Paper Multiple Regression tijdsreeks

*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: Sat, 11 Dec 2010 10:24:16 +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/11/t12920629452ligowc844upbmj.htm/, Retrieved Sat, 11 Dec 2010 11:22:35 +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/11/t12920629452ligowc844upbmj.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 «

17.848 19.592 21.092 20.899 25.890 24.965 22.225 20.977 22.897 22.785 22.769 19.637 20.203 20.450 23.083 21.738 26.766 25.280 22.574 22.729 21.378 22.902 24.989 21.116 15.169 15.846 20.927 18.273 22.538 15.596 14.034 11.366 14.861 15.149 13.577 13.026 13.190 13.196 15.826 14.733 16.307 15.703 14.589 12.043 15.057 14.053 12.698 10.888 10.045 11.549 13.767 12.434 13.116 14.211 12.266 12.602 15.714 13.742 12.745 10.491 10.057 10.900 11.771 11.992 11.933 14.504 11.727 11.477 13.578 11.555 11.846 11.397 10.066 10.269 14.279 13.870 13.695 14.420 11.424 9.704 12.464 14.301 13.464 9.893 11.572 12.380 16.692 16.052 16.459 14.761 13.654 13.480 18.068 16.560 14.530 10.650 11.651 13.735 13.360 17.818 20.613 16.231 13.862 12.004 17.734 15.034 12.609 12.320 10.833 11.350 13.648 14.890 16.325 18.045 15.616 11.926 16.855 15.083 12.520 12.355

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 8 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Pas[t] = + 17.7650666666667 -0.878527777777776M1[t] + 0.0542838383838419M2[t] + 2.64159545454546M3[t] + 2.53650707070707M4[t] + 4.70031868686869M5[t] + 3.77723030303032M6[t] + 1.67224191919192M7[t] + 0.375453535353537M8[t] + 3.47476515151516M9[t] + 2.80007676767677M10[t] + 1.92788838383839M11[t] -0.0695116161616161t + 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) 17.7650666666667 1.143005 15.5424 0 0 M1 -0.878527777777776 1.417703 -0.6197 0.536783 0.268392 M2 0.0542838383838419 1.417183 0.0383 0.969517 0.484758 M3 2.64159545454546 1.416712 1.8646 0.064979 0.032489 M4 2.53650707070707 1.416291 1.791 0.076129 0.038064 M5 4.70031868686869 1.415919 3.3196 0.001233 0.000617 M6 3.77723030303032 1.415597 2.6683 0.00881 0.004405 M7 1.67224191919192 1.415324 1.1815 0.240013 0.120007 M8 0.375453535353537 1.415101 0.2653 0.791274 0.395637 M9 3.47476515151516 1.414927 2.4558 0.015667 0.007834 M10 2.80007676767677 1.414803 1.9791 0.050371 0.025185 M11 1.92788838383839 1.414729 1.3627 0.17583 0.087915 t -0.0695116161616161 0.008378 -8.2967 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.696874486476466 R-squared 0.485634049901839 Adjusted R-squared 0.42794814895625 F-TEST (value) 8.41859175190675 F-TEST (DF numerator) 12 F-TEST (DF denominator) 107 p-value 5.10929076824596e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.16337457068026 Sum Squared Residuals 1070.74243816364 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 17.848 16.8170272727273 1.03097272727271 2 19.592 17.6803272727273 1.91167272727273 3 21.092 20.1981272727273 0.893872727272736 4 20.899 20.0235272727273 0.875472727272718 5 25.89 22.1178272727273 3.77217272727274 6 24.965 21.1252272727273 3.83977272727273 7 22.225 18.9507272727273 3.27427272727271 8 20.977 17.5844272727273 3.39257272727273 9 22.897 20.6142272727273 2.28277272727274 10 22.785 19.8700272727273 2.91497272727271 11 22.769 18.9283272727273 3.84067272727272 12 19.637 16.9309272727273 2.70607272727273 13 20.203 15.9828878787879 4.22011212121213 14 20.45 16.8461878787879 3.60381212121212 15 23.083 19.3639878787879 3.71901212121212 16 21.738 19.1893878787879 2.54861212121212 17 26.766 21.2836878787879 5.48231212121212 18 25.28 20.2910878787879 4.98891212121212 19 22.574 18.1165878787879 4.45741212121212 20 22.729 16.7502878787879 5.97871212121212 21 21.378 19.7800878787879 1.59791212121212 22 22.902 19.0358878787879 3.86611212121212 23 24.989 18.0941878787879 6.89481212121212 24 21.116 16.0967878787879 