| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 3.67573123516923 + 0.402023229674035X[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) | 3.67573123516923 | 0.649784 | 5.6568 | 0 | 0 |
| X | 0.402023229674035 | 0.074253 | 5.4143 | 1e-06 | 1e-06 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.579423898585698 |
| R-squared | 0.335732054252249 |
| Adjusted R-squared | 0.324279158635909 |
| F-TEST (value) | 29.3141634656340 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 58 |
| p-value | 1.2302241262363e-06 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.542502420533747 |
| Sum Squared Residuals | 17.0699148245285 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 8.1 | 8.05778443861623 | 0.0422155613837746 |
| 2 | 7.7 | 7.69596353190958 | 0.00403646809042381 |
| 3 | 7.5 | 7.37434494817035 | 0.12565505182965 |
| 4 | 7.6 | 7.37434494817035 | 0.225655051829650 |
| 5 | 7.8 | 7.49495191707256 | 0.305048082927439 |
| 6 | 7.8 | 7.53515424003996 | 0.264845759960036 |
| 7 | 7.8 | 7.49495191707256 | 0.305048082927439 |
| 8 | 7.5 | 7.33414262520295 | 0.165857374797053 |
| 9 | 7.5 | 7.25373797926814 | 0.24626202073186 |
| 10 | 7.1 | 7.29394030223554 | -0.193940302235544 |
| 11 | 7.5 | 7.73616585487698 | -0.236165854876981 |
| 12 | 7.5 | 7.81657050081179 | -0.316570500811789 |
| 13 | 7.6 | 7.77636817784438 | -0.176368177844385 |
| 14 | 7.7 | 7.53515424003996 | 0.164845759960036 |
| 15 | 7.7 | 7.37434494817035 | 0.32565505182965 |
| 16 | 7.9 | 7.41454727113775 | 0.485452728862246 |
| 17 | 8.1 | 7.45474959410516 | 0.645250405894842 |
| 18 | 8.2 | 7.45474959410516 | 0.745250405894842 |
| 19 | 8.2 | 7.37434494817035 | 0.82565505182965 |
| 20 | 8.2 | 7.29394030223554 | 0.906059697764456 |
| 21 | 7.9 | 7.29394030223554 | 0.606059697764457 |
| 22 | 7.3 | 7.29394030223554 | 0.00605969776445643 |
| 23 | 6.9 | 7.61555888597477 | -0.715558885974771 |
| 24 | 6.6 | 7.69596353190958 | -1.09596353190958 |
| 25 | 6.7 | 7.61555888597477 | -0.915558885974771 |
| 26 | 6.9 | 7.41454727113775 | -0.514547271137754 |
| 27 | 7 | 7.29394030223554 | -0.293940302235543 |
| 28 | 7.1 | 7.29394030223554 | -0.193940302235544 |
| 29 | 7.2 | 7.33414262520295 | -0.134142625202947 |
| 30 | 7.1 | 7.33414262520295 | -0.234142625202947 |
| 31 | 6.9 | 7.33414262520295 | -0.434142625202946 |
| 32 | 7 | 7.37434494817035 | -0.37434494817035 |
| 33 | 6.8 | 7.21353565630074 | -0.413535656300737 |
| 34 | 6.4 | 7.01252404146372 | -0.612524041463719 |
| 35 | 6.7 | 7.05272636443112 | -0.352726364431123 |
| 36 | 6.6 | 6.93211939552891 | -0.332119395528913 |
| 37 | 6.4 | 6.7713101036593 | -0.371310103659298 |
| 38 | 6.3 | 6.8517147495941 | -0.551714749594106 |
| 39 | 6.2 | 6.8517147495941 | -0.651714749594105 |
| 40 | 6.5 | 6.89191707256151 | -0.391917072561509 |
| 41 | 6.8 | 6.8517147495941 | -0.0517147495941058 |
| 42 | 6.8 | 6.7311077806919 | 0.0688922193081048 |
| 43 | 6.4 | 6.53009616585488 | -0.130096165854877 |
| 44 | 6.1 | 6.40948919695267 | -0.309489196952668 |
| 45 | 5.8 | 6.28888222805046 | -0.488882228050457 |
| 46 | 6.1 | 6.44969151992007 | -0.349691519920072 |
| 47 | 7.2 | 6.97232171849632 | 0.227678281503685 |
| 48 | 7.3 | 7.17333333333333 | 0.126666666666667 |
| 49 | 6.9 | 7.01252404146372 | -0.112524041463719 |
| 50 | 6.1 | 6.8517147495941 | -0.751714749594106 |
| 51 | 5.8 | 6.69090545772449 | -0.890905457724492 |
| 52 | 6.2 | 6.8115124266267 | -0.611512426626702 |
| 53 | 7.1 | 7.01252404146372 | 0.0874759585362801 |
| 54 | 7.7 | 7.05272636443112 | 0.647273635568877 |
| 55 | 7.9 | 6.97232171849632 | 0.927678281503685 |
| 56 | 7.7 | 6.7713101036593 | 0.928689896340702 |
| 57 | 7.4 | 6.57029848882228 | 0.829701511177719 |
| 58 | 7.5 | 6.61050081178968 | 0.889499188210315 |
| 59 | 8 | 6.93211939552891 | 1.06788060447109 |
