*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 14:38:38 +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/t12929422581rbqkhmro1dxmgh.htm/, Retrieved Tue, 21 Dec 2010 15:37:51 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh.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 «

1 1 14 41 38 13 12 1 1 18 39 32 16 11 1 1 11 30 35 19 15 1 0 12 31 33 15 6 1 1 16 34 37 14 13 1 1 18 35 29 13 10 1 1 14 39 31 19 12 1 1 14 34 36 15 14 1 1 15 36 35 14 12 1 1 15 37 38 15 9 1 0 17 38 31 16 10 1 1 19 36 34 16 12 1 0 10 38 35 16 12 1 1 16 39 38 16 11 1 1 18 33 37 17 15 1 0 14 32 33 15 12 1 0 14 36 32 15 10 1 1 17 38 38 20 12 1 0 14 39 38 18 11 1 1 16 32 32 16 12 1 0 18 32 33 16 11 1 1 11 31 31 16 12 1 1 14 39 38 19 13 1 1 12 37 39 16 11 1 0 17 39 32 17 12 1 1 9 41 32 17 13 1 0 16 36 35 16 10 1 1 14 33 37 15 14 1 1 15 33 33 16 12 1 0 11 34 33 14 10 1 1 16 31 31 15 12 1 0 13 27 32 12 8 1 1 17 37 31 14 10 1 1 15 34 37 16 12 1 0 14 34 30 14 12 1 0 16 32 33 10 7 1 0 9 29 31 10 9 1 0 15 36 33 14 12 1 1 17 29 31 16 10 1 0 13 35 33 16 10 1 0 15 37 32 16 10 1 1 16 34 33 14 12 1 0 16 38 32 20 15 1 0 12 35 33 14 10 1 1 15 38 28 14 10 1 1 11 37 35 11 12 1 1 15 38 39 14 13 1 1 15 33 34 15 11 1 1 17 36 38 16 11 1 0 13 38 32 14 12 1 1 16 32 38 16 14 1 0 14 32 3 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 16 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Software[t] = + 2.06285134721188 + 0.452576036791377Populatie[t] + 0.239169812731862Geslacht[t] -0.00908693191448484Happiness[t] -0.0132555507413528Connected[t] + 0.0243562014396462Separate[t] + 0.54734344200979Learning[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) 2.06285134721188 1.166455 1.7685 0.078066 0.039033 Populatie 0.452576036791377 0.234148 1.9329 0.054257 0.027129 Geslacht 0.239169812731862 0.219332 1.0904 0.27645 0.138225 Happiness -0.00908693191448484 0.04482 -0.2027 0.839484 0.419742 Connected -0.0132555507413528 0.031048 -0.4269 0.669755 0.334878 Separate 0.0243562014396462 0.032249 0.7552 0.450736 0.225368 Learning 0.54734344200979 0.045375 12.0627 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.664438564389672 R-squared 0.441478605848208 Adjusted R-squared 0.429552882129664 F-TEST (value) 37.0190200835981 F-TEST (DF numerator) 6 F-TEST (DF denominator) 281 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.77966607666687 Sum Squared Residuals 889.986387787314 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 10.1249029703703 1.87509702962968 2 11 11.6109594615870 -0.610959461586962 3 15 13.5089668720088 1.4910331279912 4 6 11.0093684057027 -5.00936840570268 5 13 10.7225052023013 2.27749479769868 6 10 9.94888273420403 0.0511172657959684 7 12 13.2649813138346 -1.26498131383459 8 14 11.2636663067004 2.73633369329956 9 12 10.6563686298538 1.34363137014619 10 9 11.2635251254412 -2.26352512544118 11 10 11.3697759300713 -1.36977593007127 12 12 11.6903515847758 0.309648415224199 13 12 11.5308092592312 0.469190740768752 14 11 11.7752705340538 -0.775270534053783 15 15 12.3596172152431 2.64038278475693 16 12 10.9779389911323 1.02206100886766 17 10 10.9005605867273 -0.900560586727283 18 12 13.9688129209198 -1.96881292091981 19 11 12.6489614691705 -1.64896146917047 20 12 11.7219221806054 0.278077819394625 21 11 11.4889347054842 -0.488934705484191 22 12 11.7562561894795 0.243743810520493 23 13 13.4354747239121 -0.435474723912124 24 11 11.8624855646341 -0.862485564634076 25 12 11.9282200227793 0.0717799772206508 26 13 12.2135741893444 0.786425810655615 