Multiple Linear Regression - Estimated Regression Equation |
Schoolprestaties[t] = + 6.43367253896819 + 0.450179139377826Sport[t] + 0.085372627349095GoingOut[t] -0.138164152811177Relation[t] + 0.295236033763927Family[t] -0.0749226417961014Friends[t] + 0.318308737029959Coach[t] + 0.0206352291166547Job[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) | 6.43367253896819 | 1.456809 | 4.4163 | 1.9e-05 | 1e-05 |
Sport | 0.450179139377826 | 0.176586 | 2.5494 | 0.01181 | 0.005905 |
GoingOut | 0.085372627349095 | 0.143526 | 0.5948 | 0.552869 | 0.276434 |
Relation | -0.138164152811177 | 0.100566 | -1.3739 | 0.171561 | 0.08578 |
Family | 0.295236033763927 | 0.189349 | 1.5592 | 0.121081 | 0.060541 |
Friends | -0.0749226417961014 | 0.13832 | -0.5417 | 0.588865 | 0.294433 |
Coach | 0.318308737029959 | 0.139074 | 2.2888 | 0.023508 | 0.011754 |
Job | 0.0206352291166547 | 0.167148 | 0.1235 | 0.901915 | 0.450957 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.431556935643619 |
R-squared | 0.186241388702111 |
Adjusted R-squared | 0.147752805735319 |
F-TEST (value) | 4.8388736177375 |
F-TEST (DF numerator) | 7 |
F-TEST (DF denominator) | 148 |
p-value | 6.20325530915622e-05 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 3.22513632282737 |
Sum Squared Residuals | 1539.42263652143 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 14 | 10.5533754631795 | 3.44662453682054 |
2 | 8 | 11.5200618216032 | -3.52006182160317 |
3 | 12 | 11.9390262515676 | 0.060973748432418 |
4 | 7 | 12.6266623780542 | -5.62666237805421 |
5 | 10 | 13.0925319504486 | -3.09253195044858 |
6 | 9 | 11.8050193203685 | -2.80501932036849 |
7 | 16 | 14.4905136795887 | 1.50948632041129 |
8 | 7 | 9.72264782589193 | -2.72264782589193 |
9 | 14 | 12.18177945868 | 1.81822054132005 |
10 | 6 | 11.0456118318527 | -5.04561183185268 |
11 | 16 | 12.1735423711493 | 3.82645762885071 |
12 | 11 | 11.6220327824491 | -0.622032782449136 |
13 | 17 | 13.3364679553045 | 3.66353204469552 |
14 | 12 | 11.4017103518401 | 0.598289648159931 |
15 | 7 | 12.4189472280584 | -5.41894722805835 |
16 | 13 | 10.97384759608 | 2.02615240391995 |
17 | 9 | 7.59105080808949 | 1.40894919191051 |
18 | 15 | 14.3082403200311 | 0.691759679968923 |
19 | 7 | 10.5132184711492 | -3.51321847114923 |
20 | 9 | 10.3015228853222 | -1.30152288532223 |
21 | 7 | 8.9320689990124 | -1.93206899901241 |
22 | 14 | 13.7668048172394 | 0.233195182760608 |
23 | 15 | 10.6888547504181 | 4.31114524958192 |
24 | 7 | 12.9380112607235 | -5.93801126072353 |
25 | 13 | 12.1735423711493 | 0.826457628850708 |
26 | 17 | 12.1735423711493 | 4.82645762885071 |
27 | 15 | 13.6060006198691 | 1.39399938013087 |
28 | 14 | 9.08258408991662 | 4.91741591008338 |
29 | 14 | 12.9584251189006 | 1.04157488109943 |
30 | 8 | 11.287253791427 | -3.28725379142698 |
31 | 8 | 9.3239443858446 | -1.3239443858446 |
32 | 12 | 14.1077658426571 | -2.10776584265711 |
33 | 14 | 13.0448147158304 | 0.95518528416962 |
34 | 8 | 12.4195643385144 | -4.4195643385144 |
