workshop 7

*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: Sun, 28 Nov 2010 15:24:05 +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/Nov/28/t1290957747sjj27dpqr1piskh.htm/, Retrieved Sun, 28 Nov 2010 16:22:38 +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/Nov/28/t1290957747sjj27dpqr1piskh.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 1 41 41 38 38 13 12 12 14 14 12 12 53 53 1 2 2 39 39 32 32 16 11 11 18 18 11 11 83 83 1 3 3 30 30 35 35 19 15 15 11 11 14 14 66 66 1 4 4 31 31 33 33 15 6 6 12 12 12 12 67 67 1 5 5 34 34 37 37 14 13 13 16 16 21 21 76 76 1 6 6 35 35 29 29 13 10 10 18 18 12 12 78 78 1 7 7 39 39 31 31 19 12 12 14 14 22 22 53 53 1 8 8 34 34 36 36 15 14 14 14 14 11 11 80 80 1 9 9 36 36 35 35 14 12 12 15 15 10 10 74 74 1 10 10 37 37 38 38 15 9 9 15 15 13 13 76 76 1 11 11 38 38 31 31 16 10 10 17 17 10 10 79 79 1 12 12 36 36 34 34 16 12 12 19 19 8 8 54 54 1 13 13 38 38 35 35 16 12 12 10 10 15 15 67 67 1 14 14 39 39 38 38 16 11 11 16 16 14 14 54 54 1 15 15 33 33 37 37 17 15 15 18 18 10 10 87 87 1 16 16 32 32 33 33 15 12 12 14 14 14 14 58 58 1 17 17 36 36 32 32 15 10 10 14 14 14 14 75 75 1 18 18 38 38 38 38 20 12 12 17 17 11 11 88 88 1 19 19 39 39 38 38 18 11 11 14 14 10 10 64 64 1 20 20 32 32 32 32 16 12 12 16 16 13 13 57 57 1 21 21 32 32 33 33 16 11 11 18 18 9.5 9.5 66 66 1 22 22 31 31 31 31 16 12 12 11 11 14 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 21 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Learning[t] = + 4.02213192467067 + 2.51220871915707Pop[t] -0.0041632636006461t + 0.000172174548079445Pop_t[t] -0.0555568413104866Connected[t] + 0.142876235895839Connected_p[t] + 0.157004790836634Separate[t] -0.171050529312446Separate_p[t] + 0.561688749040414Software[t] -0.0423405001257738Software_p[t] + 0.129559018015446Happiness[t] -0.0990921264717531Happiness_p[t] + 0.0223866216094604Depression[t] -0.105904658670805Depression_p[t] -0.00941064469109043Belonging[t] + 0.0247479684327582Belonging_p[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) 4.02213192467067 3.327578 1.2087 0.227919 0.11396 Pop 2.51220871915707 4.240155 0.5925 0.554069 0.277034 t -0.0041632636006461 0.006372 -0.6534 0.514113 0.257057 Pop_t 0.000172174548079445 0.007181 0.024 0.980891 0.490446 Connected -0.0555568413104866 0.052264 -1.063 0.288813 0.144406 Connected_p 0.142876235895839 0.07003 2.0402 0.042388 0.021194 Separate 0.157004790836634 0.059798 2.6256 0.009187 0.004594 Separate_p -0.171050529312446 0.074474 -2.2968 0.022465 0.011232 Software 0.561688749040414 0.082232 6.8306 0 0 Software_p -0.0423405001257738 0.109405 -0.387 0.699084 0.349542 Happiness 0.129559018015446 0.089382 1.4495 0.148462 0.074231 Happiness_p -0.0990921264717531 0.117868 -0.8407 0.401322 0.200661 Depression 0.0223866216094604 0.062207 0.3599 0.719247 0.359624 Depression_p -0.105904658670805 0.084312 -1.2561 0.210258 0.105129 Belonging -0.00941064469109043 0.019054 -0.4939 0.621816 0.310908 Belonging_p 0.0247479684327582 0.024621 1.0052 0.315801 0.1579 Multiple Linear Regression - Regression Statistics Multiple R 0.683693459674527 R-squared 0.467436746801724 Adjusted R-squared 0.435225259713119 F-TEST (value) 14.5114922982577 F-TEST (DF numerator) 15 F-TEST (DF denominator) 248 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.84570008019649 Sum Squared Residuals 844.838978937261 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 16.0460838528529 -3.04608385285288 2 16 16.0978854720564 -0.0978854720563963 3 19 16.6187187563686 2.38128124363138 4 15 12.2688445880293 2.73115541197067 5 14 15.6143076175297 -1.61430761752974 6 13 15.0952278482479 -2.09522784824792 7 19 15.1106383280845 3.88936167191549 8 15 16.9713242202552 -1.97132422025521 9 14 16.1392821471749 -2.13928214717492 