Multiple Linear Regression - Estimated Regression Equation |
Vlaanderen[t] = + 86.9586400040947 + 1.23220559598646`Walloniƫ`[t] + 0.215180265869656Brussel[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) | 86.9586400040947 | 20.028099 | 4.3418 | 4.7e-05 | 2.4e-05 |
`Walloniƫ` | 1.23220559598646 | 0.142653 | 8.6378 | 0 | 0 |
Brussel | 0.215180265869656 | 0.174624 | 1.2322 | 0.22204 | 0.11102 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.857834973293507 |
R-squared | 0.735880841405472 |
Adjusted R-squared | 0.728225213620123 |
F-TEST (value) | 96.1228604679297 |
F-TEST (DF numerator) | 2 |
F-TEST (DF denominator) | 69 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 41.4333614395668 |
Sum Squared Residuals | 118453.917372543 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 356 | 330.371102136030 | 25.6288978639695 |
2 | 386 | 370.290917738568 | 15.7090822614322 |
3 | 444 | 399.807071236949 | 44.1929287630512 |
4 | 387 | 361.919211100708 | 25.0807888992925 |
5 | 327 | 380.481494770792 | -53.4814947707922 |
6 | 448 | 384.236987557983 | 63.763012442017 |
7 | 225 | 243.138237355036 | -18.1382373550363 |
8 | 182 | 222.190742223266 | -40.1907422232665 |
9 | 460 | 377.00215344264 | 82.9978465573603 |
10 | 411 | 374.046410525759 | 36.9535894742413 |
11 | 342 | 390.946128068118 | -48.9461280681176 |
12 | 361 | 339.426901839675 | 21.5730981603252 |
13 | 377 | 340.484574631904 | 36.5154253680959 |
14 | 331 | 357.441072979557 | -26.4410729795572 |
15 | 428 | 360.199864167688 | 67.8001358323124 |
16 | 340 | 326.382200545851 | 13.6177994541492 |
17 | 352 | 408.412186677798 | -56.4121866777978 |
18 | 461 | 433.917019661006 | 27.0829803389943 |
19 | 221 | 253.426242654667 | -32.4262426546673 |
20 | 198 | 226.043663277864 | -28.0436632778640 |
21 | 422 | 436.870667383949 | -14.8706673839494 |
22 | 329 | 411.130330403816 | -82.1303304038156 |
23 | 320 | 338.625056775428 | -18.6250567754277 |
24 | 375 | 327.673282141069 | 47.3267178589313 |
25 | 364 | 395.68009391725 | -31.6800939172501 |
26 | 351 | 378.780376374891 | -27.7803763748912 |
27 | 380 | 351.495225265495 | 28.5047747345054 |
28 | 319 | 307.840240606822 | 11.1597593931776 |
29 | 322 | 364.720744944888 | -42.7207449448876 |
30 | 386 | 372.737100393422 | 13.2628996065782 |
31 | 221 | 255.693702117890 | -34.6937021178896 |
32 | 187 | 212.527953990188 | -25.5279539901882 |
33 | 344 | 378.644395839309 | -34.6443958393092 |
34 | 342 | 399.102654440108 | -57.1026544401083 |
35 | 365 | 328.787735738592 | 36.2122642614078 |
36 | 313 | 358.439869772555 | -45.4398697725551 |
37 | 356 | 339.700958104776 | 16.2990418952240 |
38 | 337 | 344.004563422169 | -7.0045634221691 |
39 | 389 | 350.987760197405 | 38.0122398025952 |
40 | 326 | 348.738529271302 | -22.7385292713015 |
41 | 343 | 328.142194940983 | 14.8578050590167 |
42 | 357 | 396.266758715628 | -39.2667587156276 |
43 | 220 | 218.553001434539 | 1.44699856546146 |
44 | 218 | 194.416354582899 | 23.5836454171009 |
45 | 391 | 412.246879195276 | -21.2468791952763 |
46 | 425 | 430.045870069289 | -5.04587006928909 |
47 | 332 | 353.490723657553 | -21.4907236575530 |
48 | 298 | 358.537298039962 | -60.5372980399618 |
49 | 360 | 371.484571066379 | -11.4845710663791 |
50 | 336 | 306.08024621169 | 29.9197537883101 |
51 | 325 | 383.437237687673 | -58.4372376876732 |
52 | 393 | 339.311245035149 | 53.6887549648508 |
53 | 301 | 345.687453280951 | -44.6874532809511 |
54 | 426 | 500.555645305619 | -74.5556453056186 |
55 | 265 | 275.392858310491 | -10.3928583104913 |
56 | 210 | 205.037292146863 | 4.9627078531373 |
57 | 429 | 445.205916947572 | -16.2059169475718 |
58 | 440 | 405.381434418504 | 34.6185655814964 |
59 | 357 | 378.096283309107 | -21.096283309107 |
60 | 431 | 422.926692758471 | 8.07330724152855 |
61 | 442 | 396.597595786023 | 45.4024042139771 |
62 | 442 | 385.763573150127 | 56.2364268498731 |
63 | 544 | 478.258192579399 | 65.7418074206007 |
64 | 420 | 391.122756065812 | 28.8772439341879 |
65 | 396 | 371.230838532334 | 24.7691614676658 |
66 | 482 | 423.298177290979 | 58.7018227090207 |
67 | 261 | 303.928443552993 | -42.9284435529933 |
68 | 211 | 222.464798488368 | -11.4647984883676 |
69 | 448 | 529.249630008696 | -81.249630008696 |
70 | 468 | 413.341009061744 | 54.6589909382564 |
