Multiple Regression + 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, 21 Dec 2010 15:23:43 +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/21/t1292944964xuwwfbxit2ql7xd.htm/, Retrieved Tue, 21 Dec 2010 16:22:55 +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/21/t1292944964xuwwfbxit2ql7xd.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 «

143827 829461 4.93 5.01 639.98 3536.15 0.94 109.57 9113 145191 837669 4.92 5.02 597.33 3240.92 0.92 107.08 9140 146832 854793 4.83 4.94 558.36 3121.58 0.91 110.33 9309 148577 850092 5.02 5.10 593.09 3302.70 0.89 110.36 9395 149873 848783 5.22 5.26 585.15 3292.49 0.87 106.50 10027 151847 846150 5.17 5.21 573.50 3162.62 0.85 104.30 10202 153252 828543 5.17 5.25 548.72 3051.60 0.86 107.21 10003 154292 830389 4.98 5.06 523.63 2848.11 0.90 109.34 9745 155657 848989 4.98 5.04 453.87 2577.68 0.91 108.20 9966 156523 841106 4.77 4.82 460.33 2680.55 0.91 109.86 10035 156416 854616 4.62 4.67 492.67 2775.70 0.89 108.68 9999 156693 832714 4.89 4.95 506.78 2879.30 0.89 113.38 9943 160312 839290 4.97 5.02 500.92 2790.11 0.88 117.12 10258 160438 840572 5.03 5.07 494.91 2764.18 0.87 116.23 10926 160882 869186 5.27 5.31 531.21 2868.37 0.88 114.75 10807 161668 856979 5.25 5.29 511.28 2740.50 0.89 115.81 10992 164391 872126 5.30 5.31 484.55 2622.87 0.92 115.86 11034 168556 868281 5.16 5.17 439.66 2376.70 0.96 11 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 9 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation SpaarNL[t] = + 163359.285691595 -0.00511639901504985Leningen[t] -4556.23358889816`10jNL`[t] + 5905.93974904935`10JEUR`[t] + 14.3954082341892AEX[t] -6.30634407009315EURO[t] + 14539.9291299438USD[t] -165.267194365423YEN[t] -0.841801515944616GOLD[t] + 1415.54540154119t + 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) 163359.285691595 7625.719442 21.4221 0 0 Leningen -0.00511639901504985 0.006574 -0.7783 0.438084 0.219042 `10jNL` -4556.23358889816 3830.29621 -1.1895 0.236842 0.118421 `10JEUR` 5905.93974904935 4132.995591 1.429 0.155898 0.077949 AEX 14.3954082341892 25.251036 0.5701 0.5698 0.2849 EURO -6.30634407009315 4.722774 -1.3353 0.184584 0.092292 USD 14539.9291299438 5423.020947 2.6811 0.008488 0.004244 YEN -165.267194365423 44.478054 -3.7157 0.000323 0.000161 GOLD -0.841801515944616 0.263546 -3.1941 0.001838 0.000919 t 1415.54540154119 61.587249 22.9844 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.99846895888183 R-squared 0.996940261850567 Adjusted R-squared 0.996685283671447 F-TEST (value) 3909.90423295619 F-TEST (DF numerator) 9 F-TEST (DF denominator) 108 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2578.58320831735 Sum Squared Residuals 718101867.11935 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 143827 142457.968658164 1369.03134183552 2 145191 145281.986279036 -90.9862790358115 3 146832 145914.332220177 917.66777982295 4 148577 146422.791752642 2154.20824735776 5 149873 147643.940623713 2229.0593762867 6 151847 149582.244574023 2264.75542597704 7 153252 151499.514362972 1752.48563702833 8 154292 154018.030716043 273.969283957106 9 155657 156069.259007234 -412.259007233676 10 156523 156294.472166544 228.527833456124 11 156416 157238.459518720 -822.459518719695 12 156693 158009.711388118 -1316.71138811800 13 160312 158889.968104668 1422.0318953316 14 160438 159837.249452076 600.750547924295 15 160882 161785.988140232 -903.98814023227 16 161668 163570.969816305 -1902.96981630491 17 164391 165548.929078877 -1157.92907887676 18 168556 168158.529577656 397.470422344337 19 169738 171078.799202706 -1340.79920270629 20 170387 172059.143926021 -1672.14392602055 21 171294 173605.876499018 -2311.87649901755 22 172202 174126.656006378 -1924.65600637841 23 172651 175359.548413569 -2708.54841356878 24 172770 177007.29886667 -4237.29886667007 25 178366 178809.407248346 -443.40724834638 26 180014 179796.251906156 