Multiple Linear Regression - Estimated Regression Equation |
marriages[t] = + 2340.27272727273 -813.727272727272M1[t] -135.272727272731M2[t] + 200.909090909092M3[t] + 1107.81818181818M4[t] + 2626.36363636363M5[t] + 3085.54545454545M6[t] + 3283.45454545455M7[t] + 3781.90909090908M8[t] + 3173.81818181818M9[t] + 908.909090909092M10[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 | -135.272727272731 | 194.64399 | -0.695 | 0.488414 | 0.244207 |
M3 | 200.909090909092 | 194.64399 | 1.0322 | 0.30406 | 0.15203 |
M4 | 1107.81818181818 | 194.64399 | 5.6915 | 0 | 0 |
M5 | 2626.36363636363 | 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 | 3781.90909090908 | 194.64399 | 19.4299 | 0 | 0 |
M9 | 3173.81818181818 | 194.64399 | 16.3058 | 0 | 0 |
M10 | 908.909090909092 | 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 | 0.925075987932612 |
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 | 25004946.7272728 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 1775 | 1526.54545454545 | 248.454545454552 |
2 | 2197 | 2205.00000000000 | -8.00000000000344 |
3 | 2920 | 2541.18181818181 | 378.818181818187 |
4 | 4240 | 3448.09090909092 | 791.909090909084 |
5 | 5415 | 4966.63636363638 | 448.363636363622 |
6 | 6136 | 5425.81818181818 | 710.181818181818 |
7 | 6719 | 5623.72727272727 | 1095.27272727273 |
8 | 6234 | 6122.18181818183 | 111.818181818174 |
9 | 7152 | 5514.09090909089 | 1637.90909090911 |
10 | 3646 | 3249.18181818181 | 396.81818181819 |
11 | 2165 | 1964.45454545455 | 200.545454545454 |
12 | 2803 | 2340.27272727273 | 462.727272727272 |
13 | 1615 | 1526.54545454546 | 88.4545454545448 |
14 | 2350 | 2205 | 145 |
15 | 3350 | 2541.18181818182 | 808.818181818181 |
16 | 3536 | 3448.09090909091 | 87.909090909091 |
17 | 5834 | 4966.63636363636 | 867.363636363638 |
18 | 6767 | 5425.81818181818 | 1341.18181818182 |
19 | 5993 | 5623.72727272727 | 369.272727272727 |
20 | 7276 | 6122.18181818182 | 1153.81818181818 |
21 | 5641 | 5514.09090909091 | 126.909090909089 |
22 | 3477 | 3249.18181818182 | 227.818181818181 |
23 | 2247 | 1964.45454545455 | 282.545454545454 |
24 | 2466 | 2340.27272727273 | 125.727272727272 |
25 | 1567 | 1526.54545454546 | 40.4545454545448 |
26 | 2237 | 2205 | 32 |
27 | 2598 | 2541.18181818182 | 56.8181818181814 |
28 | 3729 | 3448.09090909091 | 280.909090909091 |
29 | 5715 | 4966.63636363636 | 748.363636363638 |
30 | 5776 | 5425.81818181818 | 350.181818181819 |
31 | 5852 | 5623.72727272727 | 228.272727272727 |
32 | 6878 | 6122.18181818182 | 755.818181818183 |
33 | 5488 | 5514.09090909091 | -26.0909090909108 |
34 | 3583 | 3249.18181818182 | 333.818181818181 |
35 | 2054 | 1964.45454545455 | 89.5454545454546 |
36 | 2282 | 2340.27272727273 | -58.2727272727278 |
37 | 1552 | 1526.54545454546 | 25.4545454545448 |
38 | 2261 | 2205 | 56 |
39 | 2446 | 2541.18181818182 | -95.1818181818186 |
40 | 3519 | 3448.09090909091 | 70.909090909091 |
