| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 129.735271512114 + 132.441278195489X[t] + 1.56547284878861M1[t] + 5.70547284878865M2[t] + 12.7354728487886M3[t] + 17.2404728487886M4[t] + 25.3464728487887M5[t] + 32.7264728487886M6[t] + 35.6664728487887M7[t] + 33.9414728487887M8[t] + 28.1594728487886M9[t] + 24.2412531328321M10[t] + 18.6901420217210M11[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) | 129.735271512114 | 22.652312 | 5.7272 | 0 | 0 |
| X | 132.441278195489 | 15.939085 | 8.3092 | 0 | 0 |
| M1 | 1.56547284878861 | 30.842017 | 0.0508 | 0.959616 | 0.479808 |
| M2 | 5.70547284878865 | 30.842017 | 0.185 | 0.853597 | 0.426798 |
| M3 | 12.7354728487886 | 30.842017 | 0.4129 | 0.680511 | 0.340255 |
| M4 | 17.2404728487886 | 30.842017 | 0.559 | 0.577368 | 0.288684 |
| M5 | 25.3464728487887 | 30.842017 | 0.8218 | 0.413062 | 0.206531 |
| M6 | 32.7264728487886 | 30.842017 | 1.0611 | 0.291102 | 0.145551 |
| M7 | 35.6664728487887 | 30.842017 | 1.1564 | 0.250157 | 0.125078 |
| M8 | 33.9414728487887 | 30.842017 | 1.1005 | 0.273657 | 0.136829 |
| M9 | 28.1594728487886 | 30.842017 | 0.913 | 0.363342 | 0.181671 |
| M10 | 24.2412531328321 | 31.690679 | 0.7649 | 0.446044 | 0.223022 |
| M11 | 18.6901420217210 | 31.690679 | 0.5898 | 0.556625 | 0.278313 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.641911939068384 |
| R-squared | 0.412050937518533 |
| Adjusted R-squared | 0.344210661078363 |
| F-TEST (value) | 6.07383930520882 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 104 |
| p-value | 5.79472236861278e-08 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 67.1210247974531 |
| Sum Squared Residuals | 468544.124865472 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 100.01 | 131.300744360903 | -31.2907443609025 |
| 2 | 103.84 | 135.440744360902 | -31.600744360902 |
| 3 | 104.48 | 142.470744360902 | -37.9907443609022 |
| 4 | 95.43 | 146.975744360902 | -51.5457443609022 |
| 5 | 104.8 | 155.081744360902 | -50.2817443609023 |
| 6 | 108.64 | 162.461744360902 | -53.8217443609023 |
| 7 | 105.65 | 165.401744360902 | -59.7517443609023 |
| 8 | 108.42 | 163.676744360902 | -55.2567443609021 |
| 9 | 115.35 | 157.894744360902 | -42.5447443609022 |
| 10 | 113.64 | 153.976524644946 | -40.3365246449457 |
| 11 | 115.24 | 148.425413533835 | -33.1854135338346 |
| 12 | 100.33 | 129.735271512114 | -29.4052715121136 |
| 13 | 101.29 | 131.300744360902 | -30.0107443609022 |
| 14 | 104.48 | 135.440744360902 | -30.9607443609023 |
| 15 | 99.26 | 142.470744360902 | -43.2107443609022 |
| 16 | 100.11 | 146.975744360902 | -46.8657443609023 |
| 17 | 103.52 | 155.081744360902 | -51.5617443609023 |
| 18 | 101.18 | 162.461744360902 | -61.2817443609023 |
| 19 | 96.39 | 165.401744360902 | -69.0117443609023 |
| 20 | 97.56 | 163.676744360902 | -66.1167443609023 |
| 21 | 96.39 | 157.894744360902 | -61.5047443609023 |
