| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -0.207439244018707 + 0.921102813688366X[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) | -0.207439244018707 | 0.406456 | -0.5104 | 0.611476 | 0.305738 |
| X | 0.921102813688366 | 0.141354 | 6.5163 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.6228277326174 |
| R-squared | 0.387914384517331 |
| Adjusted R-squared | 0.378778778316097 |
| F-TEST (value) | 42.461811068973 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 67 |
| p-value | 1.10074940273819e-08 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1.15053961016272 |
| Sum Squared Residuals | 88.6906734350775 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1.4 | 1.63476638335802 | -0.234766383358022 |
| 2 | 1.2 | 1.63476638335802 | -0.434766383358021 |
| 3 | 1 | 1.63476638335802 | -0.634766383358023 |
| 4 | 1.7 | 1.63476638335802 | 0.0652336166419766 |
| 5 | 2.4 | 1.63476638335802 | 0.765233616641977 |
| 6 | 2 | 1.63476638335802 | 0.365233616641977 |
| 7 | 2.1 | 1.63476638335802 | 0.465233616641977 |
| 8 | 2 | 1.63476638335802 | 0.365233616641977 |
| 9 | 1.8 | 1.63476638335802 | 0.165233616641977 |
| 10 | 2.7 | 1.63476638335802 | 1.06523361664198 |
| 11 | 2.3 | 1.63476638335802 | 0.665233616641977 |
| 12 | 1.9 | 1.63476638335802 | 0.265233616641977 |
| 13 | 2 | 1.63476638335802 | 0.365233616641977 |
| 14 | 2.3 | 1.63476638335802 | 0.665233616641977 |
| 15 | 2.8 | 1.63476638335802 | 1.16523361664198 |
| 16 | 2.4 | 1.63476638335802 | 0.765233616641977 |
| 17 | 2.3 | 1.63476638335802 | 0.665233616641977 |
| 18 | 2.7 | 1.63476638335802 | 1.06523361664198 |
| 19 | 2.7 | 1.63476638335802 | 1.06523361664198 |
| 20 | 2.9 | 1.63476638335802 | 1.26523361664198 |
| 21 | 3 | 1.63476638335802 | 1.36523361664198 |
| 22 | 2.2 | 1.63476638335802 | 0.565233616641977 |
| 23 | 2.3 | 1.63476638335802 | 0.665233616641977 |
| 24 | 2.8 | 1.82819797423258 | 0.97180202576742 |
| 25 | 2.8 | 1.86504208678011 | 0.934957913219885 |
| 26 | 2.8 | 1.86504208678011 | 0.934957913219885 |
| 27 | 2.2 | 2.04926264951779 | 0.150737350482212 |
| 28 | 2.6 | 2.09531779020221 | 0.504682209797794 |
| 29 | 2.8 | 2.09531779020221 | 0.704682209797794 |
| 30 | 2.5 | 2.22427218411858 | 0.275727815881422 |
| 31 | 2.4 | 2.32559349362430 | 0.0744065063757022 |
| 32 | 2.3 | 2.49139200008820 | -0.191392000088204 |
| 33 | 1.9 | 2.55586919704639 | -0.655869197046389 |
| 34 | 1.7 | 2.71245667537341 | -1.01245667537341 |
| 35 | 2 | 2.78614490046848 | -0.78614490046848 |
| 36 | 2.1 | 2.91509929438485 | -0.815099294384852 |
| 37 | 1.7 | 3.01642060389057 | -1.31642060389057 |
| 38 | 1.8 | 3.01642060389057 | -1.21642060389057 |
| 39 | 1.8 | 3.15458602594383 | -1.35458602594383 |
| 40 | 1.8 | 3.24669630731266 | -1.44669630731266 |
| 41 | 1.3 | 3.24669630731266 | -1.94669630731266 |
| 42 | 1.3 | 3.38486172936592 | -2.08486172936592 |
| 43 | 1.3 | 3.47697201073476 | -2.17697201073475 |
