| Multiple Linear Regression - Estimated Regression Equation |
| Y[t] = -1581.71366541556 + 17.1393927894853X[t] -1.45486092444313M1[t] -0.824024568713355M2[t] + 5.5934443397917M3[t] + 41.7883174989466M4[t] + 8.69965578100341M5[t] + 10.2346763403491M6[t] + 4.92475170042933M7[t] + 7.20871783851072M8[t] + 11.3211930468029M9[t] + 30.1172787296379M10[t] -3.60510496166605M11[t] -1.50025676429478t + 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) | -1581.71366541556 | 282.09094 | -5.6071 | 1e-06 | 1e-06 |
| X | 17.1393927894853 | 2.872522 | 5.9667 | 0 | 0 |
| M1 | -1.45486092444313 | 12.93169 | -0.1125 | 0.910903 | 0.455452 |
| M2 | -0.824024568713355 | 13.566718 | -0.0607 | 0.951825 | 0.475912 |
| M3 | 5.5934443397917 | 13.56087 | 0.4125 | 0.681871 | 0.340935 |
| M4 | 41.7883174989466 | 14.652208 | 2.852 | 0.006437 | 0.003218 |
| M5 | 8.69965578100341 | 13.534018 | 0.6428 | 0.523478 | 0.261739 |
| M6 | 10.2346763403491 | 13.514681 | 0.7573 | 0.45265 | 0.226325 |
| M7 | 4.92475170042933 | 13.525463 | 0.3641 | 0.717409 | 0.358705 |
| M8 | 7.20871783851072 | 13.524981 | 0.533 | 0.59655 | 0.298275 |
| M9 | 11.3211930468029 | 13.523237 | 0.8372 | 0.406736 | 0.203368 |
| M10 | 30.1172787296379 | 13.812041 | 2.1805 | 0.03426 | 0.01713 |
| M11 | -3.60510496166605 | 13.539742 | -0.2663 | 0.791203 | 0.395601 |
| t | -1.50025676429478 | 0.612783 | -2.4483 | 0.018142 | 0.009071 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.905968603940365 |
| R-squared | 0.820779111325654 |
| Adjusted R-squared | 0.771207376160409 |
| F-TEST (value) | 16.5574012809846 |
| F-TEST (DF numerator) | 13 |
| F-TEST (DF denominator) | 47 |
| p-value | 2.46247466861860e-13 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 21.3062643774529 |
| Sum Squared Residuals | 21335.9743809301 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 108.5 | 107.160679145797 | 1.33932085420329 |
| 2 | 112.3 | 103.377561963018 | 8.9224380369823 |
| 3 | 116.6 | 102.467380558803 | 14.1326194411971 |
| 4 | 115.5 | 115.223574183122 | 0.276425816878101 |
| 5 | 120.1 | 117.312956270382 | 2.78704372961763 |
| 6 | 132.9 | 127.459961811230 | 5.44003818877033 |
| 7 | 128.1 | 123.563477181227 | 4.53652281877262 |
| 8 | 129.3 | 127.260883329227 | 2.03911667077351 |
| 9 | 132.5 | 135.700495321649 | -3.20049532164891 |
| 10 | 131 | 135.514143594914 | -4.51414359491423 |
| 11 | 124.9 | 130.971016232494 | -6.071016232494 |
| 12 | 120.8 | 133.075864429865 | -12.2758644298653 |
| 13 | 122 | 127.207049966915 | -5.20704996691508 |
| 14 | 122.1 | 124.966478135191 | -2.86647813519102 |
| 15 | 127.4 | 131.254841702560 | -3.85484170256033 |
| 16 | 135.2 | 143.154065687405 | -7.95406568740485 |
| 17 | 137.3 | 147.642962765193 | -10.3429627651933 |
| 18 | 135 | 146.477969064980 | -11.4779690649804 |
| 19 | 136 | 149.437241550772 | -13.4372415507723 |
| 20 | 138.4 | 156.391132328774 | -17.9911323287736 |
| 21 | 134.7 | 160.374502195930 | -25.6745021959297 |
| 22 | 138.4 | 158.816999046036 | -20.4169990460363 |
| 23 | 133.9 | 153.588295972037 | -19.6882959720368 |
| 24 | 133.6 | 147.294841702560 | -13.6948417025603 |
| 25 | 141.2 | 139.197906176977 | 2.00209382302308 |
| 26 | 151.8 | 142.099152182099 | 9.7008478179014 |
| 27 | 155.4 | 149.244485388942 | 6.1555146110581 |
| 28 | 156.6 | 154.116558330098 | 2.48344166990224 |
| 29 | 161.6 | 160.662182542624 | 0.937817457375732 |
| 30 | 160.7 | 160.525552409781 | 0.174447590219479 |
| 31 | 156 | 162.627855256098 | -6.62785525609819 |
| 32 | 159.5 | 161.354837495146 | -1.85483749514650 |
| 33 | 168.7 | 165.338207362303 | 3.36179263769735 |
| 34 | 169.9 | 163.609310284514 | 6.29068971548574 |
