Multiple Linear Regression - Estimated Regression Equation |
Aantalhuwelijken[t] = + 2248.6655982906 + 169.478174603174Dummy[t] -813.27090964591M1[t] -105.655525030524M2[t] + 169.036782661784M3[t] + 1065.03678266178M4[t] + 2618.65216727716M5[t] + 3073.69230769231M6[t] + 3246.07692307692M7[t] + 3903.46153846154M8[t] + 3222.84615384615M9[t] + 955.307692307692M10[t] -376.692307692306M11[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) | 2248.6655982906 | 119.134777 | 18.875 | 0 | 0 |
Dummy | 169.478174603174 | 65.859639 | 2.5733 | 0.011091 | 0.005545 |
M1 | -813.27090964591 | 160.92428 | -5.0537 | 1e-06 | 1e-06 |
M2 | -105.655525030524 | 160.92428 | -0.6566 | 0.512523 | 0.256261 |
M3 | 169.036782661784 | 160.92428 | 1.0504 | 0.295301 | 0.14765 |
M4 | 1065.03678266178 | 160.92428 | 6.6182 | 0 | 0 |
M5 | 2618.65216727716 | 160.92428 | 16.2726 | 0 | 0 |
M6 | 3073.69230769231 | 160.844515 | 19.1097 | 0 | 0 |
M7 | 3246.07692307692 | 160.844515 | 20.1815 | 0 | 0 |
M8 | 3903.46153846154 | 160.844515 | 24.2685 | 0 | 0 |
M9 | 3222.84615384615 | 160.844515 | 20.037 | 0 | 0 |
M10 | 955.307692307692 | 160.844515 | 5.9393 | 0 | 0 |
M11 | -376.692307692306 | 160.844515 | -2.342 | 0.020562 | 0.010281 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.97194288209495 |
R-squared | 0.944672966055038 |
Adjusted R-squared | 0.940030138031685 |
F-TEST (value) | 203.469299595706 |
F-TEST (DF numerator) | 12 |
F-TEST (DF denominator) | 143 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 410.074661434315 |
Sum Squared Residuals | 24047055.5969170 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 1567 | 1435.39468864469 | 131.60531135531 |
2 | 2237 | 2143.01007326007 | 93.9899267399274 |
3 | 2598 | 2417.70238095238 | 180.297619047623 |
4 | 3729 | 3313.70238095238 | 415.297619047616 |
5 | 5715 | 4867.31776556777 | 847.682234432233 |
6 | 5776 | 5322.35790598291 | 453.642094017094 |
7 | 5852 | 5494.74252136751 | 357.257478632492 |
8 | 6878 | 6152.12713675215 | 725.872863247851 |
9 | 5488 | 5471.51175213675 | 16.4882478632508 |
10 | 3583 | 3203.97329059830 | 379.026709401704 |
11 | 2054 | 1871.97329059828 | 182.026709401717 |
12 | 2282 | 2248.6655982906 | 33.3344017094019 |
13 | 1552 | 1435.39468864469 | 116.605311355312 |
14 | 2261 | 2143.01007326007 | 117.989926739927 |
15 | 2446 | 2417.70238095238 | 28.2976190476187 |
16 | 3519 | 3313.70238095238 | 205.297619047619 |
17 | 5161 | 4867.31776556777 | 293.682234432235 |
18 | 5085 | 5322.35790598291 | -237.357905982906 |
19 | 5711 | 5494.74252136752 | 216.257478632477 |
20 | 6057 | 6152.12713675214 | -95.1271367521358 |
21 | 5224 | 5471.51175213675 | -247.511752136752 |
22 | 3363 | 3203.97329059829 | 159.02670940171 |
23 | 1899 | 1871.97329059829 | 27.0267094017086 |
24 | 2115 | 2248.6655982906 | -133.665598290598 |
25 | 1491 | 1435.39468864469 | 55.6053113553113 |
26 | 2061 | 2143.01007326007 | -82.0100732600734 |
27 | 2419 | 2417.70238095238 | 1.29761904761871 |
28 | 3430 | 3313.70238095238 | 116.297619047619 |
