Multiple Linear Regression - Estimated Regression Equation |
Concernovermistakes[t] = + 21.995337995338 + 1.40151515151515Month[t] + 1.35395854145854M1[t] -2.64955877455878M2[t] -1.22450466200466M3[t] -3.47943722943723M4[t] -3.71372377622378M5[t] -4.33262570762571M6[t] -3.13625957375957M7[t] -2.4474691974692M8[t] -1.45098651348651M9[t] -0.992965367965368M10[t] -2.68879037629038M11[t] + 0.00351731601731602t + 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) | 21.995337995338 | 2.899528 | 7.5858 | 0 | 0 |
Month | 1.40151515151515 | 2.571152 | 0.5451 | 0.586528 | 0.293264 |
M1 | 1.35395854145854 | 2.209902 | 0.6127 | 0.541049 | 0.270524 |
M2 | -2.64955877455878 | 2.209966 | -1.1989 | 0.232517 | 0.116259 |
M3 | -1.22450466200466 | 2.21008 | -0.5541 | 0.580395 | 0.290198 |
M4 | -3.47943722943723 | 2.251334 | -1.5455 | 0.124405 | 0.062203 |
M5 | -3.71372377622378 | 2.251272 | -1.6496 | 0.101187 | 0.050594 |
M6 | -4.33262570762571 | 2.251259 | -1.9245 | 0.056246 | 0.028123 |
M7 | -3.13625957375957 | 2.244117 | -1.3975 | 0.164384 | 0.082192 |
M8 | -2.4474691974692 | 2.243896 | -1.0907 | 0.277204 | 0.138602 |
M9 | -1.45098651348651 | 2.243725 | -0.6467 | 0.518857 | 0.259429 |
M10 | -0.992965367965368 | 2.243603 | -0.4426 | 0.658732 | 0.329366 |
M11 | -2.68879037629038 | 2.243529 | -1.1985 | 0.232691 | 0.116346 |
t | 0.00351731601731602 | 0.010483 | 0.3355 | 0.737719 | 0.36886 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.288504216420314 |
R-squared | 0.0832346828922996 |
Adjusted R-squared | 0.001041930324023 |
F-TEST (value) | 1.01267666906711 |
F-TEST (DF numerator) | 13 |
F-TEST (DF denominator) | 145 |
p-value | 0.442297652472542 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 5.71983678896478 |
Sum Squared Residuals | 4743.89726939727 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 24 | 23.3528138528138 | 0.64718614718616 |
2 | 25 | 19.3528138528139 | 5.64718614718614 |
3 | 17 | 20.7813852813853 | -3.78138528138528 |
4 | 18 | 18.52997002997 | -0.529970029970031 |
5 | 18 | 18.2992007992008 | -0.299200799200804 |
6 | 16 | 17.6838161838162 | -1.68381618381619 |
7 | 20 | 20.2852147852148 | -0.285214785214788 |
8 | 16 | 20.9775224775225 | -4.97752247752248 |
9 | 18 | 21.9775224775225 | -3.97752247752247 |
10 | 17 | 22.4390609390609 | -5.43906093906094 |
11 | 23 | 20.7467532467532 | 2.25324675324675 |
12 | 30 | 23.4390609390609 | 6.56093906093906 |
13 | 23 | 24.7965367965368 | -1.7965367965368 |
14 | 18 | 20.7965367965368 | -2.7965367965368 |
15 | 15 | 22.2251082251082 | -7.22510822510823 |
16 | 12 | 19.973692973693 | -7.97369297369297 |
17 | 21 | 19.7429237429237 | 1.25707625707626 |
18 | 15 | 19.1275391275391 | -4.12753912753913 |
19 | 20 | 20.3274225774226 | -0.327422577422577 |
20 | 31 | 21.0197302697303 | 9.98026973026973 |
21 | 27 | 22.0197302697303 | 4.98026973026973 |
22 | 34 | 22.4812687312687 | 11.5187312687313 |
23 | 21 | 20.788961038961 | 0.211038961038961 |
24 | 31 | 23.4812687312687 | 7.51873126873127 |
