*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: Mon, 27 Dec 2010 16:54:35 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/27/t1293468822y02zrshpiwy3n55.htm/, Retrieved Mon, 27 Dec 2010 17:53:54 +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/2010/Dec/27/t1293468822y02zrshpiwy3n55.htm/}, year = {2010}, } @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 = {2010}, 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 «

1567 0 2237 0 2598 0 3729 0 5715 0 5776 0 5852 0 6878 0 5488 0 3583 0 2054 0 2282 0 1552 0 2261 0 2446 0 3519 0 5161 0 5085 0 5711 0 6057 0 5224 0 3363 0 1899 0 2115 0 1491 0 2061 0 2419 0 3430 0 4778 0 4862 0 6176 0 5664 0 5529 0 3418 0 1941 0 2402 0 1579 0 2146 0 2462 0 3695 0 4831 0 5134 0 6250 0 5760 0 6249 0 2917 0 1741 0 2359 0 1511 0 2059 0 2635 0 2867 0 4403 0 5720 0 4502 0 5749 0 5627 0 2846 0 1762 0 2429 0 1169 0 2154 0 2249 0 2687 0 4359 0 5382 0 4459 0 6398 0 4596 0 3024 0 1887 0 2070 0 1351 0 2218 0 2461 0 3028 0 4784 0 4975 0 4607 1 6249 1 4809 1 3157 1 1910 1 2228 1 1594 1 2467 1 2222 1 3607 1 4685 1 4962 1 5770 1 5480 1 5000 1 3228 1 1993 1 2288 1 1588 1 2105 1 2191 1 3591 1 4668 1 4885 1 5822 1 5599 1 5340 1 3082 1 2010 1 2301 1 1507 1 1992 1 2487 1 3490 1 4647 1 5594 1 5611 1 5788 1 6204 1 3013 1 1931 1 2549 1 1504 1 2090 1 2702 1 2939 1 4500 1 6208 1 6415 1 5657 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 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Huwelijken[t] = + 2280.23397435897 + 13.2797619047618Dummy[t] -807.055402930404M1[t] -114.824633699637M2[t] + 154.713827838829M3[t] + 1029.25228937729M4[t] + 2549.94459706960M5[t] + 3006.25228937728M6[t] + 3171.76923076923M7[t] + 3817.30769230770M8[t] + 3149.46153846154M9[t] + 933.615384615386M10[t] -368.692307692308M11[t] + 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) 2280.23397435897 113.227333 20.1385 0 0 Dummy 13.2797619047618 62.593908 0.2122 0.832286 0.416143 M1 -807.055402930404 152.944652 -5.2768 0 0 M2 -114.824633699637 152.944652 -0.7508 0.454031 0.227016 M3 154.713827838829 152.944652 1.0116 0.313453 0.156727 M4 1029.25228937729 152.944652 6.7296 0 0 M5 2549.94459706960 152.944652 16.6723 0 0 M6 3006.25228937728 152.944652 19.6558 0 0 M7 3171.76923076923 152.868843 20.7483 0 0 M8 3817.30769230770 152.868843 24.9711 0 0 M9 3149.46153846154 152.868843 20.6024 0 0 M10 933.615384615386 152.868843 6.1073 0 0 M11 -368.692307692308 152.868843 -2.4118 0.017141 0.008571 Multiple Linear Regression - Regression Statistics Multiple R 0.973352910832983 R-squared 0.94741588902704 Adjusted R-squared 0.943003236357981 F-TEST (value) 214.704387605692 F-TEST (DF numerator) 12 F-TEST (DF denominator) 143 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 389.740605971138 Sum Squared Residuals 21721376.8118132 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1567 1473.17857142856 93.821428571437 2 2237 2165.40934065934 71.5906593406562 3 2598 2434.94780219779 163.052197802205 4 3729 3309.48626373625 419.513736263746 5 5715 4830.17857142857 884.821428571427 6 5776 5286.48626373627 489.513736263732 7 5852 5452.0032051282 399.996794871796 8 6878 6097.54166666665 780.458333333354 9 5488 5429.69551282051 58.304487179488 10 3583 3213.84935897436 369.15064102564 11 2054 1911.54166666667 142.458333333328 12 2282 2280.23397435898 1.76602564102120 13 1552 1473.17857142857 78.821428571428 14 2261 2165.40934065934 95.5906593406597 15 2446 2434.94780219780 