C]9.69608121575465[/C][C]0.303918784245351[/C][/ROW]
[ROW][C]70[/C][C]10[/C][C]10.0906859809957[/C][C]-0.0906859809956775[/C][/ROW]
[ROW][C]71[/C][C]10[/C][C]9.77489566199783[/C][C]0.225104338002171[/C][/ROW]
[ROW][C]72[/C][C]10[/C][C]9.54357915796139[/C][C]0.456420842038606[/C][/ROW]
[ROW][C]73[/C][C]10[/C][C]9.57764877672946[/C][C]0.422351223270539[/C][/ROW]
[ROW][C]74[/C][C]9[/C][C]8.81208048445137[/C][C]0.187919515548633[/C][/ROW]
[ROW][C]75[/C][C]9[/C][C]9.32414317102548[/C][C]-0.324143171025482[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148216&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148216&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
198.762739578247230.237260421752771
298.598104099232290.401895900767712
398.945953240084570.0540467599154335
498.660540579476740.339459420523262
587.945201609618640.0547983903813568
698.768918834418720.231081165581284
798.529589345735720.470410654264278
898.340102255122230.659897744877766
998.779694246444840.220305753555164
10109.719310455324830.280689544675174
1198.811463730940680.188536269059321
1299.18551824410583-0.185518244105827
1398.862756266224280.137243733775719
1498.771794972587250.228205027412754
1599.03531823860939-0.0353182386093922
1699.02063601824567-0.0206360182456725
1787.977757597731590.02224240226841
1898.994092873459440.00590712654056085
1988.32159468038587-0.32159468038587
2099.10762481543886-0.107624815438862
2188.5645984547935-0.564598454793498
2299.04530437644003-0.0453043764400306
2399.20173895649092-0.201738956490925
2499.25979334924-0.259793349239997
2599.1127842473202-0.112784247320201
2688.36763169315888-0.367631693158875
2799.09627873192828-0.0962787319282783
2899.08248415235224-0.0824841523522444
2988.24642603536891-0.246426035368908
3099.5192894987379-0.519289498737897
3198.877858733233320.122141266766676
3299.38250673858998-0.382506738589979
3399.18654792592969-0.186547925929688
34109.867860665593170.132139334406833
3599.50680066642335-0.506800666423352
3699.09351780091137-0.0935178009113682
3799.40186842307429-0.401868423074288
3888.41261465229942-0.412614652299421
3998.929115542811960.0708844571880363
4099.10882665495139-0.108826654951392
4198.847959768388330.152040231611672
4299.21986783225643-0.219867832256427
4399.24505529830375-0.245055298303744
4499.56329873824642-0.563298738246422
4598.866710521331450.133289478668551
46109.874675070863230.125324929136769
47109.931693882693340.0683061173066632
4899.04174791419418-0.0417479141941824
4999.33323336139108-0.333233361391075
5098.939586559153250.0604134408467501
5198.712244469585260.287755530414745
5299.22925908104521-0.229259081045214
5398.954189941879180.0458100581208199
54109.780570089042310.21942991095769
5598.934094301582360.0659056984176386
5699.07836014713866-0.0783601471386608
5798.906367635745880.0936323642541194
5899.40216345078307-0.402163450783068
59109.773407101453880.226592898546122
60109.875843533587230.124156466412769
61109.948969347013470.0510306529865346
6299.09818753911755-0.0981875391175526
6398.956946605955060.0430533940449381
64109.898253513928740.10174648607126
6599.02846504701335-0.0284650470133505
66109.717260872085210.282739127914789
6799.09180764075898-0.0918076407589785
68109.528107305463840.471892694536158
69109.696081215754650.303918784245351
701010.0906859809957-0.0906859809956775
71109.774895661997830.225104338002171
72109.543579157961390.456420842038606
73109.577648776729460.422351223270539
7498.812080484451370.187919515548633
7599.32414317102548-0.324143171025482



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)
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')