| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 0.989987872559212 + 0.559260034717772X[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) | 0.989987872559212 | 0.476845 | 2.0761 | 0.042325 | 0.021163 |
| X | 0.559260034717772 | 0.157282 | 3.5558 | 0.000758 | 0.000379 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.423057547683513 |
| R-squared | 0.178977688651988 |
| Adjusted R-squared | 0.164822131559781 |
| F-TEST (value) | 12.6436344035177 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 58 |
| p-value | 0.000758008081633177 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1.06648468124056 |
| Sum Squared Residuals | 65.9685953686052 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1.4 | 2.10850794199477 | -0.708507941994769 |
| 2 | 1.2 | 2.10850794199476 | -0.90850794199476 |
| 3 | 1 | 2.10850794199476 | -1.10850794199476 |
| 4 | 1.7 | 2.10850794199476 | -0.408507941994758 |
| 5 | 2.4 | 2.10850794199476 | 0.291492058005242 |
| 6 | 2 | 2.10850794199476 | -0.108507941994758 |
| 7 | 2.1 | 2.10850794199476 | -0.00850794199475767 |
| 8 | 2 | 2.10850794199476 | -0.108507941994758 |
| 9 | 1.8 | 2.10850794199476 | -0.308507941994758 |
| 10 | 2.7 | 2.10850794199476 | 0.591492058005242 |
| 11 | 2.3 | 2.10850794199476 | 0.191492058005242 |
| 12 | 1.9 | 2.10850794199476 | -0.208507941994758 |
| 13 | 2 | 2.10850794199476 | -0.108507941994758 |
| 14 | 2.3 | 2.10850794199476 | 0.191492058005242 |
| 15 | 2.8 | 2.10850794199476 | 0.691492058005242 |
| 16 | 2.4 | 2.10850794199476 | 0.291492058005242 |
| 17 | 2.3 | 2.10850794199476 | 0.191492058005242 |
| 18 | 2.7 | 2.10850794199476 | 0.591492058005242 |
| 19 | 2.7 | 2.10850794199476 | 0.591492058005242 |
| 20 | 2.9 | 2.10850794199476 | 0.791492058005242 |
| 21 | 3 | 2.10850794199476 | 0.891492058005242 |
| 22 | 2.2 | 2.10850794199476 | 0.0914920580052424 |
| 23 | 2.3 | 2.10850794199476 | 0.191492058005242 |
| 24 | 2.8 | 2.22595254928549 | 0.57404745071451 |
| 25 | 2.8 | 2.2483229506742 | 0.551677049325799 |
| 26 | 2.8 | 2.2483229506742 | 0.551677049325799 |
| 27 | 2.2 | 2.36017495761776 | -0.160174957617755 |
| 28 | 2.6 | 2.38813795935364 | 0.211862040646356 |
| 29 | 2.8 | 2.38813795935364 | 0.411862040646356 |
| 30 | 2.5 | 2.46643436421413 | 0.0335656357858682 |
| 31 | 2.4 | 2.52795296803309 | -0.127952968033087 |
| 32 | 2.3 | 2.62861977428229 | -0.328619774282286 |
| 33 | 1.9 | 2.66776797671253 | -0.76776797671253 |
| 34 | 1.7 | 2.76284218261455 | -1.06284218261455 |
| 35 | 2 | 2.80758298539197 | -0.807582985391972 |
| 36 | 2.1 | 2.88587939025246 | -0.78587939025246 |
| 37 | 1.7 | 2.94739799407142 | -1.24739799407142 |
| 38 | 1.8 | 2.94739799407142 | -1.14739799407142 |
| 39 | 1.8 | 3.03128699927908 | -1.23128699927908 |
| 40 | 1.8 | 3.08721300275086 | -1.28721300275086 |
| 41 | 1.3 | 3.08721300275086 | -1.78721300275086 |
| 42 | 1.3 | 3.17110200795852 | -1.87110200795852 |
| 43 | 1.3 | 3.2270280114303 | -1.9270280114303 |
| 44 | 1.2 | 3.2270280114303 | -2.0270280114303 |
| 45 | 1.4 | 3.2270280114303 | -1.8270280114303 |
| 46 | 2.2 | 3.2270280114303 | -1.02702801143030 |
| 47 | 2.9 | 3.2270280114303 | -0.327028011430301 |
| 48 | 3.1 | 3.2270280114303 | -0.127028011430301 |
| 49 | 3.5 | 3.2270280114303 | 0.272971988569699 |
| 50 | 3.6 | 3.2270280114303 | 0.372971988569699 |
| 51 | 4.4 | 3.2270280114303 | 1.1729719885697 |
| 52 | 4.1 | 3.2270280114303 | 0.872971988569698 |
| 53 | 5.1 | 3.2270280114303 | 1.87297198856970 |
| 54 | 5.8 | 3.2270280114303 | 2.5729719885697 |
| 55 | 5.9 | 3.3276948176795 | 2.5723051823205 |
| 56 | 5.4 | 3.36684302010974 | 2.03315697989026 |
| 57 | 5.5 | 3.36684302010974 | 2.13315697989026 |
| 58 | 4.8 | 3.21025021038877 | 1.58974978961123 |
| 59 | 3.2 | 2.90265719129399 | 0.297342808706007 |