| 44 | 1.2 | 3.47697201073475 | -2.27697201073475 |
| 45 | 1.4 | 3.47697201073475 | -2.07697201073475 |
| 46 | 2.2 | 3.47697201073476 | -1.27697201073475 |
| 47 | 2.9 | 3.47697201073475 | -0.576972010734755 |
| 48 | 3.1 | 3.47697201073475 | -0.376972010734755 |
| 49 | 3.5 | 3.47697201073475 | 0.023027989265245 |
| 50 | 3.6 | 3.47697201073475 | 0.123027989265245 |
| 51 | 4.4 | 3.47697201073475 | 0.923027989265245 |
| 52 | 4.1 | 3.47697201073475 | 0.623027989265245 |
| 53 | 5.1 | 3.47697201073476 | 1.62302798926524 |
| 54 | 5.8 | 3.47697201073475 | 2.32302798926525 |
| 55 | 5.9 | 3.64277051719866 | 2.25722948280134 |
| 56 | 5.4 | 3.70724771415685 | 1.69275228584315 |
| 57 | 5.5 | 3.70724771415685 | 1.79275228584315 |
| 58 | 4.8 | 3.44933892632410 | 1.35066107367590 |
| 59 | 3.2 | 2.94273237879550 | 0.257267621204497 |
| 60 | 2.7 | 2.32559349362430 | 0.374406506375702 |
| 61 | 2.1 | 1.92030825560142 | 0.179691744398583 |
| 62 | 1.9 | 1.63476638335802 | 0.265233616641977 |
| 63 | 0.6 | 1.32159142670398 | -0.721591426703979 |
| 64 | 0.7 | 0.999205441913051 | -0.299205441913051 |
| 65 | -0.2 | 0.79656282290161 | -0.99656282290161 |
| 66 | -1 | 0.713663569669658 | -1.71366356966966 |
| 67 | -1.7 | 0.713663569669657 | -2.41366356966966 |
| 68 | -0.7 | 0.713663569669657 | -1.41366356966966 |
| 69 | -1 | 0.713663569669658 | -1.71366356966966 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.161594524268047 | 0.323189048536095 | 0.838405475731953 |
| 6 | 0.0847774589575892 | 0.169554917915178 | 0.915222541042411 |
| 7 | 0.045665412779086 | 0.091330825558172 | 0.954334587220914 |
| 8 | 0.0206990496412050 | 0.0413980992824099 | 0.979300950358795 |
| 9 | 0.00783724148119887 | 0.0156744829623977 | 0.992162758518801 |
| 10 | 0.0116752109441808 | 0.0233504218883615 | 0.98832478905582 |
| 11 | 0.00645803425019947 | 0.0129160685003989 | 0.9935419657498 |
| 12 | 0.00259312218906569 | 0.00518624437813138 | 0.997406877810934 |
| 13 | 0.00101880091269824 | 0.00203760182539649 | 0.998981199087302 |
| 14 | 0.000513221520186991 | 0.00102644304037398 | 0.999486778479813 |
| 15 | 0.000707706515875194 | 0.00141541303175039 | 0.999292293484125 |
| 16 | 0.000379582269404654 | 0.000759164538809308 | 0.999620417730595 |
| 17 | 0.000175623448813135 | 0.000351246897626271 | 0.999824376551187 |
| 18 | 0.000153294584607831 | 0.000306589169215663 | 0.999846705415392 |
| 19 | 0.000126089711709868 | 0.000252179423419735 | 0.99987391028829 |
| 20 | 0.000153931410750643 | 0.000307862821501287 | 0.99984606858925 |
| 21 | 0.000219993318616656 | 0.000439986637233311 | 0.999780006681383 |
| 22 | 0.000104873633948759 | 0.000209747267897517 | 0.999895126366051 |
| 23 | 5.21118188679677e-05 | 0.000104223637735935 | 0.999947888181132 |
| 24 | 2.78884727553605e-05 | 5.57769455107209e-05 | 0.999972111527245 |
| 25 | 1.52077590766730e-05 | 3.04155181533461e-05 | 0.999984792240923 |
