Multiple Linear Regression - Estimated Regression Equation |
Q1[t] = + 2.23897194643045 + 0.243785460782962Q2[t] -0.122438966674107Q3[t] + 0.347603426744458Q4[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) | 2.23897194643045 | 0.335983 | 6.664 | 0 | 0 |
Q2 | 0.243785460782962 | 0.079459 | 3.0681 | 0.002543 | 0.001272 |
Q3 | -0.122438966674107 | 0.086368 | -1.4176 | 0.158301 | 0.07915 |
Q4 | 0.347603426744458 | 0.079707 | 4.361 | 2.4e-05 | 1.2e-05 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.479336441707 |
R-squared | 0.229763424348329 |
Adjusted R-squared | 0.214855619658296 |
F-TEST (value) | 15.4122910197471 |
F-TEST (DF numerator) | 3 |
F-TEST (DF denominator) | 155 |
p-value | 7.9837040312114e-09 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 0.856089324065147 |
Sum Squared Residuals | 113.597784270640 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 2 | 2.93199385478886 | -0.93199385478886 |
2 | 2 | 2.5843904280444 | -0.5843904280444 |
3 | 4 | 3.50476174160366 | 0.495238258396335 |
4 | 2 | 3.17687178813707 | -1.17687178813707 |
5 | 3 | 3.17687178813707 | -0.176871788137071 |
6 | 4 | 2.68820839400589 | 1.31179160599410 |
7 | 3 | 2.68820839400590 | 0.311791605994105 |
8 | 3 | 3.17577931557182 | -0.175779315571818 |
9 | 3 | 2.5843904280444 | 0.415609571955601 |
10 | 2 | 3.62829318084302 | -1.62829318084302 |
11 | 4 | 3.54200374302889 | 0.457996256971113 |
12 | 4 | 3.27959728153331 | 0.720402718466686 |
13 | 3 | 3.29821828224593 | -0.298218282245925 |
14 | 3 | 2.93199385478886 | 0.0680061452111432 |
15 | 4 | 2.34060496726144 | 1.65939503273856 |
16 | 4 | 3.03581182075035 | 0.964188179249647 |
17 | 3 | 2.5843904280444 | 0.415609571955601 |
18 | 3 | 3.17687178813707 | -0.176871788137071 |
19 | 3 | 3.62720070827777 | -0.627200708277772 |
20 | 4 | 3.62720070827777 | 0.372799291722228 |
21 | 2 | 3.03581182075035 | -1.03581182075035 |
22 | 5 | 3.05443282146296 | 1.94556717853704 |
23 | 4 | 4.01204613644745 | -0.0120461364474518 |
24 | 2 | 2.93199385478886 | -0.931993854788857 |
25 | 3 | 3.17687178813707 | -0.176871788137071 |
26 | 4 | 3.40203624820742 | 0.597963751792578 |
27 | 4 | 3.27959728153331 | 0.720402718466686 |
28 | 3 | 3.05443282146296 | -0.054432821462964 |
29 | 4 | 3.87098616906073 | 0.129013830939266 |
30 | 4 | 2.93199385478886 | 1.06800614521114 |
31 | 1 | 2.68820839400589 | -1.68820839400590 |
32 | 4 | 3.76716820309924 | 0.232831796900762 |
33 | 5 | 3.73101867423927 | 1.26898132576073 |
34 | 2 | 2.93199385478886 | -0.931993854788857 |
35 | 4 | 3.27959728153331 | 0.720402718466686 |
36 | 3 | 2.46195146137029 | 0.538048538629708 |
37 | 2 | 2.93199385478886 | -0.931993854788857 |
38 | 4 | 3.17687178813707 | 0.823128211862929 |
39 | 5 | 3.62720070827777 | 1.37279929172223 |
40 | 4 | 2.93199385478886 | 1.06800614521114 |
41 | 4 | 3.50476174160366 | 0.495238258396335 |
42 | 4 | 3.27959728153331 | 0.720402718466686 |
43 | 3 | 3.17687178813707 | -0.176871788137071 |
44 | 4 | 3.62720070827777 | 0.372799291722228 |
45 | 2 | 2.93199385478886 | -0.931993854788857 |
