*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: Mon, 22 Nov 2010 19:57:03 +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/22/t1290455725ps8xvne9bkf9zyf.htm/, Retrieved Mon, 22 Nov 2010 20:55:25 +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/22/t1290455725ps8xvne9bkf9zyf.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:

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7 5 1 6 5 7 5 2 1 6 2 3 5 6 3 6 6 3 5 6 2 4 4 6 8 6 3 2 6 2 6 5 2 7 3 3 6 5 2 6 5 1 4 6 2 5 3 2 5 6 4 6 5 5 5 5 4 7 4 1 5 5 1 7 1 6 6 5 2 4 6 1 7 6 1 1 6 1 7 5 3 6 6 2 6 5 2 4 4 1 7 6 5 5 6 3 7 6 2 5 5 2 5 4 5 6 3 2 8 5 4 4 5 2 7 5 2 6 4 2 5 5 2 3 5 2 7 6 5 3 6 2 5 5 1 5 3 1 10 7 4 5 4 3 5 6 1 5 5 2 4 6 3 5 4 3 4 6 2 5 5 4 5 6 2 2 6 5 5 4 1 6 7 2 6 5 3 7 2 5 5 6 4 2 4 5 5 4 3 3 6 1 8 5 5 6 5 6 5 5 2 5 5 3 5 5 1 7 5 4 5 7 2 5 6 6 5 7 5 6 6 5 5 6 1 5 1 5 5 7 3 3 4 3 7 6 2 7 2 3 7 5 3 5 3 5 7 6 2 5 4 2 4 4 2 6 5 2 5 6 3 2 4 3 5 5 3 7 4 5 4 5 5 3 3 2 5 6 3 6 4 4 5 6 2 7 6 5 6 5 1 5 4 2 5 6 6 4 5 2 5 5 6 6 4 5 6 5 3 7 5 6 6 5 5 2 6 6 4 6 4 2 6 5 6 6 3 2 4 4 6 5 2 5 4 3 5 7 7 2 6 7 5 6 2 5 4 7 5 5 2 6 2 5 7 5 2 2 6 2 6 6 2 4 5 6 8 5 3 6 6 6 7 5 5 4 6 4 5 6 2 3 5 5 6 6 5 3 5 2 6 3 2 3 5 6 5 5 1 6 5 3 5 5 3 6 3 2 5 6 4 5 4 2 5 5 2 3 1 5 4 5 4 3 5 3 6 4 4 2 2 4 6 5 3 3 6 5 6 5 2 3 5 7 6 2 1 5 2 2 7 6 5 3 6 5 7 6 2 5 5 6 5 6 4 2 6 4 7 6 4 5 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 12 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Cry_Sad[t] = + 1.55818696167561 + 0.00970850787920307Age[t] + 0.216489180560649Use_hands[t] + 0.273494403108749Hand_on_hips[t] + 0.148458261933412Quiet_FirstMeeting[t] -0.138792085520547Outgoing_individual[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) 1.55818696167561 1.156205 1.3477 0.179692 0.089846 Age 0.00970850787920307 0.118536 0.0819 0.934827 0.467413 Use_hands 0.216489180560649 0.129833 1.6674 0.097406 0.048703 Hand_on_hips 0.273494403108749 0.099789 2.7407 0.006837 0.003418 Quiet_FirstMeeting 0.148458261933412 0.086712 1.7121 0.088842 0.044421 Outgoing_individual -0.138792085520547 0.103965 -1.335 0.1838 0.0919 Multiple Linear Regression - Regression Statistics Multiple R 0.294897539336513 R-squared 0.0869645587067305 Adjusted R-squared 0.0580710320835258 F-TEST (value) 3.00982845883853 F-TEST (DF numerator) 5 F-TEST (DF denominator) 158 p-value 0.0126753249430451 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.74510105898936 Sum Squared Residuals 481.169677561553 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7 3.17887596673976 3.82112403326024 2 3 2.92636766586105 0.0736323341389457 3 3 3.78414485223896 -0.784144852238956 4 6 3.49131809630448 2.50868190369552 5 2 3.21943732814292 -1.21943732814292 6 3 3.86870429494382 -0.868704294943817 7 1 3.44266186196931 -2.44266186196931 8 2 3.76885993587923 -1.76885993587923 9 5 4.19643134086825 0.803568659131747 10 1 4.26719250776156 -3.26719250776156 11 6 3.86308555499696 2.13691444500304 12 1 3.00695325258194 -2.00695325258194 13 1 2.51428175211280 -1.51428175211280 14 2 3.58707268743671 -1.58707268743671 15 1 3.28453742362303 -2.28453742362303 16 3 4.20209241228145 -1.20209241228145 17 2 3.52040128847575 -1.52040128847575 18 2 4.3145315538968 -2.3145315538968 19 2 3.71215116007839 -1.71215116007839 20 2 3.59116245536906 -1.59116245536906 21 2 2.98757856828987 -0.98757856828987 22 2 3.90517588841462 -1.90517588841462 23 1 3.28858486008904 -2.28858486008904 24 3 4.45179688441205 -1.45179688441205 25 2 3.22748986960859 -1.22748986960859 26 3 3.90356225346744 -0.903562253467436 27 4 3.49127576483814 0.50872423516186 