| 26 | 8.5563622785853e-06 | 1.71127245571706e-05 | 0.999991443637721 |
| 27 | 8.95087227484142e-06 | 1.79017445496828e-05 | 0.999991049127725 |
| 28 | 4.44112337581569e-06 | 8.88224675163139e-06 | 0.999995558876624 |
| 29 | 2.39567838302280e-06 | 4.79135676604559e-06 | 0.999997604321617 |
| 30 | 1.24355448277283e-06 | 2.48710896554566e-06 | 0.999998756445517 |
| 31 | 6.41559802630996e-07 | 1.28311960526199e-06 | 0.999999358440197 |
| 32 | 3.30520310454488e-07 | 6.61040620908977e-07 | 0.99999966947969 |
| 33 | 2.48909037153164e-07 | 4.97818074306327e-07 | 0.999999751090963 |
| 34 | 2.01382843070875e-07 | 4.0276568614175e-07 | 0.999999798617157 |
| 35 | 8.27061479452403e-08 | 1.65412295890481e-07 | 0.999999917293852 |
| 36 | 3.12397390421145e-08 | 6.2479478084229e-08 | 0.999999968760261 |
| 37 | 1.88120398222335e-08 | 3.7624079644467e-08 | 0.99999998118796 |
| 38 | 9.06790128969788e-09 | 1.81358025793958e-08 | 0.999999990932099 |
| 39 | 4.79180007751672e-09 | 9.58360015503343e-09 | 0.9999999952082 |
| 40 | 2.87388881849845e-09 | 5.74777763699689e-09 | 0.99999999712611 |
| 41 | 5.56287434702816e-09 | 1.11257486940563e-08 | 0.999999994437126 |
| 42 | 1.57685481131404e-08 | 3.15370962262808e-08 | 0.999999984231452 |
| 43 | 8.80750051018436e-08 | 1.76150010203687e-07 | 0.999999911924995 |
| 44 | 1.67573717102815e-06 | 3.35147434205631e-06 | 0.999998324262829 |
| 45 | 6.21467321689057e-05 | 0.000124293464337811 | 0.99993785326783 |
| 46 | 0.00109378534221262 | 0.00218757068442525 | 0.998906214657787 |
| 47 | 0.0128329690721842 | 0.0256659381443683 | 0.987167030927816 |
| 48 | 0.0917837014043981 | 0.183567402808796 | 0.908216298595602 |
| 49 | 0.317380423649401 | 0.634760847298801 | 0.6826195763506 |
| 50 | 0.658357087255145 | 0.68328582548971 | 0.341642912744855 |
| 51 | 0.827230918741317 | 0.345538162517367 | 0.172769081258683 |
| 52 | 0.934539737675536 | 0.130920524648927 | 0.0654602623244635 |
| 53 | 0.960988540917116 | 0.0780229181657672 | 0.0390114590828836 |
| 54 | 0.98777989328679 | 0.0244402134264212 | 0.0122201067132106 |
| 55 | 0.993364243460448 | 0.0132715130791036 | 0.00663575653955181 |
| 56 | 0.990866521307978 | 0.0182669573840431 | 0.00913347869202156 |
| 57 | 0.986498341044595 | 0.0270033179108101 | 0.0135016589554051 |
| 58 | 0.975959648840381 | 0.0480807023192372 | 0.0240403511596186 |
| 59 | 0.984440691184228 | 0.0311186176315446 | 0.0155593088157723 |
| 60 | 0.97830544000974 | 0.0433891199805204 | 0.0216945599902602 |
| 61 | 0.96454367565167 | 0.07091264869666 | 0.03545632434833 |
| 62 | 0.920938137121122 | 0.158123725757755 | 0.0790618628788775 |
| 63 | 0.963103806016237 | 0.0737923879675251 | 0.0368961939837626 |
| 64 | 0.920902815726502 | 0.158194368546995 | 0.0790971842734976 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 35 | 0.583333333333333 | NOK |
| 5% type I error level | 47 | 0.783333333333333 | NOK |
| 10% type I error level | 51 | 0.85 | NOK |