41 | 5161 | 4966.63636363636 | 194.363636363638 |
42 | 5085 | 5425.81818181818 | -340.818181818182 |
43 | 5711 | 5623.72727272727 | 87.2727272727272 |
44 | 6057 | 6122.18181818182 | -65.1818181818172 |
45 | 5224 | 5514.09090909091 | -290.090909090911 |
46 | 3363 | 3249.18181818182 | 113.818181818181 |
47 | 1899 | 1964.45454545455 | -65.4545454545453 |
48 | 2115 | 2340.27272727273 | -225.272727272727 |
49 | 1491 | 1526.54545454546 | -35.5454545454552 |
50 | 2061 | 2205 | -144 |
51 | 2419 | 2541.18181818182 | -122.181818181819 |
52 | 3430 | 3448.09090909091 | -18.0909090909090 |
53 | 4778 | 4966.63636363636 | -188.636363636362 |
54 | 4862 | 5425.81818181818 | -563.818181818182 |
55 | 6176 | 5623.72727272727 | 552.272727272727 |
56 | 5664 | 6122.18181818182 | -458.181818181817 |
57 | 5529 | 5514.09090909091 | 14.9090909090891 |
58 | 3418 | 3249.18181818182 | 168.818181818181 |
59 | 1941 | 1964.45454545455 | -23.4545454545453 |
60 | 2402 | 2340.27272727273 | 61.7272727272721 |
61 | 1579 | 1526.54545454546 | 52.4545454545448 |
62 | 2146 | 2205 | -59 |
63 | 2462 | 2541.18181818182 | -79.1818181818186 |
64 | 3695 | 3448.09090909091 | 246.909090909091 |
65 | 4831 | 4966.63636363636 | -135.636363636362 |
66 | 5134 | 5425.81818181818 | -291.818181818182 |
67 | 6250 | 5623.72727272727 | 626.272727272727 |
68 | 5760 | 6122.18181818182 | -362.181818181817 |
69 | 6249 | 5514.09090909091 | 734.90909090909 |
70 | 2917 | 3249.18181818182 | -332.181818181819 |
71 | 1741 | 1964.45454545455 | -223.454545454545 |
72 | 2359 | 2340.27272727273 | 18.7272727272722 |
73 | 1511 | 1526.54545454546 | -15.5454545454552 |
74 | 2059 | 2205 | -146 |
75 | 2635 | 2541.18181818182 | 93.8181818181814 |
76 | 2867 | 3448.09090909091 | -581.090909090909 |
77 | 4403 | 4966.63636363636 | -563.636363636362 |
78 | 5720 | 5425.81818181818 | 294.181818181819 |
79 | 4502 | 5623.72727272727 | -1121.72727272727 |
80 | 5749 | 6122.18181818182 | -373.181818181817 |
81 | 5627 | 5514.09090909091 | 112.909090909089 |
82 | 2846 | 3249.18181818182 | -403.181818181819 |
83 | 1762 | 1964.45454545455 | -202.454545454545 |
84 | 2429 | 2340.27272727273 | 88.7272727272721 |
85 | 1169 | 1526.54545454546 | -357.545454545455 |
86 | 2154 | 2205 | -50.9999999999999 |
87 | 2249 | 2541.18181818182 | -292.181818181819 |
88 | 2687 | 3448.09090909091 | -761.090909090909 |
89 | 4359 | 4966.63636363636 | -607.636363636362 |
90 | 5382 | 5425.81818181818 | -43.8181818181816 |
91 | 4459 | 5623.72727272727 | -1164.72727272727 |
92 | 6398 | 6122.18181818182 | 275.818181818183 |
93 | 4596 | 5514.09090909091 | -918.090909090911 |
94 | 3024 | 3249.18181818182 | -225.181818181819 |
95 | 1887 | 1964.45454545455 | -77.4545454545453 |
96 | 2070 | 2340.27272727273 | -270.272727272727 |
97 | 1351 | 1526.54545454546 | -175.545454545455 |
98 | 2218 | 2205 | 13.0000000000000 |
99 | 2461 | 2541.18181818182 | -80.1818181818186 |