5.01921212121213 25 15.169 15.1487484848485 0.0202515151515173 26 15.846 16.0120484848485 -0.166048484848486 27 20.927 18.5298484848485 2.39715151515152 28 18.273 18.3552484848485 -0.082248484848484 29 22.538 20.4495484848485 2.08845151515152 30 15.596 19.4569484848485 -3.86094848484849 31 14.034 17.2824484848485 -3.24844848484848 32 11.366 15.9161484848485 -4.55014848484848 33 14.861 18.9459484848485 -4.08494848484849 34 15.149 18.2017484848485 -3.05274848484848 35 13.577 17.2600484848485 -3.68304848484848 36 13.026 15.2626484848485 -2.23664848484848 37 13.19 14.3146090909091 -1.12460909090909 38 13.196 15.1779090909091 -1.98190909090909 39 15.826 17.6957090909091 -1.86970909090909 40 14.733 17.5211090909091 -2.78810909090909 41 16.307 19.6154090909091 -3.30840909090909 42 15.703 18.6228090909091 -2.91980909090909 43 14.589 16.4483090909091 -1.85930909090909 44 12.043 15.0820090909091 -3.03900909090909 45 15.057 18.1118090909091 -3.05480909090909 46 14.053 17.3676090909091 -3.31460909090909 47 12.698 16.4259090909091 -3.72790909090909 48 10.888 14.4285090909091 -3.54050909090909 49 10.045 13.4804696969697 -3.43546969696969 50 11.549 14.3437696969697 -2.7947696969697 51 13.767 16.8615696969697 -3.0945696969697 52 12.434 16.6869696969697 -4.2529696969697 53 13.116 18.7812696969697 -5.6652696969697 54 14.211 17.7886696969697 -3.5776696969697 55 12.266 15.6141696969697 -3.34816969696970 56 12.602 14.2478696969697 -1.64586969696970 57 15.714 17.2776696969697 -1.56366969696970 58 13.742 16.5334696969697 -2.79146969696970 59 12.745 15.5917696969697 -2.84676969696970 60 10.491 13.5943696969697 -3.10336969696969 61 10.057 12.6463303030303 -2.5893303030303 62 10.9 13.5096303030303 -2.60963030303030 63 11.771 16.0274303030303 -4.25643030303030 64 11.992 15.8528303030303 -3.8608303030303 65 11.933 17.9471303030303 -6.0141303030303 66 14.504 16.9545303030303 -2.45053030303031 67 11.727 14.7800303030303 -3.0530303030303 68 11.477 13.4137303030303 -1.93673030303030 69 13.578 16.4435303030303 -2.86553030303030 70 11.555 15.6993303030303 -4.1443303030303 71 11.846 14.7576303030303 -2.9116303030303 72 11.397 12.7602303030303 -1.3632303030303 73 10.066 11.8121909090909 -1.74619090909091 74 10.269 12.6754909090909 -2.40649090909091 75 14.279 15.1932909090909 -0.91429090909091 76 13.87 15.0186909090909 -1.14869090909091 77 13.695 17.1129909090909 -3.41799090909091 78 14.42 16.1203909090909 -1.70039090909091 79 11.424 13.9458909090909 -2.52189090909091 80 9.704 12.5795909090909 -2.87559090909091 81 12.464 15.6093909090909 -3.14539090909091 82 14.301 14.8651909090909 -0.564190909090909 83 13.464 13.9234909090909 -0.459490909090908 84 9.893 11.9260909090909 -2.03309090909090 85 11.572 10.9780515151515 0.593948484848486 86 12.38 11.8413515151515 0.538648484848484 87 16.692 14.3591515151515 2.33284848484848 88 16.052 14.1845515151515 1.86744848484848 89 16.459 16.2788515151515 0.180148484848486 90 14.761 15.2862515151515 -0.52525151515152 91 13.654 13.1117515151515 0.542248484848486 92 13.48 11.7454515151515 1.73454848484848 93 18.068 14.7752515151515 3.29274848484848 94 16.56 14.0310515151515 2.52894848484848 95 14.53 13.0893515151515 1.44064848484849 96 10.65 11.0919515151515 -0.441951515151513 97 11.651 10.1439121212121 1.50708787878788 98 13.735 11.0072121212121 2.72778787878788 99 13.36 13.5250121212121 -0.165012121212123 100 17.818 13.3504121212121 4.46758787878788 101 20.613 15.4447121212121 5.16828787878788 102 16.231 14.4521121212121 1.77888787878788 103 13.862 12.2776121212121 1.58438787878788 104 12.004 10.9113121212121 1.09268787878788 105 17.734 13.9411121212121 3.79288787878788 106 15.034 13.1969121212121 1.83708787878788 107 12.609 12.2552121212121 0.353787878787879 108 12.32 10.2578121212121 2.06218787878788 109 10.833 9.30977272727273 1.52322727272727 110 11.35 