*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: Thu, 30 Dec 2010 00:54:49 +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/30/t1293670372tt5c2k1f40lcrx5.htm/, Retrieved Thu, 30 Dec 2010 01:53:05 +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/30/t1293670372tt5c2k1f40lcrx5.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 «

13 8 360 175 3821 11 73 0 0 15 8 390 190 3850 8.5 70 0 0 17 8 304 150 3672 11.5 72 0 0 19.4 6 232 90 3210 17.2 78 0 0 24.3 4 151 90 3003 20.1 80 0 0 18.1 6 258 120 3410 15.1 78 0 0 20.2 6 232 90 3265 18.2 79 0 0 18 6 232 100 2789 15 73 0 0 19 6 232 100 2634 13 71 0 0 20 6 232 100 2914 16 75 0 0 21 6 199 90 2648 15 70 0 0 18 6 199 97 2774 15.5 70 0 0 18 6 232 100 2945 16 73 0 0 19 6 232 100 2901 16 74 0 0 22.5 6 232 90 3085 17.6 76 0 0 18 6 258 110 2962 13.5 71 0 0 14 8 304 150 3672 11.5 73 0 0 15 6 258 110 3730 19 75 0 0 15.5 8 304 120 3962 13.9 76 0 0 16 6 258 110 3632 18 74 0 0 18 6 232 100 3288 15.5 71 0 0 14 8 304 150 4257 15.5 74 0 0 15 8 304 150 3892 12.5 72 0 0 19 6 232 90 3211 17 75 0 0 17.5 6 258 95 3193 17.8 76 0 0 16 8 304 150 3433 12 70 0 0 27.4 4 121 80 2670 15 79 0 0 24 4 107 90 2430 14.5 70 0 1 20 4 114 91 2582 14 73 0 1 23 4 115 95 2694 15 75 0 1 34.3 4 97 78 2188 15.8 80 0 1 20.3 5 131 103 2830 15.9 78 0 1 36.4 5 121 67 2950 19.9 80 0 1 29 4 98 83 2219 16.5 74 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 30 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation MPG[t] = -17.9546020672902 -0.489709424047163Cylin[t] + 0.0239786440278725Displ[t] -0.0181834640388510HP[t] -0.00671038412737677Weight[t] + 0.0791030360112797Accel[t] + 0.77702693910102Year[t] + 2.85322822847746OriginJapan[t] + 2.63000236001736OriginEurope[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) -17.9546020672902 4.676934 -3.839 0.000145 7.2e-05 Cylin -0.489709424047163 0.321231 -1.5245 0.128215 0.064107 Displ 0.0239786440278725 0.007653 3.1331 0.001863 0.000931 HP -0.0181834640388510 0.013709 -1.3264 0.185488 0.092744 Weight -0.00671038412737677 0.000655 -10.2428 0 0 Accel 0.0791030360112797 0.098218 0.8054 0.421101 0.210551 Year 0.77702693910102 0.051784 15.0051 0 0 OriginJapan 2.85322822847746 0.552736 5.162 0 0 OriginEurope 2.63000236001736 0.566415 4.6432 5e-06 2e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.907854321965764 R-squared 0.824199469911917 Adjusted R-squared 0.820527396176396 F-TEST (value) 224.450686253692 F-TEST (DF numerator) 8 F-TEST (DF denominator) 383 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.30652953119832 Sum Squared Residuals 4187.39167808295 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 15.5306503833598 -2.53065038335978 2 15 13.2538181965878 1.74618180341217 3 17 14.9048047326538 2.09519526734622 4 19.4 23.4620154597908 -4.06201545979085 5 24.3 25.6716663386293 -1.37166633862928 6 18.1 22.0317630822510 -3.93176308225096 7 20.2 23.9490743078974 -3.74907430789742 8 18 22.0460911622980 -4.04609116229804 9 19 21.3739407518168 -2.37394075181683 10 20 22.8404500605893 -2.84045006058927 11 21 20.0517138944238 0.948286105576179 12 18 19.1184727641080 -1.11847276410803 13 18 21.0783742744385 -3.07837427443855 14 19 22.1506581151441 -3.15065811514414 15 22.5 22.7784008119154 -0.278400811915418 16 18 19.6540963803791 -1.65409638037907 17 14 15.6818316717548 -1.68183167175481 18 15 18.0436958250198 -3.04369582501984 19 15.5 16.8022522997112 -1.30225229971122 20 16 17.8451834943905 -1.84518349439046 21 18 17.1831071225406 0.816892877459366 22 14 12.8496960403855 1.15030395961445 23 15 13.5076232606422 1.49237673935781 24 19 21.1084036511582 -2.10840365115816 25 17.5 22.6020273578914 -5.10202735789141 26 16 14.9940841789004 1.00591582109956 27 27.4 26.1882471498395 