| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = + 100.808693644493 -0.421986537277549X[t] + 1.28993303416181M1[t] + 3.17167550485208M2[t] + 12.8478278608285M3[t] + 6.35093055337301M4[t] + 5.48625841420152M5[t] + 13.2690597604738M6[t] -10.4210993268639M7[t] -0.736125841420165M8[t] + 13.6835993268639M9[t] + 15.5769503365680M10[t] + 7.57947685112434M11[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) | 100.808693644493 | 6.11349 | 16.4895 | 0 | 0 |
| X | -0.421986537277549 | 0.735183 | -0.574 | 0.567509 | 0.283755 |
| M1 | 1.28993303416181 | 2.623095 | 0.4918 | 0.624172 | 0.312086 |
| M2 | 3.17167550485208 | 2.699231 | 1.175 | 0.243303 | 0.121652 |
| M3 | 12.8478278608285 | 2.703607 | 4.7521 | 8e-06 | 4e-06 |
| M4 | 6.35093055337301 | 2.716073 | 2.3383 | 0.02175 | 0.010875 |
| M5 | 5.48625841420152 | 2.737922 | 2.0038 | 0.048314 | 0.024157 |
| M6 | 13.2690597604738 | 2.751215 | 4.823 | 6e-06 | 3e-06 |
| M7 | -10.4210993268639 | 2.69934 | -3.8606 | 0.000221 | 0.000111 |
| M8 | -0.736125841420165 | 2.699481 | -0.2727 | 0.78576 | 0.39288 |
| M9 | 13.6835993268639 | 2.69934 | 5.0692 | 2e-06 | 1e-06 |
| M10 | 15.5769503365680 | 2.699153 | 5.7711 | 0 | 0 |
| M11 | 7.57947685112434 | 2.700982 | 2.8062 | 0.006229 | 0.003115 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.823138113126992 |
| R-squared | 0.677556353282265 |
| Adjusted R-squared | 0.631492975179731 |
| F-TEST (value) | 14.7092198009029 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 84 |
| p-value | 4.44089209850063e-16 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 5.3981798736166 |
| Sum Squared Residuals | 2447.78905962523 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 98.8 | 99.440111493805 | -0.64011149380493 |
| 2 | 100.5 | 101.406251271952 | -0.906251271951684 |
| 3 | 110.4 | 111.082403627928 | -0.682403627928092 |
| 4 | 96.4 | 104.501109013017 | -8.1011090130171 |
| 5 | 101.9 | 103.636436873846 | -1.73643687384559 |
| 6 | 106.2 | 111.545834181301 | -5.34583418130114 |
| 7 | 81 | 87.771277786508 | -6.77127778650797 |
| 8 | 94.7 | 97.3718539644962 | -2.67185396449618 |
| 9 | 101 | 111.622784517869 | -10.6227845178692 |
| 10 | 109.4 | 113.220744951479 | -3.82074495147908 |
| 11 | 102.3 | 105.223271466035 | -2.92327146603534 |
| 12 | 90.7 | 97.6015959611832 | -6.90159596118324 |
| 13 | 96.2 | 98.891528995345 | -2.6915289953451 |
| 14 | 96.1 | 100.857668773491 | -4.75766877349087 |
| 15 | 106 | 110.576019783195 | -4.57601978319505 |
| 16 | 103.1 | 104.163519783195 | -1.06351978319505 |
| 17 | 102 | 103.383244951479 | -1.38324495147908 |
| 18 | 104.7 | 111.208244951479 | -6.50824495147908 |
| 19 | 86 | 87.2226952880471 | -1.22269528804714 |
| 20 | 92.1 | 96.8654701197631 | -4.76547011976311 |
| 21 | 106.9 | 111.200797980592 | -4.30079798059163 |
| 22 | 112.6 | 113.009751682840 | -0.409751682840315 |
| 23 | 101.7 | 104.970079543669 | -3.27007954366883 |