100 | 3028 | 3448.09090909091 | -420.090909090909 |
101 | 4784 | 4966.63636363636 | -182.636363636362 |
102 | 4975 | 5425.81818181818 | -450.818181818181 |
103 | 4607 | 5623.72727272727 | -1016.72727272727 |
104 | 6249 | 6122.18181818182 | 126.818181818183 |
105 | 4809 | 5514.09090909091 | -705.09090909091 |
106 | 3157 | 3249.18181818182 | -92.181818181819 |
107 | 1910 | 1964.45454545455 | -54.4545454545453 |
108 | 2228 | 2340.27272727273 | -112.272727272727 |
109 | 1594 | 1526.54545454546 | 67.4545454545448 |
110 | 2467 | 2205 | 262 |
111 | 2222 | 2541.18181818182 | -319.181818181819 |
112 | 3607 | 3448.09090909091 | 158.909090909091 |
113 | 4685 | 4966.63636363636 | -281.636363636362 |
114 | 4962 | 5425.81818181818 | -463.818181818181 |
115 | 5770 | 5623.72727272727 | 146.272727272727 |
116 | 5480 | 6122.18181818182 | -642.181818181817 |
117 | 5000 | 5514.09090909091 | -514.090909090911 |
118 | 3228 | 3249.18181818182 | -21.1818181818189 |
119 | 1993 | 1964.45454545455 | 28.5454545454546 |
120 | 2288 | 2340.27272727273 | -52.2727272727278 |
121 | 1588 | 1526.54545454546 | 61.4545454545448 |
122 | 2105 | 2205 | -100 |
123 | 2191 | 2541.18181818182 | -350.181818181819 |
124 | 3591 | 3448.09090909091 | 142.909090909091 |
125 | 4668 | 4966.63636363636 | -298.636363636362 |
126 | 4885 | 5425.81818181818 | -540.818181818182 |
127 | 5822 | 5623.72727272727 | 198.272727272727 |
128 | 5599 | 6122.18181818182 | -523.181818181817 |
129 | 5340 | 5514.09090909091 | -174.090909090911 |
130 | 3082 | 3249.18181818182 | -167.181818181819 |
131 | 2010 | 1964.45454545455 | 45.5454545454546 |
132 | 2301 | 2340.27272727273 | -39.2727272727278 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
15 | 0.125186214052768 | 0.250372428105535 | 0.874813785947232 |
16 | 0.290044551783451 | 0.580089103566902 | 0.709955448216549 |
17 | 0.266075993663955 | 0.532151987327909 | 0.733924006336045 |
18 | 0.397212308109571 | 0.794424616219143 | 0.602787691890429 |
19 | 0.507404180772734 | 0.985191638454531 | 0.492595819227266 |
20 | 0.803860940506535 | 0.39227811898693 | 0.196139059493465 |
21 | 0.975254098605245 | 0.0494918027895099 | 0.0247459013947549 |
22 | 0.961737968863221 | 0.0765240622735575 | 0.0382620311367788 |
23 | 0.94286893711617 | 0.114262125767659 | 0.0571310628838294 |
24 | 0.923969591061828 | 0.152060817876345 | 0.0760304089381724 |
25 | 0.892550007213193 | 0.214899985573613 | 0.107449992786807 |
26 | 0.851274899085847 | 0.297450201828306 | 0.148725100914153 |
27 | 0.85158781872514 | 0.296824362549722 | 0.148412181274861 |
28 | 0.817344819679292 | 0.365310360641416 | 0.182655180320708 |
29 | 0.826083611253976 | 0.347832777492047 | 0.173916388746023 |
30 | 0.87374592132622 | 0.25250815734756 | 0.12625407867378 |
31 | 0.878624583509697 | 0.242750832980607 | 0.121375416490303 |
32 | 0.897845931974527 | 0.204308136050945 | 0.102154068025473 |
