Multiple Linear Regression - Estimated Regression Equation |
Learning[t] = + 4.27566163819704 + 0.108355064457799Connected[t] -0.00635413349300074Separate[t] + 0.522519287456502Software[t] + 0.0866776490697363Happiness[t] -0.0630244321133505Depression[t] + 0.0364344546113714Belonging[t] -0.0458407282060106`Belonging_Final `[t] + 1.08096691583244M1[t] + 0.439345742284376M2[t] + 0.893787137873395M3[t] + 0.9947450378243M4[t] + 0.722758968784425M5[t] + 0.987731822869931M6[t] + 0.485423725907147M7[t] + 0.96487396281522M8[t] -0.0416032140904913M9[t] + 1.20158576284122M10[t] + 0.498842225135348M11[t] -0.00408762794108934t + 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) | 4.27566163819704 | 2.805251 | 1.5242 | 0.129692 | 0.064846 |
Connected | 0.108355064457799 | 0.050373 | 2.151 | 0.033165 | 0.016583 |
Separate | -0.00635413349300074 | 0.047723 | -0.1331 | 0.894266 | 0.447133 |
Software | 0.522519287456502 | 0.072168 | 7.2403 | 0 | 0 |
Happiness | 0.0866776490697363 | 0.080633 | 1.075 | 0.284216 | 0.142108 |
Depression | -0.0630244321133505 | 0.060277 | -1.0456 | 0.297533 | 0.148766 |
Belonging | 0.0364344546113714 | 0.046771 | 0.779 | 0.437276 | 0.218638 |
`Belonging_Final ` | -0.0458407282060106 | 0.066661 | -0.6877 | 0.492783 | 0.246392 |
M1 | 1.08096691583244 | 0.7338 | 1.4731 | 0.142935 | 0.071468 |
M2 | 0.439345742284376 | 0.736031 | 0.5969 | 0.551517 | 0.275758 |
M3 | 0.893787137873395 | 0.739425 | 1.2088 | 0.228764 | 0.114382 |
M4 | 0.9947450378243 | 0.731433 | 1.36 | 0.175987 | 0.087994 |
M5 | 0.722758968784425 | 0.731102 | 0.9886 | 0.324546 | 0.162273 |
M6 | 0.987731822869931 | 0.731018 | 1.3512 | 0.178789 | 0.089394 |
M7 | 0.485423725907147 | 0.74087 | 0.6552 | 0.513394 | 0.256697 |
M8 | 0.96487396281522 | 0.757147 | 1.2744 | 0.204619 | 0.10231 |
M9 | -0.0416032140904913 | 0.743176 | -0.056 | 0.955436 | 0.477718 |
M10 | 1.20158576284122 | 0.747865 | 1.6067 | 0.110344 | 0.055172 |
M11 | 0.498842225135348 | 0.747253 | 0.6676 | 0.505493 | 0.252746 |
t | -0.00408762794108934 | 0.003308 | -1.2356 | 0.218648 | 0.109324 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.626165599110448 |
R-squared | 0.392083357509346 |
Adjusted R-squared | 0.31074239830285 |
F-TEST (value) | 4.82024506883407 |
F-TEST (DF numerator) | 19 |
F-TEST (DF denominator) | 142 |
p-value | 1.50675444343662e-08 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 1.87318265399593 |
Sum Squared Residuals | 498.251482242834 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 13 | 16.7451896390286 | -3.74518963902862 |
2 | 16 | 16.1394744167787 | -0.139474416778698 |
3 | 19 | 16.5737079754519 | 2.4262920245481 |
4 | 15 | 12.3839696879108 | 2.61603031208918 |
5 | 14 | 15.9433768202578 | -1.94337682025784 |
6 | 13 | 15.5634956846109 | -2.56349568461092 |
7 | 19 | 15.0934415248286 | 3.90655847517138 |
8 | 15 | 17.1672070082364 | -2.16720700823636 |
9 | 14 | 15.4491261572241 | -1.44912615722405 |
10 | 15 | 13.4345186019251 | 1.56548139807487 |
11 | 16 | 15.3506490869146 | 0.649350913085399 |