11.0521978021972 16 3519 3309.48626373626 209.513736263735 17 5161 4830.17857142857 330.821428571428 18 5085 5286.48626373626 -201.486263736263 19 5711 5452.0032051282 258.996794871795 20 6057 6097.54166666667 -40.5416666666685 21 5224 5429.69551282051 -205.695512820513 22 3363 3213.84935897436 149.150641025641 23 1899 1911.54166666667 -12.5416666666665 24 2115 2280.23397435898 -165.233974358975 25 1491 1473.17857142857 17.8214285714274 26 2061 2165.40934065934 -104.409340659340 27 2419 2434.94780219780 -15.9478021978028 28 3430 3309.48626373626 120.513736263735 29 4778 4830.17857142857 -52.178571428572 30 4862 5286.48626373626 -424.486263736263 31 6176 5452.0032051282 723.996794871794 32 5664 6097.54166666667 -433.541666666669 33 5529 5429.69551282051 99.3044871794869 34 3418 3213.84935897436 204.150641025641 35 1941 1911.54166666667 29.4583333333334 36 2402 2280.23397435898 121.766025641025 37 1579 1473.17857142857 105.821428571427 38 2146 2165.40934065934 -19.4093406593403 39 2462 2434.94780219780 27.0521978021972 40 3695 3309.48626373626 385.513736263735 41 4831 4830.17857142857 0.82142857142801 42 5134 5286.48626373626 -152.486263736263 43 6250 5452.0032051282 797.996794871794 44 5760 6097.54166666667 -337.541666666668 45 6249 5429.69551282051 819.304487179487 46 2917 3213.84935897436 -296.849358974359 47 1741 1911.54166666667 -170.541666666667 48 2359 2280.23397435898 78.766025641025 49 1511 1473.17857142857 37.8214285714274 50 2059 2165.40934065934 -106.409340659340 51 2635 2434.94780219780 200.052197802197 52 2867 3309.48626373626 -442.486263736265 53 4403 4830.17857142857 -427.178571428572 54 5720 5286.48626373626 433.513736263736 55 4502 5452.0032051282 -950.003205128205 56 5749 6097.54166666667 -348.541666666668 57 5627 5429.69551282051 197.304487179487 58 2846 3213.84935897436 -367.849358974359 59 1762 1911.54166666667 -149.541666666667 60 2429 2280.23397435898 148.766025641025 61 1169 1473.17857142857 -304.178571428573 62 2154 2165.40934065934 -11.4093406593403 63 2249 2434.94780219780 -185.947802197803 64 2687 3309.48626373627 -622.486263736265 65 4359 4830.17857142857 -471.178571428572 66 5382 5286.48626373626 95.5137362637365 67 4459 5452.0032051282 -993.003205128205 68 6398 6097.54166666667 300.458333333332 69 4596 5429.69551282051 -833.695512820513 70 3024 3213.84935897436 -189.849358974359 71 1887 1911.54166666667 -24.5416666666665 72 2070 2280.23397435898 -210.233974358975 73 1351 1473.17857142857 -122.178571428573 74 2218 2165.40934065934 52.5906593406597 75 2461 2434.94780219780 26.0521978021972 76 3028 3309.48626373626 -281.486263736265 77 4784 4830.17857142857 -46.178571428572 78 4975 5286.48626373626 -311.486263736263 79 4607 5465.28296703297 -858.282967032967 80 6249 6110.82142857143 138.178571428570 81 4809 5442.97527472527 -633.975274725274 82 3157 3227.12912087912 -70.1291208791209 83 1910 1924.82142857143 -14.8214285714279 84 2228 2293.51373626374 -65.5137362637364 85 1594 1486.45833333333 107.541666666666 86 2467 2178.6891025641 288.310897435898 87 2222 2448.22756410256 -226.227564102565 88 3607 3322.76602564103 284.233974358974 89 4685 4843.45833333333 -158.458333333333 90 4962 5299.76602564102 -337.766025641025 91 5770 5465.28296703297 304.717032967033 92 5480 6110.82142857143 -630.82142857143 93 5000 5442.97527472527 -442.975274725275 94 3228 3227.12912087912 0.870879120879065 95 1993 1924.82142857143 68.1785714285721 96 2288 2293.51373626374 -5.5137362637364 97 1588 1486.45833333333 101.541666666666 98 2105 2178.6891025641 -73.689102564102 99 2191 2448.22756410256 -257.227564102564 100 3591 3322.76602564103 268.233974358974 101 4668 4843.45833333333 -175.458333333333 102 4885 5299.76602564102 -414.766025641025 103 5822 5465.28296703297 356.717032967033 104 5599 6110.82142857143 -511.82142857143 105 5340 5442.97527472528 -102.975274725275 106 3082 3227.12912087912 -145.129120879121 107 2010 1924.82142857143 85.1785714285721 108 2301 2293.51373626374 7.4862637362636 109 1507 1486.45833333333 20.541666666666 110 1992 2178.6891025641 -186.689102564102 111 2487 2448.22756410256 38.7724358974355 112 3490 3322.76602564103 167.233974358974 113 4647 4843.45833333333 -196.458333333333 114 5594 5299.76602564102 294.233974358976 115 5611 5465.28296703297 145.717032967033 116 5788 6110.82142857143 -322.82142857143 117 6204 5442.97527472528 761.024725274725 118 3013 3227.12912087912 -214.129120879121 119 1931 1924.82142857143 6.1785714285721 120 2549 2293.51373626374 255.486263736263 121 1504 1486.45833333333 17.541666666666 122 2090 2178.6891025641 -88.689102564102 123 2702 2448.22756410256 253.772435897436 124 2939 3322.76602564103 -383.766025641026 125 4500 4843.45833333333 -343.458333333333 126 6208 5299.76602564102 908.233974358975 127 6415 5465.28296703297 949.717032967033 128 5657 6110.82142857143 -453.82142857143 129 5964 5442.97527472527 521.024725274725 130 3163 3227.12912087912 -64.1291208791209 131 1997 1924.82142857143 72.1785714285721 132 2422 2293.51373626374 128.486263736263 133 1376 1486.45833333333 -110.458333333334 134 2202 2178.6891025641 23.3108974358981 135 2683 2448.22756410256 234.772435897436 136 3303 3322.76602564103 -19.7660256410262 137 5202 4843.45833333333 358.541666666667 138 5231 5299.76602564102 -68.7660256410247 139 4880 5465.28296703297 -585.282967032967 140 7998 6110.82142857143 1887.17857142857 141 4977 5442.97527472527 -465.975274725275 142 3531 3227.12912087912 303.870879120879 143 2025 1924.82142857143 100.178571428572 144 2205 2293.51373626374 -88.5137362637364 145 1442 1486.45833333333 -44.458333333334 146 2238 2178.6891025641 59.3108974358981 147 2179 2448.22756410256 -269.227564102564 148 3218 3322.76602564103 -104.766025641026 149 5139 4843.45833333333 295.541666666667 150 4990 5299.76602564102 -309.766025641025 151 4914 5465.28296703297 -551.282967032967 152 6084 6110.82142857143 -26.8214285714303 153 5672 5442.97527472528 229.024725274725 154 3548 3227.12912087912 320.870879120879 155 1793 1924.82142857143 -131.821428571428 156 2086 2293.51373626374 -207.513736263736 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0267861454104122 0.0535722908208245 0.973213854589588 17 0.130573689674615 0.261147379349230 0.869426310325385 18 0.272373323901642 0.544746647803285 0.727626676098358 19 0.177822933001594 0.355645866003187 0.822177066998406 20 0.347901059855327 0.695802119710654 0.652098940144673 21 0.272045984156221 0.544091968312443 0.727954015843779 22 0.203930258818569 0.407860517637138 0.79606974118143 23 0.142867365438945 0.285734730877889 0.857132634561055 24 0.0981741916364777 0.196348383272955 0.901825808363522 25 0.0627627150432128 0.125525430086426 0.937237284956787 26 0.0426823916519221 0.0853647833038442 0.957317608348078 27 0.0263293937073492 0.0526587874146984 0.97367060629265 28 0.0176943885987410 0.0353887771974821 0.982305611401259 29 0.0402331512744438 0.0804663025488876 