Hypothese testing paper: connected

*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 09:21:09 +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/t1290504002l7jtcr4noyja1oi.htm/, Retrieved Tue, 23 Nov 2010 10:20:14 +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/t1290504002l7jtcr4noyja1oi.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 32 39 32 16 11 18 11 83 51 30 35 19 15 11 14 66 42 31 33 15 6 12 12 67 41 34 37 14 13 16 21 76 46 35 29 13 10 18 12 78 47 39 31 19 12 14 22 53 37 34 36 15 14 14 11 80 49 36 35 14 12 15 10 74 45 37 38 15 9 15 13 76 47 38 31 16 10 17 10 79 49 36 34 16 12 19 8 54 33 38 35 16 12 10 15 67 42 39 38 16 11 16 14 54 33 33 37 17 15 18 10 87 53 32 33 15 12 14 14 58 36 36 32 15 10 14 14 75 45 38 38 20 12 17 11 88 54 39 38 18 11 14 10 64 41 32 32 16 12 16 13 57 36 32 33 16 11 18 9.5 66 41 31 31 16 12 11 14 68 44 39 38 19 13 14 12 54 33 37 39 16 11 12 14 56 37 39 32 17 12 17 11 86 52 41 32 17 13 9 9 80 47 36 35 16 10 16 11 76 43 33 37 15 14 14 15 69 44 33 33 16 12 15 14 78 45 34 33 14 10 11 13 67 44 31 31 15 12 16 9 80 49 27 32 12 8 13 15 54 33 37 31 14 10 17 10 71 43 34 37 16 12 15 11 84 54 34 30 14 12 14 13 74 42 32 33 10 7 16 8 71 44 29 31 10 9 9 20 63 37 36 33 14 12 15 12 71 43 29 31 16 10 17 10 76 46 35 33 16 10 13 10 69 42 37 32 16 10 15 9 74 45 34 33 14 1 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 18 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Learning[t] = + 3.77956658273111 + 0.0469437389403786Connected[t] + 0.0419978310517143Separate[t] + 0.607405158110716Software[t] + 0.098631079258643Happiness[t] -0.0393791266630193Depression[t] + 0.0158660592613680Belonging[t] -0.0194154193631033Belonging_Final[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 3.77956658273111 1.917652 1.9709 0.049809 0.024904 Connected 0.0469437389403786 0.034787 1.3495 0.178384 0.089192 Separate 0.0419978310517143 0.035648 1.1781 0.239847 0.119923 Software 0.607405158110716 0.051845 11.7158 0 0 Happiness 0.098631079258643 0.057963 1.7016 0.09004 0.04502 Depression -0.0393791266630193 0.042557 -0.9253 0.35567 0.177835 Belonging 0.0158660592613680 0.037843 0.4193 0.675376 0.337688 Belonging_Final -0.0194154193631033 0.056444 -0.344 0.731147 0.365573 Multiple Linear Regression - Regression Statistics Multiple R 0.653394258005351 R-squared 0.426924056394364 Adjusted R-squared 0.411254011061397 F-TEST (value) 27.2445961273770 F-TEST (DF numerator) 7 F-TEST (DF denominator) 256 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.88446241278468 Sum Squared Residuals 909.106837810756 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 15.7169326674778 -2.71693266747778 2 16 15.3046452988162 0.695354701183782 3 19 16.5342266059759 2.46577339402406 4 15 11.2431990710256 3.7568009289744 5 14 15.8896873324328 -1.88968733243279 6 13 14.3424239462714 -1.34242394627140 7 19 14.8381920087898 4.16180799121016 8 15 16.6568417465609 -1.65684174656087 9 14 15.6143966049743 -1.61439660497434 10 15 13.8398822625452 1.16011773745481 11 16 14.5244132197985 1.47558678020148 12 16 15.9613451914131 0.0386548085868819 13 16 14.9654168965065 1.03458310349348 14 16 15.1305945765763 0.86940542342365 15 17 17.7266051778577 -0.726605177857671 16 15 15.0073602272847 -0.00736022728472072 17 15 14.0333112689484 0.966688731051586 18 20 16.0395466632557 3.96045333674427 19 18 15.09418616242 2.90581383758001 20 16 15.1861376221519 0.813862377848057 21 16 15.0015368334676 0.99846316653241 22 16 14.5838648261738 1.41613517382616 23 19 16.2269009876065 2.77309901239347 24 16 14.6382510537831 1.36174894621694 25 17 15.8416021360893 1.15839786391071 26 17 15.8344851325850 1.16551486741503 27 16 14.5294011985975 1.47059880140252 28 15 16.4169297769606 -1.41692977696059 29 16 15.2955174564432 0.704482543556828 30 14 13.6173944562786 0.382605543721379 31 15 15.3672314701030 -0.367231470103049 32 12 12.1577948842104 -0.157794884210425 33 14 14.4670335229458 -0.467033522945819 34 16 