1.21175285016050 28 24 22.8784120737337 1.12158792626626 29 20 24.2996300298262 -4.29963002982615 30 23 25.1324687096457 -2.13246870964574 31 34.3 32.3538434985713 1.94615650142872 32 20.3 26.3706111861237 -6.0706111861237 33 36.4 27.8506493782056 8.54935062179443 34 29 27.472093405058 1.52790659494201 35 26 23.9529226341737 2.04707736582633 36 21.5 27.0143919201809 -5.51439192018086 37 17 16.3667405177442 0.633259482255848 38 22.4 23.919075355761 -1.51907535576099 39 13 13.5768728435653 -0.576872843565337 40 25 26.6985124549422 -1.69851245494223 41 13 10.9076208453559 2.09237915464413 42 20.6 21.9137753031104 -1.31377530311037 43 12 9.3167143001292 2.68328569987079 44 14 19.4213968443725 -5.42139684437254 45 16.9 17.0082996542520 -0.108299654251955 46 13 10.5054922840415 2.49450771595848 47 30 27.8344340497555 2.16556595024448 48 17.7 20.1967452060727 -2.49674520607275 49 21 21.7167357242395 -0.716735724239508 50 20.5 20.9217944178898 -0.421794417889803 51 26.6 28.7345341875963 -2.13453418759629 52 15 14.0400984524762 0.95990154752379 53 28.4 26.8048748662984 1.59512513370155 54 23 20.838337864039 2.161662135961 55 16.5 13.8669360525985 2.63306394740150 56 25 24.7442663414816 0.255733658518398 57 16 16.7825983257136 -0.782598325713552 58 15 13.4740030756361 1.52599692436391 59 27 27.3598820747507 -0.359882074750678 60 13 12.7087087875538 0.291291212446185 61 17 19.9127985382105 -2.91279853821053 62 17.5 17.5881785298979 -0.0881785298979375 63 28 28.9581013925123 -0.95810139251228 64 34 30.2407172016434 3.75928279835664 65 27 28.6441349120428 -1.64413491204281 66 13 12.6795438972801 0.320456102719870 67 17 17.3395969658199 -0.339596965819891 68 18 14.9532521187173 3.04674788128267 69 16 16.7562387115656 -0.756238711565572 70 17.5 14.6936417463256 2.80635825367440 71 29 28.3337079207863 0.666292079213678 72 30 28.6524153461796 1.34758465382042 73 30.5 28.7037371945256 1.79626280547436 74 32.1 30.3258627047508 1.77413729524917 75 23.5 26.9053493347983 -3.40534933479826 76 28 27.5677702503861 0.432229749613906 77 28.8 26.0298941261463 2.77010587385372 78 17.5 20.6094333241187 -3.10943332411869 79 11 9.29028011968456 1.70971988031544 80 13 11.734970670678 1.26502932932201 81 14 11.3941186998565 2.60588130014354 82 14 10.9004654110139 3.0995345889861 83 13 14.8739397869971 -1.87393978699707 84 20.5 23.0519556937217 -2.55195569372168 85 19.2 20.6378264408747 -1.43782644087466 86 15 14.8972704217684 0.102729578231579 87 15.5 16.2131580942661 -0.713158094266136 88 19.2 21.4738023721633 -2.27380237216328 89 15 14.2431636790237 0.75683632097635 90 20 20.1407103758097 -0.140710375809735 91 15 19.7423596482482 -4.74235964824823 92 18 19.5239889834764 -1.52398898347638 93 22 20.8936620860624 1.10633791393758 94 16 19.4336380245463 -3.43363802454635 95 20 23.1369024756969 -3.1369024756969 96 21 24.2882044563889 -3.28820445638888 97 25 23.866759251385 1.13324074861498 98 22 22.6476263712896 -0.647626371289558 99 28 23.009758706893 4.99024129310699 100 24.5 27.6264127248051 -3.12641272480513 101 13 16.6763218317546 -3.6763218317546 102 10 8.06626378495905 1.93373621504095 103 31 28.4475379030899 2.55246209691009 104 15.5 16.0380419833115 -0.538041983311481 105 26 29.6712100724733 -3.67121007247328 106 17.6 23.9575533150052 -6.35755331500522 107 18.5 20.0070689798017 -1.50706897980174 108 13 10.588312251613 2.41168774838699 109 13 11.5257309382542 1.47426906174578 110 35 29.1805095432415 5.8194904567585 111 23.9 29.6777137526534 -5.77771375265345 112 32.9 30.5371532074897 2.36284679251029 113 31.8 33.1449785879386 -1.34497858793860 114 40.8 33.3180709555757 7.48192904442429 115 37 35.0168203590748 1.98317964092515 116 32.7 27.1252764884024 5.57472351159762 