Workshop 7 (2)

*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, 23 Nov 2010 17:11:29 +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/23/t1290532383j4oxk6db70rwscw.htm/, Retrieved Tue, 23 Nov 2010 18:13:03 +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/23/t1290532383j4oxk6db70rwscw.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 «

10 5 4 20 2 2 40 6 5 67 6 5 38 5 2 61 5 2 29 6 4 0 5 7 30 6 6 39 5 4 70 6 1 65 5 4 5 5 1 30 4 5 50 7 5 90 5 5 45 4 4 75 6 3 76 6 5 15 5 5 10 5 5 0 5 4 60 6 4 67 5 2 60 6 1 70 6 2 70 5 3 87 6 3 27 6 2 65 5 2 56 5 6 82 6 5 30 5 3 38 6 5 56 6 5 70 6 2 80 6 4 71 6 3 50 5 1 31 5 2 40 6 5 71 6 2 71 5 2 10 5 5 20 5 5 40 6 2 55 2 2 80 7 3 80 5 1 72 7 2 60 6 2 29 6 4 70 5 2 60 4 5 63 6 2 70 7 2 38 5 2 40 6 5 80 6 2 24 5 5 40 5 4 47 6 1 70 5 1 70 5 2 75 2 5 60 5 5 65 5 3 91 5 2 68 5 5 80 6 2 90 4 5 20 5 2 61 6 3 13 3 6 80 6 3 40 5 4 70 5 2 39 6 3 93 6 5 10 6 5 25 6 3 61 5 2 18 3 5 60 6 2 74 6 3 35 5 1 0 5 5 71 5 2 100 6 1 64 6 5 50 6 2 40 5 2 35 4 4 60 5 4 70 7 2 55 3 4 65 6 2 30 6 2 25 2 1 80 7 4 26 5 6 78 6 4 10 5 7 70 4 1 0 3 2 65 6 1 80 6 2 60 5 1 67 6 5 49 6 3 70 5 2 66 6 3 65 4 3 65 6 5 40 6 1 40 5 2 20 7 2 90 6 5 48 6 2 25 6 1 35 5 2 40 6 5 77 5 2 70 3 5 82 5 1 80 5 2 52 3 5 71 5 4 70 5 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 9 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Talk[t] = + 24.4193932409404 + 5.90853825248459Hands[t] -2.84218524641860`Anxiety `[t] + 0.103795203388895t + 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) 24.4193932409404 11.180542 2.1841 0.030585 0.015292 Hands 5.90853825248459 1.75744 3.362 0.000993 0.000496 `Anxiety ` -2.84218524641860 1.1976 -2.3732 0.018963 0.009481 t 0.103795203388895 0.043746 2.3727 0.018991 0.009495 Multiple Linear Regression - Regression Statistics Multiple R 0.383098887279335 R-squared 0.146764757434664 Adjusted R-squared 0.128864717380846 F-TEST (value) 8.1991301133071 F-TEST (DF numerator) 3 F-TEST (DF denominator) 143 p-value 4.49862710907301e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 22.3119148715918 Sum Squared Residuals 71188.4809689135 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 10 42.6971387210778 -32.6971387210778 2 20 30.7596896598501 -10.7596896598501 3 40 45.9710821339216 -5.97108213392158 4 67 46.0748773373105 20.9251226626895 5 38 48.7966900274706 -10.7966900274706 6 61 48.9004852308595 12.0995147691405 7 29 49.2284481938958 -20.2284481938958 8 0 34.8971494055443 -34.8971494055443 9 30 43.7516681078363 -13.7516681078363 10 39 43.6312955515779 -4.63129555157786 11 70 58.1701847467072 11.8298152532928 12 65 43.8388859583556 21.1611140416443 13 5 52.4692369010004 -47.4692369010004 14 30 35.2957528662303 -5.29575286623025 15 50 53.1251628270729 -3.12516282707290 16 90 41.4118815254926 48.5881184745074 17 45 38.4493237228155 6.55067627718446 18 75 53.2123806775922 21.7876193224078 19 76 47.6318053881439 28.3681946118561 20 15 41.8270623390482 -26.8270623390482 21 10 41.9308575424371 -31.9308575424371 22 0 44.8768379922446 -44.8768379922446 23 60 50.8891714481181 9.11082855188192 24 67 50.7687988918596 16.2312011081404 25 60 59.6233175941517 0.37668240584831 26 70 56.884927551122 13.1150724488780 27 70 48.2379992556077 21.7620007443923 28 87 54.2503327114812 32.7496672885188 29 27 57.1963131612887 -30.1963131612887 30 65 51.391570112193 13.6084298878070 31 56 40.1266243299075 15.8733756700926 32 82 48.9811430321995 33.0188569678005 33 30 48.8607704759411 -18.8607704759411 34 38 49.1887334389773 -11.1887334389773 