| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 474.520005774436 + 4.55427432377876X[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) | 474.520005774436 | 26.059968 | 18.2088 | 0 | 0 |
| X | 4.55427432377876 | 1.37548 | 3.311 | 0.00159 | 0.000795 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.395849908365107 |
| R-squared | 0.156697149952664 |
| Adjusted R-squared | 0.142403881307794 |
| F-TEST (value) | 10.9630032042323 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 59 |
| p-value | 0.00158966552042294 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 38.7250875640675 |
| Sum Squared Residuals | 88478.312003837 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 562 | 537.824418874961 | 24.1755811250391 |
| 2 | 561 | 546.932967522519 | 14.0670324774813 |
| 3 | 555 | 557.40779846721 | -2.40779846720980 |
| 4 | 544 | 564.239209952878 | -20.2392099528779 |
| 5 | 537 | 566.06091968239 | -29.0609196823895 |
| 6 | 543 | 565.150064817634 | -22.1500648176337 |
| 7 | 594 | 565.605492250012 | 28.3945077499884 |
| 8 | 611 | 577.446605491836 | 33.5533945081636 |
| 9 | 613 | 568.338056844279 | 44.6619431557212 |
| 10 | 611 | 566.06091968239 | 44.9390803176105 |
| 11 | 594 | 566.516347114767 | 27.4836528852327 |
| 12 | 595 | 573.803186032813 | 21.1968139671866 |
| 13 | 591 | 574.714040897569 | 16.2859591024309 |
| 14 | 589 | 563.328355088122 | 25.6716449118778 |
| 15 | 584 | 554.219806440565 | 29.7801935594353 |
| 16 | 573 | 557.40779846721 | 15.5922015327902 |
| 17 | 567 | 560.140363061477 | 6.85963693852293 |
| 18 | 569 | 564.239209952878 | 4.76079004712205 |
| 19 | 621 | 560.140363061477 | 60.8596369385229 |
| 20 | 629 | 558.774080764343 | 70.2259192356566 |
| 21 | 628 | 559.684935629099 | 68.3150643709008 |
| 22 | 612 | 558.774080764343 | 53.2259192356566 |
| 23 | 595 | 562.417500223366 | 32.5824997766335 |
| 24 | 597 | 560.595790493855 | 36.4042095061451 |
| 25 | 593 | 571.981476303302 | 21.0185236966982 |
| 26 | 590 | 576.991178059458 | 13.0088219405415 |
| 27 | 580 | 588.376863868905 | -8.3768638689054 |
| 28 | 574 | 578.81288778897 | -4.81288778896999 |
| 29 | 573 | 578.81288778897 | -5.81288778896999 |
| 30 | 573 | 571.526048870924 | 1.47395112907602 |
| 31 | 620 | 576.080323194703 | 43.9196768052973 |
| 32 | 626 | 569.704339141412 | 56.2956608585875 |
| 33 | 620 | 565.150064817634 | 54.8499351823663 |
| 34 | 588 | 566.516347114767 | 21.4836528852327 |
| 35 | 566 | 564.694637385256 | 1.30536261474417 |
| 36 | 557 | 555.13066130532 | 1.86933869467958 |
| 37 | 561 | 556.952371034832 | 4.04762896516806 |
| 38 | 549 | 554.675233872942 | -5.67523387294256 |
| 39 | 532 | 557.40779846721 | -25.4077984672098 |
| 40 | 526 | 547.388394954897 | -21.3883949548965 |
| 41 | 511 | 548.75467725203 | -37.7546772520302 |
| 42 | 499 | 553.308951575809 | -54.3089515758089 |
| 43 | 555 | 561.051217926233 | -6.05121792623282 |
| 44 | 565 | 559.229508196721 | 5.77049180327868 |
| 45 | 542 | 556.496943602454 | -14.4969436024541 |
| 46 | 527 | 556.041516170076 | -29.0415161700762 |
| 47 | 510 | 555.586088737698 | -45.5860887376983 |
| 48 | 514 | 558.774080764343 | -44.7740807643434 |
| 49 | 517 | 553.764379008187 | -36.7643790081868 |
| 50 | 508 | 561.051217926233 | -53.0512179262328 |
| 51 | 493 | 553.764379008187 | -60.7643790081868 |
| 52 | 490 | 568.338056844279 | -78.3380568442788 |
| 53 | 469 | 558.774080764343 | -89.7740807643434 |
| 54 | 478 | 565.605492250012 | -87.6054922500116 |
| 55 | 528 | 560.140363061477 | -32.1403630614771 |
| 56 | 534 | 560.140363061477 | -26.1403630614771 |
| 57 | 518 | 564.239209952878 | -46.2392099528779 |
| 58 | 506 | 544.200402928251 | -38.2004029282514 |
| 59 | 502 | 522.795313606491 | -20.7953136064912 |
| 60 | 516 | 502.301079149487 | 13.6989208505132 |
