Multiple Linear Regression - Estimated Regression Equation |
Popularity[t] = -1.40033179694972 -0.076094555483637Depression[t] + 0.0719081107769395Belonging[t] + 0.0941357682157757Weighted_popularity[t] + 0.083878464867039Parental_criticism[t] -0.0399931531986932Belonging_final[t] -0.0601894895057676Happiness[t] + 0.118163788663957FindingFriends[t] + 0.230029151161890KnowingPeople[t] + 0.344271299678481Liked[t] + 0.522587758027874Celebrity[t] -0.00639854118490133t + 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) | -1.40033179694972 | 2.56448 | -0.546 | 0.585877 | 0.292939 |
Depression | -0.076094555483637 | 0.063844 | -1.1919 | 0.23527 | 0.117635 |
Belonging | 0.0719081107769395 | 0.051482 | 1.3968 | 0.164632 | 0.082316 |
Weighted_popularity | 0.0941357682157757 | 0.0584 | 1.6119 | 0.109169 | 0.054585 |
Parental_criticism | 0.083878464867039 | 0.065932 | 1.2722 | 0.205353 | 0.102677 |
Belonging_final | -0.0399931531986932 | 0.073107 | -0.5471 | 0.585191 | 0.292595 |
Happiness | -0.0601894895057676 | 0.085851 | -0.7011 | 0.484374 | 0.242187 |
FindingFriends | 0.118163788663957 | 0.093894 | 1.2585 | 0.210256 | 0.105128 |
KnowingPeople | 0.230029151161890 | 0.064589 | 3.5614 | 5e-04 | 0.00025 |
Liked | 0.344271299678481 | 0.094193 | 3.655 | 0.00036 | 0.00018 |
Celebrity | 0.522587758027874 | 0.158855 | 3.2897 | 0.001261 | 0.00063 |
t | -0.00639854118490133 | 0.003744 | -1.7091 | 0.089591 | 0.044795 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.747479529845818 |
R-squared | 0.558725647538525 |
Adjusted R-squared | 0.525017190058829 |
F-TEST (value) | 16.5752362852874 |
F-TEST (DF numerator) | 11 |
F-TEST (DF denominator) | 144 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 2.02389408044419 |
Sum Squared Residuals | 589.845203835411 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 15 | 13.1041188809075 | 1.89588111909250 |
2 | 12 | 9.37957223548966 | 2.62042776451034 |
3 | 15 | 13.6692829047351 | 1.33071709526493 |
4 | 12 | 12.1780196356576 | -0.17801963565763 |
5 | 14 | 13.6340663848125 | 0.365933615187533 |
6 | 8 | 9.12171124973133 | -1.12171124973133 |
7 | 11 | 12.1232135702656 | -1.12321357026557 |
8 | 15 | 8.35269535227079 | 6.64730464772921 |
9 | 4 | 6.33029989402401 | -2.33029989402401 |
10 | 13 | 10.609066681238 | 2.39093331876199 |
11 | 19 | 14.3804043758506 | 4.61959562414936 |
12 | 10 | 11.4488108912758 | -1.44881089127583 |
13 | 15 | 17.291412674971 | -2.29141267497098 |
14 | 6 | 13.1906313519517 | -7.19063135195172 |
15 | 7 | 12.1323718286991 | -5.1323718286991 |
16 | 14 | 13.5267488143510 | 0.47325118564904 |
17 | 16 | 14.3203940197277 | 1.67960598027230 |
18 | 16 | 15.7798749483539 | 0.220125051646122 |
19 | 14 | 15.1842230800641 | -1.18422308006412 |
20 | 15 | 15.2061068182984 | -0.206106818298382 |
21 | 14 | 14.6590612639979 | -0.659061263997852 |
22 | 12 | 11.365027849543 | 0.634972150456999 |
23 | 9 | 9.07843878284137 | -0.0784387828413666 |
24 | 12 | 11.5645865588674 | 0.435413441132648 |
25 | 14 | 13.9043636743032 | 0.0956363256968038 |