46 | 2 | 2.68820839400590 | -0.688208394005895 |
47 | 4 | 3.17687178813707 | 0.823128211862929 |
48 | 2 | 2.56576942733179 | -0.565769427331788 |
49 | 4 | 2.93199385478886 | 1.06800614521114 |
50 | 4 | 3.03581182075035 | 0.964188179249647 |
51 | 1 | 2.34060496726144 | -1.34060496726144 |
52 | 4 | 2.93199385478886 | 1.06800614521114 |
53 | 2 | 2.93199385478886 | -0.931993854788857 |
54 | 1 | 2.46304393393554 | -1.46304393393554 |
55 | 4 | 4.58372155069701 | -0.583721550697007 |
56 | 3 | 2.93199385478886 | 0.0680061452111432 |
57 | 2 | 2.93199385478886 | -0.931993854788857 |
58 | 4 | 2.68820839400589 | 1.31179160599410 |
59 | 3 | 2.34060496726144 | 0.659395032738562 |
60 | 2 | 3.17687178813707 | -1.17687178813707 |
61 | 2 | 2.93199385478886 | -0.931993854788857 |
62 | 3 | 2.68820839400590 | 0.311791605994105 |
63 | 2 | 3.38341524749481 | -1.38341524749481 |
64 | 1 | 2.93199385478886 | -1.93199385478886 |
65 | 3 | 2.46304393393554 | 0.536956066064455 |
66 | 2 | 2.68820839400590 | -0.688208394005895 |
67 | 3 | 3.17687178813707 | -0.176871788137071 |
68 | 3 | 2.68820839400590 | 0.311791605994105 |
69 | 3 | 2.34060496726144 | 0.659395032738562 |
70 | 2 | 2.93199385478886 | -0.931993854788857 |
71 | 3 | 2.68820839400590 | 0.311791605994105 |
72 | 2 | 2.68820839400590 | -0.688208394005895 |
73 | 4 | 3.52338274231628 | 0.476617257683724 |
74 | 4 | 3.64582170899038 | 0.354178291009617 |
75 | 4 | 2.93199385478886 | 1.06800614521114 |
76 | 2 | 2.93199385478886 | -0.931993854788857 |
77 | 3 | 3.03581182075035 | -0.035811820750353 |
78 | 4 | 3.17577931557182 | 0.824220684428182 |
79 | 3 | 2.93199385478886 | 0.0680061452111432 |
80 | 4 | 2.93199385478886 | 1.06800614521114 |
81 | 2 | 2.93199385478886 | -0.931993854788857 |
82 | 3 | 3.17687178813707 | -0.176871788137071 |
83 | 3 | 2.46304393393554 | 0.536956066064455 |
84 | 4 | 3.64472923642513 | 0.355270763574870 |
85 | 2 | 2.81064736068 | -0.810647360680002 |
86 | 4 | 3.50585421416892 | 0.494145785831082 |
87 | 2 | 2.68820839400590 | -0.688208394005895 |
88 | 2 | 2.34060496726144 | -0.340604967261437 |
89 | 4 | 4.11477162984369 | -0.114771629843695 |
90 | 3 | 3.27959728153331 | -0.279597281533314 |
91 | 4 | 2.93199385478886 | 1.06800614521114 |
92 | 2 | 3.15825078742446 | -1.15825078742446 |
93 | 2 | 2.68820839400590 | -0.688208394005895 |
94 | 3 | 3.03581182075035 | -0.035811820750353 |
95 | 3 | 3.17577931557182 | -0.175779315571818 |
96 | 5 | 4.33993608991405 | 0.660063910085955 |
97 | 2 | 3.76716820309924 | -1.76716820309924 |
98 | 3 | 3.87098616906073 | -0.870986169060734 |
99 | 4 | 3.17687178813707 | 0.823128211862929 |
100 | 3 | 3.05443282146296 | -0.054432821462964 |
101 | 4 | 3.29821828224593 | 0.701781717754074 |
102 | 3 | 3.15825078742446 | -0.15825078742446 |
103 | 3 | 3.87098616906073 | -0.870986169060734 |
104 | 2 | 3.27959728153331 | -1.27959728153331 |
105 | 3 | 3.17687178813707 | -0.176871788137071 |
106 | 2 | 3.05443282146296 | -1.05443282146296 |
107 | 3 | 3.40203624820742 | -0.402036248207422 |
108 | 2 | 3.41956477635478 | -1.41956477635478 |
