| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 199.794899914341 -4.72130909980872X[t] + 72.3852616424894M1[t] + 86.565407098024M2[t] + 64.2131323426386M3[t] + 42.6431848758017M4[t] + 19.3504737538133M5[t] + 52.8852616424897M6[t] + 45.1972858760143M7[t] + 21.0058434646269M8[t] + 11.4042030645419M9[t] -13.4305848241345M10[t] + 1.98196364971308M11[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) | 199.794899914341 | 27.784288 | 7.1909 | 0 | 0 |
| X | -4.72130909980872 | 1.105408 | -4.2711 | 4.7e-05 | 2.3e-05 |
| M1 | 72.3852616424894 | 35.426417 | 2.0433 | 0.043856 | 0.021928 |
| M2 | 86.565407098024 | 35.437966 | 2.4427 | 0.016465 | 0.008233 |
| M3 | 64.2131323426386 | 35.357419 | 1.8161 | 0.072575 | 0.036287 |
| M4 | 42.6431848758017 | 35.437966 | 1.2033 | 0.231907 | 0.115954 |
| M5 | 19.3504737538133 | 35.334212 | 0.5476 | 0.58525 | 0.292625 |
| M6 | 52.8852616424897 | 35.426417 | 1.4928 | 0.138869 | 0.069435 |
| M7 | 45.1972858760143 | 35.341523 | 1.2789 | 0.204124 | 0.102062 |
| M8 | 21.0058434646269 | 35.475141 | 0.5921 | 0.555201 | 0.277601 |
| M9 | 11.4042030645419 | 35.530591 | 0.321 | 0.748954 | 0.374477 |
| M10 | -13.4305848241345 | 35.404587 | -0.3793 | 0.705296 | 0.352648 |
| M11 | 1.98196364971308 | 36.335694 | 0.0545 | 0.956617 | 0.478309 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.524969818507691 |
| R-squared | 0.275593310343998 |
| Adjusted R-squared | 0.182121479420643 |
| F-TEST (value) | 2.94841031379794 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 93 |
| p-value | 0.00163282736960713 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 72.595684266817 |
| Sum Squared Residuals | 490122.403797566 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 235.1 | 267.458852457024 | -32.3588524570238 |
| 2 | 280.7 | 281.638997912556 | -0.938997912556438 |
| 3 | 264.6 | 254.565414057362 | 10.0345859426381 |
| 4 | 240.7 | 242.438084790143 | -1.73808479014288 |
| 5 | 201.4 | 214.424064568346 | -13.0240645683458 |
| 6 | 240.8 | 252.680161556831 | -11.8801615568306 |
| 7 | 241.1 | 249.713494890164 | -8.6134948901641 |
| 8 | 223.8 | 234.964670678394 | -11.1646706783941 |
| 9 | 206.1 | 225.363030278309 | -19.2630302783091 |
| 10 | 174.7 | 200.528242389633 | -25.8282423896328 |
| 11 | 203.3 | 220.662099963289 | -17.3620999632890 |
| 12 | 220.5 | 237.565372712811 | -17.0653727128108 |
| 13 | 299.5 | 314.671943455109 | -15.1719434551090 |
| 14 | 347.4 | 347.737325309878 | -0.33732530987844 |
| 15 | 338.3 | 348.991596053537 | -10.6915960535365 |
| 16 | 327.7 | 294.372484888039 | 33.3275151119612 |
| 17 | 351.6 | 261.637155566433 | 89.9628444335671 |
| 18 | 396.6 | 299.893252554918 | 96.706747445082 |
| 19 | 438.8 | 306.369204087869 | 132.430795912131 |
| 20 | 395.6 | 272.735143476864 | 122.864856523136 |
| 21 | 363.5 | 234.805648477927 | 128.694351522073 |
| 22 | 378.8 | 257.183951587337 | 121.616048412663 |
| 23 | 357 | 230.104718162906 | 126.895281837094 |
| 24 | 369 | 228.122754513193 | 140.877245486807 |
| 25 | 464.8 | 286.344088856257 | 178.455911143743 |
| 26 | 479.1 | 291.081616112174 | 188.018383887826 |
| 27 | 431.3 | 278.171959556406 | 153.128040443594 |
| 28 | 366.5 | 261.323321189378 | 105.176678810622 |