| 60 | 8.1 | 7.09292868739853 | 1.00707131260147 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.0105822228305548 | 0.0211644456611096 | 0.989417777169445 |
| 6 | 0.00261828000294297 | 0.00523656000588594 | 0.997381719997057 |
| 7 | 0.000719650760157085 | 0.00143930152031417 | 0.999280349239843 |
| 8 | 0.000161031092502012 | 0.000322062185004024 | 0.999838968907498 |
| 9 | 2.60833088699367e-05 | 5.21666177398734e-05 | 0.99997391669113 |
| 10 | 0.000436205111084818 | 0.000872410222169637 | 0.999563794888915 |
| 11 | 0.000568543469934409 | 0.00113708693986882 | 0.999431456530066 |
| 12 | 0.0005673223903331 | 0.0011346447806662 | 0.999432677609667 |
| 13 | 0.000230805306514122 | 0.000461610613028245 | 0.999769194693486 |
| 14 | 7.9631048681344e-05 | 0.000159262097362688 | 0.999920368951319 |
| 15 | 3.50720239782191e-05 | 7.01440479564381e-05 | 0.999964927976022 |
| 16 | 3.84245944272907e-05 | 7.68491888545814e-05 | 0.999961575405573 |
| 17 | 0.000118759520151867 | 0.000237519040303735 | 0.999881240479848 |
| 18 | 0.000433305220527797 | 0.000866610441055594 | 0.999566694779472 |
| 19 | 0.00120583432926947 | 0.00241166865853894 | 0.99879416567073 |
| 20 | 0.00288250177360682 | 0.00576500354721365 | 0.997117498226393 |
| 21 | 0.0023419042188278 | 0.0046838084376556 | 0.997658095781172 |
| 22 | 0.00235399044557404 | 0.00470798089114808 | 0.997646009554426 |
| 23 | 0.00970699266533434 | 0.0194139853306687 | 0.990293007334666 |
| 24 | 0.0570089631166454 | 0.114017926233291 | 0.942991036883355 |
| 25 | 0.119812343004072 | 0.239624686008145 | 0.880187656995928 |
| 26 | 0.144435915875177 | 0.288871831750354 | 0.855564084124823 |
| 27 | 0.143101492697724 | 0.286202985395447 | 0.856898507302276 |
| 28 | 0.123740190872588 | 0.247480381745176 | 0.876259809127412 |
| 29 | 0.0974023760364813 | 0.194804752072963 | 0.902597623963519 |
| 30 | 0.080547860209265 | 0.16109572041853 | 0.919452139790735 |
| 31 | 0.0821027181097286 | 0.164205436219457 | 0.917897281890271 |
| 32 | 0.0768016100018586 | 0.153603220003717 | 0.923198389998141 |
| 33 | 0.0825417737943412 | 0.165083547588682 | 0.917458226205659 |
| 34 | 0.119524504654914 | 0.239049009309827 | 0.880475495345086 |
| 35 | 0.112992758302853 | 0.225985516605706 | 0.887007241697147 |
| 36 | 0.0997738475409641 | 0.199547695081928 | 0.900226152459036 |
| 37 | 0.0839493818229047 | 0.167898763645809 | 0.916050618177095 |
| 38 | 0.0880224310367037 | 0.176044862073407 | 0.911977568963296 |
| 39 | 0.107329784627382 | 0.214659569254765 | 0.892670215372618 |
| 40 | 0.0999621557543874 | 0.199924311508775 | 0.900037844245613 |
| 41 | 0.0736487294504937 | 0.147297458900987 | 0.926351270549506 |
| 42 | 0.051381245249576 | 0.102762490499152 | 0.948618754750424 |
| 43 | 0.0333019366956406 | 0.0666038733912812 | 0.96669806330436 |
| 44 | 0.0211217025272002 | 0.0422434050544004 | 0.9788782974728 |
| 45 | 0.0143217855820677 | 0.0286435711641354 | 0.985678214417932 |
| 46 | 0.0101977770995209 | 0.0203955541990418 | 0.98980222290048 |
| 47 | 0.00631289475979272 | 0.0126257895195854 | 0.993687105240207 |
| 48 | 0.00380806791567726 | 0.00761613583135452 | 0.996191932084323 |
| 49 | 0.00278007998291759 | 0.00556015996583518 | 0.997219920017082 |
| 50 | 0.0111947421952532 | 0.0223894843905064 | 0.988805257804747 |
| 51 | 0.113687444093367 | 0.227374888186734 | 0.886312555906633 |
| 52 | 0.763740294023648 | 0.472519411952704 | 0.236259705976352 |
| 53 | 0.988947078319696 | 0.0221058433606083 | 0.0110529216803042 |
| 54 | 0.999410312828243 | 0.00117937434351467 | 0.000589687171757336 |
| 55 | 0.99789148724512 | 0.00421702550976095 | 0.00210851275488048 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 21 | 0.411764705882353 | NOK |
| 5% type I error level | 29 | 0.568627450980392 | NOK |
| 10% type I error level | 30 | 0.588235294117647 | NOK |