35 | 11 | 10.3015228853222 | 0.698477114677765 |
36 | 16 | 11.6906526351407 | 4.30934736485931 |
37 | 11 | 13.0025272880164 | -2.00252728801635 |
38 | 8 | 11.2168973991191 | -3.21689739911911 |
39 | 14 | 12.3521273711106 | 1.64787262888939 |
40 | 16 | 10.0472519738302 | 5.95274802616985 |
41 | 14 | 11.7524945379063 | 2.24750546209368 |
42 | 5 | 11.3021240381773 | -6.30212403817729 |
43 | 8 | 9.42741882975867 | -1.42741882975867 |
44 | 10 | 10.3598981880733 | -0.359898188073331 |
45 | 8 | 12.2589149984984 | -4.25891499849839 |
46 | 13 | 12.636524847546 | 0.363475152453992 |
47 | 15 | 11.5120243637826 | 3.48797563621735 |
48 | 6 | 11.4103664924105 | -5.41036649241052 |
49 | 12 | 10.2918517761816 | 1.70814822381836 |
50 | 14 | 12.8190298208614 | 1.18097017913864 |
51 | 5 | 12.7869780728428 | -7.78697807284279 |
52 | 15 | 12.8586569008031 | 2.14134309919693 |
53 | 11 | 11.907718163175 | -0.907718163174993 |
54 | 8 | 10.0895071723907 | -2.08950717239074 |
55 | 13 | 11.3330747214831 | 1.66692527851693 |
56 | 14 | 12.7637336204159 | 1.2362663795841 |
57 | 12 | 9.724700660362 | 2.27529933963799 |
58 | 16 | 12.4949127304153 | 3.50508726958466 |
59 | 10 | 8.49140908684514 | 1.50859091315486 |
60 | 15 | 14.066197086093 | 0.933802913906998 |
61 | 8 | 9.47435270975693 | -1.47435270975693 |
62 | 16 | 9.09163950384027 | 6.90836049615973 |
63 | 19 | 13.3208360250463 | 5.67916397495369 |
64 | 14 | 11.4591751923887 | 2.54082480761127 |
65 | 7 | 12.3892834625206 | -5.38928346252062 |
66 | 13 | 11.907718163175 | 1.09228183682501 |
67 | 15 | 11.6661349515649 | 3.33386504843508 |
68 | 7 | 9.3174880124059 | -2.31748801240591 |
69 | 13 | 12.9056335934385 | 0.0943664065615145 |
70 | 4 | 9.61024209893835 | -5.61024209893835 |
71 | 14 | 11.7730843949627 | 2.22691560503732 |
72 | 13 | 12.6812480890645 | 0.318751910935544 |
73 | 11 | 9.61034012589545 | 1.38965987410455 |
74 | 14 | 11.6072839363646 | 2.39271606363539 |
75 | 12 | 11.1024388376955 | 0.89756116230455 |
76 | 15 | 13.4613722525627 | 1.53862774743734 |
77 | 14 | 11.9283533922916 | 2.07164660770835 |
78 | 13 | 11.3653227363627 | 1.63467726363728 |
79 | 7 | 9.98601102853903 | -2.98601102853903 |
80 | 5 | 7.96695059427243 | -2.96695059427243 |
81 | 7 | 11.8669077272697 | -4.86690772726969 |
82 | 13 | 12.9950181699905 | 0.00498183000954396 |
83 | 13 | 11.4109586564496 | 1.58904134355035 |
84 | 11 | 12.5520380345889 | -1.55203803458891 |
85 | 6 | 8.7344968837482 | -2.73449688374821 |
86 | 12 | 13.0025272880164 | -1.00252728801635 |
87 | 8 | 9.62952133606113 | -1.62952133606113 |
88 | 11 | 11.8864553811634 | -0.886455381163419 |
89 | 12 | 14.6565937709722 | -2.65659377097215 |
90 | 9 | 9.94929722274015 | -0.949297222740151 |
91 | 12 | 10.6336161537528 | 1.36638384624718 |
92 | 13 | 13.6657391099064 | -0.665739109906395 |
93 | 16 | 13.1508225722961 | 2.84917742770387 |
94 | 16 | 13.2370434075981 | 2.76295659240194 |
95 | 11 | 12.9994569257455 | -1.99945692574549 |
