Multiple Linear Regression - Estimated Regression Equation |
Schoolprestaties[t] = + 7.09477021123286 + 0.31890776231257Goingout[t] -0.124222782962212Relation[t] + 0.524420393526331Family[t] + 0.0624178602190103Friends[t] -0.0133761281617639Job[t] + 0.0047590998898964t + 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) | 7.09477021123286 | 1.524217 | 4.6547 | 7e-06 | 4e-06 |
Goingout | 0.31890776231257 | 0.131488 | 2.4254 | 0.016488 | 0.008244 |
Relation | -0.124222782962212 | 0.103833 | -1.1964 | 0.233452 | 0.116726 |
Family | 0.524420393526331 | 0.184181 | 2.8473 | 0.005032 | 0.002516 |
Friends | 0.0624178602190103 | 0.13857 | 0.4504 | 0.653046 | 0.326523 |
Job | -0.0133761281617639 | 0.174313 | -0.0767 | 0.938936 | 0.469468 |
t | 0.0047590998898964 | 0.006037 | 0.7884 | 0.43173 | 0.215865 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.336065294677035 |
R-squared | 0.112939882286363 |
Adjusted R-squared | 0.0772193406334645 |
F-TEST (value) | 3.16176286977438 |
F-TEST (DF numerator) | 6 |
F-TEST (DF denominator) | 149 |
p-value | 0.00600449399077663 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 3.35594263195998 |
Sum Squared Residuals | 1678.09029140197 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 14 | 9.04493447912672 | 4.95506552087328 |
2 | 8 | 13.0319698639731 | -5.03196986397311 |
3 | 12 | 12.5613503023939 | -0.561350302393922 |
4 | 7 | 11.8831905647296 | -4.88319056472956 |
5 | 10 | 11.8625200096427 | -1.86252000964267 |
6 | 9 | 11.4430913238081 | -2.44309132380808 |
7 | 16 | 13.5921685122462 | 2.40783148775382 |
8 | 7 | 9.55093553017966 | -2.55093553017966 |
9 | 14 | 11.873348005155 | 2.12665199484503 |
10 | 6 | 12.2159376826882 | -6.21593768268816 |
11 | 16 | 11.7560029396253 | 4.24399706037467 |
12 | 11 | 11.3036424286029 | -0.30364242860287 |
13 | 17 | 11.8224431397534 | 5.17755686024664 |
14 | 12 | 10.7490607199687 | 1.2509392800313 |
15 | 7 | 10.1863991501386 | -3.18639915013859 |
16 | 13 | 11.3713924244634 | 1.62860757553659 |
17 | 9 | 8.61833622209662 | 0.38166377790338 |
18 | 15 | 12.8441233899068 | 2.1558766100932 |
19 | 7 | 11.0043441016015 | -4.00434410160152 |
20 | 9 | 10.235788372443 | -1.235788372443 |
21 | 7 | 11.0220707054286 | -4.02207070542859 |
22 | 14 | 12.5765001433481 | 1.42349985665188 |
23 | 15 | 10.9468815692557 | 4.05311843074434 |
24 | 7 | 11.876115839889 | -4.87611583988896 |
25 | 13 | 11.8226303380839 | 1.17736966191612 |
26 | 17 | 11.8273894379738 | 5.17261056202623 |
27 | 15 | 12.3190597947208 | 2.68094020527917 |
28 | 14 | 9.16732137880732 | 4.83267862119268 |
29 | 14 | 12.2413434167806 | 1.75865658321936 |
30 | 8 | 10.6022871336545 | -2.60228713365453 |
31 | 8 | 10.5645621684314 | -2.56456216843143 |
32 | 12 | 12.3476674450475 | -0.347667445047518 |
33 | 14 | 12.3099424798244 | 1.69005752017559 |
34 | 8 | 11.7827824460116 | -3.78278244601163 |
35 | 11 | 10.3071748707914 | 0.692825129208556 |
36 | 16 | 11.2539585281105 | 4.74604147188946 |
