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Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 25 Nov 2011 03:48:38 -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/25/t1322210937hnyv7doay6xjrby.htm/, Retrieved Sat, 18 May 2024 00:47:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147255, Retrieved Sat, 18 May 2024 00:47:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact207
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]
- R  D          [Multiple Regression] [] [2011-11-25 08:48:38] [a1e1d0bae7c18896aaea36b6ddc51406] [Current]
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Dataseries X:
9 676
8 642
9 402
9 610
9 294
9 448
10 319
9 548
9 801
9 596
8 923
9 746
9 829
9 125
9 782
9 441
9 162
9 915
10 444
10 209
9 985
9 842
9 429
10 132
9 849
9 172
10 313
9 819
9 955
10 048
10 082
10 541
10 208
10 233
9 439
9 963
10 158
9 225
10 474
9 757
10 490
10 281
10 444
10 640
10 695
10 786
9 832
9 747
10 411
9 511
10 402
9 701
10 540
10 112
10 915
11 183
10 384
10 834
9 886
10 216




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147255&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147255&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147255&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Multiple Linear Regression - Estimated Regression Equation
y[t] = + 9.29579048598093 -0.000950604523242447V2[t] + 0.217357549797279M1[t] -0.637616353944412M2[t] + 0.27738502275986M3[t] -0.158752528041206M4[t] + 0.0549072147952108M5[t] + 0.11609718379375M6[t] + 0.574442530912772M7[t] + 0.540959481086575M8[t] + 0.304251567571563M9[t] + 0.327994910044561M10[t] -0.448261747482442M11[t] + 0.0177030147403732t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
y[t] =  +  9.29579048598093 -0.000950604523242447V2[t] +  0.217357549797279M1[t] -0.637616353944412M2[t] +  0.27738502275986M3[t] -0.158752528041206M4[t] +  0.0549072147952108M5[t] +  0.11609718379375M6[t] +  0.574442530912772M7[t] +  0.540959481086575M8[t] +  0.304251567571563M9[t] +  0.327994910044561M10[t] -0.448261747482442M11[t] +  0.0177030147403732t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147255&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]y[t] =  +  9.29579048598093 -0.000950604523242447V2[t] +  0.217357549797279M1[t] -0.637616353944412M2[t] +  0.27738502275986M3[t] -0.158752528041206M4[t] +  0.0549072147952108M5[t] +  0.11609718379375M6[t] +  0.574442530912772M7[t] +  0.540959481086575M8[t] +  0.304251567571563M9[t] +  0.327994910044561M10[t] -0.448261747482442M11[t] +  0.0177030147403732t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147255&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147255&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] = + 9.29579048598093 -0.000950604523242447V2[t] + 0.217357549797279M1[t] -0.637616353944412M2[t] + 0.27738502275986M3[t] -0.158752528041206M4[t] + 0.0549072147952108M5[t] + 0.11609718379375M6[t] + 0.574442530912772M7[t] + 0.540959481086575M8[t] + 0.304251567571563M9[t] + 0.327994910044561M10[t] -0.448261747482442M11[t] + 0.0177030147403732t + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)9.295790485980930.14796862.822900
V2-0.0009506045232424470.000127-7.457100
