| Multiple Linear Regression - Estimated Regression Equation |
| PSS [t] = + 17.5056184987946 -0.171507752660075month[t] -1.15792639251861IDT[t] + 0.874466763783772TGYW[t] -0.284405176049271POP[t] -0.0459412607388271t + 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) | 17.5056184987946 | 2.879982 | 6.0784 | 0 | 0 |
| month | -0.171507752660075 | 0.233938 | -0.7331 | 0.466332 | 0.233166 |
| IDT | -1.15792639251861 | 0.246396 | -4.6995 | 1.6e-05 | 8e-06 |
| TGYW | 0.874466763783772 | 0.254737 | 3.4328 | 0.001088 | 0.000544 |
| POP | -0.284405176049271 | 0.148417 | -1.9163 | 0.060099 | 0.03005 |
| t | -0.0459412607388271 | 0.017736 | -2.5903 | 0.012018 | 0.006009 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.895825388051245 |
| R-squared | 0.802503125877163 |
| Adjusted R-squared | 0.786045053033594 |
| F-TEST (value) | 48.7604553403533 |
| F-TEST (DF numerator) | 5 |
| F-TEST (DF denominator) | 60 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 1.53745837144318 |
| Sum Squared Residuals | 141.826694635242 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 14 | 15.6548446183306 | -1.65484461833064 |
| 2 | 18 | 16.7677752974248 | 1.23222470257517 |
| 3 | 11 | 12.372642548032 | -1.37264254803197 |
| 4 | 12 | 13.4846276798118 | -1.48462767981175 |
| 5 | 16 | 15.4720251226897 | 0.527974877310261 |
| 6 | 18 | 16.5840102544695 | 1.41598974553048 |
| 7 | 14 | 13.9378110326442 | 0.0621889673557955 |
| 8 | 14 | 14.7653909883747 | -0.765390988374717 |
| 9 | 15 | 15.28731453242 | -0.287314532419999 |
| 10 | 15 | 15.2413732716812 | -0.241373271681172 |
| 11 | 17 | 16.9443655385099 | 0.0556344614901121 |
| 12 | 19 | 17.4662890825552 | 1.53371091744483 |
| 13 | 10 | 13.6602723735824 | -3.66027237358238 |
| 14 | 16 | 16.2155346212445 | -0.215534621244473 |
| 15 | 18 | 16.7606004955546 | 1.23939950444542 |
| 16 | 14 | 14.3978609024641 | -0.3978609024641 |
| 17 | 14 | 14.6353792704601 | -0.635379270460111 |
| 18 | 17 | 16.0327151256036 | 0.967284874396403 |
| 19 | 14 | 13.0799139447786 | 0.920086055221384 |
| 20 | 16 | 14.7819606642929 | 1.2180393357071 |
| 21 | 18 | 17.0528177359057 | 0.947182264094274 |
| 22 | 11 | 12.3732798104636 | -1.37327981046359 |
| 23 | 14 | 14.0772176246067 | -0.0772176246067423 |
| 24 | 12 | 13.1558640527697 | -1.15586405276971 |
| 25 | 17 | 15.4267211243825 | 1.57327887561746 |
| 26 | 9 | 11.6216499627242 | -2.62164996272418 |
| 27 | 16 | 15.3348386029049 | 0.665161397095118 |
| 28 | 14 | 12.9730445571288 | 1.02695544287117 |
| 29 | 15 | 14.0850296889086 | 0.914970311091382 |
| 30 | 11 | 11.1322285080836 | -0.132228508083637 |
| 31 | 16 | 15.1510735599496 | 0.848926440050426 |
| 32 | 13 | 13.6628007306429 | -0.662800730642866 |
| 33 | 17 | 16.2171174309905 | 0.78288256900947 |
| 34 | 15 | 14.1387830139493 | 0.86121698605068 |
| 35 | 14 | 13.5249769484264 | 0.475023051573616 |
| 36 | 16 | 14.9213672562554 | 1.07863274374456 |
| 37 | 9 | 11.1162960945971 | -2.11629609459708 |
| 38 | 15 | 13.955017970994 | 1.04498202900599 |
| 39 | 17 | 14.783543474039 | 2.21645652596104 |
| 40 | 13 | 14.1687918612016 | -1.16879186120159 |
| 41 | 15 | 14.407255776512 | 0.592744223487968 |
| 42 | 16 | 14.6457196918225 | 1.35428030817752 |
| 43 | 16 | 14.3153732550344 | 1.68462674496562 |
| 44 | 12 | 12.8271004257277 | -0.82710042572767 |
| 45 | 9 | 9.91491062154575 | -0.914910621545745 |
| 46 | 9 | 10.7274536714217 | -1.72745367142172 |
| 47 | 9 | 8.72898081928735 | 0.271019180712648 |
| 48 | 9 | 8.96649918728336 | 0.033500812716637 |
| 49 | 9 | 6.14784666548354 | 2.85215333451646 |
| 50 | 9 | 9.1004115125841 | -0.100411512584101 |
| 51 | 9 | 6.51187707271523 | 2.48812292728477 |
| 52 | 9 | 9.06713932037733 | -0.0671393203773251 |
| 53 | 9 | 11.5637912387685 | -2.56379123876854 |
| 54 | 9 | 11.2930006785658 | -2.29300067856576 |
| 55 | 9 | 10.792092036432 | -1.79209203643202 |
| 56 | 9 | 8.3155094726379 | 0.684490527362092 |
| 57 | 9 | 7.11069627206604 | 1.88930372793396 |
| 58 | 9 | 7.34916018737648 | 1.65083981262352 |
| 59 | 9 | 10.0173198584278 | -1.01731985842777 |
| 60 | 9 | 8.9254040812451 | 0.0745959187548998 |