28 5 2.91681740139656 2.08318259860344 29 2 2.66538559937961 -0.665385599379614 30 5 4.28099078357311 0.719009216426887 31 5 3.74139037865515 1.25860962134485 32 1 2.90579170531742 -1.90579170531742 33 6 4.28256208705396 1.71743791294604 34 3 3.28449509215669 -0.284495092156694 35 4 3.30791721291477 0.69208278708523 36 6 3.57868136775744 2.42131863224256 37 5 4.5476228390171 0.452377160982898 38 5 3.78265821169078 1.21734178830922 39 3 3.83284341804046 -0.832843418040463 40 3 4.23369406890422 -1.23369406890422 41 5 3.85499068206494 1.14500931793506 42 2 3.6591933739963 -1.65919337399630 43 2 3.20675566565026 -1.20675566565025 44 3 3.4678959755464 -0.467895975546402 45 5 3.99369810465281 1.00630189534719 46 2 4.07593744077801 -2.07593744077801 47 4 4.06172902328005 -0.0617290232800512 48 5 3.65910871106362 1.34089128893638 49 2 3.15950128244770 -1.15950128244770 50 2 4.44650362321893 -2.44650362321893 51 5 4.66572305204565 0.334276947954352 52 6 3.86461452701147 2.13538547298853 53 6 3.53051993804136 2.46948006195864 54 5 3.45409769973485 1.54590230026515 55 4 3.47760448342561 0.522395516574395 56 3 3.43299568555644 -0.432995685556445 57 7 4.50077859750095 2.49922140249905 58 7 3.63977635823789 3.36022364176211 59 5 3.84932961065175 1.15067038934825 60 2 2.71974523659432 -0.719745236594316 61 6 3.36223451866313 2.63776548133687 62 6 3.59678119531592 2.40321880468408 63 4 3.83714496978739 0.162855030212614 64 5 3.20406774885052 1.79593225114948 65 2 4.03425946605597 -2.03425946605597 66 6 2.56430871504778 3.43569128495222 67 3 3.15945895098136 -0.159458950981358 68 2 3.98403192823995 -1.98403192823995 69 2 4.18676516445539 -2.18676516445539 70 5 3.54274691037206 1.45725308962794 71 3 3.52485886662816 -0.524858866628164 72 4 3.59570469645415 0.404295303545848 73 5 3.13198939375727 1.86801060624273 74 7 2.99728707616907 4.00271292383093 75 2 2.78761791180685 -0.787617911806846 76 5 3.90517588841462 1.09482411158538 77 6 3.52040128847575 2.47959871152425 78 4 3.46380620761406 0.536193792385944 79 3 4.34497426573434 -1.34497426573434 80 6 4.11873424582815 1.88126575417185 81 5 3.57174543961065 1.42825456038935 82 2 3.63977635823789 -1.63977635823789 83 5 3.00703791551461 1.99296208448539 84 3 3.46207887772772 -0.462078877727716 85 6 4.48777145625456 1.51222854374544 86 5 3.93987560352353 1.06012439647647 87 1 3.2371983774878 -2.23719837748780 88 5 2.25764135183541 2.74235864816459 89 2 3.28449509215669 -1.28449509215669 90 1 3.29416126856956 -2.29416126856956 91 4 4.59905165308468 -0.599051653084684 92 2 3.43299568555644 -1.43299568555644 93 3 3.22753220107493 -0.227532201074933 94 5 3.78827695163764 1.21172304836236 95 6 3.21782369319573 2.78217630680427 96 4 4.5145768733125 -0.5145768733125 97 4 3.12637065381042 0.873629346189583 98 5 2.99439858448829 2.00560141551171 99 1 2.22976165292492 -1.22976165292492 100 6 4.65336895883305 1.34663104116695 101 2 3.08874011555439 -1.08874011555438 102 3 3.21377625672972 -0.213776256729721 103 5 3.3039121079151 1.6960878920849 104 2 2.79451150848730 -0.794511508487297 105 2 3.20411008031686 -1.20411008031686 106 3 3.65357463404944 -0.65357463404944 107 2 2.78211508380836 -0.782115083808357 108 6 3.97432342036075 2.02567657963925 109 3 3.73730061072280 -0.737300610722804 110 2 2.76835913946315 -0.768359139463147 111 1 3.10399378289841 -2.10399378289841 112 1 3.06122822686396 -2.06122822686396 113 1 2.98757856828987 -1.98757856828987 114 4 3.70240032073285 0.297599679267153 115 1 2.56426638358144 -1.56426638358144 116 1 3.61094728134753 -2.61094728134753 117 1 3.6535323025831 -2.6535323025831 118 5 2.71974523659432 2.28025476340568 119 5 3.53002513342228 1.46997486657772 120 2 2.22976165292492 -0.229761652924919 121 3 3.50098427271734 -0.500984272717343 122 5 2.78079789560842 2.21920210439158 123 2 3.41391744801163 -1.41391744801163 124 2 3.49127576483814 -1.49127576483814 125 4 4.25347889488269 -0.253478894882691 126 1 2.71003672871511 -1.71003672871511 127 5 4.53799899407058 0.462001005929424 128 1 2.80148976810043 -1.80148976810043 129 2 3.19031180450531 -1.19031180450531 130 2 3.57174543961065 -1.57174543961065 131 6 3.6535323025831 2.3464676974169 132 2 3.22348476460892 -1.22348476460892 133 1 2.28804173220661 -1.28804173220661 134 3 3.05136147557005 -0.0513614755700526 135 4 3.57174543961065 0.428254560389346 136 6 2.83222670967601 3.16777329032399 137 5 4.20618218021379 0.793817819786206 138 6 4.3922286489369 1.6077713510631 139 6 3.58149627895620 2.41850372104380 140 1 3.69686624371867 -2.69686624371867 141 6 2.94165258222078 3.05834741777922 142 2 3.04012621268556 -1.04012621268556 143 2 3.27482891574383 -1.27482891574383 144 7 3.36219218719680 3.63780781280320 145 2 3.21377625672972 -1.21377625672972 146 2 3.38458014055944 -1.38458014055944 147 6 3.28449509215669 2.71550490784331 148 1 3.40817171366576 -2.40817171366576 149 2 3.28449509215669 -1.28449509215669 150 3 3.62201530889301 -0.62201530889301 151 4 4.02455095817676 -0.0245509581767641 152 5 3.33881239790506 1.66118760209494 153 5 4.35464044214721 0.645359557852794 154 6 3.94797269346477 2.05202730653523 155 3 2.74887076023193 0.251129239768074 156 1 3.5455930705865 -2.54559307058650 157 3 3.07498417120917 -0.0749841712091741 158 2 3.34690727083707 -1.34690727083707 159 3 3.65915104252996 -0.659151042529958 160 7 3.42621800082436 3.57378199917564 161 3 3.54411763897186 -0.544117638971863 162 4 2.93623441715497 1.06376558284503 163 6 3.80810410908245 2.19189589091755 164 2 3.08874011555439 -1.08874011555438 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.974996065380306 0.0500078692393887 0.0250039346196943 10 0.9565357202588 0.0869285594823997 0.0434642797411998 11 0.934663137408068 0.130673725183864 0.065336862591932 12 0.925183917830507 0.149632164338986 0.0748160821694931 13 0.915385908426075 0.169228183147851 0.0846140915739254 14 0.876217339208671 0.247565321582658 0.123782660791329 15 0.858736210101172 0.282527579797656 0.141263789898828 16 0.829552353283279 0.340895293433442 0.170447646716721 17 0.826450450784042 0.347099098431916 0.173549549215958 18 0.780126868195956 0.439746263608089 0.219873131804044 19 0.722475243573832 0.555049512852337 0.277524756426168 20 0.707773957092161 0.584452085815678 0.292226042907839 21 0.642648549369618 0.714702901260764 0.357351450630382 22 0.592087626899615 0.81582474620077 0.407912373100385 23 0.639806425502704 0.720387148994592 0.360193574497296 24 0.5938158235311 0.812368352937801 0.406184176468901 25 0.555501492210643 0.888997015578714 0.444498507789357 26 0.489555256633935 0.97911051326787 0.510444743366065 27 0.446757480732435 0.89351496146487 0.553242519267565 28 0.560298002888207 0.879403994223586 0.439701997111793 29 0.49814956386268 0.99629912772536 0.50185043613732 30 0.476916638011188 0.953833276022375 0.523083361988812 31 0.505416919361387 0.989166161277226 0.494583080638613 32 0.460933953153486 0.921867906306973 0.539066046846514 33 0.606978719130235 0.78604256173953 0.393021280869765 34 0.551021102639993 0.897957794720015 0.448978897360007 35 0.507286016868483 0.985427966263034 0.492713983131517 36 0.547733331335215 0.90453333732957 0.452266668664785 37 0.497746399245037 