| Multiple Linear Regression - Estimated Regression Equation |
| ipi[t] = -83.6948607837712 + 2.01157944981591`tip `[t] -14.6973798833694M1[t] -8.59150522082137M2[t] -9.0930245904434M3[t] -11.9610838018231M4[t] -11.4142195211682M5[t] -8.72060225971292M6[t] + 2.29366396537288M7[t] -26.1061509349583M8[t] -23.313673168531M9[t] -27.4420937616331M10[t] -19.1181103452043M11[t] + 0.119620211242018t + 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) | -83.6948607837712 | 13.818476 | -6.0567 | 0 | 0 |
| `tip ` | 2.01157944981591 | 0.132403 | 15.1928 | 0 | 0 |
| M1 | -14.6973798833694 | 3.904156 | -3.7645 | 0.000463 | 0.000232 |
| M2 | -8.59150522082137 | 4.117864 | -2.0864 | 0.042394 | 0.021197 |
| M3 | -9.0930245904434 | 4.38877 | -2.0719 | 0.043789 | 0.021894 |
| M4 | -11.9610838018231 | 4.16177 | -2.874 | 0.006068 | 0.003034 |
| M5 | -11.4142195211682 | 4.146825 | -2.7525 | 0.008378 | 0.004189 |
| M6 | -8.72060225971292 | 4.524442 | -1.9274 | 0.05998 | 0.02999 |
| M7 | 2.29366396537288 | 4.307948 | 0.5324 | 0.596939 | 0.29847 |
| M8 | -26.1061509349583 | 4.074633 | -6.407 | 0 | 0 |
| M9 | -23.313673168531 | 4.507242 | -5.1725 | 5e-06 | 2e-06 |
| M10 | -27.4420937616331 | 4.556273 | -6.0229 | 0 | 0 |
| M11 | -19.1181103452043 | 4.217408 | -4.5331 | 4e-05 | 2e-05 |
| t | 0.119620211242018 | 0.049506 | 2.4163 | 0.019618 | 0.009809 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.954042074610755 |
| R-squared | 0.910196280127594 |
| Adjusted R-squared | 0.885356953354376 |
| F-TEST (value) | 36.6433554515236 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 47 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 6.43555143585808 |
| Sum Squared Residuals | 1946.56714732802 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 99 | 92.0227954966864 | 6.9772045033136 |
| 2 | 106.3 | 100.863343655237 | 5.4366563447628 |
| 3 | 128.9 | 118.183343655237 | 10.7166563447628 |
| 4 | 111.1 | 111.612903700449 | -0.512903700449282 |
| 5 | 102.9 | 102.824964778211 | 0.0750352217886005 |
| 6 | 130 | 137.421157558 | -7.42115755800011 |
| 7 | 87 | 82.1729221504029 | 4.82707784959712 |
| 8 | 87.5 | 83.6641033185892 | 3.8358966814108 |
| 9 | 117.6 | 121.778841668037 | -4.17884166803694 |
| 10 | 103.4 | 103.085511302521 | 0.314488697479326 |
| 11 | 110.8 | 117.362695334658 | -6.56269533465769 |
| 12 | 112.6 | 123.525159467301 | -10.9251594673006 |
| 13 | 102.5 | 102.309187610781 | 0.190812389219359 |
| 14 | 112.4 | 111.954367549258 | 0.445632450742226 |
| 15 | 135.6 | 141.343844248153 | -5.74384424815325 |
| 16 | 105.1 | 108.82402939074 | -3.72402939074011 |
| 17 | 127.7 | 127.997044820943 | -0.297044820943388 |
| 18 | 137 | 140.264705707775 | -3.26470570777545 |
| 19 | 91 | 92.6604722094787 | -1.66047220947870 |
| 20 | 90.5 | 94.7551272126098 | -4.25512721260978 |
| 21 | 122.4 | 126.432811322647 | -4.03281132264659 |
| 22 | 123.3 | 125.843696005474 | -2.54369600547356 |
| 23 | 124.3 | 127.045613613807 | -2.74561361380716 |
| 24 | 120 | 124.35712816726 | -4.35712816726001 |
| 25 | 118.1 | 117.825686294396 | 0.274313705603763 |
| 26 | 119 | 122.643075553315 | -3.64307555331518 |
| 27 | 142.7 | 149.41749896745 | -6.71749896744997 |
| 28 | 123.6 | 121.122000954650 | 2.47799904534977 |
| 29 | 129.6 | 128.225539685958 | 1.37446031404194 |
| 30 | 151.6 | 146.930254812201 | 4.66974518779895 |
| 31 | 110.4 | 108.378128838076 | 2.02187116192414 |
| 32 | 99.2 | 103.633413711833 | -4.43341371183287 |
| 33 | 130.5 | 123.241621122974 | 7.25837887702577 |
| 34 | 136.2 | 139.147457294292 | -2.94745729429167 |
