| Multiple Linear Regression - Estimated Regression Equation |
| ipi[t] = -52.2182826720229 + 1.61621931142924`tip `[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) | -52.2182826720229 | 13.736251 | -3.8015 | 0.000343 | 0.000172 |
| `tip ` | 1.61621931142924 | 0.131945 | 12.2492 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.847208157154555 |
| R-squared | 0.717761661549217 |
| Adjusted R-squared | 0.712977960897509 |
| F-TEST (value) | 150.043180752315 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 59 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 10.1828542822533 |
| Sum Squared Residuals | 6117.74075868272 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 99 | 100.676064189184 | -1.6760641891836 |
| 2 | 106.3 | 102.777149294042 | 3.52285070595836 |
| 3 | 128.9 | 116.999879234619 | 11.900120765381 |
| 4 | 111.1 | 113.929062542903 | -2.82906254290342 |
| 5 | 102.9 | 106.332831779186 | -3.43283177918595 |
| 6 | 130 | 131.869096899768 | -1.86909689976804 |
| 7 | 87 | 78.533859622603 | 8.46614037739703 |
| 8 | 87.5 | 102.453905431756 | -14.9539054317558 |
| 9 | 117.6 | 130.737743381768 | -13.1377433817676 |
| 10 | 103.4 | 118.939342408334 | -15.5393424083341 |
| 11 | 110.8 | 123.626378411479 | -12.8263784114789 |
| 12 | 112.6 | 113.120952887189 | -0.520952887188796 |
| 13 | 102.5 | 107.787429159472 | -5.28742915947229 |
| 14 | 112.4 | 110.535001988902 | 1.864998011098 |
| 15 | 135.6 | 134.455047798055 | 1.14495220194517 |
| 16 | 105.1 | 110.535001988902 | -5.43500198890201 |
| 17 | 127.7 | 125.404219654051 | 2.29578034594894 |
| 18 | 137 | 133.000450417768 | 3.9995495822315 |
| 19 | 91 | 85.8068465240346 | 5.19315347596543 |
| 20 | 90.5 | 110.211758126616 | -19.7117581266162 |
| 21 | 122.4 | 133.323694280054 | -10.9236942800543 |
| 22 | 123.3 | 136.071267109484 | -12.7712671094841 |
| 23 | 124.3 | 130.252877588339 | -5.9528775883388 |
| 24 | 120 | 112.63608709376 | 7.36391290623998 |
| 25 | 118.1 | 119.100964339477 | -1.00096433947701 |
| 26 | 119 | 117.969610821477 | 1.03038917852347 |
| 27 | 142.7 | 139.788571525771 | 2.91142847422866 |
| 28 | 123.6 | 119.26258627062 | 4.33741372938008 |
| 29 | 129.6 | 124.434488067193 | 5.16551193280649 |
| 30 | 151.6 | 137.202620627485 | 14.3973793725154 |
| 31 | 110.4 | 97.2820036351822 | 13.1179963648178 |
| 32 | 99.2 | 116.191769578904 | -16.9917695789044 |
| 33 | 130.5 | 129.606389863767 | 0.893610136232906 |
| 34 | 136.2 | 145.606961046917 | -9.40696104691664 |
| 35 | 129.7 | 130.89936531291 | -1.1993653129105 |
| 36 | 128 | 109.403648470902 | 18.5963515290985 |
| 37 | 121.6 | 126.697195103194 | -5.09719510319446 |
| 38 | 135.8 | 130.091255657196 | 5.70874434280415 |
| 39 | 143.8 | 125.242597722908 | 18.5574022770919 |
| 40 | 147.5 | 137.364242558627 | 10.1357574413725 |
| 41 | 136.2 | 124.111244204908 | 12.0887557950923 |
| 42 | 156.6 | 135.101535522627 | 21.4984644773735 |
| 43 | 123.3 | 102.938771225185 | 20.3612287748154 |
| 44 | 104.5 | 109.080404608616 | -4.58040460861568 |
| 45 | 139.8 | 136.556132902913 | 3.24386709708717 |
| 46 | 136.5 | 134.778291660341 | 1.72170833965932 |
| 47 | 112.1 | 108.433916884044 | 3.666083115956 |
| 48 | 118.5 | 100.191198395755 | 18.3088016042452 |
| 49 | 94.4 | 94.8576746680383 | -0.457674668038324 |
| 50 | 102.3 | 98.4133571531827 | 3.88664284681733 |
| 51 | 111.4 | 114.413928336332 | -3.01392833633218 |
| 52 | 99.2 | 99.867954533469 | -0.667954533468976 |
| 53 | 87.8 | 96.1506501171817 | -8.35065011718173 |
| 54 | 115.8 | 113.76744061176 | 2.0325593882395 |
| 55 | 79.7 | 81.2814324520327 | -1.58143245203266 |
| 56 | 72.7 | 91.7868579763228 | -19.0868579763228 |
| 57 | 104.5 | 116.676635372333 | -12.1766353723331 |
| 58 | 103 | 117.646366959191 | -14.6463669591907 |