26 | 12 | 12.0395860686947 | -0.0395860686946777 |
27 | 14 | 13.7449173963345 | 0.255082603665467 |
28 | 10 | 11.3237347453513 | -1.32373474535133 |
29 | 14 | 12.9587063725915 | 1.04129362740849 |
30 | 16 | 16.0209419101327 | -0.0209419101327301 |
31 | 10 | 8.83074442797802 | 1.16925557202198 |
32 | 8 | 10.7103914354383 | -2.71039143543826 |
33 | 12 | 11.7448545892799 | 0.255145410720076 |
34 | 11 | 10.8912398290721 | 0.108760170927926 |
35 | 8 | 10.3166168319753 | -2.31661683197533 |
36 | 13 | 12.1237887246381 | 0.876211275361948 |
37 | 11 | 10.0155668966914 | 0.98443310330859 |
38 | 12 | 9.78578488571004 | 2.21421511428996 |
39 | 16 | 15.2696303658561 | 0.730369634143928 |
40 | 16 | 12.9784721070763 | 3.02152789292375 |
41 | 13 | 13.8822688592405 | -0.882268859240485 |
42 | 14 | 15.2715261726568 | -1.27152617265677 |
43 | 5 | 5.55350869007313 | -0.553508690073128 |
44 | 14 | 13.3175077245915 | 0.682492275408454 |
45 | 13 | 9.03216589577066 | 3.96783410422934 |
46 | 16 | 15.4830206203974 | 0.516979379602634 |
47 | 14 | 14.6731379723986 | -0.673137972398646 |
48 | 15 | 14.2082259830187 | 0.791774016981327 |
49 | 15 | 13.3012294874653 | 1.69877051253468 |
50 | 11 | 12.1583384993798 | -1.15833849937977 |
51 | 15 | 13.6027018993587 | 1.3972981006413 |
52 | 16 | 12.6145287868068 | 3.38547121319315 |
53 | 13 | 13.3125508280339 | -0.312550828033874 |
54 | 11 | 13.6932708599582 | -2.69327085995817 |
55 | 12 | 13.8771452843589 | -1.87714528435892 |
56 | 12 | 11.5368928032068 | 0.463107196793213 |
57 | 10 | 13.3738483993187 | -3.37384839931873 |
58 | 8 | 9.03838872227876 | -1.03838872227876 |
59 | 9 | 9.60405812870067 | -0.604058128700668 |
60 | 12 | 12.0926494029421 | -0.0926494029421035 |
61 | 14 | 13.9481472148274 | 0.0518527851726437 |
62 | 12 | 13.0528342079952 | -1.05283420799521 |
63 | 11 | 11.0075014050402 | -0.00750140504018929 |
64 | 14 | 13.9094005521977 | 0.0905994478022505 |
65 | 7 | 11.5459981683963 | -4.54599816839630 |
66 | 16 | 14.0447539727401 | 1.95524602725989 |
67 | 16 | 15.5371528714492 | 0.462847128550839 |
68 | 11 | 12.2647601803260 | -1.26476018032602 |
69 | 16 | 15.3546121445055 | 0.645387855494538 |
70 | 13 | 14.4183599616621 | -1.41835996166212 |
71 | 11 | 10.8207328878061 | 0.17926711219393 |
72 | 13 | 12.8031760504 | 0.19682394960001 |
73 | 14 | 14.3362199694722 | -0.336219969472208 |
74 | 15 | 13.4861689395864 | 1.51383106041364 |
75 | 10 | 9.35965940722294 | 0.640340592777062 |
76 | 15 | 14.7244744198531 | 0.275525580146891 |
77 | 11 | 12.9958102339005 | -1.99581023390055 |
78 | 11 | 11.4024329141157 | -0.402432914115743 |
79 | 6 | 8.49918198128773 | -2.49918198128773 |
80 | 11 | 9.63233741840193 | 1.36766258159807 |
81 | 12 | 11.5566437019636 | 0.443356298036368 |
82 | 13 | 13.2091406540391 | -0.209140654039053 |
83 | 12 | 12.3210617317896 | -0.321061731789568 |
84 | 8 | 10.6490833407533 | -2.64908334075331 |
85 | 9 | 10.7349212539284 | -1.73492125392839 |
86 | 10 | 11.6467410654182 | -1.64674106541819 |
