| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -1.53647721171885 + 1.07411692421246X[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) | -1.53647721171885 | 0.695836 | -2.2081 | 0.030253 | 0.015126 |
| X | 1.07411692421246 | 0.038394 | 27.9765 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.954721059341125 |
| R-squared | 0.91149230114944 |
| Adjusted R-squared | 0.910327726164563 |
| F-TEST (value) | 782.682363082568 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 76 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.817163446619703 |
| Sum Squared Residuals | 50.7494634853458 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 14.5 | 14.3604532666254 | 0.139546733374593 |
| 2 | 14.3 | 14.2530415742042 | 0.0469584257957522 |
| 3 | 15.3 | 15.6493935756804 | -0.349393575680426 |
| 4 | 14.4 | 15.0049234211530 | -0.604923421152954 |
| 5 | 13.7 | 14.5752766514680 | -0.875276651467973 |
| 6 | 14.2 | 15.1123351135742 | -0.9123351135742 |
| 7 | 13.5 | 14.6826883438892 | -1.18268834388922 |
| 8 | 11.9 | 11.0306908015669 | 0.86930919843313 |
| 9 | 14.6 | 15.9716286529442 | -1.37162865294416 |
| 10 | 15.6 | 16.4012754226291 | -0.801275422629145 |
| 11 | 14.1 | 14.5752766514680 | -0.475276651467972 |
| 12 | 14.9 | 14.4678649590467 | 0.432135040953273 |
| 13 | 14.2 | 14.145629881783 | 0.0543701182170092 |
| 14 | 14.6 | 14.8975117287317 | -0.29751172873171 |
| 15 | 17.2 | 17.6902157316841 | -0.49021573168409 |
| 16 | 15.4 | 16.0790403453654 | -0.679040345365407 |
| 17 | 14.3 | 15.0049234211530 | -0.704923421152954 |
| 18 | 17.5 | 17.6902157316841 | -0.190215731684089 |
| 19 | 14.5 | 15.5419818832592 | -1.04198188325918 |
| 20 | 14.4 | 13.3937480348343 | 1.00625196516573 |
| 21 | 16.6 | 17.5828040392628 | -0.982804039262844 |
| 22 | 16.7 | 17.6902157316841 | -0.99021573168409 |
| 23 | 16.6 | 17.1531572695779 | -0.55315726957786 |
| 24 | 16.9 | 16.4012754226291 | 0.498724577370854 |
| 25 | 15.7 | 15.6493935756804 | 0.0506064243195725 |
| 26 | 16.4 | 16.2938637302079 | 0.106136269792098 |
| 27 | 18.4 | 18.9791560407390 | -0.579156040739039 |
| 28 | 16.9 | 17.5828040392628 | -0.682804039262847 |
| 29 | 16.5 | 16.9383338847354 | -0.438333884735371 |
| 30 | 18.3 | 18.4420975786328 | -0.142097578632809 |
| 31 | 15.1 | 15.9716286529442 | -0.871628652944164 |
| 32 | 15.7 | 14.6826883438892 | 1.01731165611078 |
| 33 | 18.1 | 19.0865677331603 | -0.986567733160279 |
| 34 | 16.8 | 17.4753923468416 | -0.675392346841598 |
| 35 | 18.9 | 18.9791560407390 | -0.0791560407390388 |
| 36 | 19 | 17.7976274241053 | 1.20237257589466 |
| 37 | 18.1 | 17.2605689619991 | 0.839431038000893 |
| 38 | 17.8 | 17.5828040392628 | 0.217195960737155 |
| 39 | 21.5 | 21.1273898891639 | 0.372610110836054 |
| 40 | 17.1 | 16.9383338847354 | 0.16166611526463 |
| 41 | 18.7 | 19.3013911180028 | -0.601391118002771 |
| 42 | 19 | 19.7310378876878 | -0.731037887687754 |
| 43 | 16.4 | 17.3679806544204 | -0.967980654420357 |
| 44 | 16.9 | 15.8642169605229 | 1.03578303947708 |
| 45 | 18.6 | 19.4088028104240 | -0.808802810424016 |
| 46 | 19.3 | 19.838449580109 | -0.538449580108997 |
| 47 | 19.4 | 19.9458612725302 | -0.545861272530246 |
| 48 | 17.6 | 17.0457455771566 | 0.554254422843383 |
