| Multiple Linear Regression - Estimated Regression Equation |
| Qualityoflettersofrecommendation[t] = + 2.87926918950499 + 0.0907256384999622CollegeGPA[t] + 1.31916985763979HighSchoolGPA[t] -0.000563091457009581SATtotal[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) | 2.87926918950499 | 0.575957 | 4.9991 | 3e-06 | 1e-06 |
| CollegeGPA | 0.0907256384999622 | 0.203901 | 0.4449 | 0.657358 | 0.328679 |
| HighSchoolGPA | 1.31916985763979 | 0.199975 | 6.5967 | 0 | 0 |
| SATtotal | -0.000563091457009581 | 0.000654 | -0.8616 | 0.391063 | 0.195532 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.63037199537585 |
| R-squared | 0.397368852554131 |
| Adjusted R-squared | 0.378536629196448 |
| F-TEST (value) | 21.100474702686 |
| F-TEST (DF numerator) | 3 |
| F-TEST (DF denominator) | 96 |
| p-value | 1.39666056497845e-10 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1.17887883589416 |
| Sum Squared Residuals | 133.416509733041 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 5 | 5.11337304690064 | -0.11337304690064 |
| 2 | 6 | 6.89058765295017 | -0.890587652950168 |
| 3 | 6 | 7.24854333401823 | -1.24854333401823 |
| 4 | 4 | 4.61304640397146 | -0.613046403971464 |
| 5 | 5 | 6.87790394223787 | -1.87790394223787 |
| 6 | 3 | 2.89343438295188 | 0.106565617048121 |
| 7 | 2 | 2.88362095786913 | -0.883620957869129 |
| 8 | 7 | 5.04652607813967 | 1.95347392186033 |
| 9 | 4 | 5.06073241310514 | -1.06073241310514 |
| 10 | 7 | 5.27166745963991 | 1.72833254036009 |
| 11 | 7 | 5.3206594985471 | 1.6793405014529 |
| 12 | 3 | 4.28649131686314 | -1.28649131686314 |
| 13 | 5 | 4.50415277187583 | 0.495847228124174 |
| 14 | 6 | 6.57562392564208 | -0.575623925642083 |
| 15 | 4 | 5.25370675932148 | -1.25370675932148 |
| 16 | 5 | 5.93775633551585 | -0.937756335515848 |
| 17 | 4 | 4.94013556391842 | -0.940135563918416 |
| 18 | 6 | 6.40334760527824 | -0.403347605278241 |
| 19 | 5 | 4.58239857469656 | 0.41760142530344 |
| 20 | 4 | 5.05733127371581 | -1.05733127371581 |
| 21 | 6 | 5.02614520508141 | 0.973854794918595 |
| 22 | 3 | 4.63921857600896 | -1.63921857600896 |
| 23 | 6 | 4.76764699996227 | 1.23235300003773 |
| 24 | 7 | 4.98951972409228 | 2.01048027590772 |
| 25 | 6 | 6.84596613244375 | -0.845966132443748 |
| 26 | 5 | 3.64986601459383 | 1.35013398540617 |
| 27 | 5 | 5.45934666737212 | -0.459346667372118 |
| 28 | 3 | 4.9354288014515 | -1.9354288014515 |
| 29 | 5 | 4.8946131491016 | 0.105386850898404 |
| 30 | 3 | 3.76337018432769 | -0.76337018432769 |
| 31 | 10 | 7.15251666798783 | 2.84748333201217 |
| 32 | 5 | 5.68333184409765 | -0.683331844097648 |
| 33 | 5 | 4.81823191457738 | 0.181768085422616 |
| 34 | 5 | 4.84232624615283 | 0.157673753847165 |
| 35 | 3 | 4.36933650214671 | -1.36933650214671 |
| 36 | 4 | 4.60065807610324 | -0.600658076103244 |
| 37 | 6 | 6.03725148912549 | -0.0372514891254924 |
| 38 | 5 | 5.06935380868548 | -0.0693538086854771 |
| 39 | 6 | 6.04169406263764 | -0.0416940626376422 |
| 40 | 5 | 5.27328080286179 | -0.273280802861792 |
