| Multiple Linear Regression - Estimated Regression Equation |
| Q1_22[t] = + 1.61968772478699 -0.00918828791935026Q1_2[t] + 0.340656368476894Q1_3[t] + 0.356234894492118Q1_5[t] -0.159352120836570Q1_7[t] + 0.484170885364494Q1_8[t] -0.300030003511608Q1_12[t] + 0.097133273108172Q1_16[t] + 0.0248399368734786Q1_2v[t] -0.0351115015876335Q1_3v[t] + 0.331622895188286Q1_5v[t] -0.128426182123679Q1_7v[t] + 0.142269832219955Q1_8v[t] -0.0451005706686726Q1_12v[t] + 0.0428633491152994Q1_16v[t] -0.141230731472698Q1_22v[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) | 1.61968772478699 | 0.877904 | 1.8449 | 0.068528 | 0.034264 |
| Q1_2 | -0.00918828791935026 | 0.104501 | -0.0879 | 0.930143 | 0.465071 |
| Q1_3 | 0.340656368476894 | 0.098087 | 3.473 | 0.000812 | 0.000406 |
| Q1_5 | 0.356234894492118 | 0.130262 | 2.7348 | 0.007596 | 0.003798 |
| Q1_7 | -0.159352120836570 | 0.082334 | -1.9354 | 0.056263 | 0.028132 |
| Q1_8 | 0.484170885364494 | 0.094273 | 5.1358 | 2e-06 | 1e-06 |
| Q1_12 | -0.300030003511608 | 0.116909 | -2.5664 | 0.01203 | 0.006015 |
| Q1_16 | 0.097133273108172 | 0.114969 | 0.8449 | 0.40056 | 0.20028 |
| Q1_2v | 0.0248399368734786 | 0.109294 | 0.2273 | 0.820754 | 0.410377 |
| Q1_3v | -0.0351115015876335 | 0.107443 | -0.3268 | 0.744629 | 0.372315 |
| Q1_5v | 0.331622895188286 | 0.228915 | 1.4487 | 0.151108 | 0.075554 |
| Q1_7v | -0.128426182123679 | 0.125192 | -1.0258 | 0.30788 | 0.15394 |
| Q1_8v | 0.142269832219955 | 0.157977 | 0.9006 | 0.370361 | 0.18518 |
| Q1_12v | -0.0451005706686726 | 0.138402 | -0.3259 | 0.745327 | 0.372663 |
| Q1_16v | 0.0428633491152994 | 0.155632 | 0.2754 | 0.783665 | 0.391833 |
| Q1_22v | -0.141230731472698 | 0.147537 | -0.9573 | 0.341153 | 0.170577 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.658977147434301 |
| R-squared | 0.434250880840649 |
| Adjusted R-squared | 0.334412800988998 |
| F-TEST (value) | 4.34955160882404 |
| F-TEST (DF numerator) | 15 |
| F-TEST (DF denominator) | 85 |
| p-value | 5.89831236164073e-06 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.87092238918393 |
| Sum Squared Residuals | 64.4729936784568 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 7 | 7.02510077115959 | -0.0251007711595910 |
| 2 | 5 | 5.54783555237797 | -0.547835552377967 |
| 3 | 5 | 6.0677536234044 | -1.06775362340440 |
| 4 | 6 | 6.01797505809933 | -0.0179750580993263 |
| 5 | 7 | 5.95630522897426 | 1.04369477102574 |
| 6 | 7 | 6.179380437712 | 0.820619562287998 |
| 7 | 7 | 6.77713235996046 | 0.222867640039541 |
| 8 | 6 | 6.0307364032501 | -0.0307364032501016 |
| 9 | 5 | 5.5928576028722 | -0.592857602872204 |
| 10 | 6 | 6.57185863205907 | -0.571858632059068 |
| 11 | 7 | 6.2076897231097 | 0.792310276890294 |
| 12 | 7 | 5.83499139042263 | 1.16500860957737 |
| 13 | 6 | 6.32919667972098 | -0.329196679720977 |
| 14 | 7 | 7.1766137258019 | -0.176613725801904 |
| 15 | 6 | 5.36537287291367 | 0.634627127086326 |
| 16 | 7 | 5.77458892228821 | 1.22541107771179 |