12 | 16 | 15.7789797277346 | 0.221020272265376 |
13 | 16 | 15.9060265007212 | 0.0939734992787748 |
14 | 16 | 15.3491000461924 | 0.650899953807597 |
15 | 17 | 17.9567301750605 | -0.956730175060463 |
16 | 15 | 15.526988925255 | -0.526988925255041 |
17 | 15 | 14.8524702192245 | 0.147529780775512 |
18 | 20 | 16.8471669478825 | 3.15283305211751 |
19 | 18 | 15.4511010408893 | 2.54889895911071 |
20 | 16 | 15.6870667476161 | 0.312933252383946 |
21 | 16 | 14.7978368631116 | 1.20216313688838 |
22 | 16 | 15.35124285841 | 0.648757141589951 |
23 | 19 | 16.3695400185738 | 2.6304599814262 |
24 | 16 | 14.1886091622083 | 1.81139083779171 |
25 | 17 | 15.509523195493 | 1.49047680450705 |
26 | 17 | 16.613826257776 | 0.386173742223957 |
27 | 16 | 15.4541042139265 | 0.545895786073521 |
28 | 15 | 16.5769432383244 | -1.57694323832442 |
29 | 16 | 15.7130189448819 | 0.286981055118129 |
30 | 14 | 14.3985962238864 | -0.398596223886415 |
31 | 15 | 15.573874790707 | -0.573874790707009 |
32 | 12 | 12.648299749556 | -0.648299749555988 |
33 | 14 | 14.5954895008721 | -0.595489500872089 |
34 | 16 | 16.2494595998732 | -0.249459599873202 |
35 | 14 | 15.5601250477392 | -1.56012504773922 |
36 | 7 | 12.4963188664458 | -5.49631886644576 |
37 | 10 | 11.404694672196 | -1.40469467219596 |
38 | 14 | 15.6805713986445 | -1.68057139864454 |
39 | 16 | 14.6841636579659 | 1.31583634203413 |
40 | 16 | 15.000067184002 | 0.999932815998022 |
41 | 16 | 15.2280875681213 | 0.77191243187874 |
42 | 14 | 16.0564227136326 | -2.05642271363265 |
43 | 20 | 17.6746302985299 | 2.3253697014701 |
44 | 14 | 14.4999325015782 | -0.499932501578205 |
45 | 14 | 14.1504145720371 | -0.150414572037055 |
46 | 11 | 16.1242409855361 | -5.12424098553609 |
47 | 14 | 16.3748504141116 | -2.37485041411162 |
48 | 15 | 14.4176508285672 | 0.582349171432826 |
49 | 16 | 15.8623648037587 | 0.13763519624134 |
50 | 14 | 15.7983096217674 | -1.79830962176741 |
51 | 16 | 16.865041520318 | -0.865041520317997 |
52 | 14 | 14.4984053236201 | -0.498405323620124 |
53 | 12 | 14.7279614915831 | -2.7279614915831 |
54 | 16 | 15.5860798356923 | 0.41392016430772 |
55 | 9 | 11.4048595161903 | -2.40485951619033 |
56 | 14 | 13.1109251496804 | 0.889074850319622 |
57 | 16 | 15.4819436956478 | 0.51805630435215 |
58 | 16 | 15.6853954817826 | 0.314604518217421 |
59 | 15 | 15.1598858974952 | -0.159885897495166 |
60 | 16 | 13.5060093706318 | 2.49399062936824 |
61 | 12 | 11.7347097998497 | 0.265290200150277 |
62 | 16 | 15.7463942965977 | 0.253605703402273 |
63 | 16 | 16.628656949695 | -0.62865694969499 |
64 | 14 | 14.6977970785443 | -0.697797078544276 |
65 | 16 | 15.425613930359 | 0.574386069640979 |
66 | 17 | 16.1857534949372 | 0.81424650506276 |
67 | 18 | 15.8422741782062 | 2.15772582179382 |
68 | 18 | 14.853463326123 | 3.14653667387704 |
69 | 12 | 15.228195807044 | -3.22819580704403 |
70 | 16 | 16.0251586814133 | -0.0251586814132895 |
71 | 10 | 13.3714661102156 | -3.37146611021557 |
72 | 14 | 13.7428069355491 | 0.257193064450898 |
73 | 18 | 17.0414457122642 | 0.958554287735813 |
