| Multiple Linear Regression - Estimated Regression Equation |
| Y_t[t] = + 20.9911446404945 + 0.485054135605806X_1t[t] -0.380396689533934X_2t[t] -0.84860944516033X_4t[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) | 20.9911446404945 | 1.88913 | 11.1115 | 0 | 0 |
| X_1t | 0.485054135605806 | 0.041567 | 11.6691 | 0 | 0 |
| X_2t | -0.380396689533934 | 0.028708 | -13.2505 | 0 | 0 |
| X_4t | -0.84860944516033 | 0.198261 | -4.2803 | 5.3e-05 | 2.6e-05 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.911697011378877 |
| R-squared | 0.831191440557176 |
| Adjusted R-squared | 0.824698803655529 |
| F-TEST (value) | 128.020626002714 |
| F-TEST (DF numerator) | 3 |
| F-TEST (DF denominator) | 78 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 4.06295238811674 |
| Sum Squared Residuals | 1287.59140443207 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | -3 | -6.68868959099369 | 3.68868959099369 |
| 2 | -4 | -4.33533476767702 | 0.335334767677024 |
| 3 | -7 | -3.97177945812249 | -3.02822054187751 |
| 4 | -7 | -5.92789621192582 | -1.07210378807418 |
| 5 | -7 | -4.02136242946141 | -2.97863757053859 |
| 6 | -3 | -2.01472153571987 | -0.985278464280133 |
| 7 | 0 | -0.157770724594367 | 0.157770724594367 |
| 8 | -5 | -2.51206671651035 | -2.48793328348965 |
| 9 | -3 | -1.6793574827301 | -1.3206425172699 |
| 10 | 3 | 0.900153612709708 | 2.09984638729029 |
| 11 | 2 | -1.83359790014088 | 3.83359790014088 |
| 12 | -7 | -5.50926642763832 | -1.49073357236168 |
| 13 | -1 | -0.399827208097607 | -0.600172791902393 |
| 14 | 0 | -1.69980802890492 | 1.69980802890492 |
| 15 | -3 | 0.553439683134595 | -3.5534396831346 |
| 16 | 4 | 3.20486663328678 | 0.795133366713215 |
| 17 | 2 | 1.05533519871981 | 0.944664801280188 |
| 18 | 3 | 1.43573188825375 | 1.56426811174625 |
| 19 | 0 | -1.93825534621275 | 1.93825534621275 |
| 20 | -10 | -3.20094424086584 | -6.79905575913416 |
| 21 | -10 | -6.49166574403461 | -3.50833425596539 |
| 22 | -9 | -5.0533447171966 | -3.9466552828034 |
| 23 | -22 | -13.6041366911215 | -8.39586330887854 |
| 24 | -16 | -14.9714830318464 | -1.02851696815359 |
| 25 | -18 | -17.4304364698343 | -0.569563530165736 |
| 26 | -14 | -16.5481442647151 | 2.54814426471511 |
| 27 | -12 | -18.0865724028303 | 6.08657240283026 |
| 28 | -17 | -22.7109574867652 | 5.71095748676517 |
| 29 | -23 | -21.3445523146395 | -1.65544768536046 |
| 30 | -28 | -23.4772423692271 | -4.5227576307729 |
| 31 | -31 | -27.4960156601042 | -3.50398433989575 |
| 32 | -21 | -26.0408532532868 | 5.04085325328682 |
| 33 | -19 | -23.7575319474839 | 4.7575319474839 |
| 34 | -22 | -24.8332388333667 | 2.83323883336671 |
| 35 | -22 | -22.3247024240399 | 0.324702424039949 |
| 36 | -25 | -23.5378083473541 | -1.46219165264587 |
| 37 | -16 | -18.7682835155979 | 2.76828351559791 |
| 38 | -22 | -19.170071919906 | -2.829928080094 |
| 39 | -21 | -14.5839199307246 | -6.41608006927536 |
| 40 | -10 | -14.4624211046734 | 4.46242110467336 |
| 41 | -7 | -10.5492464284674 | 3.54924642846742 |
| 42 | -5 | -10.6743544207141 | 5.67435442071411 |
| 43 | -4 | -4.3909835412121 | 0.390983541212099 |
| 44 | 7 | -1.89379700847069 | 8.89379700847069 |
| 45 | 6 | 1.75592946945787 | 4.24407053054213 |
| 46 | 3 | 4.42325663099014 | -1.42325663099014 |
| 47 | 10 | 5.17270013347266 | 4.82729986652734 |
| 48 | 0 | 6.65605379685484 | -6.65605379685484 |
