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# PAPER

*The author of this computation has been verified*
R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Wed, 02 Dec 2009 13:23:58 -0700

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l.htm/, Retrieved Thu, 23 May 2013 11:20:05 +0000

Original text written by user:

IsPrivate?
No (this computation is public)

User-defined keywords:

System-generated keywords (parent):
t1258034831gyl7a6ypo68uqsr (pk = 55999)
Estimated Impact
31

Dataseries X:
» Textfile « » CSV « » Correlation Matrix « » Notched Boxplots «

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

 Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135

 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 613.891833030853 + 39.7441016333939X[t] -8.82574107682971M1[t] -4.33714458560193M2[t] -6.24854809437387M3[t] -12.7599516031458M4[t] -15.4713551119177M5[t] -24.3827586206896M6[t] -19.8941621294616M7[t] + 25.6456140350877M8[t] + 35.9342105263158M9[t] + 25.8228070175439M10[t] + 9.71140350877195M11[t] -2.28859649122807t + e[t]

 Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STATH0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 613.891833030853 14.483353 42.386 0 0 X 39.7441016333939 12.381497 3.21 0.002422 0.001211 M1 -8.82574107682971 16.928193 -0.5214 0.604615 0.302307 M2 -4.33714458560193 16.900815 -0.2566 0.798614 0.399307 M3 -6.24854809437387 16.879489 -0.3702 0.712943 0.356472 M4 -12.7599516031458 16.86424 -0.7566 0.453131 0.226565 M5 -15.4713551119177 16.855085 -0.9179 0.363457 0.181728 M6 -24.3827586206896 16.852031 -1.4469 0.154713 0.077356 M7 -19.8941621294616 16.855085 -1.1803 0.243946 0.121973 M8 25.6456140350877 16.828852 1.5239 0.134378 0.067189 M9 35.9342105263158 16.807435 2.138 0.037863 0.018931 M10 25.8228070175439 16.792121 1.5378 0.13095 0.065475 M11 9.71140350877195 16.782926 0.5786 0.565649 0.282825 t -2.28859649122807 0.320797 -7.1341 0 0

 Multiple Linear Regression - Regression Statistics Multiple R 0.81979497633176 R-squared 0.67206380321879 Adjusted R-squared 0.579386182389317 F-TEST (value) 7.25162986710019 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 2.02201098531418e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 26.5312876493999 Sum Squared Residuals 32379.8243194192

 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals InterpolationForecast ResidualsPrediction Error 1 595 602.777495462794 -7.77749546279383 2 591 604.977495462795 -13.9774954627950 3 589 600.777495462795 -11.777495462795 4 584 591.977495462795 -7.97749546279498 5 573 586.977495462795 -13.9774954627950 6 567 575.777495462795 -8.77749546279499 7 569 577.977495462795 -8.97749546279498 8 621 621.228675136116 -0.228675136116206 9 629 629.228675136116 -0.228675136116233 10 628 616.828675136116 11.1713248638838 11 612 598.428675136116 13.5713248638838 12 595 586.428675136116 8.5713248638838 13 597 575.314337568058 21.6856624319416 14 593 577.514337568058 15.4856624319419 15 590 573.314337568058 16.6856624319419 16 580 564.514337568058 15.4856624319419 17 574 559.514337568058 14.4856624319419 18 573 548.314337568058 24.6856624319419 19 573 550.514337568058 22.4856624319419 20 620 593.765517241379 26.2344827586207 21 626 601.765517241379 24.2344827586207 22 620 589.365517241379 30.6344827586207 23 588 570.965517241379 17.0344827586207 24 566 558.965517241379 7.03448275862069 25 557 547.851179673322 9.1488203266785 26 561 550.051179673321 10.9488203266788 27 549 545.851179673321 3.14882032667878 28 532 537.051179673321 -5.05117967332122 29 526 532.051179673321 -6.05117967332122 30 511 520.851179673321 -9.85117967332122 31 499 523.051179673321 -24.0511796733212 32 555 566.302359346642 -11.3023593466424 33 565 574.302359346642 -9.30235934664243 34 542 561.902359346642 -19.9023593466425 35 527 543.502359346642 -16.5023593466424 36 510 531.502359346642 -21.5023593466424 37 514 520.388021778585 -6.38802177858463 38 517 522.588021778584 -5.58802177858433 39 508 518.388021778584 -10.3880217785843 40 493 509.588021778584 -16.5880217785843 41 490 504.588021778584 -14.5880217785843 42 469 493.388021778584 -24.3880217785843 43 478 495.588021778584 -17.5880217785843 44 528 578.5833030853 -50.5833030852995 45 534 586.583303085299 -52.5833030852995 46 518 574.1833030853 -56.1833030852995 47 506 555.7833030853 -49.7833030852995 48 502 543.7833030853 -41.7833030852995 49 516 532.668965517242 -16.6689655172417 50 528 534.868965517241 -6.86896551724138 51 533 530.668965517241 2.33103448275864 52 536 521.868965517241 14.1310344827586 53 537 516.868965517241 20.1310344827586 54 524 505.668965517241 18.3310344827587 55 536 507.868965517241 28.1310344827587 56 587 551.120145190563 35.8798548094374 57 597 559.120145190563 37.8798548094374 58 581 546.720145190563 34.2798548094374 59 564 528.320145190563 35.6798548094374 60 564 516.320145190563 47.6798548094374