25 | 19 | 24.8387445887446 | -5.83874458874459 |
26 | 16 | 20.8387445887446 | -4.83874458874459 |
27 | 20 | 22.267316017316 | -2.26731601731602 |
28 | 21 | 20.0159007659008 | 0.984099234099234 |
29 | 22 | 19.7851315351315 | 2.21486846486846 |
30 | 17 | 19.1697469197469 | -2.16974691974692 |
31 | 24 | 20.3696303696304 | 3.63036963036963 |
32 | 25 | 21.0619380619381 | 3.93806193806194 |
33 | 26 | 22.0619380619381 | 3.93806193806194 |
34 | 25 | 22.5234765234765 | 2.47652347652348 |
35 | 17 | 20.8311688311688 | -3.83116883116883 |
36 | 32 | 23.5234765234765 | 8.47652347652348 |
37 | 33 | 24.8809523809524 | 8.11904761904762 |
38 | 13 | 20.8809523809524 | -7.88095238095239 |
39 | 32 | 22.3095238095238 | 9.69047619047619 |
40 | 25 | 20.0581085581086 | 4.94189144189144 |
41 | 29 | 19.8273393273393 | 9.17266067266068 |
42 | 22 | 19.2119547119547 | 2.78804528804529 |
43 | 18 | 20.4118381618382 | -2.41183816183816 |
44 | 17 | 21.1041458541459 | -4.10414585414585 |
45 | 20 | 22.1041458541459 | -2.10414585414585 |
46 | 15 | 22.5656843156843 | -7.56568431568432 |
47 | 20 | 20.8733766233766 | -0.873376623376624 |
48 | 33 | 23.5656843156843 | 9.43431568431568 |
49 | 29 | 24.9231601731602 | 4.07683982683982 |
50 | 23 | 20.9231601731602 | 2.07683982683983 |
51 | 26 | 22.3517316017316 | 3.6482683982684 |
52 | 18 | 20.1003163503164 | -2.10031635031635 |
53 | 20 | 19.8695471195471 | 0.13045288045288 |
54 | 11 | 19.2541625041625 | -8.2541625041625 |
55 | 28 | 20.454045954046 | 7.54595404595405 |
56 | 26 | 21.1463536463536 | 4.85364635364635 |
57 | 22 | 22.1463536463536 | -0.146353646353647 |
58 | 17 | 22.6078921078921 | -5.60789210789211 |
59 | 12 | 20.9155844155844 | -8.91558441558442 |
60 | 14 | 23.6078921078921 | -9.60789210789211 |
61 | 17 | 24.965367965368 | -7.96536796536797 |
62 | 21 | 20.965367965368 | 0.0346320346320345 |
63 | 19 | 22.3939393939394 | -3.39393939393939 |
64 | 18 | 20.1425241425241 | -2.14252414252414 |
65 | 10 | 19.9117549117549 | -9.9117549117549 |
66 | 29 | 19.2963702963703 | 9.7036297036297 |
67 | 31 | 20.4962537462537 | 10.5037462537463 |
68 | 19 | 21.1885614385614 | -2.18856143856144 |
69 | 9 | 22.1885614385614 | -13.1885614385614 |
70 | 20 | 22.6500999000999 | -2.6500999000999 |
71 | 28 | 20.9577922077922 | 7.0422077922078 |
72 | 19 | 23.6500999000999 | -4.6500999000999 |
73 | 30 | 25.0075757575758 | 4.99242424242424 |
74 | 29 | 21.0075757575758 | 7.99242424242424 |
75 | 26 | 22.4361471861472 | 3.56385281385281 |
76 | 23 | 20.1847319347319 | 2.81526806526806 |
77 | 13 | 19.9539627039627 | -6.9539627039627 |
78 | 21 | 19.3385780885781 | 1.66142191142191 |
79 | 19 | 20.5384615384615 | -1.53846153846154 |
80 | 28 | 21.2307692307692 | 6.76923076923077 |
81 | 23 | 22.2307692307692 | 0.769230769230769 |
82 | 18 | 22.6923076923077 | -4.69230769230769 |
83 | 21 | 21 | -5.43117525779457e-17 |
84 | 20 | 23.6923076923077 | -3.69230769230769 |
85 | 23 | 25.0497835497836 | -2.04978354978355 |
86 | 21 | 21.0497835497835 | -0.0497835497835497 |