217.748093844117 27 181067 182083.688305948 -1016.68830594800 28 182586 182515.010710133 70.9892898670477 29 184957 183436.339789534 1520.66021046555 30 186417 184193.359612121 2223.64038787887 31 188599 186105.958592560 2493.04140744036 32 189490 187311.848377102 2178.15162289784 33 190264 189189.408703496 1074.59129650393 34 191221 191541.91399101 -320.913991009880 35 191110 192755.335187484 -1645.33518748401 36 190674 193784.830375089 -3110.83037508885 37 195438 195417.683290467 20.3167095330140 38 196393 196478.576833867 -85.576833866655 39 197172 197435.49352453 -263.493524530107 40 198760 199097.855713035 -337.855713034768 41 200945 199907.768028736 1037.23197126447 42 203845 201680.453236028 2164.54676397171 43 204613 202964.815888099 1648.18411190094 44 205487 203809.327081385 1677.67291861455 45 206100 204823.874119742 1276.12588025843 46 206315 206030.030235034 284.969764966115 47 206291 207739.557150494 -1448.55715049436 48 207801 209254.162552281 -1453.16255228133 49 211653 210799.820741574 853.17925842625 50 211325 211682.066443877 -357.066443876836 51 211893 213035.105183719 -1142.1051837193 52 212056 213692.427181070 -1636.42718107032 53 214696 214748.23364279 -52.2336427900669 54 217455 215157.855815521 2297.14418447864 55 218884 216160.413011159 2723.58698884120 56 219816 217620.840028458 2195.15997154235 57 219984 217690.237887313 2293.76211268687 58 219062 218228.190260544 833.809739456123 59 218550 218961.390934846 -411.390934845769 60 218179 219453.822990554 -1274.82299055441 61 222218 220338.596543632 1879.40345636813 62 222196 221177.949648274 1018.05035172556 63 223393 222684.785848359 708.21415164132 64 223292 223494.810174259 -202.810174259167 65 226236 225414.834532262 821.16546773835 66 228831 227985.596775979 845.40322402126 67 228745 228211.917307692 533.082692307885 68 229140 229174.971466137 -34.9714661367844 69 229270 230684.316884183 -1414.3168841825 70 229359 231393.668434580 -2034.66843458021 71 230006 232309.880757689 -2303.88075768868 72 228810 233754.436273788 -4944.43627378755 73 232677 234135.787597984 -1458.78759798444 74 232961 235209.974312372 -2248.97431237244 75 234629 236984.581762657 -2355.58176265676 76 235660 237892.134894941 -2232.13489494124 77 240024 238855.859987355 1168.14001264511 78 243554 240460.234687148 3093.76531285201 79 244368 242521.242445963 1846.75755403741 80 244356 244512.673790935 -156.673790935265 81 245126 245414.158456990 -288.158456989506 82 246321 245336.191375218 984.808624781528 83 246797 247373.117581938 -576.117581938246 84 246735 249076.441793252 -2341.44179325163 85 251083 251242.261247465 -159.261247465163 86 251786 252284.919322666 -498.91932266632 87 252732 255759.101927368 -3027.10192736785 88 255051 257384.455687546 -2333.45568754605 89 259022 258877.267976301 144.732023699443 90 261698 260998.249793193 699.750206806899 91 263891 261723.409025846 2167.59097415413 92 265247 263254.717903359 1992.28209664062 93 262228 265472.512065377 -3244.51206537666 94 263429 268617.792576766 -5188.79257676606 95 264305 271753.038203518 -7448.0382035176 96 266371 274385.073816758 -8014.0738167583 97 273248 275912.539097832 -2664.53909783210 98 275472 275700.263768135 -228.263768134792 99 278146 276984.39029255 1161.60970744989 100 279506 277255.369775190 2250.63022480964 101 283991 278729.610811795 5261.38918820507 102 286794 280751.052380977 6042.94761902315 103 288703 281913.226125273 6789.77387472714 104 289285 282372.95297958 6912.04702042007 105 288869 284090.990500021 4778.00949997878 106 286942 285002.891929829 1939.10807017143 107 285833 285558.18176542 274.818234579835 108 284095 286444.467316664 -2349.46731666377 109 289229 288849.41869007 379.581309929754 110 289389 290484.827517952 -1095.82751795222 111 290793 289945.176359551 847.823640448599 112 291454 291388.753609349 65.2463906505897 113 294733 