| Multiple Linear Regression - Estimated Regression Equation |
| Motivation[t] = + 31.2493029952481 -4.51155152959856Month[t] + 0.646256750774323I1[t] + 0.916477777271674I2[t] + 1.23147142872843I3[t] + 1.4067809878659E1[t] + 1.04413529591756E2[t] + 0.800316870309133E3[t] -0.944759235590694A[t] + 0.163273280683192Happiness[t] + 0.437721551104317Depression[t] + 0.0347231136916052t + 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) | 31.2493029952481 | 25.071779 | 1.2464 | 0.214563 | 0.107281 |
| Month | -4.51155152959856 | 2.656561 | -1.6983 | 0.091531 | 0.045765 |
| I1 | 0.646256750774323 | 0.299591 | 2.1571 | 0.032588 | 0.016294 |
| I2 | 0.916477777271674 | 0.258207 | 3.5494 | 0.000516 | 0.000258 |
| I3 | 1.23147142872843 | 0.203604 | 6.0484 | 0 | 0 |
| E1 | 1.4067809878659 | 0.288366 | 4.8785 | 3e-06 | 1e-06 |
| E2 | 1.04413529591756 | 0.220596 | 4.7333 | 5e-06 | 3e-06 |
| E3 | 0.800316870309133 | 0.227251 | 3.5217 | 0.000568 | 0.000284 |
| A | -0.944759235590694 | 0.317306 | -2.9774 | 0.00339 | 0.001695 |
| Happiness | 0.163273280683192 | 0.377623 | 0.4324 | 0.666092 | 0.333046 |
| Depression | 0.437721551104317 | 0.28344 | 1.5443 | 0.124619 | 0.062309 |
| t | 0.0347231136916052 | 0.028309 | 1.2266 | 0.221898 | 0.110949 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.876009044196898 |
| R-squared | 0.767391845514763 |
| Adjusted R-squared | 0.750333914185846 |
| F-TEST (value) | 44.9873921237945 |
| F-TEST (DF numerator) | 11 |
| F-TEST (DF denominator) | 150 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 9.19567322980735 |
| Sum Squared Residuals | 12684.0609224093 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 127 | 124.862669557765 | 2.13733044223451 |
| 2 | 108 | 108.269836656649 | -0.269836656649063 |
| 3 | 110 | 110.613457175102 | -0.613457175101629 |
| 4 | 102 | 99.6288750000457 | 2.37112499995426 |
| 5 | 104 | 106.359011372928 | -2.35901137292809 |
| 6 | 140 | 140.725429531516 | -0.725429531516037 |
| 7 | 112 | 113.323217133878 | -1.32321713387849 |
| 8 | 115 | 117.271024252993 | -2.27102425299277 |
| 9 | 121 | 117.456492144563 | 3.54350785543679 |
| 10 | 112 | 111.03259181814 | 0.967408181859766 |
| 11 | 118 | 116.58995624344 | 1.41004375655967 |
| 12 | 122 | 119.785219229875 | 2.21478077012452 |
| 13 | 105 | 107.157900171354 | -2.15790017135396 |
| 14 | 111 | 109.867349881175 | 1.13265011882537 |
| 15 | 151 | 150.757363342316 | 0.242636657683569 |
| 16 | 106 | 105.600102290186 | 0.39989770981374 |
| 17 | 100 | 101.8295182887 | -1.82951828869995 |
| 18 | 149 | 149.121551947203 | -0.121551947202948 |
| 19 | 122 | 118.618480640434 | 3.38151935956641 |
| 20 | 115 | 115.880969586228 | -0.880969586227998 |
| 21 | 86 | 83.500695731691 | 2.499304268309 |
| 22 | 124 | 124.667419634552 | -0.667419634552071 |
| 23 | 69 | 71.2586013350266 | -2.25860133502664 |
