| Multiple Linear Regression - Estimated Regression Equation |
| Y_t[t] = + 27.6311102673683 + 0.414284391942137X_1t[t] -0.46721105468132X_2t[t] -0.0906080774295398X_3t[t] -0.847575818888379X_4t[t] + 0.0492227659404471X_5t[t] -0.880855887263957M1[t] -0.909163478628467M2[t] + 0.29762990266939M3[t] + 3.20092531029737M4[t] + 0.0785997411513749M5[t] -0.232671950536061M6[t] -1.29989292249193M7[t] -0.662633856942808M8[t] -1.7174892402748M9[t] + 0.173268888997232M10[t] + 0.898960134925918M11[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) | 27.6311102673683 | 4.873733 | 5.6694 | 0 | 0 |
| X_1t | 0.414284391942137 | 0.064379 | 6.4351 | 0 | 0 |
| X_2t | -0.46721105468132 | 0.06901 | -6.7702 | 0 | 0 |
| X_3t | -0.0906080774295398 | 0.066685 | -1.3588 | 0.178921 | 0.08946 |
| X_4t | -0.847575818888379 | 0.224397 | -3.7771 | 0.000346 | 0.000173 |
| X_5t | 0.0492227659404471 | 0.08856 | 0.5558 | 0.580249 | 0.290124 |
| M1 | -0.880855887263957 | 2.355055 | -0.374 | 0.709601 | 0.3548 |
| M2 | -0.909163478628467 | 2.370966 | -0.3835 | 0.702632 | 0.351316 |
| M3 | 0.29762990266939 | 2.349893 | 0.1267 | 0.899603 | 0.449802 |
| M4 | 3.20092531029737 | 2.382021 | 1.3438 | 0.18369 | 0.091845 |
| M5 | 0.0785997411513749 | 2.352126 | 0.0334 | 0.973445 | 0.486722 |
| M6 | -0.232671950536061 | 2.382495 | -0.0977 | 0.922504 | 0.461252 |
| M7 | -1.29989292249193 | 2.373917 | -0.5476 | 0.585861 | 0.29293 |
| M8 | -0.662633856942808 | 2.367914 | -0.2798 | 0.78049 | 0.390245 |
| M9 | -1.7174892402748 | 2.384242 | -0.7204 | 0.473892 | 0.236946 |
| M10 | 0.173268888997232 | 2.355302 | 0.0736 | 0.941582 | 0.470791 |
| M11 | 0.898960134925918 | 2.42471 | 0.3707 | 0.71203 | 0.356015 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.922061804389825 |
| R-squared | 0.850197971114621 |
| Adjusted R-squared | 0.813323625542835 |
| F-TEST (value) | 23.0566253564957 |
| F-TEST (DF numerator) | 16 |
| F-TEST (DF denominator) | 65 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 4.19270177080869 |
| Sum Squared Residuals | 1142.61862903125 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | -3 | -7.79023739771141 | 4.79023739771141 |
| 2 | -4 | -5.13604457919732 | 1.13604457919732 |
| 3 | -7 | -4.0317707810791 | -2.9682292189209 |
| 4 | -7 | -2.86464216821697 | -4.13535783178303 |
| 5 | -7 | -4.42337982765096 | -2.57662017234904 |
| 6 | -3 | -2.33520442865505 | -0.66479557134495 |
| 7 | 0 | -2.10202445338227 | 2.10202445338227 |
| 8 | -5 | -2.79225780294688 | -2.20774219705312 |
| 9 | -3 | -3.90971420015634 | 0.909714200156343 |
| 10 | 3 | 1.47981846741135 | 1.52018153258865 |
| 11 | 2 | -1.18247812647074 | 3.18247812647074 |
| 12 | -7 | -7.20122785190149 | 0.201227851901495 |
| 13 | -1 | -1.29630081988473 | 0.296300819884727 |
| 14 | 0 | -2.11481174540234 | 2.11481174540234 |
| 15 | -3 | 0.694707074332846 | -3.69470707433285 |
| 16 | 4 | 6.371578129305 | -2.371578129305 |
| 17 | 2 | 1.73715559012558 | 0.262844409874415 |
| 18 | 3 | 1.94231771905992 | 1.05768228094008 |
| 19 | 0 | -2.72205642096133 | 2.72205642096133 |
| 20 | -10 | -3.11282862918526 | -6.88717137081474 |
