model 3 ws 7

*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: Fri, 20 Nov 2009 07:17:31 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6.htm/, Retrieved Fri, 20 Nov 2009 15:19:09 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

100.01 0 103.84 0 104.48 0 95.43 0 104.80 0 108.64 0 105.65 0 108.42 0 115.35 0 113.64 0 115.24 0 100.33 0 101.29 0 104.48 0 99.26 0 100.11 0 103.52 0 101.18 0 96.39 0 97.56 0 96.39 0 85.10 0 79.77 0 79.13 0 80.84 0 82.75 0 92.55 0 96.60 0 96.92 0 95.32 0 98.52 0 100.22 0 104.91 0 103.10 0 97.13 0 103.42 0 111.72 0 118.11 0 111.62 0 100.22 0 102.03 0 105.76 0 107.68 0 110.77 0 105.44 0 112.26 0 114.07 0 117.90 0 124.72 0 126.42 0 134.73 0 135.79 0 143.36 0 140.37 0 144.74 0 151.98 0 150.92 0 163.38 0 154.43 0 146.66 0 157.95 0 162.10 0 180.42 0 179.57 0 171.58 0 185.43 0 190.64 0 203.00 0 202.36 0 193.41 0 186.17 0 192.24 0 209.60 0 206.41 0 209.82 0 230.37 0 235.80 0 232.07 0 244.64 0 242.19 0 217.48 0 209.39 0 211.73 0 221.00 0 203.11 0 214.71 0 224.19 0 238.04 0 238.36 0 246.24 0 259.87 0 249.97 0 266.48 0 282.98 0 306.31 0 301.73 1 314.62 1 332.62 1 355.51 1 370.32 1 408.13 1 433.58 1 440.51 1 386.29 1 etc...

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 47.471123246113 + 29.2155921501706X[t] + 8.03850118189862M1[t] + 10.4251146884086M2[t] + 15.7017281949185M3[t] + 18.4533417014284M4[t] + 24.8059552079383M5[t] + 30.4325687144482M6[t] + 31.6191822209582M7[t] + 28.1407957274681M8[t] + 20.6054092339780M9[t] + 16.2785054481103M10[t] + 8.97400784350905M11[t] + 1.75338649349008t + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 47.471123246113 18.709349 2.5373 0.01267 0.006335 X 29.2155921501706 15.931636 1.8338 0.06957 0.034785 M1 8.03850118189862 22.607477 0.3556 0.722891 0.361446 M2 10.4251146884086 22.602693 0.4612 0.645604 0.322802 M3 15.7017281949185 22.599407 0.6948 0.488754 0.244377 M4 18.4533417014284 22.59762 0.8166 0.416039 0.208019 M5 24.8059552079383 22.597333 1.0977 0.274878 0.137439 M6 30.4325687144482 22.598545 1.3467 0.181045 0.090523 M7 31.6191822209582 22.601256 1.399 0.164817 0.082408 M8 28.1407957274681 22.605465 1.2449 0.216006 0.108003 M9 20.6054092339780 22.611173 0.9113 0.364269 0.182134 M10 16.2785054481103 23.234101 0.7006 0.485114 0.242557 M11 8.97400784350905 23.241452 0.3861 0.700204 0.350102 t 1.75338649349008 0.184073 9.5255 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.82910426940108 R-squared 0.687413889539099 Adjusted R-squared 0.647961273655685 F-TEST (value) 17.4237848149399 F-TEST (DF numerator) 13 F-TEST (DF denominator) 103 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 49.1780861158411 Sum Squared Residuals 249103.867863759 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 100.01 57.2630109215018 42.7469890784982 2 103.84 61.4030109215014 42.4369890784986 3 104.48 68.4330109215018 36.0469890784982 4 95.43 72.9380109215016 22.4919890784984 5 104.8 81.0440109215017 23.7559890784983 6 108.64 88.4240109215017 20.2159890784983 7 105.65 91.3640109215017 14.2859890784983 8 108.42 89.6390109215017 18.7809890784983 9 115.35 83.8570109215017 31.4929890784983 10 113.64 81.283493629124 32.356506370876 11 115.24 75.7323825180129 39.5076174819871 12 100.33 68.511761167994 31.818238832006 13 101.29 78.3036488433826 22.9863511566174 14 104.48 82.4436488433828 22.0363511566172 15 99.26 89.4736488433826 9.78635115661737 16 100.11 93.9786488433826 6.13135115661735 17 103.52 102.084648843383 1.43535115661736 18 101.18 109.464648843383 -8.28464884338262 19 96.39 112.404648843383 -16.0146488433826 20 97.56 110.679648843383 -13.1196488433827 21 96.39 104.897648843383 -8.50764884338265 