WS7 Toevoeging seizoenaliteit

*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, 23 Nov 2009 17:24:54 -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/24/t12590223384opnfv45nqys1fs.htm/, Retrieved Tue, 24 Nov 2009 01:25:51 +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/24/t12590223384opnfv45nqys1fs.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 «

423.4 0 404.1 0 500 0 472.6 0 496.1 0 562 0 434.8 0 538.2 0 577.6 0 518.1 0 625.2 0 561.2 0 523.3 0 536.1 0 607.3 0 637.3 0 606.9 0 652.9 0 617.2 0 670.4 0 729.9 0 677.2 0 710 0 844.3 0 748.2 0 653.9 0 742.6 0 854.2 0 808.4 0 1819 1 1936.5 1 1966.1 1 2083.1 1 1620.1 1 1527.6 1 1795 1 1685.1 1 1851.8 1 2164.4 1 1981.8 1 1726.5 1 2144.6 1 1758.2 1 1672.9 1 1837.3 1 1596.1 1 1446 1 1898.4 1 1964.1 1 1755.9 1 2255.3 1 1881.2 1 2117.9 1 1656.5 1 1544.1 1 2098.9 1 2133.3 1 1963.5 1 1801.2 1 2365.4 1 1936.5 1 1667.6 1 1983.5 1 2058.6 1 2448.3 1 1858.1 1 1625.4 1 2130.6 1 2515.7 1 2230.2 1 2086.9 1 2235 1 2100.2 1 2288.6 1 2490 1 2573.7 1 2543.8 1 2004.7 1 2390 1 2338.4 1 2724.5 1 2292.5 1 2386 1 2477.9 1 2337 1 2605.1 1 2560.8 1 2839.3 1 2407.2 1 2085.2 1 2735.6 1 2798.7 1 3053.2 1 2405 1 2471.9 1 2727.3 1 2790.7 1 2385.4 1 3206.6 1 2705.6 1 3518.4 1 1954.9 1 2584.3 1 2535.8 1 2685.9 1 2866 1 2236.6 1 2934.9 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(Export_farma_prod)[t] = + 472.118850243288 + 874.564984681923`X(sprong)`[t] -115.286974529945M1[t] -194.639386075569M2[t] + 107.418202378807M3[t] + 15.3157908331826M4[t] + 91.1233792875589M5[t] -247.605530726257M6[t] -196.257942271881M7[t] -59.5103538175048M8[t] + 114.267234636871M9[t] -139.805176908753M10[t] -266.707588454377M11[t] + 13.6124115456238t + 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) 472.118850243288 75.243245 6.2746 0 0 `X(sprong)` 874.564984681923 65.503371 13.3514 0 0 M1 -115.286974529945 91.94054 -1.2539 0.212626 0.106313 M2 -194.639386075569 91.908568 -2.1178 0.036534 0.018267 M3 107.418202378807 91.883693 1.1691 0.244999 0.122499 M4 15.3157908331826 91.865921 0.1667 0.867909 0.433954 M5 91.1233792875589 91.855256 0.992 0.323441 0.16172 M6 -247.605530726257 91.874111 -2.6951 0.008186 0.004093 M7 -196.257942271881 91.835005 -2.1371 0.034892 0.017446 M8 -59.5103538175048 91.802996 -0.6482 0.518232 0.259116 M9 114.267234636871 91.778092 1.245 0.215863 0.107932 M10 -139.805176908753 91.7603 -1.5236 0.130589 0.065294 M11 -266.707588454377 91.749623 -2.9069 0.004446 0.002223 t 13.6124115456238 0.808155 16.8438 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.97203000679112 R-squared 0.944842334102346 Adjusted R-squared 0.938077714699803 F-TEST (value) 139.674130631388 F-TEST (DF numerator) 13 F-TEST (DF denominator) 106 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 205.150435212925 Sum Squared Residuals 4461190.31321355 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 423.4 370.444287258967 52.955712741033 2 404.1 304.70428725896 99.39571274104 3 500 620.374287258967 -120.374287258967 4 472.6 541.884287258965 -69.2842872589649 5 496.1 631.304287258966 -135.204287258967 6 562 306.187788790772 255.812211209228 7 434.8 371.147788790773 63.652211209227 8 538.2 521.507788790773 16.692211209227 9 577.6 708.897788790773 -131.297788790773 10 518.1 468.437788790774 49.6622112092263 11 625.2 355.147788790773 270.052211209227 12 561.2 635.467788790773 -74.2677887907733 13 523.3 533.793225806452 -10.4932258064518 14 536.1 468.053225806453 68.0467741935474 15 607.3 783.723225806451 -176.423225806451 16 637.3 705.233225806452 -67.9332258064518 17 606.9 794.653225806452 -187.753225806452 18 652.9 469.53672733826 183.363272661741 19 617.2 534.496727338259 82.7032726617407 20 670.4 684.856727338259 -14.4567273382594 21 729.9 872.24672733826 -142.346727338259 22 677.2 