| 17 | 5 | 5.42472270607947 | -0.42472270607947 |
| 18 | 5 | 5.40205998770025 | -0.402059987700248 |
| 19 | 7 | 6.58180263645311 | 0.418197363546885 |
| 20 | 6 | 6.45823506137093 | -0.458235061370928 |
| 21 | 6 | 5.69197489724246 | 0.308025102757538 |
| 22 | 1 | 3.5274586067484 | -2.5274586067484 |
| 23 | 7 | 6.11090461584054 | 0.889095384159459 |
| 24 | 6 | 6.29225351175008 | -0.292253511750077 |
| 25 | 7 | 6.83244107113154 | 0.16755892886846 |
| 26 | 6 | 5.94841062476645 | 0.0515893752335524 |
| 27 | 6 | 5.67797108188373 | 0.322028918116265 |
| 28 | 6 | 5.90519235513111 | 0.0948076448688896 |
| 29 | 6 | 6.03362670705345 | -0.0336267070534526 |
| 30 | 5 | 5.88389040149457 | -0.883890401494574 |
| 31 | 5 | 5.47653778082898 | -0.476537780828981 |
| 32 | 7 | 6.36042560741858 | 0.639574392581419 |
| 33 | 3 | 4.11480699037853 | -1.11480699037853 |
| 34 | 6 | 5.32912901792549 | 0.670870982074511 |
| 35 | 5 | 6.01244033580896 | -1.01244033580896 |
| 36 | 6 | 6.51116425693954 | -0.51116425693954 |
| 37 | 7 | 5.98317215615326 | 1.01682784384674 |
| 38 | 6 | 6.00779495383096 | -0.00779495383096274 |
| 39 | 5 | 5.09821386264445 | -0.0982138626444483 |
| 40 | 5 | 5.63048130696828 | -0.630481306968277 |
| 41 | 6 | 6.61846262526562 | -0.618462625265624 |
| 42 | 7 | 6.15445757578822 | 0.845542424211778 |
| 43 | 7 | 7.16687594170784 | -0.166875941707837 |
| 44 | 5 | 5.03574347968164 | -0.0357434796816424 |
| 45 | 7 | 6.13240279761086 | 0.867597202389142 |
| 46 | 5 | 5.10009225961324 | -0.100092259613243 |
| 47 | 5 | 4.74443156940751 | 0.255568430592490 |
| 48 | 5 | 5.81703059448912 | -0.817030594489116 |
| 49 | 6 | 5.98773128370064 | 0.0122687162993624 |
| 50 | 6 | 6.26785516890419 | -0.267855168904186 |
| 51 | 7 | 6.02379073955894 | 0.976209260441064 |
| 52 | 7 | 5.18382260728762 | 1.81617739271238 |
| 53 | 7 | 7.26004004461387 | -0.260040044613874 |
| 54 | 7 | 5.9895821040213 | 1.01041789597870 |
| 55 | 2 | 4.03936357270476 | -2.03936357270476 |
| 56 | 6 | 6.46013827739038 | -0.460138277390379 |
| 57 | 6 | 6.86771306664385 | -0.867713066643847 |
| 58 | 6 | 6.2500319788534 | -0.250031978853404 |
| 59 | 7 | 6.55721505189587 | 0.442784948104131 |
| 60 | 5 | 5.23799128921044 | -0.237991289210440 |
| 61 | 7 | 5.55677257337146 | 1.44322742662854 |
| 62 | 6 | 5.91071428791703 | 0.0892857120829742 |
| 63 | 6 | 6.01039560496425 | -0.0103956049642501 |
| 64 | 5 | 5.04900426128738 | -0.0490042612873828 |
| 65 | 6 | 5.94276456519716 | 0.0572354348028417 |
| 66 | 7 | 7.44626638147139 | -0.44626638147139 |
| 67 | 6 | 6.19641332492934 | -0.196413324929339 |
| 68 | 7 | 6.96821001896168 | 0.0317899810383194 |
| 69 | 7 | 6.22120208594566 | 0.778797914054345 |
| 70 | 5 | 4.9588223213712 | 0.0411776786287946 |
| 71 | 6 | 5.41125311252739 | 0.588746887472612 |
| 72 | 7 | 6.86188845793416 | 0.138111542065842 |
| 73 | 7 | 5.95456908055571 | 1.04543091944429 |
| 74 | 7 | 6.06462171301128 | 0.935378286988723 |