| 41 | 6 | 5.25300247614123 | 0.74699752385877 |
| 42 | 5 | 4.39255803591903 | 0.607441964080968 |
| 43 | 6 | 5.72304045041915 | 0.276959549580845 |
| 44 | 4 | 6.23367125419739 | -2.23367125419739 |
| 45 | 5 | 5.14587935259777 | -0.145879352597769 |
| 46 | 4 | 4.72798177127868 | -0.727981771278683 |
| 47 | 7 | 6.15902292664774 | 0.840977073352264 |
| 48 | 4 | 4.75217366197384 | -0.752173661973844 |
| 49 | 6 | 4.92714334421952 | 1.07285665578048 |
| 50 | 7 | 5.94062760410491 | 1.05937239589509 |
| 51 | 6 | 5.82212922010848 | 0.177870779891517 |
| 52 | 6 | 5.96153783803222 | 0.0384621619677803 |
| 53 | 3 | 4.66749518341426 | -1.66749518341426 |
| 54 | 4 | 5.35842267400524 | -1.35842267400524 |
| 55 | 5 | 5.4038986138021 | -0.403898613802095 |
| 56 | 6 | 4.29000600926204 | 1.70999399073796 |
| 57 | 6 | 5.15660011519672 | 0.843399884803283 |
| 58 | 3 | 4.84038396333333 | -1.84038396333333 |
| 59 | 2 | 4.00591854282824 | -2.00591854282824 |
| 60 | 7 | 6.95385085859689 | 0.0461491414031065 |
| 61 | 6 | 6.48741228999159 | -0.487412289991588 |
| 62 | 3 | 3.18389114933828 | -0.183891149338284 |
| 63 | 8 | 6.86169190810104 | 1.13830809189896 |
| 64 | 5 | 4.26003047538766 | 0.739969524612343 |
| 65 | 5 | 4.8367470016968 | 0.163252998303204 |
| 66 | 5 | 4.99914545710092 | 0.000854542899078447 |
| 67 | 6 | 6.14998702198145 | -0.149987021981447 |
| 68 | 4 | 4.58821906612859 | -0.588219066128595 |
| 69 | 6 | 4.8481241469376 | 1.1518758530624 |
| 70 | 5 | 4.04569531298866 | 0.954304687011337 |
| 71 | 6 | 3.53744177734062 | 2.46255822265938 |
| 72 | 4 | 4.85776752394112 | -0.857767523941123 |
| 73 | 2 | 4.37176638278489 | -2.37176638278489 |
| 74 | 4 | 6.15172951515756 | -2.15172951515756 |
| 75 | 4 | 4.83383467272034 | -0.833834672720343 |
| 76 | 4 | 4.18729449497612 | -0.187294494976119 |
| 77 | 5 | 4.59004540626759 | 0.409954593732412 |
| 78 | 7 | 6.31520700626212 | 0.684792993737877 |
| 79 | 6 | 4.80708351674997 | 1.19291648325003 |
| 80 | 4 | 4.73126566921398 | -0.731265669213976 |
| 81 | 4 | 4.95321799770291 | -0.953217997702908 |
| 82 | 6 | 6.79889456584031 | -0.79889456584031 |
| 83 | 6 | 4.019857780526 | 1.980142219474 |
| 84 | 5 | 4.66971980911464 | 0.330280190885363 |
| 85 | 6 | 5.4261634216772 | 0.573836578322802 |
| 86 | 8 | 6.153873202208 | 1.846126797792 |
| 87 | 6 | 5.40029280548928 | 0.599707194510722 |
| 88 | 6 | 5.0884443803624 | 0.9115556196376 |
| 89 | 9 | 7.98604485081282 | 1.01395514918718 |
| 90 | 6 | 4.89021772280302 | 1.10978227719698 |
| 91 | 7 | 5.88703319329074 | 1.11296680670926 |
| 92 | 6 | 5.10487318604012 | 0.89512681395988 |
| 93 | 7 | 5.35193703442692 | 1.64806296557308 |
| 94 | 6 | 5.45990372780322 | 0.540096272196775 |
| 95 | 7 | 5.59718201445374 | 1.40281798554626 |
| 96 | 4 | 4.77130730052278 | -0.771307300522784 |
| 97 | 6 | 4.85136124899081 | 1.14863875100919 |
| 98 | 4 | 5.72301141151797 | -1.72301141151797 |
| 99 | 6 | 4.83029067121996 | 1.16970932878004 |