631.786727338259 45.4132726617408 23 710 518.496727338259 191.503272661741 24 844.3 798.81672733826 45.4832726617404 25 748.2 697.142164353938 51.0578356460624 26 653.9 631.402164353938 22.4978356460617 27 742.6 947.072164353937 -204.472164353937 28 854.2 868.582164353938 -14.3821643539378 29 808.4 958.002164353938 -149.602164353938 30 1819 1507.45065056767 311.54934943233 31 1936.5 1572.41065056767 364.08934943233 32 1966.1 1722.77065056767 243.32934943233 33 2083.1 1910.16065056767 172.939349432330 34 1620.1 1669.70065056767 -49.6006505676697 35 1527.6 1556.41065056767 -28.8106505676698 36 1795 1836.73065056767 -41.7306505676701 37 1685.1 1735.05608758335 -49.9560875833482 38 1851.8 1669.31608758335 182.483912416651 39 2164.4 1984.98608758335 179.413912416652 40 1981.8 1906.49608758335 75.3039124166515 41 1726.5 1995.91608758335 -269.416087583348 42 2144.6 1670.79958911516 473.800410884844 43 1758.2 1735.75958911516 22.4404108848441 44 1672.9 1886.11958911516 -213.219589115156 45 1837.3 2073.50958911516 -236.209589115156 46 1596.1 1833.04958911516 -236.949589115156 47 1446 1719.75958911516 -273.759589115156 48 1898.4 2000.07958911516 -101.679589115156 49 1964.1 1898.40502613083 65.6949738691657 50 1755.9 1832.66502613083 -76.7650261308347 51 2255.3 2148.33502613083 106.964973869166 52 1881.2 2069.84502613083 -188.645026130834 53 2117.9 2159.26502613083 -41.3650261308341 54 1656.5 1834.14852766264 -177.648527662642 55 1544.1 1899.10852766264 -355.008527662642 56 2098.9 2049.46852766264 49.4314723373582 57 2133.3 2236.85852766264 -103.558527662642 58 1963.5 1996.39852766264 -32.8985276626418 59 1801.2 1883.10852766264 -81.9085276626418 60 2365.4 2163.42852766264 201.971472337358 61 1936.5 2061.75396467832 -125.253964678320 62 1667.6 1996.01396467832 -328.413964678321 63 1983.5 2311.68396467832 -328.18396467832 64 2058.6 2233.19396467832 -174.593964678321 65 2448.3 2322.61396467832 125.686035321680 66 1858.1 1997.49746621013 -139.397466210128 67 1625.4 2062.45746621013 -437.057466210128 68 2130.6 2212.81746621013 -82.217466210128 69 2515.7 2400.20746621013 115.492533789872 70 2230.2 2159.74746621013 70.452533789872 71 2086.9 2046.45746621013 40.4425337898722 72 2235 2326.77746621013 -91.7774662101283 73 2100.2 2225.10290322581 -124.902903225806 74 2288.6 2159.36290322581 129.237096774193 75 2490 2475.03290322581 14.9670967741939 76 2573.7 2396.54290322581 177.157096774193 77 2543.8 2485.96290322581 57.8370967741938 78 2004.7 2160.84640475761 -156.146404757614 79 2390 2225.80640475761 164.193595242386 80 2338.4 2376.16640475761 -37.7664047576138 81 2724.5 2563.55640475761 160.943595242386 82 2292.5 2323.09640475761 -30.5964047576139 83 2386 2209.80640475761 176.193595242386 84 2477.9 2490.12640475761 -12.2264047576142 85 2337 2388.45184177329 -51.4518417732923 86 2605.1 2322.71184177329 282.388158226707 87 2560.8 2638.38184177329 -77.581841773292 88 2839.3 2559.89184177329 279.408158226707 89 2407.2 2649.31184177329 -242.111841773293 90 2085.2 2324.1953433051 -238.995343305100 91 2735.6 2389.1553433051 346.4446566949 92 2798.7 2539.5153433051 259.1846566949 93 3053.2 2726.9053433051 326.2946566949 94 2405 2486.4453433051 -81.4453433051 95 2471.9 2373.1553433051 98.7446566949002 96 2727.3 2653.4753433051 73.8246566948999 97 2790.7 2551.80078032078 238.899219679221 98 2385.4 2486.06078032078 -100.660780320779 99 3206.6 2801.73078032078 404.869219679222 100 2705.6 2723.24078032078 -17.6407803207786 101 3518.4 2812.66078032078 705.739219679223 102 1954.9 2487.54428185259 -532.644281852586 103 2584.3 2552.50428185259 31.7957181474141 104 2535.8 2702.86428185259 -167.064281852586 105 2685.9 2890.25428185259 -204.354281852586 106 2866 2649.79428185259 216.205718147414 107 2236.6 2536.50428185259 -299.904281852586 108 2934.9 