| 49 | 18.6 | 18.7643326558965 | -0.164332655896542 |
| 50 | 18.1 | 18.4420975786328 | -0.342097578632809 |
| 51 | 20.4 | 21.4496249664277 | -1.04962496642768 |
| 52 | 18.1 | 18.4420975786328 | -0.342097578632809 |
| 53 | 19.6 | 19.7310378876878 | -0.131037887687753 |
| 54 | 19.9 | 20.8051548119002 | -0.90515481190021 |
| 55 | 19.2 | 19.5162145028453 | -0.316214502845265 |
| 56 | 17.8 | 17.4753923468416 | 0.324607653158402 |
| 57 | 19.2 | 19.7310378876878 | -0.531037887687755 |
| 58 | 22 | 22.3089185057976 | -0.308918505797645 |
| 59 | 21.1 | 20.6977431194790 | 0.402256880521039 |
| 60 | 19.5 | 17.6902157316841 | 1.80978426831591 |
| 61 | 22.2 | 20.9125665043215 | 1.28743349567855 |
| 62 | 20.9 | 21.2348015815852 | -0.334801581585191 |
| 63 | 22.2 | 21.4496249664277 | 0.75037503357232 |
| 64 | 23.5 | 23.1682120451676 | 0.331787954832392 |
| 65 | 21.5 | 21.3422132740064 | 0.157786725993563 |
| 66 | 24.3 | 24.1349172769588 | 0.165082723041184 |
| 67 | 22.8 | 22.5237418906401 | 0.276258109359867 |
| 68 | 20.3 | 18.1198625013691 | 2.18013749863093 |
| 69 | 23.7 | 22.9533886603251 | 0.746611339674881 |
| 70 | 23.3 | 22.4163301982189 | 0.88366980178111 |
| 71 | 19.6 | 17.5828040392628 | 2.01719596073716 |
| 72 | 18 | 16.0790403453654 | 1.92095965463459 |
| 73 | 17.3 | 15.6493935756804 | 1.65060642431957 |
| 74 | 16.8 | 16.0790403453654 | 0.720959654634594 |
| 75 | 18.2 | 17.4753923468416 | 0.7246076531584 |
| 76 | 16.5 | 16.2938637302079 | 0.206136269792099 |
| 77 | 16 | 15.8642169605229 | 0.135783039477083 |
| 78 | 18.4 | 18.1198625013691 | 0.280137498630926 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.177746941161458 | 0.355493882322915 | 0.822253058838542 |
| 6 | 0.120413185623959 | 0.240826371247918 | 0.879586814376041 |
| 7 | 0.157095258124916 | 0.314190516249832 | 0.842904741875084 |
| 8 | 0.0856731565477192 | 0.171346313095438 | 0.914326843452281 |
| 9 | 0.0612713925911435 | 0.122542785182287 | 0.938728607408857 |
| 10 | 0.0420027810876942 | 0.0840055621753884 | 0.957997218912306 |
| 11 | 0.0214886825258253 | 0.0429773650516505 | 0.978511317474175 |
| 12 | 0.0354875145626964 | 0.0709750291253928 | 0.964512485437304 |
| 13 | 0.0210847490481031 | 0.0421694980962062 | 0.978915250951897 |
| 14 | 0.0117209202096224 | 0.0234418404192447 | 0.988279079790378 |
| 15 | 0.0195343407679944 | 0.0390686815359889 | 0.980465659232006 |
| 16 | 0.0114813260665813 | 0.0229626521331625 | 0.988518673933419 |
| 17 | 0.00765336934512154 | 0.0153067386902431 | 0.992346630654878 |
| 18 | 0.0124051932915036 | 0.0248103865830073 | 0.987594806708496 |
| 19 | 0.0127512521710929 | 0.0255025043421859 | 0.987248747828907 |
| 20 | 0.0249982345404904 | 0.0499964690809808 | 0.97500176545951 |
| 21 | 0.0185713638545166 | 0.0371427277090332 | 0.981428636145483 |
| 22 | 0.0140723422912530 | 0.0281446845825060 | 0.985927657708747 |
| 23 | 0.0106269552604038 | 0.0212539105208076 | 0.989373044739596 |
| 24 | 0.0239047296937783 | 0.0478094593875565 | 0.976095270306222 |
| 25 | 0.0189716487342451 | 0.0379432974684901 | 0.981028351265755 |
| 26 | 0.0174640579100970 | 0.0349281158201941 | 0.982535942089903 |
| 27 | 0.0144845455528301 | 0.0289690911056602 | 0.98551545444717 |
