| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 1230.71723607144 + 87.5267609364537X[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) | 1230.71723607144 | 247.959235 | 4.9634 | 5e-06 | 2e-06 |
| X | 87.5267609364537 | 10.397695 | 8.4179 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.711795769190165 |
| R-squared | 0.506653217037018 |
| Adjusted R-squared | 0.499503263660743 |
| F-TEST (value) | 70.8610518661828 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 69 |
| p-value | 3.44013706410351e-12 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 599.406650706703 |
| Sum Squared Residuals | 24790894.9708885 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 2350.44 | 3593.93978135569 | -1243.49978135568 |
| 2 | 2440.25 | 3768.99330322859 | -1328.74330322859 |
| 3 | 2408.64 | 3593.93978135569 | -1185.29978135569 |
| 4 | 2472.81 | 3506.41302041923 | -1033.60302041923 |
| 5 | 2407.6 | 3331.35949854633 | -923.759498546327 |
| 6 | 2454.62 | 3856.52006416505 | -1401.90006416505 |
| 7 | 2448.05 | 3506.41302041923 | -1058.36302041923 |
| 8 | 2497.84 | 3681.46654229214 | -1183.62654229214 |
| 9 | 2645.64 | 3681.46654229214 | -1035.82654229214 |
| 10 | 2756.76 | 3331.35949854633 | -574.599498546327 |
| 11 | 2849.27 | 3243.83273760987 | -394.562737609873 |
| 12 | 2921.44 | 3331.35949854633 | -409.919498546327 |
| 13 | 2981.85 | 3331.35949854633 | -349.509498546327 |
| 14 | 3080.58 | 3593.93978135569 | -513.359781355688 |
| 15 | 3106.22 | 3681.46654229214 | -575.246542292142 |
| 16 | 3119.31 | 3418.88625948278 | -299.576259482781 |
| 17 | 3061.26 | 2893.72569386406 | 167.534306135942 |
| 18 | 3097.31 | 2893.72569386406 | 203.584306135942 |
| 19 | 3161.69 | 2893.72569386406 | 267.964306135942 |
| 20 | 3257.16 | 2981.25245480051 | 275.907545199488 |
| 21 | 3277.01 | 2631.14541105470 | 645.864588945303 |
| 22 | 3295.32 | 3156.30597667342 | 139.014023326581 |
| 23 | 3363.99 | 3068.77921573697 | 295.210784263034 |
| 24 | 3494.17 | 3418.88625948278 | 75.2837405172194 |
| 25 | 3667.03 | 3768.99330322860 | -101.963303228595 |
| 26 | 3813.06 | 3681.46654229214 | 131.593457707858 |
| 27 | 3917.96 | 3418.88625948278 | 499.07374051722 |
| 28 | 3895.51 | 3506.41302041923 | 389.096979580766 |
| 29 | 3801.06 | 3331.35949854633 | 469.700501453673 |
| 30 | 3570.12 | 3681.46654229214 | -111.346542292142 |
| 31 | 3701.61 | 3681.46654229214 | 20.1434577078583 |
| 32 | 3862.27 | 3681.46654229214 | 180.803457707858 |
| 33 | 3970.1 | 3681.46654229214 | 288.633457707858 |
| 34 | 4138.52 | 4031.57358603796 | 106.946413962044 |
| 35 | 4199.75 | 3944.0468251015 | 255.703174898497 |
| 36 | 4290.89 | 3156.30597667342 | 1134.58402332658 |
| 37 | 4443.91 | 3768.99330322860 | 674.916696771404 |
| 38 | 4502.64 | 3944.0468251015 | 558.593174898497 |
| 39 | 4356.98 | 3768.99330322860 | 587.986696771404 |
| 40 | 4591.27 | 4031.57358603796 | 559.696413962044 |
| 41 | 4696.96 | 4031.57358603796 | 665.386413962043 |
| 42 | 4621.4 | 3944.0468251015 | 677.353174898497 |
| 43 | 4562.84 | 3768.99330322860 | 793.846696771405 |