33 | 0.943156738363685 | 0.113686523272631 | 0.0568432616363153 |
34 | 0.93008987371127 | 0.139820252577462 | 0.0699101262887308 |
35 | 0.908827447494956 | 0.182345105010089 | 0.0911725525050444 |
36 | 0.892393103050099 | 0.215213793899802 | 0.107606896949901 |
37 | 0.86168918928848 | 0.276621621423040 | 0.138310810711520 |
38 | 0.824378187606644 | 0.351243624786713 | 0.175621812393356 |
39 | 0.824337848891392 | 0.351324302217217 | 0.175662151108608 |
40 | 0.803348496706312 | 0.393303006587377 | 0.196651503293688 |
41 | 0.82165092512341 | 0.356698149753179 | 0.178349074876589 |
42 | 0.9254233941103 | 0.149153211779399 | 0.0745766058896997 |
43 | 0.924819766779374 | 0.150360466441252 | 0.075180233220626 |
44 | 0.939552831904577 | 0.120894336190845 | 0.0604471680954227 |
45 | 0.957604809319111 | 0.0847903813617776 | 0.0423951906808888 |
46 | 0.947368432909246 | 0.105263134181508 | 0.052631567090754 |
47 | 0.933477536947277 | 0.133044926105445 | 0.0665224630527227 |
48 | 0.924238795801255 | 0.151522408397489 | 0.0757612041987446 |
49 | 0.903133714306886 | 0.193732571386229 | 0.0968662856931143 |
50 | 0.881023265362187 | 0.237953469275625 | 0.118976734637813 |
51 | 0.866276721126018 | 0.267446557747964 | 0.133723278873982 |
52 | 0.846847324668223 | 0.306305350663553 | 0.153152675331777 |
53 | 0.867615626211578 | 0.264768747576843 | 0.132384373788422 |
54 | 0.9239554312441 | 0.152089137511801 | 0.0760445687559006 |
55 | 0.9471803684005 | 0.105639263199 | 0.0528196315995 |
56 | 0.963489894976213 | 0.073020210047574 | 0.036510105023787 |
57 | 0.957136825315548 | 0.0857263493689032 | 0.0428631746844516 |
58 | 0.949318048084667 | 0.101363903830666 | 0.0506819519153329 |
59 | 0.93434833740928 | 0.131303325181440 | 0.0656516625907198 |
60 | 0.915810287784244 | 0.168379424431513 | 0.0841897122157564 |
61 | 0.893848253361692 | 0.212303493276616 | 0.106151746638308 |
62 | 0.867131398871071 | 0.265737202257857 | 0.132868601128929 |
63 | 0.842956637005812 | 0.314086725988376 | 0.157043362994188 |
64 | 0.836939206160206 | 0.326121587679588 | 0.163060793839794 |
65 | 0.83300117498588 | 0.333997650028241 | 0.166998825014121 |
66 | 0.825945007146322 | 0.348109985707356 | 0.174054992853678 |
67 | 0.925757858047526 | 0.148484283904948 | 0.0742421419524738 |
68 | 0.925822889168973 | 0.148354221662055 | 0.0741771108310274 |
69 | 0.980606314124542 | 0.0387873717509157 | 0.0193936858754579 |
70 | 0.97898884022883 | 0.0420223195423415 | 0.0210111597711708 |
71 | 0.973690882942118 | 0.052618234115763 | 0.0263091170578815 |
72 | 0.964393909775954 | 0.071212180448093 | 0.0356060902240465 |
73 | 0.952529899459964 | 0.0949402010800712 | 0.0474701005400356 |
74 | 0.939714905755292 | 0.120570188489415 | 0.0602850942447075 |
75 | 0.93064533016164 | 0.13870933967672 | 0.06935466983836 |
76 | 0.94427596019633 | 0.111448079607341 | 0.0557240398036704 |