37 | 11 | 12.6250762345359 | -1.62507623453591 |
38 | 8 | 11.1163515317186 | -3.1163515317186 |
39 | 14 | 10.5969250774781 | 3.40307492252193 |
40 | 16 | 10.4804799748329 | 5.51952002516712 |
41 | 14 | 12.2271214076684 | 1.77287859233157 |
42 | 5 | 12.196446313024 | -7.19644631302401 |
43 | 8 | 9.52359605232962 | -1.52359605232963 |
44 | 10 | 10.5012378830133 | -0.501237883013262 |
45 | 8 | 12.2367200981944 | -4.23672009819438 |
46 | 13 | 12.463008439807 | 0.536991560192978 |
47 | 15 | 9.88355238147738 | 5.11644761852262 |
48 | 6 | 11.1714659353598 | -5.17146593535975 |
49 | 12 | 10.0293007840825 | 1.97069921591751 |
50 | 14 | 12.8474458574381 | 1.15255414256194 |
51 | 5 | 10.6707358859709 | -5.6707358859709 |
52 | 15 | 12.4494071097897 | 2.55059289021031 |
53 | 11 | 11.8088519448781 | -0.808851944878103 |
54 | 8 | 9.78653450039786 | -1.78653450039786 |
55 | 13 | 11.835071754472 | 1.16492824552803 |
56 | 14 | 11.9352017742999 | 2.06479822570014 |
57 | 12 | 10.1197195623801 | 1.88028043761988 |
58 | 16 | 13.3051091865808 | 2.69489081341916 |
59 | 10 | 8.81821841747227 | 1.18178158252773 |
60 | 15 | 13.5388691722599 | 1.46113082774012 |
61 | 8 | 10.3273321439435 | -2.32733214394348 |
62 | 16 | 11.1569463189138 | 4.84305368108621 |
63 | 19 | 12.7488128316732 | 6.25118716832679 |
64 | 14 | 10.7326041845396 | 3.26739581546044 |
65 | 7 | 10.5903300943066 | -3.59033009430658 |
66 | 13 | 11.8707202434468 | 1.12927975655324 |
67 | 15 | 11.9110529411833 | 3.08894705881673 |
68 | 7 | 9.29797533801441 | -2.29797533801441 |
69 | 13 | 12.6263923917269 | 0.373607608273148 |
70 | 4 | 10.3119194412576 | -6.31191944125757 |
71 | 14 | 11.578933462236 | 2.42106653776402 |
72 | 13 | 11.1265729512135 | 1.87342704878647 |
73 | 11 | 9.87563479695915 | 1.12436520304085 |
74 | 14 | 10.9674487640956 | 3.03255123590445 |
75 | 12 | 11.4227698079536 | 0.577230192046442 |
76 | 15 | 12.789403499258 | 2.21059650074199 |
77 | 14 | 11.9096942140739 | 2.09030578592615 |
78 | 13 | 11.6252664260782 | 1.37473357392178 |
79 | 7 | 11.0659764448523 | -4.06597644485234 |
80 | 5 | 9.35508453669317 | -4.35508453669317 |
81 | 7 | 11.5095690089879 | -4.50956900898792 |
82 | 13 | 12.6184114313832 | 0.381588568616832 |
83 | 13 | 10.3737877398262 | 2.62621226017378 |
84 | 11 | 11.2951417421685 | -0.295141742168539 |
85 | 6 | 10.0355675488003 | -4.03556754880033 |
86 | 12 | 12.8582721291408 | -0.858272129140831 |
87 | 8 | 9.93676633554693 | -1.93676633554693 |
88 | 11 | 12.9283447121464 | -1.92834471214636 |
89 | 12 | 14.3383814422902 | -2.33838144229024 |
90 | 9 | 9.8285635954063 | -0.828563595406304 |
91 | 12 | 10.2461406631992 | 1.75385933680077 |
92 | 13 | 13.2285448979534 | -0.228544897953441 |
93 | 16 | 12.901020107369 | 3.098979892631 |
94 | 16 | 12.0529247663722 | 3.94707523362776 |
95 | 11 | 12.6331735367171 | -1.63317353671713 |
96 | 8 | 11.2963907475725 | -3.29639074757253 |
97 | 4 | 11.8463777678438 | -7.84637776784385 |
98 | 7 | 9.86585938917152 | -2.86585938917152 |