0.995492798490073 0.502253600754963 38 0.452931039830518 0.905862079661037 0.547068960169482 39 0.413100826000751 0.826201652001503 0.586899173999249 40 0.395897820383593 0.791795640767186 0.604102179616407 41 0.399575359537206 0.799150719074411 0.600424640462795 42 0.38947018515494 0.77894037030988 0.61052981484506 43 0.349441440292239 0.698882880584478 0.650558559707761 44 0.301296380335658 0.602592760671315 0.698703619664342 45 0.280859149865838 0.561718299731677 0.719140850134162 46 0.264357248452878 0.528714496905755 0.735642751547122 47 0.223000738639627 0.446001477279254 0.776999261360373 48 0.200797390405569 0.401594780811137 0.799202609594431 49 0.177575752489091 0.355151504978183 0.822424247510909 50 0.181639114755494 0.363278229510987 0.818360885244506 51 0.170889976536483 0.341779953072966 0.829110023463517 52 0.201612514568947 0.403225029137894 0.798387485431053 53 0.340938140746039 0.681876281492079 0.65906185925396 54 0.345839535244814 0.691679070489628 0.654160464755186 55 0.313278738861509 0.626557477723019 0.686721261138491 56 0.272145415855966 0.544290831711933 0.727854584144034 57 0.320972914106306 0.641945828212611 0.679027085893694 58 0.436537141396479 0.873074282792958 0.563462858603521 59 0.412373974177706 0.824747948355412 0.587626025822294 60 0.370247059244743 0.740494118489486 0.629752940755257 61 0.429262173527589 0.858524347055178 0.570737826472411 62 0.496597029159282 0.993194058318563 0.503402970840718 63 0.455155188797444 0.910310377594888 0.544844811202556 64 0.453653469560024 0.907306939120049 0.546346530439976 65 0.464798830318537 0.929597660637075 0.535201169681463 66 0.637954035992298 0.724091928015403 0.362045964007702 67 0.594456601740538 0.811086796518924 0.405543398259462 68 0.601969555409552 0.796060889180896 0.398030444590448 69 0.625303751698577 0.749392496602847 0.374696248301423 70 0.616677541619119 0.766644916761762 0.383322458380881 71 0.57521999755519 0.84956000488962 0.42478000244481 72 0.535965037170581 0.928069925658837 0.464034962829419 73 0.54021913527067 0.91956172945866 0.45978086472933 74 0.712326715335315 0.57534656932937 0.287673284664685 75 0.6782809052862 0.6434381894276 0.3217190947138 76 0.651704141690489 0.696591716619022 0.348295858309511 77 0.686148418082358 0.627703163835284 0.313851581917642 78 0.647527012663827 0.704945974672346 0.352472987336173 79 0.631341116391965 0.737317767216071 0.368658883608035 80 0.640493742531083 0.719012514937833 0.359506257468917 81 0.624725060127521 0.750549879744957 0.375274939872478 82 0.621720435139042 0.756559129721915 0.378279564860958 83 0.629787372007689 0.740425255984621 0.370212627992311 84 0.589612730956712 0.820774538086575 0.410387269043288 85 0.578332475673402 0.843335048653196 0.421667524326598 86 0.55284616842416 0.89430766315168 0.44715383157584 87 0.584681949566084 0.830636100867832 0.415318050433916 88 0.661989787656197 0.676020424687606 0.338010212343803 89 0.64313002258452 0.71373995483096 0.35686997741548 90 0.676596500162945 0.64680699967411 0.323403499837055 91 0.642148961120788 0.715702077758424 0.357851038879212 92 0.632037915717765 0.735924168564469 0.367962084282235 93 0.58898569011762 0.822028619764759 0.411014309882380 94 0.55976389907964 0.88047220184072 0.44023610092036 95 0.628320659248211 0.743358681503578 0.371679340751789 96 0.589242745765801 0.821514508468398 0.410757254234199 97 0.560230023225509 0.879539953548982 0.439769976774491 98 0.588592810905026 0.822814378189948 0.411407189094974 99 0.564480184885519 0.871039630228962 0.435519815114481 100 0.541115107404402 