74 | 18 | 16.9350345682719 | 1.06496543172809 |
75 | 16 | 15.8476171789353 | 0.15238282106471 |
76 | 17 | 14.2088723141696 | 2.79112768583042 |
77 | 16 | 16.4839213647992 | -0.483921364799152 |
78 | 16 | 14.7317441160654 | 1.26825588393456 |
79 | 13 | 14.6771437707371 | -1.67714377073709 |
80 | 16 | 16.0356386629328 | -0.0356386629328056 |
81 | 16 | 14.8967047313367 | 1.10329526866328 |
82 | 20 | 17.0296053738749 | 2.97039462612508 |
83 | 16 | 15.5197448656447 | 0.480255134355281 |
84 | 15 | 15.3210963938203 | -0.321096393820332 |
85 | 15 | 15.1583741065861 | -0.158374106586065 |
86 | 16 | 14.012511489833 | 1.98748851016705 |
87 | 14 | 14.5367784206284 | -0.536778420628383 |
88 | 16 | 15.5864641401771 | 0.41353585982287 |
89 | 16 | 14.4799772416247 | 1.52002275837529 |
90 | 15 | 14.3312356646173 | 0.668764335382717 |
91 | 12 | 13.4272871068829 | -1.4272871068829 |
92 | 17 | 17.0358726654063 | -0.0358726654063328 |
93 | 16 | 14.8336748840448 | 1.1663251159552 |
94 | 15 | 15.7080790784194 | -0.708079078419433 |
95 | 13 | 14.8648907828934 | -1.86489078289336 |
96 | 16 | 14.5593567136198 | 1.44064328638024 |
97 | 16 | 16.1141890237113 | -0.114189023711277 |
98 | 16 | 13.8659748430431 | 2.13402515695694 |
99 | 16 | 16.3591890561284 | -0.35918905612839 |
100 | 14 | 14.6557154812792 | -0.655715481279248 |
101 | 16 | 17.3390453472166 | -1.33904534721657 |
102 | 16 | 15.0095335781638 | 0.990466421836217 |
103 | 20 | 17.1872883542688 | 2.81271164573115 |
104 | 15 | 14.5921295882243 | 0.40787041177565 |
105 | 16 | 13.8960570840423 | 2.10394291595769 |
106 | 13 | 15.6257682838975 | -2.62576828389754 |
107 | 17 | 15.8105348569058 | 1.18946514309416 |
108 | 16 | 15.2066444933615 | 0.793355506638502 |
109 | 16 | 14.7133034459108 | 1.28669655408918 |
110 | 12 | 11.9703506700562 | 0.0296493299438496 |
111 | 16 | 15.1798172015566 | 0.82018279844344 |
112 | 16 | 15.964428222177 | 0.0355717778230328 |
113 | 17 | 14.6096060402262 | 2.39039395977375 |
114 | 13 | 14.9511735654269 | -1.9511735654269 |
115 | 12 | 14.7277066942973 | -2.72770669429725 |
116 | 18 | 16.8253291755846 | 1.17467082441538 |
117 | 14 | 14.6559700349261 | -0.655970034926068 |
118 | 14 | 13.5325577067212 | 0.467442293278842 |
119 | 13 | 14.624044736705 | -1.62404473670496 |
120 | 16 | 14.9701028473616 | 1.02989715263843 |
121 | 13 | 14.4998337483978 | -1.49983374839782 |
122 | 16 | 15.1880029928609 | 0.811997007139067 |
123 | 13 | 16.1807463520505 | -3.18074635205048 |
124 | 16 | 17.2569647518428 | -1.2569647518428 |
125 | 15 | 15.862735240263 | -0.862735240262993 |
126 | 16 | 16.8928106185355 | -0.892810618535548 |
127 | 15 | 15.2168501732006 | -0.216850173200556 |
128 | 17 | 16.5072763297195 | 0.492723670280494 |
129 | 15 | 13.2316351358545 | 1.76836486414546 |
130 | 12 | 15.3634445909989 | -3.36344459099887 |
131 | 16 | 13.8169695124099 | 2.18303048759011 |
132 | 10 | 12.4050715205078 | -2.40507152050783 |
133 | 16 | 14.4589278990992 | 1.5410721009008 |
134 | 12 | 13.539348809812 | -1.53934880981202 |