29 | 4778 | 4867.31776556777 | -89.3177655677652 |
30 | 4862 | 5322.35790598291 | -460.357905982906 |
31 | 6176 | 5494.74252136752 | 681.257478632477 |
32 | 5664 | 6152.12713675214 | -488.127136752136 |
33 | 5529 | 5471.51175213675 | 57.4882478632475 |
34 | 3418 | 3203.97329059829 | 214.02670940171 |
35 | 1941 | 1871.97329059829 | 69.0267094017081 |
36 | 2402 | 2248.6655982906 | 153.334401709402 |
37 | 1579 | 1435.39468864469 | 143.605311355311 |
38 | 2146 | 2143.01007326007 | 2.9899267399266 |
39 | 2462 | 2417.70238095238 | 44.2976190476187 |
40 | 3695 | 3313.70238095238 | 381.297619047619 |
41 | 4831 | 4867.31776556777 | -36.3177655677651 |
42 | 5134 | 5322.35790598291 | -188.357905982906 |
43 | 6250 | 5494.74252136752 | 755.257478632477 |
44 | 5760 | 6152.12713675214 | -392.127136752136 |
45 | 6249 | 5471.51175213675 | 777.488247863247 |
46 | 2917 | 3203.97329059829 | -286.97329059829 |
47 | 1741 | 1871.97329059829 | -130.973290598291 |
48 | 2359 | 2248.6655982906 | 110.334401709402 |
49 | 1511 | 1435.39468864469 | 75.6053113553113 |
50 | 2059 | 2143.01007326007 | -84.0100732600734 |
51 | 2635 | 2417.70238095238 | 217.297619047619 |
52 | 2867 | 3313.70238095238 | -446.702380952381 |
53 | 4403 | 4867.31776556777 | -464.317765567765 |
54 | 5720 | 5322.35790598291 | 397.642094017094 |
55 | 4502 | 5494.74252136752 | -992.742521367523 |
56 | 5749 | 6152.12713675214 | -403.127136752136 |
57 | 5627 | 5471.51175213675 | 155.488247863247 |
58 | 2846 | 3203.97329059829 | -357.97329059829 |
59 | 1762 | 1871.97329059829 | -109.973290598291 |
60 | 2429 | 2248.6655982906 | 180.334401709402 |
61 | 1169 | 1435.39468864469 | -266.394688644689 |
62 | 2154 | 2143.01007326007 | 10.9899267399266 |
63 | 2249 | 2417.70238095238 | -168.702380952381 |
64 | 2687 | 3313.70238095238 | -626.70238095238 |
65 | 4359 | 4867.31776556777 | -508.317765567765 |
66 | 5382 | 5322.35790598291 | 59.6420940170937 |
67 | 4459 | 5494.74252136752 | -1035.74252136752 |
68 | 6398 | 6152.12713675214 | 245.872863247864 |
69 | 4596 | 5471.51175213675 | -875.511752136752 |
70 | 3024 | 3203.97329059829 | -179.973290598290 |
71 | 1887 | 1871.97329059829 | 15.0267094017086 |
72 | 2070 | 2248.6655982906 | -178.665598290598 |
73 | 1351 | 1435.39468864469 | -84.3946886446887 |
74 | 2218 | 2143.01007326007 | 74.9899267399265 |
75 | 2461 | 2417.70238095238 | 43.2976190476187 |
76 | 3028 | 3313.70238095238 | -285.702380952381 |
77 | 4784 | 4867.31776556777 | -83.3177655677652 |
78 | 4975 | 5491.83608058608 | -516.836080586081 |
79 | 4607 | 5664.2206959707 | -1057.22069597070 |
80 | 6249 | 6321.60531135531 | -72.6053113553099 |
81 | 4809 | 5640.98992673993 | -831.989926739926 |
82 | 3157 | 3373.45146520146 | -216.451465201465 |
83 | 1910 | 2041.45146520147 | -131.451465201466 |
84 | 2228 | 2418.14377289377 | -190.143772893772 |
85 | 1673 | 1604.87286324786 | 68.1271367521368 |
86 | 2589 | 2312.48824786325 | 276.511752136752 |
87 | 2332 | 2587.18055555556 | -255.180555555556 |
88 | 3785 | 3483.18055555556 | 301.819444444444 |