27 10 11.5027987692270 -1.50279876922704 28 14 11.3012780588814 2.69872194111857 29 12 11.7421097632182 0.257890236781846 30 10 10.4313452433833 -0.4313452433833 31 12 11.1634780878973 0.836521912102709 32 8 9.38691714928457 -1.38691714928457 33 10 10.5275144095249 -0.527514409524899 34 12 11.8262790182354 0.173720981764614 35 12 10.3310158433209 1.66898415667909 36 7 8.22304791725442 -1.22304791725442 37 9 8.27771069000058 0.722289309999418 38 12 10.3684864142427 1.63151358575735 39 10 11.7282456994753 -1.72824569947530 40 10 11.4946027128326 -1.49460271283256 41 10 11.4255615460812 -1.42556154608124 42 12 10.6250803965427 1.37491960345726 43 15 13.5925928314646 1.40740716853544 44 10 10.4090027607275 -0.409002760727462 45 10 10.4593641182936 -0.459364118293577 46 12 9.03743048074102 2.96256951925898 47 13 10.7272823341297 2.27271766587031 48 11 11.219122522648 -0.21912252264801 49 11 11.8059502543634 -0.805950254363357 50 12 10.3357929751493 1.66420702485073 51 14 11.8680593892433 2.13194061075675 52 10 10.3575269448036 -0.357526944803612 53 12 9.36316946084643 2.63683053915357 54 13 11.8778960154185 1.12210398458151 55 5 7.68769600146292 -2.68769600146292 56 6 10.6431130791125 -4.64311307911245 57 12 11.6778457282952 0.322154271704802 58 12 11.8194881676232 0.180511832376788 59 11 11.0029037055735 -0.00290370557348595 60 10 11.7672156589186 -1.76721565891855 61 7 9.29516035087435 -2.29516035087435 62 12 11.4791922620481 0.520807737951855 63 14 11.8139143430140 2.18608565698597 64 11 10.7317333154751 0.268266684524943 65 12 11.6801418095975 0.319858190402492 66 13 12.1666317563444 0.833368243655612 67 14 12.8820901255509 1.11790987444909 68 11 12.5185170738355 -1.51851707383551 69 12 9.6436961008084 2.3563038991916 70 12 11.5738536547622 0.426146345237827 71 8 8.23475708095421 -0.234757080954212 72 11 10.7866280559650 0.213371944034974 73 14 12.9696783051343 1.03032169486574 74 14 12.7261986923163 1.27380130768372 75 12 11.3617210549360 0.638278945063967 76 9 12.1641120922043 -3.16411209220434 77 13 11.7683385021824 1.23166149781764 78 11 11.6983156734265 -0.698315673426478 79 12 9.8784749752844 2.12152502471561 80 12 11.3219544027120 0.678045597288026 81 12 11.5760085548052 0.423991445194768 82 12 11.8130234674940 0.186976532505967 83 12 10.8934873735966 1.10651262640339 84 11 11.2323780733894 -0.232378073389363 85 10 11.7024842922533 -1.70248429225335 86 9 10.4881125213978 -1.48811252139783 87 12 11.7755528965723 0.224447103427715 88 12 11.7889496285729 0.211050371427111 89 12 11.2674617765242 0.732538223475755 90 9 9.63414183715167 -0.634141837151667 91 15 12.2435042153932 2.75649578460679 92 12 11.9104482732526 0.0895517267473811 93 12 11.0953277966660 0.90467220333403 94 12 10.0982068996642 1.90179310033577 95 10 11.7265581311745 -1.72655813117449 96 13 11.7650607588755 1.23493924112451 97 9 11.6759731907706 -2.67597319077064 98 12 11.4561000851316 0.543899914868442 99 10 10.494577221527 -0.494577221527005 100 14 11.7307267500014 2.26927324999864 101 11 11.5258909461436 -0.52589094614363 102 15 13.9800547528774 1.01994524712264 103 11 10.8834187796776 0.116581220322435 104 11 11.8882469718560 -0.888246971856032 105 12 9.79828615931472 2.20171384068528 106 12 12.2628009224860 -0.262800922485987 107 12 11.5430327531933 0.456967246806652 108 11 11.5573203607140 -0.557320360713953 109 7 9.6848209602947 -2.68482096029471 110 12 11.8062326168819 0.193767383118141 111 14 11.8049685923588 2.1950314076412 112 11 12.5157322313154 -1.51573223131544 113 10 9.49680919790977 0.503190802090228 114 13 12.5111614981863 0.48883850181367 115 13 10.8270032211906 2.17299677880942 116 8 10.8137476704492 -2.81374767044923 117 11 10.1578787719826 0.84212122801744 118 12 11.7579875457448 0.242012454255186 119 11 9.98559522595896 1.01440477404104 120 13 11.6315705879775 1.36842941202253 121 12 10.1799388921199 1.82006110788010 122 14 11.8108685674510 2.18913143254903 123 13 11.1062872661050 1.89371273389499 124 15 11.7867947285298 3.21320527147017 125 10 10.8335331387598 -0.833533138759769 126 11 12.2716054918820 -1.27160549188197 127 9 11.2314871978694 -2.23148719786936 128 11 9.52622489369629 1.47377510630371 129 10 11.5343693650566 -1.53436936505662 130 11 8.31532244218158 2.68467755781842 131 8 11.7467457137873 -3.74674571378727 132 11 9.32003088257631 1.67996911742369 133 12 10.4770118706995 1.52298812930047 134 12 11.1015101342766 0.898489865723354 135 9 9.69561688998552 -0.695616889985518 136 11 11.0001402925289 -0.000140292528927985 137 10 9.1302193359305 0.869780664069505 138 8 9.55058109513593 -1.55058109513593 139 9 8.85962010862831 0.140379891371689 140 8 11.7797215153992 -3.77972151539915 141 9 11.0837010345447 -2.08370103454466 142 15 12.3870191922458 2.61298080775422 143 11 11.2858890375725 -0.285889037572535 144 8 8.30746092117616 -0.307460921176164 145 13 12.6948280574267 0.305171942573276 146 12 9.93055930420974 2.06944069579026 147 12 11.4947438940918 0.505256105908191 148 9 9.86456391302148 -0.864563913021481 149 7 8.52882163417604 -1.52882163417604 150 13 11.1910650341237 1.80893496587626 151 9 11.6023784750287 -2.60237847502869 152 6 11.8889966661168 -5.88899666611678 153 8 10.6600229184184 -2.66002291841837 154 8 8.4275105721091 -0.42751057210909 155 6 10.2198467256032 -4.2198467256032 156 9 11.2314871978694 -2.23148719786936 157 11 11.7226718748661 -0.722671874866125 158 8 9.71503334886203 -1.71503334886203 159 10 9.36280814160856 0.63719185839144 160 8 8.72609476897542 -0.726094768975418 161 14 11.5223426700835 2.47765732991655 162 10 10.9205066018859 -0.920506601885934 163 8 7.84888234164735 0.151117658352652 164 11 10.0045306138139 0.995469386186124 165 12 8.47801655579358 3.52198344420642 166 12 9.81055044834119 2.18944955165881 167 12 11.2818436153885 0.718156384611474 168 5 8.79560326746899 -3.79560326746899 169 12 11.3381049480468 0.661895051953185 170 10 8.85817973409113 1.14182026590887 171 7 7.33447608763545 -0.334476087635453 172 12 8.92952536705084 3.07047463294916 173 11 10.5831622891347 0.416837710865262 174 8 9.10165934690911 -1.10165934690911 175 9 8.85494898930433 0.145051010695673 176 10 10.1635586090961 -0.163558609096121 177 9 9.16765473809737 -0.167654738097374 178 12 11.3319226104361 0.668077389563862 179 6 8.23224086167329 -2.23224086167329 180 15 12.7919739455259 2.20802605447407 181 12 10.4214734484532 1.57852655154680 182 12 6.92572930939062 5.07427069060938 183 12 11.3940317453160 0.605968254683965 184 11 11.5913838368348 -0.591383836834775 185 7 8.9719142510602 -1.97191425106020 186 7 8.27631731398346 -1.27631731398346 187 5 8.4363185863642 -3.43631858636419 188 12 10.3175187251254 1.68248127487457 189 12 11.4028363147120 0.597163685287982 190 3 9.11341550912896 -6.11341550912896 191 11 11.3967951583606 -0.396795158360593 192 10 9.6364027496991 0.363597250300891 193 12 10.5990400716614 1.40095992833860 194 9 11.2366527047206 -2.23665270472061 195 12 11.3960454640998 0.603954535900156 196 9 10.0192855530767 -1.01928555307673 197 