35 56 49.2925286423662 6.70747135763378 36 70 57.9228795850109 12.0771204149891 37 80 52.3423042955626 27.6576957044374 38 71 55.2882847453701 15.7117152546299 39 50 55.1679121891116 -5.16791218911163 40 31 52.4295221460819 -21.4295221460819 41 40 49.9152998626996 -9.9152998626996 42 71 58.5456508053443 12.4543491946557 43 71 52.7409077562486 18.2590922437514 44 10 44.3181472203817 -34.3181472203817 45 20 44.4219424237706 -24.4219424237706 46 40 58.9608316188999 -18.9608316188999 47 55 35.4304738123504 19.5695261876496 48 80 62.2347750317437 17.7652249682564 49 80 56.2058642230006 23.7941357769994 50 72 65.28455068494 6.71544931505995 51 60 59.4798076358444 0.520192364155644 52 29 53.899232346396 -24.8992323463960 53 70 53.7788597901376 16.2211402098624 54 60 39.4475610017861 20.5524389982139 55 63 59.8949884493999 3.10501155060006 56 70 65.9073219052734 4.09267809472658 57 38 54.1940406036931 -16.1940406036931 58 40 51.6798183203108 -11.6798183203108 59 80 60.3101692629555 19.6898307370445 60 24 45.978870474604 -21.978870474604 61 40 48.9248509244115 -8.92485092441151 62 47 63.4637401195408 -16.4637401195408 63 70 57.6589970704451 12.3410029295549 64 70 54.9206070274154 15.0793929725846 65 75 28.7722317340947 46.2277682659053 66 60 46.6016416949374 13.3983583050626 67 65 52.3898073911635 12.6101926088365 68 91 55.335787840971 35.664212159029 69 68 46.9130273051041 21.0869726948959 70 80 61.4519165002334 18.5480834997666 71 90 41.2120794593973 48.7879205406027 72 20 55.7509686545266 -35.7509686545266 73 61 58.9211168639814 2.07888313601856 74 13 32.7727415706608 -19.7727415706608 75 80 59.1287072707592 20.8712927292408 76 40 50.4817789752449 -10.4817789752449 77 70 56.269944671471 13.7300553285290 78 39 59.4400928809259 -20.4400928809259 79 93 53.8595175914776 39.1404824085224 80 10 53.9633127948665 -43.9633127948665 81 25 59.7514784910926 -34.7514784910926 82 61 56.7889206884155 4.21107931158448 83 18 36.5490836475794 -18.5490836475794 84 60 62.9050493476779 -2.90504934767789 85 74 60.1666593046482 13.8333406953518 86 35 60.0462867483897 -25.0462867483897 87 0 48.7813409661042 -48.7813409661042 88 71 57.4116919087489 13.5883080912511 89 100 66.266210611041 33.733789388959 90 64 55.0012648287555 8.99873517124455 91 50 63.6316157714002 -13.6316157714002 92 40 57.8268727223045 -17.8268727223045 93 35 46.3377591803716 -11.3377591803716 94 60 52.350092636245 7.64990736375495 95 70 69.9553348374403 0.0446651625596758 96 55 40.7406065380537 14.2593934619463 97 65 64.2543869917335 0.74561300826647 98 30 64.3581821951224 -34.3581821951224 99 25 43.6700096349916 -18.6700096349916 100 80 64.7899403615476 15.2100596384524 101 26 47.3922885671301 -21.3922885671301 102 78 59.0889925158408 18.9110074841592 103 10 44.7576937274893 -34.7576937274893 104 70 56.0060621569052 13.9939378430948 105 0 47.3591338613909 -47.3591338613909 106 65 68.0307290686522 -3.03072906865219 107 80 65.2923390256225 14.7076609743775 108 60 62.3297812229454 -2.32978122294539 109 67 56.9733736931445 10.0266263068555 110 49 62.7615393893706 -13.7615393893706 111 70 59.7989815866935 10.2010184133065 112 66 62.9691297961484 3.03087020385165 113 65 51.2558484945681 13.7441515054319 114 65 57.4923497100889 7.50765028991107 115 40 68.9648858991523 -28.9648858991523 116 40 60.317957603638 -20.3179576036380 117 20 72.238829311996 -52.238829311996 118 90 57.9075305236445 32.0924694763555 119 48 66.5378814662892 -18.5378814662892 120 25 69.4838619160967 -44.4838619160967 121 35 60.8369336205824 -25.8369336205824 122 40 58.3227113372001 -18.3227113372001 123 77 61.0445240273602 15.9554759726398 124 70 40.8046869865241 29.1953130134759 125 82 64.0942996805566 17.9057003194434 126 80 61.3559096375269 18.6440903624731 127 52 41.1160725966908 10.8839274033092 128 71 55.8791295514675 15.1208704485325 129 70 61.6672952476936 8.33270475230642 130 50 59.1530729643112 -9.15307296431125 131 72 59.2568681677001 12.7431318322999 132 80 65.0450338639262 14.9549661360737 133 91 70.8331995601524 20.1668004398476 134 18 44.4606565071843 -26.4606565071843 135 70 53.5393429691238 16.4606570308762 136 76 59.3275086653499 16.6724913346501 137 65 68.4061951272893 -3.40619512728933 138 35 68.5099903306782 -33.5099903306782 139 62 68.6137855340671 -6.61378553406712 140 76 68.717580737456 7.28241926254398 141 50 60.2948202015891 -10.2948202015891 142 68 63.2408006513966 4.7591993486034 143 80 63.1204280951381 16.8795719048619 144 90 69.356929310659 20.6430706893410 145 79 54.8014627626601 24.1985372373399 146 30 48.9967197135644 -18.9967197135644 147 60 55.0090531694379 4.99094683056212 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.67056394384879 0.658872112302421 0.329436056151211 8 0.610575911765004 0.778848176469992 0.389424088234996 9 0.471354703588985 0.94270940717797 0.528645296411015 10 0.349134556170554 0.698269112341108 0.650865443829446 11 0.241929133221131 0.483858266442261 0.75807086677887 12 0.278649336719176 0.557298673438352 0.721350663280824 13 0.699693188029948 0.600613623940105 0.300306811970052 14 0.629820751876072 0.740358496247856 0.370179248123928 15 0.540286910138819 0.919426179722361 0.459713089861181 16 0.800998894921012 0.398002210157977 0.199001105078989 17 0.738478131711032 0.523043736577936 0.261521868288968 18 0.689142391103845 0.62171521779231 0.310857608896155 19 0.649054532732649 0.701890934534702 0.350945467267351 20 0.758294055264023 0.483411889471954 0.241705944735977 21 0.8296310821702 0.340737835659601 0.170368917829800 22 0.915365012751755 0.169269974496489 0.0846349872482447 23 0.889797089787214 0.220405820425571 0.110202910212786 24 0.869882031621839 0.260235936756322 0.130117968378161 25 0.834752677922916 0.330494644154169 0.165247322077085 26 0.795917480659858 0.408165038680284 0.204082519340142 27 0.778688786531312 0.442622426937376 0.221311213468688 28 0.78161603738513 0.436767925229741 0.218383962614871 29 0.85592418742653 0.288151625146941 0.144075812573471 30 0.824351999403946 0.351296001192109 0.175648000596054 31 0.793212869921458 0.413574260157084 0.206787130078542 32 0.796237391880487 0.407525216239026 0.203762608119513 33 0.807913831120468 0.384172337759063 0.192086168879532 34 0.796161194017905 0.407677611964191 0.203838805982095 35 0.754045715912383 0.491908568175234 0.245954284087617 36 0.710256913001224 0.579486173997553 0.289743086998777 37 0.698748552856117 0.602502894287767 0.301251447143883 38 0.656037122736709 0.687925754526582 0.343962877263291 39 0.619629533782894 0.760740932434213 0.380370466217106 40 0.638301591202303 0.723396817595395 0.361698408797697 41 0.616628097544596 0.766743804910809 0.383371902455404 42 0.569413635109088 0.861172729781824 0.430586364890912 43 0.538191535882942 0.923616928234116 0.461808464117058 44 0.622607477431366 0.754785045137267 0.377392522568634 45 0.62972862295977 0.74054275408046 0.37027137704023 46 0.634992698629243 0.730014602741514 0.365007301370757 47 0.655571670250468 0.688856659499065 0.344428329749532 48 0.621299127613674 0.757401744772651 0.378700872386326 49 0.608653504107797 