Multiple Linear Regression - Estimated Regression Equation |
Poular[t] = + 1.35086028455801 + 0.0042491286076238Friends[t] + 0.15135129972613Considerfriends[t] + 0.341801603945097FriendStudents[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) | 1.35086028455801 | 0.363066 | 3.7207 | 0.000279 | 0.00014 |
Friends | 0.0042491286076238 | 0.079078 | 0.0537 | 0.957218 | 0.478609 |
Considerfriends | 0.15135129972613 | 0.083278 | 1.8174 | 0.07112 | 0.03556 |
FriendStudents | 0.341801603945097 | 0.072283 | 4.7287 | 5e-06 | 3e-06 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.460942309224963 |
R-squared | 0.212467812433641 |
Adjusted R-squared | 0.196924413994832 |
F-TEST (value) | 13.6693280604027 |
F-TEST (DF numerator) | 3 |
F-TEST (DF denominator) | 152 |
p-value | 6.09727346390088e-08 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.698728939181563 |
Sum Squared Residuals | 74.2097638283684 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 3 | 2.84731551000220 | 0.152684489997804 |
2 | 3 | 2.50551390605709 | 0.494486093942914 |
3 | 4 | 3.18486798533965 | 0.815132014660347 |
4 | 3 | 2.16371230211199 | 0.83628769788801 |
5 | 3 | 2.34991347772333 | 0.650086522276666 |
6 | 3 | 2.35416260633096 | 0.645837393669042 |
7 | 3 | 2.99866680972831 | 0.00133319027168608 |
8 | 2 | 2.35416260633096 | -0.354162606330958 |
9 | 3 | 2.50551390605709 | 0.494486093942913 |
10 | 3 | 2.34566434911571 | 0.65433565088429 |
11 | 3 | 3.33197015645816 | -0.331970156458163 |
12 | 3 | 2.84731551000218 | 0.152684489997816 |
13 | 3 | 3.18911711394728 | -0.189117113947281 |
14 | 2 | 2.35416260633096 | -0.354162606330958 |
15 | 3 | 2.84731551000218 | 0.152684489997816 |
16 | 3 | 2.69171508166843 | 0.308284918331569 |
17 | 2 | 2.84731551000218 | -0.847315510002184 |
18 | 3 | 3.18911711394728 | -0.189117113947281 |
19 | 2 | 2.34991347772333 | -0.349913477723334 |
20 | 1 | 2.49701564884184 | -1.49701564884184 |
21 | 2 | 2.34566434911571 | -0.345664349115711 |
22 | 3 | 2.84731551000218 | 0.152684489997816 |
23 | 3 | 3.18486798533966 | -0.184867985339657 |
24 | 3 | 2.35416260633096 | 0.645837393669042 |
25 | 3 | 2.84731551000218 | 0.152684489997816 |
26 | 3 | 3.18486798533966 | -0.184867985339657 |
27 | 2 | 2.99441768112069 | -0.99441768112069 |
28 | 3 | 2.83881725278694 | 0.161182747213063 |
29 | 3 | 2.84306638139456 | 0.156933618605439 |
30 | 4 | 2.35416260633096 | 1.64583739366904 |
31 | 3 | 2.34991347772333 | 0.650086522276666 |
32 | 3 | 3.33621928506579 | -0.336219285065787 |
33 | 3 | 2.99866680972831 | 0.00133319027168608 |
34 | 3 | 2.84731551000218 | 0.152684489997816 |
35 | 2 | 2.50126477744946 | -0.501264777449464 |
36 | 3 | 3.34046841367341 | -0.340468413673411 |
37 | 3 | 2.83881725278694 | 0.161182747213063 |
38 | 3 | 2.34991347772333 | 0.650086522276666 |
39 | 3 | 2.84731551000218 | 0.152684489997816 |
40 | 4 | 3.34046841367341 | 0.659531586326589 |
41 | 3 | 3.18486798533966 | -0.184867985339657 |
42 | 3 | 2.50976303466471 | 0.490236965335289 |
43 | 1 | 2.00811187377824 | -1.00811187377824 |