10 15 14.4025490268356 0.597450973164355 11 16 15.4610456161102 0.53895438388982 12 16 16.1235117839571 -0.123511783957133 13 16 15.6206706709185 0.37932932908151 14 16 15.2094476897910 0.790552310208976 15 17 17.6741165821685 -0.674116582168514 16 15 15.1802222027614 -0.180222202761411 17 15 14.7615924363051 0.238407563694865 18 20 16.4280021978545 3.57199780214553 19 18 15.6160038471029 2.38399615289714 20 16 15.307418081434 0.692581918565983 21 16 15.2613158314681 0.7386841685319 22 16 15.1590203135979 0.840979686402122 23 19 16.3183266771825 2.68167332281749 24 16 14.8896593529274 1.11034064707260 25 17 16.5409837524434 0.459016247556603 26 17 17.0622567007993 -0.0622567007993099 27 16 15.0063695483651 0.99363045163488 28 15 16.287354596739 -1.28735459673899 29 16 15.5528708060404 0.447129193959557 30 14 14.3904425234722 -0.390442523472174 31 15 15.8770730400500 -0.87707304004998 32 12 12.4410863242391 -0.441086324239124 33 14 15.1632236724350 -1.16322367243502 34 16 15.9066298550938 0.0933701449062471 35 14 15.6500827322888 -1.65008273228881 36 10 13.265086391234 -3.26508639123401 37 10 12.7277418177310 -2.72774181773096 38 14 15.8385839962544 -1.83858399625441 39 16 14.5174086001451 1.48259139985486 40 16 14.7800135692866 1.21998643071338 41 16 15.1858454467376 0.814154553262365 42 14 15.5727609632611 -1.57276096326112 43 20 17.6691623615627 2.33083763843726 44 14 14.1387756696789 -0.138775669678926 45 14 15.0696607461849 -1.06966074618494 46 11 15.6144856270065 -4.61448562700649 47 14 16.5709069707458 -2.57090697074581 48 15 15.1481882666103 -0.148188266610254 49 16 15.0614967185108 0.938503281489162 50 14 16.0633090042108 -2.06330900421076 51 16 16.6187303550879 -0.618730355087908 52 14 14.1780196281422 -0.178019628142175 53 12 14.6837657036483 -2.68376570364832 54 16 15.6527346763494 0.347265323650556 55 9 11.6694846725896 -2.66948467258963 56 14 12.5777743435091 1.42222565649092 57 16 16.0036265752432 -0.00362657524324481 58 16 15.3226855308472 0.677314469152835 59 15 15.3869151033687 -0.386915103368735 60 16 14.2534262966507 1.74657370334928 61 12 11.5388756636925 0.4611243363075 62 16 15.9344810690503 0.0655189309496733 63 16 16.5909413491474 -0.590941349147435 64 14 14.2618668653366 -0.261866865336586 65 16 15.2400247389463 0.759975261053662 66 17 16.1718988962265 0.828101103773525 67 18 16.1173030644178 1.88269693558220 68 18 14.6991351119578 3.30086488804221 69 12 15.6722816230555 -3.67228162305553 70 16 15.3696560764777 0.630343923522344 71 10 13.5866524120327 -3.58665241203271 72 14 14.195891330998 -0.195891330997995 73 18 16.5485343575736 1.45146564242638 74 18 16.9322355961949 1.06776440380514 75 16 15.8225188056093 0.177481194390746 76 17 13.8949822443110 3.10501775568903 77 16 16.1954946350854 -0.195494635085433 78 16 14.5038462571406 1.49615374285942 79 13 15.0129915707566 -2.01299157075665 80 16 15.7714379059751 0.228562094024866 81 16 15.5690883948052 0.430911605194758 82 16 15.7700278406369 0.229972159363086 83 15 15.8074459225013 -0.807445922501296 84 15 14.7876596578462 0.212340342153845 85 16 14.3564786199950 1.64352138000496 86 14 14.1571625912085 -0.157162591208454 87 16 15.3058751714197 0.69412482858025 88 16 14.4696171221247 1.53038287787534 89 15 14.2788274441128 0.7211725558872 90 12 13.6023588239322 -1.60235882393221 91 17 16.6269243638083 0.373075636191658 92 16 15.4318857904126 0.568114209587371 93 15 15.2277147708315 -0.227714770831518 94 13 15.0813275746976 -2.0813275746976 95 16 15.0442372330375 0.955762766962496 96 16 15.7295295273941 0.270470472605877 97 16 14.1462494894847 1.85375051051534 98 16 15.9702173667754 0.0297826332246363 99 14 14.4087389652808 -0.408738965280751 100 16 17.0669910224862 -1.06699102248624 101 16 14.7322268792687 