| Multiple Linear Regression - Estimated Regression Equation |
| Happiness[t] = + 18.471365186477 -0.371850791919597Depression[t] + 0.0345840445486369Belonging[t] -0.055174226725832Popularity[t] -0.044863835273013ConcernOverMistakes[t] + 0.111652445263202ParentalExpectations[t] -0.0792229760776518ParentalCriticism[t] -0.0548112247843105Organization[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) | 18.471365186477 | 2.203709 | 8.3819 | 0 | 0 |
| Depression | -0.371850791919597 | 0.058378 | -6.3697 | 0 | 0 |
| Belonging | 0.0345840445486369 | 0.017175 | 2.0136 | 0.046131 | 0.023066 |
| Popularity | -0.055174226725832 | 0.06232 | -0.8853 | 0.377623 | 0.188811 |
| ConcernOverMistakes | -0.044863835273013 | 0.032106 | -1.3974 | 0.164698 | 0.082349 |
| ParentalExpectations | 0.111652445263202 | 0.06177 | 1.8076 | 0.073006 | 0.036503 |
| ParentalCriticism | -0.0792229760776518 | 0.078443 | -1.0099 | 0.314411 | 0.157206 |
| Organization | -0.0548112247843105 | 0.04683 | -1.1704 | 0.243988 | 0.121994 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.589629676961936 |
| R-squared | 0.347663155954237 |
| Adjusted R-squared | 0.312265032633924 |
| F-TEST (value) | 9.8215137793685 |
| F-TEST (DF numerator) | 7 |
| F-TEST (DF denominator) | 129 |
| p-value | 8.89102680368126e-10 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1.96609240890953 |
| Sum Squared Residuals | 498.651997487945 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 15 | 15.5707562793551 | -0.570756279355079 |
| 2 | 9 | 10.3104946440228 | -1.31049464402285 |
| 3 | 12 | 13.2872868490608 | -1.28728684906084 |
| 4 | 15 | 15.7596521693943 | -0.759652169394276 |
| 5 | 17 | 16.9594491810736 | 0.0405508189263842 |
| 6 | 14 | 13.6444380943195 | 0.355561905680517 |
| 7 | 9 | 11.338393560231 | -2.33839356023097 |
| 8 | 11 | 10.2353489648617 | 0.764651035138326 |
| 9 | 13 | 14.3700357514864 | -1.3700357514864 |
| 10 | 16 | 15.0322900651484 | 0.967709934851635 |
| 11 | 16 | 13.4518513150728 | 2.54814868492719 |
| 12 | 15 | 14.0146607612581 | 0.985339238741861 |
| 13 | 10 | 14.4800538394313 | -4.48005383943129 |
| 14 | 16 | 15.4035617678356 | 0.596438232164388 |
| 15 | 12 | 15.286873265127 | -3.286873265127 |
| 16 | 15 | 14.4674072723848 | 0.532592727615223 |
| 17 | 13 | 12.0935766854827 | 0.906423314517342 |
| 18 | 18 | 14.7342648329791 | 3.26573516702093 |
| 19 | 13 | 14.3342792470557 | -1.33427924705572 |
| 20 | 17 | 13.6331839923959 | 3.36681600760409 |
| 21 | 14 | 13.9204274772932 | 0.079572522706769 |
| 22 | 13 | 15.3063437098016 | -2.30634370980158 |
| 23 | 13 | 16.3897532294179 | -3.38975322941788 |
| 24 | 15 | 15.4737345070114 | -0.473734507011405 |
| 25 | 15 | 13.0121552007422 | 1.98784479925784 |
| 26 | 13 | 12.9367216053715 | 0.0632783946285424 |
| 27 | 13 | 15.2945073884385 | -2.29450738843846 |
| 28 | 16 | 13.5526424224004 | 2.44735757759957 |
| 29 | 14 | 16.030331275342 | -2.03033127534201 |
| 30 | 18 | 15.6798463080327 | 2.32015369196734 |
| 31 | 9 | 10.8608358757501 | -1.86083587575015 |
| 32 | 16 | 15.9316467667114 | 0.0683532332886011 |
| 33 | 16 | 15.1233462392428 | 0.87665376075715 |
| 34 | 17 | 14.9315112168208 | 2.06848878317921 |
| 35 | 13 | 15.1218125862326 | -2.12181258623264 |
| 36 | 17 | 13.8191280508301 | 3.18087194916987 |