89 | 4916 | 5036.79594017094 | -120.795940170940 |
90 | 5207 | 5491.83608058608 | -284.836080586081 |
91 | 6055 | 5664.2206959707 | 390.779304029303 |
92 | 5751 | 6321.60531135531 | -570.60531135531 |
93 | 5247 | 5640.98992673993 | -393.989926739927 |
94 | 3387 | 3373.45146520146 | 13.5485347985350 |
95 | 2091 | 2041.45146520147 | 49.5485347985342 |
96 | 2401 | 2418.14377289377 | -17.1437728937722 |
97 | 1664 | 1604.87286324786 | 59.1271367521368 |
98 | 2205 | 2312.48824786325 | -107.488247863248 |
99 | 2295 | 2587.18055555556 | -292.180555555556 |
100 | 3762 | 3483.18055555556 | 278.819444444445 |
101 | 4890 | 5036.79594017094 | -146.795940170940 |
102 | 5117 | 5491.83608058608 | -374.836080586081 |
103 | 6099 | 5664.2206959707 | 434.779304029303 |
104 | 5865 | 6321.60531135531 | -456.60531135531 |
105 | 5594 | 5640.98992673993 | -46.9899267399269 |
106 | 3229 | 3373.45146520146 | -144.451465201465 |
107 | 2106 | 2041.45146520147 | 64.5485347985342 |
108 | 2410 | 2418.14377289377 | -8.1437728937722 |
109 | 1583 | 1604.87286324786 | -21.8728632478631 |
110 | 2092 | 2312.48824786325 | -220.488247863248 |
111 | 2612 | 2587.18055555556 | 24.8194444444442 |
112 | 3665 | 3483.18055555556 | 181.819444444445 |
113 | 4880 | 5036.79594017094 | -156.795940170940 |
114 | 5875 | 5491.83608058608 | 383.163919413919 |
115 | 5892 | 5664.2206959707 | 227.779304029303 |
116 | 6078 | 6321.60531135531 | -243.60531135531 |
117 | 6515 | 5640.98992673993 | 874.010073260073 |
118 | 3164 | 3373.45146520146 | -209.451465201465 |
119 | 2028 | 2041.45146520147 | -13.4514652014658 |
120 | 2677 | 2418.14377289377 | 258.856227106227 |
121 | 1580 | 1604.87286324786 | -24.8728632478631 |
122 | 2196 | 2312.48824786325 | -116.488247863248 |
123 | 2838 | 2587.18055555556 | 250.819444444444 |
124 | 3087 | 3483.18055555556 | -396.180555555555 |
125 | 4726 | 5036.79594017094 | -310.795940170940 |
126 | 6521 | 5491.83608058608 | 1029.16391941392 |
127 | 6739 | 5664.2206959707 | 1074.77930402930 |
128 | 5943 | 6321.60531135531 | -378.60531135531 |
129 | 6265 | 5640.98992673993 | 624.010073260073 |
130 | 3323 | 3373.45146520146 | -50.451465201465 |
131 | 2098 | 2041.45146520147 | 56.5485347985342 |
132 | 2544 | 2418.14377289377 | 125.856227106227 |
133 | 1442 | 1604.87286324786 | -162.872863247863 |
134 | 2307 | 2312.48824786325 | -5.48824786324774 |
135 | 2811 | 2587.18055555556 | 223.819444444444 |
136 | 3461 | 3483.18055555556 | -22.1805555555554 |
137 | 5451 | 5036.79594017094 | 414.20405982906 |
138 | 5481 | 5491.83608058608 | -10.8360805860811 |
139 | 5114 | 5664.2206959707 | -550.220695970697 |
140 | 8381 | 6321.60531135531 | 2059.39468864469 |
141 | 5215 | 5640.98992673993 | -425.989926739927 |
142 | 3700 | 3373.45146520146 | 326.548534798535 |
143 | 2122 | 2041.45146520147 | 80.5485347985342 |
144 | 2311 | 2418.14377289377 | -107.143772893772 |
145 | 1515 | 1604.87286324786 | -89.8728632478631 |
146 | 2351 | 2312.48824786325 | 38.5117521367523 |
147 | 2289 | 2587.18055555556 | -298.180555555556 |
