*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: Thu, 02 Dec 2010 22:53:36 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru.htm/, Retrieved Thu, 02 Dec 2010 23:51:28 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru.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 10 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Learning[t] = + 5.45153304933176 + 0.0321668940555693Connected[t] + 0.0427653888947305Separate[t] + 0.558489671132889Software[t] + 0.0702334998707423Happiness[t] -0.0311264244363009Depression[t] + 0.00747850801958796Belonging[t] -0.00491058171792578t + 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) 5.45153304933176 1.942794 2.806 0.005401 0.0027 Connected 0.0321668940555693 0.034424 0.9344 0.350967 0.175483 Separate 0.0427653888947305 0.035076 1.2192 0.223886 0.111943 Software 0.558489671132889 0.053726 10.3952 0 0 Happiness 0.0702334998707423 0.057809 1.2149 0.225518 0.112759 Depression -0.0311264244363009 0.041759 -0.7454 0.456725 0.228362 Belonging 0.00747850801958796 0.011869 0.6301 0.529191 0.264595 t -0.00491058171792578 0.00168 -2.9227 0.00378 0.00189 Multiple Linear Regression - Regression Statistics Multiple R 0.667212929789437 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 1.85421524491435 Sum Squared Residuals 880.15722866503 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 16.0985387854796 -3.09853878547957 2 16 15.7506280756561 0.249371924343878 3 19 17.1063218899167 1.89367811008327 4 15 12.1616052410318 2.83839475896816 5 14 16.4017873467223 -2.40178734672232 6 13 14.8470133702108 -1.84701337021082 7 19 15.3941195404347 3.60588045956527 8 15 17.1034911605066 -2.10349116050658 9 14 16.0596585119288 -2.05965851192880 10 15 14.4613197202822 0.538680279717761 11 16 15.0039897785988 0.996010221401191 12 16 16.1957780658441 -0.195778065844100 13 16 15.5452007954959 0.4547992045041 14 16 15.4975704227910 0.502429577209042 15 17 18.0026152345095 -1.00261523450953 16 15 15.4966907599622 -0.496690759962225 17 15 14.5878376596391 0.412162340360936 18 20 16.4221329188422 3.57786708115779 19 18 15.5318412924009 2.46815870759907 20 16 15.598397960354 0.401602039646012 21 16 15.3944791538427 0.605520846157266 22 16 15.2136141783933 0.786385821606707 23 19 16.4921403787265 2.50785962127348 24 16 15.1609192229515 0.839080777048501 25 17 16.1483763914647 0.85162360853526 26 17 16.2218030707800 0.778196929220023 27 16 14.9083527902140 1.09164720978603 28 15 16.8091087350265 -1.80910873502655 29 16 15.6848237519473 0.31517624805274 30 14 14.263029558757 -0.263029558756991 31 15 15.7659606607022 -0.765960660702232 32 12 12.8492889523859 -0.849288952385886 33 14 14.8039620225922 -0.803962022592169 34 16 16.0017496144186 -0.00174961441855307 35 14 15.4902098814983 -1.49020988149829 36 10 13.0304769205532 -3.0304769205532 37 10 13.0355345646574 -3.03553456465737 38 14 15.7470324913881 -1.74703249138812 39 16 14.554555919938 1.44544408006200 40 16 14.4948939247229 1.50510607527713 41 16 14.7205377064971 1.27946229350293 42 14 15.7009510594818 -1.70095105948177 43 20 17.4871215566965 2.51287844330348 44 14 14.1533777639022 -0.153377763902221 45 14 14.4623553291315 -0.462355329131476 46 11 15.4909495615117 -4.49094956151171 47 14 16.6307612737306 -2.63076127373057 48 15 15.1467421663187 -0.146742166318651 49 16 15.4178766163230 0.582123383676951 50 14 15.6302473667626 -1.63024736676259 51 16 17.0252984963352 -1.02529849633517 52 14 14.1419408813432 -0.141940881343219 53 12 15.0171855791395 -3.01718557913948 54 16 16.0361860907356 -0.0361860907355918 55 9 11.3432897998035 -2.34328979980353 56 14 12.3849781445203 1.61502185547966 57 16 15.8545401093022 0.145459890697824 58 16 15.5298832287659 0.470116771234098 59 15 15.1123930302181 -0.112393030218104 60 16 14.2210605652264 1.77893943477358 61 12 11.5595534084661 0.440446591533868 62 16 15.6406817555398 0.359318244460184 63 16 16.5488168530774 -0.5488168530774 64 14 14.7109860019853 -0.710986001985263 65 16 15.3063211583342 0.69367884166577 66 17 16.0541860332013 0.945813966798677 67 18 16.3331770798611 1.6668229201389 68 18 14.3958881874426 3.60411181255739 69 12 15.8997083739692 -3.89970837396924 70 16 15.6515786730261 0.348421326973927 71 10 13.4123806085750 -3.41238060857495 72 14 14.9242951062704 -0.924295106270408 73 18 16.9280586745433 1.07194132545668 74 18 17.1409836239110 0.85901637608902 75 16 15.2322948752948 0.767705124705193 76 17 13.4918869897008 3.50811301029925 77 16 16.419099992442 -0.419099992441992 78 16 14.5311988476754 1.46880115232456 79 13 15.2165773344004 -2.21657733440038 80 16 15.1421402571568 0.857859742843152 81 16 15.6586274506278 0.341372549372198 82 16 15.7632408306316 0.236759169368357 83 15 15.6434137240469 -0.64341372404695 84 15 14.8842323819227 0.115767618077311 85 16 14.1607354722341 1.83926452776585 86 14 14.1555692846506 -0.155569284650592 87 16 15.3674881780279 0.632511821972137 88 16 14.8725888488247 1.12741115117526 89 15 14.5194813902587 0.480518609741336 90 12 13.9079725164080 -1.90797251640802 91 17 16.7584943754586 0.241505624541392 92 16 15.8055619194036 0.194438080596368 93 15 15.0531067912421 -0.0531067912420973 94 13 15.0298518503278 -2.02985185032776 95 16 14.7436133365348 1.25638666346519 96 16 15.7882428813297 0.211757118670261 97 16 13.6773839654895 2.32261603451052 98 16 15.7737083756365 0.226291624363460 99 14 14.4297816437613 -0.429781643761329 100 16 16.9922981106499 -0.992298110649857 101 16 14.6766246625527 1.32337533744731 102 20 17.4542184425634 2.54578155743657 103 15 14.2396603727495 0.76033962725048 104 16 14.9598584444853 1.04014155551469 105 13 14.8422042092773 -1.84220420927732 106 17 15.7017299648748 1.29827003512525 107 16 15.7011234587523 0.29887654124773 108 16 14.3586514687943 1.64134853120572 109 12 12.3043422991135 -0.304342299113488 110 16 15.2856808956604 0.714319104339589 111 16 15.9928271492344 0.00717285076563683 112 17 15.0564093690921 1.94359063090790 113 13 14.2811780773625 -1.28117807736248 114 12 14.5798742612205 -2.57987426122045 115 18 16.1614728444387 1.83852715556127 116 14 15.8657328435429 -1.86573284354287 117 14 13.228887828907 0.771112171092988 118 13 14.7929151358429 -1.79291513584291 119 16 15.520384206224 0.479615793776009 120 13 14.4292215835434 -1.42922158354341 121 16 15.3854232676415 0.614576732358462 122 13 15.8212093173508 -2.82120931735076 123 16 16.8545044640026 -0.854504464002573 124 15 15.8437647974654 -0.84376479746541 125 16 16.7849339139009 -0.784933913900919 126 15 14.6587216010757 0.341278398924287 127 17 15.4905839058456 1.50941609415437 128 15 14.0482521120088 0.95174788799123 129 12 14.6858650734517 -2.68586507345171 130 16 13.9402714795457 2.05972852045429 131 10 13.7239532443361 -3.72395324433605 132 16 13.4583321541629 2.54166784583713 133 12 14.1659890224415 -2.16598902244154 134 14 15.5440460090552 -1.54404600905523 135 15 15.0836566962205 -0.0836566962204945 136 13 12.1121127347309 0.887887265269134 137 15 14.5312778069589 0.468722193041143 138 11 13.4989500572246 -2.49895005722464 139 12 13.0064804164844 -1.00648041648441 140 11 13.3399564344920 -2.33995643449198 141 16 12.8564999151223 3.14350008487773 142 15 13.6441244258235 1.35587557417653 143 17 16.8413639582837 0.158636041716296 144 16 14.1244038470475 1.87559615295252 145 10 13.2667514301310 -3.26675143013095 146 18 15.4975454673630 2.50245453263695 147 13 14.9457512386837 -1.94575123868367 148 16 14.8430101053070 1.15698989469303 149 13 12.82722767011 0.172772329889989 150 10 12.9004577169405 -2.90045771694049 151 15 15.8784182905415 -0.87841829054145 152 16 13.8248630916881 2.17513690831192 153 16 11.8525810147495 4.1474189852505 154 14 12.3963025182653 1.60369748173469 155 10 12.4816282956809 -2.48162829568091 156 17 16.4393065637934 0.560693436206567 157 13 11.7066858547317 1.29331414526825 158 15 13.900934660471 1.09906533952900 159 16 14.5373961332024 1.46260386679759 160 12 12.6989037635456 -0.698903763545611 161 13 12.6931049205989 0.306895079401114 162 13 12.6702041146490 0.329795885350950 163 12 12.3813576310274 -0.381357631027421 164 17 16.2130980179022 0.786901982097807 165 15 13.6682202782511 1.33177972174891 166 10 11.6197611469958 -1.61976114699577 167 14 14.3441924705758 -0.344192470575766 168 11 14.1943469919182 -3.19434699191817 169 13 14.7895963339482 -1.78959633394817 170 16 14.3871926838976 1.61280731610237 171 12 10.4815320179531 1.5184679820469 172 16 15.3377881046553 0.66221189534468 173 12 13.8444384221823 -1.84443842218233 174 9 11.3336124343809 -2.3336124343809 175 12 14.9070414350127 -2.90704143501267 