| 75 | 7 | 6.10463371084172 | 0.895366289158283 |
| 76 | 7 | 4.67842065654389 | 2.32157934345611 |
| 77 | 6 | 5.83320515016348 | 0.166794849836516 |
| 78 | 5 | 6.62405535506921 | -1.62405535506921 |
| 79 | 5 | 4.56772531860318 | 0.432274681396818 |
| 80 | 7 | 6.94983344312298 | 0.0501665568770206 |
| 81 | 6 | 6.17138743306102 | -0.171387433061018 |
| 82 | 6 | 6.68936991494391 | -0.689369914943912 |
| 83 | 6 | 6.09230677154743 | -0.0923067715474307 |
| 84 | 6 | 6.27129245407138 | -0.271292454071381 |
| 85 | 7 | 7.5988230436906 | -0.598823043690594 |
| 86 | 6 | 6.7459773891937 | -0.745977389193694 |
| 87 | 7 | 6.45503510749454 | 0.544964892505461 |
| 88 | 5 | 6.83014836372585 | -1.83014836372585 |
| 89 | 5 | 6.21007851366726 | -1.21007851366726 |
| 90 | 7 | 5.97128439764152 | 1.02871560235848 |
| 91 | 5 | 5.77700025918297 | -0.777000259182974 |
| 92 | 7 | 6.45196134242997 | 0.548038657570027 |
| 93 | 7 | 6.73039886317847 | 0.269601136821530 |
| 94 | 5 | 5.6408353039171 | -0.640835303917097 |
| 95 | 6 | 6.28937136758725 | -0.289371367587252 |
| 96 | 7 | 5.83264405506736 | 1.16735594493264 |
| 97 | 6 | 6.42118057174751 | -0.421180571747512 |
| 98 | 5 | 6.36495373368526 | -1.36495373368526 |
| 99 | 5 | 5.92716409210019 | -0.927164092100193 |
| 100 | 7 | 5.95218998396851 | 1.04781001603149 |
| 101 | 7 | 6.62055406828976 | 0.379445931710238 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 19 | 0.298808483443559 | 0.597616966887118 | 0.701191516556441 |
| 20 | 0.270254644109751 | 0.540509288219501 | 0.72974535589025 |
| 21 | 0.155392934110984 | 0.310785868221967 | 0.844607065889016 |
| 22 | 0.348609607840317 | 0.697219215680635 | 0.651390392159683 |
| 23 | 0.275368127473243 | 0.550736254946487 | 0.724631872526757 |
| 24 | 0.188306823746288 | 0.376613647492577 | 0.811693176253712 |
| 25 | 0.146100293704662 | 0.292200587409323 | 0.853899706295338 |
| 26 | 0.0944792392154245 | 0.188958478430849 | 0.905520760784576 |
| 27 | 0.0629722593096512 | 0.125944518619302 | 0.93702774069035 |
| 28 | 0.100368106022247 | 0.200736212044494 | 0.899631893977753 |
| 29 | 0.0671683007510811 | 0.134336601502162 | 0.932831699248919 |
| 30 | 0.0663704723901064 | 0.132740944780213 | 0.933629527609894 |
| 31 | 0.0509332829101174 | 0.101866565820235 | 0.949066717089883 |
| 32 | 0.0391235803351982 | 0.0782471606703965 | 0.960876419664802 |
| 33 | 0.0334585817562925 | 0.066917163512585 | 0.966541418243708 |
| 34 | 0.0422555824143924 | 0.0845111648287848 | 0.957744417585608 |
| 35 | 0.0611042697136186 | 0.122208539427237 | 0.938895730286381 |
| 36 | 0.0592587300130289 | 0.118517460026058 | 0.940741269986971 |
| 37 | 0.0605836287992601 | 0.12116725759852 | 0.93941637120074 |
| 38 | 0.0546501124756634 | 0.109300224951327 | 0.945349887524337 |
| 39 | 0.0456269239382479 | 0.0912538478764958 | 0.954373076061752 |
| 40 | 0.0724785552548419 | 0.144957110509684 | 0.927521444745158 |