109 | 4 | 3.17577931557182 | 0.824220684428182 |
110 | 2 | 2.93308632735411 | -0.93308632735411 |
111 | 4 | 2.81064736068 | 1.18935263932000 |
112 | 4 | 3.27959728153331 | 0.720402718466686 |
113 | 1 | 2.68820839400589 | -1.68820839400590 |
114 | 5 | 3.74854720238663 | 1.25145279761337 |
115 | 2 | 2.70682939471851 | -0.706829394718506 |
116 | 3 | 3.05443282146296 | -0.054432821462964 |
117 | 4 | 3.62720070827777 | 0.372799291722228 |
118 | 1 | 2.81064736068 | -1.81064736068000 |
119 | 5 | 3.29821828224593 | 1.70178171775407 |
120 | 3 | 2.58548290060965 | 0.414517099390348 |
121 | 3 | 2.34060496726144 | 0.659395032738562 |
122 | 3 | 3.40203624820742 | -0.402036248207422 |
123 | 3 | 3.52338274231628 | -0.523382742316276 |
124 | 2 | 2.46195146137029 | -0.461951461370292 |
125 | 2 | 2.34060496726144 | -0.340604967261437 |
126 | 4 | 3.40203624820742 | 0.597963751792578 |
127 | 4 | 2.46304393393554 | 1.53695606606446 |
128 | 3 | 3.05443282146296 | -0.054432821462964 |
129 | 3 | 3.15825078742446 | -0.15825078742446 |
130 | 3 | 2.93199385478886 | 0.0680061452111432 |
131 | 4 | 3.17577931557182 | 0.824220684428182 |
132 | 3 | 3.05443282146296 | -0.054432821462964 |
133 | 4 | 2.93308632735411 | 1.06691367264589 |
134 | 4 | 2.81064736068 | 1.18935263932000 |
135 | 2 | 3.17687178813707 | -1.17687178813707 |
136 | 4 | 3.62720070827777 | 0.372799291722228 |
137 | 2 | 2.68820839400590 | -0.688208394005895 |
138 | 4 | 2.93199385478886 | 1.06800614521114 |
139 | 3 | 3.52338274231628 | -0.523382742316276 |
140 | 3 | 3.41956477635478 | -0.41956477635478 |
141 | 2 | 2.93199385478886 | -0.931993854788857 |
142 | 2 | 3.99233266316959 | -1.99233266316959 |
143 | 5 | 4.48099605730076 | 0.519003942699236 |
144 | 2 | 2.34060496726144 | -0.340604967261437 |
145 | 4 | 3.52338274231628 | 0.476617257683724 |
146 | 3 | 2.93199385478886 | 0.0680061452111432 |
147 | 3 | 3.50476174160366 | -0.504761741603665 |
148 | 3 | 3.05443282146296 | -0.054432821462964 |
149 | 3 | 2.58548290060965 | 0.414517099390348 |
150 | 4 | 3.41956477635478 | 0.58043522364522 |
151 | 4 | 3.05443282146296 | 0.945567178537036 |
152 | 4 | 3.27959728153331 | 0.720402718466686 |
153 | 4 | 4.09615062913108 | -0.096150629131084 |
154 | 4 | 2.81064736068 | 1.18935263932000 |
155 | 5 | 4.2372105965178 | 0.762789403482198 |
156 | 3 | 3.05443282146296 | -0.054432821462964 |
157 | 3 | 2.80955488811475 | 0.190445111885250 |
158 | 4 | 3.76716820309924 | 0.232831796900762 |
159 | 4 | 4.35964956319191 | -0.359649563191909 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
7 | 0.374778290690061 | 0.749556581380123 | 0.625221709309938 |
8 | 0.445023871997149 | 0.890047743994299 | 0.554976128002851 |
9 | 0.382697881968956 | 0.765395763937911 | 0.617302118031044 |
10 | 0.458237247831948 | 0.916474495663897 | 0.541762752168052 |
11 | 0.529385249723225 | 0.94122950055355 | 0.470614750276775 |
12 | 0.485034154915191 | 0.970068309830383 | 0.514965845084809 |
13 | 0.382523277001251 | 0.765046554002502 | 0.617476722998749 |
14 | 0.291675672994694 | 0.583351345989387 | 0.708324327005306 |