117 37.2 33.7312060543633 3.46879394563672 118 38 35.5140148364818 2.48598516351823 119 27.2 30.3664834788258 -3.16648347882576 120 28 25.5301705881552 2.46982941184484 121 37 31.1359941149569 5.86400588504305 122 22 25.8843992098881 -3.88439920988815 123 24 26.5732955331413 -2.57329553314133 124 32 29.3828763834963 2.61712361650369 125 22 25.7857926475817 -3.78579264758167 126 24.2 27.6486144312360 -3.44861443123596 127 32 30.7502652950378 1.24973470496223 128 31 29.5335113819027 1.46648861809732 129 39.4 31.8940533006677 7.50594669933228 130 33.5 31.8134389126685 1.68656108733151 131 27 24.9113336682058 2.08866633179415 132 27 25.6883606073069 1.31163939269313 133 29 29.8344038618583 -0.834403861858288 134 25.8 28.6514093853129 -2.85140938531294 135 18.6 20.2978927326112 -1.69789273261117 136 19.1 23.8193976980333 -4.71939769803327 137 20.6 22.6535031692065 -2.05350316920646 138 20 18.6385485508377 1.36145144916232 139 15 15.4941717677438 -0.494171767743808 140 36 30.6372042935678 5.36279570643215 141 26 26.3222285940260 -0.322228594026039 142 27.9 26.4301282707790 1.46987172922096 143 28 25.2682996410793 2.73170035892069 144 28 23.5930041319439 4.40699586805606 145 25 23.9942154787929 1.00578452120712 146 35.7 30.6556165317611 5.04438346823888 147 33.5 28.0920053550792 5.40799464492083 148 16 14.9912890814838 1.00871091851615 149 15 15.3920453907817 -0.392045390781749 150 14 11.6851141592778 2.31488584072215 151 13 17.9894092129040 -4.98940921290402 152 11 7.98927737009596 3.01072262990404 153 15 17.8099160369132 -2.80991603691325 154 19.4 19.7962229852331 -0.396222985233084 155 17.5 17.5206919792937 -0.0206919792937378 156 12 6.86716391516478 5.13283608483522 157 15.5 16.2501246723559 -0.750124672355856 158 30.9 28.0314967245269 2.86850327547308 159 32 31.0297388527053 0.970261147294687 160 18.2 20.1848868244501 -1.98488682445013 161 26 26.1800015118144 -0.180001511814401 162 26 27.6702387484031 -1.67023874840313 163 30 25.9037034793416 4.09629652065838 164 24 28.0914815672734 -4.09148156727336 165 29 29.1933092433122 -0.19330924331219 166 28 27.4642575401757 0.535742459824258 167 37.3 31.8987848114281 5.40121518857187 168 31 28.7374571990399 2.2625428009601 169 12 9.47315163259846 2.52684836740154 170 13 8.8986573046545 4.10134269534549 171 15.5 19.2745790521554 -3.77457905215541 172 29.9 29.8604428781868 0.0395571218131987 173 34.4 31.7524578988073 2.64754210119274 174 13 17.2768290505980 -4.27682905059803 175 10 7.3814951153992 2.6185048846008 176 26.4 26.1785431993189 0.221456800681091 177 20.2 24.3189160318847 -4.11891603188470 178 25.1 25.4174687429929 -0.317468742992924 179 22.3 25.2040261488613 -2.90402614886133 180 24 27.5589399807833 -3.55893998078325 181 36.1 30.9048522638523 5.19514773614765 182 18.1 22.8290456603131 -4.7290456603131 183 14 13.0292596176530 0.970740382347014 184 14 12.1240245933732 1.87597540662681 185 15 10.8673735488390 4.13262645116101 186 14 13.6247263971086 0.375273602891430 187 14.5 15.5626371959393 -1.06263719593926 188 16 13.6433233974771 2.3566766025229 189 13 11.2207868198090 1.77921318019103 190 14 10.4664685581934 3.5335314418066 191 18.5 20.9997508655774 -2.49975086557735 192 18 20.4157904570344 -2.41579045703445 193 20.2 26.0607939117851 -5.86079391178508 194 22 28.4887234650783 -6.4887234650783 195 13 12.1451393507536 0.854860649246412 196 14 11.947726453901 2.05227354609899 197 17.6 20.4725341727915 -2.87253417279153 198 15 22.4207295451384 -7.42072954513835 199 18 21.2577537597315 -3.25775375973147 200 21 20.6550463264272 0.344953673572788 201 24 22.6645934206717 1.33540657932834 202 18 18.7536684824764 -0.75366848247641 203 27 28.1080371457606 -1.10803714576059 204 13 20.9846557407931 -7.98465574079314 205 25.5 24.4190361097994 1.08096389020062 206 18 20.8439217240723 -2.84392172407230 207 19 24.1517457509621 -5.15174575096211 208 23 23.8474112178197 -0.847411217819685 209 26 23.9153197762747 2.08468022372530 210 26.5 25.0520743643356 1.44792563566440 211 22 22.588395106967 -0.588395106967016 212 21 23.7620015424993 -2.76200154249933 213 28 29.1002710025261 -1.10027100252611 214 16 15.7234435930908 0.276556406909202 215 17 14.9019408311783 2.09805916882174 216 19 17.7389789057253 1.26102109427472 217 9 6.00957597784074 2.99042402215926 218 32.4 32.3364210537643 0.0635789462356846 219 36 34.2085496006486 1.79145039935137 220 31.5 31.62496496159 -0.124964961590032 221 29.5 31.6477615608057 -2.14776156080571 222 24 26.0378226771787 -2.03782267717872 223 33 32.5434221671085 0.456577832891547 224 38 35.6204027170895 2.37959728291046 225 32 35.6757748422974 -3.67577484229744 226 35.1 36.1935156717064 -1.09351567170639 227 44.6 34.7431193703223 9.8568806296777 228 33 31.7743055316086 1.22569446839144 229 36.1 33.8575368403904 2.24246315960963 230 33.7 33.3900604373096 0.309939562690409 231 34.1 33.1545123736533 0.945487626346694 232 18 27.0094928614788 -9.0094928614788 233 31.3 30.9421277519168 0.357872248083203 234 31.6 31.1765548600197 0.423445139980348 235 46.6 33.2392156527889 13.3607843472111 236 34.1 34.7700876674134 -0.670087667413412 237 31 35.7743352260431 -4.77433522604314 238 37 35.4527259206442 1.54727407935582 239 32.8 32.687170224808 0.112829775192019 240 21.5 25.9943288374680 -4.49432883746803 241 23.7 30.2014700570826 -6.50147005708263 242 19 24.7228425438662 -5.7228425438662 243 25.4 24.5022615417679 0.89773845823214 244 30 27.0770054331579 2.92299456684206 245 16.5 18.3249409669513 -1.82494096695134 246 23 22.8274793181344 0.172520681865629 247 21 22.1205400562471 -1.12054005624706 248 15 15.1940324319628 -0.194032431962800 249 16.5 19.9246275973087 -3.42462759730871 250 36 31.9887501271363 4.01124987286371 251 11 10.3592636574698 0.640736342530218 252 12 9.21706421833176 2.78293578166824 253 15 20.7007388482540 -5.70073884825403 254 20.2 20.5063203114386 -0.30632031143863 255 20.8 23.6855184309203 -2.88551843092029 256 19.8 25.1180306542284 -5.31803065422837 257 36 34.5858542262379 1.41414577376214 258 38 28.6731041548616 9.32689584513842 259 26.6 24.0569431029270 2.54305689707296 260 19.9 21.6157446627374 -1.71574466273736 261 23.9 22.9173600968853 0.982639903114749 262 17 16.4518613811490 0.548138618851039 263 12 10.7232526337066 1.27674736629341 264 11 16.2534769308848 -5.25347693088479 265 26.8 25.4518686503898 1.34813134961023 266 23.8 25.003909041445 -1.20390904144503 267 12 10.7689607385421 1.23103926145789 268 25 29.5190606341166 -4.51906063411657 269 28 25.8917832181846 2.10821678181535 270 24 27.6023801665282 -3.60238016652819 271 26 26.8372848948843 -0.837284894884293 272 30 26.1321181902339 3.86788180976612 273 19 22.8373028082669 -3.8373028082669 274 23 23.7730212245795 -0.773021224579534 275 25 21.6182945471426 3.38170545285742 276 27.2 26.7472835734386 0.452716426561396 277 21 21.5102530105412 -0.510253010541234 278 28.1 27.5212175517463 0.578782448253719 279 16.2 22.2027813523233 -6.00278135232327 280 14 14.1780409730519 -0.178040973051911 281 25.5 26.8896301361788 -1.38963013617876 282 39 32.6394835433679 6.36051645663205 283 26 24.6674983057201 1.33250169427990 284 13 10.1900237974716 2.80997620252841 285 20 20.1170658467936 -0.117065846793644 286 22 18.7349483846426 3.26505161535737 287 23 20.6291434469076 2.37085655309242 288 18 17.1560814056771 0.843918594322912 289 14 12.463474764211 1.53652523578900 290 14 11.7369304939522 2.26306950604784 291 14 10.8979663301621 3.10203366983787 292 15 12.2918039700911 