| 24 | 117 | 117.671488954644 | -0.671488954644432 |
| 25 | 113 | 113.943416076903 | -0.943416076903167 |
| 26 | 123 | 120.884602448094 | 2.11539755190567 |
| 27 | 123 | 122.937681628777 | 0.0623183712230852 |
| 28 | 84 | 81.4719916927972 | 2.52800830720281 |
| 29 | 97 | 92.3238339343613 | 4.67616606563873 |
| 30 | 121 | 120.727946207393 | 0.2720537926072 |
| 31 | 132 | 131.439070740406 | 0.560929259594153 |
| 32 | 119 | 120.321016625333 | -1.32101662533254 |
| 33 | 98 | 99.4552023885179 | -1.45520238851795 |
| 34 | 87 | 87.6650306785593 | -0.665030678559354 |
| 35 | 101 | 98.9151868583945 | 2.08481314160552 |
| 36 | 115 | 114.514272495118 | 0.485727504881908 |
| 37 | 109 | 110.49382037113 | -1.49382037113023 |
| 38 | 109 | 110.083417555477 | -1.08341755547722 |
| 39 | 159 | 158.919457522182 | 0.0805424778177516 |
| 40 | 129 | 128.555048011259 | 0.444951988741048 |
| 41 | 119 | 119.473738521424 | -0.473738521423743 |
| 42 | 119 | 117.664364931686 | 1.33563506831351 |
| 43 | 122 | 120.448894849734 | 1.55110515026636 |
| 44 | 131 | 131.22844232799 | -0.228442327990187 |
| 45 | 120 | 116.370598424958 | 3.62940157504195 |
| 46 | 82 | 82.5253283597792 | -0.525328359779219 |
| 47 | 86 | 85.6942893335134 | 0.305710666486624 |
| 48 | 105 | 101.749058271372 | 3.25094172862828 |
| 49 | 114 | 117.864480995423 | -3.86448099542266 |
| 50 | 100 | 99.9666316613033 | 0.0333683386967008 |
| 51 | 100 | 101.552118595764 | -1.55211859576396 |
| 52 | 99 | 101.02357524534 | -2.02357524533962 |
| 53 | 132 | 134.413523765239 | -2.41352376523892 |
| 54 | 82 | 86.6301055178537 | -4.6301055178537 |
| 55 | 132 | 131.24373494464 | 0.756265055360377 |
| 56 | 107 | 107.527363811603 | -0.527363811603255 |
| 57 | 114 | 116.179189111678 | -2.17918911167801 |
| 58 | 110 | 107.668858297197 | 2.3311417028027 |
| 59 | 105 | 103.324362452546 | 1.67563754745391 |
| 60 | 121 | 118.217303057349 | 2.782696942651 |
| 61 | 109 | 106.940938827068 | 2.05906117293222 |
| 62 | 106 | 106.009113283242 | -0.00911328324167099 |
| 63 | 124 | 124.167680677846 | -0.167680677846042 |
| 64 | 120 | 121.133094963119 | -1.1330949631187 |
| 65 | 91 | 95.1375248803134 | -4.13752488031342 |
| 66 | 126 | 121.38925739071 | 4.61074260929024 |
| 67 | 138 | 137.119492020153 | 0.880507979846945 |
| 68 | 118 | 114.684153825947 | 3.3158461740531 |
| 69 | 128 | 125.517249547065 | 2.48275045293532 |
| 70 | 98 | 96.9751544706062 | 1.02484552939384 |
| 71 | 133 | 131.565468586337 | 1.43453141366297 |
| 72 | 130 | 128.086382028125 | 1.91361797187455 |
| 73 | 103 | 98.5546096242716 | 4.44539037572839 |
| 74 | 124 | 122.636237941222 | 1.3637620587784 |
| 75 | 142 | 138.67499588288 | 3.32500411712049 |
| 76 | 96 | 96.4337497025503 | -0.433749702550286 |
| 77 | 93 | 91.1634583333309 | 1.83654166666908 |
| 78 | 129 | 128.763133677065 | 0.236866322935042 |
| 79 | 150 | 148.505282000996 | 1.49471799900444 |