15.5490474808797 0.450952519120254 35 14 15.1519977706766 -1.15199777067662 36 10 12.4548067707195 -2.4548067707195 37 10 12.2908025947004 -2.29080259470041 38 14 15.4428753504870 -1.44287535048698 39 16 14.1125676496403 1.88743235035968 40 16 14.0503006909743 1.94969930902571 41 16 14.3599156612012 1.64008433879884 42 14 15.4129095162212 -1.41290951622119 43 20 17.4975592437467 2.50244075625334 44 14 13.7379997106144 0.262000289385554 45 14 14.1390257843911 -0.139025784391116 46 11 15.1505593881384 -4.1505593881384 47 14 16.4190959972096 -2.41909599720959 48 15 14.7812339122260 0.218766087773978 49 16 15.1915977233103 0.80840227668973 50 14 15.3615153637810 -1.36151536378102 51 16 16.8537398386884 -0.853739838688414 52 14 13.7316892738080 0.268310726191956 53 12 14.6138653598004 -2.61386535980045 54 16 15.5906899034319 0.409310096568081 55 9 10.7137318072366 -1.71373180723661 56 14 11.8326046050634 2.16739539493663 57 16 15.6937236900133 0.306276309986652 58 16 15.2303555712627 0.769644428737268 59 15 14.8230045585446 0.176995441455372 60 16 13.7932224493505 2.20677755064947 61 12 10.8367279492074 1.16327205079259 62 16 15.4378640177442 0.562135982255836 63 16 16.2989869704333 -0.298986970433305 64 14 14.4388877335844 -0.438887733584363 65 16 15.1500442700275 0.849955729972452 66 17 15.7438538414077 1.25614615859233 67 18 16.0903465015184 1.90965349848157 68 18 14.0764904918967 3.92350950810328 69 12 15.8084608807317 -3.80846088073167 70 16 15.4728479832678 0.527152016732215 71 10 13.0122458267498 -3.01224582674977 72 14 14.7156655383903 -0.715665538390303 73 18 16.8379895442731 1.16201045572692 74 18 17.1928281858955 0.807171814104506 75 16 15.0094686892977 0.990531310702272 76 17 13.0902524925774 3.90974750742255 77 16 16.4072325443378 -0.407232544337829 78 16 14.2122817226739 1.78771827732615 79 13 14.9614853283133 -1.96148532831330 80 16 15.0831385107766 0.916861489223383 81 16 15.5360989694856 0.463901030514361 82 16 15.6432294770163 0.356770522983692 83 15 15.6201822872087 -0.620182287208735 84 15 14.6861437075647 0.313856292435273 85 16 13.8827626275351 2.11723737246489 86 14 13.9517886120021 0.0482113879978810 87 16 15.2330941862993 0.76690581370072 88 16 14.6813029945340 1.31869700546595 89 15 14.1033381737051 0.896661826294864 90 12 13.6433035668958 -1.64330356689577 91 17 16.8321246414488 0.167875358551157 92 16 15.7294852307762 0.270514769223806 93 15 14.9057923352787 0.0942076647212783 94 13 14.8364568188003 -1.83645681880029 95 16 14.6980328060634 1.30196719393662 96 16 15.6960780466908 0.303921953309242 97 16 13.4832846792557 2.51671532074434 98 16 15.8300417014575 0.169958298542461 99 14 14.2661258632027 -0.266125863202743 100 16 17.1940865071683 -1.19408650716827 101 16 14.5059011287886 1.49409887121141 102 20 17.5790992836758 2.42090071632415 103 15 14.0226460140409 0.977353985959115 104 16 14.8383762518519 1.16162374814813 105 13 14.7124447739459 -1.71244477394589 106 17 15.7604373152473 1.23956268475275 107 16 15.7720645248471 0.227935475152921 108 16 14.2326042643852 1.76739573561481 109 12 12.0024802659182 -0.00248026591817174 110 16 15.1718385499616 0.828161450038395 111 16 15.9384880334039 0.0615119665961127 112 17 14.8625328282602 2.13746717173979 113 13 14.5286402413612 -1.52864024136121 114 12 14.614568460888 -2.61456846088799 115 18 16.2764524443605 1.72354755563947 116 14 15.9504759627417 -1.95047596274165 117 14 12.9924621951951 1.00753780480488 118 13 14.7858242392293 -1.78582423922934 119 16 15.5144579558839 0.48554204411607 120 13 14.3730308681848 -1.37303086818477 121 16 15.4072695332184 0.592730466781637 122 13 15.9001483950515 -2.90014839505153 123 16 17.0738036864139 -1.07380368641386 124 15 15.9985652529538 -0.998565252953813 125 16 16.9217558949015 -0.921755894901497 126 15 14.7501471788131 0.249852821186918 127 17 15.7672102604739 1.23278973952610 128 15 14.0042319951691 0.995768004830924 129 12 14.7455979666711 -2.74559796667113 130 16 