| 44 | 4202.52 | 3681.46654229214 | 521.053457707859 |
| 45 | 4296.49 | 3681.46654229214 | 615.023457707858 |
| 46 | 4435.23 | 3768.99330322860 | 666.236696771404 |
| 47 | 4105.18 | 3156.30597667342 | 948.87402332658 |
| 48 | 4116.68 | 3506.41302041923 | 610.266979580766 |
| 49 | 3844.49 | 3331.35949854633 | 513.130501453673 |
| 50 | 3720.98 | 3593.93978135569 | 127.040218644312 |
| 51 | 3674.4 | 3593.93978135569 | 80.460218644312 |
| 52 | 3857.62 | 3243.83273760987 | 613.787262390127 |
| 53 | 3801.06 | 3068.77921573697 | 732.280784263034 |
| 54 | 3504.37 | 2893.72569386406 | 610.644306135942 |
| 55 | 3032.6 | 2718.67217199115 | 313.927828008849 |
| 56 | 3047.03 | 2893.72569386406 | 153.304306135942 |
| 57 | 2962.34 | 3068.77921573697 | -106.439215736966 |
| 58 | 2197.82 | 2368.56512824534 | -170.745128245336 |
| 59 | 2014.45 | 1930.93132356307 | 83.5186764369328 |
| 60 | 1862.83 | 1668.35104075371 | 194.478959246294 |
| 61 | 1905.41 | 2105.98484543597 | -200.574845435975 |
| 62 | 1810.99 | 1755.87780169016 | 55.1121983098401 |
| 63 | 1670.07 | 1755.87780169016 | -85.80780169016 |
| 64 | 1864.44 | 1930.93132356307 | -66.4913235630672 |
| 65 | 2052.02 | 2193.51160637243 | -141.491606372429 |
| 66 | 2029.6 | 2281.03836730888 | -251.438367308882 |
| 67 | 2070.83 | 2368.56512824534 | -297.735128245336 |
| 68 | 2293.41 | 2893.72569386406 | -600.315693864058 |
| 69 | 2443.27 | 2893.72569386406 | -450.455693864058 |
| 70 | 2513.17 | 2806.19893292760 | -293.028932927605 |
| 71 | 2466.92 | 2981.25245480051 | -514.332454800512 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.00139129820986984 | 0.00278259641973968 | 0.99860870179013 |
| 6 | 0.000173031091682279 | 0.000346062183364557 | 0.999826968908318 |
| 7 | 2.26955247597573e-05 | 4.53910495195146e-05 | 0.99997730447524 |
| 8 | 8.00560019473845e-06 | 1.60112003894769e-05 | 0.999991994399805 |
| 9 | 0.000115603271771806 | 0.000231206543543612 | 0.999884396728228 |
| 10 | 0.000898181516208645 | 0.00179636303241729 | 0.999101818483791 |
| 11 | 0.00141391138821810 | 0.00282782277643621 | 0.998586088611782 |
| 12 | 0.00253652004315325 | 0.00507304008630649 | 0.997463479956847 |
| 13 | 0.00396384802538181 | 0.00792769605076362 | 0.996036151974618 |
| 14 | 0.0330813128689958 | 0.0661626257379916 | 0.966918687131004 |
| 15 | 0.134574786812495 | 0.269149573624991 | 0.865425213187505 |
| 16 | 0.185940309267598 | 0.371880618535196 | 0.814059690732402 |
| 17 | 0.132205556138417 | 0.264411112276835 | 0.867794443861583 |
| 18 | 0.0914310568843392 | 0.182862113768678 | 0.90856894311566 |
| 19 | 0.063044025414747 | 0.126088050829494 | 0.936955974585253 |
| 20 | 0.0492401471505761 | 0.0984802943011523 | 0.950759852849424 |
| 21 | 0.0400543026450805 | 0.080108605290161 | 0.95994569735492 |
| 22 | 0.0423939169253681 | 0.0847878338507362 | 0.957606083074632 |
| 23 | 0.041911833180375 | 0.08382366636075 | 0.958088166819625 |
| 24 | 0.122504697037721 | 0.245009394075441 | 0.877495302962279 |
| 25 | 0.499913513470486 | 0.999827026940972 | 0.500086486529514 |
