| Multiple Linear Regression - Estimated Regression Equation |
| marriages[t] = + 2340.27272727273 -813.727272727272M1[t] -135.272727272727M2[t] + 200.909090909091M3[t] + 1107.81818181818M4[t] + 2626.36363636364M5[t] + 3085.54545454545M6[t] + 3283.45454545455M7[t] + 3781.90909090909M8[t] + 3173.81818181818M9[t] + 908.90909090909M10[t] -375.818181818182M11[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) | 2340.27272727273 | 137.634085 | 17.0036 | 0 | 0 |
| M1 | -813.727272727272 | 194.64399 | -4.1806 | 5.6e-05 | 2.8e-05 |
| M2 | -135.272727272727 | 194.64399 | -0.695 | 0.488414 | 0.244207 |
| M3 | 200.909090909091 | 194.64399 | 1.0322 | 0.30406 | 0.15203 |
| M4 | 1107.81818181818 | 194.64399 | 5.6915 | 0 | 0 |
| M5 | 2626.36363636364 | 194.64399 | 13.4932 | 0 | 0 |
| M6 | 3085.54545454545 | 194.64399 | 15.8523 | 0 | 0 |
| M7 | 3283.45454545455 | 194.64399 | 16.869 | 0 | 0 |
| M8 | 3781.90909090909 | 194.64399 | 19.4299 | 0 | 0 |
| M9 | 3173.81818181818 | 194.64399 | 16.3058 | 0 | 0 |
| M10 | 908.90909090909 | 194.64399 | 4.6696 | 8e-06 | 4e-06 |
| M11 | -375.818181818182 | 194.64399 | -1.9308 | 0.055867 | 0.027933 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.96507373665963 |
| R-squared | 0.93136731719018 |
| Adjusted R-squared | 0.925075987932613 |
| F-TEST (value) | 148.039830544551 |
| F-TEST (DF numerator) | 11 |
| F-TEST (DF denominator) | 120 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 456.480619589273 |
| Sum Squared Residuals | 25004946.7272727 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1775 | 1526.54545454545 | 248.454545454546 |
| 2 | 2197 | 2205 | -8.00000000000081 |
| 3 | 2920 | 2541.18181818182 | 378.818181818182 |
| 4 | 4240 | 3448.09090909091 | 791.90909090909 |
| 5 | 5415 | 4966.63636363636 | 448.363636363636 |
| 6 | 6136 | 5425.81818181818 | 710.181818181818 |
| 7 | 6719 | 5623.72727272727 | 1095.27272727273 |
| 8 | 6234 | 6122.18181818182 | 111.818181818183 |
| 9 | 7152 | 5514.09090909091 | 1637.90909090909 |
| 10 | 3646 | 3249.18181818182 | 396.818181818179 |
| 11 | 2165 | 1964.45454545455 | 200.545454545455 |
| 12 | 2803 | 2340.27272727273 | 462.727272727273 |
| 13 | 1615 | 1526.54545454545 | 88.4545454545454 |
| 14 | 2350 | 2205 | 145 |
| 15 | 3350 | 2541.18181818182 | 808.818181818182 |
| 16 | 3536 | 3448.09090909091 | 87.909090909091 |
| 17 | 5834 | 4966.63636363636 | 867.363636363637 |
| 18 | 6767 | 5425.81818181818 | 1341.18181818182 |
| 19 | 5993 | 5623.72727272727 | 369.272727272727 |
| 20 | 7276 | 6122.18181818182 | 1153.81818181818 |
| 21 | 5641 | 5514.09090909091 | 126.909090909091 |
| 22 | 3477 | 3249.18181818182 | 227.818181818182 |
| 23 | 2247 | 1964.45454545455 | 282.545454545455 |
| 24 | 2466 | 2340.27272727273 | 125.727272727273 |
| 25 | 1567 | 1526.54545454545 | 40.4545454545454 |
| 26 | 2237 | 2205 | 32.0000000000001 |
| 27 | 2598 | 2541.18181818182 | 56.8181818181819 |
| 28 | 3729 | 3448.09090909091 | 280.909090909091 |
| 29 | 5715 | 4966.63636363636 | 748.363636363637 |
| 30 | 5776 | 5425.81818181818 | 350.181818181818 |
| 31 | 5852 | 5623.72727272727 | 228.272727272727 |
