| Multiple Linear Regression - Estimated Regression Equation |
| last[t] = + 3.42663860924614 + 0.352334244344399position[t] + 0.0449403567869172starters[t] -0.00140864859833935since[t] -0.204183757308926number[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) | 3.42663860924614 | 1.639668 | 2.0898 | 0.039249 | 0.019624 |
| position | 0.352334244344399 | 0.099933 | 3.5257 | 0.000647 | 0.000323 |
| starters | 0.0449403567869172 | 0.130371 | 0.3447 | 0.731057 | 0.365529 |
| since | -0.00140864859833935 | 0.007271 | -0.1937 | 0.846787 | 0.423394 |
| number | -0.204183757308926 | 0.093056 | -2.1942 | 0.030609 | 0.015305 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.359603331503972 |
| R-squared | 0.129314556028756 |
| Adjusted R-squared | 0.093410001638189 |
| F-TEST (value) | 3.60161985641384 |
| F-TEST (DF numerator) | 4 |
| F-TEST (DF denominator) | 97 |
| p-value | 0.00880869497153691 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 3.74917071343406 |
| Sum Squared Residuals | 1363.45926073175 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1 | 3.30203959827342 | -2.30203959827342 |
| 2 | 3 | 4.17113700985753 | -1.17113700985753 |
| 3 | 2 | 4.21089184427115 | -2.21089184427115 |
| 4 | 1 | 4.15204127680102 | -3.15204127680102 |
| 5 | 5 | 3.92133558033349 | 1.07866441966651 |
| 6 | 8 | 5.24810320747732 | 2.75189679252268 |
| 7 | 3 | 4.60635327809582 | -1.60635327809582 |
| 8 | 8 | 5.36142044266471 | 2.63857955733529 |
| 9 | 12 | 3.47757507962608 | 8.52242492037392 |
| 10 | 3 | 2.81039918602419 | 0.189600813975814 |
| 11 | 8 | 3.56405770199474 | 4.43594229800526 |
| 12 | 3 | 4.94717127307214 | -1.94717127307214 |
| 13 | 3 | 3.25625929572895 | -0.256259295728946 |
| 14 | 3 | 4.43237181230075 | -1.43237181230075 |
| 15 | 3 | 6.20835776341427 | -3.20835776341427 |
| 16 | 1 | 5.53695592401736 | -4.53695592401736 |
| 17 | 2 | 5.07537243632273 | -3.07537243632273 |
| 18 | 20 | 6.8527670360346 | 13.1472329639654 |
| 19 | 2 | 6.80659430594952 | -4.80659430594952 |
| 20 | 1 | 5.91551357466195 | -4.91551357466195 |
| 21 | 1 | 3.74548692948982 | -2.74548692948982 |
| 22 | 6 | 3.69931419940474 | 2.30068580059526 |
| 23 | 8 | 3.43909717182236 | 4.56090282817764 |
| 24 | 5 | 2.97469638693106 | 2.02530361306894 |
| 25 | 1 | 4.54931587793234 | -3.54931587793234 |
| 26 | 7 | 5.72120244870912 | 1.27879755129088 |
| 27 | 7 | 4.44006663458211 | 2.55993336541789 |
| 28 | 5 | 6.02736396296844 | -1.02736396296844 |
| 29 | 8 | 4.93632542016696 | 3.06367457983304 |
| 30 | 2 | 3.77586549630386 | -1.77586549630386 |
| 31 | 5 | 3.91415544315095 | 1.08584455684905 |
| 32 | 2 | 3.64971246977356 | -1.64971246977356 |
| 33 | 5 | 4.23017749759865 | 0.769822502401349 |
| 34 | 1 | 3.12082652301876 | -2.12082652301876 |
| 35 | 2 | 2.77186463374101 | -0.771864633741008 |
| 36 | 6 | 4.6647684185167 | 1.3352315814833 |
| 37 | 3 | 6.6505727213325 | -3.6505727213325 |
| 38 | 6 | 5.03424883025101 | 0.965751169748991 |
| 39 | 6 | 6.23282943494596 | -0.232829434945959 |
| 40 | 1 | 6.98078306707288 | -5.98078306707288 |