 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.000374983176306055 0.00074996635261211 0.999625016823694 18 8.33910223767402e-05 0.000166782044753480 0.999916608977623 19 7.82931422786308e-06 1.56586284557262e-05 0.999992170685772 20 8.09679956352492e-07 1.61935991270498e-06 0.999999190320044 21 1.45664746061371e-07 2.91329492122743e-07 0.999999854335254 22 2.09907676212598e-07 4.19815352425197e-07 0.999999790092324 23 2.22556544203143e-05 4.45113088406287e-05 0.99997774434558 24 0.000157742647651152 0.000315485295302304 0.999842257352349 25 0.00130468414216467 0.00260936828432934 0.998695315857835 26 0.00170607750057233 0.00341215500114466 0.998293922499428 27 0.0035844129530229 0.0071688259060458 0.996415587046977 28 0.00975932437505152 0.0195186487501030 0.990240675624948 29 0.0166680424300703 0.0333360848601407 0.98333195756993 30 0.059403495917502 0.118806991835004 0.940596504082498 31 0.162755413671150 0.325510827342301 0.83724458632885 32 0.228462533591116 0.456925067182232 0.771537466408884 33 0.32617520671346 0.65235041342692 0.67382479328654 34 0.54306675798808 0.91386648402384 0.45693324201192 35 0.786380833359258 0.427238333281484 0.213619166640742 36 0.924689009289031 0.150621981421938 0.075310990710969 37 0.974540426079449 0.0509191478411022 0.0254595739205511 38 0.99689822013294 0.00620355973411871 0.00310177986705935 39 0.999910964470305 0.000178071059389461 8.90355296947304e-05 40 0.999930269838352 0.000139460323296286 6.97301616481428e-05 41 0.999974321969602 5.13560607965883e-05 2.56780303982942e-05 42 0.99981235945405 0.000375281091899909 0.000187640545949955 43 0.997927841563397 0.00414431687320539 0.00207215843660269

 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 17 0.62962962962963 NOK 5% type I error level 19 0.703703703703704 NOK 10% type I error level 20 0.740740740740741 NOK

Charts produced by software:
 http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/10a2st1259785433.png (opens in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/10a2st1259785433.ps (opens in new window) Click here to open pdf file.

 http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/1k6e81259785433.png (opens in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/1k6e81259785433.ps (opens in new window) Click here to open pdf file.

 http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/2ghzs1259785433.png (opens in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/2ghzs1259785433.ps (opens in new window) Click here to open pdf file.

 http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/3swfg1259785433.png (opens in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/3swfg1259785433.ps (opens in new window) Click here to open pdf file.

 http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/40eo81259785433.png (opens in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/40eo81259785433.ps (opens in new window) Click here to open pdf file.

 http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/59x4h1259785433.png (opens in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/59x4h1259785433.ps (opens in new window) Click here to open pdf file.

 http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/6rrt11259785433.png (opens in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/6rrt11259785433.ps (opens in new window) Click here to open pdf file.

 http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/73jm31259785433.png (opens in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/73jm31259785433.ps (opens in new window) Click here to open pdf file.

 http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/8lppy1259785433.png (opens in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/8lppy1259785433.ps (opens in new window) Click here to open pdf file.

 http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/9g64l1259785433.png (opens in new window) http://www.freestatistics.org/blog/date/2009/Dec/02/t125978950882yj3d0k8fzgf4l/9g64l1259785433.ps (opens in new window) Click here to open pdf file.

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):