| Multiple Linear Regression - Estimated Regression Equation |
| ipchn[t] = + 95.1964775705906 + 0.202879658540295Tip[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) | 95.1964775705906 | 8.031714 | 11.8526 | 0 | 0 |
| Tip | 0.202879658540295 | 0.077112 | 2.631 | 0.010888 | 0.005444 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.326528131701518 |
| R-squared | 0.106620620792484 |
| Adjusted R-squared | 0.0912175280475269 |
| F-TEST (value) | 6.92202680058462 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 58 |
| p-value | 0.0108877211807719 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 5.27332636197745 |
| Sum Squared Residuals | 1612.86231335572 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 116.7 | 114.956956312416 | 1.74304368758425 |
| 2 | 109 | 114.875804448999 | -5.87580444899926 |
| 3 | 119.5 | 116.579993580738 | 2.9200064192623 |
| 4 | 115.1 | 116.032218502679 | -0.932218502678914 |
| 5 | 107.1 | 115.098972073394 | -7.99897207339356 |
| 6 | 109.7 | 116.397401888051 | -6.69740188805143 |
| 7 | 110.4 | 112.928159727012 | -2.5281597270124 |
| 8 | 105 | 113.435358873363 | -8.43535887336314 |
| 9 | 115.8 | 117.472664078315 | -1.672664078315 |
| 10 | 116.4 | 117.858135429542 | -1.45813542954155 |
| 11 | 111.1 | 115.200411902664 | -4.10041190266371 |
| 12 | 119.5 | 114.855516483145 | 4.6444835168548 |
| 13 | 110.9 | 114.490333097773 | -3.59033309777267 |
| 14 | 115.1 | 114.875804448999 | 0.224195551000763 |
| 15 | 125.2 | 118.061015088082 | 7.13898491191815 |
| 16 | 116 | 116.072794434387 | -0.0727944343869676 |
| 17 | 112.9 | 114.956956312415 | -2.05695631241534 |
| 18 | 121.7 | 117.797271531979 | 3.90272846802053 |
| 19 | 123.2 | 112.928159727012 | 10.2718402729876 |
| 20 | 116.6 | 114.835228517291 | 1.76477148270882 |
| 21 | 136.2 | 118.345046610038 | 17.8549533899617 |
| 22 | 120.9 | 117.574103907585 | 3.32589609241486 |
| 23 | 119.6 | 116.275674092927 | 3.32432590707273 |
| 24 | 125.9 | 115.809050878285 | 10.0909491217154 |
| 25 | 116.1 | 114.388893268503 | 1.71110673149747 |
| 26 | 107.5 | 114.652636824605 | -7.15263682460491 |
| 27 | 116.7 | 116.437977819759 | 0.262022180240506 |
| 28 | 112.5 | 116.052506468533 | -3.55250646853294 |
| 29 | 113 | 115.098972073394 | -2.09897207339355 |
| 30 | 126.4 | 118.304470678330 | 8.0955293216698 |
| 31 | 114.1 | 111.609441946500 | 2.4905580534995 |
| 32 | 112.5 | 114.612060892897 | -2.11206089289685 |
| 33 | 112.4 | 118.162454917352 | -5.76245491735199 |
| 34 | 113.1 | 116.681433410008 | -3.58143341000786 |
| 35 | 116.3 | 117.269784419775 | -0.969784419774704 |
| 36 | 111.7 | 115.951066639263 | -4.25106663926279 |
| 37 | 118.8 | 115.281563766080 | 3.51843623392018 |
| 38 | 116.5 | 115.626459185598 | 0.87354081440168 |
| 39 | 125.1 | 118.629078131995 | 6.47092186800532 |
| 40 | 113.1 | 115.626459185598 | -2.52645918559833 |
| 41 | 119.6 | 117.492952044169 | 2.10704795583097 |
| 42 | 114.4 | 118.446486439308 | -4.0464864393084 |
| 43 | 114 | 112.522400409932 | 1.47759959006818 |
| 44 | 117.8 | 115.585883253890 | 2.21411674610974 |
| 45 | 117 | 118.487062371016 | -1.48706237101647 |
| 46 | 120.9 | 118.831957790535 | 2.06804220946504 |
| 47 | 115 | 118.10159101979 | -3.10159101978991 |
| 48 | 117.3 | 115.890202741701 | 1.40979725829930 |
| 49 | 119.4 | 116.701721375862 | 2.69827862413813 |
| 50 | 114.9 | 116.559705614884 | -1.65970561488367 |
| 51 | 125.8 | 119.298581005178 | 6.50141899482235 |
| 52 | 117.6 | 116.722009341716 | 0.877990658284088 |
| 53 | 117.6 | 117.371224249045 | 0.228775750955146 |
| 54 | 114.9 | 118.973973551513 | -4.07397355151317 |
| 55 | 121.9 | 113.962845985568 | 7.9371540144321 |
| 56 | 117 | 116.336537990489 | 0.66346200951065 |
| 57 | 106.4 | 118.020439156374 | -11.6204391563738 |