44 | 2 | 2.34991347772333 | -0.349913477723334 |
45 | 3 | 2.84731551000218 | 0.152684489997816 |
46 | 4 | 2.99866680972831 | 1.00133319027169 |
47 | 4 | 3.34471754228103 | 0.655282457718966 |
48 | 2 | 2.34991347772333 | -0.349913477723334 |
49 | 1 | 2.84731551000218 | -1.84731551000218 |
50 | 3 | 3.18911711394728 | -0.189117113947281 |
51 | 3 | 2.49701564884184 | 0.50298435115816 |
52 | 1 | 2.35416260633096 | -1.35416260633096 |
53 | 3 | 2.99866680972831 | 0.00133319027168608 |
54 | 2 | 2.50551390605709 | -0.505513906057087 |
55 | 3 | 3.33621928506579 | -0.336219285065787 |
56 | 3 | 2.84306638139456 | 0.156933618605439 |
57 | 2 | 2.84306638139456 | -0.84306638139456 |
58 | 4 | 3.33197015645816 | 0.668029843541837 |
59 | 1 | 2.88641451449502 | -1.88641451449502 |
60 | 3 | 3.34046841367341 | -0.340468413673411 |
61 | 2 | 2.35416260633096 | -0.354162606330958 |
62 | 4 | 3.18486798533966 | 0.815132014660343 |
63 | 3 | 3.18911711394728 | -0.189117113947281 |
64 | 4 | 3.18486798533966 | 0.815132014660343 |
65 | 3 | 2.50551390605709 | 0.494486093942913 |
66 | 3 | 2.99866680972831 | 0.00133319027168608 |
67 | 3 | 2.69596421027605 | 0.304035789723945 |
68 | 3 | 2.35416260633096 | 0.645837393669042 |
69 | 3 | 3.34046841367341 | -0.340468413673411 |
70 | 1 | 1.86100970265973 | -0.861009702659732 |
71 | 3 | 2.99866680972831 | 0.00133319027168608 |
72 | 3 | 2.99866680972831 | 0.00133319027168608 |
73 | 3 | 2.49701564884184 | 0.50298435115816 |
74 | 2 | 2.34991347772333 | -0.349913477723334 |
75 | 3 | 2.84731551000218 | 0.152684489997816 |
76 | 3 | 2.84731551000218 | 0.152684489997816 |
77 | 3 | 2.84306638139456 | 0.156933618605439 |
78 | 2 | 2.84731551000218 | -0.847315510002184 |
79 | 3 | 2.99866680972831 | 0.00133319027168608 |
80 | 2 | 2.35416260633096 | -0.354162606330958 |
81 | 2 | 2.50126477744946 | -0.501264777449464 |
82 | 3 | 2.84306638139456 | 0.156933618605439 |
83 | 3 | 2.84306638139456 | 0.156933618605439 |
84 | 2 | 2.34991347772333 | -0.349913477723334 |
85 | 2 | 2.35416260633096 | -0.354162606330958 |
86 | 3 | 2.84731551000218 | 0.152684489997816 |
87 | 2 | 2.34566434911571 | -0.345664349115711 |
88 | 3 | 2.84731551000218 | 0.152684489997816 |
89 | 4 | 2.84306638139456 | 1.15693361860544 |
90 | 2 | 2.50551390605709 | -0.505513906057087 |
91 | 3 | 2.84306638139456 | 0.156933618605439 |
92 | 2 | 2.99866680972831 | -0.998666809728314 |
93 | 4 | 3.33621928506579 | 0.663780714934213 |
94 | 3 | 3.33621928506579 | -0.336219285065787 |
95 | 3 | 2.84731551000218 | 0.152684489997816 |
96 | 3 | 2.34991347772333 | 0.650086522276666 |
97 | 3 | 2.16371230211199 | 0.83628769788801 |
98 | 2 | 2.34566434911571 | -0.345664349115711 |
99 | 3 | 2.84731551000218 | 0.152684489997816 |
100 | 4 | 2.84731551000218 | 1.15268448999782 |
101 | 4 | 3.68227001761851 | 0.317729982381492 |
102 | 4 | 3.18911711394728 | 0.810882886052719 |
103 | 3 | 3.53091871789238 | -0.530918717892378 |
104 | 3 | 2.34991347772333 | 0.650086522276666 |
105 | 1 | 1.86100970265973 | -0.861009702659732 |
106 | 4 | 2.84306638139456 | 1.15693361860544 |