289143.398551749 5589.60144825073 114 293853 290199.032466541 3653.96753345884 115 294056 294068.031337972 -12.0313379725008 116 293982 295991.035532978 -2009.03553297824 117 293075 297372.287917328 -4297.28791732761 118 292391 297969.11546783 -5578.11546782984 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 13 0.017991315016941 0.035982630033882 0.98200868498306 14 0.00362145385158786 0.00724290770317572 0.996378546148412 15 0.00326429962836737 0.00652859925673474 0.996735700371633 16 0.000875454026568312 0.00175090805313662 0.999124545973432 17 0.000365034032964208 0.000730068065928415 0.999634965967036 18 0.00141343935111859 0.00282687870223717 0.998586560648881 19 0.000855173593861332 0.00171034718772266 0.999144826406139 20 0.000321233274583878 0.000642466549167756 0.999678766725416 21 0.000117551908752360 0.000235103817504720 0.999882448091248 22 6.42922296971063e-05 0.000128584459394213 0.999935707770303 23 2.23247965340882e-05 4.46495930681765e-05 0.999977675203466 24 9.06194171836306e-06 1.81238834367261e-05 0.999990938058282 25 0.000423375883023206 0.000846751766046411 0.999576624116977 26 0.000306336917402645 0.000612673834805291 0.999693663082597 27 0.000159976368820622 0.000319952737641245 0.99984002363118 28 0.000221309119612185 0.000442618239224369 0.999778690880388 29 0.000124483074582754 0.000248966149165509 0.999875516925417 30 7.51619754065383e-05 0.000150323950813077 0.999924838024594 31 0.000129440328292125 0.000258880656584250 0.999870559671708 32 0.000109028076717507 0.000218056153435015 0.999890971923282 33 5.0880365344347e-05 0.000101760730688694 0.999949119634656 34 3.78073587802619e-05 7.56147175605238e-05 0.99996219264122 35 4.59141382070229e-05 9.18282764140459e-05 0.999954085861793 36 0.000249401987134302 0.000498803974268604 0.999750598012866 37 0.000137784672980654 0.000275569345961307 0.99986221532702 38 6.79725833571144e-05 0.000135945166714229 0.999932027416643 39 3.37200371605893e-05 6.74400743211787e-05 0.99996627996284 40 1.68734337423874e-05 3.37468674847748e-05 0.999983126566258 41 7.73093478098704e-06 1.54618695619741e-05 0.99999226906522 42 6.19234578764639e-06 1.23846915752928e-05 0.999993807654212 43 3.09986016427993e-06 6.19972032855987e-06 0.999996900139836 44 1.47546301624552e-06 2.95092603249103e-06 0.999998524536984 45 7.71501240219258e-07 1.54300248043852e-06 0.99999922849876 46 5.60684586713251e-07 1.12136917342650e-06 0.999999439315413 47 7.88529321871885e-07 1.57705864374377e-06 0.999999211470678 48 6.15014093667822e-07 1.23002818733564e-06 0.999999384985906 49 3.69236387777684e-07 7.38472775555368e-07 0.999999630763612 50 1.68175040753512e-07 3.36350081507023e-07 0.99999983182496 51 1.20627283087422e-07 2.41254566174844e-07 0.999999879372717 52 1.30917026852344e-07 2.61834053704688e-07 0.999999869082973 53 6.41414575769216e-08 1.28282915153843e-07 0.999999935858542 54 5.95039348256161e-07 1.19007869651232e-06 0.999999404960652 55 6.53150512241161e-07 1.30630102448232e-06 0.999999346849488 56 4.69972744362684e-07 9.39945488725368e-07 0.999999530027256 57 9.56782935810309e-07 1.91356587162062e-06 0.999999043217064 58 1.32424022460484e-06 2.64848044920968e-06 0.999998675759775 59 1.26436860096712e-06 2.52873720193423e-06 0.9999987356314 60 7.62471951771604e-07 1.52494390354321e-06 0.999999237528048 61 2.83865373242596e-06 5.67730746485191e-06 0.999997161346268 62 2.59232651762368e-06 5.18465303524735e-06 0.999997407673482 63 3.78951503946241e-06 7.57903007892482e-06 0.99999621048496 64 2.38851114587251e-06 4.77702229174502e-06 0.999997611488854 65 5.94244385233266e-06 1.18848877046653e-05 0.999994057556148 66 1.28956853348646e-05 2.57913706697292e-05 0.999987104314665 67 3.07284423952201e-05 6.14568847904402e-05 0.999969271557605 68 5.10753396061095e-05 0.000102150679212219 0.999948924660394 69 5.28070448501469e-05 0.000105614089700294 0.99994719295515 