| 35 | 129.7 | 129.285687928638 | 0.414312071362261 |
| 36 | 128 | 121.769411802532 | 6.23058819746759 |
| 37 | 121.6 | 128.715552243435 | -7.11555224343524 |
| 38 | 135.8 | 139.165363961839 | -3.36536396183872 |
| 39 | 143.8 | 132.748726454011 | 11.0512735459890 |
| 40 | 147.5 | 145.087133327493 | 2.41286667250735 |
| 41 | 136.2 | 129.258666330899 | 6.94133366910091 |
| 42 | 156.6 | 145.750644062345 | 10.8493559376554 |
| 43 | 123.3 | 116.854099447336 | 6.44590055266422 |
| 44 | 104.5 | 96.217906667547 | 8.28209333245291 |
| 45 | 139.8 | 133.326855292087 | 6.47314470791315 |
| 46 | 136.5 | 127.105317515429 | 9.39468248457073 |
| 47 | 112.1 | 102.760176111101 | 9.33982388889919 |
| 48 | 118.5 | 111.738851473486 | 6.76114852651406 |
| 49 | 94.4 | 90.522879616966 | 3.87712038303399 |
| 50 | 102.3 | 101.173849280351 | 1.12615071964888 |
| 51 | 111.4 | 120.706586675149 | -9.3065866751486 |
| 52 | 99.2 | 99.8539326266677 | -0.653932626667735 |
| 53 | 87.8 | 95.893784383988 | -8.09378438398807 |
| 54 | 115.8 | 120.633237859679 | -4.83323785967879 |
| 55 | 79.7 | 91.3343773547068 | -11.6343773547068 |
| 56 | 72.7 | 76.129449089421 | -3.42944908942106 |
| 57 | 104.5 | 110.019870594255 | -5.51987059425538 |
| 58 | 103 | 107.218017882285 | -4.21801788228482 |
| 59 | 95.1 | 95.5458270117966 | -0.4458270117966 |
| 60 | 104.2 | 101.909449089421 | 2.29055091057893 |
| 61 | 78.3 | 82.5038987377355 | -4.20389873773546 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.350705546926428 | 0.701411093852856 | 0.649294453073572 |
| 18 | 0.315356652003748 | 0.630713304007496 | 0.684643347996252 |
| 19 | 0.193911504748982 | 0.387823009497964 | 0.806088495251018 |
| 20 | 0.117899730709766 | 0.235799461419532 | 0.882100269290234 |
| 21 | 0.0723104433869092 | 0.144620886773818 | 0.92768955661309 |
| 22 | 0.0488036576448555 | 0.097607315289711 | 0.951196342355144 |
| 23 | 0.0508296289876381 | 0.101659257975276 | 0.949170371012362 |
| 24 | 0.0572240356388942 | 0.114448071277788 | 0.942775964361106 |
| 25 | 0.0328110219184523 | 0.0656220438369047 | 0.967188978081548 |
| 26 | 0.0195470257336247 | 0.0390940514672495 | 0.980452974266375 |
| 27 | 0.0170149422603178 | 0.0340298845206355 | 0.982985057739682 |
| 28 | 0.0173783347151543 | 0.0347566694303086 | 0.982621665284846 |
| 29 | 0.0108035581028501 | 0.0216071162057002 | 0.98919644189715 |
| 30 | 0.0158955917171871 | 0.0317911834343742 | 0.984104408282813 |
| 31 | 0.0107090896129871 | 0.0214181792259743 | 0.989290910387013 |
| 32 | 0.0110174183631066 | 0.0220348367262133 | 0.988982581636893 |
| 33 | 0.00708325732107652 | 0.0141665146421530 | 0.992916742678923 |
| 34 | 0.00996502651086717 | 0.0199300530217343 | 0.990034973489133 |
| 35 | 0.0131732453467699 | 0.0263464906935397 | 0.98682675465323 |
| 36 | 0.0248521414605858 | 0.0497042829211716 | 0.975147858539414 |
| 37 | 0.217157684447213 | 0.434315368894426 | 0.782842315552787 |
| 38 | 0.460941861253163 | 0.921883722506326 | 0.539058138746837 |
| 39 | 0.557276361544705 | 0.88544727691059 | 0.442723638455295 |
| 40 | 0.984645938845046 | 0.0307081223099071 | 0.0153540611549535 |
| 41 | 0.978938433520451 | 0.0421231329590978 | 0.0210615664795489 |
| 42 | 0.950935195904115 | 0.09812960819177 | 0.049064804095885 |
| 43 | 0.94648119613933 | 0.107037607721339 | 0.0535188038606695 |
| 44 | 0.861130064584313 | 0.277739870831374 | 0.138869935415687 |
| 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 | 13 | 0.464285714285714 | NOK |
| 10% type I error level | 16 | 0.571428571428571 | NOK |