87 | 21 | 22.478354978355 | -1.47835497835498 |
88 | 15 | 20.2269397269397 | -5.22693972693973 |
89 | 28 | 19.9961704961705 | 8.0038295038295 |
90 | 19 | 19.3807858807859 | -0.380785880785881 |
91 | 26 | 20.5806693306693 | 5.41933066933067 |
92 | 10 | 21.272977022977 | -11.272977022977 |
93 | 16 | 22.272977022977 | -6.27297702297702 |
94 | 22 | 22.7345154845155 | -0.734515484515485 |
95 | 19 | 21.0422077922078 | -2.04220779220779 |
96 | 31 | 23.7345154845155 | 7.26548451548451 |
97 | 31 | 25.0919913419913 | 5.90800865800866 |
98 | 29 | 21.0919913419913 | 7.90800865800866 |
99 | 19 | 22.5205627705628 | -3.52056277056277 |
100 | 22 | 20.2691475191475 | 1.73085248085248 |
101 | 23 | 20.0383782883783 | 2.96162171162171 |
102 | 15 | 19.4229936729937 | -4.42299367299367 |
103 | 20 | 20.6228771228771 | -0.622877122877123 |
104 | 18 | 21.3151848151848 | -3.31518481518482 |
105 | 23 | 22.3151848151848 | 0.684815184815185 |
106 | 25 | 22.7767232767233 | 2.22327672327672 |
107 | 21 | 21.0844155844156 | -0.0844155844155845 |
108 | 24 | 23.7767232767233 | 0.223276723276723 |
109 | 25 | 25.1341991341991 | -0.134199134199135 |
110 | 17 | 21.1341991341991 | -4.13419913419913 |
111 | 13 | 22.5627705627706 | -9.56277056277056 |
112 | 28 | 20.3113553113553 | 7.68864468864469 |
113 | 21 | 20.0805860805861 | 0.91941391941392 |
114 | 25 | 19.4652014652015 | 5.53479853479854 |
115 | 9 | 20.6650849150849 | -11.6650849150849 |
116 | 16 | 21.3573926073926 | -5.35739260739261 |
117 | 19 | 22.3573926073926 | -3.35739260739261 |
118 | 17 | 22.8189310689311 | -5.81893106893107 |
119 | 25 | 21.1266233766234 | 3.87337662337663 |
120 | 20 | 23.8189310689311 | -3.81893106893107 |
121 | 29 | 25.1764069264069 | 3.82359307359307 |
122 | 14 | 21.1764069264069 | -7.17640692640693 |
123 | 22 | 22.6049783549784 | -0.604978354978355 |
124 | 15 | 20.3535631035631 | -5.3535631035631 |
125 | 19 | 20.1227938727939 | -1.12279387279387 |
126 | 20 | 19.5074092574093 | 0.492590742590742 |
127 | 15 | 20.7072927072927 | -5.70729270729271 |
128 | 20 | 21.3996003996004 | -1.3996003996004 |
129 | 18 | 22.3996003996004 | -4.3996003996004 |
130 | 33 | 22.8611388611389 | 10.1388611388611 |
131 | 22 | 21.1688311688312 | 0.831168831168831 |
132 | 16 | 23.8611388611389 | -7.86113886113886 |
133 | 17 | 25.2186147186147 | -8.21861471861472 |
134 | 16 | 21.2186147186147 | -5.21861471861472 |
135 | 21 | 22.6471861471861 | -1.64718614718615 |
136 | 26 | 20.3957708957709 | 5.6042291042291 |
137 | 18 | 20.1650016650017 | -2.16500166500167 |
138 | 18 | 19.549617049617 | -1.54961704961705 |
139 | 17 | 20.7495004995005 | -3.7495004995005 |
140 | 22 | 21.4418081918082 | 0.558191808191808 |
141 | 30 | 22.4418081918082 | 7.5581918081918 |
142 | 30 | 22.9033466533467 | 7.09665334665335 |
143 | 24 | 21.211038961039 | 2.78896103896104 |
144 | 21 | 23.9033466533467 | -2.90334665334665 |
145 | 21 | 25.2608225108225 | -4.26082251082251 |
146 | 29 | 21.2608225108225 | 7.73917748917749 |