107 | 1 | 2.84731551000218 | -1.84731551000218 |
108 | 3 | 3.33621928506579 | -0.336219285065787 |
109 | 2 | 2.34991347772333 | -0.349913477723334 |
110 | 2 | 2.49701564884184 | -0.49701564884184 |
111 | 3 | 2.99866680972831 | 0.00133319027168608 |
112 | 3 | 3.18911711394728 | -0.189117113947281 |
113 | 2 | 2.65686520578322 | -0.656865205783217 |
114 | 3 | 2.98591942390544 | 0.014080576094557 |
115 | 3 | 2.84731551000218 | 0.152684489997816 |
116 | 4 | 3.18911711394728 | 0.810882886052719 |
117 | 4 | 3.18911711394728 | 0.810882886052719 |
118 | 3 | 2.50126477744946 | 0.498735222550536 |
119 | 3 | 2.84731551000218 | 0.152684489997816 |
120 | 3 | 2.50551390605709 | 0.494486093942913 |
121 | 3 | 2.84306638139456 | 0.156933618605439 |
122 | 3 | 3.18911711394728 | -0.189117113947281 |
123 | 1 | 2.65686520578322 | -1.65686520578322 |
124 | 2 | 3.18911711394728 | -1.18911711394728 |
125 | 4 | 3.03776581422115 | 0.962234185778848 |
126 | 3 | 2.65686520578322 | 0.343134794216783 |
127 | 4 | 2.84306638139456 | 1.15693361860544 |
128 | 3 | 2.84306638139456 | 0.156933618605439 |
129 | 2 | 2.54461291054993 | -0.544612910549925 |
130 | 1 | 2.99866680972831 | -1.99866680972831 |
131 | 4 | 3.18911711394728 | 0.810882886052719 |
132 | 3 | 2.69596421027605 | 0.304035789723945 |
133 | 3 | 2.35416260633096 | 0.645837393669042 |
134 | 3 | 2.99866680972831 | 0.00133319027168608 |
135 | 4 | 2.84731551000218 | 1.15268448999782 |
136 | 3 | 2.99866680972831 | 0.00133319027168608 |
137 | 3 | 3.03776581422115 | -0.0377658142211516 |
138 | 1 | 2.99441768112069 | -1.99441768112069 |
139 | 4 | 3.33621928506579 | 0.663780714934213 |
140 | 2 | 3.18911711394728 | -1.18911711394728 |
141 | 2 | 3.18911711394728 | -1.18911711394728 |
142 | 3 | 2.83881725278694 | 0.161182747213063 |
143 | 3 | 2.69596421027605 | 0.304035789723945 |
144 | 2 | 2.50551390605709 | -0.505513906057087 |
145 | 3 | 2.84731551000218 | 0.152684489997816 |
146 | 3 | 2.16796143071961 | 0.832038569280386 |
147 | 2 | 2.65686520578322 | -0.656865205783217 |
148 | 3 | 3.34046841367341 | -0.340468413673411 |
149 | 4 | 3.18911711394728 | 0.810882886052719 |
150 | 4 | 2.84731551000218 | 1.15268448999782 |
151 | 4 | 2.99866680972831 | 1.00133319027169 |
152 | 2 | 3.03776581422115 | -1.03776581422115 |
153 | 3 | 2.50551390605709 | 0.494486093942913 |
154 | 3 | 3.34046841367341 | -0.340468413673411 |
155 | 3 | 2.83881725278694 | 0.161182747213063 |
156 | 3 | 2.84731551000218 | 0.152684489997816 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
7 | 0.0997077201981054 | 0.199415440396211 | 0.900292279801895 |
8 | 0.184142139262694 | 0.368284278525388 | 0.815857860737306 |
9 | 0.0972248604934743 | 0.194449720986949 | 0.902775139506526 |
10 | 0.0837658950309369 | 0.167531790061874 | 0.916234104969063 |
11 | 0.120747972569395 | 0.241495945138790 | 0.879252027430605 |
12 | 0.069600621745846 | 0.139201243491692 | 0.930399378254154 |
13 | 0.0407570976566292 | 0.0815141953132583 | 0.95924290234337 |
14 | 0.0595865857432683 | 0.119173171486537 | 0.940413414256732 |