| 29 | 326.3 | 247.473228267007 | 78.8267717329933 |
| 30 | 355.1 | 252.680161556831 | 102.419838443169 |
| 31 | 331.6 | 263.877422189590 | 67.7225778104098 |
| 32 | 261.3 | 230.243361578585 | 31.0566384214146 |
| 33 | 249 | 220.641721178500 | 28.3582788214996 |
| 34 | 205.5 | 214.692169689059 | -9.1921696890589 |
| 35 | 235.6 | 234.826027262715 | 0.7739727372848 |
| 36 | 240.9 | 228.122754513193 | 12.7772454868066 |
| 37 | 264.9 | 300.508016155683 | -35.6080161556829 |
| 38 | 253.8 | 300.524234311791 | -46.7242343117912 |
| 39 | 232.3 | 273.450650456597 | -41.150650456597 |
| 40 | 193.8 | 266.044630289186 | -72.2446302891865 |
| 41 | 177 | 271.079773766050 | -94.0797737660503 |
| 42 | 213.2 | 304.614561654727 | -91.4145616547267 |
| 43 | 207.2 | 296.926585888251 | -89.7265858882513 |
| 44 | 180.6 | 268.013834377055 | -87.4138343770552 |
| 45 | 188.6 | 277.297430376205 | -88.697430376205 |
| 46 | 175.4 | 224.134787888676 | -48.7347878886763 |
| 47 | 199 | 244.268645462333 | -45.2686454623326 |
| 48 | 179.6 | 223.401445413385 | -43.8014454133847 |
| 49 | 225.8 | 276.901470656639 | -51.1014706566392 |
| 50 | 234 | 295.802925211982 | -61.8029252119825 |
| 51 | 200.2 | 287.614577756023 | -87.4145777560232 |
| 52 | 183.6 | 261.323321189378 | -77.7233211893777 |
| 53 | 178.2 | 247.473228267007 | -69.2732282670067 |
| 54 | 203.2 | 262.122779756448 | -58.9227797564483 |
| 55 | 208.5 | 254.434803989973 | -45.9348039899728 |
| 56 | 191.8 | 230.243361578585 | -38.4433615785854 |
| 57 | 172.8 | 220.641721178500 | -47.8417211785004 |
| 58 | 148 | 176.921696890589 | -28.9216968905891 |
| 59 | 159.4 | 197.055554464245 | -37.6555544642454 |
| 60 | 154.5 | 237.565372712811 | -83.0653727128108 |
| 61 | 213.2 | 276.901470656639 | -63.7014706566393 |
| 62 | 196.4 | 281.638997912556 | -85.2389979125563 |
| 63 | 182.8 | 268.729341356788 | -85.9293413567882 |
| 64 | 176.4 | 232.995466590525 | -56.5954665905254 |
| 65 | 153.6 | 209.702755468537 | -56.1027554685369 |
| 66 | 173.2 | 247.958852457022 | -74.758852457022 |
| 67 | 171 | 249.713494890164 | -78.7134948901641 |
| 68 | 151.2 | 230.243361578585 | -79.0433615785854 |
| 69 | 161.9 | 220.641721178500 | -58.7417211785004 |
| 70 | 157.2 | 191.085624190015 | -33.8856241900153 |
| 71 | 201.7 | 239.547336362524 | -37.8473363625239 |
| 72 | 236.4 | 218.680136313576 | 17.7198636864240 |
| 73 | 356.1 | 300.508016155683 | 55.5919838443172 |
| 74 | 398.3 | 300.524234311791 | 97.7757656882088 |
| 75 | 403.7 | 278.171959556406 | 125.528040443594 |
| 76 | 384.6 | 275.487248488804 | 109.112751511196 |
| 77 | 365.8 | 261.637155566433 | 104.162844433567 |
| 78 | 368.1 | 304.614561654727 | 63.4854383452733 |
| 79 | 367.9 | 306.369204087869 | 61.5307959121312 |
| 80 | 347 | 272.735143476864 | 74.2648565231361 |
| 81 | 343.3 | 253.690884877161 | 89.6091151228385 |
| 82 | 292.9 | 266.626569786955 | 26.2734302130451 |
| 83 | 311.5 | 305.645663759846 | 5.854336240154 |
| 84 | 300.9 | 317.827627409559 | -16.9276274095591 |
| 85 | 366.9 | 366.606343553005 | 0.293656446995033 |
| 86 | 356.9 | 399.671725407774 | -42.7717254077743 |
| 87 | 329.7 | 377.319450652389 | -47.6194506523889 |
| 88 | 316.2 | 346.306884985935 | -30.1068849859347 |
