Multiple Linear Regression - Estimated Regression Equation |
Depression[t] = + 9.24355550579304 + 0.493286378792209Month[t] -0.00260207016403223Expect[t] -0.0557478262810437Criticism[t] -0.214965647664329Concerns[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) | 9.24355550579304 | 3.305874 | 2.7961 | 0.005832 | 0.002916 |
Month | 0.493286378792209 | 0.30908 | 1.596 | 0.112542 | 0.056271 |
Expect | -0.00260207016403223 | 0.183669 | -0.0142 | 0.988715 | 0.494357 |
Criticism | -0.0557478262810437 | 0.232612 | -0.2397 | 0.810912 | 0.405456 |
Concerns | -0.214965647664329 | 0.210983 | -1.0189 | 0.30986 | 0.15493 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.161389265252687 |
R-squared | 0.0260464949388022 |
Adjusted R-squared | 0.000749001300848984 |
F-TEST (value) | 1.02960772761003 |
F-TEST (DF numerator) | 4 |
F-TEST (DF denominator) | 154 |
p-value | 0.393886977846912 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 3.1442247281482 |
Sum Squared Residuals | 1522.46696772919 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 12 | 12.1885676692836 | -0.188567669283605 |
2 | 11 | 12.2558253632110 | -1.25582536321096 |
3 | 14 | 12.6254538652333 | 1.37454613476669 |
4 | 12 | 12.5872686683213 | -0.587268668321266 |
5 | 21 | 12.5567926850167 | 8.44320731498329 |
6 | 12 | 12.7071253962701 | -0.70712539627006 |
7 | 22 | 12.6028784008290 | 9.39712159917097 |
8 | 11 | 12.59693077879 | -1.59693077878999 |
9 | 10 | 12.6125405112978 | -2.61254051129776 |
10 | 13 | 12.6585319187019 | 0.341468081298108 |
11 | 10 | 12.2319570065237 | -2.23195700652371 |
12 | 8 | 11.9497563522844 | -3.94975635228437 |
13 | 15 | 12.2916079380508 | 2.7083920619492 |
14 | 14 | 12.5872686683213 | 1.41273133167873 |
15 | 10 | 12.7299946171744 | -2.72999461717435 |
16 | 14 | 12.9781634568668 | 1.02183654313317 |
17 | 14 | 12.4166688063277 | 1.58333119367234 |
18 | 11 | 12.7299946171744 | -1.72999461717435 |
19 | 10 | 12.5114504509154 | -2.51145045091537 |
20 | 13 | 11.8732889615757 | 1.12671103842432 |
21 | 7 | 12.1281624247701 | -5.12816242477007 |
22 | 14 | 11.7279609425586 | 2.27203905744144 |
23 | 12 | 12.2986679783555 | -0.298667978355491 |
24 | 14 | 11.9660179465714 | 2.03398205342865 |
25 | 11 | 12.5386751907531 | -1.53867519075310 |
26 | 9 | 12.6474744647430 | -3.64747446474297 |
27 | 11 | 12.5419264342199 | -1.54192643421992 |
28 | 15 | 12.4114646659996 | 2.58853533400041 |
29 | 14 | 12.3602691182674 | 1.63973088173261 |
30 | 13 | 12.6864058318424 | 0.313594168157586 |
31 | 9 | 12.3584132182908 | -3.35841321829077 |
32 | 15 | 12.0185226721846 | 2.98147732781539 |
33 | 10 | 12.2778432742442 | -2.27784327424420 |
34 | 11 | 12.2771941009414 | -1.27719410094140 |
35 | 13 | 12.5975799520928 | 0.402420047907216 |
36 | 8 | 11.9757743654483 | -3.97577436544826 |
37 | 20 | 11.9284819229621 | 8.0715180770379 |
38 | 12 | 12.9069002064862 | -0.906900206486205 |
39 | 10 | 11.7968215708670 | -1.79682157086698 |
40 | 10 | 12.2771941009414 | -2.2771941009414 |
41 | 9 | 11.9965963810831 | -2.99659638108313 |
42 | 14 | 12.3628711884314 | 1.63712881156857 |
