Multiple Regression (with seasonal dummies and linear trend)

*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: Tue, 15 Dec 2009 01:59:22 -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/Dec/15/t1260867622pa94lq4okebdlqw.htm/, Retrieved Tue, 15 Dec 2009 10:00:35 +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/2009/Dec/15/t1260867622pa94lq4okebdlqw.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 «

8715.1 0 8919.9 0 10085.8 0 9511.7 0 8991.3 0 10311.2 0 8895.4 0 7449.8 0 10084.0 0 9859.4 0 9100.1 0 8920.8 0 8502.7 0 8599.6 0 10394.4 0 9290.4 0 8742.2 0 10217.3 0 8639.0 0 8139.6 0 10779.1 0 10427.7 0 10349.1 0 10036.4 0 9492.1 0 10638.8 0 12054.5 0 10324.7 0 11817.3 0 11008.9 0 9996.6 0 9419.5 0 11958.8 0 12594.6 0 11890.6 0 10871.7 0 11835.7 0 11542.2 0 13093.7 0 11180.2 0 12035.7 0 12112.0 0 10875.2 0 9897.3 0 11672.1 1 12385.7 1 11405.6 1 9830.9 1 11025.1 1 10853.8 1 12252.6 1 11839.4 1 11669.1 1 11601.4 1 11178.4 1 9516.4 1 12102.8 1 12989.0 1 11610.2 1 10205.5 1 11356.2 1 11307.1 1 12648.6 1 11947.2 1 11714.1 1 12192.5 1 11268.8 1 9097.4 1 12639.8 1 13040.1 1 11687.3 1 11191.7 1 11391.9 1 11793.1 1 13933.2 1 12778.1 1 11810.3 1 13698.4 1 11956.6 1 10723.8 1 13938.9 1 13979.8 1 13807.4 1 12973.9 1 12509.8 1 12934.1 1 14908.3 1 13 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 Uitvoer[t] = + 7642.02272727274 -1159.29000000000Dummie[t] + 865.746704545459M1[t] + 930.747499999996M2[t] + 2447.96647727272M3[t] + 1249.24909090908M4[t] + 1178.82261363636M5[t] + 1960.31431818182M6[t] + 386.769659090908M7[t] -843.738636363637M8[t] + 1856.41579545454M9[t] + 2115.68022727273M10[t] + 1269.36284090909M11[t] + 65.5810227272728t + 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) 7642.02272727274 238.458163 32.0476 0 0 Dummie -1159.29000000000 222.750579 -5.2044 1e-06 0 M1 865.746704545459 296.322438 2.9216 0.004174 0.002087 M2 930.747499999996 296.207095 3.1422 0.00212 0.00106 M3 2447.96647727272 296.117353 8.2669 0 0 M4 1249.24909090908 296.053235 4.2197 4.8e-05 2.4e-05 M5 1178.82261363636 296.014757 3.9823 0.000118 5.9e-05 M6 1960.31431818182 296.00193 6.6226 0 0 M7 386.769659090908 296.014757 1.3066 0.193893 0.096947 M8 -843.738636363637 296.053235 -2.85 0.005162 0.002581 M9 1856.41579545454 295.886462 6.2741 0 0 M10 2115.68022727273 295.822294 7.1519 0 0 M11 1269.36284090909 295.783786 4.2915 3.7e-05 1.8e-05 t 65.5810227272728 2.755683 23.7985 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.959898822723858 R-squared 0.921405749866648 Adjusted R-squared 0.912747061292634 F-TEST (value) 106.414007385828 F-TEST (DF numerator) 13 F-TEST (DF denominator) 118 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 693.644360927177 Sum Squared Residuals 56774814.9346364 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8715.1 8573.3504545454 141.749545454594 2 8919.9 8703.93227272728 215.967727272721 3 10085.8 10286.7322727273 -200.932272727282 4 9511.7 9153.59590909092 358.104090909085 5 8991.3 9148.75045454544 -157.450454545440 6 10311.2 9995.82318181817 315.376818181833 7 8895.4 8487.85954545454 407.540454545457 8 7449.8 7322.93227272727 126.867727272732 9 10084 10088.6677272727 -4.66772727272951 10 9859.4 10413.5131818182 -554.113181818184 11 9100.1 9632.77681818182 -532.676818181816 12 8920.8 8428.995 491.804999999998 13 8502.7 9360.32272727273 -857.622727272733 14 8599.6 9490.90454545456 -891.304545454558 15 10394.4 11073.7045454545 -679.304545454547 16 9290.4 9940.56818181818 -650.168181818183 17 8742.2 9935.72272727273 -1193.52272727273 18 10217.3 10782.7954545455 -565.495454545458 19 8639 9274.83181818182 -635.83181818182 20 8139.6 8109.90454545455 29.6954545454531 21 10779.1 10875.64 -96.5400000000012 22 10427.7 11200.4854545455 -772.785454545455 23 10349.1 10419.7490909091 -70.6490909090922 24 10036.4 9215.96727272727 820.432727272725 25 9492.1 10147.295 -655.195000000006 26 10638.8 10277.8768181818 360.923181818182 27 12054.5 11860.6768181818 193.823181818181 28 10324.7 10727.5404545455 -402.840454545455 29 11817.3 10722.695 1094.60500000000 30 11008.9 11569.7677272727 -560.86772727273 31 9996.6 10061.8040909091 -65.2040909090914 32 9419.5 8896.87681818182 522.623181818180 33 11958.8 11662.6122727273 296.187727272726 34 12594.6 11987.4577272727 607.142272727273 35 11890.6 11206.7213636364 683.878636363635 36 10871.7 10002.9395454545 868.760454545453 37 11835.7 10934.2672727273 901.432727272722 38 11542.2 11064.8490909091 477.350909090912 39 13093.7 12647.6490909091 446.050909090910 40 11180.2 11514.5127272727 -334.312727272728 41 12035.7 11509.6672727273 526.032727272725 42 12112 12356.74 -244.740000000002 43 10875.2 10848.7763636364 26.4236363636358 44 9897.3 9683.8490909091 213.450909090907 45 11672.1 11290.2945454545 381.805454545455 46 12385.7 11615.14 770.56 47 11405.6 10834.4036363636 571.196363636364 48 9830.9 9630.62181818182 200.278181818181 49 11025.1 10561.9495454546 463.150454545449 50 10853.8 10692.5313636364 161.268636363638 51 12252.6 12275.3313636364 -22.7313636363633 52 11839.4 11142.195 697.205 53 11669.1 11137.3495454545 531.750454545453 54 11601.4 11984.4222727273 -383.022272727274 55 11178.4 10476.4586363636 701.941363636363 56 9516.4 9311.53136363636 204.868636363635 57 12102.8 12077.2668181818 25.5331818181810 58 12989 12402.1122727273 586.887727272727 59 11610.2 11621.3759090909 -11.1759090909087 60 10205.5 10417.5940909091 -212.094090909091 61 11356.2 11348.9218181818 7.27818181817804 62 11307.1 11479.5036363636 -172.403636363635 63 12648.6 13062.3036363636 -413.703636363635 64 11947.2 11929.1672727273 18.0327272727283 65 11714.1 11924.3218181818 -210.221818181819 66 12192.5 12771.3945454545 -578.894545454546 67 11268.8 11263.4309090909 5.36909090909034 68 9097.4 10098.5036363636 -1001.10363636364 69 12639.8 12864.2390909091 -224.439090909092 70 13040.1 13189.0845454545 -148.984545454545 71 11687.3 12408.3481818182 -721.048181818183 72 11191.7 11204.5663636364 -12.8663636363630 73 11391.9 12135.8940909091 -743.994090909095 74 11793.1 12266.4759090909 -473.375909090906 75 13933.2 13849.2759090909 83.9240909090925 76 12778.1 12716.1395454545 61.9604545454555 77 11810.3 12711.2940909091 -900.994090909093 78 13698.4 13558.3668181818 140.033181818181 79 11956.6 12050.4031818182 -93.8031818181809 80 10723.8 10885.4759090909 -161.67590909091 81 13938.9 13651.2113636364 287.688636363636 82 13979.8 13976.0568181818 3.74318181818114 83 13807.4 13195.3204545455 612.079545454545 84 12973.9 11991.5386363636 982.361363636363 85 12509.8 12922.8663636364 -413.066363636369 86 12934.1 13053.4481818182 -119.348181818179 87 14908.3 14636.2481818182 272.051818181819 88 13772.1 13503.1118181818 268.988181818183 89 13012.6 13498.2663636364 -485.666363636364 90 14049.9 14345.3390909091 -295.439090909092 91 11816.5 12837.3754545455 -1020.87545454545 92 11593.2 11672.4481818182 -79.2481818181807 93 14466.2 14438.1836363636 28.0163636363649 94 13615.9 14763.0290909091 -1147.12909090909 95 14733.9 13982.2927272727 751.607272727273 96 13880.7 12778.5109090909 1102.18909090909 97 13527.5 13709.8386363636 -182.338636363640 98 13584 13840.4204545455 -256.420454545451 99 16170.2 15423.2204545455 746.979545454548 100 13260.6 14290.0840909091 -1029.48409090909 101 14741.9 14285.2386363636 456.661363636363 102 15486.5 15132.3113636364 354.188636363636 103 13154.5 13624.3477272727 -469.847727272726 104 12621.2 12459.4204545455 161.779545454547 105 15031.6 15225.1559090909 -193.555909090908 106 15452.4 15550.0013636364 -97.6013636363633 107 15428 14769.265 658.735 108 13105.9 