0.782692991784406 0.391346495892203 50 0.56305455600913 0.87389088798174 0.43694544399087 51 0.516787171659211 0.966425656681578 0.483212828340789 52 0.544635413376129 0.910729173247742 0.455364586623871 53 0.512212824717463 0.975574350565074 0.487787175282537 54 0.501811008038784 0.996377983922433 0.498188991961216 55 0.454324064185136 0.908648128370273 0.545675935814864 56 0.408681488865842 0.817362977731685 0.591318511134158 57 0.397509753779794 0.795019507559588 0.602490246220206 58 0.367923129855174 0.735846259710347 0.632076870144826 59 0.347015673845593 0.694031347691185 0.652984326154407 60 0.348340620051534 0.696681240103068 0.651659379948466 61 0.312267768178312 0.624535536356624 0.687732231821688 62 0.304436078018594 0.608872156037189 0.695563921981406 63 0.271827067155893 0.543654134311787 0.728172932844107 64 0.246700084553629 0.493400169107258 0.753299915446371 65 0.377148189288415 0.754296378576829 0.622851810711585 66 0.341948706318311 0.683897412636622 0.658051293681689 67 0.307982998941384 0.615965997882767 0.692017001058616 68 0.361686190757266 0.723372381514532 0.638313809242734 69 0.348735927859267 0.697471855718534 0.651264072140733 70 0.334090570703171 0.668181141406342 0.665909429296829 71 0.497947832752172 0.995895665504344 0.502052167247828 72 0.599285189499979 0.801429621000043 0.400714810500021 73 0.559182689757083 0.881634620485834 0.440817310242917 74 0.563222356776715 0.87355528644657 0.436777643223285 75 0.563663770487821 0.872672459024358 0.436336229512179 76 0.533479161901617 0.933041676196765 0.466520838098383 77 0.515806088111293 0.968387823777413 0.484193911888707 78 0.511795718395567 0.976408563208866 0.488204281604433 79 0.631886932255784 0.736226135488433 0.368113067744216 80 0.74521125706578 0.50957748586844 0.25478874293422 81 0.790251639977637 0.419496720044727 0.209748360022363 82 0.761624925288038 0.476750149423925 0.238375074711962 83 0.74600740622646 0.50798518754708 0.25399259377354 84 0.70848782617095 0.583024347658101 0.291512173829050 85 0.693313617898338 0.613372764203324 0.306686382101662 86 0.694651107995057 0.610697784009886 0.305348892004943 87 0.822291996306271 0.355416007387457 0.177708003693729 88 0.809222781213768 0.381554437572465 0.190777218786232 89 0.875656120434487 0.248687759131025 0.124343879565513 90 0.857239821158232 0.285520357683535 0.142760178841768 91 0.833997464123938 0.332005071752123 0.166002535876062 92 0.814150959854737 0.371698080290525 0.185849040145263 93 0.783716806622736 0.432566386754527 0.216283193377264 94 0.75564533651153 0.488709326976941 0.244354663488471 95 0.720641179251297 0.558717641497406 0.279358820748703 96 0.708367381327561 0.583265237344877 0.291632618672439 97 0.672581988504357 0.654836022991286 0.327418011495643 98 0.700691635541425 0.598616728917151 0.299308364458576 99 0.671931191234062 0.656137617531877 0.328068808765939 100 0.665951246668313 0.668097506663374 0.334048753331687 101 0.650593460572996 0.698813078854008 0.349406539427004 102 0.659982327098215 0.680035345803569 0.340017672901785 103 0.734992349605684 0.530015300788633 0.265007650394316 104 0.732713496470639 0.534573007058722 0.267286503529361 105 0.862540251492215 0.274919497015569 0.137459748507785 106 0.832741900515462 0.334516198969076 0.167258099484538 107 0.832468588453123 0.335062823093754 0.167531411546877 108 0.798323888390408 0.403352223219184 0.201676111609592 109 0.766357067725589 0.467285864548823 0.233642932274411 110 0.727611293192718 0.544777413614564 0.272388706807282 111 