| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 15.1707908539916 + 2.58019404216615D[t] + 1.2970254593017Y1[t] -0.140546777544707Y2[t] -0.292873046833665Y3[t] + 0.300136115162012t + 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) | 15.1707908539916 | 6.134386 | 2.4731 | 0.01566 | 0.00783 |
| D | 2.58019404216615 | 7.636126 | 0.3379 | 0.736388 | 0.368194 |
| Y1 | 1.2970254593017 | 0.112758 | 11.5027 | 0 | 0 |
| Y2 | -0.140546777544707 | 0.190226 | -0.7388 | 0.46231 | 0.231155 |
| Y3 | -0.292873046833665 | 0.114306 | -2.5622 | 0.012407 | 0.006204 |
| t | 0.300136115162012 | 0.175054 | 1.7145 | 0.090561 | 0.04528 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.978714772026642 |
| R-squared | 0.957882604983162 |
| Adjusted R-squared | 0.955074778648706 |
| F-TEST (value) | 341.147382667025 |
| F-TEST (DF numerator) | 5 |
| F-TEST (DF denominator) | 75 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 18.5544241079048 |
| Sum Squared Residuals | 25819.9990482000 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 107.1 | 99.7967981200193 | 7.30320187998065 |
| 2 | 115.2 | 115.667880023444 | -0.467880023443807 |
| 3 | 106.1 | 122.232297825913 | -16.1322978259132 |
| 4 | 89.5 | 106.428044457514 | -16.9280444575143 |
| 5 | 91.3 | 84.1042619445722 | 7.1957380554278 |
| 6 | 97.6 | 91.7372651199057 | 5.86273488009425 |
| 7 | 100.7 | 104.817370006527 | -4.11737000652681 |
| 8 | 104.6 | 107.725668862692 | -3.12566886269187 |
| 9 | 94.7 | 110.803409063690 | -16.1034090636898 |
| 10 | 101.8 | 96.8069542541563 | 4.99304574584372 |
| 11 | 102.5 | 106.565179345402 | -4.06517934540167 |
| 12 | 105.3 | 109.674794325161 | -4.37479432516073 |
| 13 | 110.3 | 111.428820349567 | -1.12882034956719 |
| 14 | 109.8 | 117.615541651329 | -7.81554165132895 |
| 15 | 117.3 | 115.744386617982 | 1.55561338201768 |
| 16 | 118.8 | 124.378121832511 | -5.57812183251111 |
| 17 | 131.3 | 125.716131828457 | 5.58386817154281 |
| 18 | 125.9 | 139.821718167321 | -13.9217181673209 |
| 19 | 133.1 | 130.921772512694 | 2.17822748730556 |
| 20 | 147 | 137.658531448149 | 9.34146855185073 |
| 21 | 145.8 | 156.556899102185 | -10.7568991021848 |
| 22 | 164.4 | 151.238318521111 | 13.161681478889 |
| 23 | 149.8 | 171.760848961350 | -21.9608489613503 |
| 24 | 137.7 | 150.861690964576 | -13.1616909645764 |
| 25 | 151.7 | 132.072363303234 | 19.6276366967656 |
| 26 | 156.8 | 156.507418340683 | 0.292581659317393 |
| 27 | 180 | 164.998493279345 | 15.0015067206552 |
| 28 | 180.4 | 190.572608829157 | -10.1726088291569 |
| 29 | 170.4 | 186.637217350151 | -16.2372173501507 |
| 30 | 191.6 | 167.116225474737 | 24.4837745252632 |
| 31 | 199.5 | 196.201619883808 | 3.29838011619154 |
| 32 | 218.2 | 206.697395911843 | 11.5026040881572 |
| 33 | 217.5 | 223.932679980470 | -6.43267998046969 |
| 34 | 205 | 218.382976464049 | -13.3829764640485 |
| 35 | 194 | 197.091951106431 | -3.09195110643108 |
| 36 | 199.3 | 185.086653021367 | 14.2133469786332 |
| 37 | 219.3 | 197.467951709240 | 21.8320482907596 |
| 38 | 211.1 | 226.185302604620 | -15.0853026046198 |
| 39 | 215.2 | 211.486667254395 | 3.71333274560472 |
| 40 | 240.2 | 212.399630391888 | 27.8003696081124 |
| 41 | 242.2 | 246.950720185695 | -4.75072018569482 |
| 42 | 240.7 | 245.130458288825 | -4.43045828882452 |
| 43 | 255.4 | 235.882136489103 | 19.5178635108971 |
| 44 | 253 | 254.873620928650 | -1.87362092864971 |