147 | 31 | 22.6893939393939 | 8.31060606060606 |
148 | 20 | 20.4379786879787 | -0.437978687978688 |
149 | 16 | 20.2072094572095 | -4.20720945720946 |
150 | 22 | 19.5918248418248 | 2.40817515817516 |
151 | 20 | 20.7917082917083 | -0.791708291708292 |
152 | 28 | 21.484015984016 | 6.51598401598402 |
153 | 38 | 22.484015984016 | 15.515984015984 |
154 | 22 | 22.9455544455544 | -0.945554445554446 |
155 | 20 | 21.2532467532468 | -1.25324675324675 |
156 | 17 | 23.9455544455544 | -6.94555444555444 |
157 | 28 | 25.3030303030303 | 2.6969696969697 |
158 | 22 | 21.3030303030303 | 0.696969696969697 |
159 | 31 | 22.7316017316017 | 8.26839826839827 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
17 | 0.186018245597383 | 0.372036491194766 | 0.813981754402617 |
18 | 0.0871965062102043 | 0.174393012420409 | 0.912803493789796 |
19 | 0.0355563794863127 | 0.0711127589726255 | 0.964443620513687 |
20 | 0.14682813559267 | 0.293656271185341 | 0.85317186440733 |
21 | 0.085210864009095 | 0.17042172801819 | 0.914789135990905 |
22 | 0.111005306867716 | 0.222010613735432 | 0.888994693132284 |
23 | 0.198881959077544 | 0.397763918155088 | 0.801118040922456 |
24 | 0.184910538779579 | 0.369821077559157 | 0.815089461220421 |
25 | 0.24764662066856 | 0.49529324133712 | 0.75235337933144 |
26 | 0.280449515854607 | 0.560899031709213 | 0.719550484145393 |
27 | 0.217821319767851 | 0.435642639535703 | 0.782178680232149 |
28 | 0.17494415839584 | 0.349888316791681 | 0.82505584160416 |
29 | 0.125938773715723 | 0.251877547431446 | 0.874061226284277 |
30 | 0.0894230722895998 | 0.1788461445792 | 0.9105769277104 |
31 | 0.0643144472637689 | 0.128628894527538 | 0.935685552736231 |
32 | 0.0516832168581026 | 0.103366433716205 | 0.948316783141897 |
33 | 0.0357299117193272 | 0.0714598234386545 | 0.964270088280673 |
34 | 0.0311984262040937 | 0.0623968524081874 | 0.968801573795906 |
35 | 0.044919271689992 | 0.089838543379984 | 0.955080728310008 |
36 | 0.0362867212116559 | 0.0725734424233118 | 0.963713278788344 |
37 | 0.0516055594394931 | 0.103211118878986 | 0.948394440560507 |
38 | 0.0889468954655244 | 0.177893790931049 | 0.911053104534476 |
39 | 0.176743474006825 | 0.35348694801365 | 0.823256525993175 |
40 | 0.156589791502145 | 0.31317958300429 | 0.843410208497855 |
41 | 0.158716555885576 | 0.317433111771152 | 0.841283444114424 |
42 | 0.126660498348342 | 0.253320996696685 | 0.873339501651658 |
43 | 0.155236009913409 | 0.310472019826819 | 0.84476399008659 |
44 | 0.230857181527133 | 0.461714363054266 | 0.769142818472867 |
45 | 0.233179534966863 | 0.466359069933725 | 0.766820465033137 |
46 | 0.356837199447941 | 0.713674398895881 | 0.643162800552059 |
47 | 0.309232222690182 | 0.618464445380364 | 0.690767777309818 |
48 | 0.321300914400207 | 0.642601828800413 | 0.678699085599793 |
49 | 0.286292647787165 | 0.572585295574329 | 0.713707352212835 |
50 | 0.247420875825799 | 0.494841751651599 | 0.7525791241742 |
51 | 0.216646878193444 | 0.433293756386888 | 0.783353121806556 |
52 | 0.188135712363596 | 0.376271424727191 | 0.811864287636404 |