| 59 | 95.1 | 101.484173844898 | -6.38417384489823 |
| 60 | 104.2 | 91.1403702517511 | 13.0596297482489 |
| 61 | 78.3 | 87.2614439043209 | -8.96144390432088 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.233263058219805 | 0.46652611643961 | 0.766736941780195 |
| 6 | 0.184131309046911 | 0.368262618093821 | 0.81586869095309 |
| 7 | 0.123871964078668 | 0.247743928157336 | 0.876128035921332 |
| 8 | 0.351161450582471 | 0.702322901164942 | 0.648838549417529 |
| 9 | 0.346509112632392 | 0.693018225264783 | 0.653490887367609 |
| 10 | 0.396575108343172 | 0.793150216686344 | 0.603424891656828 |
| 11 | 0.352909740369222 | 0.705819480738444 | 0.647090259630778 |
| 12 | 0.269888297196818 | 0.539776594393637 | 0.730111702803182 |
| 13 | 0.199708281593313 | 0.399416563186626 | 0.800291718406687 |
| 14 | 0.152104954247203 | 0.304209908494405 | 0.847895045752797 |
| 15 | 0.143291778243611 | 0.286583556487222 | 0.85670822175639 |
| 16 | 0.102118317740118 | 0.204236635480236 | 0.897881682259882 |
| 17 | 0.08422020331362 | 0.16844040662724 | 0.91577979668638 |
| 18 | 0.0773784965732228 | 0.154756993146446 | 0.922621503426777 |
| 19 | 0.0552923811178863 | 0.110584762235773 | 0.944707618882114 |
| 20 | 0.154996590673079 | 0.309993181346159 | 0.84500340932692 |
| 21 | 0.138600803981079 | 0.277201607962158 | 0.861399196018921 |
| 22 | 0.138035826355402 | 0.276071652710803 | 0.861964173644598 |
| 23 | 0.107583997029549 | 0.215167994059097 | 0.892416002970452 |
| 24 | 0.107977463742366 | 0.215954927484732 | 0.892022536257634 |
| 25 | 0.0786331231686774 | 0.157266246337355 | 0.921366876831323 |
| 26 | 0.057542848147071 | 0.115085696294142 | 0.942457151852929 |
| 27 | 0.0516591620372754 | 0.103318324074551 | 0.948340837962725 |
| 28 | 0.0411334188413259 | 0.0822668376826518 | 0.958866581158674 |
| 29 | 0.0343950942575223 | 0.0687901885150445 | 0.965604905742478 |
| 30 | 0.0676114657346181 | 0.135222931469236 | 0.932388534265382 |
| 31 | 0.0867773113742927 | 0.173554622748585 | 0.913222688625707 |
| 32 | 0.155802356107687 | 0.311604712215375 | 0.844197643892313 |
| 33 | 0.118871035622943 | 0.237742071245885 | 0.881128964377057 |
| 34 | 0.130379821663218 | 0.260759643326436 | 0.869620178336782 |
| 35 | 0.103212176228542 | 0.206424352457083 | 0.896787823771458 |
| 36 | 0.201872633628875 | 0.403745267257749 | 0.798127366371125 |
| 37 | 0.181603513585824 | 0.363207027171648 | 0.818396486414176 |
| 38 | 0.149584229487472 | 0.299168458974943 | 0.850415770512528 |
| 39 | 0.240015282546624 | 0.480030565093248 | 0.759984717453376 |
| 40 | 0.218744996378279 | 0.437489992756558 | 0.781255003621721 |
| 41 | 0.218378071550886 | 0.436756143101773 | 0.781621928449113 |
| 42 | 0.411830216536242 | 0.823660433072484 | 0.588169783463758 |
| 43 | 0.667974343656194 | 0.664051312687612 | 0.332025656343806 |
| 44 | 0.597589847561456 | 0.804820304877087 | 0.402410152438544 |
| 45 | 0.529523006769836 | 0.940953986460329 | 0.470476993230164 |
| 46 | 0.464220027071545 | 0.92844005414309 | 0.535779972928455 |
| 47 | 0.408048950717125 | 0.81609790143425 | 0.591951049282875 |
| 48 | 0.713489549784749 | 0.573020900430501 | 0.286510450215251 |
| 49 | 0.631630834377686 | 0.736738331244627 | 0.368369165622314 |
| 50 | 0.597361939648125 | 0.80527612070375 | 0.402638060351875 |
| 51 | 0.511368237135366 | 0.977263525729267 | 0.488631762864634 |
| 52 | 0.425426724398597 | 0.850853448797194 | 0.574573275601403 |
| 53 | 0.33241365068466 | 0.66482730136932 | 0.66758634931534 |
| 54 | 0.350055590912318 | 0.700111181824636 | 0.649944409087682 |
| 55 | 0.230488385153196 | 0.460976770306391 | 0.769511614846804 |
| 56 | 0.414457077682764 | 0.828914155365527 | 0.585542922317236 |
| 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 | 2 | 0.0384615384615385 | OK |
