| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 2.83141091127098 + 0.230588729016787X[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) | 2.83141091127098 | 0.400232 | 7.0744 | 0 | 0 |
| X | 0.230588729016787 | 0.020918 | 11.0235 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.8028671994604 |
| R-squared | 0.644595739969386 |
| Adjusted R-squared | 0.6392911987749 |
| F-TEST (value) | 121.517717807403 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 67 |
| p-value | 1.11022302462516e-16 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.398324831007973 |
| Sum Squared Residuals | 10.6303989568345 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 8.2 | 7.51236211031176 | 0.687637889688239 |
| 2 | 8 | 7.51236211031175 | 0.487637889688249 |
| 3 | 7.5 | 7.51236211031175 | -0.0123621103117507 |
| 4 | 6.8 | 6.47471282973621 | 0.325287170263789 |
| 5 | 6.5 | 6.47471282973621 | 0.0252871702637894 |
| 6 | 6.6 | 6.47471282973621 | 0.125287170263789 |
| 7 | 7.6 | 8.18106942446043 | -0.581069424460432 |
| 8 | 8 | 8.18106942446043 | -0.181069424460432 |
| 9 | 8.1 | 8.18106942446043 | -0.081069424460432 |
| 10 | 7.7 | 7.65071534772182 | 0.049284652278178 |
| 11 | 7.5 | 7.65071534772182 | -0.150715347721822 |
| 12 | 7.6 | 7.65071534772182 | -0.0507153477218226 |
| 13 | 7.8 | 7.39706774580336 | 0.402932254196643 |
| 14 | 7.8 | 7.39706774580336 | 0.402932254196643 |
| 15 | 7.8 | 7.39706774580336 | 0.402932254196643 |
| 16 | 7.5 | 7.58153872901679 | -0.0815387290167869 |
| 17 | 7.5 | 7.58153872901679 | -0.0815387290167869 |
| 18 | 7.1 | 7.58153872901679 | -0.481538729016787 |
| 19 | 7.5 | 7.69683309352518 | -0.19683309352518 |
| 20 | 7.5 | 7.69683309352518 | -0.19683309352518 |
| 21 | 7.6 | 7.69683309352518 | -0.0968330935251805 |
| 22 | 7.7 | 7.996598441247 | -0.296598441247002 |
| 23 | 7.7 | 7.996598441247 | -0.296598441247002 |
| 24 | 7.9 | 7.996598441247 | -0.096598441247002 |
| 25 | 8.1 | 7.55847985611511 | 0.541520143884892 |
| 26 | 8.2 | 7.55847985611511 | 0.641520143884891 |
| 27 | 8.2 | 7.55847985611511 | 0.641520143884891 |
| 28 | 8.2 | 7.07424352517986 | 1.12575647482014 |
| 29 | 7.9 | 7.07424352517986 | 0.825756474820145 |
| 30 | 7.3 | 7.07424352517986 | 0.225756474820144 |
| 31 | 6.9 | 6.88977254196643 | 0.0102274580335736 |
| 32 | 6.6 | 6.88977254196643 | -0.289772541966427 |
| 33 | 6.7 | 6.88977254196643 | -0.189772541966427 |
| 34 | 6.9 | 7.09730239808153 | -0.197302398081534 |
| 35 | 7 | 7.09730239808153 | -0.0973023980815344 |
| 36 | 7.1 | 7.09730239808153 | 0.00269760191846521 |
| 37 | 7.2 | 6.82059592326139 | 0.379404076738610 |
| 38 | 7.1 | 6.82059592326139 | 0.279404076738609 |
| 39 | 6.9 | 6.82059592326139 | 0.0794040767386097 |
| 40 | 7 | 6.56694832134292 | 0.433051678657075 |
| 41 | 6.8 | 6.56694832134292 | 0.233051678657075 |