| 35 | 169.9 | 155.981092219987 | 13.9189077800132 |
| 36 | 185.9 | 154.658061859461 | 31.2419381405390 |
| 37 | 190.8 | 160.101246637571 | 30.698753362429 |
| 38 | 195.8 | 174.657279739543 | 21.1427202604575 |
| 39 | 211.9 | 186.087461143757 | 25.8125388562426 |
| 40 | 227.1 | 197.301109417023 | 29.7988905829774 |
| 41 | 251.3 | 206.931824331657 | 44.3681756683434 |
| 42 | 256.7 | 220.506708430401 | 36.193291569599 |
| 43 | 251.9 | 217.467193439873 | 34.4328065601268 |
| 44 | 251.2 | 234.361932035776 | 16.8380679642241 |
| 45 | 270.3 | 250.000088999782 | 20.2999110002179 |
| 46 | 267.2 | 249.813737273047 | 17.3862627269528 |
| 47 | 243 | 234.301398525357 | 8.69860147464335 |
| 48 | 229.9 | 234.520913515885 | -4.62091351588456 |
| 49 | 187.2 | 228.480705125039 | -41.2807051250392 |
| 50 | 178.2 | 215.09952798015 | -36.8995279801501 |
| 51 | 175.2 | 217.445831205937 | -42.2458312059375 |
| 52 | 192.4 | 217.004692382353 | -24.6046923823529 |
| 53 | 187 | 224.750074090143 | -37.7500740901435 |
| 54 | 184 | 214.329808283608 | -30.3298082836084 |
| 55 | 194.1 | 213.004232572029 | -18.904232572029 |
| 56 | 212.7 | 211.731214811078 | 0.968785188922443 |
| 57 | 217.5 | 212.286706120337 | 5.21329387966342 |
| 58 | 200.5 | 199.245809801488 | 1.25419019851200 |
| 59 | 205.9 | 202.758197050126 | 3.14180294987420 |
| 60 | 196.5 | 197.150318492229 | -0.65031849222889 |
| 61 | 206.3 | 193.852412947701 | 12.4475870522989 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 17 | 0.00212462027808544 | 0.00424924055617088 | 0.997875379721915 |
| 18 | 0.000692759857787616 | 0.00138551971557523 | 0.999307240142212 |
| 19 | 0.000135820792718360 | 0.000271641585436719 | 0.999864179207282 |
| 20 | 3.01176146051441e-05 | 6.02352292102883e-05 | 0.999969882385395 |
| 21 | 1.5122937970789e-05 | 3.0245875941578e-05 | 0.99998487706203 |
| 22 | 2.66196150550665e-06 | 5.32392301101329e-06 | 0.999997338038495 |
| 23 | 4.89844127617984e-07 | 9.79688255235967e-07 | 0.999999510155872 |
| 24 | 2.75890669522639e-07 | 5.51781339045279e-07 | 0.99999972410933 |
| 25 | 3.17759141901912e-07 | 6.35518283803824e-07 | 0.999999682240858 |
| 26 | 9.41698248552693e-07 | 1.88339649710539e-06 | 0.999999058301752 |
| 27 | 8.36624539081892e-07 | 1.67324907816378e-06 | 0.99999916337546 |
| 28 | 2.4593381047624e-07 | 4.9186762095248e-07 | 0.99999975406619 |
| 29 | 9.530040488934e-08 | 1.9060080977868e-07 | 0.999999904699595 |
| 30 | 2.24664589048073e-08 | 4.49329178096146e-08 | 0.999999977533541 |
| 31 | 7.9373040972106e-09 | 1.58746081944212e-08 | 0.999999992062696 |
| 32 | 3.40417084429783e-09 | 6.80834168859566e-09 | 0.99999999659583 |
| 33 | 2.60978357669981e-09 | 5.21956715339962e-09 | 0.999999997390216 |
| 34 | 2.88085556322412e-09 | 5.76171112644824e-09 | 0.999999997119144 |
| 35 | 9.18010066600592e-09 | 1.83602013320118e-08 | 0.9999999908199 |
| 36 | 9.74112769617927e-07 | 1.94822553923585e-06 | 0.99999902588723 |
| 37 | 0.000374097117799097 | 0.000748194235598194 | 0.9996259028822 |
| 38 | 0.00583504778395467 | 0.0116700955679093 | 0.994164952216045 |
| 39 | 0.0201564796083976 | 0.0403129592167952 | 0.979843520391602 |
| 40 | 0.0490322668703238 | 0.0980645337406477 | 0.950967733129676 |
| 41 | 0.0700843453675452 | 0.140168690735090 | 0.929915654632455 |
| 42 | 0.0724986856499544 | 0.144997371299909 | 0.927501314350046 |
| 43 | 0.0927558348738917 | 0.185511669747783 | 0.907244165126108 |
| 44 | 0.0991995667485483 | 0.198399133497097 | 0.900800433251452 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 21 | 0.75 | NOK |
| 5% type I error level | 23 | 0.821428571428571 | NOK |
| 10% type I error level | 24 | 0.857142857142857 | NOK |