| 58 | 110.5 | 120.028947775923 | -9.5289477759227 |
| 59 | 113.6 | 118.182742883206 | -4.58274288320603 |
| 60 | 114.2 | 115.48444342462 | -1.28444342462011 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.430981937929004 | 0.861963875858008 | 0.569018062070996 |
| 6 | 0.523475437600216 | 0.953049124799569 | 0.476524562399784 |
| 7 | 0.412588145259399 | 0.825176290518798 | 0.587411854740601 |
| 8 | 0.388609447866592 | 0.777218895733184 | 0.611390552133408 |
| 9 | 0.275625665629396 | 0.551251331258792 | 0.724374334370604 |
| 10 | 0.185163819157073 | 0.370327638314146 | 0.814836180842927 |
| 11 | 0.124394909359656 | 0.248789818719311 | 0.875605090640344 |
| 12 | 0.246334656863434 | 0.492669313726869 | 0.753665343136566 |
| 13 | 0.180832350365894 | 0.361664700731787 | 0.819167649634106 |
| 14 | 0.142212846361368 | 0.284425692722735 | 0.857787153638632 |
| 15 | 0.201318969158368 | 0.402637938316736 | 0.798681030841632 |
| 16 | 0.143779244790235 | 0.28755848958047 | 0.856220755209765 |
| 17 | 0.101366125208590 | 0.202732250417181 | 0.89863387479141 |
| 18 | 0.0772833153682086 | 0.154566630736417 | 0.922716684631791 |
| 19 | 0.417788988959023 | 0.835577977918045 | 0.582211011040977 |
| 20 | 0.354531192768073 | 0.709062385536146 | 0.645468807231927 |
| 21 | 0.916722976563763 | 0.166554046872474 | 0.083277023436237 |
| 22 | 0.892621299831472 | 0.214757400337056 | 0.107378700168528 |
| 23 | 0.864529413284814 | 0.270941173430372 | 0.135470586715186 |
| 24 | 0.944311625254616 | 0.111376749490768 | 0.0556883747453842 |
| 25 | 0.923378067086969 | 0.153243865826062 | 0.0766219329130312 |
| 26 | 0.94715258577094 | 0.105694828458119 | 0.0528474142290594 |
| 27 | 0.924219713201563 | 0.151560573596875 | 0.0757802867984373 |
| 28 | 0.913525886663696 | 0.172948226672608 | 0.0864741133363041 |
| 29 | 0.887666288528875 | 0.224667422942251 | 0.112333711471125 |
| 30 | 0.936027195267452 | 0.127945609465096 | 0.0639728047325481 |
| 31 | 0.932387194402056 | 0.135225611195888 | 0.0676128055979438 |
| 32 | 0.915126719445238 | 0.169746561109524 | 0.084873280554762 |
| 33 | 0.930505708106249 | 0.138988583787503 | 0.0694942918937514 |
| 34 | 0.91994634234361 | 0.160107315312779 | 0.0800536576563893 |
| 35 | 0.889376542525103 | 0.221246914949795 | 0.110623457474897 |
| 36 | 0.887506905589005 | 0.224986188821989 | 0.112493094410995 |
| 37 | 0.85760330595386 | 0.284793388092279 | 0.142396694046139 |
| 38 | 0.807090195988412 | 0.385819608023175 | 0.192909804011588 |
| 39 | 0.876664721976324 | 0.246670556047353 | 0.123335278023676 |
| 40 | 0.853317040083518 | 0.293365919832964 | 0.146682959916482 |
| 41 | 0.819302032673474 | 0.361395934653052 | 0.180697967326526 |
| 42 | 0.789099223491208 | 0.421801553017585 | 0.210900776508792 |
| 43 | 0.767522255526932 | 0.464955488946137 | 0.232477744473068 |
| 44 | 0.696075873656859 | 0.607848252686283 | 0.303924126343141 |
| 45 | 0.623399823863064 | 0.753200352273872 | 0.376600176136936 |
| 46 | 0.625167945573741 | 0.749664108852517 | 0.374832054426259 |
| 47 | 0.545547439974018 | 0.908905120051963 | 0.454452560025982 |
| 48 | 0.446967187611859 | 0.893934375223717 | 0.553032812388141 |
| 49 | 0.374800321442782 | 0.749600642885565 | 0.625199678557218 |
| 50 | 0.288683831212053 | 0.577367662424105 | 0.711316168787947 |
| 51 | 0.824441769251564 | 0.351116461496873 | 0.175558230748436 |
| 52 | 0.747734155159822 | 0.504531689680356 | 0.252265844840178 |
| 53 | 0.696066704403977 | 0.607866591192045 | 0.303933295596023 |
| 54 | 0.682818786167544 | 0.634362427664911 | 0.317181213832456 |
| 55 | 0.619467756586638 | 0.761064486826725 | 0.380532243413363 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 0 | 0 | OK |
| 5% type I error level | 0 | 0 | OK |
| 10% type I error level | 0 | 0 | OK |