99 | 14 | 11.4066566250023 | 2.59334337499772 |
100 | 11 | 11.8147247869069 | -0.814724786906851 |
101 | 17 | 13.1842129907603 | 3.81578700923972 |
102 | 15 | 12.9572281345398 | 2.04277186546016 |
103 | 14 | 12.4960462819943 | 1.50395371800571 |
104 | 5 | 11.7606576427565 | -6.7606576427565 |
105 | 4 | 11.4750500867612 | -7.47505008676117 |
106 | 19 | 13.7310355108716 | 5.26896448912841 |
107 | 11 | 10.2142229223314 | 0.785777077668605 |
108 | 15 | 10.4526368525883 | 4.54736314741166 |
109 | 10 | 9.91795341403337 | 0.0820465859666293 |
110 | 9 | 11.4799062566951 | -2.47990625669509 |
111 | 12 | 10.5070425367433 | 1.49295746325668 |
112 | 15 | 11.535116042314 | 3.46488395768603 |
113 | 7 | 12.986767826168 | -5.98676782616803 |
114 | 13 | 12.2893580023912 | 0.710641997608773 |
115 | 14 | 14.9374967008966 | -0.937496700896634 |
116 | 14 | 12.2557084280644 | 1.74429157193555 |
117 | 14 | 11.5161673394968 | 2.48383266050322 |
118 | 8 | 11.1367207747657 | -3.1367207747657 |
119 | 15 | 11.9510779654216 | 3.04892203457843 |
120 | 15 | 10.3841545600062 | 4.61584543999377 |
121 | 9 | 11.1924490602674 | -2.19244906026743 |
122 | 16 | 12.1238537091192 | 3.87614629088081 |
123 | 9 | 12.0215405054586 | -3.02154050545861 |
124 | 15 | 13.6125800505405 | 1.38741994945953 |
125 | 15 | 12.2985403270735 | 2.70145967292648 |
126 | 6 | 11.6822775182012 | -5.68227751820122 |
127 | 8 | 11.9309061628458 | -3.93090616284576 |
128 | 15 | 12.2726892422579 | 2.72731075774209 |
129 | 10 | 10.7466499921507 | -0.746649992150716 |
130 | 9 | 10.6451172238788 | -1.64511722387884 |
131 | 14 | 13.9525592528233 | 0.0474407471766966 |
132 | 12 | 13.0771907240761 | -1.07719072407606 |
133 | 8 | 12.7611785846601 | -4.76117858466012 |
134 | 11 | 11.8386283708142 | -0.838628370814164 |
135 | 13 | 12.7458080051097 | 0.254191994890344 |
136 | 9 | 11.3114873478434 | -2.31148734784336 |
137 | 15 | 11.8253551742753 | 3.17464482572473 |
138 | 13 | 9.97571054186978 | 3.02428945813022 |
139 | 15 | 12.3651677255321 | 2.63483227446793 |
140 | 14 | 12.2228936352991 | 1.77710636470091 |
141 | 16 | 11.096976503892 | 4.90302349610801 |
142 | 12 | 12.3794450252018 | -0.379445025201756 |
143 | 14 | 11.1978351984328 | 2.80216480156722 |
144 | 10 | 11.0824066608837 | -1.08240666088371 |
145 | 10 | 11.5673306182425 | -1.56733061824253 |
146 | 4 | 13.1304419943729 | -9.13044199437285 |
147 | 8 | 11.5815889070702 | -3.58158890707025 |
148 | 17 | 11.1323685752909 | 5.86763142470914 |
149 | 16 | 12.6000123050881 | 3.39998769491194 |
150 | 12 | 13.9805642905123 | -1.98056429051232 |
151 | 12 | 11.0423107801524 | 0.957689219847574 |
152 | 15 | 13.1951831290347 | 1.80481687096535 |
153 | 9 | 12.9334263448874 | -3.93342634488739 |
154 | 13 | 12.0177194646798 | 0.982280535320237 |
155 | 14 | 11.938569468502 | 2.06143053149801 |
156 | 11 | 10.9620733656727 | 0.0379266343272837 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
10 | 0.947193326477199 | 0.105613347045601 | 0.0528066735228007 |