2.70819602990887 293 16 12.2661183851677 3.7338816148323 294 34.2 28.9979185608288 5.20208143917117 295 34.7 30.7130760866114 3.98692391338865 296 38 32.078216989974 5.92178301002597 297 34.5 29.4679129284168 5.03208707158315 298 27.2 29.2685094564121 -2.06850945641207 299 30 29.7516112889550 0.248388711044954 300 23.2 25.4270825024087 -2.22708250240866 301 18 15.2305510068972 2.76944899310276 302 16 15.9110712909174 0.0889287090826203 303 14 12.7205577674846 1.27944223251538 304 18 17.1536483060682 0.846351693931836 305 18 19.6781303576365 -1.67813035763651 306 22 21.2615521332552 0.738447866744777 307 19 20.4148824280065 -1.41488242800655 308 20.5 21.6360458031843 -1.13604580318434 309 19 19.5564935566136 -0.55649355661361 310 13 16.6847057205303 -3.68470572053029 311 23 24.3723711460176 -1.37237114601757 312 14 12.0072155935443 1.99278440645572 313 14 10.4361924978150 3.56380750218495 314 16 12.4906235049883 3.50937649501166 315 14 10.6605167903749 3.33948320962514 316 19 17.6154335018010 1.38456649819904 317 16 12.3044055221096 3.69559447789039 318 16 16.8374536174621 -0.837453617462145 319 31 28.9450129860118 2.05498701398821 320 21.5 23.3832282446142 -1.88322824461423 321 27 28.8579867873446 -1.85798678734458 322 33.5 27.3483701559878 6.15162984401218 323 19.2 21.1426160858053 -1.94261608580532 324 13 6.1638486382738 6.8361513617262 325 24.5 24.8174610272577 -0.317461027257735 326 18.5 18.9777877618933 -0.477787761893321 327 26 26.4446168131823 -0.44461681318234 328 27 29.1172361022955 -2.11723610229552 329 36 32.6121743086129 3.38782569138712 330 25 23.3219390564954 1.67806094350457 331 21.6 26.6213754386819 -5.02137543868186 332 24 23.5985847593477 0.401415240652298 333 25 24.9483555739487 0.0516444260512951 334 26 26.5199819674882 -0.519981967488218 335 32.3 34.5376977302497 -2.23769773024966 336 30 31.8556764536199 -1.85567645361993 337 33.8 33.2396606681608 0.560339331839241 338 20 26.5985309125805 -6.59853091258053 339 32 31.5796681646640 0.420331835336043 340 21.1 29.3277077835367 -8.22770778353667 341 28 29.7924165005541 -1.79241650055405 342 29 28.8763822010105 0.123617798989512 343 32.2 32.3312234440398 -0.131223444039747 344 32.4 32.6644325899318 -0.264432589931794 345 34 34.2448774862028 -0.244877486202757 346 31 28.2347063310000 2.76529366899997 347 32 30.3012390203009 1.69876097969909 348 27 26.8249051422518 0.175094857748248 349 26 29.9736866504639 -3.97368665046393 350 38.1 34.4261361835644 3.67386381643556 351 24 25.6207677235606 -1.62076772356064 352 25 25.2475655009923 -0.247565500992309 353 27.5 28.9782786761979 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35.5286687656404 0.471331234359568 378 31.5 31.9927080412287 -0.492708041228663 379 26 29.5049329836817 -3.50493298368169 380 23 26.7402391475755 -3.74023914757553 381 19 22.2851124867926 -3.28511248679255 382 18 20.9928075434008 -2.99280754340076 383 22 23.4979322477192 -1.49793224771922 384 20 23.137328024017 -3.13732802401699 385 17 23.986026099801 -6.986026099801 386 30.7 27.1168915960262 3.58310840397380 387 43.4 32.3699844293064 11.0300155706936 388 44 35.4659764380706 8.53402356192944 389 29 30.7810945046364 -1.78109450463642 390 41.5 32.622432632669 8.87756736733098 391 44.3 33.8893743891281 10.4106256108719 392 31.9 33.134717216199 -1.23471721619902 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.239204321578649 0.478408643157297 0.760795678421351 13 0.127450171550827 0.254900343101653 0.872549828449173 14 0.0598635064608886 0.119727012921777 0.940136493539111 15 0.0813597982759425 0.162719596551885 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0.648095498105514 346 0.339927240309454 0.679854480618908 0.660072759690546 347 0.305179081315747 