148 | 3380 | 3483.18055555556 | -103.180555555555 |
149 | 5398 | 5036.79594017094 | 361.20405982906 |
150 | 5242 | 5491.83608058608 | -249.836080586081 |
151 | 5162 | 5664.2206959707 | -502.220695970697 |
152 | 6391 | 6321.60531135531 | 69.39468864469 |
153 | 5958 | 5640.98992673993 | 317.010073260073 |
154 | 3727 | 3373.45146520146 | 353.548534798535 |
155 | 1883 | 2041.45146520147 | -158.451465201466 |
156 | 2191 | 2418.14377289377 | -227.143772893772 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
16 | 0.0224569505085652 | 0.0449139010171303 | 0.977543049491435 |
17 | 0.106502278896379 | 0.213004557792758 | 0.89349772110362 |
18 | 0.222203030457395 | 0.444406060914789 | 0.777796969542605 |
19 | 0.137115485791067 | 0.274230971582135 | 0.862884514208933 |
20 | 0.275289865607203 | 0.550579731214407 | 0.724710134392797 |
21 | 0.206275266673710 | 0.412550533347421 | 0.79372473332629 |
22 | 0.147428028567830 | 0.294856057135659 | 0.85257197143217 |
23 | 0.0981135054955831 | 0.196227010991166 | 0.901886494504417 |
24 | 0.063876871516078 | 0.127753743032156 | 0.936123128483922 |
25 | 0.0386495282021686 | 0.0772990564043372 | 0.961350471797831 |
26 | 0.024957432584119 | 0.049914865168238 | 0.975042567415881 |
27 | 0.0145529323346813 | 0.0291058646693626 | 0.985447067665319 |
28 | 0.00927222547555814 | 0.0185444509511163 | 0.990727774524442 |
29 | 0.0216401029112766 | 0.0432802058225532 | 0.978359897088723 |
30 | 0.0313961965548904 | 0.0627923931097808 | 0.96860380344511 |
31 | 0.0336300899156815 | 0.067260179831363 | 0.966369910084318 |
32 | 0.0784795782824617 | 0.156959156564923 | 0.921520421717538 |
33 | 0.0572864466560922 | 0.114572893312184 | 0.942713553343908 |
34 | 0.0403288841676651 | 0.0806577683353302 | 0.959671115832335 |
35 | 0.0270739132362832 | 0.0541478264725663 | 0.972926086763717 |
36 | 0.0194985657368962 | 0.0389971314737924 | 0.980501434263104 |
37 | 0.0128113215378100 | 0.0256226430756200 | 0.98718867846219 |
38 | 0.0080917288949488 | 0.0161834577898976 | 0.991908271105051 |
39 | 0.0050154641316135 | 0.010030928263227 | 0.994984535868386 |
40 | 0.00362141748142747 | 0.00724283496285494 | 0.996378582518572 |
41 | 0.00341479101421986 | 0.00682958202843973 | 0.99658520898578 |
42 | 0.00212945193196431 | 0.00425890386392861 | 0.997870548068036 |
43 | 0.00293060247147311 | 0.00586120494294621 | 0.997069397528527 |
44 | 0.00321185407391571 | 0.00642370814783143 | 0.996788145926084 |
45 | 0.0157331339527781 | 0.0314662679055562 | 0.984266866047222 |
46 | 0.0186825385237882 | 0.0373650770475763 | 0.981317461476212 |
47 | 0.0140470475017306 | 0.0280940950034612 | 0.98595295249827 |
48 | 0.00996888748179733 | 0.0199377749635947 | 0.990031112518203 |
49 | 0.00690847993058095 | 0.0138169598611619 | 0.993091520069419 |
50 | 0.00468652003481925 | 0.0093730400696385 | 0.99531347996518 |
51 | 0.00352181337114639 | 0.00704362674229279 | 0.996478186628854 |
52 | 0.00752739121825487 | 0.0150547824365097 | 0.992472608781745 |