| 41 | 2 | 6.01807212562084 | -4.01807212562084 |
| 42 | 10 | 5.73672536906337 | 4.26327463093663 |
| 43 | 1 | 5.90318828787726 | -4.90318828787726 |
| 44 | 2 | 2.31149937854283 | -0.311499378542833 |
| 45 | 1 | 4.07339884367296 | -3.07339884367296 |
| 46 | 1 | 4.63977738551466 | -3.63977738551466 |
| 47 | 1 | 2.74186435366586 | -1.74186435366586 |
| 48 | 6 | 4.93607835958561 | 1.06392164041439 |
| 49 | 4 | 5.89110333566841 | -1.89110333566841 |
| 50 | 9 | 4.61841941313144 | 4.38158058686856 |
| 51 | 10 | 5.79453192970324 | 4.20546807029676 |
| 52 | 6 | 5.52727165912916 | 0.472728340870837 |
| 53 | 1 | 6.0950588495692 | -5.0950588495692 |
| 54 | 6 | 5.41943106437728 | 0.580568935622723 |
| 55 | 18 | 6.8954451534948 | 11.1045548465052 |
| 56 | 3 | 6.3212400673833 | -3.3212400673833 |
| 57 | 4 | 3.79638352292951 | 0.203616477070485 |
| 58 | 1 | 3.13343357512264 | -2.13343357512264 |
| 59 | 3 | 2.25080473542511 | 0.749195264574888 |
| 60 | 5 | 2.70308274080132 | 2.29691725919868 |
| 61 | 4 | 2.5414711151027 | 1.4585288848973 |
| 62 | 4 | 5.75237796177206 | -1.75237796177206 |
| 63 | 1 | 5.29502041987246 | -4.29502041987246 |
| 64 | 17 | 6.84569288470196 | 10.154307115298 |
| 65 | 2 | 4.16062644418258 | -2.16062644418258 |
| 66 | 1 | 5.12832925765044 | -4.12832925765044 |
| 67 | 6 | 7.11554220906458 | -1.11554220906458 |
| 68 | 10 | 4.79376652801619 | 5.20623347198381 |
| 69 | 9 | 7.61602694044445 | 1.38397305955555 |
| 70 | 5 | 7.15162615555315 | -2.15162615555315 |
| 71 | 1 | 7.08714099368966 | -6.08714099368966 |
| 72 | 13 | 5.78487545058756 | 7.21512454941244 |
| 73 | 11 | 8.59727532282745 | 2.40272467717255 |
| 74 | 9 | 8.3525534298268 | 0.647446570173197 |
| 75 | 4 | 7.07564356149482 | -3.07564356149482 |
| 76 | 4 | 3.53237597660137 | 0.46762402339863 |
| 77 | 5 | 4.49726149287255 | 0.502738507127454 |
| 78 | 2 | 4.43559362820574 | -2.43559362820574 |
| 79 | 1 | 3.57268586888496 | -2.57268586888496 |
| 80 | 2 | 3.50679205842313 | -1.50679205842313 |
| 81 | 4 | 3.6549425454586 | 0.345057454541398 |
| 82 | 12 | 6.05474895728562 | 5.94525104271438 |
| 83 | 14 | 5.38616441508539 | 8.61383558491461 |
| 84 | 2 | 5.92718728215698 | -3.92718728215698 |
| 85 | 7 | 6.49920041839204 | 0.500799581607963 |
| 86 | 4 | 6.22912285062128 | -2.22912285062128 |
| 87 | 1 | 6.17308958034783 | -5.17308958034783 |
| 88 | 6 | 5.90301201257708 | 0.0969879874229223 |
| 89 | 2 | 3.9772319564161 | -1.9772319564161 |
| 90 | 1 | 2.83407341547607 | -1.83407341547607 |
| 91 | 4 | 4.27212428188871 | -0.27212428188871 |
| 92 | 6 | 5.23137520376653 | 0.768624796233471 |
| 93 | 7 | 2.94904168347164 | 4.05095831652836 |
| 94 | 9 | 4.67149898784827 | 4.32850101215173 |
| 95 | 1 | 4.47044520139615 | -3.47044520139615 |
| 96 | 3 | 5.62965393478787 | -2.62965393478787 |
| 97 | 6 | 4.68497426731313 | 1.31502573268687 |
| 98 | 8 | 6.50892456022047 | 1.49107543977953 |
| 99 | 8 | 7.29920793974785 | 0.700792060252152 |
| 100 | 4 | 5.58998353062624 | -1.58998353062624 |
| 101 | 8 | 6.10705937152606 | 1.89294062847394 |