13.9018224660129 2.09817753398713 131 10 13.4900189227280 -3.49001892272798 132 16 13.4847293488174 2.51527065118258 133 12 14.1318955712898 -2.13189557128976 134 14 15.6891601643807 -1.68916016438072 135 15 15.1349525324793 -0.134952532479329 136 13 11.8798702989229 1.12012970107707 137 15 14.5406759892864 0.459324010713589 138 11 13.3639577865016 -2.36395778650162 139 12 12.9948717800782 -0.994871780078202 140 11 13.2797734052426 -2.27977340524255 141 16 12.8706670328481 3.12933296715187 142 15 13.5777970081450 1.42220299185502 143 17 17.0126296693111 -0.0126296693111276 144 16 14.2177232846361 1.78227671536388 145 10 13.3076482519712 -3.30764825197124 146 18 15.7108182646390 2.28918173536104 147 13 15.057515844885 -2.05751584488500 148 16 14.9198086004653 1.08019139953471 149 13 12.6377638044032 0.362236195596831 150 10 12.8783257394112 -2.8783257394112 151 15 16.1550432712530 -1.15504327125297 152 16 13.9923608515066 2.00763914849345 153 16 11.7040450513149 4.29595494868507 154 14 12.2499675462609 1.75003245373915 155 10 12.3106299805489 -2.31062998054890 156 17 16.8321246414488 0.167875358551157 157 13 11.5695393191606 1.43046068083939 158 15 14.0042319951691 0.995768004830924 159 16 14.6713955204085 1.32860447959148 160 12 12.5736517546432 -0.573651754643187 161 13 12.6006036915371 0.39939630846291 162 13 12.4665513538839 0.53344864611615 163 12 12.3881607885568 -0.388160788556804 164 17 16.5737899268770 0.42621007312302 165 15 13.6726004456851 1.32739955431489 166 10 11.4206728334644 -1.42067283346442 167 14 14.4691619974894 -0.469161997489407 168 11 14.2909865799885 -3.29098657998851 169 13 14.8482927619942 -1.84829276199418 170 16 14.4308747459494 1.56912525405060 171 12 10.3653118162962 1.63468818370377 172 16 15.7059483938507 0.294051606149257 173 12 13.9883936528962 -1.98839365289617 174 9 11.3120335908731 -2.31203359087306 175 12 15.2885887877223 -3.28858878772229 176 15 14.7442131156564 0.255786884343579 177 12 12.2632972969965 -0.263297296996452 178 12 12.6879346718068 -0.68793467180684 179 14 14.0621066117256 -0.0621066117256398 180 12 13.4762697050290 -1.47626970502904 181 16 15.4340480772343 0.565951922765726 182 11 11.5217489928797 -0.521748992879665 183 19 17.1604632713109 1.83953672868908 184 15 15.5206096079202 -0.520609607920211 185 8 14.7662880903322 -6.76628809033216 186 16 14.9680927196659 1.03190728033408 187 17 14.7476768686274 2.2523231313726 188 12 12.5418032885651 -0.541803288565062 189 11 11.5269675255856 -0.526967525585558 190 11 10.2993224089426 0.700677591057419 191 14 15.0449039081772 -1.04490390817718 192 16 15.8549236374795 0.145076362520500 193 12 9.65799989258033 2.34200010741967 194 16 14.3005132593300 1.69948674067001 195 13 13.9159846340245 -0.915984634024543 196 15 15.3686335282855 -0.368633528285528 197 16 13.0983431475463 2.90165685245371 198 16 15.3129697531759 0.687030246824146 199 14 12.4874552007084 1.51254479929164 200 16 14.7705797810563 1.22942021894372 201 16 14.1953897769368 1.80461022306323 202 14 13.5652608133924 0.434739186607567 203 11 13.7622976777595 -2.76229767775952 204 12 14.9165699771728 -2.91656997717275 205 15 12.9696665181991 2.03033348180092 206 15 14.8369644200455 0.163035579954474 207 16 14.847026495686 1.15297350431399 208 16 15.4339487103626 0.566051289637426 209 11 13.9167631437977 -2.91676314379775 210 15 14.3031594704995 0.696840529500508 211 12 14.507489606999 -2.507489606999 212 12 16.2896849694461 -4.28968496944614 213 15 14.3091704811001 0.690829518899902 214 15 12.1674958883062 2.83250411169378 215 16 14.8832893443442 1.11671065565580 216 14 13.4207878308238 0.57921216917622 217 17 15.0626619782301 1.93733802176992 218 14 14.3279169397482 -0.327916939748238 219 13 11.9902889016349 1.00971109836511 220 15 15.6158919610783 -0.615891961078344 221 13 15.0224913327296 -2.02249133272956 222 14 14.5733033465195 -0.573303346519544 223 15 14.5664459129041 0.43355408709592 224 12 13.4585313702885 -1.45853137028855 225 13 