43 | 8 | 12.5807634929112 | -4.58076349291118 |
44 | 14 | 12.7103766397369 | 1.28962336026311 |
45 | 11 | 12.4926837833490 | -1.49268378334896 |
46 | 13 | 12.7299946171744 | 0.27000538282565 |
47 | 9 | 12.4317318167399 | -3.43173181673985 |
48 | 11 | 11.9284819229621 | -0.928481922962108 |
49 | 15 | 12.0601504178563 | 2.93984958214373 |
50 | 11 | 12.3674234669803 | -1.36742346698027 |
51 | 10 | 12.3226306434509 | -2.32263064345093 |
52 | 14 | 12.5846665981572 | 1.41533340184277 |
53 | 18 | 12.4900817131849 | 5.50991828681507 |
54 | 14 | 13.5326012503600 | 0.46739874964002 |
55 | 11 | 12.2506298604642 | -1.25062986046418 |
56 | 12 | 12.6953141241069 | -0.695314124106936 |
57 | 13 | 12.8866335505282 | 0.113366449471811 |
58 | 9 | 13.1783911755526 | -4.17839117555261 |
59 | 10 | 13.4818581163152 | -3.48185811631517 |
60 | 15 | 13.2679713682887 | 1.73202863171132 |
61 | 20 | 13.0973715062951 | 6.90262849370493 |
62 | 12 | 12.9883727842134 | -0.98837278421337 |
63 | 12 | 13.0559323774398 | -1.05593237743978 |
64 | 14 | 13.0552832041370 | 0.944716795863015 |
65 | 13 | 13.5455146042955 | -0.545514604295531 |
66 | 11 | 12.6409616413161 | -1.64096164131609 |
67 | 17 | 12.4580032902815 | 4.54199670971845 |
68 | 12 | 13.0293594993813 | -1.02935949938127 |
69 | 13 | 13.5662341687232 | -0.566234168723177 |
70 | 14 | 12.9846691270592 | 1.01533087294085 |
71 | 13 | 12.6286031522752 | 0.371396847724847 |
72 | 15 | 13.0624375528499 | 1.93756244715014 |
73 | 13 | 12.4722176792991 | 0.527782320700887 |
74 | 10 | 12.4620088467348 | -2.46200884673482 |
75 | 11 | 12.7471588451419 | -1.74715884514193 |
76 | 19 | 12.8393411080420 | 6.16065889195796 |
77 | 13 | 13.3710116370559 | -0.371011637055876 |
78 | 17 | 12.9034500097098 | 4.09654999029021 |
79 | 13 | 13.0332626046273 | -0.0332626046273222 |
80 | 9 | 12.6551760303337 | -3.65517603033366 |
81 | 11 | 12.7822922466790 | -1.78229224667898 |
82 | 10 | 13.0792540120315 | -3.07925401203146 |
83 | 9 | 12.9326249579323 | -3.93262495793233 |
84 | 12 | 12.9224161253680 | -0.92241612536803 |
85 | 12 | 12.9281669877917 | -0.928166987791667 |
86 | 13 | 12.9565957658268 | 0.0434042341732009 |
87 | 13 | 13.0188487675179 | -0.0188487675179233 |
88 | 12 | 13.2258830661306 | -1.22588306613059 |
89 | 15 | 12.4282816199634 | 2.57171838003656 |
90 | 22 | 13.0585344476038 | 8.94146555239619 |
91 | 13 | 12.6927120539429 | 0.307287946057096 |
92 | 15 | 13.5215437964011 | 1.47845620359894 |
93 | 13 | 13.2600627065894 | -0.260062706589361 |
94 | 15 | 12.9384782715632 | 2.06152172843681 |
95 | 10 | 12.9762137432643 | -2.97621374326426 |
96 | 11 | 12.3334972868993 | -1.33349728689930 |
97 | 16 | 12.4262262718950 | 3.57377372810502 |
98 | 11 | 12.4341349335943 | -1.43413493359429 |
99 | 11 | 13.0585344476038 | -2.05853444760381 |
100 | 10 | 12.8853325154462 | -2.88533251544617 |
101 | 10 | 12.7796901765149 | -2.77969017651495 |
102 | 16 | 13.2777277871656 | 2.72227221283441 |
103 | 12 | 12.9185130201220 | -0.918513020121981 |
104 | 11 | 13.0183020454224 | -2.01830204542235 |