10.1730727272727 1.17692727272727 111 13.648 12.6908727272727 0.95712727272727 112 14.89 12.5162727272727 2.37372727272727 113 16.325 14.6105727272727 1.71442727272727 114 18.045 13.6179727272727 4.42702727272727 115 15.616 11.4434727272727 4.17252727272727 116 11.926 10.0771727272727 1.84882727272727 117 16.855 13.1069727272727 3.74802727272727 118 15.083 12.3627727272727 2.72022727272727 119 12.52 11.4210727272727 1.09892727272727 120 12.355 9.42367272727273 2.93132727272727 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.00818438454552243 0.0163687690910449 0.991815615454477 17 0.00191871134144154 0.00383742268288308 0.998081288658558 18 0.000843664412573147 0.00168732882514629 0.999156335587427 19 0.000304198990097878 0.000608397980195757 0.999695801009902 20 0.000118282251684664 0.000236564503369328 0.999881717748315 21 0.000876826611342432 0.00175365322268486 0.999123173388658 22 0.00044556917443213 0.00089113834886426 0.999554430825568 23 0.000800458291199774 0.00160091658239955 0.9991995417088 24 0.000860538718411278 0.00172107743682256 0.999139461281589 25 0.080217472588655 0.16043494517731 0.919782527411345 26 0.249016051761470 0.498032103522941 0.75098394823853 27 0.29828222859988 0.59656445719976 0.70171777140012 28 0.364340381301363 0.728680762602726 0.635659618698637 29 0.651688023262952 0.696623953474096 0.348311976737048 30 0.984401426748668 0.0311971465026636 0.0155985732513318 31 0.997414081562938 0.00517183687412447 0.00258591843706223 32 0.999832663873947 0.000334672252106268 0.000167336126053134 33 0.999862099930116 0.000275800139767689 0.000137900069883844 34 0.99990451631522 0.000190967369559644 9.5483684779822e-05 35 0.99997778196126 4.44360774804321e-05 2.22180387402161e-05 36 0.9999840038822 3.19922355998212e-05 1.59961177999106e-05 37 0.999988032334065 2.39353318695694e-05 1.19676659347847e-05 38 0.999985799264255 2.84014714892668e-05 1.42007357446334e-05 39 0.999986963840785 2.60723184297817e-05 1.30361592148909e-05 40 0.999978566033436 4.28679331270897e-05 2.14339665635448e-05 41 0.999982625231477 3.47495370451112e-05 1.73747685225556e-05 42 0.999973962572518 5.20748549638262e-05 2.60374274819131e-05 43 0.999978121836116 4.37563277688306e-05 2.18781638844153e-05 44 0.999968417134956 6.31657300871102e-05 3.15828650435551e-05 45 0.999949272263952 0.000101455472096070 5.07277360480349e-05 46 0.999920315631397 0.000159368737206335 7.96843686031677e-05 47 0.999896914230415 0.000206171539170235 0.000103085769585118 48 0.999854358519346 0.00029128296130798 0.00014564148065399 49 0.999765990836591 0.00046801832681755 0.000234009163408775 50 0.999698710924231 0.000602578151536984 0.000301289075768492 51 0.999580920500627 0.00083815899874618 0.00041907949937309 52 0.999350270472505 0.00129945905499029 0.000649729527495143 53 0.999232401664142 0.00153519667171526 0.00076759833585763 54 0.998807875821734 0.00238424835653176 0.00119212417826588 55 0.998225640670093 0.00354871865981347 0.00177435932990673 56 0.998779519754862 0.00244096049027529 0.00122048024513765 57 0.999186046144065 0.00162790771187068 0.00081395385593534 58 0.998928741950917 0.00214251609816625 0.00107125804908312 59 0.998668991552664 0.00266201689467294 0.00133100844733647 60 0.998155097069281 0.00368980586143771 0.00184490293071886 61 0.997806767423186 0.00438646515362794 0.00219323257681397 62 0.997301961815947 0.00539607636810515 0.00269803818405257 63 0.99607113982475 0.00785772035050128 0.00392886017525064 64 0.995940189732812 0.00811962053437692 0.00405981026718846 65 0.997415024088687 0.00516995182262605 0.00258497591131303 66 0.996822166067957 0.00635566786408583 0.00317783393204291 67 0.995626522773585 0.0087469544528303 0.00437347722641515 68 0.995125046655314 0.00974990668937154 0.00487495334468577 69 0.994497927068464 0.0110041458630729 0.00550207293153646 