*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: Wed, 17 Nov 2010 09:20:01 +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/17/t1289985955fvo4s598b8e1dgh.htm/, Retrieved Wed, 17 Nov 2010 10:26:11 +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/17/t1289985955fvo4s598b8e1dgh.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 «

41 38 13 12 14 12 53 39 32 16 11 18 11 83 30 35 19 15 11 14 66 31 33 15 6 12 12 67 34 37 14 13 16 21 76 35 29 13 10 18 12 78 39 31 19 12 14 22 53 34 36 15 14 14 11 80 36 35 14 12 15 10 74 37 38 15 9 15 13 76 38 31 16 10 17 10 79 36 34 16 12 19 8 54 38 35 16 12 10 15 67 39 38 16 11 16 14 54 33 37 17 15 18 10 87 32 33 15 12 14 14 58 36 32 15 10 14 14 75 38 38 20 12 17 11 88 39 38 18 11 14 10 64 32 32 16 12 16 13 57 32 33 16 11 18 9.5 66 31 31 16 12 11 14 68 39 38 19 13 14 12 54 37 39 16 11 12 14 56 39 32 17 12 17 11 86 41 32 17 13 9 9 80 36 35 16 10 16 11 76 33 37 15 14 14 15 69 33 33 16 12 15 14 78 34 33 14 10 11 13 67 31 31 15 12 16 9 80 27 32 12 8 13 15 54 37 31 14 10 17 10 71 34 37 16 12 15 11 84 34 30 14 12 14 13 74 32 33 10 7 16 8 71 29 31 10 9 9 20 63 36 33 14 12 15 12 71 29 31 16 10 17 10 76 35 33 16 10 13 10 69 37 32 16 10 15 9 74 34 33 14 12 16 14 75 38 32 20 15 16 8 54 35 33 14 10 12 14 52 38 28 14 10 15 11 69 37 35 11 12 11 13 68 38 39 14 13 15 9 65 33 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 15 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Learning[t] = + 5.45153304933195 + 0.0321668940555692Connected[t] + 0.0427653888947307Separate[t] + 0.558489671132888Software[t] + 0.0702334998707389Happiness[t] -0.0311264244363035Depression[t] + 0.00747850801958737Belonging[t] -0.00491058171792585t + 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) 5.45153304933195 1.942794 2.806 0.005401 0.0027 Connected 0.0321668940555692 0.034424 0.9344 0.350967 0.175483 Separate 0.0427653888947307 0.035076 1.2192 0.223886 0.111943 Software 0.558489671132888 0.053726 10.3952 0 0 Happiness 0.0702334998707389 0.057809 1.2149 0.225518 0.112759 Depression -0.0311264244363035 0.041759 -0.7454 0.456725 0.228362 Belonging 0.00747850801958737 0.011869 0.6301 0.529191 0.264595 t -0.00491058171792585 0.00168 -2.9227 0.00378 0.00189 Multiple Linear Regression - Regression Statistics Multiple R 0.667212929789438 R-squared 0.445173093678205 Adjusted R-squared 0.430002045458468 F-TEST (value) 29.3435949336093 F-TEST (DF numerator) 7 F-TEST (DF denominator) 256 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.85421524491434 Sum Squared Residuals 880.157228665026 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 16.0985387854790 -3.09853878547897 2 16 15.7506280756561 0.249371924343889 3 19 17.1063218899167 1.89367811008325 4 15 12.1616052410319 2.83839475896812 5 14 16.4017873467223 -2.40178734672229 6 13 14.8470133702108 -1.84701337021082 7 19 15.3941195404347 3.60588045956527 8 15 17.1034911605066 -2.10349116050658 9 14 16.0596585119288 -2.05965851192881 10 15 14.4613197202822 0.538680279717755 11 16 15.0039897785988 0.996010221401189 12 16 16.1957780658441 -0.195778065844116 13 16 15.5452007954959 0.45479920450408 14 16 15.4975704227910 0.502429577209031 15 17 18.0026152345095 -1.00261523450952 16 15 15.4966907599622 -0.496690759962239 17 15 14.5878376596391 0.412162340360932 18 20 16.4221329188422 3.5778670811578 19 18 15.5318412924009 2.46815870759905 20 16 15.598397960354 0.401602039646002 21 16 15.3944791538427 0.605520846157257 22 16 15.2136141783933 0.78638582160669 23 19 16.4921403787265 2.50785962127346 24 16 15.1609192229515 0.839080777048478 25 17 16.1483763914647 0.851623608535269 26 17 16.22180307078 0.778196929219997 27 16 14.9083527902140 1.09164720978602 28 15 16.8091087350266 -1.80910873502655 29 16 