53 | 0.171207377920909 | 0.342414755841818 | 0.828792622079091 |
54 | 0.207618742651455 | 0.415237485302911 | 0.792381257348544 |
55 | 0.21997439388624 | 0.439948787772481 | 0.78002560611376 |
56 | 0.200120143745262 | 0.400240287490524 | 0.799879856254738 |
57 | 0.171574870031624 | 0.343149740063247 | 0.828425129968376 |
58 | 0.183107767218234 | 0.366215534436468 | 0.816892232781766 |
59 | 0.238536082883487 | 0.477072165766973 | 0.761463917116513 |
60 | 0.472239165721288 | 0.944478331442576 | 0.527760834278712 |
61 | 0.510104345831749 | 0.979791308336503 | 0.489895654168251 |
62 | 0.462378926274308 | 0.924757852548616 | 0.537621073725692 |
63 | 0.422650205563764 | 0.845300411127528 | 0.577349794436236 |
64 | 0.376324287268961 | 0.752648574537921 | 0.623675712731039 |
65 | 0.470269939124361 | 0.940539878248723 | 0.529730060875639 |
66 | 0.599819244168103 | 0.800361511663794 | 0.400180755831897 |
67 | 0.707193787174976 | 0.585612425650048 | 0.292806212825024 |
68 | 0.672472457940178 | 0.655055084119645 | 0.327527542059822 |
69 | 0.816442070232577 | 0.367115859534845 | 0.183557929767423 |
70 | 0.786331637341229 | 0.427336725317542 | 0.213668362658771 |
71 | 0.81787052437534 | 0.364258951249321 | 0.182129475624661 |
72 | 0.814804087063487 | 0.370391825873025 | 0.185195912936513 |
73 | 0.813766314253921 | 0.372467371492157 | 0.186233685746079 |
74 | 0.852412164728547 | 0.295175670542906 | 0.147587835271453 |
75 | 0.838778868144973 | 0.322442263710055 | 0.161221131855027 |
76 | 0.817808803326274 | 0.364382393347452 | 0.182191196673726 |
77 | 0.824391633209693 | 0.351216733580614 | 0.175608366790307 |
78 | 0.795752173958979 | 0.408495652082043 | 0.204247826041021 |
79 | 0.770892061565009 | 0.458215876869981 | 0.229107938434991 |
80 | 0.804835125162985 | 0.39032974967403 | 0.195164874837015 |
81 | 0.771694544327323 | 0.456610911345354 | 0.228305455672677 |
82 | 0.752926712349396 | 0.494146575301208 | 0.247073287650604 |
83 | 0.712592638462758 | 0.574814723074483 | 0.287407361537242 |
84 | 0.689662501955171 | 0.620674996089658 | 0.310337498044829 |
85 | 0.6465874253648 | 0.706825149270401 | 0.353412574635201 |
86 | 0.60076183692244 | 0.79847632615512 | 0.39923816307756 |
87 | 0.552448608346904 | 0.895102783306193 | 0.447551391653096 |
88 | 0.536091274300361 | 0.927817451399278 | 0.463908725699639 |
89 | 0.60251954379202 | 0.79496091241596 | 0.39748045620798 |
90 | 0.553556383964299 | 0.892887232071403 | 0.446443616035701 |
91 | 0.610928835334718 | 0.778142329330565 | 0.389071164665282 |
92 | 0.701056376288969 | 0.597887247422063 | 0.298943623711031 |
93 | 0.710059397890488 | 0.579881204219024 | 0.289940602109512 |
94 | 0.669332396960966 | 0.661335206078069 | 0.330667603039034 |
95 | 0.625504603458845 | 0.748990793082311 | 0.374495396541155 |
96 | 0.724772941352192 | 0.550454117295617 | 0.275227058647808 |
97 | 0.760579220737819 | 0.478841558524362 | 0.239420779262181 |
98 | 0.844832340115653 | 0.310335319768693 | 0.155167659884347 |