87 | 16 | 13.1158790701389 | 2.88412092986111 |
88 | 15 | 12.7652299159938 | 2.23477008400617 |
89 | 14 | 13.5696071875676 | 0.430392812432445 |
90 | 12 | 13.6433703651392 | -1.64337036513920 |
91 | 12 | 10.2682747618807 | 1.73172523811934 |
92 | 10 | 8.82033206271318 | 1.17966793728682 |
93 | 12 | 11.4263746133836 | 0.573625386616377 |
94 | 8 | 9.3413456607946 | -1.34134566079460 |
95 | 16 | 14.0520765069226 | 1.94792349307736 |
96 | 11 | 7.75087376463123 | 3.24912623536877 |
97 | 12 | 11.4922744805770 | 0.507725519422968 |
98 | 9 | 10.2998349775947 | -1.29983497759473 |
99 | 14 | 11.3107199255873 | 2.68928007441269 |
100 | 15 | 14.4417914627296 | 0.558208537270431 |
101 | 8 | 10.7050914338505 | -2.70509143385053 |
102 | 12 | 12.2985131903579 | -0.298513190357948 |
103 | 10 | 10.4127573387016 | -0.412757338701639 |
104 | 16 | 14.7838902026429 | 1.21610979735713 |
105 | 17 | 14.2719966698276 | 2.72800333017243 |
106 | 8 | 10.0794170593795 | -2.07941705937948 |
107 | 9 | 10.5838716669164 | -1.58387166691636 |
108 | 8 | 11.3755467072374 | -3.37554670723741 |
109 | 11 | 12.3744237176035 | -1.37442371760347 |
110 | 16 | 15.2759600290629 | 0.724039970937076 |
111 | 13 | 13.4306727557511 | -0.430672755751130 |
112 | 5 | 7.71119025790909 | -2.71119025790909 |
113 | 15 | 12.7846787100066 | 2.21532128999339 |
114 | 15 | 13.940839216779 | 1.05916078322099 |
115 | 12 | 11.3972919071503 | 0.60270809284972 |
116 | 12 | 11.3956027799066 | 0.60439722009336 |
117 | 16 | 15.7234388724739 | 0.276561127526108 |
118 | 12 | 12.4369449584 | -0.436944958399993 |
119 | 10 | 11.6255542363726 | -1.62555423637263 |
120 | 12 | 10.5660991565575 | 1.43390084344252 |
121 | 4 | 6.22293211352812 | -2.22293211352812 |
122 | 11 | 12.9176944639492 | -1.91769446394925 |
123 | 16 | 14.6788101160740 | 1.32118988392603 |
124 | 7 | 8.79712611731686 | -1.79712611731686 |
125 | 9 | 10.7125218131455 | -1.71252181314545 |
126 | 14 | 10.8281029013784 | 3.17189709862156 |
127 | 11 | 9.64537312488019 | 1.35462687511981 |
128 | 10 | 10.7811590578546 | -0.781159057854605 |
129 | 6 | 8.4773317134976 | -2.47733171349761 |
130 | 14 | 12.8023524491645 | 1.19764755083547 |
131 | 11 | 10.8201744273176 | 0.179825572682416 |
132 | 11 | 9.11860432423373 | 1.88139567576627 |
133 | 9 | 13.8648278690724 | -4.86482786907245 |
134 | 16 | 11.372357927454 | 4.62764207254599 |
135 | 7 | 8.44596341492404 | -1.44596341492404 |
136 | 8 | 8.78090798916263 | -0.780907989162627 |
137 | 10 | 9.90724711312378 | 0.0927528868762226 |
138 | 14 | 11.9107259183342 | 2.08927408166581 |
139 | 9 | 9.55187003377597 | -0.551870033775968 |
140 | 13 | 12.2440385058042 | 0.755961494195762 |
141 | 13 | 9.5840268701916 | 3.41597312980839 |
142 | 12 | 11.6521364140392 | 0.347863585960838 |
143 | 11 | 12.5351681163983 | -1.53516811639827 |
144 | 10 | 14.9020014400070 | -4.90200144000698 |
145 | 12 | 11.9172044351705 | 0.0827955648294793 |
146 | 14 | 13.2419318675388 | 0.758068132461205 |
147 | 11 | 13.3186321462926 | -2.3186321462926 |
148 | 13 | 10.9918777612751 | 2.00812223872485 |