15.6848237519473 0.315176248052743 30 14 14.2630295587570 -0.263029558757013 31 15 15.7659606607022 -0.765960660702237 32 12 12.8492889523859 -0.849288952385907 33 14 14.8039620225922 -0.803962022592174 34 16 16.0017496144186 -0.00174961441855540 35 14 15.4902098814983 -1.49020988149829 36 10 13.0304769205532 -3.03047692055322 37 10 13.0355345646574 -3.03553456465739 38 14 15.7470324913881 -1.74703249138813 39 16 14.554555919938 1.44544408006200 40 16 14.4948939247229 1.50510607527711 41 16 14.7205377064971 1.27946229350291 42 14 15.7009510594818 -1.70095105948177 43 20 17.4871215566965 2.51287844330346 44 14 14.1533777639022 -0.153377763902245 45 14 14.4623553291315 -0.462355329131485 46 11 15.4909495615117 -4.49094956151173 47 14 16.6307612737306 -2.63076127373059 48 15 15.1467421663187 -0.146742166318659 49 16 15.4178766163230 0.58212338367696 50 14 15.6302473667626 -1.6302473667626 51 16 17.0252984963352 -1.02529849633518 52 14 14.1419408813432 -0.141940881343227 53 12 15.0171855791395 -3.01718557913949 54 16 16.0361860907356 -0.0361860907356081 55 9 11.3432897998036 -2.34328979980356 56 14 12.3849781445203 1.61502185547966 57 16 15.8545401093022 0.145459890697828 58 16 15.5298832287659 0.47011677123408 59 15 15.1123930302181 -0.112393030218124 60 16 14.2210605652264 1.77893943477357 61 12 11.5595534084662 0.440446591533846 62 16 15.6406817555398 0.359318244460177 63 16 16.5488168530774 -0.548816853077411 64 14 14.7109860019853 -0.710986001985279 65 16 15.3063211583342 0.693678841665758 66 17 16.0541860332013 0.945813966798659 67 18 16.3331770798611 1.66682292013889 68 18 14.3958881874426 3.60411181255738 69 12 15.8997083739692 -3.89970837396925 70 16 15.6515786730261 0.348421326973927 71 10 13.4123806085750 -3.41238060857496 72 14 14.9242951062704 -0.924295106270414 73 18 16.9280586745433 1.07194132545669 74 18 17.140983623911 0.85901637608901 75 16 15.2322948752948 0.76770512470519 76 17 13.4918869897007 3.50811301029926 77 16 16.419099992442 -0.419099992441987 78 16 14.5311988476754 1.46880115232456 79 13 15.2165773344004 -2.21657733440037 80 16 15.1421402571569 0.857859742843126 81 16 15.6586274506278 0.341372549372196 82 16 15.7632408306317 0.236759169368344 83 15 15.6434137240469 -0.643413724046948 84 15 14.8842323819227 0.115767618077307 85 16 14.1607354722341 1.83926452776585 86 14 14.1555692846506 -0.155569284650594 87 16 15.3674881780279 0.632511821972129 88 16 14.8725888488247 1.12741115117525 89 15 14.5194813902587 0.480518609741331 90 12 13.9079725164080 -1.90797251640802 91 17 16.7584943754586 0.241505624541383 92 16 15.8055619194036 0.194438080596370 93 15 15.0531067912421 -0.0531067912420874 94 13 15.0298518503278 -2.02985185032776 95 16 14.7436133365348 1.25638666346519 96 16 15.7882428813297 0.211757118670259 97 16 13.6773839654895 2.32261603451051 98 16 15.7737083756365 0.226291624363468 99 14 14.4297816437613 -0.429781643761336 100 16 16.9922981106499 -0.992298110649853 101 16 14.6766246625527 1.32337533744731 102 20 17.4542184425634 2.54578155743658 103 15 14.2396603727495 0.760339627250459 104 16 14.9598584444853 1.04014155551470 105 13 14.8422042092773 -1.84220420927732 106 17 15.7017299648747 1.29827003512525 107 16 15.7011234587523 0.298876541247739 108 16 14.3586514687943 1.64134853120570 109 12 12.3043422991135 -0.304342299113495 110 16 15.2856808956604 0.714319104339601 111 16 15.9928271492344 0.00717285076563326 112 17 15.0564093690921 1.94359063090789 113 13 14.2811780773625 -1.28117807736249 114 12 14.5798742612204 -2.57987426122044 115 18 16.1614728444387 1.83852715556128 116 14 15.8657328435429 -1.86573284354288 117 14 13.2288878289070 0.771112171092978 118 13 14.7929151358429 -1.79291513584292 119 16 15.5203842062240 0.479615793776025 120 13 