| 22 | 85.1 | 153.976524644946 | -68.8765246449457 |
| 23 | 79.77 | 148.425413533835 | -68.6554135338346 |
| 24 | 79.13 | 129.735271512114 | -50.6052715121136 |
| 25 | 80.84 | 131.300744360902 | -50.4607443609022 |
| 26 | 82.75 | 135.440744360902 | -52.6907443609023 |
| 27 | 92.55 | 142.470744360902 | -49.9207443609023 |
| 28 | 96.6 | 146.975744360902 | -50.3757443609023 |
| 29 | 96.92 | 155.081744360902 | -58.1617443609023 |
| 30 | 95.32 | 162.461744360902 | -67.1417443609023 |
| 31 | 98.52 | 165.401744360902 | -66.8817443609023 |
| 32 | 100.22 | 163.676744360902 | -63.4567443609023 |
| 33 | 104.91 | 157.894744360902 | -52.9847443609023 |
| 34 | 103.1 | 153.976524644946 | -50.8765246449457 |
| 35 | 97.13 | 148.425413533835 | -51.2954135338346 |
| 36 | 103.42 | 129.735271512114 | -26.3152715121136 |
| 37 | 111.72 | 131.300744360902 | -19.5807443609023 |
| 38 | 118.11 | 135.440744360902 | -17.3307443609023 |
| 39 | 111.62 | 142.470744360902 | -30.8507443609023 |
| 40 | 100.22 | 146.975744360902 | -46.7557443609023 |
| 41 | 102.03 | 155.081744360902 | -53.0517443609023 |
| 42 | 105.76 | 162.461744360902 | -56.7017443609023 |
| 43 | 107.68 | 165.401744360902 | -57.7217443609023 |
| 44 | 110.77 | 163.676744360902 | -52.9067443609023 |
| 45 | 105.44 | 157.894744360902 | -52.4547443609023 |
| 46 | 112.26 | 153.976524644946 | -41.7165246449457 |
| 47 | 114.07 | 148.425413533835 | -34.3554135338346 |
| 48 | 117.9 | 129.735271512114 | -11.8352715121136 |
| 49 | 124.72 | 131.300744360902 | -6.58074436090226 |
| 50 | 126.42 | 135.440744360902 | -9.02074436090227 |
| 51 | 134.73 | 142.470744360902 | -7.74074436090228 |
| 52 | 135.79 | 146.975744360902 | -11.1857443609023 |
| 53 | 143.36 | 155.081744360902 | -11.7217443609023 |
| 54 | 140.37 | 162.461744360902 | -22.0917443609023 |
| 55 | 144.74 | 165.401744360902 | -20.6617443609023 |
| 56 | 151.98 | 163.676744360902 | -11.6967443609023 |
| 57 | 150.92 | 157.894744360902 | -6.97474436090226 |
| 58 | 163.38 | 153.976524644946 | 9.40347535505432 |
| 59 | 154.43 | 148.425413533835 | 6.00458646616543 |
| 60 | 146.66 | 129.735271512114 | 16.9247284878864 |
| 61 | 157.95 | 131.300744360902 | 26.6492556390977 |
| 62 | 162.1 | 135.440744360902 | 26.6592556390977 |
| 63 | 180.42 | 142.470744360902 | 37.9492556390977 |
| 64 | 179.57 | 146.975744360902 | 32.5942556390977 |
| 65 | 171.58 | 155.081744360902 | 16.4982556390977 |
| 66 | 185.43 | 162.461744360902 | 22.9682556390977 |
| 67 | 190.64 | 165.401744360902 | 25.2382556390977 |
| 68 | 203 | 163.676744360902 | 39.3232556390977 |
| 69 | 202.36 | 157.894744360902 | 44.4652556390978 |
| 70 | 193.41 | 153.976524644946 | 39.4334753550543 |
| 71 | 186.17 | 148.425413533835 | 37.7445864661654 |
| 72 | 192.24 | 129.735271512114 | 62.5047284878864 |
| 73 | 209.6 | 131.300744360902 | 78.2992556390977 |