M10.2173575497972790.1540631.41080.1650190.08251
M2-0.6376163539444120.156759-4.06750.0001849.2e-05
M30.277385022759860.1541041.80.0784240.039212
M4-0.1587525280412060.153917-1.03140.3077380.153869
M50.05490721479521080.1536060.35750.7223870.361193
M60.116097183793750.155370.74720.4587280.229364
M70.5744425309127720.1538353.73420.0005180.000259
M80.5409594810865750.1539543.51380.0010040.000502
M90.3042515675715630.1529591.98910.0526560.026328
M100.3279949100445610.153252.14030.0376690.018834
M11-0.4482617474824420.153773-2.91510.0054770.002739
t0.01770301474037320.0018429.608900

\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) & 9.29579048598093 & 0.147968 & 62.8229 & 0 & 0 \tabularnewline
V2 & -0.000950604523242447 & 0.000127 & -7.4571 & 0 & 0 \tabularnewline
M1 & 0.217357549797279 & 0.154063 & 1.4108 & 0.165019 & 0.08251 \tabularnewline
M2 & -0.637616353944412 & 0.156759 & -4.0675 & 0.000184 & 9.2e-05 \tabularnewline
M3 & 0.27738502275986 & 0.154104 & 1.8 & 0.078424 & 0.039212 \tabularnewline
M4 & -0.158752528041206 & 0.153917 & -1.0314 & 0.307738 & 0.153869 \tabularnewline
M5 & 0.0549072147952108 & 0.153606 & 0.3575 & 0.722387 & 0.361193 \tabularnewline
M6 & 0.11609718379375 & 0.15537 & 0.7472 & 0.458728 & 0.229364 \tabularnewline
M7 & 0.574442530912772 & 0.153835 & 3.7342 & 0.000518 & 0.000259 \tabularnewline
M8 & 0.540959481086575 & 0.153954 & 3.5138 & 0.001004 & 0.000502 \tabularnewline
M9 & 0.304251567571563 & 0.152959 & 1.9891 & 0.052656 & 0.026328 \tabularnewline
M10 & 0.327994910044561 & 0.15325 & 2.1403 & 0.037669 & 0.018834 \tabularnewline
M11 & -0.448261747482442 & 0.153773 & -2.9151 & 0.005477 & 0.002739 \tabularnewline
t & 0.0177030147403732 & 0.001842 & 9.6089 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147255&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]9.29579048598093[/C][C]0.147968[/C][C]62.8229[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]V2[/C][C]-0.000950604523242447[/C][C]0.000127[/C][C]-7.4571[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]M1[/C][C]0.217357549797279[/C][C]0.154063[/C][C]1.4108[/C][C]0.165019[/C][C]0.08251[/C][/ROW]
[ROW][C]M2[/C][C]-0.637616353944412[/C][C]0.156759[/C][C]-4.0675[/C][C]0.000184[/C][C]9.2e-05[/C][/ROW]
[ROW][C]M3[/C][C]0.27738502275986[/C][C]0.154104[/C][C]1.8[/C][C]0.078424[/C][C]0.039212[/C][/ROW]
[ROW][C]M4[/C][C]-0.158752528041206[/C][C]0.153917[/C][C]-1.0314[/C][C]0.307738[/C][C]0.153869[/C][/ROW]
[ROW][C]M5[/C][C]0.0549072147952108[/C][C]0.153606[/C][C]0.3575[/C][C]0.722387[/C][C]0.361193[/C][/ROW]
[ROW][C]M6[/C][C]0.11609718379375[/C][C]0.15537[/C][C]0.7472[/C][C]0.458728[/C][C]0.229364[/C][/ROW]
[ROW][C]M7[/C][C]0.574442530912772[/C][C]0.153835[/C][C]3.7342[/C][C]0.000518[/C][C]0.000259[/C][/ROW]
[ROW][C]M8[/C][C]0.540959481086575[/C][C]0.153954[/C][C]3.5138[/C][C]0.001004[/C][C]0.000502[/C][/ROW]
[ROW][C]M9[/C][C]0.304251567571563[/C][C]0.152959[/C][C]1.9891[/C][C]0.052656[/C][C]0.026328[/C][/ROW]
[ROW][C]M10[/C][C]0.327994910044561[/C][C]0.15325[/C][C]2.1403[/C][C]0.037669[/C][C]0.018834[/C][/ROW]
[ROW][C]M11[/C][C]-0.448261747482442[/C][C]0.153773[/C][C]-2.9151[/C][C]0.005477[/C][C]0.002739[/C][/ROW]