14.4292215835434 -1.42922158354343 121 16 15.3854232676415 0.614576732358469 122 13 15.8212093173508 -2.82120931735076 123 16 16.8545044640026 -0.85450446400258 124 15 15.8437647974654 -0.84376479746541 125 16 16.7849339139009 -0.784933913900921 126 15 14.6587216010757 0.341278398924294 127 17 15.4905839058456 1.50941609415438 128 15 14.0482521120088 0.951747887991243 129 12 14.6858650734517 -2.68586507345170 130 16 13.9402714795457 2.05972852045428 131 10 13.7239532443361 -3.72395324433606 132 16 13.4583321541629 2.54166784583712 133 12 14.1659890224415 -2.16598902244154 134 14 15.5440460090552 -1.54404600905523 135 15 15.0836566962205 -0.0836566962204762 136 13 12.1121127347309 0.887887265269139 137 15 14.5312778069589 0.46872219304114 138 11 13.4989500572247 -2.49895005722466 139 12 13.0064804164844 -1.00648041648442 140 11 13.339956434492 -2.33995643449199 141 16 12.8564999151223 3.14350008487771 142 15 13.6441244258235 1.35587557417655 143 17 16.8413639582837 0.158636041716305 144 16 14.1244038470475 1.87559615295253 145 10 13.2667514301309 -3.26675143013094 146 18 15.4975454673630 2.50245453263696 147 13 14.9457512386837 -1.94575123868368 148 16 14.8430101053070 1.15698989469302 149 13 12.82722767011 0.172772329889987 150 10 12.9004577169405 -2.90045771694048 151 15 15.8784182905414 -0.878418290541436 152 16 13.8248630916881 2.17513690831192 153 16 11.8525810147495 4.14741898525048 154 14 12.3963025182653 1.60369748173468 155 10 12.4816282956809 -2.4816282956809 156 17 16.4393065637934 0.560693436206563 157 13 11.7066858547318 1.29331414526825 158 15 13.9009346604710 1.09906533952902 159 16 14.5373961332024 1.46260386679759 160 12 12.6989037635456 -0.6989037635456 161 13 12.6931049205989 0.306895079401114 162 13 12.6702041146490 0.329795885350963 163 12 12.3813576310274 -0.381357631027413 164 17 16.2130980179022 0.786901982097844 165 15 13.6682202782511 1.33177972174891 166 10 11.6197611469958 -1.61976114699577 167 14 14.3441924705758 -0.344192470575764 168 11 14.1943469919182 -3.19434699191817 169 13 14.7895963339482 -1.78959633394817 170 16 14.3871926838976 1.61280731610236 171 12 10.4815320179531 1.51846798204690 172 16 15.3377881046553 0.662211895344686 173 12 13.8444384221823 -1.84443842218235 174 9 11.3336124343809 -2.3336124343809 175 12 14.9070414350127 -2.90704143501266 176 15 14.4730075744532 0.526992425546797 177 12 12.2943276210920 -0.294327621092045 178 12 12.6503684441930 -0.650368444193027 179 14 13.7938681954925 0.206131804507502 180 12 13.2889048934373 -1.28890489343726 181 16 15.0068737606415 0.993126239358496 182 11 11.4515058779588 -0.451505877958803 183 19 16.7015767685106 2.29842323148939 184 15 15.1109818809655 -0.110981880965516 185 8 14.5969865862610 -6.59698658626102 186 16 14.6989355568994 1.30106444310065 187 17 14.3895807084944 2.61041929150556 188 12 12.3486229107255 -0.348622910725456 189 11 11.4120697144516 -0.412069714451611 190 11 10.4549680631895 0.545031936810458 191 14 14.4364908904417 -0.436490890441748 192 16 15.3764277982820 0.62357220171798 193 12 9.72248141934327 2.27751858065673 194 16 14.0886404643777 1.91135953562229 195 13 13.6328845134380 -0.632884513437968 196 15 14.9989754108533 0.00102458914673653 197 16 12.9126260121705 3.08737398782951 198 16 14.9919436450660 1.00805635493404 199 14 12.4076330969111 1.59236690308889 200 16 14.4603615475735 1.53963845242654 201 16 14.0333200029035 1.96667999709652 202 14 13.2954618359923 0.704538164007682 203 11 13.3129603848872 -2.31296038488723 204 12 14.4949222642595 -2.4949222642595 205 15 12.6778762991469 2.32212370085312 206 15 14.4188365698392 0.581163430160789 207 16 14.5320147838526 1.46798521614739 208 16 14.8431254461590 1.15687455384097 209 11 13.5801453187234 -2.58014531872336 