96 | 8 | 10.4229255234411 | -2.42292552344109 |
97 | 4 | 8.1138599594134 | -4.11385995941341 |
98 | 7 | 9.7152682026098 | -2.7152682026098 |
99 | 14 | 11.2168973991191 | 2.78310260088089 |
100 | 11 | 11.3916288110257 | -0.391628811025697 |
101 | 17 | 13.0262328794039 | 3.97376712059613 |
102 | 15 | 13.1301873431795 | 1.86981265682053 |
103 | 14 | 12.7789905078561 | 1.22100949214392 |
104 | 5 | 11.6686587670628 | -6.6686587670628 |
105 | 4 | 11.3215144329553 | -7.32151443295527 |
106 | 19 | 12.1976151221466 | 6.80238487785344 |
107 | 11 | 9.82127605907555 | 1.17872394092445 |
108 | 15 | 12.3732226225553 | 2.62677737744474 |
109 | 10 | 9.30360745505874 | 0.696392544941258 |
110 | 9 | 10.939552123916 | -1.93955212391604 |
111 | 12 | 9.61024209893835 | 2.38975790106165 |
112 | 15 | 12.5534789228418 | 2.4465210771582 |
113 | 7 | 13.0025272880164 | -6.00252728801635 |
114 | 13 | 11.4195775792231 | 1.58042242077689 |
115 | 14 | 13.0962647952358 | 0.903735204764227 |
116 | 14 | 12.1735423711493 | 1.82645762885071 |
117 | 14 | 13.8820013733315 | 0.117998626668537 |
118 | 8 | 11.0325721496547 | -3.03257214965466 |
119 | 15 | 12.0881697438002 | 2.9118302561998 |
120 | 15 | 10.6336161537528 | 4.36638384624717 |
121 | 9 | 9.7264194213023 | -0.726419421302312 |
122 | 16 | 11.9283533922916 | 4.07164660770835 |
123 | 9 | 11.4922945182892 | -2.49229451828918 |
124 | 15 | 13.5617846461308 | 1.43821535386921 |
125 | 15 | 12.1735423711493 | 2.82645762885071 |
126 | 6 | 11.6906526351407 | -5.69065263514069 |
127 | 8 | 13.5745965511151 | -5.57459655111509 |
128 | 15 | 12.2354480584993 | 2.76455194150074 |
129 | 10 | 8.37038994441404 | 1.62961005558596 |
130 | 9 | 10.6421637836354 | -1.64216378363544 |
131 | 14 | 13.9706392151802 | 0.0293607848197538 |
132 | 12 | 13.9574534991062 | -1.95745349910623 |
133 | 8 | 10.4709000451427 | -2.47090004514272 |
134 | 11 | 11.8349900823126 | -0.834990082312648 |
135 | 13 | 11.1577085613893 | 1.84229143861074 |
136 | 9 | 10.8129090383336 | -1.81290903833363 |
137 | 15 | 12.66103677862 | 2.33896322138003 |
138 | 13 | 9.42741882975867 | 3.57258117024133 |
139 | 15 | 12.1735423711493 | 2.82645762885071 |
140 | 14 | 11.907718163175 | 2.09228183682501 |
141 | 16 | 11.2414150826949 | 4.75858491730513 |
142 | 12 | 12.1735423711493 | -0.173542371149291 |
143 | 14 | 9.48645575819956 | 4.51354424180044 |
144 | 10 | 10.1435094174375 | -0.143509417437472 |
145 | 10 | 9.76124310315073 | 0.238756896849271 |
146 | 4 | 13.023162517133 | -9.023162517133 |
147 | 8 | 11.2994383155857 | -3.29943831558573 |
148 | 17 | 13.1825892798864 | 3.81741072011361 |
149 | 16 | 11.948774445761 | 4.05122555423901 |
150 | 12 | 14.3638705940063 | -2.36387059400631 |
151 | 12 | 11.5527639653642 | 0.447236034635813 |
152 | 15 | 13.1301873431795 | 1.86981265682053 |
153 | 9 | 9.52159653403442 | -0.521596534034424 |
154 | 13 | 12.8501354611744 | 0.149864538825616 |
155 | 14 | 11.8349900823126 | 2.16500991768735 |