| 32 | 6878 | 6122.18181818182 | 755.818181818182 |
| 33 | 5488 | 5514.09090909091 | -26.0909090909091 |
| 34 | 3583 | 3249.18181818182 | 333.818181818182 |
| 35 | 2054 | 1964.45454545455 | 89.5454545454544 |
| 36 | 2282 | 2340.27272727273 | -58.2727272727272 |
| 37 | 1552 | 1526.54545454545 | 25.4545454545454 |
| 38 | 2261 | 2205 | 56 |
| 39 | 2446 | 2541.18181818182 | -95.1818181818181 |
| 40 | 3519 | 3448.09090909091 | 70.9090909090911 |
| 41 | 5161 | 4966.63636363636 | 194.363636363636 |
| 42 | 5085 | 5425.81818181818 | -340.818181818182 |
| 43 | 5711 | 5623.72727272727 | 87.2727272727273 |
| 44 | 6057 | 6122.18181818182 | -65.1818181818184 |
| 45 | 5224 | 5514.09090909091 | -290.090909090909 |
| 46 | 3363 | 3249.18181818182 | 113.818181818182 |
| 47 | 1899 | 1964.45454545455 | -65.4545454545456 |
| 48 | 2115 | 2340.27272727273 | -225.272727272727 |
| 49 | 1491 | 1526.54545454545 | -35.5454545454546 |
| 50 | 2061 | 2205 | -144 |
| 51 | 2419 | 2541.18181818182 | -122.181818181818 |
| 52 | 3430 | 3448.09090909091 | -18.0909090909089 |
| 53 | 4778 | 4966.63636363636 | -188.636363636364 |
| 54 | 4862 | 5425.81818181818 | -563.818181818182 |
| 55 | 6176 | 5623.72727272727 | 552.272727272727 |
| 56 | 5664 | 6122.18181818182 | -458.181818181818 |
| 57 | 5529 | 5514.09090909091 | 14.9090909090909 |
| 58 | 3418 | 3249.18181818182 | 168.818181818182 |
| 59 | 1941 | 1964.45454545455 | -23.4545454545456 |
| 60 | 2402 | 2340.27272727273 | 61.7272727272728 |
| 61 | 1579 | 1526.54545454545 | 52.4545454545454 |
| 62 | 2146 | 2205 | -59 |
| 63 | 2462 | 2541.18181818182 | -79.1818181818182 |
| 64 | 3695 | 3448.09090909091 | 246.909090909091 |
| 65 | 4831 | 4966.63636363636 | -135.636363636364 |
| 66 | 5134 | 5425.81818181818 | -291.818181818182 |
| 67 | 6250 | 5623.72727272727 | 626.272727272727 |
| 68 | 5760 | 6122.18181818182 | -362.181818181818 |
| 69 | 6249 | 5514.09090909091 | 734.909090909091 |
| 70 | 2917 | 3249.18181818182 | -332.181818181818 |
| 71 | 1741 | 1964.45454545455 | -223.454545454545 |
| 72 | 2359 | 2340.27272727273 | 18.7272727272728 |
| 73 | 1511 | 1526.54545454545 | -15.5454545454546 |
| 74 | 2059 | 2205 | -146 |
| 75 | 2635 | 2541.18181818182 | 93.8181818181818 |
| 76 | 2867 | 3448.09090909091 | -581.090909090909 |
| 77 | 4403 | 4966.63636363636 | -563.636363636364 |
| 78 | 5720 | 5425.81818181818 | 294.181818181818 |
| 79 | 4502 | 5623.72727272727 | -1121.72727272727 |
| 80 | 5749 | 6122.18181818182 | -373.181818181818 |
| 81 | 5627 | 5514.09090909091 | 112.909090909091 |
| 82 | 2846 | 3249.18181818182 | -403.181818181818 |
| 83 | 1762 | 1964.45454545455 | -202.454545454546 |
| 84 | 2429 | 2340.27272727273 | 88.7272727272728 |
| 85 | 1169 | 1526.54545454545 | -357.545454545455 |
| 86 | 2154 | 2205 | -51 |
| 87 | 2249 | 2541.18181818182 | -292.181818181818 |
| 88 | 2687 | 3448.09090909091 | -761.090909090909 |
| 89 | 4359 | 4966.63636363636 | -607.636363636364 |
| 90 | 5382 | 5425.81818181818 | -43.8181818181818 |
| 91 | 4459 | 5623.72727272727 | -1164.72727272727 |
| 92 | 6398 | 6122.18181818182 | 275.818181818182 |
| 93 | 4596 | 5514.09090909091 | -918.09090909091 |