| 74 | 206.41 | 135.440744360902 | 70.9692556390977 |
| 75 | 209.82 | 142.470744360902 | 67.3492556390977 |
| 76 | 230.37 | 146.975744360902 | 83.3942556390977 |
| 77 | 235.8 | 155.081744360902 | 80.7182556390977 |
| 78 | 232.07 | 162.461744360902 | 69.6082556390977 |
| 79 | 244.64 | 165.401744360902 | 79.2382556390977 |
| 80 | 242.19 | 163.676744360902 | 78.5132556390977 |
| 81 | 217.48 | 157.894744360902 | 59.5852556390978 |
| 82 | 209.39 | 153.976524644946 | 55.4134753550543 |
| 83 | 211.73 | 148.425413533835 | 63.3045864661654 |
| 84 | 221 | 129.735271512114 | 91.2647284878864 |
| 85 | 203.11 | 131.300744360902 | 71.8092556390978 |
| 86 | 214.71 | 135.440744360902 | 79.2692556390977 |
| 87 | 224.19 | 142.470744360902 | 81.7192556390977 |
| 88 | 238.04 | 146.975744360902 | 91.0642556390977 |
| 89 | 238.36 | 155.081744360902 | 83.2782556390978 |
| 90 | 246.24 | 162.461744360902 | 83.7782556390977 |
| 91 | 259.87 | 165.401744360902 | 94.4682556390977 |
| 92 | 249.97 | 163.676744360902 | 86.2932556390977 |
| 93 | 266.48 | 157.894744360902 | 108.585255639098 |
| 94 | 282.98 | 153.976524644946 | 129.003475355054 |
| 95 | 306.31 | 148.425413533835 | 157.884586466165 |
| 96 | 301.73 | 262.176549707602 | 39.5534502923977 |
| 97 | 314.62 | 263.742022556391 | 50.8779774436091 |
| 98 | 332.62 | 267.882022556391 | 64.737977443609 |
| 99 | 355.51 | 274.912022556391 | 80.597977443609 |
| 100 | 370.32 | 279.417022556391 | 90.902977443609 |
| 101 | 408.13 | 287.523022556391 | 120.606977443609 |
| 102 | 433.58 | 294.903022556391 | 138.676977443609 |
| 103 | 440.51 | 297.843022556391 | 142.666977443609 |
| 104 | 386.29 | 296.118022556391 | 90.171977443609 |
| 105 | 342.84 | 290.336022556391 | 52.5039774436090 |
| 106 | 254.97 | 286.417802840434 | -31.4478028404344 |
| 107 | 203.42 | 280.866691729323 | -77.4466917293233 |
| 108 | 170.09 | 262.176549707602 | -92.0865497076023 |
| 109 | 174.03 | 263.742022556391 | -89.712022556391 |
| 110 | 167.85 | 267.882022556391 | -100.032022556391 |
| 111 | 177.01 | 274.912022556391 | -97.902022556391 |
| 112 | 188.19 | 279.417022556391 | -91.227022556391 |
| 113 | 211.2 | 287.523022556391 | -76.323022556391 |
| 114 | 240.91 | 294.903022556391 | -53.993022556391 |
| 115 | 230.26 | 297.843022556391 | -67.583022556391 |
| 116 | 251.25 | 296.118022556391 | -44.868022556391 |
| 117 | 241.66 | 290.336022556391 | -48.6760225563909 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.000100568613409031 | 0.000201137226818061 | 0.999899431386591 |
| 17 | 3.66648240437122e-06 | 7.33296480874243e-06 | 0.999996333517596 |
| 18 | 7.0463081447607e-07 | 1.40926162895214e-06 | 0.999999295369186 |
| 19 | 1.72434686863373e-07 | 3.44869373726745e-07 | 0.999999827565313 |
| 20 | 4.84653420864804e-08 | 9.69306841729608e-08 | 0.999999951534658 |
| 21 | 6.5388538386515e-08 | 1.3077707677303e-07 | 0.999999934611462 |