15 | 0.417372997754567 | 0.834745995509134 | 0.582627002245433 |
16 | 0.397649037230417 | 0.795298074460834 | 0.602350962769583 |
17 | 0.319265600774192 | 0.638531201548385 | 0.680734399225808 |
18 | 0.273415696024939 | 0.546831392049877 | 0.726584303975061 |
19 | 0.236913072229273 | 0.473826144458545 | 0.763086927770727 |
20 | 0.198880203291997 | 0.397760406583995 | 0.801119796708003 |
21 | 0.279419062587415 | 0.55883812517483 | 0.720580937412585 |
22 | 0.618771362478365 | 0.76245727504327 | 0.381228637521635 |
23 | 0.582405358768509 | 0.835189282462983 | 0.417594641231491 |
24 | 0.642489801810588 | 0.715020396378823 | 0.357510198189412 |
25 | 0.580143673157277 | 0.839712653685446 | 0.419856326842723 |
26 | 0.56508639564939 | 0.86982720870122 | 0.43491360435061 |
27 | 0.53336953657518 | 0.933260926849639 | 0.466630463424820 |
28 | 0.469697043023122 | 0.939394086046244 | 0.530302956976878 |
29 | 0.408330927474781 | 0.816661854949563 | 0.591669072525219 |
30 | 0.402697635937668 | 0.805395271875337 | 0.597302364062332 |
31 | 0.630059647813811 | 0.739880704372378 | 0.369940352186189 |
32 | 0.574486050614173 | 0.851027898771655 | 0.425513949385827 |
33 | 0.64629707609601 | 0.70740584780798 | 0.35370292390399 |
34 | 0.677892332475199 | 0.644215335049602 | 0.322107667524801 |
35 | 0.64848929231282 | 0.70302141537436 | 0.35151070768718 |
36 | 0.602270040562342 | 0.795459918875316 | 0.397729959437658 |
37 | 0.630555024686505 | 0.738889950626991 | 0.369444975313495 |
38 | 0.64873118761508 | 0.70253762476984 | 0.35126881238492 |
39 | 0.694874774222383 | 0.610250451555235 | 0.305125225777617 |
40 | 0.701579535513153 | 0.596840928973694 | 0.298420464486847 |
41 | 0.661789799241109 | 0.676420401517782 | 0.338210200758891 |
42 | 0.63419629580567 | 0.73160740838866 | 0.36580370419433 |
43 | 0.584876346532735 | 0.830247306934529 | 0.415123653467265 |
44 | 0.538619733240357 | 0.922760533519286 | 0.461380266759643 |
45 | 0.56830680751865 | 0.8633863849627 | 0.43169319248135 |
46 | 0.557485387512356 | 0.885029224975288 | 0.442514612487644 |
47 | 0.565862540831114 | 0.868274918337773 | 0.434137459168886 |
48 | 0.54894340858668 | 0.90211318282664 | 0.45105659141332 |
49 | 0.563913400699232 | 0.872173198601535 | 0.436086599300768 |
50 | 0.569468778394227 | 0.861062443211546 | 0.430531221605773 |
51 | 0.633532123245473 | 0.732935753509054 | 0.366467876754527 |
52 | 0.64904684275534 | 0.701906314489321 | 0.350953157244661 |
53 | 0.665699171537022 | 0.668601656925957 | 0.334300828462978 |
54 | 0.722532205881726 | 0.554935588236548 | 0.277467794118274 |
55 | 0.747835137384785 | 0.50432972523043 | 0.252164862615215 |
56 | 0.707862579292357 | 0.584274841415287 | 0.292137420707643 |
57 | 0.716786919784025 | 0.56642616043195 | 0.283213080215975 |
58 | 0.765954977725335 | 0.468090044549329 | 0.234045022274665 |
59 | 0.750553416930239 | 0.498893166139522 | 0.249446583069761 |
60 | 0.778633000928734 | 0.442733998142533 | 0.221366999071266 |
61 | 0.786273022338975 | 0.42745395532205 | 0.213726977661025 |