| 37 | 15 | 12.9661713672121 | 2.03382863278794 |
| 38 | 14 | 13.9754544326756 | 0.0245455673244031 |
| 39 | 10 | 12.2188287717503 | -2.21882877175033 |
| 40 | 13 | 14.1477302007365 | -1.14773020073655 |
| 41 | 11 | 13.8299133460184 | -2.82991334601836 |
| 42 | 11 | 13.1604469223968 | -2.16044692239679 |
| 43 | 15 | 15.6721109996737 | -0.672110999673656 |
| 44 | 15 | 15.4522148076881 | -0.452214807688086 |
| 45 | 12 | 12.7666518496131 | -0.766651849613136 |
| 46 | 17 | 15.0257319155093 | 1.97426808449065 |
| 47 | 15 | 13.5365404694218 | 1.46345953057819 |
| 48 | 16 | 15.3471296410326 | 0.652870358967448 |
| 49 | 14 | 13.8361917074415 | 0.163808292558475 |
| 50 | 17 | 14.7708232574782 | 2.22917674252177 |
| 51 | 10 | 10.1667732862057 | -0.166773286205738 |
| 52 | 11 | 14.3742513001651 | -3.37425130016508 |
| 53 | 15 | 13.9650213652633 | 1.03497863473669 |
| 54 | 15 | 14.8739562956362 | 0.126043704363799 |
| 55 | 7 | 10.8213126923863 | -3.82131269238629 |
| 56 | 17 | 15.0204441000745 | 1.97955589992549 |
| 57 | 14 | 12.5899954853358 | 1.41000451466421 |
| 58 | 18 | 16.2121583093109 | 1.78784169068912 |
| 59 | 14 | 13.8022396066041 | 0.197760393395936 |
| 60 | 14 | 15.1021069058429 | -1.1021069058429 |
| 61 | 9 | 15.5227535945348 | -6.52275359453481 |
| 62 | 14 | 14.4643505477734 | -0.464350547773396 |
| 63 | 11 | 12.4456382773282 | -1.44563827732819 |
| 64 | 16 | 13.8024934184012 | 2.19750658159875 |
| 65 | 17 | 15.2301181212198 | 1.7698818787802 |
| 66 | 12 | 15.2717598774344 | -3.27175987743435 |
| 67 | 15 | 13.7623377654847 | 1.23766223451528 |
| 68 | 15 | 15.3076249728366 | -0.30762497283657 |
| 69 | 16 | 16.18366555304 | -0.183665553040031 |
| 70 | 16 | 16.3694197038323 | -0.369419703832316 |
| 71 | 11 | 12.7190564215049 | -1.71905642150492 |
| 72 | 12 | 12.8950548880976 | -0.8950548880976 |
| 73 | 14 | 14.109227977714 | -0.109227977713956 |
| 74 | 15 | 15.6425332638628 | -0.642533263862847 |
| 75 | 17 | 15.4105009188413 | 1.58949908115866 |
| 76 | 19 | 14.711572918669 | 4.288427081331 |
| 77 | 15 | 13.9436180294779 | 1.05638197052208 |
| 78 | 16 | 13.2126280746209 | 2.78737192537908 |
| 79 | 14 | 14.4413997796972 | -0.441399779697186 |
| 80 | 16 | 11.3168274791738 | 4.68317252082618 |
| 81 | 15 | 14.7454605985579 | 0.254539401442148 |
| 82 | 17 | 14.6290650709815 | 2.37093492901845 |
| 83 | 12 | 14.2089367767596 | -2.20893677675965 |
| 84 | 18 | 14.8776549168948 | 3.12234508310518 |
| 85 | 13 | 14.4011155726877 | -1.40111557268766 |
| 86 | 14 | 12.8606483847811 | 1.13935161521892 |
| 87 | 14 | 14.0491281612205 | -0.0491281612205215 |
| 88 | 14 | 13.9519378920334 | 0.0480621079665583 |
| 89 | 12 | 14.1331993767643 | -2.13319937676426 |
| 90 | 14 | 12.9474394971082 | 1.05256050289177 |
| 91 | 12 | 13.6058479814505 | -1.60584798145048 |
| 92 | 15 | 14.5151070508531 | 0.484892949146905 |
| 93 | 11 | 12.3297013138244 | -1.3297013138244 |
| 94 | 15 | 15.1267383115133 | -0.12673831151334 |
| 95 | 14 | 14.2524491044696 | -0.252449104469553 |
| 96 | 15 | 13.7132596746007 | 1.28674032539932 |
| 97 | 16 | 14.4006607685608 | 1.59933923143919 |
| 98 | 14 | 11.3082983628279 | 2.69170163717206 |
| 99 | 18 | 16.0653976837292 | 1.93460231627078 |
| 100 | 14 | 15.1794376843252 | -1.17943768432516 |