210 15 13.8885534096533 1.11144659034666 211 12 14.2037853885328 -2.20378538853276 212 12 15.7224255491506 -3.72242554915059 213 15 14.1090793589769 0.890920641023053 214 15 12.0905788116402 2.90942118835982 215 16 14.4647432573063 1.53525674269368 216 14 13.0805138671753 0.919486132824675 217 17 14.5748713248213 2.42512867517873 218 14 13.9049231073214 0.0950768926785521 219 13 11.8321054700474 1.16789452995262 220 15 15.1299096914369 -0.129909691436863 221 13 14.5726876835671 -1.57268768356711 222 14 13.8921489634354 0.107851036564569 223 15 14.1999876889948 0.800012311005216 224 12 13.0554532006112 -1.05545320061118 225 13 12.2689174915128 0.731082508487161 226 8 11.6573695969631 -3.65736959696312 227 14 13.6832791328481 0.316720867151934 228 14 12.8142890945427 1.18571090545734 229 11 12.1978908737620 -1.19789087376204 230 12 12.8303898458872 -0.83038984588718 231 13 11.1854887383650 1.81451126163496 232 10 13.2189058291037 -3.21890582910369 233 16 11.348787511322 4.65121248867801 234 18 15.7737516733149 2.22624832668513 235 13 13.7266606548843 -0.72666065488433 236 11 13.2215618348084 -2.22156183480842 237 4 10.9938193483991 -6.99381934839914 238 13 14.1796817218455 -1.17968172184546 239 16 14.1367439630088 1.86325603699122 240 10 11.5930618646107 -1.59306186461068 241 12 12.1626452683162 -0.162645268316154 242 12 13.3960154190304 -1.39601541903039 243 10 8.81036730048707 1.18963269951293 244 13 10.9797489991871 2.02025100081286 245 15 13.5802095891207 1.41979041087934 246 12 11.8071329179159 0.192867082084079 247 14 12.745833303401 1.25416669659900 248 10 12.3830320431314 -2.38303204313137 249 12 10.7045626835548 1.29543731644515 250 12 11.5222473456141 0.477752654385854 251 11 11.7208297915302 -0.720829791530176 252 10 11.5207040112402 -1.52070401124024 253 12 11.2737442088263 0.726255791173698 254 16 12.7074968396978 3.29250316030215 255 12 13.2078556645355 -1.20785566453552 256 14 13.7197084126368 0.280291587363209 257 16 14.1388849696129 1.86111503038709 258 14 11.5536798517218 2.44632014827823 259 13 14.0549432381567 -1.05494323815667 260 4 9.3330935436994 -5.33309354369941 261 15 13.5531018279656 1.44689817203439 262 11 14.7741198188765 -3.77411981887649 263 11 11.1662281765916 -0.166228176591611 264 14 12.6310833706034 1.36891662939664 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.402475229471653 0.804950458943307 0.597524770528347 12 0.799813019552283 0.400373960895434 0.200186980447717 13 0.760826664987249 0.478346670025502 0.239173335012751 14 0.673552621178249 0.652894757643502 0.326447378821751 15 0.618114699975933 0.763770600048135 0.381885300024067 16 0.680833200974806 0.638333598050388 0.319166799025194 17 0.608142628027366 0.783714743945269 0.391857371972634 18 0.857694380421813 0.284611239156373 0.142305619578187 19 0.830980289213744 0.338039421572512 0.169019710786256 20 0.780467388615392 0.439065222769216 0.219532611384608 21 0.716435090676601 0.567129818646798 0.283564909323399 22 0.677924859700136 0.644150280599728 0.322075140299864 23 0.64008062396809 0.71983875206382 0.35991937603191 24 0.608002819411591 0.783994361176817 0.391997180588409 25 0.544602520253449 0.910794959493103 0.455397479746551 26 0.495118873916556 0.990237747833111 0.504881126083444 27 0.435695066526812 0.871390133053624 0.564304933473188 28 0.489428727652138 0.978857455304276 0.510571272347862 29 0.429531193251687 0.859062386503374 0.570468806748313 30 0.43911069134142 0.87822138268284 0.56088930865858 31 0.390777631300563 0.781555262601126 0.609222368699437 32 0.386536250945879 0.773072501891758 0.613463749054121 33 0.367573743538395 0.735147487076789 0.632426256461605 34 0.311946111516887 0.623892223033773 0.688053888483113 35 0.300790075632003 0.601580151264006 