| 80 | 88 | 85.2454865632715 | 2.75451343672849 |
| 81 | 125 | 121.738614406248 | 3.26138559375185 |
| 82 | 92 | 89.0680039111323 | 2.93199608886772 |
| 83 | 0 | 109.345352779391 | -109.345352779391 |
| 84 | 117 | 114.916343470473 | 2.08365652952656 |
| 85 | 112 | 111.250818714449 | 0.749181285551013 |
| 86 | 144 | 140.878719281316 | 3.12128071868435 |
| 87 | 130 | 127.269479903801 | 2.73052009619872 |
| 88 | 87 | 84.2500765897112 | 2.74992341028881 |
| 89 | 92 | 91.0489561744283 | 0.951043825571687 |
| 90 | 114 | 112.93135863501 | 1.0686413649898 |
| 91 | 81 | 78.4283016135663 | 2.57169838643365 |
| 92 | 127 | 124.843208774412 | 2.15679122558791 |
| 93 | 115 | 113.515990410046 | 1.48400958995443 |
| 94 | 123 | 123.494500923936 | -0.49450092393635 |
| 95 | 115 | 113.434105828135 | 1.56589417186466 |
| 96 | 117 | 115.047186865778 | 1.95281313422219 |
| 97 | 117 | 113.947019305653 | 3.05298069434722 |
| 98 | 103 | 100.411634377619 | 2.58836562238079 |
| 99 | 108 | 106.192559903607 | 1.80744009639313 |
| 100 | 139 | 135.934809691971 | 3.06519030802865 |
| 101 | 113 | 110.064534195754 | 2.9354658042464 |
| 102 | 97 | 93.7144696479281 | 3.28553035207193 |
| 103 | 117 | 113.950842425141 | 3.04915757485889 |
| 104 | 133 | 130.707868956701 | 2.29213104329864 |
| 105 | 115 | 115.035404137852 | -0.0354041378522152 |
| 106 | 103 | 103.739583482592 | -0.739583482592092 |
| 107 | 95 | 93.427528710251 | 1.57247128974904 |
| 108 | 117 | 117.401220015821 | -0.401220015820747 |
| 109 | 113 | 111.802004413137 | 1.19799558686324 |
| 110 | 127 | 129.194700004463 | -2.19470000446266 |
| 111 | 126 | 124.38825326896 | 1.61174673103982 |
| 112 | 119 | 116.796142082432 | 2.20385791756761 |
| 113 | 97 | 93.3042688150122 | 3.69573118498784 |
| 114 | 105 | 103.840130598964 | 1.15986940103565 |
| 115 | 140 | 139.944881460882 | 0.0551185391177514 |
| 116 | 91 | 88.2265144189182 | 2.77348558108179 |
| 117 | 112 | 111.121023823852 | 0.878976176147543 |
| 118 | 113 | 112.699075353706 | 0.300924646294279 |
| 119 | 102 | 96.2595972670768 | 5.74040273292323 |
| 120 | 92 | 90.3254841362672 | 1.67451586373277 |
| 121 | 98 | 98.6999320588694 | -0.699932058869385 |
| 122 | 122 | 121.966247911501 | 0.0337520884991126 |
| 123 | 100 | 99.192919945795 | 0.807080054205019 |
| 124 | 84 | 81.5105492983808 | 2.48945070161924 |
| 125 | 142 | 137.432563588255 | 4.56743641174508 |
| 126 | 124 | 122.229731427864 | 1.77026857213554 |
| 127 | 137 | 134.480235016388 | 2.51976498361221 |
| 128 | 105 | 103.982394559463 | 1.01760544053655 |
| 129 | 106 | 105.487042659469 | 0.512957340531429 |
| 130 | 125 | 123.413272734891 | 1.58672726510915 |
| 131 | 104 | 102.569290967179 | 1.4307090328214 |
| 132 | 130 | 132.385261152476 | -2.38526115247623 |
| 133 | 79 | 79.9380332079596 | -0.938033207959584 |
| 134 | 108 | 109.29243204455 | -1.29243204454953 |
| 135 | 136 | 134.529351336077 | 1.47064866392296 |