105 | 16 | 12.784894316843 | 3.21510568315699 |
106 | 19 | 12.8275293410967 | 6.17247065890333 |
107 | 11 | 12.9644019763189 | -1.96440197631890 |
108 | 16 | 12.7349998041928 | 3.26500019580718 |
109 | 15 | 13.1483681007177 | 1.85163189928232 |
110 | 24 | 13.6742796245088 | 10.3257203754912 |
111 | 14 | 13.8377251377896 | 0.162274862210421 |
112 | 15 | 12.9773158250367 | 2.02268417496331 |
113 | 11 | 13.3474937376310 | -2.34749373763103 |
114 | 15 | 13.1444649954716 | 1.85553500452836 |
115 | 12 | 13.9227530519768 | -1.92275305197681 |
116 | 10 | 13.7481449450535 | -3.74814494505351 |
117 | 14 | 13.5174417378454 | 0.482558262154581 |
118 | 13 | 13.6781827297549 | -0.678182729754896 |
119 | 9 | 13.2041159269987 | -4.20411592699873 |
120 | 15 | 13.5933542636595 | 1.4066457363405 |
121 | 15 | 13.1647240034129 | 1.83527599658714 |
122 | 14 | 13.7904326953034 | 0.209567304696573 |
123 | 11 | 13.2936961197348 | -2.2936961197348 |
124 | 8 | 13.7788203764499 | -5.77882037644989 |
125 | 11 | 13.5570249667241 | -2.55702496672408 |
126 | 11 | 13.4701492953593 | -2.47014929535927 |
127 | 8 | 13.8293640624029 | -5.82936406240287 |
128 | 10 | 13.4779555058514 | -3.47795550585136 |
129 | 11 | 13.5407633724371 | -2.54076337243710 |
130 | 13 | 12.8567047841015 | 0.143295215898550 |
131 | 11 | 13.2949971548168 | -2.29499715481682 |
132 | 20 | 13.6658242407140 | 6.33417575928604 |
133 | 10 | 13.7034545727314 | -3.70345457273139 |
134 | 15 | 13.7812229985221 | 1.21877700147791 |
135 | 12 | 13.4272123718066 | -1.42721237180655 |
136 | 14 | 13.1224443959620 | 0.877555604038027 |
137 | 23 | 13.6269871820227 | 9.3730128179773 |
138 | 14 | 13.5420644075191 | 0.457935592480886 |
139 | 16 | 13.5906578850873 | 2.40934211491272 |
140 | 11 | 13.2405503636178 | -2.24055036361779 |
141 | 12 | 12.9733102685834 | -0.973310268583418 |
142 | 10 | 12.9376301449508 | -2.9376301449508 |
143 | 14 | 12.9352356656776 | 1.06476433432236 |
144 | 12 | 13.5173392866382 | -1.51733928663820 |
145 | 12 | 13.3370854569749 | -1.33708545697490 |
146 | 11 | 13.1037720368037 | -2.10377203680375 |
147 | 12 | 12.9156095454411 | -0.915609545441137 |
148 | 13 | 13.5058294189919 | -0.505829418991884 |
149 | 11 | 13.6379503275734 | -2.63795032757343 |
150 | 19 | 13.3215700328753 | 5.67842996712468 |
151 | 12 | 13.4500815927108 | -1.45008159271084 |
152 | 17 | 13.0888114775988 | 3.91118852240122 |
153 | 9 | 12.6329564775144 | -3.63295647751441 |
154 | 12 | 13.4330656854374 | -1.43306568543741 |
155 | 19 | 13.3268766244106 | 5.67312337558939 |
156 | 18 | 13.6729785894268 | 4.32702141057317 |
157 | 15 | 13.0953166530089 | 1.90468334699114 |
158 | 14 | 13.3202689977933 | 0.679731002206694 |
159 | 11 | 12.7178900832935 | -1.71789008329345 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
8 | 0.980771638345918 | 0.038456723308165 | 0.0192283616540825 |
9 | 0.987695177828852 | 0.0246096443422956 | 0.0123048221711478 |
10 | 0.977801610586647 | 0.0443967788267052 | 0.0221983894133526 |
11 | 0.963569994217362 | 0.0728600115652757 | 0.0364300057826378 |
12 | 0.959984339774789 | 0.0800313204504226 | 0.0400156602252113 |