0.699209924367997 36 0.399446956221477 0.798893912442955 0.600553043778523 37 0.480233640547253 0.960467281094507 0.519766359452747 38 0.456414493869952 0.912828987739904 0.543585506130048 39 0.504036781673619 0.991926436652762 0.495963218326381 40 0.484662564347358 0.969325128694716 0.515337435652642 41 0.448981538814127 0.897963077628253 0.551018461185873 42 0.419330929144973 0.838661858289946 0.580669070855027 43 0.435488787174067 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0.00293161983497722 0.00586323966995445 0.997068380165023 230 0.00207599045903008 0.00415198091806016 0.99792400954097 231 0.00226850989205011 0.00453701978410022 0.99773149010795 232 0.0077985191670701 0.0155970383341402 0.99220148083293 233 0.0293698404957630 0.0587396809915259 0.970630159504237 234 0.0449507472439715 0.089901494487943 0.955049252756029 235 0.0330914105808940 0.0661828211617879 0.966908589419106 236 0.0271011514226525 0.054202302845305 0.972898848577348 237 0.238959015911461 0.477918031822922 0.761040984088539 238 0.19294927201925 0.3858985440385 0.80705072798075 239 0.163289925162300 0.326579850324601 0.8367100748377 240 0.130447620662191 0.260895241324381 0.86955237933781 241 0.116817470818194 0.233634941636387 0.883182529181806 242 0.177907984064825 0.35581596812965 0.822092015935175 243 0.150453950204245 0.300907900408490 0.849546049795755 244 0.151452822534991 0.302905645069982 0.84854717746501 245 0.132852249443852 0.265704498887705 0.867147750556148 246 0.116475820843447 0.232951641686895 0.883524179156553 247 0.0792562973088716 0.158512594617743 0.920743702691128 248 0.0704290884946226 0.140858176989245 0.929570911505377 249 0.0534977901152154 0.106995580230431 0.946502209884785 250 0.130779813206018 0.261559626412036 0.869220186793982 251 0.107472861596092 0.214945723192184 0.892527138403908 252 0.54397838950358 0.91204322099284 0.45602161049642 253 0.382288727481096 0.764577454962192 0.617711272518904 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 10 0.0411522633744856 NOK 5% type I error level 86 0.353909465020576 NOK 10% type I error level 125 0.51440329218107 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/10htaw1289985584.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/10htaw1289985584.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/1l1cn1289985584.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/1l1cn1289985584.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/2l1cn1289985584.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/2l1cn1289985584.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/3l1cn1289985584.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/3l1cn1289985584.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/4eab81289985584.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/4eab81289985584.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/5eab81289985584.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/5eab81289985584.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/6eab81289985584.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/6eab81289985584.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/77jst1289985584.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/77jst1289985584.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/8htaw1289985584.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/8htaw1289985584.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/9htaw1289985584.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/17/t1289985955fvo4s598b8e1dgh/9htaw1289985584.ps (open in new window)

Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 3 ; 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') }

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