15 | 0.0343135974349097 | 0.0686271948698193 | 0.96568640256509 |
16 | 0.0192565188736376 | 0.0385130377472752 | 0.980743481126362 |
17 | 0.0466764180855753 | 0.0933528361711505 | 0.953323581914425 |
18 | 0.0282662942727469 | 0.0565325885454937 | 0.971733705727253 |
19 | 0.0380036463569691 | 0.0760072927139381 | 0.96199635364303 |
20 | 0.280344394183375 | 0.56068878836675 | 0.719655605816625 |
21 | 0.229403280068110 | 0.458806560136219 | 0.77059671993189 |
22 | 0.176252536968684 | 0.352505073937368 | 0.823747463031316 |
23 | 0.132468062866502 | 0.264936125733004 | 0.867531937133498 |
24 | 0.109851137094607 | 0.219702274189214 | 0.890148862905393 |
25 | 0.0797527641977912 | 0.159505528395582 | 0.920247235802209 |
26 | 0.0567459837377677 | 0.113491967475535 | 0.943254016262232 |
27 | 0.062669653517619 | 0.125339307035238 | 0.937330346482381 |
28 | 0.0538503222202304 | 0.107700644440461 | 0.94614967777977 |
29 | 0.0399357270362183 | 0.0798714540724366 | 0.960064272963782 |
30 | 0.108999833333925 | 0.217999666667851 | 0.891000166666075 |
31 | 0.0933940921865981 | 0.186788184373196 | 0.906605907813402 |
32 | 0.0714613734202051 | 0.142922746840410 | 0.928538626579795 |
33 | 0.0535129392528578 | 0.107025878505716 | 0.946487060747142 |
34 | 0.0387710811561712 | 0.0775421623123424 | 0.961228918843829 |
35 | 0.0330800542089557 | 0.0661601084179114 | 0.966919945791044 |
36 | 0.0240956247095152 | 0.0481912494190303 | 0.975904375290485 |
37 | 0.0197599559820310 | 0.0395199119640619 | 0.980240044017969 |
38 | 0.0162255966016325 | 0.0324511932032650 | 0.983774403398368 |
39 | 0.0111769177282006 | 0.0223538354564013 | 0.9888230822718 |
40 | 0.0146494307969997 | 0.0292988615939993 | 0.985350569203 |
41 | 0.0103318435500736 | 0.0206636871001471 | 0.989668156449926 |
42 | 0.00753757971402405 | 0.0150751594280481 | 0.992462420285976 |
43 | 0.0188767164876127 | 0.0377534329752255 | 0.981123283512387 |
44 | 0.0164235212985376 | 0.0328470425970752 | 0.983576478701462 |
45 | 0.0116247438152610 | 0.0232494876305221 | 0.988375256184739 |
46 | 0.0209552544855553 | 0.0419105089711106 | 0.979044745514445 |
47 | 0.017757680899154 | 0.035515361798308 | 0.982242319100846 |
48 | 0.0147704070227463 | 0.0295408140454926 | 0.985229592977254 |
49 | 0.134356518325722 | 0.268713036651445 | 0.865643481674278 |
50 | 0.113730990282218 | 0.227461980564436 | 0.886269009717782 |
51 | 0.115440018814416 | 0.230880037628831 | 0.884559981185584 |
52 | 0.237122355699519 | 0.474244711399037 | 0.762877644300481 |
53 | 0.200080847315928 | 0.400161694631856 | 0.799919152684072 |
54 | 0.188557813670264 | 0.377115627340528 | 0.811442186329736 |
55 | 0.161450094800665 | 0.322900189601331 | 0.838549905199335 |
56 | 0.135063355262932 | 0.270126710525865 | 0.864936644737068 |
57 | 0.145690184131426 | 0.291380368262851 | 0.854309815868574 |
58 | 0.157520478548005 | 0.315040957096009 | 0.842479521451995 |
59 | 0.368002495860407 | 0.736004991720814 | 0.631997504139593 |
60 | 0.334184411278982 | 0.668368822557964 | 0.665815588721018 |