22 85.1 102.324131551005 -17.2241315510050 23 79.77 96.7730204398938 -17.0030204398938 24 79.13 89.5523990898749 -10.4223990898749 25 80.84 99.3442867652635 -18.5042867652635 26 82.75 103.484286765264 -20.7342867652636 27 92.55 110.514286765264 -17.9642867652636 28 96.6 115.019286765264 -18.4192867652636 29 96.92 123.125286765264 -26.2052867652636 30 95.32 130.505286765264 -35.1852867652635 31 98.52 133.445286765264 -34.9252867652636 32 100.22 131.720286765264 -31.5002867652636 33 104.91 125.938286765264 -21.0282867652636 34 103.1 123.364769472886 -20.2647694728859 35 97.13 117.813658361775 -20.6836583617748 36 103.42 110.593037011756 -7.17303701175578 37 111.72 120.384924687144 -8.66492468714446 38 118.11 124.524924687145 -6.41492468714453 39 111.62 131.554924687144 -19.9349246871445 40 100.22 136.059924687144 -35.8399246871445 41 102.03 144.165924687144 -42.1359246871445 42 105.76 151.545924687144 -45.7859246871445 43 107.68 154.485924687144 -46.8059246871445 44 110.77 152.760924687144 -41.9909246871445 45 105.44 146.978924687144 -41.5389246871445 46 112.26 144.405407394767 -32.1454073947668 47 114.07 138.854296283656 -24.7842962836557 48 117.9 131.633674933637 -13.7336749336367 49 124.72 141.425562609025 -16.7055626090254 50 126.42 145.565562609025 -19.1455626090255 51 134.73 152.595562609025 -17.8655626090254 52 135.79 157.100562609025 -21.3105626090254 53 143.36 165.206562609025 -21.8465626090254 54 140.37 172.586562609025 -32.2165626090254 55 144.74 175.526562609025 -30.7865626090254 56 151.98 173.801562609025 -21.8215626090254 57 150.92 168.019562609025 -17.0995626090254 58 163.38 165.446045316648 -2.06604531664770 59 154.43 159.894934205537 -5.4649342055366 60 146.66 152.674312855518 -6.01431285551764 61 157.95 162.466200530906 -4.51620053090632 62 162.1 166.606200530906 -4.50620053090638 63 180.42 173.636200530906 6.78379946909365 64 179.57 178.141200530906 1.42879946909366 65 171.58 186.247200530906 -14.6672005309063 66 185.43 193.627200530906 -8.19720053090631 67 190.64 196.567200530906 -5.92720053090635 68 203 194.842200530906 8.15779946909364 69 202.36 189.060200530906 13.2997994690937 70 193.41 186.486683238529 6.92331676147138 71 186.17 180.935572127418 5.23442787258247 72 192.24 173.714950777399 18.5250492226014 73 209.6 183.506838452787 26.0931615472128 74 206.41 187.646838452787 18.7631615472127 75 209.82 194.676838452787 15.1431615472127 76 230.37 199.181838452787 31.1881615472127 77 235.8 207.287838452787 28.5121615472128 78 232.07 214.667838452787 17.4021615472127 79 244.64 217.607838452787 27.0321615472127 80 242.19 215.882838452787 26.3071615472128 81 217.48 210.100838452787 7.37916154721275 82 209.39 207.527321160410 1.86267883959044 83 211.73 201.976210049298 9.75378995070157 84 221 194.755588699279 26.2444113007205 85 203.11 204.547476374668 -1.43747637466814 86 214.71 208.687476374668 6.02252362533179 87 224.19 215.717476374668 8.47252362533183 88 238.04 220.222476374668 17.8175236253318 89 238.36 228.328476374668 10.0315236253318 90 246.24 235.708476374668 10.5315236253318 91 259.87 238.648476374668 21.2215236253318 92 249.97 236.923476374668 13.0465236253318 93 266.48 231.141476374668 35.3385236253318 94 282.98 228.567959082290 54.4120409177096 95 306.31 223.016847971179 83.2931520288207 96 301.73 245.011818771331 56.718181228669 97 314.62 254.803706446720 59.8162935532803 98 332.62 258.943706446720 73.6762935532802 99 355.51 265.973706446720 89.5362935532803 100 370.32 270.478706446720 99.8412935532803 101 408.13 278.58470644672 129.545293553280 102 433.58 285.96470644672 147.615293553280 103 440.51 288.90470644672 151.605293553280 