62 | 0.75557426511813 | 0.488851469763739 | 0.244425734881869 |
63 | 0.814021492892214 | 0.371957014215572 | 0.185978507107786 |
64 | 0.912831219220578 | 0.174337561558844 | 0.0871687807794218 |
65 | 0.902082186417057 | 0.195835627165886 | 0.097917813582943 |
66 | 0.893661873047822 | 0.212676253904357 | 0.106338126952178 |
67 | 0.872311455370715 | 0.255377089258571 | 0.127688544629285 |
68 | 0.850450029671153 | 0.299099940657694 | 0.149549970328847 |
69 | 0.839720205908489 | 0.320559588183022 | 0.160279794091511 |
70 | 0.843941521866012 | 0.312116956267976 | 0.156058478133988 |
71 | 0.819296446518641 | 0.361407106962718 | 0.180703553481359 |
72 | 0.80651606714366 | 0.38696786571268 | 0.19348393285634 |
73 | 0.78300245931902 | 0.433995081361960 | 0.216997540680980 |
74 | 0.753031069350287 | 0.493937861299426 | 0.246968930649713 |
75 | 0.772158370955865 | 0.45568325808827 | 0.227841629044135 |
76 | 0.777463783266586 | 0.445072433466828 | 0.222536216733414 |
77 | 0.742083566578456 | 0.515832866843087 | 0.257916433421544 |
78 | 0.736593933466275 | 0.526812133067449 | 0.263406066533725 |
79 | 0.697924217984631 | 0.604151564030738 | 0.302075782015369 |
80 | 0.720454821512502 | 0.559090356974996 | 0.279545178487498 |
81 | 0.72590825262061 | 0.54818349475878 | 0.27409174737939 |
82 | 0.689423095168575 | 0.62115380966285 | 0.310576904831425 |
83 | 0.665968046455304 | 0.668063907089392 | 0.334031953544696 |
84 | 0.632016151665758 | 0.735967696668485 | 0.367983848334242 |
85 | 0.624845063578691 | 0.750309872842618 | 0.375154936421309 |
86 | 0.596960560872602 | 0.806078878254796 | 0.403039439127398 |
87 | 0.576846903634023 | 0.846306192731954 | 0.423153096365977 |
88 | 0.536711322722032 | 0.926577354555936 | 0.463288677277968 |
89 | 0.49319988558539 | 0.98639977117078 | 0.506800114414609 |
90 | 0.451361708400619 | 0.902723416801238 | 0.548638291599381 |
91 | 0.478315204893607 | 0.956630409787215 | 0.521684795106393 |
92 | 0.51317411503645 | 0.973651769927101 | 0.486825884963551 |
93 | 0.493309090092435 | 0.98661818018487 | 0.506690909907565 |
94 | 0.446534942493333 | 0.893069884986666 | 0.553465057506667 |
95 | 0.402633705446227 | 0.805267410892454 | 0.597366294553773 |
96 | 0.395738037328478 | 0.791476074656957 | 0.604261962671522 |
97 | 0.543980913467317 | 0.912038173065367 | 0.456019086532683 |
98 | 0.540471190476433 | 0.919057619047135 | 0.459528809523567 |
99 | 0.531152870392716 | 0.937694259214568 | 0.468847129607284 |
100 | 0.484074216178035 | 0.96814843235607 | 0.515925783821965 |
101 | 0.464273619737135 | 0.92854723947427 | 0.535726380262865 |
102 | 0.418385340212127 | 0.836770680424253 | 0.581614659787873 |
103 | 0.415900085901055 | 0.83180017180211 | 0.584099914098945 |
104 | 0.471193287941412 | 0.942386575882824 | 0.528806712058588 |
105 | 0.428502184544098 | 0.857004369088197 | 0.571497815455902 |
106 | 0.459419331351806 | 0.918838662703612 | 0.540580668648194 |
107 | 0.426221340891763 | 0.852442681783525 | 0.573778659108237 |
108 | 0.51654733724562 | 0.96690532550876 | 0.48345266275438 |