| 24 | 92 | 97.3484040388167 | -5.34840403881674 |
| 25 | 97.4 | 98.5961384192508 | -1.19613841925080 |
| 26 | 97 | 100.520079543669 | -3.52007954366882 |
| 27 | 105.4 | 110.280629207101 | -4.88062920710076 |
| 28 | 102.7 | 103.825930553373 | -1.12593055337301 |
| 29 | 98.1 | 103.087854375385 | -4.9878543753848 |
| 30 | 104.5 | 110.870655721657 | -6.37065572165704 |
| 31 | 87.4 | 86.8851060582251 | 0.514893941774906 |
| 32 | 89.9 | 96.527880889941 | -6.62788088994106 |
| 33 | 109.8 | 110.947606058225 | -1.14760605822511 |
| 34 | 111.7 | 112.840957067929 | -1.14095706792928 |
| 35 | 98.6 | 104.843483582486 | -6.24348358248557 |
| 36 | 96.9 | 97.1796094239057 | -0.279609423905713 |
| 37 | 95.1 | 98.3429464968843 | -3.24294649688429 |
| 38 | 97 | 100.266887621302 | -3.26688762130230 |
| 39 | 112.7 | 110.154033245918 | 2.5459667540825 |
| 40 | 102.9 | 103.994725168284 | -1.09472516828402 |
| 41 | 97.4 | 103.256648990296 | -5.85664899029581 |
| 42 | 111.4 | 110.955053029113 | 0.444946970887453 |
| 43 | 87.4 | 86.6741127895863 | 0.725887210413681 |
| 44 | 96.8 | 96.1480930063913 | 0.651906993608724 |
| 45 | 114.1 | 110.567818174675 | 3.53218182532468 |
| 46 | 110.3 | 112.714361106746 | -2.41436110674603 |
| 47 | 103.9 | 104.927880889941 | -1.02788088994107 |
| 48 | 101.6 | 97.306205385089 | 4.29379461491101 |
| 49 | 94.6 | 98.5117411117953 | -3.9117411117953 |
| 50 | 95.9 | 100.351284928758 | -4.45128492875780 |
| 51 | 104.7 | 110.069635938462 | -5.36963593846199 |
| 52 | 102.8 | 103.699334592190 | -0.899334592189746 |
| 53 | 98.1 | 102.876861106746 | -4.77686110674603 |
| 54 | 113.9 | 110.744059760474 | 3.15594023952623 |
| 55 | 80.9 | 86.7585100970418 | -5.85851009704183 |
| 56 | 95.7 | 96.4012849287578 | -0.701284928757804 |
| 57 | 113.2 | 110.821010097042 | 2.37898990295816 |
| 58 | 105.9 | 112.798758414202 | -6.89875841420153 |
| 59 | 108.8 | 104.843483582486 | 3.95651641751443 |
| 60 | 102.3 | 97.2218080776335 | 5.07819192236652 |
| 61 | 99 | 98.4273438043398 | 0.572656195660208 |
| 62 | 100.7 | 100.30908627503 | 0.390913724969953 |
| 63 | 115.5 | 110.027437284734 | 5.47256271526576 |
| 64 | 100.7 | 103.572738631006 | -2.87273863100648 |
| 65 | 109.9 | 102.792463799291 | 7.10753620070949 |
| 66 | 114.6 | 110.701861106746 | 3.89813889325398 |
| 67 | 85.4 | 86.9273047119529 | -1.52730471195285 |
| 68 | 100.5 | 96.6544768511243 | 3.84552314887567 |
| 69 | 114.8 | 111.074202019408 | 3.72579798059163 |
| 70 | 116.5 | 113.009751682840 | 3.49024831715969 |
| 71 | 112.9 | 105.054476851124 | 7.84552314887566 |
| 72 | 102 | 97.475 | 4.52499999999999 |
| 73 | 106 | 98.722734380434 | 7.27726561956593 |
| 74 | 105.3 | 100.604476851124 | 4.69552314887566 |
| 75 | 118.8 | 110.322827860829 | 8.47717213917147 |
| 76 | 106.1 | 103.783731899645 | 2.31626810035474 |
| 77 | 109.3 | 103.045655721657 | 6.25434427834296 |
| 78 | 117.2 | 111.039450336568 | 6.16054966343194 |
| 79 | 92.5 | 87.2226952880471 | 5.27730471195286 |