| 61 | 9 | 12.7524356921294 | -3.75243569212943 |
| 62 | 9 | 9.59509090016202 | -0.595090900162022 |
| 63 | 9 | 10.0584041149364 | -1.05840411493642 |
| 64 | 9 | 8.34433643885133 | 0.655663561148675 |
| 65 | 10 | 6.85606360954462 | 3.14393639045538 |
| 66 | 9 | 11.2509600252131 | -2.25096002521306 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 9 | 0.0508553784643286 | 0.101710756928657 | 0.949144621535671 |
| 10 | 0.014223071001873 | 0.0284461420037459 | 0.985776928998127 |
| 11 | 0.0142793445502125 | 0.0285586891004249 | 0.985720655449787 |
| 12 | 0.00455648151819255 | 0.0091129630363851 | 0.995443518481807 |
| 13 | 0.00265737598490926 | 0.00531475196981851 | 0.99734262401509 |
| 14 | 0.000807127103066684 | 0.00161425420613337 | 0.999192872896933 |
| 15 | 0.000259693492902676 | 0.000519386985805352 | 0.999740306507097 |
| 16 | 7.6947538608061e-05 | 0.000153895077216122 | 0.999923052461392 |
| 17 | 3.46611313405893e-05 | 6.93222626811787e-05 | 0.99996533886866 |
| 18 | 8.06905416258587e-05 | 0.000161381083251717 | 0.999919309458374 |
| 19 | 2.66415559411341e-05 | 5.32831118822683e-05 | 0.99997335844406 |
| 20 | 3.36145325744151e-05 | 6.72290651488301e-05 | 0.999966385467426 |
| 21 | 5.01806712810311e-05 | 0.000100361342562062 | 0.999949819328719 |
| 22 | 2.76827459556968e-05 | 5.53654919113935e-05 | 0.999972317254044 |
| 23 | 7.16250412062119e-05 | 0.000143250082412424 | 0.999928374958794 |
| 24 | 3.91666940771074e-05 | 7.83333881542148e-05 | 0.999960833305923 |
| 25 | 3.30701734512487e-05 | 6.61403469024975e-05 | 0.999966929826549 |
| 26 | 7.13859699099079e-05 | 0.000142771939819816 | 0.99992861403009 |
| 27 | 2.9572617810938e-05 | 5.91452356218761e-05 | 0.99997042738219 |
| 28 | 1.30211043228384e-05 | 2.60422086456767e-05 | 0.999986978895677 |
| 29 | 4.94348378870604e-06 | 9.8869675774121e-06 | 0.999995056516211 |
| 30 | 5.72630980663803e-06 | 1.14526196132761e-05 | 0.999994273690193 |
| 31 | 2.37966959502994e-06 | 4.75933919005989e-06 | 0.999997620330405 |
| 32 | 1.43550374544622e-06 | 2.87100749089244e-06 | 0.999998564496255 |
| 33 | 8.93272368581025e-07 | 1.78654473716205e-06 | 0.999999106727631 |
| 34 | 3.2854865588301e-07 | 6.57097311766019e-07 | 0.999999671451344 |
| 35 | 1.70580524162992e-07 | 3.41161048325985e-07 | 0.999999829419476 |
| 36 | 8.23142123841174e-08 | 1.64628424768235e-07 | 0.999999917685788 |
| 37 | 0.000325960022649595 | 0.000651920045299189 | 0.99967403997735 |
| 38 | 0.000245720011723078 | 0.000491440023446155 | 0.999754279988277 |
| 39 | 0.000933467845772229 | 0.00186693569154446 | 0.999066532154228 |
| 40 | 0.000551327373360392 | 0.00110265474672078 | 0.99944867262664 |
| 41 | 0.000425037762487219 | 0.000850075524974438 | 0.999574962237513 |
| 42 | 0.00106276749590839 | 0.00212553499181677 | 0.998937232504092 |
| 43 | 0.975958349067142 | 0.048083301865717 | 0.0240416509328585 |
| 44 | 0.99992404763559 | 0.000151904728817567 | 7.59523644087837e-05 |
| 45 | 0.999999838995521 | 3.22008957078708e-07 | 1.61004478539354e-07 |
| 46 | 0.999999410054888 | 1.17989022348579e-06 | 5.89945111742897e-07 |
| 47 | 0.999998766238296 | 2.46752340808802e-06 | 1.23376170404401e-06 |
| 48 | 0.999996232825573 | 7.53434885313917e-06 | 3.76717442656958e-06 |
| 49 | 0.99999847308227 | 3.05383545943855e-06 | 1.52691772971927e-06 |
| 50 | 0.999992473063763 | 1.50538724747327e-05 | 7.52693623736636e-06 |
| 51 | 0.999975494296955 | 4.9011406089139e-05 | 2.45057030445695e-05 |
| 52 | 0.999922033988623 | 0.000155932022754489 | 7.79660113772444e-05 |
| 53 | 0.999946477697151 | 0.000107044605697134 | 5.35223028485669e-05 |
| 54 | 0.999990929823395 | 1.8140353209934e-05 | 9.07017660496699e-06 |
| 55 | 0.99998587489681 | 2.82502063807623e-05 | 1.41251031903812e-05 |
| 56 | 0.999831510821697 | 0.000336978356605745 | 0.000168489178302873 |
| 57 | 0.998315452203347 | 0.00336909559330587 | 0.00168454779665294 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 45 | 0.918367346938776 | NOK |
| 5% type I error level | 48 | 0.979591836734694 | NOK |
| 10% type I error level | 48 | 0.979591836734694 | NOK |