12.8042807399043 0.195719260095656 226 8 11.9668684285413 -3.96686842854126 227 14 14.3096831383973 -0.309683138397306 228 14 13.2737435527865 0.726256447213536 229 11 12.3432695732266 -1.34326957322662 230 12 13.1609985574185 -1.16099855741854 231 13 11.4799323515281 1.52006764847186 232 10 13.4650403340905 -3.46504033409047 233 16 11.7004538222459 4.29954617775412 234 18 16.4558663707500 1.54413362925002 235 13 14.3053988244790 -1.30539882447904 236 11 13.6549207425401 -2.65492074254014 237 4 11.1700281372820 -7.17002813728201 238 13 14.8152140281387 -1.81521402813869 239 16 14.5923633054321 1.40763669456793 240 10 11.9287261285823 -1.92872612858232 241 12 12.4071970658913 -0.407197065891325 242 12 13.7956003816510 -1.79560038165098 243 10 8.88634470078797 1.11365529921203 244 13 11.2770068802368 1.72299311976323 245 15 14.0926273160205 0.907372683979529 246 12 12.0467701780665 -0.0467701780665329 247 14 13.1538828662063 0.846117133793704 248 10 12.8902928435778 -2.89029284357777 249 12 10.8009658204609 1.19903417953906 250 12 11.8839336289646 0.116066371035425 251 11 12.1379198030589 -1.13791980305892 252 10 11.8622634576053 -1.86226345760533 253 12 11.6631437816570 0.336856218342975 254 16 13.1782247636368 2.82177523636317 255 12 13.7152063049677 -1.71520630496769 256 14 14.2640878596850 -0.264087859685045 257 16 14.6811885572799 1.31881144272010 258 14 11.8239286814975 2.17607131850247 259 13 14.7816409840600 -1.78164098406003 260 4 9.48330674262236 -5.48330674262236 261 15 14.174366651485 0.825633348514991 262 11 15.5502096888069 -4.55020968880690 263 11 11.4716452522508 -0.471645252250818 264 14 13.1672908525232 0.83270914747681 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.234449524103323 0.468899048206647 0.765550475896677 12 0.120293517840557 0.240587035681113 0.879706482159443 13 0.0815541573457802 0.163108314691560 0.91844584265422 14 0.102874776497918 0.205749552995836 0.897125223502082 15 0.0587519756515502 0.117503951303100 0.94124802434845 16 0.0391686675931634 0.0783373351863268 0.960831332406837 17 0.0630191184441749 0.126038236888350 0.936980881555825 18 0.25586432793531 0.51172865587062 0.74413567206469 19 0.194216632900151 0.388433265800301 0.80578336709985 20 0.137764883334639 0.275529766669278 0.862235116665361 21 0.0986062615513702 0.197212523102740 0.90139373844863 22 0.0968533990427727 0.193706798085545 0.903146600957227 23 0.257054377911139 0.514108755822278 0.742945622088861 24 0.321495418423947 0.642990836847893 0.678504581576054 25 0.294869538595019 0.589739077190038 0.705130461404981 26 0.277447857711977 0.554895715423954 0.722552142288023 27 0.352098888872558 0.704197777745116 0.647901111127442 28 0.363849648859342 0.727699297718684 0.636150351140658 29 0.346785592147590 0.693571184295181 0.65321440785241 30 0.380898386272267 0.761796772544533 0.619101613727733 31 0.328675803111161 0.657351606222323 0.671324196888839 32 0.289492867969932 0.578985735939864 0.710507132030068 33 0.262490777406898 0.524981554813796 0.737509222593102 34 0.226304417033047 0.452608834066093 0.773695582966953 35 0.187880541814586 0.375761083629173 0.812119458185414 36 0.304929814888216 0.609859629776433 0.695070185111784 37 0.334971074151198 0.669942148302397 0.665028925848802 38 0.325963622584243 0.651927245168487 0.674036377415757 39 0.35602273985543 0.71204547971086 0.64397726014457 40 0.334209449134650 0.668418898269301 0.66579055086535 41 0.298001365293739 0.596002730587478 0.701998634706261 42 0.263835728828234 0.527671457656468 0.736164271171766 43 0.278274265211429 0.556548530422857 0.721725734788571 44 0.236536521323935 0.47307304264787 0.763463478676065 45 0.214442280198149 0.428884560396298 0.78555771980185 46 0.392689717772571 0.785379435545142 0.607310282227429 47 0.545519033485654 0.908961933028692 0.454480966514346 48 0.496548776402329 0.993097552804658 0.503451223597671 49 0.483216160724748 0.966432321449497 0.516783839275252 50 0.468390230644651 