61 | 0.301291341032095 | 0.60258268206419 | 0.698708658967905 |
62 | 0.332207429013259 | 0.664414858026518 | 0.667792570986741 |
63 | 0.291883996658072 | 0.583767993316143 | 0.708116003341928 |
64 | 0.316157892642315 | 0.63231578528463 | 0.683842107357685 |
65 | 0.291693523190468 | 0.583387046380937 | 0.708306476809532 |
66 | 0.253841542708134 | 0.507683085416269 | 0.746158457291866 |
67 | 0.227225028796191 | 0.454450057592382 | 0.772774971203809 |
68 | 0.222187210118659 | 0.444374420237318 | 0.777812789881341 |
69 | 0.197089190294300 | 0.394178380588601 | 0.8029108097057 |
70 | 0.212758089861184 | 0.425516179722367 | 0.787241910138816 |
71 | 0.181261365238067 | 0.362522730476133 | 0.818738634761933 |
72 | 0.152823869818969 | 0.305647739637939 | 0.84717613018103 |
73 | 0.137759225531377 | 0.275518451062753 | 0.862240774468623 |
74 | 0.119343487163615 | 0.238686974327231 | 0.880656512836385 |
75 | 0.098502503256754 | 0.197005006513508 | 0.901497496743246 |
76 | 0.0804658994578013 | 0.160931798915603 | 0.919534100542199 |
77 | 0.0650720056054062 | 0.130144011210812 | 0.934927994394594 |
78 | 0.0723674781228154 | 0.144734956245631 | 0.927632521877185 |
79 | 0.0580018478189396 | 0.116003695637879 | 0.94199815218106 |
80 | 0.0486030293810799 | 0.0972060587621597 | 0.95139697061892 |
81 | 0.0440477845731427 | 0.0880955691462854 | 0.955952215426857 |
82 | 0.0346391989240108 | 0.0692783978480216 | 0.96536080107599 |
83 | 0.0269417091806120 | 0.0538834183612241 | 0.973058290819388 |
84 | 0.0221311164018527 | 0.0442622328037053 | 0.977868883598147 |
85 | 0.0180896292900084 | 0.0361792585800169 | 0.981910370709992 |
86 | 0.0136813580661717 | 0.0273627161323433 | 0.986318641933828 |
87 | 0.0112393484612302 | 0.0224786969224605 | 0.98876065153877 |
88 | 0.00833714630466 | 0.01667429260932 | 0.99166285369534 |
89 | 0.0139406014249339 | 0.0278812028498678 | 0.986059398575066 |
90 | 0.0123325054172013 | 0.0246650108344026 | 0.987667494582799 |
91 | 0.00915576404333714 | 0.0183115280866743 | 0.990844235956663 |
92 | 0.0127437632071105 | 0.0254875264142210 | 0.98725623679289 |
93 | 0.0124596024120148 | 0.0249192048240296 | 0.987540397587985 |
94 | 0.00977168325470277 | 0.0195433665094055 | 0.990228316745297 |
95 | 0.0071886754290659 | 0.0143773508581318 | 0.992811324570934 |
96 | 0.00664965852224185 | 0.0132993170444837 | 0.993350341477758 |
97 | 0.0071692770393711 | 0.0143385540787422 | 0.992830722960629 |
98 | 0.00571877785940844 | 0.0114375557188169 | 0.994281222140592 |
99 | 0.0041144772462355 | 0.008228954492471 | 0.995885522753765 |
100 | 0.00715618910625302 | 0.0143123782125060 | 0.992843810893747 |
101 | 0.00562901604410624 | 0.0112580320882125 | 0.994370983955894 |
102 | 0.0063996817551195 | 0.012799363510239 | 0.99360031824488 |
103 | 0.00528663442241695 | 0.0105732688448339 | 0.994713365577583 |
104 | 0.00478400645235927 | 0.00956801290471854 | 0.99521599354764 |
105 | 0.00665535125353362 | 0.0133107025070672 | 0.993344648746466 |
106 | 0.0109518134048810 | 0.0219036268097619 | 0.989048186595119 |