| 89 | 269 | 308.85024656452 | -39.8502465645201 |
| 90 | 289.3 | 337.663725353388 | -48.3637253533877 |
| 91 | 266.2 | 325.254440487104 | -59.0544404871036 |
| 92 | 253.6 | 272.735143476864 | -19.1351434768639 |
| 93 | 233.8 | 263.133503076779 | -29.3335030767789 |
| 94 | 228.4 | 243.020024287911 | -14.6200242879112 |
| 95 | 253.6 | 248.989954562141 | 4.61004543785864 |
| 96 | 260.1 | 270.614536411472 | -10.5145364114719 |
| 97 | 306.6 | 342.999798053961 | -36.3997980539613 |
| 98 | 309.2 | 357.179943509496 | -47.9799435094959 |
| 99 | 309.5 | 325.385050554493 | -15.8850505544929 |
| 100 | 271 | 280.208557588613 | -9.20855758861259 |
| 101 | 279.9 | 280.522391965668 | -0.622391965667762 |
| 102 | 317.9 | 295.171943455109 | 22.7280565448907 |
| 103 | 298.4 | 278.041349489016 | 20.3586505109836 |
| 104 | 246.7 | 239.685979778203 | 7.01402022179714 |
| 105 | 227.3 | 230.084339378118 | -2.78433937811783 |
| 106 | 209.1 | 195.806933289824 | 13.2930667101760 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.0153452455842658 | 0.0306904911685317 | 0.984654754415734 |
| 17 | 0.0738001070073879 | 0.147600214014776 | 0.926199892992612 |
| 18 | 0.0952423478053775 | 0.190484695610755 | 0.904757652194623 |
| 19 | 0.140734580508482 | 0.281469161016963 | 0.859265419491518 |
| 20 | 0.173601364378849 | 0.347202728757698 | 0.826398635621151 |
| 21 | 0.284647148005408 | 0.569294296010817 | 0.715352851994592 |
| 22 | 0.290343731134587 | 0.580687462269174 | 0.709656268865413 |
| 23 | 0.384078185558495 | 0.76815637111699 | 0.615921814441505 |
| 24 | 0.566598111425118 | 0.866803777149765 | 0.433401888574882 |
| 25 | 0.865938011999626 | 0.268123976000748 | 0.134061988000374 |
| 26 | 0.977875921533613 | 0.0442481569327738 | 0.0221240784663869 |
| 27 | 0.994308399633995 | 0.0113832007320102 | 0.00569160036600509 |
| 28 | 0.99570021170341 | 0.00859957659318112 | 0.00429978829659056 |
| 29 | 0.99501369439902 | 0.0099726112019611 | 0.00498630560098055 |
| 30 | 0.99640551932009 | 0.00718896135981818 | 0.00359448067990909 |
| 31 | 0.995870902409248 | 0.00825819518150445 | 0.00412909759075223 |
| 32 | 0.993953903497812 | 0.0120921930043765 | 0.00604609650218824 |
| 33 | 0.991351448535656 | 0.0172971029286884 | 0.00864855146434421 |
| 34 | 0.987422285206533 | 0.0251554295869341 | 0.0125777147934671 |
| 35 | 0.983130365827109 | 0.0337392683457829 | 0.0168696341728915 |
| 36 | 0.977687245353234 | 0.0446255092935315 | 0.0223127546467657 |
| 37 | 0.974426298312586 | 0.0511474033748276 | 0.0255737016874138 |
| 38 | 0.974008969008363 | 0.0519820619832742 | 0.0259910309916371 |
| 39 | 0.968921974131752 | 0.0621560517364968 | 0.0310780258682484 |
| 40 | 0.973012890003715 | 0.0539742199925708 | 0.0269871099962854 |
| 41 | 0.985525597602521 | 0.0289488047949577 | 0.0144744023974788 |
| 42 | 0.992005493339951 | 0.0159890133200980 | 0.00799450666004902 |
| 43 | 0.994996527284598 | 0.0100069454308049 | 0.00500347271540246 |
| 44 | 0.996397330356081 | 0.00720533928783742 | 0.00360266964391871 |
| 45 | 0.997420396041416 | 0.00515920791716853 | 0.00257960395858427 |
| 46 | 0.996729631445375 | 0.0065407371092496 | 0.0032703685546248 |
| 47 | 0.995632353468882 | 0.0087352930622353 | 0.00436764653111765 |
