| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 97.1336370267663 + 0.0352680312321223X[t] -0.994110622434554M1[t] -0.687493175700802M2[t] -0.466465397677703M3[t] -2.20315379946010M4[t] + 0.00931861749677947M5[t] -0.271665593540829M6[t] -0.305962182715962M7[t] -0.447910526269306M8[t] -0.704493275398668M9[t] -2.09188703780570M10[t] -0.159814522917262M11[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) | 97.1336370267663 | 2.264442 | 42.8952 | 0 | 0 |
| X | 0.0352680312321223 | 0.007098 | 4.969 | 9e-06 | 5e-06 |
| M1 | -0.994110622434554 | 2.137059 | -0.4652 | 0.643953 | 0.321976 |
| M2 | -0.687493175700802 | 2.143613 | -0.3207 | 0.749847 | 0.374923 |
| M3 | -0.466465397677703 | 2.149238 | -0.217 | 0.829119 | 0.414559 |
| M4 | -2.20315379946010 | 2.144095 | -1.0275 | 0.309423 | 0.154712 |
| M5 | 0.00931861749677947 | 2.140064 | 0.0044 | 0.996544 | 0.498272 |
| M6 | -0.271665593540829 | 2.131882 | -0.1274 | 0.899144 | 0.449572 |
| M7 | -0.305962182715962 | 2.127209 | -0.1438 | 0.886248 | 0.443124 |
| M8 | -0.447910526269306 | 2.125494 | -0.2107 | 0.834007 | 0.417004 |
| M9 | -0.704493275398668 | 2.127379 | -0.3312 | 0.741999 | 0.371 |
| M10 | -2.09188703780570 | 2.129257 | -0.9824 | 0.330909 | 0.165455 |
| M11 | -0.159814522917262 | 2.12708 | -0.0751 | 0.940428 | 0.470214 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.627797045839455 |
| R-squared | 0.394129130764746 |
| Adjusted R-squared | 0.239438696066384 |
| F-TEST (value) | 2.54785715440825 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 47 |
| p-value | 0.0111036875022026 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 3.36067973745561 |
| Sum Squared Residuals | 530.825909994002 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 98.71 | 101.549642395339 | -2.83964239533927 |
| 2 | 98.54 | 101.560008379723 | -3.02000837972326 |
| 3 | 98.2 | 101.523579529752 | -3.32357952975187 |
| 4 | 96.92 | 100.16073225903 | -3.24073225902997 |
| 5 | 99.06 | 102.510749997792 | -3.45074999779212 |
| 6 | 99.65 | 102.836375923947 | -3.18637592394701 |
| 7 | 99.82 | 102.773864909786 | -2.95386490978619 |
| 8 | 99.99 | 102.367406331992 | -2.37740633199193 |
| 9 | 100.33 | 102.569307988880 | -2.23930798888015 |
| 10 | 99.31 | 101.354727579511 | -2.04472757951052 |
| 11 | 101.1 | 103.695909256692 | -2.59590925669158 |
| 12 | 101.1 | 103.834562960870 | -2.73456296086957 |
| 13 | 100.93 | 102.544200876085 | -1.61420087608518 |
| 14 | 100.85 | 102.610995710441 | -1.76099571044051 |
| 15 | 100.93 | 103.033051266487 | -2.1030512664867 |
| 16 | 99.6 | 101.871231773788 | -2.27123177378791 |
| 17 | 101.88 | 103.977900097048 | -2.09790009704842 |
| 18 | 101.81 | 103.809773585954 | -1.99977358595359 |
| 19 | 102.38 | 104.456149999558 | -2.07614999955843 |
| 20 | 102.74 | 104.494068615289 | -1.75406861528891 |
| 21 | 102.82 | 104.114047756847 | -1.29404775684712 |
| 22 | 101.72 | 103.142816762979 | -1.42281676297912 |
| 23 | 103.47 | 104.993772806034 | -1.52377280603368 |
| 24 | 102.98 | 104.335369004366 | -1.3553690043657 |
| 25 | 102.68 | 103.073221344567 | -0.393221344567015 |
| 26 | 102.9 | 103.457428460011 | -0.557428460011436 |
| 27 | 103.03 | 103.985288109754 | -0.955288109754006 |
| 28 | 101.29 | 101.656096783272 | -0.366096783271949 |
| 29 | 103.69 | 104.252990740659 | -0.562990740658968 |
| 30 | 103.68 | 104.285892007587 | -0.60589200758724 |
| 31 | 104.2 | 104.710079824430 | -0.510079824429701 |
| 32 | 104.08 | 104.578711890246 | -0.498711890245997 |
| 33 | 104.16 | 104.583112572234 | -0.423112572234342 |
| 34 | 103.05 | 103.647149609598 | -0.597149609598473 |
| 35 | 104.66 | 105.251229434028 | -0.591229434028176 |
