| Multiple Linear Regression - Estimated Regression Equation |
| tip[t] = + 121.394817113588 -0.179452244652004wrk[t] -0.400730340464006M1[t] + 2.3M2[t] + 11.1832865320880M3[t] + 4.16136800241036M4[t] + 1.88465453449834M5[t] + 11.9041067791503M6[t] -8.33396914733354M7[t] + 3.81041566736967M8[t] + 18.2956207291353M9[t] + 16.2375364868936M10[t] + 8.15835673395602M11[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) | 121.394817113588 | 5.920244 | 20.505 | 0 | 0 |
| wrk | -0.179452244652004 | 0.046266 | -3.8787 | 0.000319 | 0.00016 |
| M1 | -0.400730340464006 | 2.94741 | -0.136 | 0.892421 | 0.446211 |
| M2 | 2.3 | 3.077795 | 0.7473 | 0.458535 | 0.229267 |
| M3 | 11.1832865320880 | 3.090288 | 3.6188 | 0.00071 | 0.000355 |
| M4 | 4.16136800241036 | 3.111013 | 1.3376 | 0.187322 | 0.093661 |
| M5 | 1.88465453449834 | 3.163415 | 0.5958 | 0.554131 | 0.277065 |
| M6 | 11.9041067791503 | 3.153045 | 3.7754 | 0.00044 | 0.00022 |
| M7 | -8.33396914733354 | 3.190904 | -2.6118 | 0.011986 | 0.005993 |
| M8 | 3.81041566736967 | 3.284717 | 1.16 | 0.251769 | 0.125884 |
| M9 | 18.2956207291353 | 3.250561 | 5.6285 | 1e-06 | 0 |
| M10 | 16.2375364868936 | 3.12584 | 5.1946 | 4e-06 | 2e-06 |
| M11 | 8.15835673395602 | 3.080923 | 2.648 | 0.010923 | 0.005462 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.878569063356793 |
| R-squared | 0.771883599087633 |
| Adjusted R-squared | 0.714854498859542 |
| F-TEST (value) | 13.5349075472072 |
| F-TEST (DF numerator) | 12 |
| F-TEST (DF denominator) | 48 |
| p-value | 1.36221034452433e-11 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 4.86642040031007 |
| Sum Squared Residuals | 1136.73828060259 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 95.1 | 96.588581500452 | -1.48858150045198 |
| 2 | 97 | 99.827668574872 | -2.82766857487196 |
| 3 | 112.7 | 109.967120819524 | 2.73287918047606 |
| 4 | 102.9 | 104.021915757758 | -1.12191575775836 |
| 5 | 97.4 | 102.821915757758 | -5.42191575775836 |
| 6 | 111.4 | 112.482463513106 | -1.08246351310636 |
| 7 | 87.4 | 85.6046545344984 | 1.79534546550166 |
| 8 | 96.8 | 96.1339691473335 | 0.66603085266646 |
| 9 | 114.1 | 110.798626453751 | 3.30137354624887 |
| 10 | 110.3 | 110.893969147334 | -0.59396914733352 |
| 11 | 103.9 | 104.609311840916 | -0.709311840915936 |
| 12 | 101.6 | 97.168764085568 | 4.43123591443206 |
| 13 | 94.6 | 97.665294968364 | -3.06529496836396 |
| 14 | 95.9 | 100.904382042784 | -5.00438204278396 |
| 15 | 104.7 | 110.684929798132 | -5.98492979813197 |
| 16 | 102.8 | 104.560272491714 | -1.76027249171437 |
| 17 | 98.1 | 103.180820247062 | -5.08082024706237 |
| 18 | 113.9 | 113.020820247062 | 0.879179752937634 |
| 19 | 80.9 | 86.3224635131064 | -5.42246351310636 |
| 20 | 95.7 | 97.0312303705935 | -1.33123037059355 |
| 21 | 113.2 | 111.516435432359 | 1.68356456764086 |
| 22 | 105.9 | 111.252873636638 | -5.35287363663755 |
| 23 | 108.8 | 104.96821633022 | 3.83178366978005 |
| 24 | 102.3 | 97.707120819524 | 4.59287918047604 |
| 25 | 99 | 98.562556191624 | 0.437443808376024 |
| 26 | 100.7 | 101.622191021392 | -0.92219102139198 |
| 27 | 115.5 | 111.582191021392 | 3.91780897860801 |
| 28 | 100.7 | 105.098629225670 | -4.39862922567038 |
| 29 | 109.9 | 103.360272491714 | 6.53972750828563 |
| 30 | 114.6 | 113.200272491714 | 1.39972750828562 |
| 31 | 85.4 | 87.2197247363664 | -1.81972473636638 |
| 32 | 100.5 | 98.2873960831576 | 2.21260391684242 |
| 33 | 114.8 | 112.952053389575 | 1.84794661042483 |
| 34 | 116.5 | 113.585752817114 | 2.91424718288641 |
| 35 | 112.9 | 107.480547755348 | 5.41945224465201 |
| 36 | 102 | 100.578356733956 | 1.42164326604399 |