| 42 | 6.4 | 6.56694832134292 | -0.166948321342924 |
| 43 | 6.7 | 7.09730239808153 | -0.397302398081534 |
| 44 | 6.6 | 7.09730239808153 | -0.497302398081535 |
| 45 | 6.4 | 7.09730239808153 | -0.697302398081534 |
| 46 | 6.3 | 6.5900071942446 | -0.290007194244604 |
| 47 | 6.2 | 6.5900071942446 | -0.390007194244604 |
| 48 | 6.5 | 6.5900071942446 | -0.0900071942446039 |
| 49 | 6.8 | 6.705301558753 | 0.0946984412470026 |
| 50 | 6.8 | 6.705301558753 | 0.0946984412470026 |
| 51 | 6.4 | 6.705301558753 | -0.305301558752997 |
| 52 | 6.1 | 6.24412410071942 | -0.144124100719424 |
| 53 | 5.8 | 6.24412410071942 | -0.444124100719424 |
| 54 | 6.1 | 6.24412410071942 | -0.144124100719424 |
| 55 | 7.2 | 7.76600971223022 | -0.566009712230215 |
| 56 | 7.3 | 7.76600971223022 | -0.466009712230216 |
| 57 | 6.9 | 7.76600971223022 | -0.866009712230215 |
| 58 | 6.1 | 6.54388944844125 | -0.443889448441247 |
| 59 | 5.8 | 6.54388944844125 | -0.743889448441247 |
| 60 | 6.2 | 6.54388944844125 | -0.343889448441246 |
| 61 | 7.1 | 7.35095 | -0.250950000000001 |
| 62 | 7.7 | 7.35095 | 0.34905 |
| 63 | 7.9 | 7.35095 | 0.54905 |
| 64 | 7.7 | 7.18953788968825 | 0.510462110311751 |
| 65 | 7.4 | 7.18953788968825 | 0.210462110311752 |
| 66 | 7.5 | 7.18953788968825 | 0.310462110311751 |
| 67 | 8 | 7.88130407673861 | 0.118695923261391 |
| 68 | 8.1 | 7.88130407673861 | 0.218695923261391 |
| 69 | 8 | 7.88130407673861 | 0.118695923261391 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.410779322406094 | 0.821558644812188 | 0.589220677593906 |
| 6 | 0.249308135825926 | 0.498616271651852 | 0.750691864174074 |
| 7 | 0.664821767623725 | 0.670356464752549 | 0.335178232376275 |
| 8 | 0.551070329572687 | 0.897859340854626 | 0.448929670427313 |
| 9 | 0.428858746873263 | 0.857717493746526 | 0.571141253126737 |
| 10 | 0.317806993429051 | 0.635613986858103 | 0.682193006570949 |
| 11 | 0.243276224372036 | 0.486552448744072 | 0.756723775627964 |
| 12 | 0.168652273645345 | 0.33730454729069 | 0.831347726354655 |
| 13 | 0.158178368203229 | 0.316356736406458 | 0.841821631796771 |
| 14 | 0.143419546057798 | 0.286839092115595 | 0.856580453942202 |
| 15 | 0.126945023237601 | 0.253890046475202 | 0.8730549767624 |
| 16 | 0.091656871391938 | 0.183313742783876 | 0.908343128608062 |
| 17 | 0.0641826134958258 | 0.128365226991652 | 0.935817386504174 |
| 18 | 0.103372298195755 | 0.206744596391510 | 0.896627701804245 |
| 19 | 0.0787449753703466 | 0.157489950740693 | 0.921255024629653 |
| 20 | 0.0586680497171225 | 0.117336099434245 | 0.941331950282877 |
| 21 | 0.0389889198471232 | 0.0779778396942464 | 0.961011080152877 |
| 22 | 0.0297545684708475 | 0.0595091369416949 | 0.970245431529153 |
| 23 | 0.0227119970539866 | 0.0454239941079733 | 0.977288002946013 |
| 24 | 0.0146109295024639 | 0.0292218590049277 | 0.985389070497536 |