1.26777312073132 102 20 17.3302055136579 2.66979448634214 103 15 14.6657299251388 0.334270074861174 104 16 14.4982176969474 1.50178230305259 105 13 15.1210647666331 -2.12106476663310 106 17 15.9044088002123 1.09559119978766 107 16 15.5814492454538 0.418550754546173 108 16 14.3481449641976 1.65185503580237 109 12 11.9053155487678 0.094684451232151 110 16 15.0609499367424 0.93905006325765 111 16 15.8229243141858 0.177075685814236 112 17 14.8455704288842 2.15442957111575 113 13 13.8834738038531 -0.883473803853104 114 12 14.7379256798790 -2.73792567987903 115 18 16.5795463429740 1.42045365702602 116 14 15.2281114767074 -1.22811147670738 117 14 12.99760178337 1.00239821663001 118 13 14.8993115345838 -1.89931153458377 119 16 15.6581955051037 0.341804494896255 120 13 14.0711360179465 -1.07113601794654 121 16 15.5535329647761 0.44646703522391 122 13 15.953286738566 -2.95328673856601 123 16 16.9658873937755 -0.965887393775536 124 15 16.1569827481446 -1.15698274814463 125 16 16.7580898664056 -0.758089866405574 126 15 15.4110906664556 -0.411090666455589 127 17 15.8522913759244 1.14770862407563 128 15 13.9760046762488 1.02399532375120 129 12 14.8005465356512 -2.80054653565118 130 16 14.1060139812216 1.89398601877845 131 10 13.3359227827828 -3.33592278278282 132 16 13.9381832706654 2.06181672933455 133 12 13.8537668978712 -1.85376689787117 134 14 15.5185421206393 -1.51854212063931 135 15 15.2365070835216 -0.236507083521641 136 13 12.0440600114522 0.955939988547835 137 15 14.4011861094136 0.598813890586377 138 11 13.1320965306762 -2.13209653067623 139 12 13.2328826440951 -1.23288264409513 140 11 13.3171512856996 -2.31715128569959 141 16 12.8930870818786 3.10691291812139 142 15 13.3481826926909 1.65181730730911 143 17 16.6251495125964 0.37485048740358 144 16 14.6920646620491 1.30793533795092 145 10 14.1015702832193 -4.10157028321931 146 18 15.7690449902574 2.23095500974265 147 13 14.9873219097028 -1.98732190970275 148 16 15.1318447564792 0.868155243520766 149 13 13.0275017473578 -0.0275017473578213 150 10 13.1303945600366 -3.13039456003662 151 15 16.0188472173771 -1.01884721737712 152 16 13.8617086186959 2.13829138130414 153 16 12.0158620853918 3.98413791460823 154 14 12.6607154650181 1.33928453498189 155 10 12.6056861353773 -2.60568613537734 156 17 16.3675035753915 0.63249642460849 157 13 11.6139167601168 1.38608323988323 158 15 13.8562720046718 1.1437279953282 159 16 15.0647264580226 0.935273541977356 160 12 12.4616481771048 -0.461648177104788 161 13 12.6278304637159 0.372169536284084 162 13 12.758427107309 0.241572892691002 163 12 11.5618691659864 0.438130834013596 164 17 16.0220011643078 0.977998835692165 165 15 14.2073181104066 0.792681889593414 166 10 12.6331863748027 -2.63318637480265 167 14 14.3683314267263 -0.368331426726333 168 11 13.7153437366674 -2.71534373666737 169 13 14.8885990551029 -1.88859905510292 170 16 15.2457979352778 0.754202064722216 171 12 10.2854991539590 1.71450084604098 172 16 15.5194638774246 0.480536122575433 173 12 12.8367523332627 -0.836752333262726 174 9 11.0531284391401 -2.05312843914015 175 12 14.1163175907024 -2.11631759070238 176 15 14.3370390705290 0.662960929471016 177 12 11.7885924976967 0.211407502303261 178 12 12.6880411523742 -0.688041152374181 179 14 13.7049789759084 0.295021024091621 180 12 13.0681347026367 -1.06813470263669 181 16 15.2128766609814 0.787123339018608 182 11 10.6554383572104 0.344561642789593 183 19 17.1463892904118 1.85361070958823 184 15 14.1941906406341 0.805809359365865 185 8 14.6477265300753 -6.64772653007528 186 16 15.2567874798764 0.743212520123645 187 17 14.1911457196704 2.80885428032959 188 12 11.2649899572791 0.735010042720903 189 11 11.4971440575779 -0.497144057577914 190 11 11.2351280597453 -0.235128059745261 191 14 15.2001378944469 -1.20013789444691 192 16 15.4639760819775 0.536023918022513 193 12 9.9368775832289 2.06312241677111 194 16 14.4575980137519 1.54240198624806 195 13 13.6527489527911 -0.652748952791132 196 15 15.0215787178556 -0.0215787178556023 197 16 12.7311147802860 3.26888521971396 198 16 15.2447717061704 0.75522829382964 199 14 12.4749815277244 1.52501847227564 200 16 14.7600932996358 1.23990670036416 201 16 13.8662886610248 2.13371133897524 202 14 13.7375099472516 0.262490052748416 203 11 12.9533618586172 -1.95336185861718 204 12 14.5378169642539 -2.53781696425391 205 15 12.6790316942382 2.32096830576176 206 15 14.6443393719584 0.355660628041642 207 16 14.4861613266570 1.51383867334304 208 16 15.5235111969253 0.47648880307465 209 11 13.2889439413281 -2.28894394132806 210 15 13.6080491455005 1.39195085449946 211 12 14.1204962557417 -2.12049625574171 212 12 16.0388683048002 -4.03886830480018 213 15 14.6686832368861 0.331316763113950 214 15 11.8253269043947 3.17467309560533 215 16 14.5931820436595 1.40681795634047 216 14 12.7320021377912 1.26799786220875 217 17 14.6079232240351 2.39207677596492 218 14 13.2042562296398 0.79574377036023 219 13 12.0539370739323 0.946062926067694 220 15 15.4547445845594 -0.454744584559391 221 13 14.0575639701153 -1.05756397011527 222 14 14.0515537515291 -0.0515537515290932 223 15 14.0233630034945 0.97663699650547 224 12 12.9139492925952 -0.913949292595166 225 13 13.1823819391275 -0.182381939127515 226 8 11.8885006117870 -3.88850061178705 227 14 14.1955491705540 -0.195549170553975 228 14 12.8633707502467 1.13662924975327 229 11 12.3464306860680 -1.34643068606797 230 12 12.7834452633280 -0.783445263327967 231 13 10.6660715861687 2.3339284138313 232 10 13.6996524618582 -3.69965246185824 233 16 11.5816154391062 4.41838456089384 234 18 15.2021717163673 2.79782828363267 235 13 13.3927306361125 -0.392730636112459 236 11 12.6034082064065 -1.60340820640646 237 4 10.2801833291943 -6.28018332919432 238 13 13.5153843221827 -0.515384322182697 239 16 13.8876536306327 2.11234636936726 240 10 10.6255327401344 -0.625532740134409 241 12 11.9868516800914 0.0131483199086112 242 12 13.7069303922495 -1.70693039224951 243 10 8.90314447342048 1.09685552657952 244 13 10.9048883644221 2.09511163557788 245 15 12.9156903284589 2.08430967154114 246 12 12.5990454991870 -0.599045499186962 247 14 13.1464960333700 0.853503966630049 248 10 12.9835984954948 -2.98359849549476 249 12 10.9368364127457 1.06316358725425 250 12 11.4240469083942 0.57595309160577 251 11 12.1229276563996 -1.12292765639964 252 10 11.4263977997735 -1.42639779977352 253 12 10.9394396280551 1.06056037194486 254 16 12.5083661523618 3.49163384763824 255 12 12.9982991105830 -0.99829911058297 256 14 13.6871325214264 0.312867478573634 257 16 14.4874778469839 1.51252215301612 258 14 11.7289415144362 2.27105848556385 259 13 14.0536540515759 -1.05365405157594 260 4 8.08400355852552 -4.08400355852552 261 15 13.8043898253624 1.19561017463758 262 11 15.3209721875729 -4.32097218757294 263 11 11.1048724893516 -0.104872489351615 264 14 12.7961332780032 1.20386672199677 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.99834241093483 0.00331517813033992 0.00165758906516996 20 0.995906117462993 0.00818776507401351 0.00409388253700675 21 0.990826282065173 0.0183474358696531 0.00917371793482656 22 0.98492508770394 0.0301498245921189 0.0150749122960595 23 0.977370010363987 0.0452599792720258 0.0226299896360129 24 0.968584787741185 0.0628304245176307 0.0314152122588153 25 0.95049422143068 0.0990115571386415 0.0495057785693208 26 0.930080053838236 0.139839892323528 0.0699199461617642 27 0.901301656325489 0.197396687349023 0.0986983436745114 28 0.912931732035046 0.174136535929909 0.0870682679649545 29 0.880683701505507 0.238632596988985 0.119316298494493 