11 | 0.956904464665324 | 0.0861910706693512 | 0.0430955353346756 |
12 | 0.920697888667066 | 0.158604222665867 | 0.0793021113329336 |
13 | 0.882492531993626 | 0.235014936012748 | 0.117507468006374 |
14 | 0.831787362559643 | 0.336425274880715 | 0.168212637440357 |
15 | 0.833637665347259 | 0.332724669305483 | 0.166362334652741 |
16 | 0.772337166541829 | 0.455325666916341 | 0.227662833458171 |
17 | 0.702449654958027 | 0.595100690083946 | 0.297550345041973 |
18 | 0.632540296200812 | 0.734919407598376 | 0.367459703799188 |
19 | 0.682909876885509 | 0.634180246228983 | 0.317090123114491 |
20 | 0.608275275154214 | 0.783449449691572 | 0.391724724845786 |
21 | 0.591743521167003 | 0.816512957665995 | 0.408256478832997 |
22 | 0.556714998106944 | 0.886570003786111 | 0.443285001893056 |
23 | 0.646721021452639 | 0.706557957094723 | 0.353278978547361 |
24 | 0.705613423368859 | 0.588773153262282 | 0.294386576631141 |
25 | 0.655107069104288 | 0.689785861791424 | 0.344892930895712 |
26 | 0.721708149004592 | 0.556583701990816 | 0.278291850995408 |
27 | 0.708669496827631 | 0.582661006344739 | 0.291330503172369 |
28 | 0.7334035966462 | 0.533192806707601 | 0.2665964033538 |
29 | 0.688634669337594 | 0.622730661324812 | 0.311365330662406 |
30 | 0.712517610918986 | 0.574964778162027 | 0.287482389081014 |
31 | 0.756236342798999 | 0.487527314402002 | 0.243763657201001 |
32 | 0.708319232636352 | 0.583361534727296 | 0.291680767363648 |
33 | 0.656095459510699 | 0.687809080978602 | 0.343904540489301 |
34 | 0.642051843077262 | 0.715896313845475 | 0.357948156922738 |
35 | 0.585402013702521 | 0.829195972594959 | 0.414597986297479 |
36 | 0.563956326029157 | 0.872087347941685 | 0.436043673970843 |
37 | 0.511256840223565 | 0.977486319552869 | 0.488743159776435 |
38 | 0.524822655514506 | 0.950354688970988 | 0.475177344485494 |
39 | 0.503337879784778 | 0.993324240430445 | 0.496662120215222 |
40 | 0.502932964222003 | 0.994134071555994 | 0.497067035777997 |
41 | 0.495023160033715 | 0.990046320067431 | 0.504976839966285 |
42 | 0.735243870547754 | 0.529512258904491 | 0.264756129452246 |
43 | 0.719873123327977 | 0.560253753344047 | 0.280126876672023 |
44 | 0.675280114393177 | 0.649439771213646 | 0.324719885606823 |
45 | 0.70403386234207 | 0.591932275315861 | 0.29596613765793 |
46 | 0.656899842586546 | 0.686200314826907 | 0.343100157413454 |
47 | 0.693100856542594 | 0.613798286914812 | 0.306899143457406 |
48 | 0.741266019954485 | 0.517467960091031 | 0.258733980045515 |
49 | 0.714501470205834 | 0.570997059588332 | 0.285498529794166 |
50 | 0.67272915264572 | 0.65454169470856 | 0.32727084735428 |
51 | 0.7674943066196 | 0.4650113867608 | 0.2325056933804 |
52 | 0.745930311351737 | 0.508139377296526 | 0.254069688648263 |
53 | 0.705616439853054 | 0.588767120293892 | 0.294383560146946 |
54 | 0.676797856010564 | 0.646404287978872 | 0.323202143989436 |
55 | 0.636718001879889 | 0.726563996240222 | 0.363281998120111 |
56 | 0.599352402040276 | 0.801295195919447 | 0.400647597959724 |