71 | 464 | 409.920543732823 | 54.0794562671774 |
72 | 425 | 367.183060942923 | 57.8169390570768 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
6 | 0.759060281570113 | 0.481879436859774 | 0.240939718429887 |
7 | 0.652132384360399 | 0.695735231279202 | 0.347867615639601 |
8 | 0.538894987922612 | 0.922210024154776 | 0.461105012077388 |
9 | 0.509162729141888 | 0.981674541716223 | 0.490837270858112 |
10 | 0.416684413400884 | 0.833368826801768 | 0.583315586599116 |
11 | 0.708643441167009 | 0.582713117665981 | 0.291356558832991 |
12 | 0.633563315445071 | 0.732873369109857 | 0.366436684554929 |
13 | 0.552048851384107 | 0.895902297231786 | 0.447951148615893 |
14 | 0.530283227601438 | 0.939433544797124 | 0.469716772398562 |
15 | 0.548371502213831 | 0.903256995572338 | 0.451628497786169 |
16 | 0.462858923523821 | 0.925717847047641 | 0.53714107647618 |
17 | 0.67061216580384 | 0.65877566839232 | 0.32938783419616 |
18 | 0.603270242871023 | 0.793459514257954 | 0.396729757128977 |
19 | 0.548808301269428 | 0.902383397461143 | 0.451191698730571 |
20 | 0.481448699329475 | 0.96289739865895 | 0.518551300670525 |
21 | 0.464814192194541 | 0.929628384389082 | 0.535185807805459 |
22 | 0.685614864921974 | 0.628770270156051 | 0.314385135078026 |
23 | 0.623627574782897 | 0.752744850434206 | 0.376372425217103 |
24 | 0.601687219976111 | 0.796625560047777 | 0.398312780023889 |
25 | 0.64156999092858 | 0.716860018142841 | 0.358430009071420 |
26 | 0.614178411160342 | 0.771643177679316 | 0.385821588839658 |
27 | 0.577699041582131 | 0.844601916835738 | 0.422300958417869 |
28 | 0.507741260590869 | 0.984517478818262 | 0.492258739409131 |
29 | 0.628493283497198 | 0.743013433005605 | 0.371506716502802 |
30 | 0.563860450705576 | 0.872279098588849 | 0.436139549294424 |
31 | 0.535412931808378 | 0.929174136383244 | 0.464587068191622 |
32 | 0.491102781552647 | 0.982205563105293 | 0.508897218447353 |
33 | 0.47856147060984 | 0.95712294121968 | 0.52143852939016 |
34 | 0.552479146382333 | 0.895041707235334 | 0.447520853617667 |
35 | 0.530051598414301 | 0.939896803171397 | 0.469948401585699 |
36 | 0.545322812574414 | 0.909354374851173 | 0.454677187425586 |
37 | 0.484159615175062 | 0.968319230350123 | 0.515840384824938 |
38 | 0.419067175750518 | 0.838134351501036 | 0.580932824249482 |
39 | 0.401598248661878 | 0.803196497323756 | 0.598401751338122 |
40 | 0.35610822848396 | 0.71221645696792 | 0.64389177151604 |
41 | 0.298360913826166 | 0.596721827652332 | 0.701639086173834 |
42 | 0.297078100205677 | 0.594156200411353 | 0.702921899794323 |
43 | 0.240331580212594 | 0.480663160425189 | 0.759668419787406 |
44 | 0.199648153908241 | 0.399296307816483 | 0.800351846091759 |
45 | 0.164915392352372 | 0.329830784704745 | 0.835084607647627 |
46 | 0.124405827621739 | 0.248811655243477 | 0.875594172378261 |
47 | 0.102791336872274 | 0.205582673744547 | 0.897208663127726 |
48 | 0.152114254476135 | 0.304228508952271 | 0.847885745523865 |
49 | 0.125688902147935 | 0.25137780429587 | 0.874311097852065 |
50 | 0.102145487401737 | 0.204290974803473 | 0.897854512598263 |
51 | 0.129701589099069 | 0.259403178198139 | 0.87029841090093 |
52 | 0.142380003678013 | 0.284760007356025 | 0.857619996321987 |
53 | 0.157335742917031 | 0.314671485834062 | 0.842664257082969 |
54 | 0.369896590311134 | 0.739793180622269 | 0.630103409688866 |
55 | 0.296750290119870 | 0.593500580239741 | 0.70324970988013 |
56 | 0.229576486812867 | 0.459152973625735 | 0.770423513187133 |
57 | 0.176002239481633 | 0.352004478963266 | 0.823997760518367 |
58 | 0.138726496171919 | 0.277452992343838 | 0.861273503828081 |
59 | 0.130231418143649 | 0.260462836287298 | 0.86976858185635 |
60 | 0.0894649236640546 | 0.178929847328109 | 0.910535076335945 |
61 | 0.0645683172658091 | 0.129136634531618 | 0.93543168273419 |
62 | 0.0567473456820624 | 0.113494691364125 | 0.943252654317938 |
63 | 0.0626085847420472 | 0.125217169484094 | 0.937391415257953 |
64 | 0.0372512596963209 | 0.0745025193926418 | 0.96274874030368 |
65 | 0.0196199202201570 | 0.0392398404403139 | 0.980380079779843 |
66 | 0.0179278055452604 | 0.0358556110905208 | 0.98207219445474 |
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 | 2 | 0.0327868852459016 | OK |
10% type I error level | 3 | 0.0491803278688525 | OK |