| 80 | 104.2 | 96.9920660809464 | 7.20793391905363 |
| 81 | 112.5 | 111.538387210414 | 0.961612789586324 |
| 82 | 122.4 | 113.431738220118 | 8.96826177988215 |
| 83 | 113.3 | 105.434264734674 | 7.86573526532586 |
| 84 | 100 | 97.7703905760943 | 2.22960942390571 |
| 85 | 110.7 | 99.0181249565284 | 11.6818750434716 |
| 86 | 112.8 | 100.984264734674 | 11.8157352653259 |
| 87 | 109.8 | 110.787013051834 | -0.987013051833833 |
| 88 | 117.3 | 104.458910359289 | 12.8410896407107 |
| 89 | 109.1 | 103.720834181301 | 5.37916581869887 |
| 90 | 115.9 | 111.334840912662 | 4.56515908733766 |
| 91 | 96 | 87.1382979805916 | 8.86170201940837 |
| 92 | 99.8 | 96.7388741585798 | 3.06112584142015 |
| 93 | 116.8 | 111.327393941775 | 5.4726060582251 |
| 94 | 115.7 | 113.473936873846 | 2.22606312615439 |
| 95 | 99.4 | 105.603059349585 | -6.20305934958515 |
| 96 | 94.3 | 97.8969865372776 | -3.59698653727756 |
| 97 | 91 | 98.8493303416173 | -7.84933034161734 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.293730444507971 | 0.587460889015942 | 0.706269555492029 |
| 17 | 0.158249967339331 | 0.316499934678662 | 0.841750032660669 |
| 18 | 0.0839358006837008 | 0.167871601367402 | 0.916064199316299 |
| 19 | 0.101745477994550 | 0.203490955989100 | 0.89825452200545 |
| 20 | 0.0615388342185457 | 0.123077668437091 | 0.938461165781454 |
| 21 | 0.0769674978779492 | 0.153934995755898 | 0.92303250212205 |
| 22 | 0.0510950549135213 | 0.102190109827043 | 0.948904945086479 |
| 23 | 0.0279842888753446 | 0.0559685777506892 | 0.972015711124655 |
| 24 | 0.0162221938317037 | 0.0324443876634073 | 0.983777806168296 |
| 25 | 0.0080679249614446 | 0.0161358499228892 | 0.991932075038555 |
| 26 | 0.00439178142147315 | 0.0087835628429463 | 0.995608218578527 |
| 27 | 0.00299515663886491 | 0.00599031327772983 | 0.997004843361135 |
| 28 | 0.00211388486199971 | 0.00422776972399941 | 0.997886115138 |
| 29 | 0.00186274383235201 | 0.00372548766470402 | 0.998137256167648 |
| 30 | 0.00122103273722899 | 0.00244206547445798 | 0.998778967262771 |
| 31 | 0.00111364143568897 | 0.00222728287137793 | 0.99888635856431 |
| 32 | 0.00111255422252478 | 0.00222510844504956 | 0.998887445777475 |
| 33 | 0.00188579054956729 | 0.00377158109913458 | 0.998114209450433 |
| 34 | 0.000965181632262513 | 0.00193036326452503 | 0.999034818367738 |
| 35 | 0.000865796511221119 | 0.00173159302244224 | 0.99913420348878 |
| 36 | 0.00109446410095447 | 0.00218892820190895 | 0.998905535899046 |
| 37 | 0.000703053261031495 | 0.00140610652206299 | 0.999296946738969 |
| 38 | 0.000404431114824305 | 0.00080886222964861 | 0.999595568885176 |
| 39 | 0.000528702032005832 | 0.00105740406401166 | 0.999471297967994 |
| 40 | 0.000344619050986396 | 0.000689238101972791 | 0.999655380949014 |
| 41 | 0.000456954741542652 | 0.000913909483085304 | 0.999543045258457 |
| 42 | 0.000776226134315593 | 0.00155245226863119 | 0.999223773865684 |