0.959766848725556 30 0.0578069181759679 0.115613836351936 0.942193081824032 31 0.0657084886424916 0.131416977284983 0.934291511357508 32 0.141355237750147 0.282710475500294 0.858644762249853 33 0.109218055527841 0.218436111055682 0.89078194447216 34 0.0815515119215645 0.163103023843129 0.918448488078436 35 0.0579911142314806 0.115982228462961 0.94200888576852 36 0.0438558632733829 0.0877117265467659 0.956144136726617 37 0.0304303299755616 0.0608606599511231 0.969569670024439 38 0.0204158940145405 0.040831788029081 0.97958410598546 39 0.013443609205058 0.026887218410116 0.986556390794942 40 0.0103912078741313 0.0207824157482626 0.989608792125869 41 0.0101511438823067 0.0203022877646134 0.989848856117693 42 0.00671451441716006 0.0134290288343201 0.99328548558284 43 0.0104762270537192 0.0209524541074384 0.98952377294628 44 0.0114563369203733 0.0229126738407466 0.988543663079627 45 0.0523569830516194 0.104713966103239 0.94764301694838 46 0.061491865474115 0.12298373094823 0.938508134525885 47 0.0491638529705815 0.098327705941163 0.950836147029419 48 0.0372683850741155 0.074536770148231 0.962731614925885 49 0.0275325012010619 0.0550650024021239 0.972467498798938 50 0.0200575535806589 0.0401151071613177 0.97994244641934 51 0.0160222044585094 0.0320444089170187 0.98397779554149 52 0.0311173660279841 0.0622347320559682 0.968882633972016 53 0.0516539161304914 0.103307832260983 0.948346083869509 54 0.0652695918599219 0.130539183719844 0.934730408140078 55 0.386341997059546 0.772683994119093 0.613658002940454 56 0.36155018056772 0.72310036113544 0.63844981943228 57 0.335111623347106 0.670223246694212 0.664888376652894 58 0.329185914646086 0.658371829292171 0.670814085353914 59 0.286479495031790 0.572958990063579 0.71352050496821 60 0.257292482491960 0.514584964983919 0.74270751750804 61 0.238304112910271 0.476608225820542 0.761695887089729 62 0.20208948504504 0.40417897009008 0.79791051495496 63 0.176309250138465 0.352618500276930 0.823690749861535 64 0.229781654847390 0.459563309694781 0.77021834515261 65 0.248763017142131 0.497526034284263 0.751236982857869 66 0.217816844768214 0.435633689536428 0.782183155231786 67 0.454901771897018 0.909803543794037 0.545098228102982 68 0.449940524128691 0.899881048257383 0.550059475871309 69 0.599728782742628 0.800542434514744 0.400271217257372 70 0.556873819802628 0.886252360394744 0.443126180197372 71 0.507542646301406 0.984914707397188 0.492457353698594 72 0.466974792889946 0.933949585779893 0.533025207110054 73 0.419844373490712 0.839688746981423 0.580155626509288 74 0.375535933683526 0.751071867367051 0.624464066316474 75 0.335305568932140 0.670611137864279 0.66469443106786 76 0.303049142506629 0.606098285013258 0.696950857493371 77 0.266506636560929 0.533013273121857 0.733493363439071 78 0.24036986414675 0.4807397282935 0.75963013585325 79 0.291100335850342 0.582200671700684 0.708899664149658 80 0.315392676527235 0.63078535305447 0.684607323472765 81 0.336231672500603 0.672463345001206 0.663768327499397 82 0.308306952115272 0.616613904230544 0.691693047884728 83 0.278454785152489 0.556909570304978 0.721545214847511 84 0.243010417272914 0.486020834545827 0.756989582727086 85 0.217852135623341 0.435704271246681 0.78214786437666 86 0.211763916786364 0.423527833572727 0.788236083213636 87 0.182772771352659 0.365545542705317 0.817227228647341 88 0.173481031930931 0.346962063861861 0.82651896806907 89 0.145225954696284 0.290451909392568 0.854774045303716 