| Multiple Linear Regression - Estimated Regression Equation |
| X[t] = + 39.5718545572898 + 1.4428225092746Y[t] + 0.462651817415592`y(t)`[t] + 0.456836619187371`y(t-1)`[t] -12.0357634082612M1[t] -35.1685550498614M2[t] -43.9263346792956M3[t] -39.5414071812871M4[t] -25.9417353094251M5[t] -15.6128526883177M6[t] -27.0108528497098M7[t] -31.7675430580503M8[t] -12.4005152354837M9[t] -53.5642426604347M10[t] -38.356705110219M11[t] -0.0981315636876872t + 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) | 39.5718545572898 | 14.916987 | 2.6528 | 0.011062 | 0.005531 |
| Y | 1.4428225092746 | 3.352062 | 0.4304 | 0.668985 | 0.334493 |
| `y(t)` | 0.462651817415592 | 0.134518 | 3.4393 | 0.001287 | 0.000644 |
| `y(t-1)` | 0.456836619187371 | 0.155403 | 2.9397 | 0.005218 | 0.002609 |
| M1 | -12.0357634082612 | 5.673619 | -2.1214 | 0.039562 | 0.019781 |
| M2 | -35.1685550498614 | 5.876229 | -5.9849 | 0 | 0 |
| M3 | -43.9263346792956 | 6.513124 | -6.7443 | 0 | 0 |
| M4 | -39.5414071812871 | 5.828352 | -6.7843 | 0 | 0 |
| M5 | -25.9417353094251 | 5.317747 | -4.8783 | 1.4e-05 | 7e-06 |
| M6 | -15.6128526883177 | 5.046647 | -3.0937 | 0.003429 | 0.001715 |
| M7 | -27.0108528497098 | 5.191112 | -5.2033 | 5e-06 | 2e-06 |
| M8 | -31.7675430580503 | 5.75193 | -5.5229 | 2e-06 | 1e-06 |
| M9 | -12.4005152354837 | 5.350115 | -2.3178 | 0.025172 | 0.012586 |
| M10 | -53.5642426604347 | 5.698954 | -9.399 | 0 | 0 |
| M11 | -38.356705110219 | 7.794011 | -4.9213 | 1.2e-05 | 6e-06 |
| t | -0.0981315636876872 | 0.067336 | -1.4573 | 0.152124 | 0.076062 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.932787352234213 |
| R-squared | 0.870092244488114 |
| Adjusted R-squared | 0.825805509654517 |
| F-TEST (value) | 19.6467914773439 |
| F-TEST (DF numerator) | 15 |
| F-TEST (DF denominator) | 44 |
| p-value | 1.04360964314765e-14 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 7.91699716280575 |
| Sum Squared Residuals | 2757.86913933847 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 112.3 | 125.882537323786 | -13.5825373237857 |
| 2 | 117.3 | 109.704087244584 | 7.5959127554161 |
| 3 | 111.1 | 102.365758213796 | 8.73424178620351 |
| 4 | 102.2 | 106.068295976077 | -3.86829597607748 |
| 5 | 104.3 | 112.619848070291 | -8.31984807029128 |
| 6 | 122.9 | 119.756322033516 | 3.14367796648385 |
| 7 | 107.6 | 117.82487101266 | -10.2248710126599 |
| 8 | 121.3 | 114.388637551058 | 6.91136244894178 |
| 9 | 131.5 | 133.006263434964 | -1.50626343496396 |
| 10 | 89 | 102.722114666831 | -13.7221146668313 |
| 11 | 104.4 | 102.828551928908 | 1.57144807109218 |
| 12 | 128.9 | 128.796407148176 | 0.103592851824 |
| 13 | 135.9 | 135.032765638395 | 0.867234361605378 |
| 14 | 133.3 | 126.232902325106 | 7.06709767489355 |
| 15 | 121.3 | 119.371952741016 | 1.92804725898431 |
| 16 | 120.5 | 115.476329147188 | 5.02367085281238 |
| 17 | 120.4 | 123.125708571181 | -2.72570857118096 |
| 18 | 137.9 | 132.944725151509 | 4.95527484849077 |
| 19 | 126.1 | 129.499316569284 | -3.39931656928365 |
| 20 | 133.2 | 127.17984418753 | 6.0201558124696 |
| 21 | 151.1 | 144.342896243649 | 6.75710375635096 |
| 22 | 105 | 114.60604478298 | -9.60604478297976 |
| 23 | 119 | 116.564577470103 | 2.43542252989708 |
| 24 | 140.4 | 140.240108315915 | 0.159891684085257 |
| 25 | 156.6 | 144.402674905283 | 12.1973250947173 |
| 26 | 137.1 | 138.443014792737 | -1.34301479273715 |
| 27 | 122.7 | 127.966146390847 | -5.26614639084666 |
| 28 | 125.8 | 116.682442080229 | 9.11755791977077 |
| 29 | 139.3 | 125.039755706094 | 14.2602442939063 |