156 | 11 | 9.78802851272559 | 1.21197148727442 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
11 | 0.587126822409171 | 0.825746355181657 | 0.412873177590829 |
12 | 0.429450037876422 | 0.858900075752843 | 0.570549962123578 |
13 | 0.505456961119181 | 0.989086077761637 | 0.494543038880819 |
14 | 0.600688244853181 | 0.798623510293638 | 0.399311755146819 |
15 | 0.854124657107087 | 0.291750685785826 | 0.145875342892913 |
16 | 0.790394778879301 | 0.419210442241397 | 0.209605221120699 |
17 | 0.791295491300824 | 0.417409017398351 | 0.208704508699176 |
18 | 0.719782156361532 | 0.560435687276936 | 0.280217843638468 |
19 | 0.746296943891649 | 0.507406112216703 | 0.253703056108351 |
20 | 0.67921955258671 | 0.64156089482658 | 0.32078044741329 |
21 | 0.605578077038303 | 0.788843845923394 | 0.394421922961697 |
22 | 0.52933307861911 | 0.94133384276178 | 0.47066692138089 |
23 | 0.624742490984215 | 0.75051501803157 | 0.375257509015785 |
24 | 0.738753659161786 | 0.522492681676428 | 0.261246340838214 |
25 | 0.681120939101208 | 0.637758121797584 | 0.318879060898792 |
26 | 0.742614200878264 | 0.514771598243473 | 0.257385799121736 |
27 | 0.690066496228128 | 0.619867007543743 | 0.309933503771872 |
28 | 0.755249761015867 | 0.489500477968266 | 0.244750238984133 |
29 | 0.745491177351696 | 0.509017645296607 | 0.254508822648304 |
30 | 0.761183733834948 | 0.477632532330103 | 0.238816266165052 |
31 | 0.74004139723416 | 0.519917205531681 | 0.259958602765841 |
32 | 0.693602170177103 | 0.612795659645795 | 0.306397829822897 |
33 | 0.639309203019263 | 0.721381593961473 | 0.360690796980737 |
34 | 0.62523914701655 | 0.7495217059669 | 0.37476085298345 |
35 | 0.567727442500207 | 0.864545114999587 | 0.432272557499793 |
36 | 0.56488931918188 | 0.87022136163624 | 0.43511068081812 |
37 | 0.513394504866874 | 0.973210990266253 | 0.486605495133126 |
38 | 0.510542310642881 | 0.978915378714237 | 0.489457689357119 |
39 | 0.45587914193311 | 0.91175828386622 | 0.54412085806689 |
40 | 0.49285853067525 | 0.985717061350501 | 0.507141469324749 |
41 | 0.546560185344698 | 0.906879629310605 | 0.453439814655302 |
42 | 0.666254367720535 | 0.66749126455893 | 0.333745632279465 |
43 | 0.631470296859949 | 0.737059406280102 | 0.368529703140051 |
44 | 0.580154899915991 | 0.839690200168018 | 0.419845100084009 |
45 | 0.591239580939614 | 0.817520838120773 | 0.408760419060386 |
46 | 0.539058333674798 | 0.921883332650404 | 0.460941666325202 |
47 | 0.510718856958197 | 0.978562286083606 | 0.489281143041803 |
48 | 0.567991791852708 | 0.864016416294583 | 0.432008208147292 |
49 | 0.536459308359299 | 0.927081383281402 | 0.463540691640701 |
50 | 0.500127692443653 | 0.999744615112694 | 0.499872307556347 |
51 | 0.78309365194723 | 0.433812696105541 | 0.21690634805277 |
52 | 0.764596152018235 | 0.47080769596353 | 0.235403847981765 |
53 | 0.727048305545746 | 0.545903388908509 | 0.272951694454254 |
54 | 0.70482318287871 | 0.59035363424258 | 0.29517681712129 |
55 | 0.669908185851781 | 0.660183628296437 | 0.330091814148219 |