| 102 | 7 | 5.88205855890217 | 1.11794144109783 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 8 | 0.103429947544564 | 0.206859895089127 | 0.896570052455436 |
| 9 | 0.0403502035219053 | 0.0807004070438106 | 0.959649796478095 |
| 10 | 0.165999867060003 | 0.331999734120005 | 0.834000132939997 |
| 11 | 0.0973737973458012 | 0.194747594691602 | 0.902626202654199 |
| 12 | 0.440882663225413 | 0.881765326450826 | 0.559117336774587 |
| 13 | 0.394605710657369 | 0.789211421314738 | 0.605394289342631 |
| 14 | 0.364671350143335 | 0.729342700286669 | 0.635328649856665 |
| 15 | 0.349883646342643 | 0.699767292685286 | 0.650116353657357 |
| 16 | 0.348417910198731 | 0.696835820397461 | 0.651582089801269 |
| 17 | 0.283232299505971 | 0.566464599011941 | 0.716767700494029 |
| 18 | 0.950644830626652 | 0.0987103387466963 | 0.0493551693733482 |
| 19 | 0.963561475930184 | 0.0728770481396311 | 0.0364385240698155 |
| 20 | 0.961779557990184 | 0.0764408840196313 | 0.0382204420098156 |
| 21 | 0.954548768252043 | 0.090902463495914 | 0.045451231747957 |
| 22 | 0.942786776857195 | 0.11442644628561 | 0.0572132231428052 |
| 23 | 0.953647777932294 | 0.0927044441354113 | 0.0463522220677057 |
| 24 | 0.943545798917349 | 0.112908402165302 | 0.0564542010826512 |
| 25 | 0.935145012081988 | 0.129709975836023 | 0.0648549879180115 |
| 26 | 0.915160814321137 | 0.169678371357727 | 0.0848391856788634 |
| 27 | 0.908037477114475 | 0.183925045771051 | 0.0919625228855253 |
| 28 | 0.877720657848455 | 0.24455868430309 | 0.122279342151545 |
| 29 | 0.875590479193472 | 0.248819041613057 | 0.124409520806528 |
| 30 | 0.854682263876642 | 0.290635472246716 | 0.145317736123358 |
| 31 | 0.816126464264929 | 0.367747071470143 | 0.183873535735071 |
| 32 | 0.782153468385622 | 0.435693063228756 | 0.217846531614378 |
| 33 | 0.733977582307575 | 0.53204483538485 | 0.266022417692425 |
| 34 | 0.695772237509987 | 0.608455524980026 | 0.304227762490013 |
| 35 | 0.640402837065793 | 0.719194325868414 | 0.359597162934207 |
| 36 | 0.5906738073573 | 0.8186523852854 | 0.4093261926427 |
| 37 | 0.576933449562231 | 0.846133100875539 | 0.423066550437769 |
| 38 | 0.519594341335154 | 0.960811317329692 | 0.480405658664846 |
| 39 | 0.460812033549628 | 0.921624067099256 | 0.539187966450372 |
| 40 | 0.607972287904853 | 0.784055424190294 | 0.392027712095147 |
| 41 | 0.592158712220774 | 0.815682575558453 | 0.407841287779227 |
| 42 | 0.631181415511268 | 0.737637168977463 | 0.368818584488732 |
| 43 | 0.646477327945165 | 0.707045344109671 | 0.353522672054835 |
| 44 | 0.592149323043242 | 0.815701353913517 | 0.407850676956758 |
| 45 | 0.570596602205582 | 0.858806795588835 | 0.429403397794418 |
| 46 | 0.559534206176705 | 0.88093158764659 | 0.440465793823295 |
| 47 | 0.510160990803186 | 0.979678018393628 | 0.489839009196814 |
| 48 | 0.459805484649879 | 0.919610969299757 | 0.540194515350121 |
| 49 | 0.416078799255717 | 0.832157598511434 | 0.583921200744283 |
| 50 | 0.451433940364685 | 0.902867880729371 | 0.548566059635315 |
| 51 | 0.48097828820622 | 0.961956576412439 | 0.51902171179378 |