| 30 | 134.9 | 142.932499818105 | -8.03249981810474 |
| 31 | 149.2 | 135.567994455426 | 13.6320055445741 |
| 32 | 132.3 | 135.319012548016 | -3.01901254801619 |
| 33 | 149 | 153.301856746951 | -4.30185674695104 |
| 34 | 117.2 | 112.045744244886 | 5.15425575511385 |
| 35 | 119.6 | 120.071993978027 | -0.471993978027431 |
| 36 | 152 | 144.913527396198 | 7.08647260380221 |
| 37 | 149.4 | 148.865959194564 | 0.534040805436261 |
| 38 | 127.3 | 139.233647725666 | -11.9336477256661 |
| 39 | 114.1 | 118.965356157773 | -4.86535615777254 |
| 40 | 102.1 | 107.049058818167 | -4.94905881816664 |
| 41 | 107.7 | 108.96853394408 | -1.26853394408049 |
| 42 | 104.4 | 116.308095748779 | -11.9080957487791 |
| 43 | 102.1 | 105.843498093677 | -3.7434980936772 |
| 44 | 96 | 99.8598388075494 | -3.85983880754935 |
| 45 | 109.3 | 113.813012246788 | -4.51301224678761 |
| 46 | 90 | 77.3605415620079 | 12.6394584379921 |
| 47 | 83.9 | 89.616694507607 | -5.71669450760702 |
| 48 | 112 | 116.236145217587 | -4.23614521758701 |
| 49 | 114.3 | 114.316062937973 | -0.0160629379732617 |
| 50 | 103.6 | 104.986347911906 | -1.38634791190635 |
| 51 | 91.7 | 92.2307864965686 | -0.530786496568621 |
| 52 | 80.8 | 86.123873978339 | -5.32387397833903 |
| 53 | 87.2 | 89.1461537083536 | -1.94615370835361 |
| 54 | 109.2 | 97.3583572480908 | 11.8416427519092 |
| 55 | 102.7 | 98.9643198689533 | 3.73568013104673 |
| 56 | 95.1 | 101.152666905846 | -6.05266690584585 |
| 57 | 117.5 | 113.935971327648 | 3.56402867235165 |
| 58 | 85.1 | 79.5655547432949 | 5.53444525670511 |
| 59 | 92.1 | 89.9181821153548 | 2.18181788464518 |
| 60 | 113.5 | 116.613811922124 | -3.11381192212449 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 19 | 0.0103166245804497 | 0.0206332491608995 | 0.98968337541955 |
| 20 | 0.0043575351734827 | 0.00871507034696539 | 0.995642464826517 |
| 21 | 0.00202856761597113 | 0.00405713523194227 | 0.997971432384029 |
| 22 | 0.000944964467037782 | 0.00188992893407556 | 0.999055035532962 |
| 23 | 0.000209186042294785 | 0.000418372084589569 | 0.999790813957705 |
| 24 | 0.000368108455547481 | 0.000736216911094961 | 0.999631891544453 |
| 25 | 0.000134538808541602 | 0.000269077617083203 | 0.999865461191458 |
| 26 | 0.0011168879489944 | 0.00223377589798881 | 0.998883112051006 |
| 27 | 0.0781291569964193 | 0.156258313992839 | 0.921870843003581 |
| 28 | 0.221697272512877 | 0.443394545025754 | 0.778302727487123 |
| 29 | 0.237274728586044 | 0.474549457172087 | 0.762725271413956 |
| 30 | 0.514763555358584 | 0.970472889282833 | 0.485236444641416 |
| 31 | 0.601748122144278 | 0.796503755711444 | 0.398251877855722 |
| 32 | 0.574134690284324 | 0.851730619431352 | 0.425865309715676 |
| 33 | 0.668014633116484 | 0.663970733767033 | 0.331985366883516 |
| 34 | 0.576248945884107 | 0.847502108231786 | 0.423751054115893 |
| 35 | 0.513339139610988 | 0.973321720778024 | 0.486660860389012 |
| 36 | 0.655682687559172 | 0.688634624881656 | 0.344317312440828 |
| 37 | 0.634153740103837 | 0.731692519792327 | 0.365846259896163 |
| 38 | 0.713955851244151 | 0.572088297511698 | 0.286044148755849 |
| 39 | 0.665646565351917 | 0.668706869296167 | 0.334353434648083 |
| 40 | 0.656596651836922 | 0.686806696326155 | 0.343403348163078 |
| 41 | 0.948782465762291 | 0.102435068475418 | 0.0512175342377092 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 7 | 0.304347826086957 | NOK |
| 5% type I error level | 8 | 0.347826086956522 | NOK |
| 10% type I error level | 8 | 0.347826086956522 | NOK |