| 49 | -2 | 1.98208574158102 | -3.98208574158102 |
| 50 | -1 | 3.23248359104944 | -4.23248359104944 |
| 51 | 2 | -0.554641924310487 | 2.55464192431049 |
| 52 | 8 | 3.97057721694661 | 4.02942278305339 |
| 53 | -6 | -1.98841261635376 | -4.01158738364624 |
| 54 | -4 | -0.742565101680088 | -3.25743489831991 |
| 55 | 4 | 2.22283418668772 | 1.77716581331228 |
| 56 | 7 | 6.40039822977038 | 0.599601770229623 |
| 57 | 3 | 2.12366824400991 | 0.876331755990091 |
| 58 | 3 | -2.53345843128449 | 5.53345843128449 |
| 59 | 8 | 0.188943204980747 | 7.81105679501925 |
| 60 | 3 | -1.09513740444649 | 4.09513740444649 |
| 61 | -3 | -1.63071567999052 | -1.36928432000948 |
| 62 | 4 | 0.866470852750887 | 3.13352914724911 |
| 63 | -5 | -6.27874168569545 | 1.27874168569545 |
| 64 | -1 | -2.24406818343822 | 1.24406818343822 |
| 65 | 5 | -0.182352814963714 | 5.18235281496371 |
| 66 | 0 | -1.40000907307263 | 1.40000907307263 |
| 67 | -6 | -3.26830976078348 | -2.73169023921652 |
| 68 | -13 | -10.6487792409424 | -2.35122075905755 |
| 69 | -15 | -5.75414641693954 | -9.24585358306046 |
| 70 | -8 | -10.1523752287513 | 2.15237522875129 |
| 71 | -20 | -16.1441066534112 | -3.85589334658884 |
| 72 | -10 | -15.2245225221378 | 5.22452252213778 |
| 73 | -22 | -16.9554241724173 | -5.04457582758274 |
| 74 | -25 | -19.1927716730767 | -5.80722832692331 |
| 75 | -10 | -14.6516523204395 | 4.65165232043951 |
| 76 | -8 | -13.2833648111152 | 5.28336481111522 |
| 77 | -9 | -8.24584144628689 | -0.754158553713111 |
| 78 | -5 | -5.89154545437091 | 0.891545454370909 |
| 79 | -7 | -2.09986960421625 | -4.90013039578375 |
| 80 | -11 | -5.04293600921058 | -5.95706399078942 |
| 81 | -11 | -6.22235917256594 | -4.77764082743406 |
| 82 | -16 | -11.6243790155481 | -4.37562098445188 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 7 | 0.224225643155923 | 0.448451286311845 | 0.775774356844077 |
| 8 | 0.106825211489846 | 0.213650422979692 | 0.893174788510154 |
| 9 | 0.0535711865976839 | 0.107142373195368 | 0.946428813402316 |
| 10 | 0.0482788277644166 | 0.0965576555288332 | 0.951721172235583 |
| 11 | 0.0252449507428286 | 0.0504899014856573 | 0.974755049257171 |
| 12 | 0.0269521659414338 | 0.0539043318828675 | 0.973047834058566 |
| 13 | 0.0201134515164077 | 0.0402269030328153 | 0.979886548483592 |
| 14 | 0.00968907229038997 | 0.0193781445807799 | 0.99031092770961 |
| 15 | 0.0145920148769335 | 0.029184029753867 | 0.985407985123066 |
| 16 | 0.00712950986095098 | 0.014259019721902 | 0.992870490139049 |
| 17 | 0.00347157390395451 | 0.00694314780790901 | 0.996528426096046 |
| 18 | 0.00184846897341192 | 0.00369693794682384 | 0.998151531026588 |
| 19 | 0.00089634822605367 | 0.00179269645210734 | 0.999103651773946 |
| 20 | 0.00946941844167321 | 0.0189388368833464 | 0.990530581558327 |
| 21 | 0.0058995367258437 | 0.0117990734516874 | 0.994100463274156 |
| 22 | 0.00377471507562602 | 0.00754943015125204 | 0.996225284924374 |
| 23 | 0.0034526758561251 | 0.0069053517122502 | 0.996547324143875 |
| 24 | 0.0141656519532084 | 0.0283313039064168 | 0.985834348046792 |
| 25 | 0.0212621880939066 | 0.0425243761878132 | 0.978737811906093 |
| 26 | 0.0358248957957663 | 0.0716497915915325 | 0.964175104204234 |
| 27 | 0.0989291465828652 | 0.19785829316573 | 0.901070853417135 |
| 28 | 0.120599996248353 | 0.241199992496706 | 0.879400003751647 |