[ROW][C]t[/C][C]0.0177030147403732[/C][C]0.001842[/C][C]9.6089[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147255&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147255&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)9.295790485980930.14796862.822900
V2-0.0009506045232424470.000127-7.457100
M10.2173575497972790.1540631.41080.1650190.08251
M2-0.6376163539444120.156759-4.06750.0001849.2e-05
M30.277385022759860.1541041.80.0784240.039212
M4-0.1587525280412060.153917-1.03140.3077380.153869
M50.05490721479521080.1536060.35750.7223870.361193
M60.116097183793750.155370.74720.4587280.229364
M70.5744425309127720.1538353.73420.0005180.000259
M80.5409594810865750.1539543.51380.0010040.000502
M90.3042515675715630.1529591.98910.0526560.026328
M100.3279949100445610.153252.14030.0376690.018834
M11-0.4482617474824420.153773-2.91510.0054770.002739
t0.01770301474037320.0018429.608900







Multiple Linear Regression - Regression Statistics
Multiple R0.933073645856127
R-squared0.870626428591245
Adjusted R-squared0.834064332323553
F-TEST (value)23.812267825589
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value4.44089209850063e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.241478479576812
Sum Squared Residuals2.68234538054153

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.933073645856127 \tabularnewline
R-squared & 0.870626428591245 \tabularnewline
Adjusted R-squared & 0.834064332323553 \tabularnewline
F-TEST (value) & 23.812267825589 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 4.44089209850063e-16 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.241478479576812 \tabularnewline
Sum Squared Residuals & 2.68234538054153 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147255&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.933073645856127[/C][/ROW]
[ROW][C]R-squared[/C][C]0.870626428591245[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.834064332323553[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]23.812267825589[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/C][/ROW]
[ROW][C]p-value[/C][C]4.44089209850063e-16[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.241478479576812[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]2.68234538054153[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147255&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147255&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 R0.933073645856127
R-squared0.870626428591245
Adjusted R-squared0.834064332323553
F-TEST (value)23.812267825589
F-TEST (DF numerator)13
F-TEST (DF denominator)46
p-value4.44089209850063e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.241478479576812
Sum Squared Residuals2.68234538054153







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
198.888242392806670.111757607193332
288.08329205759561-0.0832920575956113
399.24414153461844-0.244141534618444
498.627981257723320.372018742276677
599.15973504464472-0.159735044644726
699.0922349318043-0.0922349318043011
7109.690911277161970.309088722838027
899.45744280625363-0.457442806253628
998.997934963098650.0020650369013496
1099.23425524757672-0.234255247576723
1188.16485392568981-0.164853925689813
1298.799075688526540.200924311473459
1398.955236077635070.0447639223649291