104 386.29 287.17970644672 99.1102935532803 105 342.84 281.39770644672 61.4422935532802 106 254.97 278.824189154342 -23.8541891543421 107 203.42 273.273078043231 -69.853078043231 108 170.09 266.052456693212 -95.962456693212 109 174.03 275.844344368601 -101.814344368601 110 167.85 279.984344368601 -112.134344368601 111 177.01 287.014344368601 -110.004344368601 112 188.19 291.519344368601 -103.329344368601 113 211.2 299.625344368601 -88.4253443686007 114 240.91 307.005344368601 -66.0953443686007 115 230.26 309.945344368601 -79.6853443686007 116 251.25 308.220344368601 -56.9703443686007 117 241.66 302.438344368601 -60.7783443686007 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.000274435732045288 0.000548871464090576 0.999725564267955 18 4.56351542180012e-05 9.12703084360024e-05 0.999954364845782 19 7.97251293144967e-06 1.59450258628993e-05 0.999992027487069 20 1.46627834597354e-06 2.93255669194708e-06 0.999998533721654 21 1.15894958300442e-06 2.31789916600884e-06 0.999998841050417 22 2.23395829906392e-06 4.46791659812783e-06 0.9999977660417 23 3.62575293254753e-06 7.25150586509505e-06 0.999996374247067 24 8.3507134585288e-07 1.67014269170576e-06 0.999999164928654 25 1.41006894240002e-07 2.82013788480004e-07 0.999999858993106 26 2.3473061863232e-08 4.6946123726464e-08 0.999999976526938 27 4.69234905624935e-09 9.3846981124987e-09 0.99999999530765 28 1.78166766397197e-09 3.56333532794395e-09 0.999999998218332 29 3.35716477220309e-10 6.71432954440617e-10 0.999999999664284 30 5.39253076050422e-11 1.07850615210084e-10 0.999999999946075 31 1.31515389333556e-11 2.63030778667113e-11 0.999999999986849 32 2.85612006558114e-12 5.71224013116228e-12 0.999999999997144 33 6.7122422994813e-13 1.34244845989626e-12 0.999999999999329 34 2.383381794753e-13 4.766763589506e-13 0.999999999999762 35 4.99473028280626e-14 9.98946056561252e-14 0.99999999999995 36 5.81390115915307e-14 1.16278023183061e-13 0.999999999999942 37 1.45086669253644e-13 2.90173338507287e-13 0.999999999999855 38 2.66258535816818e-13 5.32517071633636e-13 0.999999999999734 39 1.07664687666786e-13 2.15329375333572e-13 0.999999999999892 40 2.18339443086272e-14 4.36678886172544e-14 0.999999999999978 41 4.17473788040758e-15 8.34947576081516e-15 0.999999999999996 42 8.95158320562925e-16 1.79031664112585e-15 1 43 2.26142220583709e-16 4.52284441167417e-16 1 44 5.78393912593834e-17 1.15678782518767e-16 1 45 1.08088894302196e-17 2.16177788604391e-17 1 46 3.10145538010868e-18 6.20291076021736e-18 1 47 1.28053798966470e-18 2.56107597932940e-18 1 48 1.02229840148895e-18 2.04459680297790e-18 1 49 9.03835324941757e-19 1.80767064988351e-18 1 50 4.73554254443513e-19 9.47108508887027e-19 1 51 5.90284583743365e-19 1.18056916748673e-18 1 52 1.06309076366634e-18 2.12618152733269e-18 1 53 2.22582565382329e-18 4.45165130764658e-18 1 54 2.51453061830056e-18 5.02906123660112e-18 1 55 4.32544597199891e-18 8.65089194399782e-18 1 56 9.34677257035783e-18 1.86935451407157e-17 1 57 1.16029251890089e-17 2.32058503780177e-17 1 58 4.70455430969171e-17 9.40910861938343e-17 1 59 6.47087971969078e-17 1.29417594393816e-16 1 60 4.25762382359724e-17 8.51524764719448e-17 1 61 3.1949867275225e-17 6.389973455045e-17 1 62 2.26502340451146e-17 4.53004680902293e-17 1 63 5.4936819069854e-17 1.09873638139708e-16 1 64 1.34198046833590e-16 2.68396093667179e-16 1 65 1.60201829192070e-16 3.20403658384140e-16 1 66 5.42507736824333e-16 1.08501547364867e-15 1 67 2.86324180675846e-15 5.72648361351691e-15 0.999999999999997 68 1.94459292182849e-14 3.88918584365698e-14 0.99999999999998 69 8.50181412539746e-14 1.70036282507949e-13 0.999999999999915 70 1.84491284437922e-13 