56 | 0.632452588156524 | 0.735094823686951 | 0.367547411843476 |
57 | 0.61341015662073 | 0.77317968675854 | 0.38658984337927 |
58 | 0.63426075078659 | 0.731478498426821 | 0.365739249213411 |
59 | 0.593708336493013 | 0.812583327013975 | 0.406291663506987 |
60 | 0.551347141540331 | 0.897305716919338 | 0.448652858459669 |
61 | 0.508673717932448 | 0.982652564135104 | 0.491326282067552 |
62 | 0.730620681098382 | 0.538758637803236 | 0.269379318901618 |
63 | 0.819056394150068 | 0.361887211699864 | 0.180943605849932 |
64 | 0.803195672628212 | 0.393608654743577 | 0.196804327371788 |
65 | 0.849793955133992 | 0.300412089732016 | 0.150206044866008 |
66 | 0.82555905028772 | 0.34888189942456 | 0.17444094971228 |
67 | 0.829685829225226 | 0.340628341549549 | 0.170314170774774 |
68 | 0.829268051076505 | 0.341463897846989 | 0.170731948923495 |
69 | 0.797282777909896 | 0.405434444180208 | 0.202717222090104 |
70 | 0.861166612869722 | 0.277666774260555 | 0.138833387130278 |
71 | 0.845982960342542 | 0.308034079314916 | 0.154017039657458 |
72 | 0.821947171478489 | 0.356105657043022 | 0.178052828521511 |
73 | 0.79645611237148 | 0.407087775257042 | 0.203543887628521 |
74 | 0.779109619186169 | 0.441780761627662 | 0.220890380813831 |
75 | 0.74393683132905 | 0.512126337341901 | 0.256063168670951 |
76 | 0.715957969823542 | 0.568084060352915 | 0.284042030176458 |
77 | 0.69254197755547 | 0.614916044889058 | 0.307458022444529 |
78 | 0.660508572861893 | 0.678982854276214 | 0.339491427138107 |
79 | 0.65488584354891 | 0.69022831290218 | 0.34511415645109 |
80 | 0.647915740110383 | 0.704168519779233 | 0.352084259889617 |
81 | 0.701759434132432 | 0.596481131735137 | 0.298240565867568 |
82 | 0.658836466290165 | 0.68232706741967 | 0.341163533709835 |
83 | 0.622788274333295 | 0.75442345133341 | 0.377211725666705 |
84 | 0.598944050968878 | 0.802111898062243 | 0.401055949031122 |
85 | 0.580974560337853 | 0.838050879324293 | 0.419025439662147 |
86 | 0.537098365346624 | 0.925803269306751 | 0.462901634653376 |
87 | 0.500160706619741 | 0.999678586760517 | 0.499839293380259 |
88 | 0.457386090463361 | 0.914772180926723 | 0.542613909536639 |
89 | 0.437520180293789 | 0.875040360587579 | 0.56247981970621 |
90 | 0.397456367334306 | 0.794912734668611 | 0.602543632665694 |
91 | 0.357973113561379 | 0.715946227122758 | 0.642026886438621 |
92 | 0.316605995025794 | 0.633211990051588 | 0.683394004974206 |
93 | 0.301054577608383 | 0.602109155216766 | 0.698945422391617 |
94 | 0.280906193742387 | 0.561812387484774 | 0.719093806257613 |
95 | 0.254239834183062 | 0.508479668366125 | 0.745760165816938 |
96 | 0.236124720456608 | 0.472249440913216 | 0.763875279543392 |
97 | 0.264972415935738 | 0.529944831871476 | 0.735027584064262 |
98 | 0.258308912147867 | 0.516617824295734 | 0.741691087852133 |
99 | 0.24135704662909 | 0.482714093258179 | 0.75864295337091 |
100 | 0.206179248088148 | 0.412358496176295 | 0.793820751911852 |
101 | 0.22504336303099 | 0.450086726061979 | 0.77495663696901 |