| 26 | 0.769064056988565 | 0.461871886022869 | 0.230935943011435 |
| 27 | 0.880612254466208 | 0.238775491067584 | 0.119387745533792 |
| 28 | 0.930804189714262 | 0.138391620571476 | 0.0691958102857382 |
| 29 | 0.94398140786477 | 0.112037184270460 | 0.0560185921352301 |
| 30 | 0.958218535738274 | 0.0835629285234519 | 0.0417814642617259 |
| 31 | 0.968302702605266 | 0.0633945947894682 | 0.0316972973947341 |
| 32 | 0.975987164267529 | 0.0480256714649426 | 0.0240128357324713 |
| 33 | 0.981435658597274 | 0.0371286828054526 | 0.0185643414027263 |
| 34 | 0.990364041502209 | 0.0192719169955818 | 0.00963595849779088 |
| 35 | 0.993259760897316 | 0.0134804782053674 | 0.00674023910268372 |
| 36 | 0.998870357348588 | 0.00225928530282375 | 0.00112964265141188 |
| 37 | 0.999236060641206 | 0.00152787871758853 | 0.000763939358794263 |
| 38 | 0.999331485602202 | 0.00133702879559548 | 0.000668514397797741 |
| 39 | 0.999266814643275 | 0.00146637071344894 | 0.000733185356724468 |
| 40 | 0.99918683188983 | 0.00162633622034128 | 0.00081316811017064 |
| 41 | 0.999085900202096 | 0.00182819959580755 | 0.000914099797903774 |
| 42 | 0.998878439679827 | 0.00224312064034546 | 0.00112156032017273 |
| 43 | 0.998880508062642 | 0.00223898387471649 | 0.00111949193735824 |
| 44 | 0.99826339089889 | 0.00347321820221945 | 0.00173660910110972 |
| 45 | 0.997624958619227 | 0.00475008276154614 | 0.00237504138077307 |
| 46 | 0.997021433728135 | 0.00595713254372943 | 0.00297856627186471 |
| 47 | 0.998941319903612 | 0.00211736019277644 | 0.00105868009638822 |
| 48 | 0.99885892895619 | 0.00228214208761829 | 0.00114107104380915 |
| 49 | 0.998660671749893 | 0.00267865650021345 | 0.00133932825010673 |
| 50 | 0.99736923950844 | 0.00526152098312127 | 0.00263076049156064 |
| 51 | 0.994970636385864 | 0.0100587272282726 | 0.00502936361413628 |
| 52 | 0.996432220547817 | 0.00713555890436513 | 0.00356777945218256 |
| 53 | 0.999364838187062 | 0.00127032362587688 | 0.000635161812938438 |
| 54 | 0.999964211331383 | 7.15773372341817e-05 | 3.57886686170908e-05 |
| 55 | 0.999994319144778 | 1.13617104443095e-05 | 5.68085522215477e-06 |
| 56 | 0.999999692000631 | 6.159987383117e-07 | 3.0799936915585e-07 |
| 57 | 0.999999994044788 | 1.19104242687244e-08 | 5.95521213436222e-09 |
| 58 | 0.999999968164416 | 6.36711686589598e-08 | 3.18355843294799e-08 |
| 59 | 0.999999915260016 | 1.69479968359174e-07 | 8.4739984179587e-08 |
| 60 | 0.999999870629 | 2.58742002736166e-07 | 1.29371001368083e-07 |
| 61 | 0.999999102302198 | 1.79539560418813e-06 | 8.97697802094066e-07 |
| 62 | 0.999995096358603 | 9.80728279384703e-06 | 4.90364139692352e-06 |
| 63 | 0.999971541968912 | 5.69160621756804e-05 | 2.84580310878402e-05 |
| 64 | 0.999780003615494 | 0.000439992769012873 | 0.000219996384506437 |
| 65 | 0.998652971269015 | 0.00269405746196916 | 0.00134702873098458 |
| 66 | 0.99113280828997 | 0.0177343834200587 | 0.00886719171002934 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 38 | 0.612903225806452 | NOK |
| 5% type I error level | 44 | 0.709677419354839 | NOK |
| 10% type I error level | 51 | 0.82258064516129 | NOK |