| 136 | 98 | 96.8992058627791 | 1.10079413722089 |
| 137 | 120 | 124.667401840036 | -4.66740184003587 |
| 138 | 108 | 108.631281225528 | -0.631281225527681 |
| 139 | 139 | 140.005831042139 | -1.00583104213871 |
| 140 | 123 | 122.501921065389 | 0.498078934610773 |
| 141 | 90 | 87.7976083662166 | 2.20239163378343 |
| 142 | 119 | 119.472628515234 | -0.472628515233945 |
| 143 | 105 | 108.023426764516 | -3.02342676451573 |
| 144 | 110 | 108.572080952126 | 1.42791904787438 |
| 145 | 135 | 135.31413342072 | -0.314133420719566 |
| 146 | 101 | 98.001534797802 | 2.99846520219805 |
| 147 | 114 | 112.840863043874 | 1.15913695612575 |
| 148 | 118 | 116.563984372029 | 1.43601562797111 |
| 149 | 120 | 118.817905397025 | 1.18209460297456 |
| 150 | 108 | 111.329981234971 | -3.32998123497107 |
| 151 | 114 | 111.876330455609 | 2.12366954439092 |
| 152 | 122 | 122.392379108571 | -0.392379108570879 |
| 153 | 132 | 131.094601012271 | 0.905398987729093 |
| 154 | 130 | 133.544146301127 | -3.5441463011267 |
| 155 | 130 | 132.623215246069 | -2.62321524606894 |
| 156 | 112 | 113.468987690843 | -1.46898769084313 |
| 157 | 114 | 118.258862627077 | -4.25886262707715 |
| 158 | 103 | 104.553528363456 | -1.55352836345567 |
| 159 | 115 | 115.585365934216 | -0.585365934215644 |
| 160 | 108 | 107.15704216147 | 0.842957838530111 |
| 161 | 94 | 95.8386040915634 | -1.83860409156343 |
| 162 | 105 | 102.198678564215 | 2.80132143578484 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 15 | 4.3961443679384e-46 | 8.7922887358768e-46 | 1 |
| 16 | 1.12221471856813e-60 | 2.24442943713627e-60 | 1 |
| 17 | 5.99671501062401e-79 | 1.1993430021248e-78 | 1 |
| 18 | 5.32631583480094e-95 | 1.06526316696019e-94 | 1 |
| 19 | 1.4720224798454e-104 | 2.9440449596908e-104 | 1 |
| 20 | 2.44561317863365e-119 | 4.89122635726729e-119 | 1 |
| 21 | 2.14155152992171e-137 | 4.28310305984341e-137 | 1 |
| 22 | 9.94150224642491e-156 | 1.98830044928498e-155 | 1 |
| 23 | 4.17429663289577e-163 | 8.34859326579154e-163 | 1 |
| 24 | 3.70193208154878e-179 | 7.40386416309755e-179 | 1 |
| 25 | 2.80820170756337e-201 | 5.61640341512673e-201 | 1 |
| 26 | 1.71765420184186e-214 | 3.43530840368372e-214 | 1 |
| 27 | 7.79588057965603e-229 | 1.55917611593121e-228 | 1 |
| 28 | 5.15258856484324e-246 | 1.03051771296865e-245 | 1 |
| 29 | 1.52797521124352e-251 | 3.05595042248705e-251 | 1 |
| 30 | 5.50363328832411e-279 | 1.10072665766482e-278 | 1 |
| 31 | 6.47102081610366e-293 | 1.29420416322073e-292 | 1 |
| 32 | 2.39805282214752e-308 | 4.79610564429504e-308 | 1 |
| 33 | 1.18995710800864e-319 | 2.37991421601728e-319 | 1 |
| 34 | 0 | 0 | 1 |
| 35 | 0 | 0 | 1 |
| 36 | 0 | 0 | 1 |
| 37 | 0 | 0 | 1 |
| 38 | 0 | 0 | 1 |
| 39 | 0 | 0 | 1 |
| 40 | 0 | 0 | 1 |
| 41 | 0 | 0 | 1 |
| 42 | 0 | 0 | 1 |
| 43 | 0 | 0 | 1 |
| 44 | 0 | 0 | 1 |
| 45 | 0 | 0 | 1 |
| 46 | 0 | 0 | 1 |
| 47 | 0 | 0 | 1 |