| 100 | 2 | 4.05650781808143 | -2.05650781808143 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 7 | 0.128199313157727 | 0.256398626315455 | 0.871800686842273 |
| 8 | 0.578403878635478 | 0.843192242729044 | 0.421596121364522 |
| 9 | 0.602711507800439 | 0.794576984399122 | 0.397288492199561 |
| 10 | 0.73428120891711 | 0.53143758216578 | 0.26571879108289 |
| 11 | 0.807276765512683 | 0.385446468974635 | 0.192723234487317 |
| 12 | 0.833576673059948 | 0.332846653880104 | 0.166423326940052 |
| 13 | 0.768515193581228 | 0.462969612837544 | 0.231484806418772 |
| 14 | 0.69292667332938 | 0.61414665334124 | 0.30707332667062 |
| 15 | 0.647945930349456 | 0.704108139301088 | 0.352054069650544 |
| 16 | 0.576957367683183 | 0.846085264633634 | 0.423042632316817 |
| 17 | 0.502318076813654 | 0.995363846372691 | 0.497681923186346 |
| 18 | 0.426327498445344 | 0.852654996890689 | 0.573672501554656 |
| 19 | 0.356979442576168 | 0.713958885152336 | 0.643020557423832 |
| 20 | 0.329321826873428 | 0.658643653746856 | 0.670678173126572 |
| 21 | 0.320692704245552 | 0.641385408491105 | 0.679307295754448 |
| 22 | 0.469456280742041 | 0.938912561484083 | 0.530543719257959 |
| 23 | 0.473673770904564 | 0.947347541809129 | 0.526326229095435 |
| 24 | 0.626659073437625 | 0.746681853124751 | 0.373340926562375 |
| 25 | 0.602644217631708 | 0.794711564736584 | 0.397355782368292 |
| 26 | 0.580138650001896 | 0.839722699996208 | 0.419861349998104 |
| 27 | 0.521273629527015 | 0.95745274094597 | 0.478726370472985 |
| 28 | 0.591973490959349 | 0.816053018081302 | 0.408026509040651 |
| 29 | 0.527145711763448 | 0.945708576473105 | 0.472854288236552 |
| 30 | 0.499441302201549 | 0.998882604403098 | 0.500558697798451 |
| 31 | 0.778132516671033 | 0.443734966657935 | 0.221867483328967 |
| 32 | 0.746840756332207 | 0.506318487335586 | 0.253159243667793 |
| 33 | 0.694307265548766 | 0.611385468902469 | 0.305692734451234 |
| 34 | 0.65843492495688 | 0.683130150086241 | 0.34156507504312 |
| 35 | 0.671211883428003 | 0.657576233143995 | 0.328788116571997 |
| 36 | 0.623338558473471 | 0.753322883053058 | 0.376661441526529 |
| 37 | 0.564881206264272 | 0.870237587471456 | 0.435118793735728 |
| 38 | 0.5170383411048 | 0.9659233177904 | 0.4829616588952 |
| 39 | 0.461760260557694 | 0.923520521115388 | 0.538239739442306 |
| 40 | 0.404324656510941 | 0.808649313021881 | 0.595675343489059 |
| 41 | 0.401894077678387 | 0.803788155356774 | 0.598105922321613 |
| 42 | 0.369213892155594 | 0.738427784311187 | 0.630786107844406 |
| 43 | 0.316114245991879 | 0.632228491983757 | 0.683885754008121 |
| 44 | 0.431663096903513 | 0.863326193807027 | 0.568336903096487 |
| 45 | 0.383339688586334 | 0.766679377172669 | 0.616660311413666 |
| 46 | 0.352246140362815 | 0.70449228072563 | 0.647753859637185 |
| 47 | 0.343583174138099 | 0.687166348276198 | 0.656416825861901 |
| 48 | 0.310849369952079 | 0.621698739904158 | 0.689150630047921 |
| 49 | 0.308490593474744 | 0.616981186949488 | 0.691509406525256 |
| 50 | 0.306984751113382 | 0.613969502226763 | 0.693015248886618 |