13 | 0.954570021246807 | 0.0908599575063868 | 0.0454299787531934 |
14 | 0.928252451758952 | 0.143495096482095 | 0.0717475482410476 |
15 | 0.93566213444809 | 0.128675731103818 | 0.0643378655519092 |
16 | 0.915130911819663 | 0.169738176360674 | 0.084869088180337 |
17 | 0.88139965530035 | 0.237200689399300 | 0.118600344699650 |
18 | 0.858228433835611 | 0.283543132328778 | 0.141771566164389 |
19 | 0.839059811245035 | 0.321880377509929 | 0.160940188754965 |
20 | 0.814140152849397 | 0.371719694301206 | 0.185859847150603 |
21 | 0.885371119833343 | 0.229257760333313 | 0.114628880166657 |
22 | 0.879051358789927 | 0.241897282420145 | 0.120948641210073 |
23 | 0.847587888176407 | 0.304824223647187 | 0.152412111823593 |
24 | 0.808767107634988 | 0.382465784730024 | 0.191232892365012 |
25 | 0.775853044839257 | 0.448293910321486 | 0.224146955160743 |
26 | 0.771037761993226 | 0.457924476013547 | 0.228962238006774 |
27 | 0.744105546995202 | 0.511788906009596 | 0.255894453004798 |
28 | 0.727251280167363 | 0.545497439665273 | 0.272748719832637 |
29 | 0.690239729564482 | 0.619520540871036 | 0.309760270435518 |
30 | 0.634353435874215 | 0.73129312825157 | 0.365646564125785 |
31 | 0.67944895967099 | 0.641102080658021 | 0.320551040329010 |
32 | 0.693070766984524 | 0.613858466030953 | 0.306929233015476 |
33 | 0.67300436211643 | 0.65399127576714 | 0.32699563788357 |
34 | 0.626587212002158 | 0.746825575995684 | 0.373412787997842 |
35 | 0.570813731911616 | 0.858372536176768 | 0.429186268088384 |
36 | 0.580083053146585 | 0.83983389370683 | 0.419916946853415 |
37 | 0.826786108696956 | 0.346427782606089 | 0.173213891303044 |
38 | 0.791459918639452 | 0.417080162721097 | 0.208540081360548 |
39 | 0.763164664940106 | 0.473670670119789 | 0.236835335059894 |
40 | 0.743317049199077 | 0.513365901601845 | 0.256682950800922 |
41 | 0.731840176988317 | 0.536319646023365 | 0.268159823011683 |
42 | 0.69885886510105 | 0.602282269797899 | 0.301141134898949 |
43 | 0.737177112766546 | 0.525645774466908 | 0.262822887233454 |
44 | 0.702369600046359 | 0.595260799907283 | 0.297630399953641 |
45 | 0.667659718987027 | 0.664680562025946 | 0.332340281012973 |
46 | 0.619604889662289 | 0.760790220675422 | 0.380395110337711 |
47 | 0.624159126521768 | 0.751681746956464 | 0.375840873478232 |
48 | 0.583152949339276 | 0.833694101321448 | 0.416847050660724 |
49 | 0.570332855874996 | 0.859334288250008 | 0.429667144125004 |
50 | 0.530025772100259 | 0.939948455799481 | 0.469974227899741 |
51 | 0.518482020182186 | 0.963035959635628 | 0.481517979817814 |
52 | 0.477777714088025 | 0.95555542817605 | 0.522222285911975 |
53 | 0.568772511374607 | 0.862454977250786 | 0.431227488625393 |
54 | 0.519815921878011 | 0.960368156243978 | 0.480184078121989 |
55 | 0.476257049193074 | 0.952514098386147 | 0.523742950806926 |
56 | 0.429154480891607 | 0.858308961783213 | 0.570845519108394 |
57 | 0.381969605085021 | 0.763939210170043 | 0.618030394914978 |
58 | 0.402060965903614 | 0.804121931807227 | 0.597939034096386 |
59 | 0.394794813902535 | 0.78958962780507 | 0.605205186097465 |