| 28 | 0.0109620341836494 | 0.0219240683672988 | 0.989037965816351 |
| 29 | 0.00798953376024327 | 0.0159790675204865 | 0.992010466239757 |
| 30 | 0.00772714403539668 | 0.0154542880707934 | 0.992272855964603 |
| 31 | 0.00925282091341402 | 0.0185056418268280 | 0.990747179086586 |
| 32 | 0.0185919324359145 | 0.0371838648718290 | 0.981408067564085 |
| 33 | 0.0175111594395508 | 0.0350223188791015 | 0.98248884056045 |
| 34 | 0.0158283382240311 | 0.0316566764480621 | 0.984171661775969 |
| 35 | 0.0164543451605829 | 0.0329086903211657 | 0.983545654839417 |
| 36 | 0.0714121940677841 | 0.142824388135568 | 0.928587805932216 |
| 37 | 0.09985077025645 | 0.1997015405129 | 0.90014922974355 |
| 38 | 0.0866052888517718 | 0.173210577703544 | 0.913394711148228 |
| 39 | 0.0924747164885937 | 0.184949432977187 | 0.907525283511406 |
| 40 | 0.0749546518579667 | 0.149909303715933 | 0.925045348142033 |
| 41 | 0.0655715903311415 | 0.131143180662283 | 0.934428409668858 |
| 42 | 0.0611410095421159 | 0.122282019084232 | 0.938858990457884 |
| 43 | 0.0921079782770567 | 0.184215956554113 | 0.907892021722943 |
| 44 | 0.111217334399249 | 0.222434668798498 | 0.888782665600751 |
| 45 | 0.120233692639495 | 0.24046738527899 | 0.879766307360505 |
| 46 | 0.110207411152452 | 0.220414822304904 | 0.889792588847548 |
| 47 | 0.102630209748876 | 0.205260419497752 | 0.897369790251124 |
| 48 | 0.0938507250800404 | 0.187701450160081 | 0.90614927491996 |
| 49 | 0.0809500557862985 | 0.161900111572597 | 0.919049944213702 |
| 50 | 0.078124903182811 | 0.156249806365622 | 0.921875096817189 |
| 51 | 0.104946786076985 | 0.209893572153970 | 0.895053213923015 |
| 52 | 0.110848156806613 | 0.221696313613226 | 0.889151843193387 |
| 53 | 0.100138343603609 | 0.200276687207217 | 0.899861656396391 |
| 54 | 0.152037524871120 | 0.304075049742239 | 0.84796247512888 |
| 55 | 0.167174186164417 | 0.334348372328835 | 0.832825813835583 |
| 56 | 0.160878541905601 | 0.321757083811201 | 0.8391214580944 |
| 57 | 0.229316160731851 | 0.458632321463703 | 0.770683839268149 |
| 58 | 0.233365599491366 | 0.466731198982732 | 0.766634400508634 |
| 59 | 0.215207751542808 | 0.430415503085616 | 0.784792248457192 |
| 60 | 0.382453514965244 | 0.764907029930489 | 0.617546485034756 |
| 61 | 0.458512861685673 | 0.917025723371345 | 0.541487138314327 |
| 62 | 0.495102797110866 | 0.990205594221733 | 0.504897202889134 |
| 63 | 0.447804237498385 | 0.89560847499677 | 0.552195762501615 |
| 64 | 0.375551772745261 | 0.751103545490522 | 0.624448227254739 |
| 65 | 0.329658947071558 | 0.659317894143116 | 0.670341052928442 |
| 66 | 0.270837824962788 | 0.541675649925576 | 0.729162175037212 |
| 67 | 0.232641193278676 | 0.465282386557351 | 0.767358806721324 |
| 68 | 0.459654102518473 | 0.919308205036945 | 0.540345897481527 |
| 69 | 0.364705878521766 | 0.729411757043531 | 0.635294121478234 |
| 70 | 0.275802844581225 | 0.551605689162449 | 0.724197155418775 |
| 71 | 0.524679343733932 | 0.950641312532135 | 0.475320656266068 |
| 72 | 0.714233072104219 | 0.571533855791562 | 0.285766927895781 |
| 73 | 0.92710491694909 | 0.145790166101822 | 0.0728950830509108 |
| 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 | 24 | 0.347826086956522 | NOK |
| 10% type I error level | 26 | 0.376811594202899 | NOK |