| 101 | 13 | 12.4563851303547 | 0.543614869645329 |
| 102 | 14 | 12.7252032024807 | 1.27479679751933 |
| 103 | 14 | 14.5040805009936 | -0.504080500993641 |
| 104 | 17 | 15.461191467573 | 1.53880853242703 |
| 105 | 12 | 12.9555294479144 | -0.955529447914446 |
| 106 | 16 | 13.6300280235476 | 2.36997197645239 |
| 107 | 10 | 12.3794950924766 | -2.37949509247661 |
| 108 | 13 | 14.4168279574073 | -1.41682795740732 |
| 109 | 15 | 15.1445316493511 | -0.144531649351138 |
| 110 | 16 | 15.2859758777211 | 0.714024122278923 |
| 111 | 14 | 13.0353068514408 | 0.96469314855916 |
| 112 | 13 | 12.6952172676047 | 0.30478273239527 |
| 113 | 17 | 14.95902685886 | 2.04097314113998 |
| 114 | 14 | 13.8979020363115 | 0.102097963688514 |
| 115 | 16 | 13.4668499087546 | 2.53315009124543 |
| 116 | 12 | 14.099801047829 | -2.09980104782901 |
| 117 | 16 | 13.5077902144144 | 2.49220978558559 |
| 118 | 8 | 10.5537521962536 | -2.55375219625362 |
| 119 | 9 | 12.507835916133 | -3.50783591613298 |
| 120 | 13 | 12.3707429819561 | 0.629257018043905 |
| 121 | 19 | 15.3553962924165 | 3.64460370758352 |
| 122 | 11 | 12.5044640495103 | -1.50446404951033 |
| 123 | 15 | 14.947035987839 | 0.0529640121609898 |
| 124 | 11 | 13.773210223737 | -2.77321022373699 |
| 125 | 15 | 16.0277814283964 | -1.0277814283964 |
| 126 | 16 | 15.8196278046792 | 0.18037219532082 |
| 127 | 15 | 12.8976148830332 | 2.10238511696677 |
| 128 | 12 | 12.8995675520869 | -0.899567552086856 |
| 129 | 16 | 14.8933794716469 | 1.10662052835308 |
| 130 | 15 | 13.4283449652334 | 1.57165503476662 |
| 131 | 13 | 14.6943120567262 | -1.69431205672624 |
| 132 | 14 | 14.2004979440111 | -0.200497944011147 |
| 133 | 11 | 12.9876136044835 | -1.98761360448346 |
| 134 | 15 | 14.5003007559447 | 0.499699244055297 |
| 135 | 14 | 12.7727428883851 | 1.22725711161494 |
| 136 | 13 | 15.9077684621914 | -2.90776846219141 |
| 137 | 15 | 15.8460007999241 | -0.84600079992406 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 11 | 0.267906305087992 | 0.535812610175984 | 0.732093694912008 |
| 12 | 0.221244775804694 | 0.442489551609388 | 0.778755224195306 |
| 13 | 0.7308467126837 | 0.5383065746326 | 0.2691532873163 |
| 14 | 0.619263802395307 | 0.761472395209386 | 0.380736197604693 |
| 15 | 0.657639606945299 | 0.684720786109402 | 0.342360393054701 |
| 16 | 0.60224114395102 | 0.79551771209796 | 0.39775885604898 |
| 17 | 0.520363099415867 | 0.959273801168266 | 0.479636900584133 |
| 18 | 0.646598862653734 | 0.706802274692533 | 0.353401137346266 |
| 19 | 0.566288537947937 | 0.867422924104127 | 0.433711462052063 |
| 20 | 0.684409144382555 | 0.63118171123489 | 0.315590855617445 |
| 21 | 0.613016803502164 | 0.773966392995672 | 0.386983196497836 |
| 22 | 0.651369188998589 | 0.697261622002822 | 0.348630811001411 |
| 23 | 0.709534693158385 | 0.58093061368323 | 0.290465306841615 |
| 24 | 0.651542321018505 | 0.69691535796299 | 0.348457678981495 |
| 25 | 0.604558351347433 | 0.790883297305135 | 0.395441648652567 |
| 26 | 0.549754419831305 | 0.90049116033739 | 0.450245580168695 |
| 27 | 0.546052932472836 | 0.907894135054328 | 0.453947067527164 |
| 28 | 0.658252262437962 | 0.683495475124076 | 0.341747737562038 |
| 29 | 0.618286768404771 | 0.763426463190457 | 0.381713231595229 |
| 30 | 0.664834520661414 | 0.670330958677172 | 0.335165479338586 |