13565.4831818182 -459.583181818182 109 14716.8 14496.8109090909 219.989090909087 110 14180 14627.3927272727 -447.392727272724 111 16202.2 16210.1927272727 -7.99272727272485 112 14392.4 15077.0563636364 -684.656363636363 113 15140.6 15072.2109090909 68.3890909090913 114 15960.1 15919.2836363636 40.816363636364 115 14351.3 14411.32 -60.0199999999996 116 13230.2 13246.3927272727 -16.1927272727258 117 15202.1 16012.1281818182 -810.02818181818 118 17056 16336.9736363636 719.026363636364 119 16077.7 15556.2372727273 521.462727272728 120 13348.2 14352.4554545455 -1004.25545454545 121 16402.4 15283.7831818182 1118.61681818182 122 16559.1 15414.365 1144.73500000000 123 16579 16997.165 -418.164999999999 124 17561.2 15864.0286363636 1697.17136363637 125 16129.6 15859.1831818182 270.416818181817 126 18484.3 16706.2559090909 1778.04409090909 127 16402.6 15198.2922727273 1204.30772727273 128 14032.3 14033.365 -1.06499999999910 129 17109.1 16799.1004545455 309.999545454546 130 17157.2 17123.9459090909 33.2540909090923 131 13879.8 16343.2095454545 -2463.40954545455 132 12362.4 15139.4277272727 -2777.02772727273 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0322720764943533 0.0645441529887065 0.967727923505647 18 0.00779957449306438 0.0155991489861288 0.992200425506936 19 0.00193387672679884 0.00386775345359768 0.998066123273201 20 0.0106707490228408 0.0213414980456817 0.98932925097716 21 0.0136514555663406 0.0273029111326811 0.98634854443366 22 0.0102028034795844 0.0204056069591688 0.989797196520416 23 0.0308661336835502 0.0617322673671004 0.96913386631645 24 0.0384465165962809 0.0768930331925618 0.96155348340372 25 0.0288096960423794 0.0576193920847589 0.97119030395762 26 0.0844390570061641 0.168878114012328 0.915560942993836 27 0.112399510638943 0.224799021277887 0.887600489361057 28 0.0782332134089368 0.156466426817874 0.921766786591063 29 0.329002542080954 0.658005084161909 0.670997457919046 30 0.284511337885564 0.569022675771129 0.715488662114436 31 0.225259265228137 0.450518530456274 0.774740734771863 32 0.189244106245812 0.378488212491624 0.810755893754188 33 0.149826630539865 0.299653261079730 0.850173369460135 34 0.197356936110762 0.394713872221524 0.802643063889238 35 0.196461631888879 0.392923263777758 0.803538368111121 36 0.160374362685837 0.320748725371673 0.839625637314164 37 0.196950291761246 0.393900583522491 0.803049708238754 38 0.15794848064915 0.3158969612983 0.84205151935085 39 0.126363757843121 0.252727515686242 0.873636242156879 40 0.106358712916830 0.212717425833660 0.89364128708317 41 0.0834340569937186 0.166868113987437 0.916565943006281 42 0.0653592004516723 0.130718400903345 0.934640799548328 43 0.0482694809183359 0.0965389618366718 0.951730519081664 44 0.035932964122488 0.071865928244976 0.964067035877512 45 0.0254915414822807 0.0509830829645614 0.97450845851772 46 0.0215884535639277 0.0431769071278555 0.978411546436072 47 0.0156999915260176 0.0313999830520351 0.984300008473982 48 0.0195060037829708 0.0390120075659416 0.98049399621703 49 0.0139349942705929 0.0278699885411858 0.986065005729407 50 0.009938609389188 0.019877218778376 0.990061390610812 51 0.00700381801805979 0.0140076360361196 0.99299618198194 52 0.00619776744135567 0.0123955348827113 0.993802232558644 53 0.00446282364885925 0.0089256472977185 0.99553717635114 54 0.00363633842998940 0.00727267685997879 0.99636366157001 55 0.00298922109739953 0.00597844219479906 0.9970107789026 56 0.00223633106290489 0.00447266212580977 0.997763668937095 57 0.00166735780280354 0.00333471560560709 0.998332642197197 58 0.00126576574151532 0.00253153148303064 0.998734234258485 59 0.00096434957544318 0.00192869915088636 0.999035650424557 60 0.00147466183730927 0.00294932367461853 0.99852533816269 61 0.000989325141815622 0.00197865028363124 0.999010674858184 