| 29 | 0.0930197840084552 | 0.18603956801691 | 0.906980215991545 |
| 30 | 0.0978279989168685 | 0.195655997833737 | 0.902172001083131 |
| 31 | 0.0779831971311883 | 0.155966394262377 | 0.922016802868812 |
| 32 | 0.123366925972342 | 0.246733851944685 | 0.876633074027658 |
| 33 | 0.129375670128599 | 0.258751340257198 | 0.870624329871401 |
| 34 | 0.11969895505202 | 0.23939791010404 | 0.88030104494798 |
| 35 | 0.0908553055053136 | 0.181710611010627 | 0.909144694494686 |
| 36 | 0.0683671214683793 | 0.136734242936759 | 0.931632878531621 |
| 37 | 0.0645938225084159 | 0.129187645016832 | 0.935406177491584 |
| 38 | 0.0535719374838071 | 0.107143874967614 | 0.946428062516193 |
| 39 | 0.0580783727481459 | 0.116156745496292 | 0.941921627251854 |
| 40 | 0.0881737223664305 | 0.176347444732861 | 0.911826277633569 |
| 41 | 0.116156522883617 | 0.232313045767234 | 0.883843477116383 |
| 42 | 0.148630013565923 | 0.297260027131846 | 0.851369986434077 |
| 43 | 0.122485622365813 | 0.244971244731626 | 0.877514377634187 |
| 44 | 0.342762180206364 | 0.685524360412728 | 0.657237819793636 |
| 45 | 0.371491624865072 | 0.742983249730144 | 0.628508375134928 |
| 46 | 0.342800707795982 | 0.685601415591964 | 0.657199292204018 |
| 47 | 0.446925401783825 | 0.89385080356765 | 0.553074598216175 |
| 48 | 0.519348221452321 | 0.961303557095359 | 0.480651778547679 |
| 49 | 0.499453625813615 | 0.998907251627229 | 0.500546374186385 |
| 50 | 0.466021130956546 | 0.932042261913092 | 0.533978869043454 |
| 51 | 0.464283836103163 | 0.928567672206326 | 0.535716163896837 |
| 52 | 0.489698888562752 | 0.979397777125504 | 0.510301111437248 |
| 53 | 0.44575659575362 | 0.891513191507239 | 0.55424340424638 |
| 54 | 0.39038195418143 | 0.780763908362859 | 0.60961804581857 |
| 55 | 0.3758130623317 | 0.7516261246634 | 0.6241869376683 |
| 56 | 0.350728537140758 | 0.701457074281515 | 0.649271462859242 |
| 57 | 0.296083053172266 | 0.592166106344532 | 0.703916946827734 |
| 58 | 0.299073828010772 | 0.598147656021545 | 0.700926171989227 |
| 59 | 0.426664601742866 | 0.853329203485733 | 0.573335398257134 |
| 60 | 0.471851159887991 | 0.943702319775983 | 0.528148840112008 |
| 61 | 0.402677575589198 | 0.805355151178396 | 0.597322424410802 |
| 62 | 0.409952809720659 | 0.819905619441318 | 0.590047190279341 |
| 63 | 0.353331986307485 | 0.70666397261497 | 0.646668013692515 |
| 64 | 0.295458024495441 | 0.590916048990882 | 0.704541975504559 |
| 65 | 0.252129620239563 | 0.504259240479127 | 0.747870379760437 |
| 66 | 0.201739891103271 | 0.403479782206541 | 0.798260108896729 |
| 67 | 0.211743483915892 | 0.423486967831785 | 0.788256516084108 |
| 68 | 0.429758057194802 | 0.859516114389603 | 0.570241942805198 |
| 69 | 0.512820976013451 | 0.974358047973098 | 0.487179023986549 |
| 70 | 0.56927171806901 | 0.861456563861979 | 0.43072828193099 |
| 71 | 0.46953251229152 | 0.939065024583041 | 0.53046748770848 |
| 72 | 0.651663655134721 | 0.696672689730558 | 0.348336344865279 |
| 73 | 0.879479231152751 | 0.241041537694498 | 0.120520768847249 |
| 74 | 0.80028640192071 | 0.399427196158581 | 0.19971359807929 |
| 75 | 0.71651878628178 | 0.56696242743644 | 0.28348121371822 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 5 | 0.072463768115942 | NOK |
| 5% type I error level | 13 | 0.188405797101449 | NOK |
| 10% type I error level | 17 | 0.246376811594203 | NOK |