70 0.000124180031797735 0.000248360063595471 0.999875819968202 71 0.000270956397865418 0.000541912795730836 0.999729043602135 72 0.00108320338821173 0.00216640677642346 0.998916796611788 73 0.00103152496993607 0.00206304993987214 0.998968475030064 74 0.000681477247946558 0.00136295449589312 0.999318522752053 75 0.000452612872675077 0.000905225745350153 0.999547387127325 76 0.000268463295262545 0.000536926590525089 0.999731536704737 77 0.000404818368560072 0.000809636737120144 0.99959518163144 78 0.000899367306371433 0.00179873461274287 0.999100632693629 79 0.000948213606961687 0.00189642721392337 0.999051786393038 80 0.0005885129854486 0.0011770259708972 0.999411487014551 81 0.000362546063240341 0.000725092126480681 0.99963745393676 82 0.000249174445522540 0.000498348891045081 0.999750825554477 83 0.000470020617210872 0.000940041234421745 0.99952997938279 84 0.000304925495787193 0.000609850991574385 0.999695074504213 85 0.000610249536725303 0.00122049907345061 0.999389750463275 86 0.00125044310502108 0.00250088621004215 0.998749556894979 87 0.00198713839367244 0.00397427678734489 0.998012861606328 88 0.0103078525387085 0.020615705077417 0.989692147461291 89 0.0415989218129557 0.0831978436259114 0.958401078187044 90 0.0376872484393439 0.0753744968786878 0.962312751560656 91 0.170901598036506 0.341803196073012 0.829098401963494 92 0.152567713133320 0.305135426266640 0.84743228686668 93 0.130952920637620 0.261905841275239 0.86904707936238 94 0.377047602769689 0.754095205539378 0.622952397230311 95 0.467135346689962 0.934270693379923 0.532864653310038 96 0.474067406726303 0.948134813452606 0.525932593273697 97 0.519458958695257 0.961082082609486 0.480541041304743 98 0.544461809850435 0.911076380299131 0.455538190149565 99 0.482087317439402 0.964174634878803 0.517912682560598 100 0.905103310087828 0.189793379824343 0.0948966899121716 101 0.957671103719514 0.0846577925609712 0.0423288962804856 102 0.949013399045477 0.101973201909047 0.0509866009545235 103 0.912984883135451 0.174030233729098 0.0870151168645488 104 0.867746250920009 0.264507498159982 0.132253749079991 105 0.92691917610027 0.146161647799461 0.0730808238997303 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 74 0.795698924731183 NOK 5% type I error level 76 0.817204301075269 NOK 10% type I error level 79 0.849462365591398 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/107nqi1292945013.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/107nqi1292945013.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/1tva91292945013.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/1tva91292945013.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/2tva91292945013.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/2tva91292945013.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/3tva91292945013.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/3tva91292945013.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/4l5rc1292945013.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/4l5rc1292945013.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/5l5rc1292945013.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/5l5rc1292945013.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/6l5rc1292945013.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/6l5rc1292945013.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/7eeqf1292945013.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/7eeqf1292945013.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/8eeqf1292945013.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/8eeqf1292945013.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/97nqi1292945013.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292944964xuwwfbxit2ql7xd/97nqi1292945013.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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