149 | 14 | 13.5428872367616 | 0.457112763238448 |
150 | 13 | 12.5641894932098 | 0.435810506790199 |
151 | 16 | 16.0433459968011 | -0.0433459968011405 |
152 | 13 | 12.1290136015778 | 0.87098639842222 |
153 | 12 | 11.1692656051966 | 0.83073439480335 |
154 | 9 | 9.09291427494277 | -0.0929142749427714 |
155 | 14 | 11.2577678270325 | 2.74223217296746 |
156 | 15 | 14.5279979189494 | 0.472002081050603 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
15 | 0.933649257395563 | 0.132701485208874 | 0.066350742604437 |
16 | 0.999930621874146 | 0.000138756251707923 | 6.93781258539613e-05 |
17 | 0.99982533042272 | 0.000349339154560413 | 0.000174669577280207 |
18 | 0.999578824249336 | 0.000842351501327179 | 0.000421175750663589 |
19 | 0.99944246296334 | 0.00111507407331862 | 0.000557537036659311 |
20 | 0.998941708262373 | 0.00211658347525386 | 0.00105829173762693 |
21 | 0.999034755321167 | 0.00193048935766501 | 0.000965244678832506 |
22 | 0.999567250471365 | 0.000865499057270978 | 0.000432749528635489 |
23 | 0.999157827831607 | 0.00168434433678615 | 0.000842172168393073 |
24 | 0.998445326001666 | 0.00310934799666861 | 0.00155467399833431 |
25 | 0.997235517460621 | 0.00552896507875728 | 0.00276448253937864 |
26 | 0.995267882314468 | 0.00946423537106505 | 0.00473211768553253 |
27 | 0.995942688768337 | 0.00811462246332684 | 0.00405731123166342 |
28 | 0.993516932421401 | 0.0129661351571970 | 0.00648306757859852 |
29 | 0.996582457718479 | 0.00683508456304207 | 0.00341754228152104 |
30 | 0.995217176268008 | 0.0095656474639834 | 0.0047828237319917 |
31 | 0.992921336992382 | 0.0141573260152365 | 0.00707866300761823 |
32 | 0.996284334548904 | 0.00743133090219159 | 0.00371566545109579 |
33 | 0.994330861757432 | 0.0113382764851356 | 0.00566913824256779 |
34 | 0.992277437072564 | 0.0154451258548714 | 0.00772256292743568 |
35 | 0.991279356100053 | 0.0174412877998932 | 0.00872064389994661 |
36 | 0.987757815396007 | 0.0244843692079857 | 0.0122421846039929 |
37 | 0.984893642637731 | 0.0302127147245372 | 0.0151063573622686 |
38 | 0.986023059249697 | 0.0279538815006067 | 0.0139769407503034 |
39 | 0.985261760143423 | 0.0294764797131537 | 0.0147382398565768 |
40 | 0.989836355867045 | 0.0203272882659101 | 0.0101636441329550 |
41 | 0.98602298353575 | 0.0279540329285006 | 0.0139770164642503 |
42 | 0.98077854240216 | 0.0384429151956809 | 0.0192214575978405 |
43 | 0.973489036583066 | 0.0530219268338682 | 0.0265109634169341 |
44 | 0.96769041426965 | 0.064619171460701 | 0.0323095857303505 |
45 | 0.991292554964444 | 0.0174148900711116 | 0.00870744503555578 |
46 | 0.988013678177197 | 0.0239726436456056 | 0.0119863218228028 |
47 | 0.983986894232742 | 0.0320262115345167 | 0.0160131057672583 |
48 | 0.979021719539053 | 0.0419565609218936 | 0.0209782804609468 |
49 | 0.976520832207837 | 0.0469583355843252 | 0.0234791677921626 |
50 | 0.972010259031866 | 0.0559794819362689 | 0.0279897409681344 |
51 | 0.969431950633464 | 0.0611360987330716 | 0.0305680493665358 |
52 | 0.982138988658216 | 0.0357220226835678 | 0.0178610113417839 |