12 11.0715835530869 0.928416446913057 198 10 10.0019083820286 -0.00190838202856881 199 9 8.23350488619634 0.766495113803655 200 12 8.84155225730372 3.15844774269628 201 8 10.7665464858566 -2.76654648585663 202 11 10.8020033379946 0.197996662005431 203 11 11.3695343626171 -0.369534362617138 204 12 11.0878344846167 0.91216551538334 205 10 8.29205391525087 1.70794608474913 206 10 10.4806779890293 -0.480677989029284 207 12 9.14142599913317 2.85857400086683 208 12 9.01377702364655 2.98622297635345 209 11 10.6987609587223 0.301239041277706 210 8 10.5638655820420 -2.56386558204196 211 12 11.3480827554813 0.6519172445187 212 10 9.82710517186493 0.172894828135075 213 11 11.8674157074869 -0.867415707486885 214 10 10.1487566713132 -0.148756671313207 215 8 9.48088786172217 -1.48088786172217 216 12 10.8485608408308 1.15143915916920 217 12 9.41817021384078 2.58182978615922 218 10 9.95338094837302 0.0466190516269787 219 12 10.7632687425498 1.23673125745024 220 9 8.86314504569881 0.136854954301189 221 6 6.98802341349426 -0.988023413494258 222 10 9.92148420206045 0.0785157979395493 223 9 10.0072940268584 -1.00729402685843 224 9 8.363999676306 0.636000323693995 225 9 8.93279472545163 0.067205274548368 226 6 9.5702661772516 -3.57026617725160 227 10 7.94260586032131 2.05739413967869 228 6 11.0879756658759 -5.08797566587591 229 14 12.2963500683445 1.7036499316555 230 10 9.60080471630192 0.399195283698082 231 10 8.26151537620055 1.73848462379945 232 6 4.38341259803653 1.61658740196347 233 12 9.24060359063258 2.75939640936742 234 12 11.3392781860853 0.660721813914683 235 7 7.67656018200976 -0.676560182009761 236 8 8.94342804440768 -0.943428044407678 237 11 8.94679997045374 2.05320002954627 238 3 7.73806080388816 -4.73806080388816 239 6 9.4090832819263 -3.40908328192629 240 8 8.9990724791584 -0.999072479158396 241 9 10.0358188471249 -1.03581884712495 242 9 7.95043715261881 1.04956284738119 243 8 9.03889791106322 -1.03889791106322 244 9 8.9698567443119 0.0301432556881003 245 7 8.36451400656831 -1.36451400656831 246 7 7.7601209240255 -0.760120924025495 247 6 9.10292337143217 -3.10292337143217 248 9 11.2833513888161 -2.28335138881610 249 10 8.8352287384338 1.16477126156620 250 11 9.96968227467744 1.03031772532257 251 12 11.1757992094577 0.824200790542298 252 8 10.2515233339372 -2.25152333393716 253 11 9.61883739887164 1.38116260112836 254 3 4.66726737608007 -1.66726737608007 255 11 10.7577419164606 0.242258083539354 256 12 8.42217216010284 3.57782783989716 257 7 8.36662190809131 -1.36662190809131 258 9 9.99342996311558 -0.993429963115582 259 12 10.5247074428194 1.4752925571806 260 8 10.2270259512383 -2.22702595123827 261 11 9.43943685175287 1.56056314824713 262 8 8.26769771381123 -0.267697713811227 263 10 10.7184425959788 -0.718442595978835 264 8 8.31959707351283 -0.31959707351283 265 7 9.45779568480558 -2.45779568480558 266 8 9.55930670781255 -1.55930670781255 267 10 11.2770278699462 -1.27702786994617 268 8 9.56229370369485 -1.56229370369485 269 12 11.3542650930920 0.645734906908023 270 14 11.0643691586970 2.93563084130299 271 7 9.0749044965219 -2.07490449652189 272 6 6.26601794258008 -0.266017942580075 273 11 11.0441815760842 -0.0441815760842363 274 4 5.40407478477717 -1.40407478477717 275 9 11.1638076832394 -2.16380768323941 276 5 4.25160999543932 0.748390004560678 277 9 8.84342479482828 0.156575205171720 278 11 10.4612401006773 0.538759899322745 279 12 10.2192030438468 1.78079695615316 280 9 8.37004083265743 0.62995916734257 281 12 10.9353737571089 1.06462624289115 