0.705187779762991 0.589624440474018 0.294812220237009 112 0.664334062714632 0.671331874570737 0.335665937285368 113 0.640455667322077 0.719088665355846 0.359544332677923 114 0.59862086402985 0.802758271940299 0.401379135970149 115 0.578287227690546 0.843425544618907 0.421712772309454 116 0.541768107100484 0.916463785799032 0.458231892899516 117 0.727987546376758 0.544024907246485 0.272012453623242 118 0.786556320430843 0.426887359138314 0.213443679569157 119 0.757738732233045 0.48452253553391 0.242261267766955 120 0.897961410150518 0.204077179698963 0.102038589849482 121 0.940279103214078 0.119441793571844 0.0597208967859222 122 0.966441257936538 0.0671174841269237 0.0335587420634618 123 0.951942344079318 0.0961153118413638 0.0480576559206819 124 0.954627398040992 0.0907452039180161 0.0453726019590081 125 0.938399441111121 0.123201117777757 0.0616005588888786 126 0.921154087043854 0.157691825912293 0.0788459129561464 127 0.89804145545564 0.203917089088719 0.101958544544360 128 0.874853937462801 0.250292125074398 0.125146062537199 129 0.831797914780391 0.336404170439218 0.168202085219609 130 0.800952081201036 0.398095837597929 0.199047918798964 131 0.738876560171049 0.522246879657903 0.261123439828951 132 0.689118313582949 0.621763372834102 0.310881686417051 133 0.683102013756669 0.633795972486662 0.316897986243331 134 0.698258444798024 0.603483110403953 0.301741555201976 135 0.712066143164299 0.575867713671403 0.287933856835701 136 0.862791422134519 0.274417155730962 0.137208577865481 137 0.835889661133835 0.328220677732331 0.164110338866165 138 0.883438887393833 0.233122225212334 0.116561112606167 139 0.812100389237606 0.375799221524787 0.187899610762394 140 0.669569932748201 0.660860134503598 0.330430067251799 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 3 0.0223880597014925 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/10n4xs1290532276.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/10n4xs1290532276.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/1y3ih1290532276.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/1y3ih1290532276.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/29czk1290532276.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/29czk1290532276.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/39czk1290532276.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/39czk1290532276.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/49czk1290532276.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/49czk1290532276.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/59czk1290532276.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/59czk1290532276.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/61lg51290532276.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/61lg51290532276.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/7cdy81290532276.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/7cdy81290532276.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/8cdy81290532276.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/8cdy81290532276.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/9cdy81290532276.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290532383j4oxk6db70rwscw/9cdy81290532276.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

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

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

Copyright

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

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by