| 31 | 0.63489507380949 | 0.730209852381019 | 0.365104926190509 |
| 32 | 0.572279928189967 | 0.855440143620066 | 0.427720071810033 |
| 33 | 0.514426987626673 | 0.971146024746654 | 0.485573012373327 |
| 34 | 0.536378975033684 | 0.927242049932633 | 0.463621024966316 |
| 35 | 0.539832066588601 | 0.920335866822799 | 0.460167933411399 |
| 36 | 0.642739305432647 | 0.714521389134706 | 0.357260694567353 |
| 37 | 0.689409922252719 | 0.621180155494563 | 0.310590077747281 |
| 38 | 0.642095936594981 | 0.715808126810038 | 0.357904063405019 |
| 39 | 0.622372622364435 | 0.75525475527113 | 0.377627377635565 |
| 40 | 0.596323436769128 | 0.807353126461744 | 0.403676563230872 |
| 41 | 0.678792808767049 | 0.642414382465902 | 0.321207191232951 |
| 42 | 0.705380014511917 | 0.589239970976166 | 0.294619985488083 |
| 43 | 0.657802725307396 | 0.684394549385208 | 0.342197274692604 |
| 44 | 0.605495286632869 | 0.789009426734261 | 0.394504713367131 |
| 45 | 0.5623772787866 | 0.8752454424268 | 0.4376227212134 |
| 46 | 0.580980905003055 | 0.83803818999389 | 0.419019094996945 |
| 47 | 0.583028088141574 | 0.833943823716852 | 0.416971911858426 |
| 48 | 0.548285696036745 | 0.90342860792651 | 0.451714303963255 |
| 49 | 0.494460683298863 | 0.988921366597726 | 0.505539316701137 |
| 50 | 0.514129282017002 | 0.971741435965996 | 0.485870717982998 |
| 51 | 0.468659360351272 | 0.937318720702545 | 0.531340639648728 |
| 52 | 0.546287926467576 | 0.907424147064848 | 0.453712073532424 |
| 53 | 0.509044306244229 | 0.98191138751154 | 0.49095569375577 |
| 54 | 0.456195980212432 | 0.912391960424864 | 0.543804019787568 |
| 55 | 0.605761758962616 | 0.788476482074768 | 0.394238241037384 |
| 56 | 0.59891177445751 | 0.80217645108498 | 0.40108822554249 |
| 57 | 0.585346924409466 | 0.829306151181067 | 0.414653075590533 |
| 58 | 0.583203335352553 | 0.833593329294894 | 0.416796664647447 |
| 59 | 0.53341217694313 | 0.933175646113739 | 0.466587823056869 |
| 60 | 0.50082169265435 | 0.9983566146913 | 0.49917830734565 |
| 61 | 0.890056061770577 | 0.219887876458845 | 0.109943938229423 |
| 62 | 0.866091844477667 | 0.267816311044666 | 0.133908155522333 |
| 63 | 0.850296273540294 | 0.299407452919413 | 0.149703726459706 |
| 64 | 0.856356346542124 | 0.287287306915752 | 0.143643653457876 |
| 65 | 0.850487017156492 | 0.299025965687017 | 0.149512982843508 |
| 66 | 0.903513510033248 | 0.192972979933503 | 0.0964864899667516 |
| 67 | 0.887872848752004 | 0.224254302495991 | 0.112127151247995 |
| 68 | 0.862415284449876 | 0.275169431100247 | 0.137584715550124 |
| 69 | 0.83275437172842 | 0.33449125654316 | 0.16724562827158 |
| 70 | 0.802756223504256 | 0.394487552991488 | 0.197243776495744 |
| 71 | 0.800008954196511 | 0.399982091606978 | 0.199991045803489 |
| 72 | 0.76827845431229 | 0.46344309137542 | 0.23172154568771 |
| 73 | 0.726883789841948 | 0.546232420316103 | 0.273116210158052 |
| 74 | 0.695887867315551 | 0.608224265368899 | 0.304112132684449 |
| 75 | 0.67865465157035 | 0.6426906968593 | 0.32134534842965 |
| 76 | 0.8215232250656 | 0.356953549868798 | 0.178476774934399 |
| 77 | 0.797684517824846 | 0.404630964350309 | 0.202315482175154 |
| 78 | 0.852541376768685 | 0.29491724646263 | 0.147458623231315 |
| 79 | 0.822141055237019 | 0.355717889525962 | 0.177858944762981 |