1498.787190772996440.212809227003565
1599.09534799267079-0.0953479926707931
1699.00106959903577-0.00106959903577493
1799.49765101859721-0.497651018597207
1898.860738796334560.139261203665443
19109.784521888641150.215478111358855
20109.99213391651730.00786608348270403
2199.03545990770652-0.0354599077065188
2299.21284271174356-0.21284271174356
2398.846888737056060.153111262943939
24109.595183042681880.404816957318117
2599.1486601640547-0.148660164054701
2698.954948537288520.0450514627114811
27109.753617690955980.246382309044021
2898.854177266134610.145822733865391
2998.956257808550430.0437421914495744
30109.897349094870240.102650905129763
311010.3410769029394-0.34107690293939
32109.888969391685280.111030608314718
33109.986515799150380.0134842008496209
341010.0041970432827-0.00419704328268858
3599.04981886870812-0.049818868708115
3699.01766686075189-0.0176668607518877
371010.0179640664997-0.0179640664997102
3899.11700267444115-0.117002674441148
39109.813006539598420.186993460401576
4099.12555092346012-0.125550923460119
41109.610725088742640.389274911257358
42109.888294417839230.111705582160774
431010.2093942424101-0.209394242410103
441010.0072957207688-0.00729572076875843
45109.736007573215790.263992426784214
46109.690948918814090.309051081185906
4798.888667467958310.111332532041688
4899.43543361465673-0.435433614656735
49109.989897299003850.0101027009961502
5099.05756595767829-0.0575659576782866
511010.0938862421564-0.093886242156359
5299.39122095364617-0.391220953646175
53109.7756310394650.224368960535001
541010.2613827591517-0.261382759151678
55109.974095688847390.0259043111526111
561110.6541581647750.345841835224964
571010.2440817568287-0.244081756828666
58109.857756078582940.142243921417065
5999.0497710005877-0.0497710005876985
601010.152640793383-0.152640793382953

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 9 & 8.88824239280667 & 0.111757607193332 \tabularnewline
2 & 8 & 8.08329205759561 & -0.0832920575956113 \tabularnewline
3 & 9 & 9.24414153461844 & -0.244141534618444 \tabularnewline
4 & 9 & 8.62798125772332 & 0.372018742276677 \tabularnewline
5 & 9 & 9.15973504464472 & -0.159735044644726 \tabularnewline
6 & 9 & 9.0922349318043 & -0.0922349318043011 \tabularnewline
7 & 10 & 9.69091127716197 & 0.309088722838027 \tabularnewline
8 & 9 & 9.45744280625363 & -0.457442806253628 \tabularnewline
9 & 9 & 8.99793496309865 & 0.0020650369013496 \tabularnewline
10 & 9 & 9.23425524757672 & -0.234255247576723 \tabularnewline
11 & 8 & 8.16485392568981 & -0.164853925689813 \tabularnewline
12 & 9 & 8.79907568852654 & 0.200924311473459 \tabularnewline
13 & 9 & 8.95523607763507 & 0.0447639223649291 \tabularnewline
14 & 9 & 8.78719077299644 & 0.212809227003565 \tabularnewline
15 & 9 & 9.09534799267079 & -0.0953479926707931 \tabularnewline
16 & 9 & 9.00106959903577 & -0.00106959903577493 \tabularnewline
17 & 9 & 9.49765101859721 & -0.497651018597207 \tabularnewline
18 & 9 & 8.86073879633456 & 0.139261203665443 \tabularnewline
19 & 10 & 9.78452188864115 & 0.215478111358855 \tabularnewline
20 & 10 & 9.9921339165173 & 0.00786608348270403 \tabularnewline
21 & 9 & 9.03545990770652 & -0.0354599077065188 \tabularnewline
22 & 9 & 9.21284271174356 & -0.21284271174356 \tabularnewline