135 | 14 | 15.7868784601568 | -1.78687846015677 |
136 | 15 | 15.3303799356065 | -0.330379935606529 |
137 | 13 | 11.9938487535088 | 1.00615124649115 |
138 | 15 | 14.6098955797817 | 0.390104420218339 |
139 | 11 | 12.7544535040939 | -1.75445350409391 |
140 | 12 | 13.5298806558592 | -1.52988065585925 |
141 | 8 | 12.5020125617428 | -4.50201256174277 |
142 | 16 | 13.4529169900714 | 2.54708300992862 |
143 | 15 | 13.1543754342146 | 1.84562456578539 |
144 | 17 | 15.7140881912821 | 1.28591180871787 |
145 | 16 | 14.9651476507307 | 1.03485234926925 |
146 | 10 | 13.8505924817137 | -3.85059248171373 |
147 | 18 | 15.9021721885407 | 2.09782781145932 |
148 | 13 | 15.1859588320983 | -2.18595883209831 |
149 | 16 | 14.9007530515701 | 1.09924694842993 |
150 | 13 | 13.0756941618866 | -0.0756941618866246 |
151 | 10 | 12.9690890471681 | -2.96908904716813 |
152 | 15 | 16.5069784394832 | -1.50697843948319 |
153 | 16 | 13.2809389721161 | 2.7190610278839 |
154 | 16 | 12.4176117670764 | 3.58238823292364 |
155 | 14 | 12.0229232361766 | 1.97707676382336 |
156 | 10 | 11.6932649489102 | -1.69326494891016 |
157 | 17 | 16.8862698022527 | 0.113730197747253 |
158 | 13 | 11.3105081066524 | 1.68949189334757 |
159 | 15 | 14.0443966495857 | 0.955603350414254 |
160 | 16 | 15.1270448849928 | 0.872955115007213 |
161 | 12 | 12.4395839863638 | -0.439583986363836 |
162 | 13 | 12.7603978148808 | 0.23960218511924 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
23 | 0.697302694397424 | 0.605394611205151 | 0.302697305602576 |
24 | 0.863589139185205 | 0.27282172162959 | 0.136410860814795 |
25 | 0.824658795323634 | 0.350682409352731 | 0.175341204676366 |
26 | 0.73532831804981 | 0.52934336390038 | 0.26467168195019 |
27 | 0.63640575313108 | 0.72718849373784 | 0.36359424686892 |
28 | 0.646743890601233 | 0.706512218797534 | 0.353256109398767 |
29 | 0.558408366499841 | 0.883183267000318 | 0.441591633500159 |
30 | 0.720222650629362 | 0.559554698741275 | 0.279777349370638 |
31 | 0.771361164416005 | 0.45727767116799 | 0.228638835583995 |
32 | 0.719998684913336 | 0.560002630173329 | 0.280001315086664 |
33 | 0.662291805788389 | 0.675416388423222 | 0.337708194211611 |
34 | 0.60525205060076 | 0.78949589879848 | 0.39474794939924 |
35 | 0.542489164912092 | 0.915021670175815 | 0.457510835087908 |
36 | 0.908490506479382 | 0.183018987041235 | 0.0915094935206176 |
37 | 0.883142272717856 | 0.233715454564288 | 0.116857727282144 |
38 | 0.859450974939424 | 0.281098050121152 | 0.140549025060576 |
39 | 0.827651580411873 | 0.344696839176254 | 0.172348419588127 |
40 | 0.785720390297831 | 0.428559219404339 | 0.214279609702169 |
41 | 0.734991258315898 | 0.530017483368205 | 0.265008741684102 |
42 | 0.698292602193214 | 0.603414795613572 | 0.301707397806786 |
43 | 0.702402216278634 | 0.595195567442732 | 0.297597783721366 |
44 | 0.650705373031574 | 0.698589253936852 | 0.349294626968426 |
45 | 0.595628509930698 | 0.808742980138604 | 0.404371490069302 |
46 | 0.793197716994534 | 0.413604566010931 | 0.206802283005466 |
47 | 0.86821082317828 | 0.26357835364344 | 0.13178917682172 |