176 15 14.4730075744532 0.526992425546806 177 12 12.2943276210920 -0.294327621092033 178 12 12.6503684441930 -0.650368444193032 179 14 13.7938681954925 0.206131804507505 180 12 13.2889048934373 -1.28890489343725 181 16 15.0068737606415 0.99312623935851 182 11 11.4515058779588 -0.451505877958785 183 19 16.7015767685106 2.29842323148939 184 15 15.1109818809655 -0.110981880965518 185 8 14.5969865862610 -6.59698658626104 186 16 14.6989355568994 1.30106444310063 187 17 14.3895807084944 2.61041929150556 188 12 12.3486229107255 -0.348622910725467 189 11 11.4120697144516 -0.412069714451598 190 11 10.4549680631895 0.545031936810458 191 14 14.4364908904417 -0.43649089044172 192 16 15.3764277982820 0.623572201717984 193 12 9.72248141934327 2.27751858065673 194 16 14.0886404643777 1.9113595356223 195 13 13.6328845134380 -0.632884513437977 196 15 14.9989754108533 0.00102458914674346 197 16 12.9126260121705 3.08737398782949 198 16 14.9919436450660 1.00805635493403 199 14 12.4076330969111 1.59236690308890 200 16 14.4603615475735 1.53963845242653 201 16 14.0333200029035 1.96667999709652 202 14 13.2954618359923 0.704538164007681 203 11 13.3129603848872 -2.31296038488724 204 12 14.4949222642595 -2.49492226425949 205 15 12.6778762991469 2.32212370085313 206 15 14.4188365698392 0.581163430160781 207 16 14.5320147838526 1.46798521614738 208 16 14.8431254461590 1.15687455384097 209 11 13.5801453187234 -2.58014531872336 210 15 13.8885534096534 1.11144659034664 211 12 14.2037853885328 -2.20378538853275 212 12 15.7224255491506 -3.72242554915061 213 15 14.1090793589770 0.890920641023038 214 15 12.0905788116402 2.90942118835982 215 16 14.4647432573063 1.53525674269367 216 14 13.0805138671753 0.91948613282467 217 17 14.5748713248213 2.42512867517871 218 14 13.9049231073215 0.0950768926785433 219 13 11.8321054700474 1.16789452995262 220 15 15.1299096914369 -0.129909691436880 221 13 14.5726876835671 -1.57268768356711 222 14 13.8921489634354 0.107851036564569 223 15 14.1999876889948 0.800012311005213 224 12 13.0554532006112 -1.05545320061118 225 13 12.2689174915128 0.731082508487175 226 8 11.6573695969631 -3.65736959696312 227 14 13.6832791328481 0.316720867151929 228 14 12.8142890945427 1.18571090545735 229 11 12.1978908737621 -1.19789087376205 230 12 12.8303898458872 -0.830389845887172 231 13 11.1854887383650 1.81451126163496 232 10 13.2189058291037 -3.21890582910368 233 16 11.3487875113220 4.65121248867802 234 18 15.7737516733149 2.22624832668511 235 13 13.7266606548843 -0.726660654884331 236 11 13.2215618348084 -2.22156183480842 237 4 10.9938193483991 -6.99381934839915 238 13 14.1796817218455 -1.17968172184545 239 16 14.1367439630088 1.86325603699123 240 10 11.5930618646107 -1.59306186461067 241 12 12.1626452683162 -0.162645268316152 242 12 13.3960154190304 -1.39601541903038 243 10 8.81036730048706 1.18963269951294 244 13 10.9797489991871 2.02025100081286 245 15 13.5802095891207 1.41979041087932 246 12 11.8071329179159 0.192867082084070 247 14 12.745833303401 1.25416669659900 248 10 12.3830320431314 -2.38303204313139 249 12 10.7045626835548 1.29543731644515 250 12 11.5222473456141 0.477752654385858 251 11 11.7208297915302 -0.720829791530184 252 10 11.5207040112403 -1.52070401124025 253 12 11.2737442088263 0.726255791173704 254 16 12.7074968396979 3.29250316030215 255 12 13.2078556645355 -1.20785566453553 256 14 13.7197084126368 0.280291587363206 257 16 14.1388849696129 1.86111503038708 258 14 11.5536798517218 2.44632014827823 259 13 14.0549432381567 -1.05494323815668 260 4 9.3330935436994 -5.33309354369939 261 15 13.5531018279656 1.44689817203439 262 11 14.7741198188765 -3.7741198188765 263 11 11.1662281765916 -0.166228176591609 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 0.760826664987248 0.478346670025504 0.239173335012752 14 0.673552621178249 0.652894757643502 0.326447378821751 15 0.618114699975934 0.763770600048132 0.381885300024066 16 0.680833200974805 0.638333598050389 0.319166799025195 17 0.608142628027363 0.783714743945274 0.391857371972637 18 0.857694380421812 0.284611239156376 0.142305619578188 19 0.830980289213743 0.338039421572513 0.169019710786257 20 0.780467388615395 0.439065222769211 0.219532611384605 21 0.716435090676602 0.567129818646795 0.283564909323398 22 0.677924859700133 0.644150280599733 