| 36 | 104.46 | 105.957698441043 | -1.49769844104334 |
| 37 | 104.95 | 105.510242302707 | -0.56024230270667 |
| 38 | 105.85 | 106.589229633424 | -0.73922963342391 |
| 39 | 106.23 | 106.658604877149 | -0.428604877148875 |
| 40 | 104.86 | 105.348659653275 | -0.488659653275163 |
| 41 | 107.44 | 108.157161798055 | -0.71716179805491 |
| 42 | 108.23 | 108.634440258508 | -0.404440258507925 |
| 43 | 108.45 | 109.090369303459 | -0.640369303459294 |
| 44 | 109.39 | 110.200436068646 | -0.810436068646293 |
| 45 | 110.15 | 110.786759265965 | -0.636759265964651 |
| 46 | 109.13 | 109.628607706566 | -0.498607706566422 |
| 47 | 110.28 | 109.765537431740 | 0.51446256826017 |
| 48 | 110.17 | 108.486416280387 | 1.6835837196135 |
| 49 | 109.99 | 104.582693081302 | 5.40730691869814 |
| 50 | 109.26 | 103.182337816401 | 6.07766218359912 |
| 51 | 109.11 | 102.299476216859 | 6.81052378314144 |
| 52 | 107.06 | 100.693279530635 | 6.36672046936499 |
| 53 | 109.53 | 102.701197366446 | 6.82880263355442 |
| 54 | 108.92 | 102.723518224004 | 6.19648177599577 |
| 55 | 109.24 | 103.059535962766 | 6.18046403723362 |
| 56 | 109.12 | 103.679377093827 | 5.44062290617313 |
| 57 | 109 | 104.406772416074 | 4.59322758392627 |
| 58 | 107.23 | 102.666698341345 | 4.56330165865453 |
| 59 | 109.49 | 105.293551071507 | 4.19644892849327 |
| 60 | 109.04 | 105.135953313335 | 3.90404668666512 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.0010699946216479 | 0.0021399892432958 | 0.998930005378352 |
| 17 | 9.03722580906049e-05 | 0.000180744516181210 | 0.99990962774191 |
| 18 | 1.13370937557175e-05 | 2.26741875114349e-05 | 0.999988662906244 |
| 19 | 2.75200155473553e-06 | 5.50400310947105e-06 | 0.999997247998445 |
| 20 | 2.52730321115333e-06 | 5.05460642230665e-06 | 0.999997472696789 |
| 21 | 3.15259649148898e-07 | 6.30519298297797e-07 | 0.99999968474035 |
| 22 | 7.1782861872708e-08 | 1.43565723745416e-07 | 0.999999928217138 |
| 23 | 1.08193775816879e-08 | 2.16387551633758e-08 | 0.999999989180622 |
| 24 | 1.37238712068433e-08 | 2.74477424136866e-08 | 0.99999998627613 |
| 25 | 2.54795327754182e-08 | 5.09590655508363e-08 | 0.999999974520467 |
| 26 | 1.45513626366300e-08 | 2.91027252732601e-08 | 0.999999985448637 |
| 27 | 4.56497269100838e-09 | 9.12994538201676e-09 | 0.999999995435027 |
| 28 | 6.42818989219183e-08 | 1.28563797843837e-07 | 0.999999935718101 |
| 29 | 1.03680137988326e-07 | 2.07360275976653e-07 | 0.999999896319862 |
| 30 | 1.17627070202785e-07 | 2.3525414040557e-07 | 0.99999988237293 |
| 31 | 1.1307243890761e-07 | 2.2614487781522e-07 | 0.999999886927561 |
| 32 | 9.79050966051753e-08 | 1.95810193210351e-07 | 0.999999902094903 |
| 33 | 1.24347037638512e-07 | 2.48694075277024e-07 | 0.999999875652962 |
| 34 | 2.46677310881236e-07 | 4.93354621762471e-07 | 0.99999975332269 |
| 35 | 1.56085044927271e-06 | 3.12170089854542e-06 | 0.99999843914955 |
| 36 | 6.95325746222679e-05 | 0.000139065149244536 | 0.999930467425378 |
| 37 | 0.00424843733960981 | 0.00849687467921962 | 0.99575156266039 |
| 38 | 0.0366396932670628 | 0.0732793865341255 | 0.963360306732937 |
| 39 | 0.0972195695501208 | 0.194439139100242 | 0.90278043044988 |
| 40 | 0.197830534359731 | 0.395661068719462 | 0.802169465640269 |
| 41 | 0.513430724690708 | 0.973138550618585 | 0.486569275309292 |
| 42 | 0.581647190148437 | 0.836705619703126 | 0.418352809851563 |
| 43 | 0.861814319871053 | 0.276371360257894 | 0.138185680128947 |
| 44 | 0.961649199654906 | 0.076701600690188 | 0.038350800345094 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 22 | 0.758620689655172 | NOK |
| 5% type I error level | 22 | 0.758620689655172 | NOK |
| 10% type I error level | 24 | 0.827586206896552 | NOK |