| 45 | 218.2 | 250.434167881831 | -32.2341678818310 |
| 46 | 203.7 | 201.629896490946 | 2.07010350905378 |
| 47 | 205.6 | 188.717086617190 | 16.8829133828098 |
| 48 | 215.6 | 203.711481409235 | 11.8885185907648 |
| 49 | 188.5 | 220.961492419167 | -32.4614924191674 |
| 50 | 202.9 | 184.150312022822 | 18.7496879771777 |
| 51 | 214 | 204.007701955054 | 9.99229804494628 |
| 52 | 230.3 | 224.617806641013 | 5.68219335898689 |
| 53 | 230 | 240.282016637642 | -10.2820166376418 |
| 54 | 241 | 234.651241821181 | 6.34875817881907 |
| 55 | 259.6 | 247.067185400702 | 12.5328145992977 |
| 56 | 247.8 | 270.033842419934 | -22.2338424199343 |
| 57 | 270.3 | 249.193304537834 | 21.1066954621656 |
| 58 | 289.7 | 274.887526791206 | 14.8124732087940 |
| 59 | 322.7 | 300.643556274702 | 22.0564437252977 |
| 60 | 315 | 334.429281508696 | -19.4292815086957 |
| 61 | 320.2 | 314.422540819686 | 5.77745918031379 |
| 62 | 329.5 | 312.884608964800 | 16.6153910351997 |
| 63 | 360.6 | 326.771361068855 | 33.8286389311451 |
| 64 | 382.2 | 364.578964093599 | 17.621035906401 |
| 65 | 435.4 | 385.800126012484 | 49.5998739875157 |
| 66 | 464 | 442.957854411004 | 21.042145588996 |
| 67 | 468.8 | 466.549772285209 | 2.25022771479086 |
| 68 | 403 | 453.47514667569 | -50.4751466756897 |
| 69 | 351.6 | 359.380213897142 | -7.78021389714243 |
| 70 | 252 | 300.855428741837 | -48.8554287418372 |
| 71 | 188 | 198.466979958003 | -10.4669799580030 |
| 72 | 146.5 | 144.809620328559 | 1.69037967144065 |
| 73 | 152.9 | 129.448349110195 | 23.4516508898050 |
| 74 | 148.1 | 162.626014430348 | -14.5260144303478 |
| 75 | 165.1 | 167.955160408173 | -2.85516040817264 |
| 76 | 177 | 189.104966363943 | -12.1049663639427 |
| 77 | 206.1 | 203.856200851336 | 2.24379914866349 |
| 78 | 244.9 | 235.248429383224 | 9.65157061677632 |
| 79 | 228.6 | 278.29805283542 | -49.6980528354201 |
| 80 | 253.4 | 243.48085333237 | 9.91914666762991 |
| 81 | 241.1 | 266.874659095047 | -25.7746590950468 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 9 | 0.0223044695175946 | 0.0446089390351892 | 0.977695530482405 |
| 10 | 0.0143262870721759 | 0.0286525741443517 | 0.985673712927824 |
| 11 | 0.00753719623978628 | 0.0150743924795726 | 0.992462803760214 |
| 12 | 0.00255452718312488 | 0.00510905436624976 | 0.997445472816875 |
| 13 | 0.0020224471564735 | 0.004044894312947 | 0.997977552843527 |
| 14 | 0.000763281773093224 | 0.00152656354618645 | 0.999236718226907 |
| 15 | 0.000920010997375257 | 0.00184002199475051 | 0.999079989002625 |
| 16 | 0.000361933144679982 | 0.000723866289359964 | 0.99963806685532 |
| 17 | 0.000680982628736677 | 0.00136196525747335 | 0.999319017371263 |
| 18 | 0.000286502198658711 | 0.000573004397317422 | 0.999713497801341 |
| 19 | 0.000226575180265881 | 0.000453150360531761 | 0.999773424819734 |
| 20 | 0.000192554728961195 | 0.00038510945792239 | 0.999807445271039 |
| 21 | 8.03599389054704e-05 | 0.000160719877810941 | 0.999919640061095 |
| 22 | 0.000155523949869902 | 0.000311047899739803 | 0.99984447605013 |
| 23 | 0.000265152080315990 | 0.000530304160631981 | 0.999734847919684 |
| 24 | 0.000236423380414597 | 0.000472846760829193 | 0.999763576619585 |
| 25 | 0.000148189929612245 | 0.00029637985922449 | 0.999851810070388 |
| 26 | 6.41929908395996e-05 | 0.000128385981679199 | 0.99993580700916 |
| 27 | 0.00016881281120564 | 0.00033762562241128 | 0.999831187188794 |