| 22 | 2.03430697890715e-07 | 4.0686139578143e-07 | 0.999999796569302 |
| 23 | 5.31374261310877e-07 | 1.06274852262175e-06 | 0.999999468625739 |
| 24 | 1.95922753030058e-07 | 3.91845506060116e-07 | 0.999999804077247 |
| 25 | 8.13379082974152e-08 | 1.62675816594830e-07 | 0.999999918662092 |
| 26 | 3.8205229898219e-08 | 7.6410459796438e-08 | 0.99999996179477 |
| 27 | 8.62674149687276e-09 | 1.72534829937455e-08 | 0.999999991373258 |
| 28 | 1.62736212930182e-09 | 3.25472425860364e-09 | 0.999999998372638 |
| 29 | 3.48234297539373e-10 | 6.96468595078746e-10 | 0.999999999651766 |
| 30 | 8.57328725031319e-11 | 1.71465745006264e-10 | 0.999999999914267 |
| 31 | 1.74971305352516e-11 | 3.49942610705032e-11 | 0.999999999982503 |
| 32 | 3.51033075336154e-12 | 7.02066150672307e-12 | 0.99999999999649 |
| 33 | 6.47507085385451e-13 | 1.29501417077090e-12 | 0.999999999999353 |
| 34 | 1.21930121353381e-13 | 2.43860242706762e-13 | 0.999999999999878 |
| 35 | 2.18429622580665e-14 | 4.36859245161331e-14 | 0.999999999999978 |
| 36 | 6.19592078100283e-15 | 1.23918415620057e-14 | 0.999999999999994 |
| 37 | 2.82749818775683e-15 | 5.65499637551365e-15 | 0.999999999999997 |
| 38 | 1.87349335107131e-15 | 3.74698670214263e-15 | 0.999999999999998 |
| 39 | 5.62562178111483e-16 | 1.12512435622297e-15 | 1 |
| 40 | 1.20216437593701e-16 | 2.40432875187402e-16 | 1 |
| 41 | 2.71558684721833e-17 | 5.43117369443665e-17 | 1 |
| 42 | 7.1077210350425e-18 | 1.4215442070085e-17 | 1 |
| 43 | 2.29551865196965e-18 | 4.59103730393931e-18 | 1 |
| 44 | 7.74584013088524e-19 | 1.54916802617705e-18 | 1 |
| 45 | 1.99562235729663e-19 | 3.99124471459325e-19 | 1 |
| 46 | 7.57149618309897e-20 | 1.51429923661979e-19 | 1 |
| 47 | 4.41448819736285e-20 | 8.8289763947257e-20 | 1 |
| 48 | 5.14806215383661e-20 | 1.02961243076732e-19 | 1 |
| 49 | 9.01734905629325e-20 | 1.80346981125865e-19 | 1 |
| 50 | 1.02804419678468e-19 | 2.05608839356935e-19 | 1 |
| 51 | 3.90091143625552e-19 | 7.80182287251104e-19 | 1 |
| 52 | 2.62587654223401e-18 | 5.25175308446802e-18 | 1 |
| 53 | 2.23785230506030e-17 | 4.47570461012061e-17 | 1 |
| 54 | 1.02415848378172e-16 | 2.04831696756345e-16 | 1 |
| 55 | 7.31188228357852e-16 | 1.46237645671570e-15 | 1 |
| 56 | 5.99212988801057e-15 | 1.19842597760211e-14 | 0.999999999999994 |
| 57 | 2.54164444812026e-14 | 5.08328889624051e-14 | 0.999999999999975 |
| 58 | 2.84008850603266e-13 | 5.68017701206532e-13 | 0.999999999999716 |
| 59 | 1.10050723185393e-12 | 2.20101446370787e-12 | 0.9999999999989 |
| 60 | 1.99053489249126e-12 | 3.98106978498252e-12 | 0.99999999999801 |
| 61 | 5.69877812457117e-12 | 1.13975562491423e-11 | 0.999999999994301 |
| 62 | 1.45940474976291e-11 | 2.91880949952581e-11 | 0.999999999985406 |
| 63 | 9.7387260189417e-11 | 1.94774520378834e-10 | 0.999999999902613 |
| 64 | 5.69296437894212e-10 | 1.13859287578842e-09 | 0.999999999430704 |