53 | 0.0137316776901667 | 0.0274633553803335 | 0.986268322309833 |
54 | 0.0171306558161259 | 0.0342613116322518 | 0.982869344183874 |
55 | 0.177205100351373 | 0.354410200702745 | 0.822794899648628 |
56 | 0.162034353718286 | 0.324068707436573 | 0.837965646281714 |
57 | 0.138996978151436 | 0.277993956302873 | 0.861003021848564 |
58 | 0.134246495650416 | 0.268492991300831 | 0.865753504349584 |
59 | 0.109588688512528 | 0.219177377025055 | 0.890411311487472 |
60 | 0.0938261171966572 | 0.187652234393314 | 0.906173882803343 |
61 | 0.0833960498432985 | 0.166792099686597 | 0.916603950156702 |
62 | 0.0662238124961096 | 0.132447624992219 | 0.93377618750389 |
63 | 0.0546876815303646 | 0.109375363060729 | 0.945312318469635 |
64 | 0.0772552403949966 | 0.154510480789993 | 0.922744759605003 |
65 | 0.0868224410639883 | 0.173644882127977 | 0.913177558936012 |
66 | 0.0704234310134558 | 0.140846862026912 | 0.929576568986544 |
67 | 0.208734432661900 | 0.417468865323800 | 0.7912655673381 |
68 | 0.19521734856645 | 0.3904346971329 | 0.80478265143355 |
69 | 0.320412635583143 | 0.640825271166287 | 0.679587364416857 |
70 | 0.282558157928667 | 0.565116315857334 | 0.717441842071333 |
71 | 0.242104145843017 | 0.484208291686035 | 0.757895854156982 |
72 | 0.211127380830380 | 0.422254761660759 | 0.78887261916962 |
73 | 0.178099527915418 | 0.356199055830835 | 0.821900472084582 |
74 | 0.149295531820929 | 0.298591063641857 | 0.850704468179071 |
75 | 0.125131339095946 | 0.250262678191891 | 0.874868660904054 |
76 | 0.107805445782328 | 0.215610891564656 | 0.892194554217672 |
77 | 0.0868013450275972 | 0.173602690055194 | 0.913198654972403 |
78 | 0.0809904815703343 | 0.161980963140669 | 0.919009518429666 |
79 | 0.140837632097271 | 0.281675264194541 | 0.85916236790273 |
80 | 0.145554974320011 | 0.291109948640022 | 0.85444502567999 |
81 | 0.189091743339445 | 0.378183486678889 | 0.810908256660555 |
82 | 0.172543504877151 | 0.345087009754303 | 0.827456495122849 |
83 | 0.153055114095358 | 0.306110228190717 | 0.846944885904642 |
84 | 0.131091845730247 | 0.262183691460495 | 0.868908154269753 |
85 | 0.119028071859263 | 0.238056143718527 | 0.880971928140737 |
86 | 0.123582555363563 | 0.247165110727126 | 0.876417444636437 |
87 | 0.102734946123872 | 0.205469892247743 | 0.897265053876128 |
88 | 0.105789319451817 | 0.211578638903634 | 0.894210680548183 |
89 | 0.0863050844696556 | 0.172610168939311 | 0.913694915530344 |
90 | 0.076079824891809 | 0.152159649783618 | 0.923920175108191 |
91 | 0.0834322856602698 | 0.166864571320540 | 0.91656771433973 |
92 | 0.098945258755573 | 0.197890517511146 | 0.901054741244427 |
93 | 0.101665706711472 | 0.203331413422945 | 0.898334293288528 |
94 | 0.0832028497769755 | 0.166405699553951 | 0.916797150223025 |
95 | 0.0672631583837464 | 0.134526316767493 | 0.932736841616254 |
96 | 0.0527752000454015 | 0.105550400090803 | 0.947224799954599 |
97 | 0.041649357465942 | 0.083298714931884 | 0.958350642534058 |
98 | 0.0314420113376828 | 0.0628840226753655 | 0.968557988662317 |