0.917769785191197 0.458884892595598 101 0.512816916935891 0.974366166128217 0.487183083064109 102 0.466693590018455 0.93338718003691 0.533306409981545 103 0.457851110652312 0.915702221304623 0.542148889347688 104 0.418497371767018 0.836994743534036 0.581502628232982 105 0.391358388666072 0.782716777332144 0.608641611333928 106 0.352249779196565 0.70449955839313 0.647750220803435 107 0.316077398098936 0.632154796197873 0.683922601901063 108 0.332967986764845 0.66593597352969 0.667032013235155 109 0.295423269175015 0.59084653835003 0.704576730824985 110 0.260132102366225 0.52026420473245 0.739867897633775 111 0.301832995924026 0.603665991848053 0.698167004075974 112 0.305451680309493 0.610903360618985 0.694548319690507 113 0.303882450737785 0.60776490147557 0.696117549262215 114 0.262373043450682 0.524746086901364 0.737626956549318 115 0.245978977269208 0.491957954538416 0.754021022730792 116 0.307074518959040 0.614149037918079 0.69292548104096 117 0.361877048423927 0.723754096847855 0.638122951576073 118 0.39558071806424 0.79116143612848 0.60441928193576 119 0.365459139807773 0.730918279615545 0.634540860192227 120 0.317320274797212 0.634640549594423 0.682679725202788 121 0.275595833998396 0.551191667996792 0.724404166001604 122 0.311454673154099 0.622909346308198 0.688545326845901 123 0.328602996372559 0.657205992745118 0.671397003627441 124 0.303580902671088 0.607161805342177 0.696419097328912 125 0.269081513082065 0.53816302616413 0.730918486917935 126 0.255735034914187 0.511470069828374 0.744264965085813 127 0.213822241517179 0.427644483034358 0.786177758482821 128 0.207043729341392 0.414087458682783 0.792956270658609 129 0.181481121273278 0.362962242546557 0.818518878726722 130 0.178974100314505 0.357948200629011 0.821025899685495 131 0.214579853874768 0.429159707749536 0.785420146125232 132 0.197487266941452 0.394974533882904 0.802512733058548 133 0.182128977914174 0.364257955828349 0.817871022085826 134 0.145045634275589 0.290091268551178 0.854954365724411 135 0.114302335895837 0.228604671791674 0.885697664104163 136 0.223882087797174 0.447764175594348 0.776117912202826 137 0.18064149280325 0.3612829856065 0.81935850719675 138 0.154519174441734 0.309038348883468 0.845480825558266 139 0.211982744888525 0.423965489777049 0.788017255111475 140 0.219277895852672 0.438555791705345 0.780722104147328 141 0.326154613320955 0.65230922664191 0.673845386679045 142 0.287388035481624 0.574776070963247 0.712611964518376 143 0.240750004039749 0.481500008079497 0.759249995960251 144 0.484064967446122 0.968129934892244 0.515935032553878 145 0.436992607599138 0.873985215198276 0.563007392400862 146 0.367498736490788 0.734997472981576 0.632501263509212 147 0.658412225852456 0.683175548295088 0.341587774147544 148 0.665802146519045 0.66839570696191 0.334197853480955 149 0.590309720491302 0.819380559017396 0.409690279508698 150 0.603525609248655 0.79294878150269 0.396474390751345 151 0.571704446033106 0.856591107933788 0.428295553966894 152 0.494102837791862 0.988205675583725 0.505897162208138 153 0.374992225269011 0.749984450538022 0.625007774730989 154 0.258609892777430 0.517219785554859 0.74139010722257 155 0.541951122606672 0.916097754786655 0.458048877393328 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 0 0 OK 10% type I error level 2 0.0136054421768707 OK

Charts produced by software:

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Parameters (Session):

par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 6 ; 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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