| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 44.6238087674328 + 0.648372618794754X[t] + 2.73643325933069M1[t] + 8.11863080589267M2[t] + 5.54052302280312M3[t] + 10.6327205693652M4[t] + 15.9723299978759M5[t] + 11.9014141427661M6[t] + 18.2417059744356M7[t] + 15.2405881180513M8[t] + 8.69991469123985M9[t] -2.07156680759192M10[t] + 2.99600897634725M11[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) | 44.6238087674328 | 11.967091 | 3.7289 | 0.000517 | 0.000258 |
| X | 0.648372618794754 | 0.101102 | 6.413 | 0 | 0 |
| M1 | 2.73643325933069 | 3.507264 | 0.7802 | 0.439174 | 0.219587 |
| M2 | 8.11863080589267 | 3.653685 | 2.222 | 0.031132 | 0.015566 |
| M3 | 5.54052302280312 | 3.376909 | 1.6407 | 0.107534 | 0.053767 |
| M4 | 10.6327205693652 | 3.452856 | 3.0794 | 0.003459 | 0.00173 |
| M5 | 15.9723299978759 | 3.458734 | 4.618 | 3e-05 | 1.5e-05 |
| M6 | 11.9014141427661 | 3.353047 | 3.5494 | 0.000889 | 0.000444 |
| M7 | 18.2417059744356 | 3.42548 | 5.3253 | 3e-06 | 1e-06 |
| M8 | 15.2405881180513 | 3.37643 | 4.5138 | 4.3e-05 | 2.1e-05 |
| M9 | 8.69991469123985 | 3.366723 | 2.5841 | 0.012931 | 0.006466 |
| M10 | -2.07156680759192 | 3.440674 | -0.6021 | 0.550013 | 0.275007 |
| M11 | 2.99600897634725 | 3.353436 | 0.8934 | 0.376187 | 0.188094 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.837478632407121 |
| R-squared | 0.701370459738502 |
| Adjusted R-squared | 0.625124619671736 |
| F-TEST (value) | 9.19880296583182 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 47 |
| p-value | 9.2879609558949e-09 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 5.30132070747676 |
| Sum Squared Residuals | 1320.88805844553 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 104.08 | 111.678805811202 | -7.59880581120246 |
| 2 | 103.86 | 113.430116692514 | -9.57011669251427 |
| 3 | 107.47 | 117.724758668649 | -10.2547586686491 |
| 4 | 111.1 | 117.046439907938 | -5.94643990793789 |
| 5 | 117.33 | 127.184006715530 | -9.85400671552983 |
| 6 | 119.04 | 123.372439907938 | -4.33243990793787 |
| 7 | 123.68 | 127.702776621344 | -4.02277662134366 |
| 8 | 125.9 | 129.369941620282 | -3.4699416202816 |
| 9 | 124.54 | 122.699593669711 | 1.84040633028884 |
| 10 | 119.39 | 119.708583596416 | -0.318583596416448 |
| 11 | 118.8 | 119.200154858721 | -0.400154858720747 |
| 12 | 114.81 | 110.563304098859 | 4.24669590114087 |
| 13 | 117.9 | 113.753598191346 | 4.14640180865386 |
| 14 | 120.53 | 116.801654310247 | 3.72834568975299 |
| 15 | 125.15 | 118.632480334962 | 6.51751966503823 |
| 16 | 126.49 | 122.946630738970 | 3.54336926102984 |
| 17 | 131.85 | 129.518148143191 | 2.33185185680907 |
| 18 | 127.4 | 126.030767644996 | 1.36923235500362 |
| 19 | 131.08 | 133.213943881099 | -2.13394388109904 |
| 20 | 122.37 | 129.175429834643 | -6.80542983464318 |
| 21 | 124.34 | 127.367876525033 | -3.0278765250334 |
| 22 | 119.61 | 124.182354666100 | -4.57235466610025 |
| 23 | 119.97 | 119.329829382480 | 0.640170617520318 |
| 24 | 116.46 | 116.268983144253 | 0.191016855747034 |
| 25 | 117.03 | 116.541600452164 | 0.488399547836416 |
| 26 | 120.96 | 120.627052761136 | 0.332947238863934 |
| 27 | 124.71 | 119.799551048792 | 4.91044895120766 |
| 28 | 127.08 | 126.447842880462 | 0.632157119538181 |
| 29 | 131.91 | 127.637867548686 | 4.27213245131386 |
| 30 | 137.69 | 130.958399547837 | 6.73160045216349 |
| 31 | 142.46 | 136.974505070109 | 5.4854949298914 |
| 32 | 144.32 | 130.926035905389 | 13.393964094611 |
| 33 | 138.06 | 130.026204262092 | 8.03379573790812 |
| 34 | 124.45 | 125.090076332413 | -0.6400763324129 |