23 & 9 & 8.84688873705606 & 0.153111262943939 \tabularnewline
24 & 10 & 9.59518304268188 & 0.404816957318117 \tabularnewline
25 & 9 & 9.1486601640547 & -0.148660164054701 \tabularnewline
26 & 9 & 8.95494853728852 & 0.0450514627114811 \tabularnewline
27 & 10 & 9.75361769095598 & 0.246382309044021 \tabularnewline
28 & 9 & 8.85417726613461 & 0.145822733865391 \tabularnewline
29 & 9 & 8.95625780855043 & 0.0437421914495744 \tabularnewline
30 & 10 & 9.89734909487024 & 0.102650905129763 \tabularnewline
31 & 10 & 10.3410769029394 & -0.34107690293939 \tabularnewline
32 & 10 & 9.88896939168528 & 0.111030608314718 \tabularnewline
33 & 10 & 9.98651579915038 & 0.0134842008496209 \tabularnewline
34 & 10 & 10.0041970432827 & -0.00419704328268858 \tabularnewline
35 & 9 & 9.04981886870812 & -0.049818868708115 \tabularnewline
36 & 9 & 9.01766686075189 & -0.0176668607518877 \tabularnewline
37 & 10 & 10.0179640664997 & -0.0179640664997102 \tabularnewline
38 & 9 & 9.11700267444115 & -0.117002674441148 \tabularnewline
39 & 10 & 9.81300653959842 & 0.186993460401576 \tabularnewline
40 & 9 & 9.12555092346012 & -0.125550923460119 \tabularnewline
41 & 10 & 9.61072508874264 & 0.389274911257358 \tabularnewline
42 & 10 & 9.88829441783923 & 0.111705582160774 \tabularnewline
43 & 10 & 10.2093942424101 & -0.209394242410103 \tabularnewline
44 & 10 & 10.0072957207688 & -0.00729572076875843 \tabularnewline
45 & 10 & 9.73600757321579 & 0.263992426784214 \tabularnewline
46 & 10 & 9.69094891881409 & 0.309051081185906 \tabularnewline
47 & 9 & 8.88866746795831 & 0.111332532041688 \tabularnewline
48 & 9 & 9.43543361465673 & -0.435433614656735 \tabularnewline
49 & 10 & 9.98989729900385 & 0.0101027009961502 \tabularnewline
50 & 9 & 9.05756595767829 & -0.0575659576782866 \tabularnewline
51 & 10 & 10.0938862421564 & -0.093886242156359 \tabularnewline
52 & 9 & 9.39122095364617 & -0.391220953646175 \tabularnewline
53 & 10 & 9.775631039465 & 0.224368960535001 \tabularnewline
54 & 10 & 10.2613827591517 & -0.261382759151678 \tabularnewline
55 & 10 & 9.97409568884739 & 0.0259043111526111 \tabularnewline
56 & 11 & 10.654158164775 & 0.345841835224964 \tabularnewline
57 & 10 & 10.2440817568287 & -0.244081756828666 \tabularnewline
58 & 10 & 9.85775607858294 & 0.142243921417065 \tabularnewline
59 & 9 & 9.0497710005877 & -0.0497710005876985 \tabularnewline
60 & 10 & 10.152640793383 & -0.152640793382953 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147255&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]8.88824239280667[/C][C]0.111757607193332[/C][/ROW]
[ROW][C]2[/C][C]8[/C][C]8.08329205759561[/C][C]-0.0832920575956113[/C][/ROW]
[ROW][C]3[/C][C]9[/C][C]9.24414153461844[/C][C]-0.244141534618444[/C][/ROW]
[ROW][C]4[/C][C]9[/C][C]8.62798125772332[/C][C]0.372018742276677[/C][/ROW]
[ROW][C]5[/C][C]9[/C][C]9.15973504464472[/C][C]-0.159735044644726[/C][/ROW]
[ROW][C]6[/C][C]9[/C][C]9.0922349318043[/C][C]-0.0922349318043011[/C][/ROW]
[ROW][C]7[/C][C]10[/C][C]9.69091127716197[/C][C]0.309088722838027[/C][/ROW]
[ROW][C]8[/C][C]9[/C][C]9.45744280625363[/C][C]-0.457442806253628[/C][/ROW]
[ROW][C]9[/C][C]9[/C][C]8.99793496309865[/C][C]0.0020650369013496[/C][/ROW]