| 21 | -10 | -7.37455270300499 | -2.62544729699501 |
| 22 | -9 | -3.96165148186391 | -5.03834851813609 |
| 23 | -22 | -12.2791351927626 | -9.72086480723738 |
| 24 | -16 | -14.2930307820924 | -1.7069692179076 |
| 25 | -18 | -17.789700635039 | -0.210299364961043 |
| 26 | -14 | -16.2526617011354 | 2.25266170113545 |
| 27 | -12 | -17.0135298411411 | 5.0135298411411 |
| 28 | -17 | -19.1975449679354 | 2.19754496793544 |
| 29 | -23 | -20.6575623303272 | -2.34243766967277 |
| 30 | -28 | -22.4034280135916 | -5.59657198640841 |
| 31 | -31 | -27.1309192057283 | -3.86908079427173 |
| 32 | -21 | -25.7116848059518 | 4.71168480595179 |
| 33 | -19 | -24.1582497975117 | 5.15824979751174 |
| 34 | -22 | -24.906433231362 | 2.90643323136196 |
| 35 | -22 | -22.8499158280208 | 0.849915828020826 |
| 36 | -25 | -25.3135180621996 | 0.313518062199576 |
| 37 | -16 | -20.1203163580656 | 4.12031635806558 |
| 38 | -22 | -20.5529291216478 | -1.44707087835223 |
| 39 | -21 | -14.3204470286286 | -6.67955297137143 |
| 40 | -10 | -11.5346041878856 | 1.53460418788559 |
| 41 | -7 | -10.447780926934 | 3.447780926934 |
| 42 | -5 | -10.1961020132764 | 5.19610201327636 |
| 43 | -4 | -4.2135981830537 | 0.213598183053699 |
| 44 | 7 | -1.29268545664458 | 8.29268545664458 |
| 45 | 6 | 1.63775665659068 | 4.36224334340932 |
| 46 | 3 | 6.10145797346419 | -3.10145797346419 |
| 47 | 10 | 6.62257559687232 | 3.37742440312768 |
| 48 | 0 | 7.36529661201433 | -7.36529661201433 |
| 49 | -2 | 1.82525999024326 | -3.82525999024326 |
| 50 | -1 | 2.29261895274308 | -3.29261895274308 |
| 51 | 2 | -0.530232445616788 | 2.53023244561679 |
| 52 | 8 | 6.94403506515045 | 1.05596493484955 |
| 53 | -6 | -1.82238470539301 | -4.17761529460699 |
| 54 | -4 | 0.0461977099928985 | -4.0461977099929 |
| 55 | 4 | 1.68438047459319 | 2.31561952540681 |
| 56 | 7 | 6.00253843320673 | 0.997461566793265 |
| 57 | 3 | 0.815343400370414 | 2.18465659962959 |
| 58 | 3 | -2.07466532940227 | 5.07466532940227 |
| 59 | 8 | 0.925728427040373 | 7.07427157295963 |
| 60 | 3 | -0.453966894241842 | 3.45396689424184 |
| 61 | -3 | -1.80948074516408 | -1.19051925483592 |
| 62 | 4 | 0.35525724690188 | 3.64474275309812 |
| 63 | -5 | -5.99135750774511 | 0.991357507745113 |
| 64 | -1 | 0.871640774176823 | -1.87164077417682 |
| 65 | 5 | -0.423500652894297 | 5.4235006528943 |
| 66 | 0 | -1.70816323499905 | 1.70816323499905 |
| 67 | -6 | -4.48427685141141 | -1.51572314858859 |
| 68 | -13 | -11.1683890607042 | -1.83161093929584 |
| 69 | -15 | -6.75352276947239 | -8.24647723052761 |
| 70 | -8 | -9.13380104620559 | 1.13380104620559 |
| 71 | -20 | -15.2367748766585 | -4.7632251233415 |
| 72 | -10 | -15.103553021579 | 5.10355302157902 |
| 73 | -22 | -18.0192240343785 | -3.98077596562149 |
| 74 | -25 | -20.5914290522621 | -4.40857094773793 |
| 75 | -10 | -14.8073694701222 | 4.80736947012218 |
| 76 | -8 | -11.5904626445943 | 3.59046264459428 |
| 77 | -9 | -8.96254714692609 | -0.037452853073911 |
| 78 | -5 | -7.34561773853076 | 2.34561773853076 |
| 79 | -7 | -5.03150536005622 | -1.96849463994378 |
| 80 | -11 | -7.92469267777407 | -3.07530732222593 |
| 81 | -11 | -9.25706058681563 | -1.74293941318437 |