| 51 | 0.259150815135788 | 0.518301630271576 | 0.740849184864212 |
| 52 | 0.215205163451794 | 0.430410326903589 | 0.784794836548206 |
| 53 | 0.261525417484919 | 0.523050834969837 | 0.738474582515081 |
| 54 | 0.281147228671214 | 0.562294457342428 | 0.718852771328786 |
| 55 | 0.241461098839942 | 0.482922197679884 | 0.758538901160058 |
| 56 | 0.291481243178425 | 0.582962486356849 | 0.708518756821575 |
| 57 | 0.266996606954055 | 0.53399321390811 | 0.733003393045945 |
| 58 | 0.343969261328418 | 0.687938522656835 | 0.656030738671582 |
| 59 | 0.456957687471486 | 0.913915374942973 | 0.543042312528514 |
| 60 | 0.399694203206981 | 0.799388406413961 | 0.60030579679302 |
| 61 | 0.358669591254134 | 0.717339182508267 | 0.641330408745866 |
| 62 | 0.305040321371257 | 0.610080642742514 | 0.694959678628743 |
| 63 | 0.30756115853007 | 0.61512231706014 | 0.69243884146993 |
| 64 | 0.275873176595622 | 0.551746353191243 | 0.724126823404378 |
| 65 | 0.227333720480382 | 0.454667440960764 | 0.772666279519618 |
| 66 | 0.188561961586096 | 0.377123923172192 | 0.811438038413904 |
| 67 | 0.15121504456154 | 0.302430089123079 | 0.84878495543846 |
| 68 | 0.132912576759266 | 0.265825153518532 | 0.867087423240734 |
| 69 | 0.122928984526984 | 0.245857969053967 | 0.877071015473016 |
| 70 | 0.105763165170603 | 0.211526330341206 | 0.894236834829397 |
| 71 | 0.223083097331947 | 0.446166194663894 | 0.776916902668053 |
| 72 | 0.189839720354538 | 0.379679440709076 | 0.810160279645462 |
| 73 | 0.344468040043362 | 0.688936080086724 | 0.655531959956638 |
| 74 | 0.580243966321798 | 0.839512067356404 | 0.419756033678202 |
| 75 | 0.555545455694101 | 0.888909088611799 | 0.444454544305899 |
| 76 | 0.492386206093615 | 0.98477241218723 | 0.507613793906385 |
| 77 | 0.422844453807721 | 0.845688907615441 | 0.577155546192279 |
| 78 | 0.363043278017342 | 0.726086556034684 | 0.636956721982658 |
| 79 | 0.3413460455143 | 0.682692091028601 | 0.6586539544857 |
| 80 | 0.31575358827441 | 0.63150717654882 | 0.68424641172559 |
| 81 | 0.336399346743211 | 0.672798693486422 | 0.663600653256789 |
| 82 | 0.38555179611426 | 0.77110359222852 | 0.61444820388574 |
| 83 | 0.499712862515343 | 0.999425725030686 | 0.500287137484657 |
| 84 | 0.413999132396524 | 0.827998264793048 | 0.586000867603476 |
| 85 | 0.334072719010767 | 0.668145438021535 | 0.665927280989233 |
| 86 | 0.334282344829568 | 0.668564689659136 | 0.665717655170432 |
| 87 | 0.254500305959622 | 0.509000611919244 | 0.745499694040378 |
| 88 | 0.1960404210251 | 0.392080842050199 | 0.8039595789749 |
| 89 | 0.165086235275155 | 0.330172470550309 | 0.834913764724845 |
| 90 | 0.137293051974971 | 0.274586103949941 | 0.86270694802503 |
| 91 | 0.0873729134018217 | 0.174745826803643 | 0.912627086598178 |
| 92 | 0.050123441900381 | 0.100246883800762 | 0.949876558099619 |
| 93 | 0.0488822164566401 | 0.0977644329132801 | 0.95111778354336 |
| 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 | 1 | 0.0114942528735632 | OK |