| 52 | 0.424940591722046 | 0.849881183444091 | 0.575059408277954 |
| 53 | 0.456638918375078 | 0.913277836750157 | 0.543361081624922 |
| 54 | 0.402834817864022 | 0.805669635728044 | 0.597165182135978 |
| 55 | 0.774572904491615 | 0.450854191016769 | 0.225427095508385 |
| 56 | 0.758858730361797 | 0.482282539276405 | 0.241141269638203 |
| 57 | 0.711546316881818 | 0.576907366236364 | 0.288453683118182 |
| 58 | 0.671235008025068 | 0.657529983949864 | 0.328764991974932 |
| 59 | 0.620028010545394 | 0.759943978909213 | 0.379971989454606 |
| 60 | 0.577149202631245 | 0.84570159473751 | 0.422850797368755 |
| 61 | 0.530993325502895 | 0.93801334899421 | 0.469006674497105 |
| 62 | 0.485866246173615 | 0.971732492347229 | 0.514133753826385 |
| 63 | 0.508935170730429 | 0.982129658539141 | 0.491064829269571 |
| 64 | 0.813603369296484 | 0.372793261407032 | 0.186396630703516 |
| 65 | 0.781815629748329 | 0.436368740503341 | 0.218184370251671 |
| 66 | 0.795556049655748 | 0.408887900688505 | 0.204443950344252 |
| 67 | 0.75329532019806 | 0.49340935960388 | 0.24670467980194 |
| 68 | 0.787979086559713 | 0.424041826880575 | 0.212020913440287 |
| 69 | 0.745154645371625 | 0.509690709256749 | 0.254845354628375 |
| 70 | 0.707118024031003 | 0.585763951937995 | 0.292881975968997 |
| 71 | 0.821886453622645 | 0.35622709275471 | 0.178113546377355 |
| 72 | 0.914299088394346 | 0.171401823211309 | 0.0857009116056543 |
| 73 | 0.894992145932811 | 0.210015708134378 | 0.105007854067189 |
| 74 | 0.866111228200989 | 0.267777543598022 | 0.133888771799011 |
| 75 | 0.836886248496849 | 0.326227503006302 | 0.163113751503151 |
| 76 | 0.789785967947107 | 0.420428064105787 | 0.210214032052893 |
| 77 | 0.734079473209486 | 0.531841053581029 | 0.265920526790515 |
| 78 | 0.698376646147989 | 0.603246707704021 | 0.301623353852011 |
| 79 | 0.661194408321166 | 0.677611183357668 | 0.338805591678834 |
| 80 | 0.604868920110252 | 0.790262159779496 | 0.395131079889748 |
| 81 | 0.527609252252489 | 0.944781495495022 | 0.472390747747511 |
| 82 | 0.629916309468871 | 0.740167381062259 | 0.370083690531129 |
| 83 | 0.966463682804525 | 0.06707263439095 | 0.033536317195475 |
| 84 | 0.954387024653367 | 0.0912259506932668 | 0.0456129753466334 |
| 85 | 0.948933638199486 | 0.102132723601028 | 0.0510663618005142 |
| 86 | 0.918750972086821 | 0.162498055826358 | 0.0812490279131792 |
| 87 | 0.927933415245782 | 0.144133169508437 | 0.0720665847542184 |
| 88 | 0.881820229427039 | 0.236359541145922 | 0.118179770572961 |
| 89 | 0.832630890689383 | 0.334738218621234 | 0.167369109310617 |
| 90 | 0.807512711930903 | 0.384974576138194 | 0.192487288069097 |
| 91 | 0.71959599076282 | 0.560808018474361 | 0.28040400923718 |
| 92 | 0.593110476623631 | 0.813779046752738 | 0.406889523376369 |
| 93 | 0.631628369734874 | 0.736743260530252 | 0.368371630265126 |
| 94 | 0.961170109250675 | 0.0776597814986495 | 0.0388298907493247 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 0 | 0 | OK |
| 5% type I error level | 0 | 0 | OK |
| 10% type I error level | 9 | 0.103448275862069 | NOK |