| 43 | 0.000464976044477627 | 0.000929952088955254 | 0.999535023955522 |
| 44 | 0.000350455147675001 | 0.000700910295350001 | 0.999649544852325 |
| 45 | 0.00071084351105 | 0.0014216870221 | 0.99928915648895 |
| 46 | 0.000408746931639050 | 0.000817493863278101 | 0.999591253068361 |
| 47 | 0.000273276837968217 | 0.000546553675936434 | 0.999726723162032 |
| 48 | 0.00074292430634312 | 0.00148584861268624 | 0.999257075693657 |
| 49 | 0.000596688630745976 | 0.00119337726149195 | 0.999403311369254 |
| 50 | 0.000617542804768237 | 0.00123508560953647 | 0.999382457195232 |
| 51 | 0.000868382569683474 | 0.00173676513936695 | 0.999131617430317 |
| 52 | 0.000542391856141581 | 0.00108478371228316 | 0.999457608143858 |
| 53 | 0.0007145580035043 | 0.0014291160070086 | 0.999285441996496 |
| 54 | 0.000913366723759769 | 0.00182673344751954 | 0.99908663327624 |
| 55 | 0.00159257323656935 | 0.00318514647313869 | 0.99840742676343 |
| 56 | 0.00111099697977535 | 0.0022219939595507 | 0.998889003020225 |
| 57 | 0.000929338477844018 | 0.00185867695568804 | 0.999070661522156 |
| 58 | 0.00234015785324282 | 0.00468031570648564 | 0.997659842146757 |
| 59 | 0.00280509302944386 | 0.00561018605888773 | 0.997194906970556 |
| 60 | 0.00386202267103595 | 0.00772404534207189 | 0.996137977328964 |
| 61 | 0.00247489566949674 | 0.00494979133899349 | 0.997525104330503 |
| 62 | 0.00237994471572415 | 0.0047598894314483 | 0.997620055284276 |
| 63 | 0.00260590131182205 | 0.00521180262364411 | 0.997394098688178 |
| 64 | 0.00392825125522085 | 0.0078565025104417 | 0.99607174874478 |
| 65 | 0.00588959122609823 | 0.0117791824521965 | 0.994110408773902 |
| 66 | 0.00470473488681766 | 0.00940946977363532 | 0.995295265113182 |
| 67 | 0.00568855134245127 | 0.0113771026849025 | 0.994311448657549 |
| 68 | 0.00511168619090299 | 0.0102233723818060 | 0.994888313809097 |
| 69 | 0.00401205661588896 | 0.00802411323177793 | 0.995987943384111 |
| 70 | 0.00364850683525539 | 0.00729701367051078 | 0.996351493164745 |
| 71 | 0.00686481005235964 | 0.0137296201047193 | 0.99313518994764 |
| 72 | 0.00650494174212236 | 0.0130098834842447 | 0.993495058257878 |
| 73 | 0.00876539451257772 | 0.0175307890251554 | 0.991234605487422 |
| 74 | 0.00907420549480598 | 0.0181484109896120 | 0.990925794505194 |
| 75 | 0.0189444008239603 | 0.0378888016479207 | 0.98105559917604 |
| 76 | 0.0219144817452674 | 0.0438289634905348 | 0.978085518254733 |
| 77 | 0.0151777285515092 | 0.0303554571030185 | 0.98482227144849 |
| 78 | 0.0101026945427356 | 0.0202053890854711 | 0.989897305457264 |
| 79 | 0.00692290957370739 | 0.0138458191474148 | 0.993077090426293 |
| 80 | 0.00545554672740167 | 0.0109110934548033 | 0.994544453272598 |
| 81 | 0.00236411698880378 | 0.00472823397760755 | 0.997635883011196 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 43 | 0.651515151515151 | NOK |
| 5% type I error level | 58 | 0.878787878787879 | NOK |
| 10% type I error level | 59 | 0.893939393939394 | NOK |