77 | 0.952752878746522 | 0.0944942425069551 | 0.0472471212534776 |
78 | 0.962919915670134 | 0.0741601686597323 | 0.0370800843298662 |
79 | 0.993151179293998 | 0.0136976414120041 | 0.00684882070600203 |
80 | 0.99177776924463 | 0.0164444615107412 | 0.00822223075537058 |
81 | 0.994861182828325 | 0.0102776343433499 | 0.00513881717167493 |
82 | 0.994189275368446 | 0.0116214492631072 | 0.00581072463155362 |
83 | 0.991953150279963 | 0.0160936994400737 | 0.00804684972003685 |
84 | 0.988802111672032 | 0.0223957766559361 | 0.0111978883279680 |
85 | 0.987308288265266 | 0.0253834234694673 | 0.0126917117347336 |
86 | 0.981643042345557 | 0.0367139153088854 | 0.0183569576544427 |
87 | 0.975509323621777 | 0.0489813527564457 | 0.0244906763782229 |
88 | 0.988888501298392 | 0.0222229974032168 | 0.0111114987016084 |
89 | 0.989668403097329 | 0.0206631938053422 | 0.0103315969026711 |
90 | 0.989263211657017 | 0.021473576685965 | 0.0107367883429825 |
91 | 0.999053132724169 | 0.00189373455166259 | 0.000946867275831297 |
92 | 0.99949112692883 | 0.00101774614234066 | 0.000508873071170332 |
93 | 0.999755867717568 | 0.00048826456486385 | 0.000244132282431925 |
94 | 0.999571968074408 | 0.000856063851184716 | 0.000428031925592358 |
95 | 0.99921060479531 | 0.00157879040937813 | 0.000789395204689064 |
96 | 0.998767694371546 | 0.00246461125690816 | 0.00123230562845408 |
97 | 0.998101340197 | 0.00379731960599932 | 0.00189865980299966 |
98 | 0.996625166880246 | 0.00674966623950814 | 0.00337483311975407 |
99 | 0.99500523090759 | 0.00998953818482185 | 0.00499476909241093 |
100 | 0.996515672525706 | 0.00696865494858684 | 0.00348432747429342 |
101 | 0.99404542527874 | 0.0119091494425209 | 0.00595457472126044 |
102 | 0.990594990172649 | 0.0188100196547030 | 0.00940500982735148 |
103 | 0.999976888507988 | 4.62229840248883e-05 | 2.31114920124441e-05 |
104 | 0.999999877681874 | 2.44636251704274e-07 | 1.22318125852137e-07 |
105 | 0.999999983068729 | 3.38625420164111e-08 | 1.69312710082055e-08 |
106 | 0.999999916722175 | 1.66555650718955e-07 | 8.32778253594773e-08 |
107 | 0.99999968456997 | 6.3086005828563e-07 | 3.15430029142815e-07 |
108 | 0.999998696015347 | 2.60796930561416e-06 | 1.30398465280708e-06 |
109 | 0.999994142784828 | 1.17144303438595e-05 | 5.85721517192973e-06 |
110 | 0.999998548639398 | 2.90272120405385e-06 | 1.45136060202692e-06 |
111 | 0.999992429093433 | 1.51418131343729e-05 | 7.57090656718644e-06 |
112 | 0.999960802218585 | 7.83955628300839e-05 | 3.91977814150419e-05 |
113 | 0.99981046011736 | 0.000379079765279558 | 0.000189539882639779 |
114 | 0.99923922693195 | 0.00152154613609819 | 0.000760773068049093 |
115 | 0.996788561468464 | 0.00642287706307131 | 0.00321143853153566 |
116 | 0.989547244545645 | 0.0209055109087104 | 0.0104527554543552 |
117 | 0.997255127706328 | 0.00548974458734433 | 0.00274487229367217 |
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 |