Multiple Linear Regression - Estimated Regression Equation |
bewegingen[t] = + 8650.42436770292 + 0.00580420016496377passagiers[t] + 0.0857171609177784cargo[t] -0.00293593909601016auto[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) | 8650.42436770292 | 759.800383 | 11.3851 | 0 | 0 |
passagiers | 0.00580420016496377 | 0.000943 | 6.1565 | 0 | 0 |
cargo | 0.0857171609177784 | 0.009401 | 9.1178 | 0 | 0 |
auto | -0.00293593909601016 | 0.006804 | -0.4315 | 0.667454 | 0.333727 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.899279511857937 |
R-squared | 0.808703640447449 |
Adjusted R-squared | 0.800264095173072 |
F-TEST (value) | 95.8231295829055 |
F-TEST (DF numerator) | 3 |
F-TEST (DF denominator) | 68 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 831.41292487375 |
Sum Squared Residuals | 47004826.7120045 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 18919 | 17782.7409819661 | 1136.25901803386 |
2 | 19147 | 18425.5537723079 | 721.446227692107 |
3 | 21518 | 19932.5562460665 | 1585.44375393354 |
4 | 20941 | 20592.5021524865 | 348.497847513514 |
5 | 22401 | 21200.7080484380 | 1200.29195156204 |
6 | 22181 | 21017.1470244345 | 1163.85297556553 |
7 | 22494 | 22573.6313708935 | -79.6313708935403 |
8 | 21479 | 21803.2336143818 | -324.233614381789 |
9 | 22322 | 21759.9588920445 | 562.0411079555 |
10 | 21829 | 20835.5746687345 | 993.425331265515 |
11 | 20370 | 19857.3223676994 | 512.677632300595 |
12 | 18467 | 19002.0287899932 | -535.028789993215 |
13 | 18780 | 18621.2126612955 | 158.787338704461 |
14 | 18815 | 18832.6225748896 | -17.6225748896364 |
15 | 20881 | 20603.8555974171 | 277.144402582912 |
16 | 21443 | 21294.2248372602 | 148.77516273981 |
17 | 22333 | 21403.1705134291 | 929.829486570876 |
18 | 22944 | 21720.2663716138 | 1223.73362838624 |
19 | 22536 | 23155.5457661379 | -619.545766137909 |
20 | 21658 | 21922.5769183946 | -264.576918394605 |
21 | 23035 | 22421.5780552314 | 613.421944768598 |
22 | 21969 | 21587.8447699248 | 381.155230075214 |
23 | 20297 | 20238.4638402976 | 58.5361597024423 |
24 | 18564 | 19508.4944602152 | -944.494460215215 |
25 | 18844 | 18855.4464284892 | -11.4464284892372 |
26 | 18762 | 19118.9648985290 | -356.964898529045 |
27 | 21757 | 21129.8939205317 | 627.106079468262 |
28 | 20501 | 21865.0146098044 | -1364.01460980440 |
29 | 23181 | 22042.3924488696 | 1138.60755113037 |
30 | 23015 | 21998.5277150599 | 1016.47228494008 |
31 | 22828 | 23028.0412693063 | -200.041269306311 |
32 | 21597 | 22228.2994871935 | -631.299487193493 |
33 | 23005 | 22704.8013737244 | 300.198626275595 |
34 | 22243 | 22115.2315957811 | 127.768404218927 |
35 | 20729 | 20952.1901617987 | -223.190161798678 |
36 | 18310 | 19926.9979389178 | -1616.9979389178 |
37 | 19427 | 19102.5729987587 | 324.427001241292 |
38 | 18849 | 19346.6526981843 | -497.652698184289 |
39 | 21817 | 21890.9565687611 | -73.9565687610673 |
40 | 21101 | 21983.9324573532 | -882.932457353157 |
41 | 23546 | 22477.6183173241 | 1068.38168267594 |
42 | 23456 | 23130.374288379 | 325.625711620978 |
43 | 23649 | 24418.3584332168 | -769.358433216772 |
44 | 22432 | 23692.4535416175 | -1260.45354161749 |
45 | 23745 | 23993.5246642741 | -248.5246642741 |
46 | 23874 | 23530.9659176217 | 343.034082378254 |
47 | 22327 | 22565.3720483289 | -238.372048328859 |
48 | 20143 | 21673.6195892778 | -1530.61958927781 |
49 | 21252 | 20840.7340354881 | 411.265964511864 |
50 | 21094 | 21506.8154382875 | -412.815438287461 |
51 | 21800 | 23173.1965867395 | -1373.19658673951 |
52 | 22480 | 22358.7210107259 | 121.278989274102 |
53 | 23055 | 22776.9834281942 | 278.016571805777 |
54 | 23352 | 22554.0843791709 | 797.91562082907 |
55 | 23171 | 23132.4486984251 | 38.5513015749356 |
56 | 20691 | 22526.9611669726 | -1835.96116697258 |
57 | 23183 | 22399.4420172848 | 783.557982715187 |
58 | 22412 | 21606.0931157503 | 805.906884249725 |
59 | 18958 | 19709.8384717453 | -751.838471745263 |
60 | 17347 | 18580.5557362545 | -1233.55573625446 |
61 | 17353 | 17300.8190649193 | 52.1809350806783 |
62 | 17153 | 17519.9476274078 | -366.947627407826 |
63 | 20141 | 19132.281253019 | 1008.71874698101 |
64 | 19699 | 20083.3279558204 | -384.32795582037 |
65 | 20780 | 20124.8236742848 | 655.176325715155 |
66 | 21101 | 20292.9050713577 | 808.094928642293 |
67 | 20871 | 21618.7056567799 | -747.705656779926 |