0.610358162631493 0.694820918684253 348 0.270263762070035 0.540527524140071 0.729736237929965 349 0.423438108518423 0.846876217036846 0.576561891481577 350 0.396437273056671 0.792874546113342 0.603562726943329 351 0.352603165809497 0.705206331618995 0.647396834190503 352 0.357555438991203 0.715110877982407 0.642444561008797 353 0.317369627948768 0.634739255897537 0.682630372051232 354 0.272028879339509 0.544057758679018 0.727971120660491 355 0.230865004362475 0.46173000872495 0.769134995637525 356 0.217133987253902 0.434267974507804 0.782866012746098 357 0.241150639359730 0.482301278719461 0.75884936064027 358 0.206629032706721 0.413258065413442 0.793370967293279 359 0.20257576416839 0.40515152833678 0.79742423583161 360 0.253477326464665 0.506954652929329 0.746522673535335 361 0.221654859340653 0.443309718681305 0.778345140659347 362 0.241429433422859 0.482858866845718 0.758570566577141 363 0.196167024460087 0.392334048920174 0.803832975539913 364 0.192519924268099 0.385039848536197 0.807480075731901 365 0.409675866444954 0.819351732889908 0.590324133555046 366 0.363753923486601 0.727507846973201 0.636246076513399 367 0.316246332902289 0.632492665804578 0.683753667097711 368 0.332786985373042 0.665573970746083 0.667213014626958 369 0.346139046114959 0.692278092229918 0.653860953885041 370 0.277466395981654 0.554932791963308 0.722533604018346 371 0.24606343065014 0.49212686130028 0.75393656934986 372 0.316326621399135 0.632653242798269 0.683673378600866 373 0.247189313885861 0.494378627771722 0.752810686114139 374 0.234049310920844 0.468098621841688 0.765950689079156 375 0.169430442636410 0.338860885272821 0.83056955736359 376 0.336224772714279 0.672449545428559 0.663775227285721 377 0.268589595106043 0.537179190212087 0.731410404893956 378 0.237610766678842 0.475221533357684 0.762389233321158 379 0.191519739792931 0.383039479585862 0.80848026020707 380 0.106968571841866 0.213937143683733 0.893031428158134 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 171 0.463414634146341 NOK 5% type I error level 192 0.520325203252033 NOK 10% type I error level 202 0.547425474254743 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/10br8i1293670458.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/10br8i1293670458.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/1fzar1293670458.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/1fzar1293670458.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/2fzar1293670458.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/2fzar1293670458.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/38qrc1293670458.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/38qrc1293670458.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/48qrc1293670458.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/48qrc1293670458.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/58qrc1293670458.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/58qrc1293670458.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/6izrx1293670458.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/6izrx1293670458.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/7izrx1293670458.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/7izrx1293670458.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/8br8i1293670458.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/8br8i1293670458.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/9br8i1293670458.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/30/t1293670372tt5c2k1f40lcrx5/9br8i1293670458.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 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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