0.936780461289303 0.531609769355349 51 0.42367172034991 0.84734344069982 0.57632827965009 52 0.378169197572531 0.756338395145061 0.621830802427469 53 0.386603609576097 0.773207219152193 0.613396390423903 54 0.369709551282599 0.739419102565198 0.630290448717401 55 0.360937557172319 0.721875114344638 0.639062442827681 56 0.339385238523737 0.678770477047474 0.660614761476263 57 0.299777754262648 0.599555508525295 0.700222245737352 58 0.271157720239429 0.542315440478858 0.728842279760571 59 0.23669426979653 0.47338853959306 0.76330573020347 60 0.242458614750553 0.484917229501107 0.757541385249447 61 0.218650159104958 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0.0121936684864218 0.993903165756789 230 0.00441036251732997 0.00882072503465995 0.99558963748267 231 0.00439461457994107 0.00878922915988214 0.99560538542006 232 0.00814497957146643 0.0162899591429329 0.991855020428534 233 0.0377565442118784 0.0755130884237568 0.962243455788122 234 0.0542942200569106 0.108588440113821 0.94570577994309 235 0.0405065857547010 0.0810131715094021 0.959493414245299 236 0.0361101125951766 0.0722202251903533 0.963889887404823 237 0.246505700570198 0.493011401140395 0.753494299429802 238 0.200782130963978 0.401564261927957 0.799217869036022 239 0.180044405468033 0.360088810936067 0.819955594531967 240 0.142128535333137 0.284257070666275 0.857871464666863 241 0.113707343103352 0.227414686206705 0.886292656896648 242 0.0945301032407307 0.189060206481461 0.90546989675927 243 0.0879023187197933 0.175804637439587 0.912097681280207 244 0.153550434222244 0.307100868444488 0.846449565777756 245 0.137630339717254 0.275260679434508 0.862369660282746 246 0.110109330538686 0.220218661077373 0.889890669461314 247 0.0777706008222238 0.155541201644448 0.922229399177776 248 0.0666948470256238 0.133389694051248 0.933305152974376 249 0.0624888270323013 0.124977654064603 0.937511172967699 250 0.0773809930539605 0.154761986107921 0.92261900694604 251 0.0460549764082260 0.0921099528164521 0.953945023591774 252 0.112285664162278 0.224571328324556 0.887714335837722 253 0.234998511095394 0.469997022190787 0.765001488904606 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 4 0.0164609053497942 NOK 5% type I error level 79 0.325102880658436 NOK 10% type I error level 128 0.526748971193416 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/10g77d1290504050.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/10g77d1290504050.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/19oak1290504050.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/19oak1290504050.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/29oak1290504050.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/29oak1290504050.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/3kf9n1290504050.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/3kf9n1290504050.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/4kf9n1290504050.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/4kf9n1290504050.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/5kf9n1290504050.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/5kf9n1290504050.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/6u6q81290504050.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/6u6q81290504050.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/7ngqb1290504050.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/7ngqb1290504050.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/8ngqb1290504050.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/8ngqb1290504050.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/9ngqb1290504050.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t1290504002l7jtcr4noyja1oi/9ngqb1290504050.ps (open in new window)

Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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

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

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