| 61 | 528 | 478.618852665837 | 49.3811473341628 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.00299330295407347 | 0.00598660590814694 | 0.997006697045927 |
| 6 | 0.000314382321867891 | 0.000628764643735783 | 0.999685617678132 |
| 7 | 0.0667740025018575 | 0.133548005003715 | 0.933225997498143 |
| 8 | 0.145755564676377 | 0.291511129352754 | 0.854244435323623 |
| 9 | 0.180519849332671 | 0.361039698665342 | 0.819480150667329 |
| 10 | 0.184933350353786 | 0.369866700707572 | 0.815066649646214 |
| 11 | 0.130239759137240 | 0.260479518274480 | 0.86976024086276 |
| 12 | 0.0826842738850585 | 0.165368547770117 | 0.917315726114942 |
| 13 | 0.0493985558999449 | 0.0987971117998897 | 0.950601444100055 |
| 14 | 0.0310960078744596 | 0.0621920157489192 | 0.96890399212554 |
| 15 | 0.0208907221296325 | 0.0417814442592650 | 0.979109277870368 |
| 16 | 0.0114322989793561 | 0.0228645979587121 | 0.988567701020644 |
| 17 | 0.00620090904245518 | 0.0124018180849104 | 0.993799090957545 |
| 18 | 0.00334334176185157 | 0.00668668352370314 | 0.996656658238148 |
| 19 | 0.00871659126913478 | 0.0174331825382696 | 0.991283408730865 |
| 20 | 0.0279014305250720 | 0.0558028610501441 | 0.972098569474928 |
| 21 | 0.0615776613444012 | 0.123155322688802 | 0.938422338655599 |
| 22 | 0.0753034798717058 | 0.150606959743412 | 0.924696520128294 |
| 23 | 0.0628692845740217 | 0.125738569148043 | 0.937130715425978 |
| 24 | 0.0566738966209028 | 0.113347793241806 | 0.943326103379097 |
| 25 | 0.044301957064568 | 0.088603914129136 | 0.955698042935432 |
| 26 | 0.0336421861491779 | 0.0672843722983558 | 0.966357813850822 |
| 27 | 0.0260873439701704 | 0.0521746879403409 | 0.97391265602983 |
| 28 | 0.0195362963008291 | 0.0390725926016582 | 0.980463703699171 |
| 29 | 0.0143400482439805 | 0.0286800964879611 | 0.98565995175602 |
| 30 | 0.0104762727372787 | 0.0209525454745573 | 0.989523727262721 |
| 31 | 0.0224935745379435 | 0.0449871490758869 | 0.977506425462057 |
| 32 | 0.0851535323272297 | 0.170307064654459 | 0.91484646767277 |
| 33 | 0.285685153093215 | 0.57137030618643 | 0.714314846906785 |
| 34 | 0.414129076528555 | 0.82825815305711 | 0.585870923471445 |
| 35 | 0.484801502510684 | 0.969603005021367 | 0.515198497489316 |
| 36 | 0.536716600997166 | 0.926566798005667 | 0.463283399002834 |
| 37 | 0.621673294422018 | 0.756653411155965 | 0.378326705577982 |
| 38 | 0.671867052195312 | 0.656265895609375 | 0.328132947804688 |
| 39 | 0.705188553571087 | 0.589622892857826 | 0.294811446428913 |
| 40 | 0.702476896801277 | 0.595046206397446 | 0.297523103198723 |
| 41 | 0.717574790302602 | 0.564850419394797 | 0.282425209697399 |
| 42 | 0.773674835324355 | 0.45265032935129 | 0.226325164675645 |
| 43 | 0.831524957763732 | 0.336950084472537 | 0.168475042236268 |
| 44 | 0.945691693087483 | 0.108616613825034 | 0.0543083069125169 |
| 45 | 0.966918497185705 | 0.0661630056285898 | 0.0330815028142949 |
| 46 | 0.967874566137706 | 0.0642508677245883 | 0.0321254338622942 |
| 47 | 0.959018795662236 | 0.0819624086755287 | 0.0409812043377643 |
| 48 | 0.94906788786092 | 0.101864224278158 | 0.0509321121390792 |
| 49 | 0.932312552468493 | 0.135374895063014 | 0.0676874475315071 |
| 50 | 0.911964508335428 | 0.176070983329143 | 0.0880354916645716 |
| 51 | 0.887019524495885 | 0.22596095100823 | 0.112980475504115 |
| 52 | 0.873996066000006 | 0.252007867999988 | 0.126003933999994 |
| 53 | 0.947309124613964 | 0.105381750772072 | 0.0526908753860359 |
| 54 | 0.988857825983778 | 0.0222843480324437 | 0.0111421740162219 |
| 55 | 0.971641875378966 | 0.0567162492420685 | 0.0283581246210342 |
| 56 | 0.97348787288619 | 0.0530242542276203 | 0.0265121271138101 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 3 | 0.0576923076923077 | NOK |
| 5% type I error level | 12 | 0.230769230769231 | NOK |
| 10% type I error level | 23 | 0.442307692307692 | NOK |