| 65 | 1.62136047855522e-09 | 3.24272095711043e-09 | 0.99999999837864 |
| 66 | 8.31149672393442e-09 | 1.66229934478688e-08 | 0.999999991688503 |
| 67 | 4.38166503089528e-08 | 8.76333006179057e-08 | 0.99999995618335 |
| 68 | 2.15220067810186e-07 | 4.30440135620372e-07 | 0.999999784779932 |
| 69 | 6.83275341266936e-07 | 1.36655068253387e-06 | 0.999999316724659 |
| 70 | 1.28098406921397e-06 | 2.56196813842793e-06 | 0.99999871901593 |
| 71 | 1.94765197416549e-06 | 3.89530394833097e-06 | 0.999998052348026 |
| 72 | 3.16064121013635e-06 | 6.32128242027271e-06 | 0.99999683935879 |
| 73 | 7.1932863886061e-06 | 1.43865727772122e-05 | 0.999992806713611 |
| 74 | 1.17015702942845e-05 | 2.34031405885690e-05 | 0.999988298429706 |
| 75 | 1.71338090827164e-05 | 3.42676181654329e-05 | 0.999982866190917 |
| 76 | 3.89588663396852e-05 | 7.79177326793705e-05 | 0.99996104113366 |
| 77 | 8.14895087762972e-05 | 0.000162979017552594 | 0.999918510491224 |
| 78 | 0.000143958930487626 | 0.000287917860975252 | 0.999856041069512 |
| 79 | 0.000268998696282618 | 0.000537997392565235 | 0.999731001303717 |
| 80 | 0.000382733155075396 | 0.000765466310150792 | 0.999617266844925 |
| 81 | 0.000387045200139966 | 0.000774090400279932 | 0.99961295479986 |
| 82 | 0.00035091499168611 | 0.00070182998337222 | 0.999649085008314 |
| 83 | 0.000314337368526072 | 0.000628674737052145 | 0.999685662631474 |
| 84 | 0.000303182754724941 | 0.000606365509449881 | 0.999696817245275 |
| 85 | 0.000226996645131987 | 0.000453993290263973 | 0.999773003354868 |
| 86 | 0.000179702858102073 | 0.000359405716204145 | 0.999820297141898 |
| 87 | 0.000145589173602592 | 0.000291178347205183 | 0.999854410826397 |
| 88 | 0.000130202975146880 | 0.000260405950293761 | 0.999869797024853 |
| 89 | 0.000117379865301225 | 0.00023475973060245 | 0.999882620134699 |
| 90 | 0.000127539761028856 | 0.000255079522057711 | 0.99987246023897 |
| 91 | 0.000146766066197943 | 0.000293532132395886 | 0.999853233933802 |
| 92 | 0.000159304806688577 | 0.000318609613377155 | 0.999840695193311 |
| 93 | 0.000178161791216886 | 0.000356323582433772 | 0.999821838208783 |
| 94 | 0.000189736683947811 | 0.000379473367895623 | 0.999810263316052 |
| 95 | 0.000214226862457526 | 0.000428453724915051 | 0.999785773137542 |
| 96 | 0.000184758307621591 | 0.000369516615243182 | 0.999815241692378 |
| 97 | 0.000175707560296316 | 0.000351415120592632 | 0.999824292439704 |
| 98 | 0.000233492769348395 | 0.000466985538696791 | 0.999766507230652 |
| 99 | 0.00040709003945135 | 0.0008141800789027 | 0.999592909960549 |
| 100 | 0.000813132444481021 | 0.00162626488896204 | 0.99918686755552 |
| 101 | 0.00250427175494105 | 0.0050085435098821 | 0.997495728245059 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 86 | 1 | NOK |
| 5% type I error level | 86 | 1 | NOK |
| 10% type I error level | 86 | 1 | NOK |