2816.82428185259 118.075718147414 109 2668.6 2715.14971886826 -46.5497188682645 110 2371.2 2649.40971886826 -278.209718868265 111 3165.9 2965.07971886826 200.820281131736 112 2887.2 2886.58971886826 0.610281131735011 113 3112.2 2976.00971886826 136.190281131735 114 2671.2 2650.89322040007 20.3067795999276 115 2432.6 2715.85322040007 -283.253220400072 116 2812.3 2866.21322040007 -53.913220400072 117 3095.7 3053.60322040007 42.0967795999279 118 2862.9 2813.14322040007 49.7567795999281 119 2607.3 2699.85322040007 -92.5532204000718 120 2862.5 2980.17322040007 -117.673220400073 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.00136049548565108 0.00272099097130215 0.998639504514349 18 0.000191839335201649 0.000383678670403299 0.999808160664798 19 8.95729806534943e-05 0.000179145961306989 0.999910427019347 20 9.75641441404676e-06 1.95128288280935e-05 0.999990243585586 21 1.28020089534354e-06 2.56040179068708e-06 0.999998719799105 22 1.79721535441836e-07 3.59443070883671e-07 0.999999820278465 23 5.0378347251856e-08 1.00756694503712e-07 0.999999949621653 24 1.24056793811648e-06 2.48113587623297e-06 0.999998759432062 25 4.12153113856137e-07 8.24306227712274e-07 0.999999587846886 26 9.96409406059555e-08 1.99281881211911e-07 0.99999990035906 27 2.0158895327569e-08 4.0317790655138e-08 0.999999979841105 28 1.27541965640027e-08 2.55083931280054e-08 0.999999987245803 29 2.68166879090223e-09 5.36333758180445e-09 0.999999997318331 30 6.34151656966387e-10 1.26830331393277e-09 0.999999999365848 31 5.36196931684638e-09 1.07239386336928e-08 0.99999999463803 32 1.76765653891894e-09 3.53531307783789e-09 0.999999998232344 33 1.21859754681983e-09 2.43719509363966e-09 0.999999998781402 34 5.90443088427099e-07 1.18088617685420e-06 0.999999409556912 35 7.82238354857151e-05 0.000156447670971430 0.999921776164514 36 4.78583942099387e-05 9.57167884198774e-05 0.99995214160579 37 3.75672005295841e-05 7.51344010591682e-05 0.99996243279947 38 2.23821512839676e-05 4.47643025679352e-05 0.999977617848716 39 7.72498676212473e-05 0.000154499735242495 0.999922750132379 40 3.78549461877936e-05 7.57098923755871e-05 0.999962145053812 41 5.93832759805872e-05 0.000118766551961174 0.99994061672402 42 0.000266159439465591 0.000532318878931182 0.999733840560534 43 0.000337465596728041 0.000674931193456082 0.999662534403272 44 0.00116951865463583 0.00233903730927166 0.998830481345364 45 0.00149808167024227 0.00299616334048453 0.998501918329758 46 0.00226656057894911 0.00453312115789822 0.99773343942105 47 0.00849708951322944 0.0169941790264589 0.99150291048677 48 0.00560667700746569 0.0112133540149314 0.994393322992534 49 0.00410322691815107 0.00820645383630213 0.995896773081849 50 0.00300837126186058 0.00601674252372116 0.99699162873814 51 0.00335723209378749 0.00671446418757499 0.996642767906213 52 0.00275787946380521 0.00551575892761042 0.997242120536195 53 0.00253916757842770 0.00507833515685541 0.997460832421572 54 0.00719092792907754 0.0143818558581551 0.992809072070922 55 0.0165207373512522 0.0330414747025044 0.983479262648748 56 0.0136230714651316 0.0272461429302632 0.986376928534868 57 0.0103603801222215 0.0207207602444429 0.989639619877779 58 0.00758727882543021 0.0151745576508604 0.99241272117457 59 0.00498971231582186 0.00997942463164372 0.995010287684178 60 0.00843580394435844 0.0168716078887169 0.991564196055642 61 0.00580495012484927 0.0116099002496985 0.99419504987515 62 0.00863247378075162 0.0172649475615032 0.991367526219248 63 0.0133521588938644 0.0267043177877289 0.986647841106136 64 0.0121906231560214 0.0243812463120427 0.987809376843979 65 0.0203429978210581 0.0406859956421162 0.979657002178942 66 0.0177107075998662 0.0354214151997324 0.982289292400134 67 0.0487759499200259 0.0975518998400518 0.951224050079974 68 0.0384837976785629 