| 41 | 0.214891037314293 | 0.429782074628586 | 0.785108962685707 |
| 42 | 0.1995133642342 | 0.3990267284684 | 0.8004866357658 |
| 43 | 0.174297001238803 | 0.348594002477605 | 0.825702998761197 |
| 44 | 0.134335289895580 | 0.268670579791159 | 0.86566471010442 |
| 45 | 0.148628012573951 | 0.297256025147903 | 0.851371987426049 |
| 46 | 0.116610775203375 | 0.23322155040675 | 0.883389224796625 |
| 47 | 0.131737583026597 | 0.263475166053195 | 0.868262416973403 |
| 48 | 0.126564464612648 | 0.253128929225297 | 0.873435535387352 |
| 49 | 0.0973804339594581 | 0.194760867918916 | 0.902619566040542 |
| 50 | 0.0872817938536332 | 0.174563587707266 | 0.912718206146367 |
| 51 | 0.0946478315808648 | 0.189295663161730 | 0.905352168419135 |
| 52 | 0.338524215535318 | 0.677048431070637 | 0.661475784464682 |
| 53 | 0.408670513485931 | 0.817341026971862 | 0.591329486514069 |
| 54 | 0.386094527469081 | 0.772189054938162 | 0.613905472530919 |
| 55 | 0.537122298706111 | 0.925755402587779 | 0.462877701293889 |
| 56 | 0.503695875439141 | 0.992608249121718 | 0.496304124560859 |
| 57 | 0.483204920756455 | 0.96640984151291 | 0.516795079243545 |
| 58 | 0.418156309104462 | 0.836312618208924 | 0.581843690895538 |
| 59 | 0.351746715359801 | 0.703493430719603 | 0.648253284640199 |
| 60 | 0.288749648409777 | 0.577499296819554 | 0.711250351590223 |
| 61 | 0.288283135542555 | 0.576566271085109 | 0.711716864457445 |
| 62 | 0.231483220853061 | 0.462966441706122 | 0.768516779146939 |
| 63 | 0.180076208775864 | 0.360152417551728 | 0.819923791224136 |
| 64 | 0.165322676671074 | 0.330645353342148 | 0.834677323328926 |
| 65 | 0.123545425688593 | 0.247090851377185 | 0.876454574311407 |
| 66 | 0.0928326309044379 | 0.185665261808876 | 0.907167369095562 |
| 67 | 0.0655626933257484 | 0.131125386651497 | 0.934437306674252 |
| 68 | 0.0507263757390604 | 0.101452751478121 | 0.94927362426094 |
| 69 | 0.0472061667572856 | 0.0944123335145711 | 0.952793833242714 |
| 70 | 0.040293901566274 | 0.080587803132548 | 0.959706098433726 |
| 71 | 0.0292403701775057 | 0.0584807403550113 | 0.970759629822494 |
| 72 | 0.0267545696401430 | 0.0535091392802861 | 0.973245430359857 |
| 73 | 0.0474495250533333 | 0.0948990501066665 | 0.952550474946667 |
| 74 | 0.035631874920469 | 0.071263749840938 | 0.964368125079531 |
| 75 | 0.0411201981226624 | 0.0822403962453248 | 0.958879801877338 |
| 76 | 0.192211882660583 | 0.384423765321166 | 0.807788117339417 |
| 77 | 0.13306911074952 | 0.26613822149904 | 0.86693088925048 |
| 78 | 0.157501743855071 | 0.315003487710143 | 0.842498256144929 |
| 79 | 0.100645112428822 | 0.201290224857644 | 0.899354887571178 |
| 80 | 0.101144799952543 | 0.202289599905086 | 0.898855200047457 |
| 81 | 0.0657335647886768 | 0.131467129577354 | 0.934266435211323 |
| 82 | 0.0380556574351226 | 0.0761113148702452 | 0.961944342564877 |
| 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 | 0 | 0 | OK |
| 10% type I error level | 12 | 0.1875 | NOK |