48 | 0.887174482129183 | 0.225651035741633 | 0.112825517870817 |
49 | 0.896091088952706 | 0.207817822094587 | 0.103908911047294 |
50 | 0.881802130268035 | 0.23639573946393 | 0.118197869731965 |
51 | 0.85817953801207 | 0.283640923975862 | 0.141820461987931 |
52 | 0.824447159146211 | 0.351105681707578 | 0.175552840853789 |
53 | 0.831803152164876 | 0.336393695670248 | 0.168196847835124 |
54 | 0.79512535858705 | 0.409749282825899 | 0.20487464141295 |
55 | 0.827905288902006 | 0.344189422195988 | 0.172094711097994 |
56 | 0.79136870879464 | 0.41726258241072 | 0.20863129120536 |
57 | 0.755719621392757 | 0.488560757214487 | 0.244280378607243 |
58 | 0.760464830860557 | 0.479070338278887 | 0.239535169139443 |
59 | 0.727367750505166 | 0.545264498989667 | 0.272632249494834 |
60 | 0.77851769888259 | 0.442964602234821 | 0.22148230111741 |
61 | 0.749311644241368 | 0.501376711517264 | 0.250688355758632 |
62 | 0.718605313835782 | 0.562789372328437 | 0.281394686164218 |
63 | 0.677079797631274 | 0.645840404737452 | 0.322920202368726 |
64 | 0.631425780867186 | 0.737148438265629 | 0.368574219132814 |
65 | 0.592298567627169 | 0.815402864745662 | 0.407701432372831 |
66 | 0.578355473978365 | 0.84328905204327 | 0.421644526021635 |
67 | 0.606411463899784 | 0.787177072200432 | 0.393588536100216 |
68 | 0.725903940590054 | 0.548192118819892 | 0.274096059409946 |
69 | 0.771325134053018 | 0.457349731893965 | 0.228674865946983 |
70 | 0.735817931231675 | 0.528364137536649 | 0.264182068768325 |
71 | 0.838306159748342 | 0.323387680503316 | 0.161693840251658 |
72 | 0.813316393486356 | 0.373367213027289 | 0.186683606513644 |
73 | 0.798413981058257 | 0.403172037883486 | 0.201586018941743 |
74 | 0.786499914351603 | 0.427000171296794 | 0.213500085648397 |
75 | 0.74964751125112 | 0.50070497749776 | 0.25035248874888 |
76 | 0.763828839097291 | 0.472342321805418 | 0.236171160902709 |
77 | 0.731307817929068 | 0.537384364141865 | 0.268692182070932 |
78 | 0.700574240364984 | 0.598851519270032 | 0.299425759635016 |
79 | 0.686599201686892 | 0.626801596626217 | 0.313400798313108 |
80 | 0.645451073355433 | 0.709097853289134 | 0.354548926644567 |
81 | 0.631092879372731 | 0.737814241254537 | 0.368907120627269 |
82 | 0.71459180656148 | 0.570816386877039 | 0.285408193438519 |
83 | 0.68475217756174 | 0.63049564487652 | 0.31524782243826 |
84 | 0.64283244109777 | 0.71433511780446 | 0.35716755890223 |
85 | 0.612025741643143 | 0.775948516713715 | 0.387974258356857 |
86 | 0.614704076495453 | 0.770591847009095 | 0.385295923504547 |
87 | 0.575009453053845 | 0.84998109389231 | 0.424990546946155 |
88 | 0.527640597372726 | 0.944718805254548 | 0.472359402627274 |
89 | 0.510536657876996 | 0.978926684246008 | 0.489463342123004 |
90 | 0.465431234492334 | 0.930862468984669 | 0.534568765507666 |
91 | 0.43862480525773 | 0.87724961051546 | 0.56137519474227 |
92 | 0.39750441762225 | 0.7950088352445 | 0.60249558237775 |
93 | 0.366354942510826 | 0.732709885021653 | 0.633645057489174 |
94 | 0.326757572030473 | 0.653515144060945 | 0.673242427969527 |