57 | 0.56216862171532 | 0.87566275656936 | 0.43783137828468 |
58 | 0.5463336336521 | 0.907332732695799 | 0.4536663663479 |
59 | 0.499360675956351 | 0.998721351912701 | 0.50063932404365 |
60 | 0.456507089370293 | 0.913014178740585 | 0.543492910629707 |
61 | 0.435066052861484 | 0.870132105722969 | 0.564933947138516 |
62 | 0.509243951454315 | 0.98151209709137 | 0.490756048545685 |
63 | 0.617218964432564 | 0.765562071134872 | 0.382781035567436 |
64 | 0.600277378171986 | 0.799445243656027 | 0.399722621828014 |
65 | 0.619703762561743 | 0.760592474876514 | 0.380296237438257 |
66 | 0.577188055200848 | 0.845623889598304 | 0.422811944799152 |
67 | 0.565077179793268 | 0.869845640413463 | 0.434922820206732 |
68 | 0.590020889566676 | 0.819958220866648 | 0.409979110433324 |
69 | 0.545625666579154 | 0.908748666841693 | 0.454374333420846 |
70 | 0.670034528269929 | 0.659930943460141 | 0.329965471730071 |
71 | 0.645189996874679 | 0.709620006250643 | 0.354810003125321 |
72 | 0.611289658181353 | 0.777420683637294 | 0.388710341818647 |
73 | 0.569427975638134 | 0.861144048723733 | 0.430572024361866 |
74 | 0.560469665135126 | 0.879060669729749 | 0.439530334864874 |
75 | 0.516967027186257 | 0.966065945627486 | 0.483032972813743 |
76 | 0.491058804023234 | 0.982117608046467 | 0.508941195976766 |
77 | 0.464425361646178 | 0.928850723292357 | 0.535574638353822 |
78 | 0.426566662913753 | 0.853133325827506 | 0.573433337086247 |
79 | 0.4494974957461 | 0.898994991492201 | 0.5505025042539 |
80 | 0.490760437076865 | 0.98152087415373 | 0.509239562923135 |
81 | 0.530385183278234 | 0.939229633443532 | 0.469614816721766 |
82 | 0.490805473083941 | 0.981610946167882 | 0.509194526916059 |
83 | 0.472187615418773 | 0.944375230837546 | 0.527812384581227 |
84 | 0.426227021628653 | 0.852454043257305 | 0.573772978371347 |
85 | 0.437395877823804 | 0.874791755647607 | 0.562604122176196 |
86 | 0.39541108354172 | 0.79082216708344 | 0.60458891645828 |
87 | 0.36190624051444 | 0.723812481028879 | 0.63809375948556 |
88 | 0.331052722256962 | 0.662105444513923 | 0.668947277743038 |
89 | 0.305189232469919 | 0.610378464939837 | 0.694810767530081 |
90 | 0.26731091417689 | 0.534621828353779 | 0.73268908582311 |
91 | 0.239541545166722 | 0.479083090333445 | 0.760458454833278 |
92 | 0.204082032150348 | 0.408164064300696 | 0.795917967849652 |
93 | 0.203623598860265 | 0.40724719772053 | 0.796376401139735 |
94 | 0.21908926013509 | 0.438178520270179 | 0.78091073986491 |
95 | 0.190872882642197 | 0.381745765284395 | 0.809127117357803 |
96 | 0.182709903914024 | 0.365419807828049 | 0.817290096085976 |
97 | 0.333919549065621 | 0.667839098131242 | 0.666080450934379 |
98 | 0.325933084371378 | 0.651866168742756 | 0.674066915628622 |
99 | 0.306153405850402 | 0.612306811700804 | 0.693846594149598 |
100 | 0.271262908020791 | 0.542525816041582 | 0.728737091979209 |
101 | 0.291122665403136 | 0.582245330806273 | 0.708877334596864 |
102 | 0.270926343492743 | 0.541852686985486 | 0.729073656507257 |