107 | 0.0545922181716176 | 0.109184436343235 | 0.945407781828382 |
108 | 0.0438336264125004 | 0.0876672528250008 | 0.9561663735875 |
109 | 0.0392129632904552 | 0.0784259265809104 | 0.960787036709545 |
110 | 0.0370762462014605 | 0.074152492402921 | 0.96292375379854 |
111 | 0.0285484500106334 | 0.0570969000212669 | 0.971451549989367 |
112 | 0.0214193006675377 | 0.0428386013350754 | 0.978580699332462 |
113 | 0.0200155535268614 | 0.0400311070537228 | 0.979984446473139 |
114 | 0.0146173493018105 | 0.0292346986036211 | 0.98538265069819 |
115 | 0.0105685528863733 | 0.0211371057727466 | 0.989431447113627 |
116 | 0.0121136623474940 | 0.0242273246949880 | 0.987886337652506 |
117 | 0.0143442184862325 | 0.0286884369724651 | 0.985655781513767 |
118 | 0.0110001121545370 | 0.0220002243090739 | 0.988999887845463 |
119 | 0.00779950682316354 | 0.0155990136463271 | 0.992200493176836 |
120 | 0.00595279371435628 | 0.0119055874287126 | 0.994047206285644 |
121 | 0.00406507702728397 | 0.00813015405456795 | 0.995934922972716 |
122 | 0.00272283912847722 | 0.00544567825695444 | 0.997277160871523 |
123 | 0.0121535461332177 | 0.0243070922664353 | 0.987846453866782 |
124 | 0.0179366175445403 | 0.0358732350890807 | 0.98206338245546 |
125 | 0.0219635671802370 | 0.0439271343604741 | 0.978036432819763 |
126 | 0.0161574806681968 | 0.0323149613363936 | 0.983842519331803 |
127 | 0.0250729387337287 | 0.0501458774674574 | 0.974927061266271 |
128 | 0.0179424277960161 | 0.0358848555920321 | 0.982057572203984 |
129 | 0.0198863701503634 | 0.0397727403007269 | 0.980113629849637 |
130 | 0.110662057605004 | 0.221324115210007 | 0.889337942394996 |
131 | 0.126129656862796 | 0.252259313725592 | 0.873870343137204 |
132 | 0.0967792373539926 | 0.193558474707985 | 0.903220762646007 |
133 | 0.0766458511958595 | 0.153291702391719 | 0.92335414880414 |
134 | 0.0552538168648388 | 0.110507633729678 | 0.94474618313516 |
135 | 0.0814371528435614 | 0.162874305687123 | 0.918562847156439 |
136 | 0.0582041234208045 | 0.116408246841609 | 0.941795876579196 |
137 | 0.0405168619454216 | 0.0810337238908432 | 0.959483138054578 |
138 | 0.286707146718020 | 0.573414293436039 | 0.71329285328198 |
139 | 0.289746661466465 | 0.57949332293293 | 0.710253338533535 |
140 | 0.341146988148944 | 0.682293976297889 | 0.658853011851056 |
141 | 0.450307508455385 | 0.90061501691077 | 0.549692491544615 |
142 | 0.363274125722073 | 0.726548251444146 | 0.636725874277927 |
143 | 0.284862182285023 | 0.569724364570045 | 0.715137817714977 |
144 | 0.305020075416075 | 0.610040150832151 | 0.694979924583925 |
145 | 0.219713365063883 | 0.439426730127766 | 0.780286634936117 |
146 | 0.155540620159322 | 0.311081240318644 | 0.844459379840678 |
147 | 0.364695391717337 | 0.729390783434673 | 0.635304608282663 |
148 | 0.306309818380505 | 0.61261963676101 | 0.693690181619495 |
149 | 0.463510206974237 | 0.927020413948475 | 0.536489793025763 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 4 | 0.0279720279720280 | NOK |
5% type I error level | 54 | 0.377622377622378 | NOK |
10% type I error level | 72 | 0.503496503496504 | NOK |