282 10 10.7867340684694 -0.786734068469408 283 9 8.86127250817425 0.138727491825746 284 6 5.80078624883922 0.199213751160785 285 10 11.1433377381081 -1.14333773810813 286 9 7.79051828181657 1.20948171818343 287 13 10.8966177321885 2.10338226781147 288 12 10.2437004265457 1.75629957345426 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.72842669149035 0.543146617019301 0.271573308509650 11 0.93211129196143 0.135777416077138 0.0678887080385691 12 0.883927528921358 0.232144942157284 0.116072471078642 13 0.907996117292558 0.184007765414884 0.092003882707442 14 0.882918643366776 0.234162713266449 0.117081356633224 15 0.893372416642965 0.21325516671407 0.106627583357035 16 0.901444286069359 0.197111427861282 0.0985557139306408 17 0.860478230620102 0.279043538759797 0.139521769379899 18 0.850882361745292 0.298235276509416 0.149117638254708 19 0.800875673969819 0.398248652060362 0.199124326030181 20 0.741526955513361 0.516946088973278 0.258473044486639 21 0.68004537451535 0.639909250969299 0.319954625484650 22 0.611980281908264 0.776039436183472 0.388019718091736 23 0.538947837607392 0.922104324785216 0.461052162392608 24 0.514659703331384 0.970680593337232 0.485340296668616 25 0.513177509267377 0.973644981465246 0.486822490732623 26 0.479991010742595 0.95998202148519 0.520008989257405 27 0.421395820416826 0.842791640833652 0.578604179583174 28 0.425690363172463 0.851380726344925 0.574309636827537 29 0.365084395759665 0.730168791519331 0.634915604240335 30 0.306802040898218 0.613604081796436 0.693197959101782 31 0.254354709798710 0.508709419597421 0.74564529020129 32 0.248959157202431 0.497918314404862 0.751040842797569 33 0.217421178977288 0.434842357954576 0.782578821022712 34 0.178369234649196 0.356738469298392 0.821630765350804 35 0.217867818066175 0.435735636132351 0.782132181933824 36 0.201215205990948 0.402430411981897 0.798784794009052 37 0.165356409024524 0.330712818049049 0.834643590975476 38 0.193459404854362 0.386918809708723 0.806540595145638 39 0.206894025939872 0.413788051879744 0.793105974060128 40 0.177929302829723 0.355858605659446 0.822070697170277 41 0.149026371730436 0.298052743460872 0.850973628269564 42 0.126655282221277 0.253310564442554 0.873344717778723 43 0.183568354774128 0.367136709548257 0.816431645225872 44 0.151176229122688 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215 0.475073243768378 0.950146487536755 0.524926756231622 216 0.463329927494324 0.926659854988647 0.536670072505676 217 0.50100231508737 0.99799536982526 0.49899768491263 218 0.460515567197673 0.921031134395345 0.539484432802327 219 0.448083060958644 0.896166121917289 0.551916939041356 220 0.408872581656281 0.817745163312563 0.591127418343719 221 0.375727178988077 0.751454357976153 0.624272821011923 222 0.337751749601660 0.675503499203319 0.66224825039834 223 0.309783299840621 0.619566599681243 0.690216700159379 224 0.278692799114202 0.557385598228404 0.721307200885798 225 0.24513558682899 0.49027117365798 0.75486441317101 226 0.348811289317032 0.697622578634065 0.651188710682968 227 0.394249562604279 0.788499125208558 0.605750437395721 228 0.698373733901906 0.603252532196188 0.301626266098094 229 0.68000035730657 0.639999285386861 0.319999642693430 230 0.640145693983217 0.719708612033565 0.359854306016783 231 0.634317602264253 0.731364795471493 0.365682397735747 232 0.631447483369072 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0.267468332335415 0.133734166167708 250 0.843303151232435 0.313393697535130 0.156696848767565 