[ROW][C]10[/C][C]9[/C][C]9.23425524757672[/C][C]-0.234255247576723[/C][/ROW]
[ROW][C]11[/C][C]8[/C][C]8.16485392568981[/C][C]-0.164853925689813[/C][/ROW]
[ROW][C]12[/C][C]9[/C][C]8.79907568852654[/C][C]0.200924311473459[/C][/ROW]
[ROW][C]13[/C][C]9[/C][C]8.95523607763507[/C][C]0.0447639223649291[/C][/ROW]
[ROW][C]14[/C][C]9[/C][C]8.78719077299644[/C][C]0.212809227003565[/C][/ROW]
[ROW][C]15[/C][C]9[/C][C]9.09534799267079[/C][C]-0.0953479926707931[/C][/ROW]
[ROW][C]16[/C][C]9[/C][C]9.00106959903577[/C][C]-0.00106959903577493[/C][/ROW]
[ROW][C]17[/C][C]9[/C][C]9.49765101859721[/C][C]-0.497651018597207[/C][/ROW]
[ROW][C]18[/C][C]9[/C][C]8.86073879633456[/C][C]0.139261203665443[/C][/ROW]
[ROW][C]19[/C][C]10[/C][C]9.78452188864115[/C][C]0.215478111358855[/C][/ROW]
[ROW][C]20[/C][C]10[/C][C]9.9921339165173[/C][C]0.00786608348270403[/C][/ROW]
[ROW][C]21[/C][C]9[/C][C]9.03545990770652[/C][C]-0.0354599077065188[/C][/ROW]
[ROW][C]22[/C][C]9[/C][C]9.21284271174356[/C][C]-0.21284271174356[/C][/ROW]
[ROW][C]23[/C][C]9[/C][C]8.84688873705606[/C][C]0.153111262943939[/C][/ROW]
[ROW][C]24[/C][C]10[/C][C]9.59518304268188[/C][C]0.404816957318117[/C][/ROW]
[ROW][C]25[/C][C]9[/C][C]9.1486601640547[/C][C]-0.148660164054701[/C][/ROW]
[ROW][C]26[/C][C]9[/C][C]8.95494853728852[/C][C]0.0450514627114811[/C][/ROW]
[ROW][C]27[/C][C]10[/C][C]9.75361769095598[/C][C]0.246382309044021[/C][/ROW]
[ROW][C]28[/C][C]9[/C][C]8.85417726613461[/C][C]0.145822733865391[/C][/ROW]
[ROW][C]29[/C][C]9[/C][C]8.95625780855043[/C][C]0.0437421914495744[/C][/ROW]
[ROW][C]30[/C][C]10[/C][C]9.89734909487024[/C][C]0.102650905129763[/C][/ROW]
[ROW][C]31[/C][C]10[/C][C]10.3410769029394[/C][C]-0.34107690293939[/C][/ROW]
[ROW][C]32[/C][C]10[/C][C]9.88896939168528[/C][C]0.111030608314718[/C][/ROW]
[ROW][C]33[/C][C]10[/C][C]9.98651579915038[/C][C]0.0134842008496209[/C][/ROW]
[ROW][C]34[/C][C]10[/C][C]10.0041970432827[/C][C]-0.00419704328268858[/C][/ROW]
[ROW][C]35[/C][C]9[/C][C]9.04981886870812[/C][C]-0.049818868708115[/C][/ROW]
[ROW][C]36[/C][C]9[/C][C]9.01766686075189[/C][C]-0.0176668607518877[/C][/ROW]
[ROW][C]37[/C][C]10[/C][C]10.0179640664997[/C][C]-0.0179640664997102[/C][/ROW]
[ROW][C]38[/C][C]9[/C][C]9.11700267444115[/C][C]-0.117002674441148[/C][/ROW]
[ROW][C]39[/C][C]10[/C][C]9.81300653959842[/C][C]0.186993460401576[/C][/ROW]
[ROW][C]40[/C][C]9[/C][C]9.12555092346012[/C][C]-0.125550923460119[/C][/ROW]
[ROW][C]41[/C][C]10[/C][C]9.61072508874264[/C][C]0.389274911257358[/C][/ROW]
[ROW][C]42[/C][C]10[/C][C]9.88829441783923[/C][C]0.111705582160774[/C][/ROW]
[ROW][C]43[/C][C]10[/C][C]10.2093942424101[/C][C]-0.209394242410103[/C][/ROW]
[ROW][C]44[/C][C]10[/C][C]10.0072957207688[/C][C]-0.00729572076875843[/C][/ROW]
[ROW][C]45[/C][C]10[/C][C]9.73600757321579[/C][C]0.263992426784214[/C][/ROW]
[ROW][C]46[/C][C]10[/C][C]9.69094891881409[/C][C]0.309051081185906[/C][/ROW]
[ROW][C]47[/C][C]9[/C][C]8.88866746795831[/C][C]0.111332532041688[/C][/ROW]
[ROW][C]48[/C][C]9[/C][C]9.43543361465673[/C][C]-0.435433614656735[/C][/ROW]
[ROW][C]49[/C][C]10[/C][C]9.98989729900385[/C][C]0.0101027009961502[/C][/ROW]
[ROW][C]50[/C][C]9[/C][C]9.05756595767829[/C][C]-0.0575659576782866[/C][/ROW]
[ROW][C]51[/C][C]10[/C][C]10.0938862421564[/C][C]-0.093886242156359[/C][/ROW]