62 0.000748263132494009 0.00149652626498802 0.999251736867506 63 0.00062967911493938 0.00125935822987876 0.99937032088506 64 0.000386967041063199 0.000773934082126399 0.999613032958937 65 0.000301247701175002 0.000602495402350004 0.999698752298825 66 0.000258219097183663 0.000516438194367325 0.999741780902816 67 0.000161537194768924 0.000323074389537847 0.99983846280523 68 0.000452059844446501 0.000904119688893003 0.999547940155553 69 0.000315263914615592 0.000630527829231185 0.999684736085384 70 0.000206674088411668 0.000413348176823335 0.999793325911588 71 0.000248294463192553 0.000496588926385105 0.999751705536807 72 0.000186046567538993 0.000372093135077986 0.99981395343246 73 0.000204881784284586 0.000409763568569171 0.999795118215715 74 0.000153510781571641 0.000307021563143282 0.999846489218428 75 9.08903634365807e-05 0.000181780726873161 0.999909109636563 76 5.18304145051469e-05 0.000103660829010294 0.999948169585495 77 7.77738091395676e-05 0.000155547618279135 0.99992222619086 78 5.42983639813143e-05 0.000108596727962629 0.99994570163602 79 3.06261826756508e-05 6.12523653513015e-05 0.999969373817324 80 1.72970963769533e-05 3.45941927539067e-05 0.999982702903623 81 1.02178725198224e-05 2.04357450396449e-05 0.99998978212748 82 5.39175225463969e-06 1.07835045092794e-05 0.999994608247745 83 4.59750167148491e-06 9.19500334296983e-06 0.999995402498329 84 1.22590324934066e-05 2.45180649868132e-05 0.999987740967507 85 8.40719595525944e-06 1.68143919105189e-05 0.999991592804045 86 4.43160347562469e-06 8.86320695124938e-06 0.999995568396524 87 2.50316600626629e-06 5.00633201253257e-06 0.999997496833994 88 1.39733051715075e-06 2.79466103430150e-06 0.999998602669483 89 9.760360042219e-07 1.9520720084438e-06 0.999999023963996 90 7.1523162905904e-07 1.43046325811808e-06 0.999999284768371 91 1.71793913094001e-06 3.43587826188002e-06 0.999998282060869 92 8.48055543874453e-07 1.69611108774891e-06 0.999999151944456 93 4.05579895019356e-07 8.11159790038712e-07 0.999999594420105 94 1.54898070528949e-06 3.09796141057897e-06 0.999998451019295 95 1.7467188511311e-06 3.4934377022622e-06 0.999998253281149 96 3.14789040984718e-05 6.29578081969437e-05 0.999968521095902 97 2.08687392575693e-05 4.17374785151386e-05 0.999979131260742 98 1.22296385291071e-05 2.44592770582142e-05 0.99998777036147 99 1.513393149448e-05 3.026786298896e-05 0.999984866068506 100 3.94180632934344e-05 7.88361265868688e-05 0.999960581936707 101 2.43766583732477e-05 4.87533167464953e-05 0.999975623341627 102 1.67349083049768e-05 3.34698166099535e-05 0.999983265091695 103 1.68495599009735e-05 3.36991198019469e-05 0.9999831504401 104 7.88499809247384e-06 1.57699961849477e-05 0.999992115001908 105 3.64601524129532e-06 7.29203048259063e-06 0.999996353984759 106 1.996895215816e-06 3.993790431632e-06 0.999998003104784 107 4.13222991558085e-06 8.2644598311617e-06 0.999995867770084 108 1.66971145842672e-05 3.33942291685345e-05 0.999983302885416 109 9.08018662203781e-06 1.81603732440756e-05 0.999990919813378 110 1.12796393488283e-05 2.25592786976566e-05 0.999988720360651 111 4.92254972202066e-06 9.84509944404131e-06 0.999995077450278 112 5.46202248963554e-05 0.000109240449792711 0.999945379775104 113 2.12221780586569e-05 4.24443561173139e-05 0.999978777821941 114 0.000123938687599835 0.000247877375199671 0.9998760613124 115 0.000596759816266123 0.00119351963253225 0.999403240183734 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 64 0.646464646464647 NOK 5% type I error level 75 0.757575757575758 NOK 10% type I error level 82 0.828282828282828 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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Software written by Ed van Stee & Patrick Wessa

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