0.0769675953571258 0.961516202321437 69 0.0467550038999331 0.0935100077998662 0.953244996100067 70 0.0432286033644389 0.0864572067288779 0.956771396635561 71 0.0339188181632297 0.0678376363264595 0.96608118183677 72 0.0267482690794838 0.0534965381589677 0.973251730920516 73 0.0227023297322374 0.0454046594644748 0.977297670267763 74 0.0215239163668552 0.0430478327337104 0.978476083633145 75 0.0218235208976324 0.0436470417952647 0.978176479102368 76 0.0237213668773671 0.0474427337547342 0.976278633122633 77 0.0245522671169802 0.0491045342339605 0.97544773288302 78 0.0199363019923911 0.0398726039847822 0.980063698007609 79 0.0185504654584787 0.0371009309169574 0.981449534541521 80 0.0135901813251850 0.0271803626503701 0.986409818674815 81 0.0119393298936034 0.0238786597872067 0.988060670106397 82 0.00928021492385571 0.0185604298477114 0.990719785076144 83 0.0078391443406636 0.0156782886813272 0.992160855659336 84 0.0054702018081245 0.0109404036162490 0.994529798191875 85 0.00432498658585523 0.00864997317171046 0.995675013414145 86 0.00702625296933968 0.0140525059386794 0.99297374703066 87 0.0117225547788564 0.0234451095577128 0.988277445221144 88 0.0122869151445936 0.0245738302891871 0.987713084855406 89 0.126489789359588 0.252979578719177 0.873510210640412 90 0.121260228352399 0.242520456704798 0.8787397716476 91 0.162599591272528 0.325199182545056 0.837400408727472 92 0.165232728132736 0.330465456265473 0.834767271867264 93 0.204261061009699 0.408522122019398 0.795738938990301 94 0.228639008981976 0.457278017963952 0.771360991018024 95 0.194319953331094 0.388639906662188 0.805680046668906 96 0.139348801501412 0.278697603002825 0.860651198498588 97 0.123701570721141 0.247403141442283 0.876298429278859 98 0.0904457040660556 0.180891408132111 0.909554295933944 99 0.0827331909358937 0.165466381871787 0.917266809064106 100 0.049204801404871 0.098409602809742 0.95079519859513 101 0.217148738504443 0.434297477008886 0.782851261495557 102 0.506785395546698 0.986429208906604 0.493214604453302 103 0.530665434447814 0.938669131104372 0.469334565552186 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 37 0.425287356321839 NOK 5% type I error level 66 0.758620689655172 NOK 10% type I error level 73 0.839080459770115 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/10z8dn1259022288.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/10z8dn1259022288.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/1tjf91259022288.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/1tjf91259022288.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/2gtcn1259022288.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/2gtcn1259022288.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/3f5bc1259022288.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/3f5bc1259022288.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/4gcjr1259022288.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/4gcjr1259022288.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/5myf81259022288.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/5myf81259022288.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/6ybe51259022288.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/6ybe51259022288.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/76x9d1259022288.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/76x9d1259022288.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/8x8r41259022288.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/8x8r41259022288.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/9xcxt1259022288.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/24/t12590223384opnfv45nqys1fs/9xcxt1259022288.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') }

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