99 | 0.816300972913863 | 0.367398054172274 | 0.183699027086137 |
100 | 0.785820189823091 | 0.428359620353818 | 0.214179810176909 |
101 | 0.786965171018474 | 0.426069657963051 | 0.213034828981526 |
102 | 0.761415260144725 | 0.47716947971055 | 0.238584739855275 |
103 | 0.769935924738837 | 0.460128150522327 | 0.230064075261163 |
104 | 0.731124767503707 | 0.537750464992585 | 0.268875232496293 |
105 | 0.688008161639485 | 0.623983676721029 | 0.311991838360515 |
106 | 0.65140953162603 | 0.697180936747941 | 0.348590468373971 |
107 | 0.60181931372742 | 0.79636137254516 | 0.39818068627258 |
108 | 0.634958372140219 | 0.730083255719562 | 0.365041627859781 |
109 | 0.611472555133294 | 0.777054889733411 | 0.388527444866706 |
110 | 0.567233800668374 | 0.865532398663252 | 0.432766199331626 |
111 | 0.636132269379813 | 0.727735461240374 | 0.363867730620187 |
112 | 0.730728249134147 | 0.538543501731706 | 0.269271750865853 |
113 | 0.72971658933161 | 0.54056682133678 | 0.27028341066839 |
114 | 0.776021807021449 | 0.447956385957103 | 0.223978192978551 |
115 | 0.797347917393948 | 0.405304165212104 | 0.202652082606052 |
116 | 0.768649336354943 | 0.462701327290114 | 0.231350663645057 |
117 | 0.757497437827841 | 0.485005124344318 | 0.242502562172159 |
118 | 0.782468206890621 | 0.435063586218757 | 0.217531793109379 |
119 | 0.780304698484758 | 0.439390603030485 | 0.219695301515242 |
120 | 0.771786512645749 | 0.456426974708502 | 0.228213487354251 |
121 | 0.86125170885184 | 0.277496582296321 | 0.13874829114816 |
122 | 0.842581844891156 | 0.314836310217688 | 0.157418155108844 |
123 | 0.799985468136654 | 0.400029063726691 | 0.200014531863345 |
124 | 0.779205079248669 | 0.441589841502663 | 0.220794920751331 |
125 | 0.754803708784304 | 0.490392582431391 | 0.245196291215696 |
126 | 0.710301171609216 | 0.579397656781569 | 0.289698828390784 |
127 | 0.652143204950105 | 0.695713590099789 | 0.347856795049894 |
128 | 0.583959173519173 | 0.832081652961654 | 0.416040826480827 |
129 | 0.770170177431137 | 0.459659645137725 | 0.229829822568863 |
130 | 0.861160993906304 | 0.277678012187392 | 0.138839006093696 |
131 | 0.824618292418221 | 0.350763415163558 | 0.175381707581779 |
132 | 0.775192619666197 | 0.449614760667607 | 0.224807380333803 |
133 | 0.742933253799374 | 0.514133492401252 | 0.257066746200626 |
134 | 0.757388024431814 | 0.485223951136372 | 0.242611975568186 |
135 | 0.836470666407129 | 0.327058667185742 | 0.163529333592871 |
136 | 0.822722785065846 | 0.354554429868308 | 0.177277214934154 |
137 | 0.751127561136396 | 0.497744877727207 | 0.248872438863604 |
138 | 0.676297219755388 | 0.647405560489225 | 0.323702780244612 |
139 | 0.579103675929108 | 0.841792648141784 | 0.420896324070892 |
140 | 0.545079109696102 | 0.909841780607796 | 0.454920890303898 |
141 | 0.660976805407795 | 0.678046389184409 | 0.339023194592205 |
142 | 0.605059311031694 | 0.789881377936613 | 0.394940688968306 |
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 | 5 | 0.0396825396825397 | OK |