3.68982568875843e-13 0.999999999999815 71 4.23992432527825e-13 8.47984865055649e-13 0.999999999999576 72 4.66926665911313e-13 9.33853331822626e-13 0.999999999999533 73 5.65914716072277e-13 1.13182943214455e-12 0.999999999999434 74 4.93719390967793e-13 9.87438781935585e-13 0.999999999999506 75 4.74622760678002e-13 9.49245521356004e-13 0.999999999999525 76 1.30782940530446e-12 2.61565881060892e-12 0.999999999998692 77 5.08310163718688e-12 1.01662032743738e-11 0.999999999994917 78 3.2024736795388e-11 6.4049473590776e-11 0.999999999967975 79 3.81877395603373e-10 7.63754791206745e-10 0.999999999618123 80 3.59399590826126e-09 7.18799181652252e-09 0.999999996406004 81 1.03675906267600e-07 2.07351812535201e-07 0.999999896324094 82 1.50480090936069e-06 3.00960181872138e-06 0.99999849519909 83 2.89383185352590e-05 5.78766370705181e-05 0.999971061681465 84 1.78851971396527e-05 3.57703942793055e-05 0.99998211480286 85 8.99001916723703e-06 1.79800383344741e-05 0.999991009980833 86 4.25132766164832e-06 8.50265532329663e-06 0.999995748672338 87 2.10241885470461e-06 4.20483770940923e-06 0.999997897581145 88 1.16302185079410e-06 2.32604370158820e-06 0.99999883697815 89 1.22619193211801e-06 2.45238386423603e-06 0.999998773808068 90 5.39590701415312e-06 1.07918140283062e-05 0.999994604092986 91 4.42258707027308e-05 8.84517414054617e-05 0.999955774129297 92 0.00212017673342080 0.00424035346684161 0.997879823266579 93 0.298313690288161 0.596627380576321 0.701686309711839 94 0.429010340756011 0.858020681512022 0.570989659243989 95 0.410178383127036 0.820356766254072 0.589821616872964 96 0.380411181516313 0.760822363032625 0.619588818483688 97 0.324948216852113 0.649896433704227 0.675051783147887 98 0.224034759041403 0.448069518082807 0.775965240958597 99 0.142387611127018 0.284775222254037 0.857612388872982 100 0.0826161993529477 0.165232398705895 0.917383800647052 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 76 0.904761904761905 NOK 5% type I error level 76 0.904761904761905 NOK 10% type I error level 76 0.904761904761905 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/10kcrt1258726645.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/10kcrt1258726645.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/1x4mb1258726645.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/1x4mb1258726645.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/2pkij1258726645.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/2pkij1258726645.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/3kjiy1258726645.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/3kjiy1258726645.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/45gh91258726645.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/45gh91258726645.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/5xmio1258726645.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/5xmio1258726645.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/6ubd31258726645.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/6ubd31258726645.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/7tmyn1258726645.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/7tmyn1258726645.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/85g7d1258726645.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/85g7d1258726645.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/9ms9i1258726645.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/20/t1258726737r8cxfhvqg02uzp6/9ms9i1258726645.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$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$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by