99 | 0.0258712307034809 | 0.0517424614069617 | 0.97412876929652 |
100 | 0.0236637712176412 | 0.0473275424352825 | 0.976336228782359 |
101 | 0.0179790737712938 | 0.0359581475425877 | 0.982020926228706 |
102 | 0.0188000304518922 | 0.0376000609037845 | 0.981199969548108 |
103 | 0.0200459750592483 | 0.0400919501184966 | 0.979954024940752 |
104 | 0.026399766076411 | 0.052799532152822 | 0.973600233923589 |
105 | 0.0226950635024775 | 0.0453901270049549 | 0.977304936497523 |
106 | 0.0173178299322224 | 0.0346356598644448 | 0.982682170067778 |
107 | 0.0126399172937594 | 0.0252798345875189 | 0.98736008270624 |
108 | 0.00890960816274954 | 0.0178192163254991 | 0.99109039183725 |
109 | 0.00616211360549316 | 0.0123242272109863 | 0.993837886394507 |
110 | 0.00439018741080737 | 0.00878037482161474 | 0.995609812589193 |
111 | 0.00296818270959089 | 0.00593636541918178 | 0.99703181729041 |
112 | 0.00231287492411378 | 0.00462574984822757 | 0.997687125075886 |
113 | 0.00164855023552359 | 0.00329710047104719 | 0.998351449764476 |
114 | 0.00142927378683192 | 0.00285854757366384 | 0.998570726213168 |
115 | 0.00103303176695592 | 0.00206606353391184 | 0.998966968233044 |
116 | 0.00139253208564243 | 0.00278506417128486 | 0.998607467914358 |
117 | 0.00373685716957970 | 0.00747371433915939 | 0.99626314283042 |
118 | 0.00293051030799662 | 0.00586102061599325 | 0.997069489692003 |
119 | 0.00184456490939793 | 0.00368912981879586 | 0.998155435090602 |
120 | 0.00138530212946806 | 0.00277060425893612 | 0.998614697870532 |
121 | 0.000843717270372868 | 0.00168743454074574 | 0.999156282729627 |
122 | 0.000507034634590998 | 0.00101406926918200 | 0.99949296536541 |
123 | 0.000346238182095778 | 0.000692476364191555 | 0.999653761817904 |
124 | 0.000252144945537366 | 0.000504289891074732 | 0.999747855054463 |
125 | 0.000262000815576652 | 0.000524001631153304 | 0.999737999184423 |
126 | 0.00189800264273973 | 0.00379600528547945 | 0.99810199735726 |
127 | 0.0366053905811792 | 0.0732107811623584 | 0.96339460941882 |
128 | 0.197410532890698 | 0.394821065781396 | 0.802589467109302 |
129 | 0.248363982048039 | 0.496727964096078 | 0.751636017951961 |
130 | 0.218327980098889 | 0.436655960197778 | 0.78167201990111 |
131 | 0.164194721163796 | 0.328389442327592 | 0.835805278836204 |
132 | 0.129314398937784 | 0.258628797875569 | 0.870685601062216 |
133 | 0.0898303694761895 | 0.179660738952379 | 0.91016963052381 |
134 | 0.0586223926950855 | 0.117244785390171 | 0.941377607304914 |
135 | 0.0486693740867543 | 0.0973387481735086 | 0.951330625913246 |
136 | 0.0287124702766257 | 0.0574249405532514 | 0.971287529723374 |
137 | 0.016722024530169 | 0.033444049060338 | 0.983277975469831 |
138 | 0.0088592226532433 | 0.0177184453064866 | 0.991140777346757 |
139 | 0.00442666973594812 | 0.00885333947189624 | 0.995573330264052 |
140 | 0.629076330187278 | 0.741847339625445 | 0.370923669812722 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 25 | 0.2 | NOK |
5% type I error level | 53 | 0.424 | NOK |
10% type I error level | 65 | 0.52 | NOK |