| 28 | 8.80625258630217e-05 | 0.000176125051726043 | 0.999911937474137 |
| 29 | 6.7636498666953e-05 | 0.000135272997333906 | 0.999932363501333 |
| 30 | 9.79538793228484e-05 | 0.000195907758645697 | 0.999902046120677 |
| 31 | 4.78995994222496e-05 | 9.57991988444991e-05 | 0.999952100400578 |
| 32 | 6.88650748277579e-05 | 0.000137730149655516 | 0.999931134925172 |
| 33 | 3.65537540240901e-05 | 7.31075080481801e-05 | 0.999963446245976 |
| 34 | 3.89079716364752e-05 | 7.78159432729505e-05 | 0.999961092028363 |
| 35 | 3.42426127995193e-05 | 6.84852255990387e-05 | 0.9999657573872 |
| 36 | 1.53029244667751e-05 | 3.06058489335501e-05 | 0.999984697075533 |
| 37 | 1.21800553574767e-05 | 2.43601107149534e-05 | 0.999987819944643 |
| 38 | 1.23070600818785e-05 | 2.46141201637571e-05 | 0.999987692939918 |
| 39 | 5.83025304774715e-06 | 1.16605060954943e-05 | 0.999994169746952 |
| 40 | 8.96665696003511e-06 | 1.79333139200702e-05 | 0.99999103334304 |
| 41 | 4.32367556395301e-06 | 8.64735112790601e-06 | 0.999995676324436 |
| 42 | 2.11257081655950e-06 | 4.22514163311901e-06 | 0.999997887429183 |
| 43 | 1.52600449770315e-06 | 3.05200899540631e-06 | 0.999998473995502 |
| 44 | 7.038922921419e-07 | 1.4077845842838e-06 | 0.999999296107708 |
| 45 | 2.18288626453530e-05 | 4.36577252907060e-05 | 0.999978171137355 |
| 46 | 2.40806152129645e-05 | 4.8161230425929e-05 | 0.999975919384787 |
| 47 | 1.83930006808305e-05 | 3.67860013616611e-05 | 0.99998160699932 |
| 48 | 9.5895617048996e-06 | 1.91791234097992e-05 | 0.999990410438295 |
| 49 | 0.000182510005595050 | 0.000365020011190100 | 0.999817489994405 |
| 50 | 0.000113421289773695 | 0.000226842579547391 | 0.999886578710226 |
| 51 | 6.13296360600287e-05 | 0.000122659272120057 | 0.99993867036394 |
| 52 | 3.38716547974193e-05 | 6.77433095948387e-05 | 0.999966128345203 |
| 53 | 1.97693057429495e-05 | 3.9538611485899e-05 | 0.999980230694257 |
| 54 | 9.76853525306571e-06 | 1.95370705061314e-05 | 0.999990231464747 |
| 55 | 4.5704691866225e-06 | 9.140938373245e-06 | 0.999995429530813 |
| 56 | 3.72365684482919e-05 | 7.44731368965839e-05 | 0.999962763431552 |
| 57 | 3.21014241942270e-05 | 6.42028483884541e-05 | 0.999967898575806 |
| 58 | 1.83229603378106e-05 | 3.66459206756212e-05 | 0.999981677039662 |
| 59 | 2.11520315738060e-05 | 4.23040631476119e-05 | 0.999978847968426 |
| 60 | 0.000200018144877199 | 0.000400036289754399 | 0.999799981855123 |
| 61 | 0.00054423414478525 | 0.0010884682895705 | 0.999455765855215 |
| 62 | 0.000423189596154421 | 0.000846379192308843 | 0.999576810403846 |
| 63 | 0.000395740136484996 | 0.000791480272969992 | 0.999604259863515 |
| 64 | 0.000254685533350103 | 0.000509371066700205 | 0.99974531446665 |
| 65 | 0.00299341158889442 | 0.00598682317778884 | 0.997006588411106 |
| 66 | 0.0145077659072498 | 0.0290155318144996 | 0.98549223409275 |
| 67 | 0.0852218769917232 | 0.170443753983446 | 0.914778123008277 |
| 68 | 0.165872193872886 | 0.331744387745771 | 0.834127806127114 |
| 69 | 0.368567655229419 | 0.737135310458839 | 0.63143234477058 |
| 70 | 0.502371032855588 | 0.995257934288824 | 0.497628967144412 |
| 71 | 0.367151491591172 | 0.734302983182343 | 0.632848508408828 |
| 72 | 0.229209002948359 | 0.458418005896717 | 0.770790997051641 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 54 | 0.84375 | NOK |
| 5% type I error level | 58 | 0.90625 | NOK |
| 10% type I error level | 58 | 0.90625 | NOK |