60 | 0.379235908113109 | 0.758471816226217 | 0.620764091886891 |
61 | 0.567247407767017 | 0.865505184465966 | 0.432752592232983 |
62 | 0.524134130812679 | 0.951731738374642 | 0.475865869187321 |
63 | 0.481502933096219 | 0.963005866192438 | 0.518497066903781 |
64 | 0.437448269115526 | 0.874896538231052 | 0.562551730884474 |
65 | 0.393025237691986 | 0.786050475383971 | 0.606974762308014 |
66 | 0.358229675674672 | 0.716459351349343 | 0.641770324325328 |
67 | 0.406385840789508 | 0.812771681579015 | 0.593614159210492 |
68 | 0.366827622486175 | 0.733655244972349 | 0.633172377513825 |
69 | 0.325903183990047 | 0.651806367980093 | 0.674096816009953 |
70 | 0.287865490109079 | 0.575730980218158 | 0.712134509890921 |
71 | 0.24947245195372 | 0.49894490390744 | 0.75052754804628 |
72 | 0.224687385756475 | 0.44937477151295 | 0.775312614243525 |
73 | 0.191793431476297 | 0.383586862952594 | 0.808206568523703 |
74 | 0.179748942396755 | 0.35949788479351 | 0.820251057603245 |
75 | 0.159742107043393 | 0.319484214086786 | 0.840257892956607 |
76 | 0.246507428746144 | 0.493014857492289 | 0.753492571253856 |
77 | 0.213007585438418 | 0.426015170876836 | 0.786992414561582 |
78 | 0.231202194491193 | 0.462404388982386 | 0.768797805508807 |
79 | 0.198186095309901 | 0.396372190619802 | 0.801813904690099 |
80 | 0.211056380801244 | 0.422112761602487 | 0.788943619198756 |
81 | 0.190508430453558 | 0.381016860907116 | 0.809491569546442 |
82 | 0.192085188790509 | 0.384170377581018 | 0.807914811209491 |
83 | 0.213701414557844 | 0.427402829115688 | 0.786298585442156 |
84 | 0.186152173712903 | 0.372304347425807 | 0.813847826287097 |
85 | 0.159814833234888 | 0.319629666469776 | 0.840185166765112 |
86 | 0.135654047758287 | 0.271308095516573 | 0.864345952241714 |
87 | 0.112755933804864 | 0.225511867609727 | 0.887244066195136 |
88 | 0.0964927396980605 | 0.192985479396121 | 0.90350726030194 |
89 | 0.0886449380455549 | 0.177289876091110 | 0.911355061954445 |
90 | 0.27519074321418 | 0.55038148642836 | 0.72480925678582 |
91 | 0.237585228859789 | 0.475170457719578 | 0.762414771140211 |
92 | 0.208264111920328 | 0.416528223840656 | 0.791735888079672 |
93 | 0.176661622964874 | 0.353323245929747 | 0.823338377035126 |
94 | 0.157288963577690 | 0.314577927155379 | 0.84271103642231 |
95 | 0.154476600174884 | 0.308953200349769 | 0.845523399825115 |
96 | 0.134995301627934 | 0.269990603255868 | 0.865004698372066 |
97 | 0.139556121224431 | 0.279112242448861 | 0.86044387877557 |
98 | 0.120414015638087 | 0.240828031276174 | 0.879585984361913 |
99 | 0.109629705281964 | 0.219259410563929 | 0.890370294718036 |
100 | 0.111158658138069 | 0.222317316276138 | 0.88884134186193 |
101 | 0.115794764870287 | 0.231589529740573 | 0.884205235129713 |
102 | 0.102018043363988 | 0.204036086727975 | 0.897981956636012 |
103 | 0.0955648932696374 | 0.191129786539275 | 0.904435106730363 |
104 | 0.107462801011949 | 0.214925602023898 | 0.89253719898805 |
105 | 0.0941334797198106 | 0.188266959439621 | 0.90586652028019 |
106 | 0.128170935062323 | 0.256341870124645 | 0.871829064937677 |