[ROW][C]52[/C][C]9[/C][C]9.39122095364617[/C][C]-0.391220953646175[/C][/ROW]
[ROW][C]53[/C][C]10[/C][C]9.775631039465[/C][C]0.224368960535001[/C][/ROW]
[ROW][C]54[/C][C]10[/C][C]10.2613827591517[/C][C]-0.261382759151678[/C][/ROW]
[ROW][C]55[/C][C]10[/C][C]9.97409568884739[/C][C]0.0259043111526111[/C][/ROW]
[ROW][C]56[/C][C]11[/C][C]10.654158164775[/C][C]0.345841835224964[/C][/ROW]
[ROW][C]57[/C][C]10[/C][C]10.2440817568287[/C][C]-0.244081756828666[/C][/ROW]
[ROW][C]58[/C][C]10[/C][C]9.85775607858294[/C][C]0.142243921417065[/C][/ROW]
[ROW][C]59[/C][C]9[/C][C]9.0497710005877[/C][C]-0.0497710005876985[/C][/ROW]
[ROW][C]60[/C][C]10[/C][C]10.152640793383[/C][C]-0.152640793382953[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147255&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147255&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
198.888242392806670.111757607193332
288.08329205759561-0.0832920575956113
399.24414153461844-0.244141534618444
498.627981257723320.372018742276677
599.15973504464472-0.159735044644726
699.0922349318043-0.0922349318043011
7109.690911277161970.309088722838027
899.45744280625363-0.457442806253628
998.997934963098650.0020650369013496
1099.23425524757672-0.234255247576723
1188.16485392568981-0.164853925689813
1298.799075688526540.200924311473459
1398.955236077635070.0447639223649291
1498.787190772996440.212809227003565
1599.09534799267079-0.0953479926707931
1699.00106959903577-0.00106959903577493
1799.49765101859721-0.497651018597207
1898.860738796334560.139261203665443
19109.784521888641150.215478111358855
20109.99213391651730.00786608348270403
2199.03545990770652-0.0354599077065188
2299.21284271174356-0.21284271174356
2398.846888737056060.153111262943939
24109.595183042681880.404816957318117
2599.1486601640547-0.148660164054701
2698.954948537288520.0450514627114811
27109.753617690955980.246382309044021
2898.854177266134610.145822733865391
2998.956257808550430.0437421914495744
30109.897349094870240.102650905129763
311010.3410769029394-0.34107690293939
32109.888969391685280.111030608314718
33109.986515799150380.0134842008496209
341010.0041970432827-0.00419704328268858
3599.04981886870812-0.049818868708115
3699.01766686075189-0.0176668607518877
371010.0179640664997-0.0179640664997102
3899.11700267444115-0.117002674441148
39109.813006539598420.186993460401576
4099.12555092346012-0.125550923460119
41109.610725088742640.389274911257358
42109.888294417839230.111705582160774
431010.2093942424101-0.209394242410103
441010.0072957207688-0.00729572076875843
45109.736007573215790.263992426784214
46109.690948918814090.309051081185906
4798.888667467958310.111332532041688
4899.43543361465673-0.435433614656735
49109.989897299003850.0101027009961502
5099.05756595767829-0.0575659576782866
511010.0938862421564-0.093886242156359
5299.39122095364617-0.391220953646175
53109.7756310394650.224368960535001
541010.2613827591517-0.261382759151678
55109.974095688847390.0259043111526111
561110.6541581647750.345841835224964
571010.2440817568287-0.244081756828666
58109.857756078582940.142243921417065
5999.0497710005877-0.0497710005876985
601010.152640793383-0.152640793382953



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')