| 94 | 3024 | 3249.18181818182 | -225.181818181818 |
| 95 | 1887 | 1964.45454545455 | -77.4545454545455 |
| 96 | 2070 | 2340.27272727273 | -270.272727272727 |
| 97 | 1351 | 1526.54545454545 | -175.545454545455 |
| 98 | 2218 | 2205 | 13.0000000000001 |
| 99 | 2461 | 2541.18181818182 | -80.1818181818182 |
| 100 | 3028 | 3448.09090909091 | -420.090909090909 |
| 101 | 4784 | 4966.63636363636 | -182.636363636364 |
| 102 | 4975 | 5425.81818181818 | -450.818181818182 |
| 103 | 4607 | 5623.72727272727 | -1016.72727272727 |
| 104 | 6249 | 6122.18181818182 | 126.818181818182 |
| 105 | 4809 | 5514.09090909091 | -705.090909090909 |
| 106 | 3157 | 3249.18181818182 | -92.181818181818 |
| 107 | 1910 | 1964.45454545455 | -54.4545454545456 |
| 108 | 2228 | 2340.27272727273 | -112.272727272727 |
| 109 | 1594 | 1526.54545454545 | 67.4545454545454 |
| 110 | 2467 | 2205 | 262 |
| 111 | 2222 | 2541.18181818182 | -319.181818181818 |
| 112 | 3607 | 3448.09090909091 | 158.909090909091 |
| 113 | 4685 | 4966.63636363636 | -281.636363636364 |
| 114 | 4962 | 5425.81818181818 | -463.818181818182 |
| 115 | 5770 | 5623.72727272727 | 146.272727272727 |
| 116 | 5480 | 6122.18181818182 | -642.181818181818 |
| 117 | 5000 | 5514.09090909091 | -514.090909090909 |
| 118 | 3228 | 3249.18181818182 | -21.181818181818 |
| 119 | 1993 | 1964.45454545455 | 28.5454545454544 |
| 120 | 2288 | 2340.27272727273 | -52.2727272727272 |
| 121 | 1588 | 1526.54545454545 | 61.4545454545454 |
| 122 | 2105 | 2205 | -100 |
| 123 | 2191 | 2541.18181818182 | -350.181818181818 |
| 124 | 3591 | 3448.09090909091 | 142.909090909091 |
| 125 | 4668 | 4966.63636363636 | -298.636363636364 |
| 126 | 4885 | 5425.81818181818 | -540.818181818182 |
| 127 | 5822 | 5623.72727272727 | 198.272727272727 |
| 128 | 5599 | 6122.18181818182 | -523.181818181818 |
| 129 | 5340 | 5514.09090909091 | -174.090909090909 |
| 130 | 3082 | 3249.18181818182 | -167.181818181818 |
| 131 | 2010 | 1964.45454545455 | 45.5454545454544 |
| 132 | 2301 | 2340.27272727273 | -39.2727272727272 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 15 | 0.125186214052768 | 0.250372428105537 | 0.874813785947232 |
| 16 | 0.290044551783452 | 0.580089103566904 | 0.709955448216548 |
| 17 | 0.266075993663952 | 0.532151987327905 | 0.733924006336048 |
| 18 | 0.397212308109574 | 0.794424616219148 | 0.602787691890426 |
| 19 | 0.507404180772738 | 0.985191638454525 | 0.492595819227262 |
| 20 | 0.803860940506534 | 0.392278118986932 | 0.196139059493466 |
| 21 | 0.975254098605245 | 0.0494918027895096 | 0.0247459013947548 |
| 22 | 0.961737968863222 | 0.0765240622735565 | 0.0382620311367782 |
| 23 | 0.942868937116171 | 0.114262125767658 | 0.0571310628838291 |
| 24 | 0.923969591061827 | 0.152060817876347 | 0.0760304089381734 |
| 25 | 0.892550007213193 | 0.214899985573614 | 0.107449992786807 |
| 26 | 0.851274899085846 | 0.297450201828307 | 0.148725100914154 |
| 27 | 0.85158781872514 | 0.296824362549721 | 0.148412181274861 |
| 28 | 0.817344819679293 | 0.365310360641415 | 0.182655180320707 |
| 29 | 0.826083611253977 | 0.347832777492045 | 0.173916388746023 |
| 30 | 0.873745921326218 | 0.252508157347563 | 0.126254078673782 |