30 0.877212884686702 0.245574230626595 0.122787115313298 31 0.843656349020963 0.312687301958074 0.156343650979037 32 0.832330458063174 0.335339083873652 0.167669541936826 33 0.812231119340063 0.375537761319873 0.187768880659937 34 0.762488577442033 0.475022845115933 0.237511422557967 35 0.744420190177096 0.511159619645807 0.255579809822904 36 0.813288143244134 0.373423713511732 0.186711856755866 37 0.853115244027231 0.293769511945537 0.146884755972769 38 0.834344304551198 0.331311390897603 0.165655695448801 39 0.856005333760673 0.287989332478654 0.143994666239327 40 0.839466318647917 0.321067362704166 0.160533681352083 41 0.81114890516292 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0.000345001316703971 0.000690002633407943 0.999654998683296 227 0.000240104335768227 0.000480208671536454 0.999759895664232 228 0.000149924611790221 0.000299849223580443 0.99985007538821 229 9.76700348352581e-05 0.000195340069670516 0.999902329965165 230 5.84420960566556e-05 0.000116884192113311 0.999941557903943 231 6.14139037689193e-05 0.000122827807537839 0.999938586096231 232 0.000281736732812232 0.000563473465624465 0.999718263267188 233 0.00140086117832112 0.00280172235664225 0.99859913882168 234 0.0022897409492983 0.0045794818985966 0.997710259050702 235 0.00133784764113804 0.00267569528227608 0.998662152358862 236 0.00087359733824157 0.00174719467648314 0.999126402661758 237 0.0191809140129544 0.0383618280259088 0.980819085987046 238 0.0116537111785717 0.0233074223571434 0.988346288821428 239 0.00794413414283247 0.0158882682856649 0.992055865857168 240 0.0045361448222641 0.0090722896445282 0.995463855177736 241 0.00312583339726639 0.00625166679453277 0.996874166602734 242 0.00511790268749596 0.0102358053749919 0.994882097312504 243 0.00293062144810698 0.00586124289621395 0.997069378551893 244 0.00212476806185601 0.00424953612371202 0.997875231938144 245 0.00111381482442245 0.0022276296488449 0.998886185175577 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 62 0.273127753303965 NOK 5% type I error level 95 0.418502202643172 NOK 10% type I error level 123 0.541850220264317 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/10dpd41290957822.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/10dpd41290957822.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/1p7hb1290957822.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/1p7hb1290957822.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/2hgye1290957822.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/2hgye1290957822.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/3hgye1290957822.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/3hgye1290957822.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/4hgye1290957822.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/4hgye1290957822.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/5hgye1290957822.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/5hgye1290957822.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/6s7fh1290957822.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/6s7fh1290957822.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/73yw21290957822.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/73yw21290957822.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/83yw21290957822.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/83yw21290957822.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/9dpd41290957822.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290957747sjj27dpqr1piskh/9dpd41290957822.ps (open in new window)

Parameters (Session):

par1 = 8 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 8 ; 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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