53 | 0.976067376203782 | 0.0478652475924353 | 0.0239326237962177 |
54 | 0.976737935371232 | 0.046524129257535 | 0.0232620646287675 |
55 | 0.973376010621936 | 0.053247978756128 | 0.026623989378064 |
56 | 0.966385646299197 | 0.0672287074016055 | 0.0336143537008028 |
57 | 0.975072812968049 | 0.0498543740639027 | 0.0249271870319513 |
58 | 0.968604685384795 | 0.0627906292304099 | 0.0313953146152050 |
59 | 0.958784031714412 | 0.0824319365711752 | 0.0412159682855876 |
60 | 0.946744710982143 | 0.106510578035714 | 0.0532552890178569 |
61 | 0.93284309119605 | 0.134313817607899 | 0.0671569088039494 |
62 | 0.919899115767245 | 0.160201768465510 | 0.0801008842327551 |
63 | 0.900251949790252 | 0.199496100419497 | 0.0997480502097483 |
64 | 0.884622774641366 | 0.230754450717268 | 0.115377225358634 |
65 | 0.936158227263073 | 0.127683545473854 | 0.0638417727369268 |
66 | 0.941302434161088 | 0.117395131677823 | 0.0586975658389117 |
67 | 0.928161402578554 | 0.143677194842892 | 0.0718385974214462 |
68 | 0.915566004464006 | 0.168867991071989 | 0.0844339955359943 |
69 | 0.898446226792583 | 0.203107546414835 | 0.101553773207417 |
70 | 0.885460236405788 | 0.229079527188424 | 0.114539763594212 |
71 | 0.862778079944178 | 0.274443840111644 | 0.137221920055822 |
72 | 0.83686833746627 | 0.326263325067459 | 0.163131662533729 |
73 | 0.820712211572717 | 0.358575576854567 | 0.179287788427283 |
74 | 0.815138334240323 | 0.369723331519353 | 0.184861665759677 |
75 | 0.79024755103446 | 0.41950489793108 | 0.20975244896554 |
76 | 0.756152108081876 | 0.487695783836248 | 0.243847891918124 |
77 | 0.74665857493936 | 0.506682850121282 | 0.253341425060641 |
78 | 0.705733685052797 | 0.588532629894405 | 0.294266314947203 |
79 | 0.711337750520457 | 0.577324498959087 | 0.288662249479543 |
80 | 0.697204070710098 | 0.605591858579805 | 0.302795929289902 |
81 | 0.661898688272877 | 0.676202623454246 | 0.338101311727123 |
82 | 0.619964852095304 | 0.760070295809392 | 0.380035147904696 |
83 | 0.57265445659414 | 0.85469108681172 | 0.42734554340586 |
84 | 0.581423658877749 | 0.837152682244502 | 0.418576341122251 |
85 | 0.563090203733514 | 0.873819592532972 | 0.436909796266486 |
86 | 0.539508849729024 | 0.920982300541952 | 0.460491150270976 |
87 | 0.59179092784014 | 0.81641814431972 | 0.40820907215986 |
88 | 0.62074372516261 | 0.758512549674781 | 0.379256274837390 |
89 | 0.58586147562107 | 0.82827704875786 | 0.41413852437893 |
90 | 0.569916826068621 | 0.860166347862758 | 0.430083173931379 |
91 | 0.558209635856616 | 0.883580728286768 | 0.441790364143384 |
92 | 0.526465841611335 | 0.94706831677733 | 0.473534158388665 |
93 | 0.482947475442566 | 0.965894950885132 | 0.517052524557434 |
94 | 0.465465526368109 | 0.930931052736217 | 0.534534473631892 |
95 | 0.479307314937569 | 0.958614629875137 | 0.520692685062431 |
96 | 0.619056654163523 | 0.761886691672954 | 0.380943345836477 |
97 | 0.573905600368762 | 0.852188799262475 | 0.426094399631238 |
98 | 0.537911331018487 | 0.924177337963026 | 0.462088668981513 |