| 31 | 0.878624583509699 | 0.242750832980602 | 0.121375416490301 |
| 32 | 0.897845931974527 | 0.204308136050945 | 0.102154068025473 |
| 33 | 0.943156738363684 | 0.113686523272631 | 0.0568432616363156 |
| 34 | 0.930089873711269 | 0.139820252577463 | 0.0699101262887314 |
| 35 | 0.908827447494956 | 0.182345105010088 | 0.091172552505044 |
| 36 | 0.892393103050096 | 0.215213793899809 | 0.107606896949904 |
| 37 | 0.861689189288479 | 0.276621621423042 | 0.138310810711521 |
| 38 | 0.824378187606643 | 0.351243624786714 | 0.175621812393357 |
| 39 | 0.824337848891395 | 0.35132430221721 | 0.175662151108605 |
| 40 | 0.80334849670631 | 0.39330300658738 | 0.19665150329369 |
| 41 | 0.821650925123414 | 0.356698149753172 | 0.178349074876586 |
| 42 | 0.9254233941103 | 0.149153211779399 | 0.0745766058896996 |
| 43 | 0.924819766779374 | 0.150360466441251 | 0.0751802332206255 |
| 44 | 0.939552831904577 | 0.120894336190847 | 0.0604471680954235 |
| 45 | 0.957604809319111 | 0.0847903813617771 | 0.0423951906808886 |
| 46 | 0.947368432909245 | 0.105263134181509 | 0.0526315670907547 |
| 47 | 0.933477536947278 | 0.133044926105444 | 0.0665224630527219 |
| 48 | 0.924238795801254 | 0.151522408397491 | 0.0757612041987457 |
| 49 | 0.903133714306886 | 0.193732571386228 | 0.0968662856931139 |
| 50 | 0.881023265362185 | 0.23795346927563 | 0.118976734637815 |
| 51 | 0.866276721126022 | 0.267446557747956 | 0.133723278873978 |
| 52 | 0.846847324668222 | 0.306305350663556 | 0.153152675331778 |
| 53 | 0.867615626211578 | 0.264768747576844 | 0.132384373788422 |
| 54 | 0.9239554312441 | 0.152089137511801 | 0.0760445687559003 |
| 55 | 0.947180368400501 | 0.105639263198998 | 0.052819631599499 |
| 56 | 0.963489894976213 | 0.0730202100475749 | 0.0365101050237874 |
| 57 | 0.95713682531555 | 0.0857263493689002 | 0.0428631746844501 |
| 58 | 0.949318048084666 | 0.101363903830668 | 0.0506819519153342 |
| 59 | 0.93434833740928 | 0.131303325181439 | 0.0656516625907195 |
| 60 | 0.915810287784243 | 0.168379424431514 | 0.0841897122157569 |
| 61 | 0.89384825336169 | 0.212303493276619 | 0.10615174663831 |
| 62 | 0.867131398871073 | 0.265737202257854 | 0.132868601128927 |
| 63 | 0.842956637005812 | 0.314086725988377 | 0.157043362994188 |
| 64 | 0.836939206160205 | 0.32612158767959 | 0.163060793839795 |
| 65 | 0.833001174985884 | 0.333997650028232 | 0.166998825014116 |
| 66 | 0.825945007146323 | 0.348109985707353 | 0.174054992853677 |
| 67 | 0.925757858047528 | 0.148484283904944 | 0.0742421419524721 |
| 68 | 0.925822889168973 | 0.148354221662053 | 0.0741771108310265 |
| 69 | 0.980606314124542 | 0.0387873717509156 | 0.0193936858754578 |
| 70 | 0.97898884022883 | 0.0420223195423419 | 0.021011159771171 |
| 71 | 0.973690882942118 | 0.0526182341157638 | 0.0263091170578819 |
| 72 | 0.964393909775953 | 0.071212180448094 | 0.035606090224047 |
| 73 | 0.952529899459966 | 0.0949402010800687 | 0.0474701005400343 |
| 74 | 0.939714905755292 | 0.120570188489417 | 0.0602850942447084 |
| 75 | 0.930645330161638 | 0.138709339676724 | 0.0693546698383621 |
| 76 | 0.944275960196329 | 0.111448079607343 | 0.0557240398036715 |