103 | 0.245207554814281 | 0.490415109628563 | 0.754792445185719 |
104 | 0.35176117280371 | 0.70352234560742 | 0.64823882719629 |
105 | 0.591330021562691 | 0.817339956874619 | 0.408669978437309 |
106 | 0.673463029544408 | 0.653073940911184 | 0.326536970455592 |
107 | 0.627268380985699 | 0.745463238028601 | 0.372731619014301 |
108 | 0.642554984093959 | 0.714890031812082 | 0.357445015906041 |
109 | 0.594825475717706 | 0.810349048564588 | 0.405174524282294 |
110 | 0.57200349754713 | 0.855993004905739 | 0.42799650245287 |
111 | 0.523172454994647 | 0.953655090010705 | 0.476827545005353 |
112 | 0.512416965653708 | 0.975166068692584 | 0.487583034346292 |
113 | 0.606296224550446 | 0.787407550899108 | 0.393703775449554 |
114 | 0.553582515218695 | 0.892834969562609 | 0.446417484781305 |
115 | 0.50206811674886 | 0.995863766502281 | 0.49793188325114 |
116 | 0.463000773371962 | 0.926001546743925 | 0.536999226628038 |
117 | 0.438711543015197 | 0.877423086030395 | 0.561288456984803 |
118 | 0.459230982695065 | 0.91846196539013 | 0.540769017304935 |
119 | 0.448118644333165 | 0.896237288666329 | 0.551881355666835 |
120 | 0.4895174603782 | 0.979034920756401 | 0.5104825396218 |
121 | 0.454114137148908 | 0.908228274297816 | 0.545885862851092 |
122 | 0.512404230727213 | 0.975191538545574 | 0.487595769272787 |
123 | 0.527571913677075 | 0.94485617264585 | 0.472428086322925 |
124 | 0.538126827901501 | 0.923746344196997 | 0.461873172098498 |
125 | 0.540538811636947 | 0.918922376726106 | 0.459461188363053 |
126 | 0.717743294637346 | 0.564513410725308 | 0.282256705362654 |
127 | 0.828659303310928 | 0.342681393378144 | 0.171340696689072 |
128 | 0.808872961036705 | 0.382254077926589 | 0.191127038963295 |
129 | 0.762083539901145 | 0.475832920197711 | 0.237916460098855 |
130 | 0.74531913545375 | 0.509361729092501 | 0.25468086454625 |
131 | 0.683055534797616 | 0.633888930404768 | 0.316944465202384 |
132 | 0.621428688754112 | 0.757142622491776 | 0.378571311245888 |
133 | 0.667643631906929 | 0.664712736186142 | 0.332356368093071 |
134 | 0.606933133249548 | 0.786133733500904 | 0.393066866750452 |
135 | 0.563389720720028 | 0.873220558559944 | 0.436610279279972 |
136 | 0.548723803912352 | 0.902552392175295 | 0.451276196087648 |
137 | 0.540433562909047 | 0.919132874181906 | 0.459566437090953 |
138 | 0.482943944234027 | 0.965887888468055 | 0.517056055765973 |
139 | 0.432114738837496 | 0.864229477674991 | 0.567885261162504 |
140 | 0.555935954665696 | 0.888128090668609 | 0.444064045334304 |
141 | 0.615825878917114 | 0.768348242165771 | 0.384174121082886 |
142 | 0.537130082558964 | 0.925739834882073 | 0.462869917441036 |
143 | 0.785392237316999 | 0.429215525366002 | 0.214607762683001 |
144 | 0.685253206457179 | 0.629493587085642 | 0.314746793542821 |
145 | 0.662856074469117 | 0.674287851061765 | 0.337143925530883 |
146 | 0.567429159577552 | 0.865141680844895 | 0.432570840422448 |
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 | 1 | 0.0072992700729927 | OK |