| 25 | 0.0254160245127901 | 0.0508320490255803 | 0.97458397548721 |
| 26 | 0.0532808192990594 | 0.106561638598119 | 0.94671918070094 |
| 27 | 0.0933878036191835 | 0.186775607238367 | 0.906612196380816 |
| 28 | 0.397437004886946 | 0.794874009773891 | 0.602562995113054 |
| 29 | 0.576155738524188 | 0.847688522951625 | 0.423844261475812 |
| 30 | 0.531107966096581 | 0.937784067806837 | 0.468892033903419 |
| 31 | 0.503030646348662 | 0.993938707302676 | 0.496969353651338 |
| 32 | 0.547342160103699 | 0.905315679792603 | 0.452657839896301 |
| 33 | 0.537333542615282 | 0.925332914769437 | 0.462666457384718 |
| 34 | 0.508402144569951 | 0.983195710860097 | 0.491597855430049 |
| 35 | 0.456935159774739 | 0.913870319549477 | 0.543064840225261 |
| 36 | 0.396404615735285 | 0.792809231470569 | 0.603595384264715 |
| 37 | 0.389274996491767 | 0.778549992983533 | 0.610725003508233 |
| 38 | 0.362407786413580 | 0.724815572827159 | 0.63759221358642 |
| 39 | 0.314822224343188 | 0.629644448686375 | 0.685177775656812 |
| 40 | 0.346315332308344 | 0.692630664616688 | 0.653684667691656 |
| 41 | 0.334680625551125 | 0.66936125110225 | 0.665319374448875 |
| 42 | 0.313099603286194 | 0.626199206572388 | 0.686900396713806 |
| 43 | 0.320531824773139 | 0.641063649546278 | 0.679468175226861 |
| 44 | 0.360200258353042 | 0.720400516706085 | 0.639799741646958 |
| 45 | 0.504438971883416 | 0.991122056233168 | 0.495561028116584 |
| 46 | 0.46840147067835 | 0.9368029413567 | 0.53159852932165 |
| 47 | 0.45260894713281 | 0.90521789426562 | 0.54739105286719 |
| 48 | 0.385163445505860 | 0.770326891011719 | 0.614836554494140 |
| 49 | 0.33215543706978 | 0.66431087413956 | 0.66784456293022 |
| 50 | 0.284687053643325 | 0.56937410728665 | 0.715312946356675 |
| 51 | 0.241658295716038 | 0.483316591432076 | 0.758341704283962 |
| 52 | 0.191801515154857 | 0.383603030309715 | 0.808198484845143 |
| 53 | 0.169891090436399 | 0.339782180872799 | 0.830108909563601 |
| 54 | 0.125523004224611 | 0.251046008449222 | 0.874476995775389 |
| 55 | 0.165538024848352 | 0.331076049696704 | 0.834461975151648 |
| 56 | 0.198664064418893 | 0.397328128837786 | 0.801335935581107 |
| 57 | 0.718280571731045 | 0.563438856537909 | 0.281719428268955 |
| 58 | 0.657775758294092 | 0.684448483411816 | 0.342224241705908 |
| 59 | 0.829339540995622 | 0.341320918008756 | 0.170660459004378 |
| 60 | 0.923272012081324 | 0.153455975837351 | 0.0767279879186757 |
| 61 | 0.995299124134247 | 0.00940175173150685 | 0.00470087586575342 |
| 62 | 0.985306605161027 | 0.0293867896779467 | 0.0146933948389733 |
| 63 | 0.988067572763725 | 0.0238648544725498 | 0.0119324272362749 |
| 64 | 0.995164576872942 | 0.00967084625411643 | 0.00483542312705821 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 2 | 0.0333333333333333 | NOK |
| 5% type I error level | 6 | 0.1 | NOK |
| 10% type I error level | 9 | 0.15 | NOK |