107 | 0.127408540751861 | 0.254817081503722 | 0.872591459248139 |
108 | 0.110836560233573 | 0.221673120467145 | 0.889163439766427 |
109 | 0.0957010341922642 | 0.191402068384528 | 0.904298965807736 |
110 | 0.416982750530948 | 0.833965501061895 | 0.583017249469052 |
111 | 0.369424630178139 | 0.738849260356278 | 0.630575369821861 |
112 | 0.340767655411977 | 0.681535310823954 | 0.659232344588023 |
113 | 0.318431028157305 | 0.63686205631461 | 0.681568971842695 |
114 | 0.283484521505919 | 0.566969043011838 | 0.716515478494081 |
115 | 0.255802707585252 | 0.511605415170505 | 0.744197292414748 |
116 | 0.284471943373689 | 0.568943886747377 | 0.715528056626311 |
117 | 0.241456159701519 | 0.482912319403038 | 0.758543840298481 |
118 | 0.204149716024803 | 0.408299432049606 | 0.795850283975197 |
119 | 0.23211469868313 | 0.46422939736626 | 0.76788530131687 |
120 | 0.205218556241390 | 0.410437112482781 | 0.79478144375861 |
121 | 0.210339272145149 | 0.420678544290298 | 0.789660727854851 |
122 | 0.172732564431027 | 0.345465128862054 | 0.827267435568973 |
123 | 0.154521300318496 | 0.309042600636991 | 0.845478699681504 |
124 | 0.214814867089528 | 0.429629734179055 | 0.785185132910472 |
125 | 0.192699444913650 | 0.385398889827301 | 0.80730055508635 |
126 | 0.192351875161354 | 0.384703750322709 | 0.807648124838646 |
127 | 0.35004081425552 | 0.70008162851104 | 0.64995918574448 |
128 | 0.370598971592271 | 0.741197943184543 | 0.629401028407729 |
129 | 0.396829366284867 | 0.793658732569735 | 0.603170633715133 |
130 | 0.378359717576874 | 0.756719435153749 | 0.621640282423126 |
131 | 0.351585209243346 | 0.703170418486692 | 0.648414790756654 |
132 | 0.439121550227746 | 0.878243100455493 | 0.560878449772254 |
133 | 0.56341002323029 | 0.87317995353942 | 0.43658997676971 |
134 | 0.50348373804852 | 0.99303252390296 | 0.49651626195148 |
135 | 0.468468029222388 | 0.936936058444775 | 0.531531970777612 |
136 | 0.402658586872525 | 0.805317173745051 | 0.597341413127475 |
137 | 0.76845811952334 | 0.463083760953321 | 0.231541880476660 |
138 | 0.709730843463607 | 0.580538313072787 | 0.290269156536393 |
139 | 0.653101299836227 | 0.693797400327546 | 0.346898700163773 |
140 | 0.610071883792312 | 0.779856232415375 | 0.389928116207688 |
141 | 0.54630846547453 | 0.90738306905094 | 0.45369153452547 |
142 | 0.492027083953053 | 0.984054167906106 | 0.507972916046947 |
143 | 0.418132524161946 | 0.836265048323892 | 0.581867475838054 |
144 | 0.337276773541877 | 0.674553547083753 | 0.662723226458123 |
145 | 0.330352711222166 | 0.660705422444332 | 0.669647288777834 |
146 | 0.248397216102346 | 0.496794432204693 | 0.751602783897654 |
147 | 0.175015640006478 | 0.350031280012955 | 0.824984359993522 |
148 | 0.120747282010673 | 0.241494564021346 | 0.879252717989327 |
149 | 0.225327650624311 | 0.450655301248621 | 0.77467234937569 |
150 | 0.250821764923187 | 0.501643529846374 | 0.749178235076813 |
151 | 0.257020965074454 | 0.514041930148908 | 0.742979034925546 |
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 | 3 | 0.0208333333333333 | OK |
10% type I error level | 6 | 0.0416666666666667 | OK |