99 | 0.604984796249609 | 0.790030407500782 | 0.395015203750391 |
100 | 0.57059121340375 | 0.8588175731925 | 0.42940878659625 |
101 | 0.590821822007804 | 0.818356355984392 | 0.409178177992196 |
102 | 0.544423758730519 | 0.911152482538961 | 0.455576241269481 |
103 | 0.494212308851229 | 0.988424617702457 | 0.505787691148771 |
104 | 0.500220397650356 | 0.999559204699287 | 0.499779602349644 |
105 | 0.551934366440812 | 0.896131267118377 | 0.448065633559188 |
106 | 0.554892150976265 | 0.890215698047471 | 0.445107849023735 |
107 | 0.511942038192078 | 0.976115923615844 | 0.488057961807922 |
108 | 0.60972456271276 | 0.78055087457448 | 0.39027543728724 |
109 | 0.593066740902704 | 0.813866518194592 | 0.406933259097296 |
110 | 0.550577261245747 | 0.898845477508505 | 0.449422738754253 |
111 | 0.494826599668513 | 0.989653199337027 | 0.505173400331487 |
112 | 0.616809343277845 | 0.76638131344431 | 0.383190656722155 |
113 | 0.626154390803578 | 0.747691218392843 | 0.373845609196422 |
114 | 0.615235488097312 | 0.769529023805377 | 0.384764511902688 |
115 | 0.559987629609119 | 0.880024740781762 | 0.440012370390881 |
116 | 0.521138877655042 | 0.957722244689916 | 0.478861122344958 |
117 | 0.477016181848517 | 0.954032363697034 | 0.522983818151483 |
118 | 0.463883416582805 | 0.92776683316561 | 0.536116583417195 |
119 | 0.49473937214882 | 0.98947874429764 | 0.50526062785118 |
120 | 0.44153085835672 | 0.88306171671344 | 0.558469141643279 |
121 | 0.413482952204301 | 0.826965904408603 | 0.586517047795699 |
122 | 0.368587832917053 | 0.737175665834107 | 0.631412167082947 |
123 | 0.426064031980692 | 0.852128063961384 | 0.573935968019308 |
124 | 0.387390103702172 | 0.774780207404344 | 0.612609896297828 |
125 | 0.415133168427088 | 0.830266336854177 | 0.584866831572912 |
126 | 0.444862550468138 | 0.889725100936275 | 0.555137449531862 |
127 | 0.432032123037265 | 0.86406424607453 | 0.567967876962735 |
128 | 0.361613594633677 | 0.723227189267353 | 0.638386405366323 |
129 | 0.598066118848158 | 0.803867762303684 | 0.401933881151842 |
130 | 0.738468831650333 | 0.523062336699334 | 0.261531168349667 |
131 | 0.741820011049845 | 0.516359977900309 | 0.258179988950155 |
132 | 0.789267218156797 | 0.421465563686407 | 0.210732781843203 |
133 | 0.762622726087927 | 0.474754547824146 | 0.237377273912073 |
134 | 0.808958022446945 | 0.382083955106110 | 0.191041977553055 |
135 | 0.732637529174614 | 0.534724941650772 | 0.267362470825386 |
136 | 0.668174881262813 | 0.663650237474374 | 0.331825118737187 |
137 | 0.758245179336002 | 0.483509641327995 | 0.241754820663998 |
138 | 0.704237223954689 | 0.591525552090623 | 0.295762776045311 |
139 | 0.646950914700121 | 0.706098170599757 | 0.353049085299879 |
140 | 0.503093950827842 | 0.993812098344316 | 0.496906049172158 |
141 | 0.40212766654133 | 0.80425533308266 | 0.59787233345867 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 15 | 0.118110236220472 | NOK |
5% type I error level | 36 | 0.283464566929134 | NOK |
10% type I error level | 44 | 0.346456692913386 | NOK |