68 | 19574 | 20239.8620421468 | -665.86204214681 |
69 | 21002 | 20514.1432314818 | 487.856768518228 |
70 | 20105 | 20150.3115235848 | -45.311523584763 |
71 | 17772 | 18789.8590567933 | -1017.85905679328 |
72 | 16117 | 18126.1220907098 | -2009.12209070978 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
7 | 0.231968237748975 | 0.463936475497951 | 0.768031762251025 |
8 | 0.113701425034541 | 0.227402850069081 | 0.88629857496546 |
9 | 0.0514425731733788 | 0.102885146346758 | 0.948557426826621 |
10 | 0.0239918039687801 | 0.0479836079375603 | 0.97600819603122 |
11 | 0.0467272115478025 | 0.093454423095605 | 0.953272788452198 |
12 | 0.227353013937551 | 0.454706027875102 | 0.772646986062449 |
13 | 0.157836805464755 | 0.31567361092951 | 0.842163194535245 |
14 | 0.134438054202568 | 0.268876108405136 | 0.865561945797432 |
15 | 0.101662219592079 | 0.203324439184158 | 0.898337780407921 |
16 | 0.098244397732677 | 0.196488795465354 | 0.901755602267323 |
17 | 0.0843185046042436 | 0.168637009208487 | 0.915681495395756 |
18 | 0.0798675921588242 | 0.159735184317648 | 0.920132407841176 |
19 | 0.0775624508741231 | 0.155124901748246 | 0.922437549125877 |
20 | 0.0578823539679545 | 0.115764707935909 | 0.942117646032046 |
21 | 0.0436602542690680 | 0.0873205085381359 | 0.956339745730932 |
22 | 0.0536739001188255 | 0.107347800237651 | 0.946326099881175 |
23 | 0.0539428124038628 | 0.107885624807726 | 0.946057187596137 |
24 | 0.103910908902323 | 0.207821817804646 | 0.896089091097677 |
25 | 0.0931427898388888 | 0.186285579677778 | 0.906857210161111 |
26 | 0.122806676909924 | 0.245613353819848 | 0.877193323090076 |
27 | 0.114755694402456 | 0.229511388804912 | 0.885244305597544 |
28 | 0.388579187815333 | 0.777158375630666 | 0.611420812184667 |
29 | 0.386735393459922 | 0.773470786919845 | 0.613264606540078 |
30 | 0.397013727186267 | 0.794027454372534 | 0.602986272813733 |
31 | 0.364917552878686 | 0.729835105757371 | 0.635082447121314 |
32 | 0.355442960874143 | 0.710885921748286 | 0.644557039125857 |
33 | 0.319179889994313 | 0.638359779988626 | 0.680820110005687 |
34 | 0.263163166871704 | 0.526326333743409 | 0.736836833128296 |
35 | 0.215539150284052 | 0.431078300568104 | 0.784460849715948 |
36 | 0.324304410217052 | 0.648608820434104 | 0.675695589782948 |
37 | 0.344488569726822 | 0.688977139453644 | 0.655511430273178 |
38 | 0.323419938674555 | 0.646839877349111 | 0.676580061325445 |
39 | 0.277145236989512 | 0.554290473979025 | 0.722854763010488 |
40 | 0.302158098453160 | 0.604316196906319 | 0.69784190154684 |
41 | 0.36224528986408 | 0.72449057972816 | 0.63775471013592 |
42 | 0.359540149898821 | 0.719080299797641 | 0.640459850101179 |
43 | 0.317521252822061 | 0.635042505644121 | 0.68247874717794 |
44 | 0.300916219017074 | 0.601832438034147 | 0.699083780982926 |
45 | 0.241043731542508 | 0.482087463085017 | 0.758956268457492 |
46 | 0.200692077135279 | 0.401384154270558 | 0.799307922864721 |
47 | 0.165066076342867 | 0.330132152685735 | 0.834933923657132 |
48 | 0.163555518001719 | 0.327111036003438 | 0.836444481998281 |
49 | 0.205116737072232 | 0.410233474144464 | 0.794883262927768 |
50 | 0.159946113185379 | 0.319892226370759 | 0.84005388681462 |
51 | 0.192363279843737 | 0.384726559687475 | 0.807636720156263 |
52 | 0.151570636295789 | 0.303141272591578 | 0.848429363704211 |
53 | 0.121157427698475 | 0.242314855396949 | 0.878842572301525 |
54 | 0.100314644491739 | 0.200629288983479 | 0.89968535550826 |
55 | 0.0953034718800017 | 0.190606943760003 | 0.904696528119998 |
56 | 0.355265450183737 | 0.710530900367475 | 0.644734549816263 |
57 | 0.279384145071889 | 0.558768290143777 | 0.720615854928111 |
58 | 0.230848684133917 | 0.461697368267833 | 0.769151315866083 |
59 | 0.199855730423384 | 0.399711460846768 | 0.800144269576616 |
60 | 0.227607365070658 | 0.455214730141316 | 0.772392634929342 |
61 | 0.222100840527121 | 0.444201681054242 | 0.777899159472879 |
62 | 0.194880886382961 | 0.389761772765922 | 0.805119113617039 |
63 | 0.365332927445117 | 0.730665854890234 | 0.634667072554883 |
64 | 0.304595600082816 | 0.609191200165632 | 0.695404399917184 |
65 | 0.208768127149027 | 0.417536254298054 | 0.791231872850973 |
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 | 1 | 0.0169491525423729 | OK |
10% type I error level | 3 | 0.0508474576271186 | OK |