| 35 | 126.71 | 120.432062834431 | 6.27793716556923 |
| 36 | 121.83 | 119.121822666950 | 2.70817733305012 |
| 37 | 122.51 | 117.514159380356 | 4.99584061964429 |
| 38 | 125.48 | 121.080913594292 | 4.39908640570762 |
| 39 | 127.77 | 129.330628545075 | -1.56062854507522 |
| 40 | 128.03 | 128.846821570002 | -0.816821570002408 |
| 41 | 132.84 | 131.917126832731 | 0.922873167268494 |
| 42 | 133.41 | 137.766312045181 | -4.35631204518143 |
| 43 | 139.99 | 136.974505070109 | 3.01549492989139 |
| 44 | 138.53 | 134.816271618158 | 3.71372838184247 |
| 45 | 136.12 | 135.731883307486 | 0.388116692514287 |
| 46 | 124.75 | 122.302074071595 | 2.44792592840454 |
| 47 | 122.88 | 126.850951760499 | -3.97095176049883 |
| 48 | 121.46 | 126.578107783090 | -5.11810778308955 |
| 49 | 118.4 | 120.431836164932 | -2.0318361649321 |
| 50 | 122.45 | 121.340262641810 | 1.10973735818972 |
| 51 | 128.94 | 128.552581402522 | 0.387418597478484 |
| 52 | 133.25 | 130.662264902628 | 2.58773509737228 |
| 53 | 137.94 | 135.612850759862 | 2.32714924013839 |
| 54 | 140.04 | 139.452080854048 | 0.587919145952199 |
| 55 | 130.74 | 133.08426935734 | -2.34426935734009 |
| 56 | 131.55 | 138.382321021529 | -6.83232102152867 |
| 57 | 129.47 | 136.704442235678 | -7.23444223567785 |
| 58 | 125.45 | 122.366911333475 | 3.08308866652507 |
| 59 | 127.87 | 130.41700116387 | -2.54700116386997 |
| 60 | 124.68 | 126.707782306848 | -2.02778230684848 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.926941902908301 | 0.146116194183398 | 0.073058097091699 |
| 17 | 0.88706768483201 | 0.225864630335981 | 0.112932315167990 |
| 18 | 0.820285115720262 | 0.359429768559475 | 0.179714884279738 |
| 19 | 0.88741086406543 | 0.225178271869141 | 0.112589135934571 |
| 20 | 0.926191656197284 | 0.147616687605432 | 0.0738083438027159 |
| 21 | 0.977242972912232 | 0.0455140541755353 | 0.0227570270877676 |
| 22 | 0.983702225703043 | 0.0325955485939144 | 0.0162977742969572 |
| 23 | 0.97533256924043 | 0.0493348615191416 | 0.0246674307595708 |
| 24 | 0.980256324381556 | 0.0394873512368874 | 0.0197436756184437 |
| 25 | 0.967969453864816 | 0.0640610922703673 | 0.0320305461351836 |
| 26 | 0.949502796781631 | 0.100994406436738 | 0.050497203218369 |
| 27 | 0.938573426100455 | 0.122853147799090 | 0.0614265738995452 |
| 28 | 0.916445907100514 | 0.167108185798973 | 0.0835540928994865 |
| 29 | 0.921915856853262 | 0.156168286293476 | 0.0780841431467381 |
| 30 | 0.886176666031354 | 0.227646667937291 | 0.113823333968646 |
| 31 | 0.89719698997548 | 0.205606020049040 | 0.102803010024520 |
| 32 | 0.98034360451614 | 0.0393127909677223 | 0.0196563954838611 |
| 33 | 0.979664171349014 | 0.0406716573019721 | 0.0203358286509860 |
| 34 | 0.963332827478874 | 0.0733343450422513 | 0.0366671725211256 |
| 35 | 0.951236319335284 | 0.0975273613294315 | 0.0487636806647158 |
| 36 | 0.929058228502285 | 0.141883542995429 | 0.0709417714977147 |
| 37 | 0.924736307629298 | 0.150527384741404 | 0.0752636923707021 |
| 38 | 0.887401984353007 | 0.225196031293987 | 0.112598015646993 |
| 39 | 0.861532119475264 | 0.276935761049472 | 0.138467880524736 |
| 40 | 0.80558319263871 | 0.38883361472258 | 0.19441680736129 |
| 41 | 0.706496574189177 | 0.587006851621646 | 0.293503425810823 |
| 42 | 0.692489542451993 | 0.615020915096013 | 0.307510457548007 |
| 43 | 0.751785812822064 | 0.496428374355873 | 0.248214187177936 |
| 44 | 0.770929676560268 | 0.458140646879465 | 0.229070323439732 |
| 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 | 6 | 0.206896551724138 | NOK |
| 10% type I error level | 9 | 0.310344827586207 | NOK |