| 82 | -16 | -13.5047253520418 | -2.49527464795818 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 20 | 0.107440651909577 | 0.214881303819154 | 0.892559348090423 |
| 21 | 0.0689179788244487 | 0.137835957648897 | 0.931082021175551 |
| 22 | 0.0335644555025773 | 0.0671289110051547 | 0.966435544497423 |
| 23 | 0.0191523672598244 | 0.0383047345196489 | 0.980847632740176 |
| 24 | 0.00993463692439768 | 0.0198692738487954 | 0.990065363075602 |
| 25 | 0.100195672044192 | 0.200391344088385 | 0.899804327955808 |
| 26 | 0.160379939875852 | 0.320759879751704 | 0.839620060124148 |
| 27 | 0.354610181584688 | 0.709220363169377 | 0.645389818415312 |
| 28 | 0.36820096420141 | 0.736401928402821 | 0.63179903579859 |
| 29 | 0.284520247953938 | 0.569040495907876 | 0.715479752046062 |
| 30 | 0.265560943355425 | 0.531121886710851 | 0.734439056644575 |
| 31 | 0.231937914631909 | 0.463875829263818 | 0.768062085368091 |
| 32 | 0.539073779604474 | 0.921852440791053 | 0.460926220395526 |
| 33 | 0.593225362917709 | 0.813549274164582 | 0.406774637082291 |
| 34 | 0.526823229431606 | 0.946353541136787 | 0.473176770568394 |
| 35 | 0.440710626350214 | 0.881421252700428 | 0.559289373649786 |
| 36 | 0.365676260307437 | 0.731352520614874 | 0.634323739692563 |
| 37 | 0.396599381629213 | 0.793198763258426 | 0.603400618370787 |
| 38 | 0.359262259081126 | 0.718524518162251 | 0.640737740918874 |
| 39 | 0.378910626367761 | 0.757821252735521 | 0.621089373632239 |
| 40 | 0.374685301399407 | 0.749370602798814 | 0.625314698600593 |
| 41 | 0.417410903541324 | 0.834821807082648 | 0.582589096458676 |
| 42 | 0.459199849578626 | 0.918399699157251 | 0.540800150421374 |
| 43 | 0.388201711555107 | 0.776403423110215 | 0.611798288444892 |
| 44 | 0.640167053924615 | 0.71966589215077 | 0.359832946075385 |
| 45 | 0.749558103773163 | 0.500883792453673 | 0.250441896226837 |
| 46 | 0.705343800554927 | 0.589312398890145 | 0.294656199445073 |
| 47 | 0.72880358349248 | 0.54239283301504 | 0.27119641650752 |
| 48 | 0.853356041486586 | 0.293287917026828 | 0.146643958513414 |
| 49 | 0.824169706671719 | 0.351660586656563 | 0.175830293328281 |
| 50 | 0.7788996533049 | 0.442200693390199 | 0.2211003466951 |
| 51 | 0.728128435665469 | 0.543743128669061 | 0.271871564334531 |
| 52 | 0.650886575620697 | 0.698226848758605 | 0.349113424379303 |
| 53 | 0.668512423207435 | 0.662975153585131 | 0.331487576792565 |
| 54 | 0.713370286574342 | 0.573259426851315 | 0.286629713425658 |
| 55 | 0.630727432562486 | 0.738545134875029 | 0.369272567437514 |
| 56 | 0.536113947905897 | 0.927772104188206 | 0.463886052094103 |
| 57 | 0.52991695147729 | 0.94016609704542 | 0.47008304852271 |
| 58 | 0.491375972444217 | 0.982751944888434 | 0.508624027555783 |
| 59 | 0.599899043003237 | 0.800201913993527 | 0.400100956996763 |
| 60 | 0.63417111746557 | 0.731657765068859 | 0.36582888253443 |
| 61 | 0.530217685100762 | 0.939564629798477 | 0.469782314899238 |
| 62 | 0.505242241421008 | 0.989515517157984 | 0.494757758578992 |
| 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 | 0.0465116279069767 | OK |
| 10% type I error level | 3 | 0.0697674418604651 | OK |