| 77 | 0.952752878746522 | 0.0944942425069562 | 0.0472471212534781 |
| 78 | 0.962919915670134 | 0.0741601686597325 | 0.0370800843298663 |
| 79 | 0.993151179293998 | 0.0136976414120034 | 0.00684882070600172 |
| 80 | 0.99177776924463 | 0.0164444615107411 | 0.00822223075537054 |
| 81 | 0.994861182828325 | 0.01027763434335 | 0.00513881717167498 |
| 82 | 0.994189275368446 | 0.0116214492631074 | 0.00581072463155371 |
| 83 | 0.991953150279963 | 0.0160936994400737 | 0.00804684972003683 |
| 84 | 0.988802111672032 | 0.022395776655936 | 0.011197888327968 |
| 85 | 0.987308288265266 | 0.0253834234694672 | 0.0126917117347336 |
| 86 | 0.981643042345557 | 0.0367139153088858 | 0.0183569576544429 |
| 87 | 0.975509323621777 | 0.0489813527564466 | 0.0244906763782233 |
| 88 | 0.988888501298392 | 0.0222229974032168 | 0.0111114987016084 |
| 89 | 0.989668403097329 | 0.0206631938053423 | 0.0103315969026711 |
| 90 | 0.989263211657018 | 0.0214735766859646 | 0.0107367883429823 |
| 91 | 0.999053132724169 | 0.00189373455166259 | 0.000946867275831297 |
| 92 | 0.99949112692883 | 0.00101774614234065 | 0.000508873071170326 |
| 93 | 0.999755867717568 | 0.000488264564863856 | 0.000244132282431928 |
| 94 | 0.999571968074408 | 0.000856063851184678 | 0.000428031925592339 |
| 95 | 0.99921060479531 | 0.0015787904093781 | 0.00078939520468905 |
| 96 | 0.998767694371546 | 0.0024646112569082 | 0.0012323056284541 |
| 97 | 0.998101340197 | 0.00379731960599944 | 0.00189865980299972 |
| 98 | 0.996625166880246 | 0.00674966623950798 | 0.00337483311975399 |
| 99 | 0.99500523090759 | 0.00998953818482158 | 0.00499476909241079 |
| 100 | 0.996515672525706 | 0.00696865494858736 | 0.00348432747429368 |
| 101 | 0.99404542527874 | 0.0119091494425204 | 0.00595457472126021 |
| 102 | 0.990594990172648 | 0.0188100196547039 | 0.00940500982735193 |
| 103 | 0.999976888507988 | 4.62229840248892e-05 | 2.31114920124446e-05 |
| 104 | 0.999999877681874 | 2.44636251704263e-07 | 1.22318125852132e-07 |
| 105 | 0.999999983068729 | 3.38625420164111e-08 | 1.69312710082056e-08 |
| 106 | 0.999999916722175 | 1.66555650718953e-07 | 8.32778253594767e-08 |
| 107 | 0.99999968456997 | 6.30860058285634e-07 | 3.15430029142817e-07 |
| 108 | 0.999998696015347 | 2.60796930561417e-06 | 1.30398465280709e-06 |
| 109 | 0.999994142784828 | 1.17144303438604e-05 | 5.85721517193022e-06 |
| 110 | 0.999998548639398 | 2.90272120405374e-06 | 1.45136060202687e-06 |
| 111 | 0.999992429093433 | 1.51418131343731e-05 | 7.57090656718655e-06 |
| 112 | 0.999960802218585 | 7.83955628300864e-05 | 3.91977814150432e-05 |
| 113 | 0.99981046011736 | 0.000379079765279564 | 0.000189539882639782 |
| 114 | 0.99923922693195 | 0.00152154613609814 | 0.000760773068049068 |
| 115 | 0.996788561468465 | 0.00642287706307106 | 0.00321143853153553 |
| 116 | 0.989547244545645 | 0.0209055109087108 | 0.0104527554543554 |
| 117 | 0.997255127706328 | 0.00548974458734464 | 0.00274487229367232 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 24 | 0.233009708737864 | NOK |
| 5% type I error level | 42 | 0.407766990291262 | NOK |
| 10% type I error level | 51 | 0.495145631067961 | NOK |