| 60 | 2.7 | 2.52795296803309 | 0.172047031966914 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.200072967767426 | 0.400145935534852 | 0.799927032232574 |
| 6 | 0.112556220434799 | 0.225112440869599 | 0.8874437795652 |
| 7 | 0.0646251308724237 | 0.129250261744847 | 0.935374869127576 |
| 8 | 0.0314141943650823 | 0.0628283887301646 | 0.968585805634918 |
| 9 | 0.0129303919768203 | 0.0258607839536407 | 0.98706960802318 |
| 10 | 0.0191566888484000 | 0.0383133776967999 | 0.9808433111516 |
| 11 | 0.0109683541828002 | 0.0219367083656004 | 0.9890316458172 |
| 12 | 0.00470296536408427 | 0.00940593072816855 | 0.995297034635916 |
| 13 | 0.00195323651189147 | 0.00390647302378295 | 0.998046763488109 |
| 14 | 0.000999212390519086 | 0.00199842478103817 | 0.99900078760948 |
| 15 | 0.00128814032288588 | 0.00257628064577176 | 0.998711859677114 |
| 16 | 0.000674625381837698 | 0.00134925076367540 | 0.999325374618162 |
| 17 | 0.000304496085784720 | 0.000608992171569441 | 0.999695503914215 |
| 18 | 0.000239702238881494 | 0.000479404477762987 | 0.999760297761119 |
| 19 | 0.000173843275123097 | 0.000347686550246194 | 0.999826156724877 |
| 20 | 0.000177061399639548 | 0.000354122799279095 | 0.99982293860036 |
| 21 | 0.000203338303489169 | 0.000406676606978338 | 0.99979666169651 |
| 22 | 8.4902033518996e-05 | 0.000169804067037992 | 0.99991509796648 |
| 23 | 3.54032884184309e-05 | 7.08065768368618e-05 | 0.999964596711582 |
| 24 | 1.52146335384930e-05 | 3.04292670769861e-05 | 0.999984785366462 |
| 25 | 6.63575890205921e-06 | 1.32715178041184e-05 | 0.999993364241098 |
| 26 | 3.00114723492254e-06 | 6.00229446984507e-06 | 0.999996998852765 |
| 27 | 2.79922027178866e-06 | 5.59844054357731e-06 | 0.999997200779728 |
| 28 | 1.2171555156696e-06 | 2.4343110313392e-06 | 0.999998782844484 |
| 29 | 6.20558491794676e-07 | 1.24111698358935e-06 | 0.999999379441508 |
| 30 | 3.28208097868096e-07 | 6.56416195736192e-07 | 0.999999671791902 |
| 31 | 1.83652697894670e-07 | 3.67305395789341e-07 | 0.999999816347302 |
| 32 | 1.00992403915410e-07 | 2.01984807830820e-07 | 0.999999899007596 |
| 33 | 7.36703682021473e-08 | 1.47340736404295e-07 | 0.999999926329632 |
| 34 | 5.0938801869688e-08 | 1.01877603739376e-07 | 0.999999949061198 |
| 35 | 1.83197362199678e-08 | 3.66394724399356e-08 | 0.999999981680264 |
| 36 | 5.86017794595607e-09 | 1.17203558919121e-08 | 0.999999994139822 |
| 37 | 2.76940340495631e-09 | 5.53880680991261e-09 | 0.999999997230597 |
| 38 | 1.05147609657173e-09 | 2.10295219314346e-09 | 0.999999998948524 |
| 39 | 4.49973488474852e-10 | 8.99946976949704e-10 | 0.999999999550026 |
| 40 | 2.25935512652416e-10 | 4.51871025304831e-10 | 0.999999999774065 |
| 41 | 3.94265703448335e-10 | 7.8853140689667e-10 | 0.999999999605734 |
| 42 | 1.09970340046032e-09 | 2.19940680092065e-09 | 0.999999998900297 |
| 43 | 6.63395393669835e-09 | 1.32679078733967e-08 | 0.999999993366046 |
| 44 | 1.68162014191063e-07 | 3.36324028382127e-07 | 0.999999831837986 |
| 45 | 1.09723346631841e-05 | 2.19446693263683e-05 | 0.999989027665337 |
| 46 | 0.000319193710727251 | 0.000638387421454502 | 0.999680806289273 |
| 47 | 0.00501239223657857 | 0.0100247844731571 | 0.994987607763421 |
| 48 | 0.0497833902009396 | 0.0995667804018792 | 0.95021660979906 |
| 49 | 0.210380131697049 | 0.420760263394098 | 0.789619868302951 |
| 50 | 0.559563427171843 | 0.880873145656315 | 0.440436572828157 |
| 51 | 0.686497405892803 | 0.627005188214395 | 0.313502594107197 |
| 52 | 0.864145325325663 | 0.271709349348673 | 0.135854674674337 |
| 53 | 0.845683699729879 | 0.308632600540242 | 0.154316300270121 |
| 54 | 0.9222686651026 | 0.155462669794802 | 0.0777313348974008 |
| 55 | 0.942503322180677 | 0.114993355638646 | 0.0574966778193231 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 35 | 0.686274509803922 | NOK |
| 5% type I error level | 39 | 0.764705882352941 | NOK |
| 10% type I error level | 41 | 0.80392156862745 | NOK |