0.322075140299867 23 0.640080623968092 0.719838752063816 0.359919376031908 24 0.608002819411591 0.783994361176818 0.391997180588409 25 0.544602520253453 0.910794959493094 0.455397479746547 26 0.495118873916558 0.990237747833116 0.504881126083442 27 0.435695066526806 0.871390133053611 0.564304933473195 28 0.489428727652136 0.978857455304273 0.510571272347864 29 0.429531193251683 0.859062386503366 0.570468806748317 30 0.439110691341422 0.878221382682843 0.560889308658578 31 0.390777631300561 0.781555262601123 0.609222368699439 32 0.386536250945878 0.773072501891755 0.613463749054122 33 0.367573743538395 0.73514748707679 0.632426256461605 34 0.311946111516884 0.623892223033768 0.688053888483116 35 0.300790075632009 0.601580151264018 0.699209924367991 36 0.399446956221478 0.798893912442955 0.600553043778522 37 0.480233640547256 0.960467281094513 0.519766359452744 38 0.456414493869953 0.912828987739905 0.543585506130048 39 0.504036781673621 0.991926436652758 0.495963218326379 40 0.48466256434735 0.9693251286947 0.51533743565265 41 0.448981538814123 0.897963077628246 0.551018461185877 42 0.419330929144965 0.83866185828993 0.580669070855035 43 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0.00824523551913891 0.99587738224043 229 0.00293161983497726 0.00586323966995452 0.997068380165023 230 0.00207599045903004 0.00415198091806009 0.99792400954097 231 0.00226850989205013 0.00453701978410026 0.99773149010795 232 0.00779851916707025 0.0155970383341405 0.99220148083293 233 0.0293698404957628 0.0587396809915256 0.970630159504237 234 0.0449507472439721 0.0899014944879442 0.955049252756028 235 0.0330914105808945 0.0661828211617889 0.966908589419106 236 0.0271011514226524 0.0542023028453049 0.972898848577348 237 0.238959015911466 0.477918031822931 0.761040984088534 238 0.192949272019248 0.385898544038497 0.807050727980752 239 0.163289925162307 0.326579850324614 0.836710074837693 240 0.130447620662190 0.260895241324380 0.86955237933781 241 0.116817470818194 0.233634941636388 0.883182529181806 242 0.177907984064823 0.355815968129646 0.822092015935177 243 0.150453950204244 0.300907900408489 0.849546049795756 244 0.151452822534993 0.302905645069986 0.848547177465007 245 0.132852249443854 0.265704498887708 0.867147750556146 246 0.116475820843446 0.232951641686892 0.883524179156554 247 0.079256297308871 0.158512594617742 0.920743702691129 248 0.0704290884946231 0.140858176989246 0.929570911505377 249 0.0534977901152146 0.106995580230429 0.946502209884785 250 0.130779813206018 0.261559626412037 0.869220186793982 251 0.107472861596092 0.214945723192185 0.892527138403908 252 0.54397838950358 0.91204322099284 0.45602161049642 253 0.382288727481099 0.764577454962197 0.617711272518901 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/Dec/02/t1291330288vtjtozuicq4ftru/10fqkw1291330402.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/10fqkw1291330402.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/18pn31291330402.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/18pn31291330402.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/28pn31291330402.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/28pn31291330402.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/38pn31291330402.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/38pn31291330402.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/41g461291330402.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/41g461291330402.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/51g461291330402.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/51g461291330402.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/61g461291330402.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/61g461291330402.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/7uq391291330402.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/7uq391291330402.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/8nz3u1291330402.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/8nz3u1291330402.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/9nz3u1291330402.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/02/t1291330288vtjtozuicq4ftru/9nz3u1291330402.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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