| 48 | 0 | 0 | 1 |
| 49 | 0 | 0 | 1 |
| 50 | 0 | 0 | 1 |
| 51 | 0 | 0 | 1 |
| 52 | 0 | 0 | 1 |
| 53 | 0 | 0 | 1 |
| 54 | 0 | 0 | 1 |
| 55 | 0 | 0 | 1 |
| 56 | 0 | 0 | 1 |
| 57 | 0 | 0 | 1 |
| 58 | 0 | 0 | 1 |
| 59 | 0 | 0 | 1 |
| 60 | 0 | 0 | 1 |
| 61 | 0 | 0 | 1 |
| 62 | 0 | 0 | 1 |
| 63 | 0 | 0 | 1 |
| 64 | 0 | 0 | 1 |
| 65 | 0 | 0 | 1 |
| 66 | 0 | 0 | 1 |
| 67 | 0 | 0 | 1 |
| 68 | 0 | 0 | 1 |
| 69 | 0 | 0 | 1 |
| 70 | 0 | 0 | 1 |
| 71 | 0 | 0 | 1 |
| 72 | 0 | 0 | 1 |
| 73 | 0 | 0 | 1 |
| 74 | 0 | 0 | 1 |
| 75 | 0 | 0 | 1 |
| 76 | 0 | 0 | 1 |
| 77 | 0 | 0 | 1 |
| 78 | 0 | 0 | 1 |
| 79 | 0 | 0 | 1 |
| 80 | 0 | 0 | 1 |
| 81 | 0 | 0 | 1 |
| 82 | 0 | 0 | 1 |
| 83 | 1 | 0 | 0 |
| 84 | 1 | 0 | 0 |
| 85 | 1 | 0 | 0 |
| 86 | 1 | 0 | 0 |
| 87 | 1 | 0 | 0 |
| 88 | 1 | 0 | 0 |
| 89 | 1 | 0 | 0 |
| 90 | 1 | 0 | 0 |
| 91 | 1 | 0 | 0 |
| 92 | 1 | 0 | 0 |
| 93 | 1 | 0 | 0 |
| 94 | 1 | 0 | 0 |
| 95 | 1 | 0 | 0 |
| 96 | 1 | 0 | 0 |
| 97 | 1 | 0 | 0 |
| 98 | 1 | 0 | 0 |
| 99 | 1 | 0 | 0 |
| 100 | 1 | 0 | 0 |
| 101 | 1 | 0 | 0 |
| 102 | 1 | 0 | 0 |
| 103 | 1 | 0 | 0 |
| 104 | 1 | 0 | 0 |
| 105 | 1 | 0 | 0 |
| 106 | 1 | 0 | 0 |
| 107 | 1 | 0 | 0 |
| 108 | 1 | 0 | 0 |
| 109 | 1 | 0 | 0 |
| 110 | 1 | 0 | 0 |
| 111 | 1 | 0 | 0 |
| 112 | 1 | 0 | 0 |
| 113 | 1 | 0 | 0 |
| 114 | 1 | 0 | 0 |
| 115 | 1 | 0 | 0 |
| 116 | 1 | 0 | 0 |
| 117 | 1 | 0 | 0 |
| 118 | 1 | 0 | 0 |
| 119 | 1 | 0 | 0 |
| 120 | 1 | 0 | 0 |
| 121 | 1 | 0 | 0 |
| 122 | 1 | 0 | 0 |
| 123 | 1 | 0 | 0 |
| 124 | 1 | 0 | 0 |
| 125 | 1 | 0 | 0 |
| 126 | 1 | 0 | 0 |
| 127 | 1 | 0 | 0 |
| 128 | 1 | 0 | 0 |
| 129 | 1 | 4.94065645841247e-323 | 2.47032822920623e-323 |
| 130 | 1 | 1.70732243613907e-298 | 8.53661218069533e-299 |
| 131 | 1 | 5.26242879649718e-288 | 2.63121439824859e-288 |
| 132 | 1 | 1.28955340515892e-270 | 6.44776702579459e-271 |
| 133 | 1 | 9.93391705898235e-251 | 4.96695852949118e-251 |
| 134 | 1 | 7.79117096707144e-251 | 3.89558548353572e-251 |
| 135 | 1 | 4.77822810408425e-233 | 2.38911405204213e-233 |
| 136 | 1 | 5.96737173054915e-212 | 2.98368586527458e-212 |
| 137 | 1 | 2.74094761413078e-194 | 1.37047380706539e-194 |
| 138 | 1 | 4.41484685992468e-183 | 2.20742342996234e-183 |
| 139 | 1 | 5.14291306299364e-168 | 2.57145653149682e-168 |
| 140 | 1 | 2.81237820049952e-149 | 1.40618910024976e-149 |
| 141 | 1 | 3.03123157598842e-134 | 1.51561578799421e-134 |
| 142 | 1 | 1.19426104293487e-124 | 5.97130521467434e-125 |
| 143 | 1 | 6.18615291565865e-109 | 3.09307645782933e-109 |
| 144 | 1 | 3.91663943767624e-94 | 1.95831971883812e-94 |
| 145 | 1 | 1.63048519310666e-78 | 8.15242596553329e-79 |
| 146 | 1 | 1.98365506502173e-61 | 9.91827532510865e-62 |
| 147 | 1 | 4.32101645611691e-45 | 2.16050822805846e-45 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 133 | 1 | NOK |
| 5% type I error level | 133 | 1 | NOK |
| 10% type I error level | 133 | 1 | NOK |