| 48 | 0.994351572721903 | 0.0112968545561937 | 0.00564842727809684 |
| 49 | 0.992627334220558 | 0.0147453315588838 | 0.00737266577944192 |
| 50 | 0.991267950719983 | 0.0174640985600337 | 0.00873204928001687 |
| 51 | 0.992108200765648 | 0.0157835984687049 | 0.00789179923435245 |
| 52 | 0.99215409771059 | 0.0156918045788186 | 0.0078459022894093 |
| 53 | 0.991448982794882 | 0.0171020344102367 | 0.00855101720511833 |
| 54 | 0.98950415605459 | 0.0209916878908219 | 0.0104958439454110 |
| 55 | 0.985993640723603 | 0.0280127185527938 | 0.0140063592763969 |
| 56 | 0.980785509294147 | 0.0384289814117062 | 0.0192144907058531 |
| 57 | 0.975333423402335 | 0.0493331531953299 | 0.0246665765976649 |
| 58 | 0.965461123456287 | 0.0690777530874263 | 0.0345388765437132 |
| 59 | 0.953288489457833 | 0.0934230210843341 | 0.0467115105421671 |
| 60 | 0.953945073890242 | 0.0921098522195164 | 0.0460549261097582 |
| 61 | 0.947887517056566 | 0.104224965886867 | 0.0521124829434335 |
| 62 | 0.950665224331443 | 0.098669551337114 | 0.049334775668557 |
| 63 | 0.960207688751998 | 0.0795846224960032 | 0.0397923112480016 |
| 64 | 0.960711407647612 | 0.0785771847047762 | 0.0392885923523881 |
| 65 | 0.964117120585648 | 0.0717657588287037 | 0.0358828794143518 |
| 66 | 0.97449186338663 | 0.0510162732267413 | 0.0255081366133706 |
| 67 | 0.983842651358607 | 0.0323146972827856 | 0.0161573486413928 |
| 68 | 0.991202081242179 | 0.0175958375156423 | 0.00879791875782114 |
| 69 | 0.99360489572065 | 0.0127902085587004 | 0.0063951042793502 |
| 70 | 0.993919615447783 | 0.0121607691044349 | 0.00608038455221743 |
| 71 | 0.993977477556998 | 0.0120450448860045 | 0.00602252244300226 |
| 72 | 0.991574180204732 | 0.0168516395905365 | 0.00842581979526824 |
| 73 | 0.986399224041986 | 0.0272015519160286 | 0.0136007759580143 |
| 74 | 0.984885226157227 | 0.030229547685546 | 0.015114773842773 |
| 75 | 0.990320299704728 | 0.0193594005905441 | 0.00967970029527204 |
| 76 | 0.994878492645896 | 0.0102430147082090 | 0.00512150735410451 |
| 77 | 0.9979974342862 | 0.00400513142760196 | 0.00200256571380098 |
| 78 | 0.99810718385377 | 0.00378563229246049 | 0.00189281614623024 |
| 79 | 0.998693371377452 | 0.00261325724509601 | 0.00130662862254800 |
| 80 | 0.999369711991037 | 0.00126057601792619 | 0.000630288008963094 |
| 81 | 0.999970808200197 | 5.83835996064726e-05 | 2.91917998032363e-05 |
| 82 | 0.999973613724755 | 5.27725504908949e-05 | 2.63862752454474e-05 |
| 83 | 0.99994323350418 | 0.000113532991641342 | 5.6766495820671e-05 |
| 84 | 0.999843560182532 | 0.00031287963493542 | 0.00015643981746771 |
| 85 | 0.999865651686408 | 0.000268696627184785 | 0.000134348313592393 |
| 86 | 0.99979802109611 | 0.000403957807780151 | 0.000201978903890075 |
| 87 | 0.999206100712194 | 0.00158779857561202 | 0.00079389928780601 |
| 88 | 0.999385013542166 | 0.00122997291566759 | 0.000614986457833794 |
| 89 | 0.996610957762558 | 0.00677808447488424 | 0.00338904223744212 |
| 90 | 0.989190273090963 | 0.0216194538180733 | 0.0108097269090367 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 21 | 0.28 | NOK |
| 5% type I error level | 53 | 0.706666666666667 | NOK |
| 10% type I error level | 65 | 0.866666666666667 | NOK |