102 | 0.198959404556689 | 0.397918809113379 | 0.80104059544331 |
103 | 0.170972989606511 | 0.341945979213022 | 0.829027010393489 |
104 | 0.284377012368414 | 0.568754024736828 | 0.715622987631586 |
105 | 0.514653480967052 | 0.970693038065895 | 0.485346519032948 |
106 | 0.683495874065833 | 0.633008251868334 | 0.316504125934167 |
107 | 0.638617939922173 | 0.722764120155654 | 0.361382060077827 |
108 | 0.610617892028748 | 0.778764215942503 | 0.389382107971252 |
109 | 0.562725788018748 | 0.874548423962505 | 0.437274211981252 |
110 | 0.536201503876763 | 0.927596992246475 | 0.463798496123237 |
111 | 0.494603716188115 | 0.98920743237623 | 0.505396283811885 |
112 | 0.464766611756559 | 0.929533223513117 | 0.535233388243441 |
113 | 0.58320325205918 | 0.83359349588164 | 0.41679674794082 |
114 | 0.5370060248115 | 0.925987950376999 | 0.4629939751885 |
115 | 0.533767558661498 | 0.932464882677004 | 0.466232441338502 |
116 | 0.490510047501311 | 0.981020095002622 | 0.509489952498689 |
117 | 0.434607360521024 | 0.869214721042049 | 0.565392639478976 |
118 | 0.435187847761727 | 0.870375695523455 | 0.564812152238273 |
119 | 0.416387293982483 | 0.832774587964966 | 0.583612706017517 |
120 | 0.43832535871419 | 0.87665071742838 | 0.56167464128581 |
121 | 0.387595329141303 | 0.775190658282607 | 0.612404670858697 |
122 | 0.434885804817546 | 0.869771609635092 | 0.565114195182454 |
123 | 0.436631251373214 | 0.873262502746428 | 0.563368748626786 |
124 | 0.4435803076663 | 0.8871606153326 | 0.5564196923337 |
125 | 0.419850753619922 | 0.839701507239844 | 0.580149246380078 |
126 | 0.710899070760386 | 0.578201858479228 | 0.289100929239614 |
127 | 0.911050906213778 | 0.177898187572443 | 0.0889490937862215 |
128 | 0.90209164884093 | 0.195816702318139 | 0.0979083511590696 |
129 | 0.872627070517085 | 0.254745858965831 | 0.127372929482915 |
130 | 0.87845767967242 | 0.243084640655159 | 0.12154232032758 |
131 | 0.837057897969687 | 0.325884204060625 | 0.162942102030313 |
132 | 0.791873435939686 | 0.416253128120629 | 0.208126564060314 |
133 | 0.73676484877877 | 0.52647030244246 | 0.26323515122123 |
134 | 0.666001600836124 | 0.667996798327753 | 0.333998399163876 |
135 | 0.648886259694257 | 0.702227480611487 | 0.351113740305743 |
136 | 0.652473491528836 | 0.695053016942328 | 0.347526508471164 |
137 | 0.634856173172046 | 0.730287653655908 | 0.365143826827954 |
138 | 0.568078264944734 | 0.863843470110532 | 0.431921735055266 |
139 | 0.499112472967588 | 0.998224945935176 | 0.500887527032412 |
140 | 0.558002691633374 | 0.883994616733251 | 0.441997308366626 |
141 | 0.565678953617903 | 0.868642092764195 | 0.434321046382097 |
142 | 0.459930043714572 | 0.919860087429145 | 0.540069956285428 |
143 | 0.367141189829509 | 0.734282379659019 | 0.63285881017049 |
144 | 0.259499056202997 | 0.518998112405994 | 0.740500943797003 |
145 | 0.194639704117767 | 0.389279408235533 | 0.805360295882233 |
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 |