95 | 0.353356171168203 | 0.706712342336405 | 0.646643828831797 |
96 | 0.32530680491389 | 0.65061360982778 | 0.67469319508611 |
97 | 0.284560194742448 | 0.569120389484895 | 0.715439805257552 |
98 | 0.299723940360554 | 0.599447880721107 | 0.700276059639446 |
99 | 0.259652695351026 | 0.519305390702053 | 0.740347304648974 |
100 | 0.224270062319114 | 0.448540124638229 | 0.775729937680886 |
101 | 0.209131998078951 | 0.418263996157903 | 0.790868001921049 |
102 | 0.18072323042987 | 0.361446460859739 | 0.81927676957013 |
103 | 0.279910150564197 | 0.559820301128395 | 0.720089849435803 |
104 | 0.239796596285798 | 0.479593192571596 | 0.760203403714202 |
105 | 0.251144923702565 | 0.502289847405129 | 0.748855076297435 |
106 | 0.267168481935988 | 0.534336963871975 | 0.732831518064012 |
107 | 0.232174252773439 | 0.464348505546878 | 0.767825747226561 |
108 | 0.212040462803197 | 0.424080925606393 | 0.787959537196803 |
109 | 0.19049928733419 | 0.38099857466838 | 0.80950071266581 |
110 | 0.220696388414807 | 0.441392776829613 | 0.779303611585193 |
111 | 0.194505271203578 | 0.389010542407156 | 0.805494728796422 |
112 | 0.178216435210383 | 0.356432870420766 | 0.821783564789617 |
113 | 0.197961332376106 | 0.395922664752212 | 0.802038667623894 |
114 | 0.176201497916102 | 0.352402995832204 | 0.823798502083898 |
115 | 0.175386652367843 | 0.350773304735686 | 0.824613347632157 |
116 | 0.173759712760187 | 0.347519425520375 | 0.826240287239813 |
117 | 0.145177475326993 | 0.290354950653987 | 0.854822524673007 |
118 | 0.119708518207234 | 0.239417036414469 | 0.880291481792766 |
119 | 0.142482295086064 | 0.284964590172129 | 0.857517704913936 |
120 | 0.167290345290536 | 0.334580690581072 | 0.832709654709464 |
121 | 0.134767282771008 | 0.269534565542015 | 0.865232717228992 |
122 | 0.184644952231467 | 0.369289904462934 | 0.815355047768533 |
123 | 0.178593347360673 | 0.357186694721345 | 0.821406652639327 |
124 | 0.141372475360712 | 0.282744950721424 | 0.858627524639288 |
125 | 0.115325277865035 | 0.230650555730071 | 0.884674722134965 |
126 | 0.0882881540410715 | 0.176576308082143 | 0.911711845958929 |
127 | 0.0852538460650295 | 0.170507692130059 | 0.91474615393497 |
128 | 0.083826455126268 | 0.167652910252536 | 0.916173544873732 |
129 | 0.201605846308179 | 0.403211692616357 | 0.798394153691821 |
130 | 0.297930773469587 | 0.595861546939175 | 0.702069226530412 |
131 | 0.243291622027789 | 0.486583244055578 | 0.756708377972211 |
132 | 0.226110926362301 | 0.452221852724602 | 0.773889073637699 |
133 | 0.315708785200919 | 0.631417570401838 | 0.684291214799081 |
134 | 0.303588843919512 | 0.607177687839024 | 0.696411156080488 |
135 | 0.225489273554873 | 0.450978547109746 | 0.774510726445127 |
136 | 0.323616945213333 | 0.647233890426665 | 0.676383054786667 |
137 | 0.439358329809253 | 0.878716659618506 | 0.560641670190747 |
138 | 0.484364763553653 | 0.968729527107305 | 0.515635236446347 |
139 | 0.457466066225943 | 0.914932132451886 | 0.542533933774057 |
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 |