70 0.994541777168753 0.0109164456624937 0.00545822283124684 71 0.992058663413326 0.0158826731733473 0.00794133658667363 72 0.9919915165329 0.0160169669341985 0.00800848346709924 73 0.990920861891885 0.0181582762162295 0.00907913810811477 74 0.989364381402027 0.0212712371959458 0.0106356185979729 75 0.98911087871045 0.0217782425791011 0.0108891212895506 76 0.990229106668796 0.0195417866624078 0.0097708933312039 77 0.993200672667942 0.0135986546641165 0.00679932733205827 78 0.992027849060926 0.0159443018781482 0.00797215093907411 79 0.99246799077802 0.0150640184439608 0.00753200922198038 80 0.992545628150344 0.0149087436993119 0.00745437184965594 81 0.999151493622438 0.00169701275512417 0.000848506377562085 82 0.99916100150604 0.00167799698792172 0.00083899849396086 83 0.998772534026897 0.00245493194620556 0.00122746597310278 84 0.998891221352352 0.00221755729529662 0.00110877864764831 85 0.99862947267147 0.00274105465706078 0.00137052732853039 86 0.99825767131596 0.00348465736808013 0.00174232868404007 87 0.999324343043245 0.00135131391350896 0.000675656956754481 88 0.999196721108208 0.00160655778358434 0.000803278891792172 89 0.999345073759949 0.00130985248010228 0.000654926240051142 90 0.999658767015484 0.000682465969032088 0.000341232984516044 91 0.999643220720453 0.000713558559094867 0.000356779279547434 92 0.999397618002257 0.00120476399548692 0.000602381997743459 93 0.99909925271642 0.00180149456716082 0.00090074728358041 94 0.998506225881276 0.00298754823744758 0.00149377411872379 95 0.99769085465754 0.00461829068491872 0.00230914534245936 96 0.997782378825144 0.00443524234971243 0.00221762117485622 97 0.995179844031834 0.00964031193633192 0.00482015596816596 98 0.993274387927807 0.0134512241443856 0.00672561207219278 99 0.98539852261549 0.0292029547690191 0.0146014773845096 100 0.985883979880737 0.0282320402385253 0.0141160201192626 101 0.999372705380494 0.00125458923901274 0.000627294619506369 102 0.99916843884505 0.00166312230989765 0.000831561154948823 103 0.999880302660346 0.000239394679308196 0.000119697339654098 104 0.998616946890175 0.00276610621964977 0.00138305310982488 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 67 0.752808988764045 NOK 5% type I error level 84 0.943820224719101 NOK 10% type I error level 84 0.943820224719101 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/1045b71292063046.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/1045b71292063046.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/18vvg1292063046.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/18vvg1292063046.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/28vvg1292063046.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/28vvg1292063046.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/38vvg1292063046.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/38vvg1292063046.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/404c11292063046.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/404c11292063046.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/504c11292063046.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/504c11292063046.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/6tvc41292063046.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/6tvc41292063046.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/7tvc41292063046.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/7tvc41292063046.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/845b71292063046.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/845b71292063046.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/945b71292063046.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920629452ligowc844upbmj/945b71292063046.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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