| 37 | 106 | 99.99817414884 | 6.00182585115999 |
| 38 | 105.3 | 103.775617957216 | 1.52438204278397 |
| 39 | 118.8 | 113.735617957216 | 5.06438204278397 |
| 40 | 106.1 | 107.252056161494 | -1.15205616149443 |
| 41 | 109.3 | 106.231508406146 | 3.06849159385357 |
| 42 | 117.2 | 116.609865140102 | 0.590134859897562 |
| 43 | 92.5 | 90.8087696294065 | 1.69123037059355 |
| 44 | 104.2 | 101.876440976198 | 2.32355902380235 |
| 45 | 112.5 | 117.438359505875 | -4.93835950587527 |
| 46 | 122.4 | 116.995345465502 | 5.40465453449834 |
| 47 | 113.3 | 110.531235914432 | 2.76876408556794 |
| 48 | 100 | 102.552331425128 | -2.55233142512805 |
| 49 | 110.7 | 102.151601084664 | 8.54839891533596 |
| 50 | 112.8 | 105.570140403736 | 7.22985959626394 |
| 51 | 109.8 | 115.530140403736 | -5.73014040373607 |
| 52 | 117.3 | 108.867126363362 | 8.43287363663755 |
| 53 | 109.1 | 108.205483097318 | 0.894516902681529 |
| 54 | 115.9 | 117.686578608014 | -1.78657860801446 |
| 55 | 96 | 92.2443875866225 | 3.75561241337752 |
| 56 | 99.8 | 103.670963422718 | -3.87096342271769 |
| 57 | 116.8 | 118.694525218439 | -1.89452521843929 |
| 58 | 115.7 | 118.072058933414 | -2.37205893341368 |
| 59 | 99.4 | 110.710688159084 | -11.3106881590841 |
| 60 | 94.3 | 102.193426935824 | -7.89342693582405 |
| 61 | 91 | 101.433792106056 | -10.4337921060560 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 16 | 0.155807742206136 | 0.311615484412272 | 0.844192257793864 |
| 17 | 0.076846625956661 | 0.153693251913322 | 0.92315337404334 |
| 18 | 0.0474884735704068 | 0.0949769471408135 | 0.952511526429593 |
| 19 | 0.0477199697815761 | 0.0954399395631522 | 0.952280030218424 |
| 20 | 0.0219261381343761 | 0.0438522762687523 | 0.978073861865624 |
| 21 | 0.00908073518397626 | 0.0181614703679525 | 0.990919264816024 |
| 22 | 0.00786877003815199 | 0.0157375400763040 | 0.992131229961848 |
| 23 | 0.00955812919828087 | 0.0191162583965617 | 0.99044187080172 |
| 24 | 0.00513985914235924 | 0.0102797182847185 | 0.99486014085764 |
| 25 | 0.00761270150024891 | 0.0152254030004978 | 0.99238729849975 |
| 26 | 0.0075653230722832 | 0.0151306461445664 | 0.992434676927717 |
| 27 | 0.00931214718811198 | 0.0186242943762240 | 0.990687852811888 |
| 28 | 0.00924918128439385 | 0.0184983625687877 | 0.990750818715606 |
| 29 | 0.0526308169487893 | 0.105261633897579 | 0.94736918305121 |
| 30 | 0.0315075174139895 | 0.063015034827979 | 0.96849248258601 |
| 31 | 0.0255704308216063 | 0.0511408616432125 | 0.974429569178394 |
| 32 | 0.0149995939161897 | 0.0299991878323794 | 0.98500040608381 |
| 33 | 0.00812724110279539 | 0.0162544822055908 | 0.991872758897205 |
| 34 | 0.00611448857758184 | 0.0122289771551637 | 0.993885511422418 |
| 35 | 0.00378625815004067 | 0.00757251630008134 | 0.99621374184996 |
| 36 | 0.00358091881440668 | 0.00716183762881336 | 0.996419081185593 |
| 37 | 0.00402778060465449 | 0.00805556120930899 | 0.995972219395346 |
| 38 | 0.00250945357175160 | 0.00501890714350321 | 0.997490546428248 |
| 39 | 0.00278917250609998 | 0.00557834501219996 | 0.9972108274939 |
| 40 | 0.00271486404368972 | 0.00542972808737944 | 0.99728513595631 |
| 41 | 0.00118937713576875 | 0.00237875427153749 | 0.998810622864231 |
| 42 | 0.000591390796176683 | 0.00118278159235337 | 0.999408609203823 |
| 43 | 0.000218101638430536 | 0.000436203276861072 | 0.99978189836157 |
| 44 | 0.000142087401796409 | 0.000284174803592818 | 0.999857912598204 |
| 45 | 0.00023004963601989 | 0.00046009927203978 | 0.99976995036398 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 11 | 0.366666666666667 | NOK |
| 5% type I error level | 23 | 0.766666666666667 | NOK |
| 10% type I error level | 27 | 0.9 | NOK |