| 80 | 0.957440711120714 | 0.085118577758572 | 0.042559288879286 |
| 81 | 0.944161381781243 | 0.111677236437513 | 0.0558386182187565 |
| 82 | 0.949565398893566 | 0.100869202212868 | 0.050434601106434 |
| 83 | 0.952443528639113 | 0.0951129427217737 | 0.0475564713608868 |
| 84 | 0.973169238232161 | 0.0536615235356773 | 0.0268307617678386 |
| 85 | 0.967985776428156 | 0.0640284471436882 | 0.0320142235718441 |
| 86 | 0.959818761238725 | 0.0803624775225508 | 0.0401812387612754 |
| 87 | 0.94634638260515 | 0.107307234789701 | 0.0536536173948504 |
| 88 | 0.930728254349649 | 0.138543491300702 | 0.0692717456503512 |
| 89 | 0.934018407818188 | 0.131963184363625 | 0.0659815921818124 |
| 90 | 0.920344838325637 | 0.159310323348726 | 0.0796551616743628 |
| 91 | 0.923596019022385 | 0.15280796195523 | 0.076403980977615 |
| 92 | 0.90617881461078 | 0.187642370778441 | 0.0938211853892204 |
| 93 | 0.889655428231102 | 0.220689143537797 | 0.110344571768898 |
| 94 | 0.86005568622936 | 0.279888627541279 | 0.139944313770639 |
| 95 | 0.827886083901078 | 0.344227832197843 | 0.172113916098922 |
| 96 | 0.804739778181151 | 0.390520443637697 | 0.195260221818848 |
| 97 | 0.809230810276744 | 0.381538379446512 | 0.190769189723256 |
| 98 | 0.844103643313096 | 0.311792713373807 | 0.155896356686904 |
| 99 | 0.8762884191157 | 0.247423161768599 | 0.123711580884299 |
| 100 | 0.846417002065755 | 0.30716599586849 | 0.153582997934245 |
| 101 | 0.818392150942188 | 0.363215698115624 | 0.181607849057812 |
| 102 | 0.797682816737323 | 0.404634366525355 | 0.202317183262677 |
| 103 | 0.752120476958767 | 0.495759046082467 | 0.247879523041233 |
| 104 | 0.732568375197845 | 0.53486324960431 | 0.267431624802155 |
| 105 | 0.690985245134709 | 0.618029509730583 | 0.309014754865291 |
| 106 | 0.810567079289447 | 0.378865841421106 | 0.189432920710553 |
| 107 | 0.809164599337758 | 0.381670801324484 | 0.190835400662242 |
| 108 | 0.777083454341987 | 0.445833091316026 | 0.222916545658013 |
| 109 | 0.726264912604441 | 0.547470174791118 | 0.273735087395559 |
| 110 | 0.665832686119982 | 0.668334627760036 | 0.334167313880018 |
| 111 | 0.609822680300012 | 0.780354639399976 | 0.390177319699988 |
| 112 | 0.5438837859433 | 0.9122324281134 | 0.4561162140567 |
| 113 | 0.539737075403439 | 0.920525849193122 | 0.460262924596561 |
| 114 | 0.461860613461328 | 0.923721226922657 | 0.538139386538672 |
| 115 | 0.573600787684625 | 0.85279842463075 | 0.426399212315375 |
| 116 | 0.661364236778515 | 0.67727152644297 | 0.338635763221485 |
| 117 | 0.611035737132192 | 0.777928525735615 | 0.388964262867808 |
| 118 | 0.705526106285814 | 0.588947787428371 | 0.294473893714186 |
| 119 | 0.836964953462618 | 0.326070093074763 | 0.163035046537382 |
| 120 | 0.787506824552378 | 0.424986350895243 | 0.212493175447622 |
| 121 | 0.86578825848455 | 0.268423483030898 | 0.134211741515449 |
| 122 | 0.832577113744846 | 0.334845772510308 | 0.167422886255154 |
| 123 | 0.738616303892379 | 0.522767392215241 | 0.261383696107621 |
| 124 | 0.90254947291138 | 0.194901054177239 | 0.0974505270886195 |
| 125 | 0.820856218646843 | 0.358287562706314 | 0.179143781353157 |
| 126 | 0.81908140633684 | 0.36183718732632 | 0.18091859366316 |
| 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 | 5 | 0.0431034482758621 | OK |