109 | 0.506959145445685 | 0.98608170910863 | 0.493040854554315 |
110 | 0.543007376391255 | 0.913985247217491 | 0.456992623608745 |
111 | 0.574269073659107 | 0.851461852681786 | 0.425730926340893 |
112 | 0.559575511302245 | 0.88084897739551 | 0.440424488697755 |
113 | 0.702687896106623 | 0.594624207786755 | 0.297312103893378 |
114 | 0.77431289555669 | 0.451374208886621 | 0.225687104443310 |
115 | 0.784129534649345 | 0.431740930701309 | 0.215870465350655 |
116 | 0.74762823470347 | 0.504743530593059 | 0.252371765296530 |
117 | 0.719844324245086 | 0.560311351509828 | 0.280155675754914 |
118 | 0.897960906955542 | 0.204078186088916 | 0.102039093044458 |
119 | 0.94829649125816 | 0.103407017483680 | 0.0517035087418399 |
120 | 0.934675999843293 | 0.130648000313414 | 0.0653240001567069 |
121 | 0.92353062775851 | 0.152938744482979 | 0.0764693722414893 |
122 | 0.91422001326533 | 0.171559973469339 | 0.0857799867346696 |
123 | 0.89867081735236 | 0.202658365295279 | 0.101329182647640 |
124 | 0.876468780368465 | 0.247062439263069 | 0.123531219631535 |
125 | 0.859095719318141 | 0.281808561363718 | 0.140904280681859 |
126 | 0.832757530025908 | 0.334484939948184 | 0.167242469974092 |
127 | 0.875779240288612 | 0.248441519422776 | 0.124220759711388 |
128 | 0.845626916994732 | 0.308746166010536 | 0.154373083005268 |
129 | 0.816830469011507 | 0.366339061976985 | 0.183169530988493 |
130 | 0.771321092596035 | 0.45735781480793 | 0.228678907403965 |
131 | 0.775315774079142 | 0.449368451841715 | 0.224684225920858 |
132 | 0.730054960416882 | 0.539890079166237 | 0.269945039583118 |
133 | 0.705002122988244 | 0.589995754023511 | 0.294997877011756 |
134 | 0.724896581624881 | 0.550206836750237 | 0.275103418375119 |
135 | 0.869106762091254 | 0.261786475817491 | 0.130893237908746 |
136 | 0.83691419886101 | 0.326171602277981 | 0.163085801138991 |
137 | 0.836899462853213 | 0.326201074293574 | 0.163100537146787 |
138 | 0.867181641251044 | 0.265636717497913 | 0.132818358748956 |
139 | 0.837170122276516 | 0.325659755446968 | 0.162829877723484 |
140 | 0.793131677526034 | 0.413736644947933 | 0.206868322473966 |
141 | 0.831012243017961 | 0.337975513964077 | 0.168987756982039 |
142 | 0.986035812248661 | 0.0279283755026774 | 0.0139641877513387 |
143 | 0.97577140108915 | 0.0484571978217005 | 0.0242285989108502 |
144 | 0.978893022821635 | 0.0422139543567297 | 0.0211069771783648 |
145 | 0.96406327120947 | 0.0718734575810583 | 0.0359367287905291 |
146 | 0.94315965455635 | 0.113680690887301 | 0.0568403454436506 |
147 | 0.941461802519 | 0.117076394961999 | 0.0585381974809996 |
148 | 0.92794249185595 | 0.144115016288099 | 0.0720575081440496 |
149 | 0.892944793303478 | 0.214110413393043 | 0.107055206696522 |
150 | 0.828539792427558 | 0.342920415144884 | 0.171460207572442 |
151 | 0.742471431830197 | 0.515057136339606 | 0.257528568169803 |
152 | 0.605076237990254 | 0.789847524019492 | 0.394923762009746 |
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 | 0.0205479452054795 | OK |
10% type I error level | 4 | 0.0273972602739726 | OK |