251 0.82780869469585 0.344382610608299 0.172191305304150 252 0.821910790091086 0.356178419817828 0.178089209908914 253 0.801542566836721 0.396914866326558 0.198457433163279 254 0.770086329806592 0.459827340386815 0.229913670193408 255 0.722155187290488 0.555689625419024 0.277844812709512 256 0.875956133185436 0.248087733629128 0.124043866814564 257 0.849459041060549 0.301081917878902 0.150540958939451 258 0.826345905359565 0.347308189280870 0.173654094640435 259 0.831923223562796 0.336153552874408 0.168076776437204 260 0.848636175155275 0.302727649689449 0.151363824844725 261 0.845162514771797 0.309674970456405 0.154837485228203 262 0.801396042671901 0.397207914656198 0.198603957328099 263 0.778310490480682 0.443379019038636 0.221689509519318 264 0.71971541635734 0.560569167285319 0.280284583642660 265 0.772381154804038 0.455237690391925 0.227618845195962 266 0.839922673999482 0.320154652001036 0.160077326000518 267 0.926917810431742 0.146164379136515 0.0730821895682577 268 0.90667151793294 0.186656964134120 0.0933284820670598 269 0.865007780153338 0.269984439693324 0.134992219846662 270 0.926659218945848 0.146681562108304 0.0733407810541522 271 0.904538175266072 0.190923649467857 0.0954618247339284 272 0.943421373055725 0.113157253888551 0.0565786269442753 273 0.902042733934533 0.195914532130934 0.0979572660654672 274 0.903071709349389 0.193856581301222 0.0969282906506112 275 0.88993391842091 0.220132163158182 0.110066081579091 276 0.811762000333418 0.376475999333165 0.188237999666582 277 0.719977651286748 0.560044697426505 0.280022348713252 278 0.555516235808126 0.888967528383748 0.444483764191874 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 33 0.122676579925651 NOK 10% type I error level 62 0.230483271375465 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/10tste1292942301.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/10tste1292942301.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/1fiw51292942301.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/1fiw51292942301.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/2fiw51292942301.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/2fiw51292942301.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/3fiw51292942301.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/3fiw51292942301.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/48rv81292942301.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/48rv81292942301.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/58rv81292942301.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/58rv81292942301.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/68rv81292942301.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/68rv81292942301.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/710ct1292942301.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/710ct1292942301.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/8tste1292942301.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/8tste1292942301.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/9tste1292942301.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12929422581rbqkhmro1dxmgh/9tste1292942301.ps (open in new window)

Parameters (Session):

par1 = 7 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = no ;

Parameters (R input):

par1 = 7 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = no ;

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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