90 0.133107976429199 0.266215952858399 0.8668920235708 91 0.126118812445928 0.252237624891855 0.873881187554072 92 0.160058572167801 0.320117144335601 0.8399414278322 93 0.167997772182592 0.335995544365183 0.832002227817408 94 0.139557747810160 0.279115495620320 0.86044225218984 95 0.115729925286861 0.231459850573722 0.88427007471314 96 0.0932764105713006 0.186552821142601 0.9067235894287 97 0.0761155189497139 0.152231037899428 0.923884481050286 98 0.059346411623747 0.118692823247494 0.940653588376253 99 0.0498181975523148 0.0996363951046297 0.950181802447685 100 0.0449054117399659 0.0898108234799318 0.955094588260034 101 0.03517521572663 0.07035043145326 0.96482478427337 102 0.0372266011788852 0.0744532023577705 0.962773398821115 103 0.0357808544234354 0.0715617088468707 0.964219145576565 104 0.0474118494781049 0.0948236989562097 0.952588150521895 105 0.040019167934751 0.080038335869502 0.959980832065249 106 0.0312052701744513 0.0624105403489026 0.968794729825549 107 0.0234692385644281 0.0469384771288562 0.976530761435572 108 0.0170196066722731 0.0340392133445462 0.982980393327727 109 0.0121571214887014 0.0243142429774029 0.987842878511299 110 0.00884589888724445 0.0176917977744889 0.991154101112756 111 0.0061486988323863 0.0122973976647726 0.993851301167614 112 0.00479781197483775 0.0095956239496755 0.995202188025162 113 0.00353307291971619 0.00706614583943238 0.996466927080284 114 0.00277107297941552 0.00554214595883104 0.997228927020585 115 0.00192706212657924 0.00385412425315848 0.99807293787342 116 0.00260000309417717 0.00520000618835434 0.997399996905823 117 0.00535100533677687 0.0107020106735537 0.994648994663223 118 0.00424838886741215 0.0084967777348243 0.995751611132588 119 0.00271931129716628 0.00543862259433256 0.997280688702834 120 0.00205399142576962 0.00410798285153925 0.99794600857423 121 0.00127135927204565 0.00254271854409131 0.998728640727954 122 0.000774541948323765 0.00154908389664753 0.999225458051676 123 0.000533586157710259 0.00106717231542052 0.99946641384229 124 0.000394737652673695 0.00078947530534739 0.999605262347326 125 0.000420839761830071 0.000841679523660142 0.99957916023817 126 0.00233450249373211 0.00466900498746421 0.997665497506268 127 0.0366570901165631 0.0733141802331261 0.963342909883437 128 0.200867076215583 0.401734152431165 0.799132923784417 129 0.242967013562078 0.485934027124157 0.757032986437922 130 0.213664539664747 0.427329079329494 0.786335460335253 131 0.160320681073061 0.320641362146122 0.839679318926939 132 0.125727579636562 0.251455159273123 0.874272420363438 133 0.0867670984641593 0.173534196928319 0.913232901535841 134 0.0564407168536965 0.112881433707393 0.943559283146304 135 0.0471135191661803 0.0942270383323606 0.95288648083382 136 0.0277624658474629 0.0555249316949259 0.972237534152537 137 0.0159240266505748 0.0318480533011496 0.984075973349425 138 0.00850456155309412 0.0170091231061882 0.991495438446906 139 0.00438114638817711 0.00876229277635422 0.995618853611823 140 0.636241927052665 0.72751614589467 0.363758072947335 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 15 0.12 NOK 5% type I error level 33 0.264 NOK 10% type I error level 54 0.432 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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') }

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Software written by Ed van Stee & Patrick Wessa

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