Multiple Linear Regression - Estimated Regression Equation |
PS[t] = + 21.3846153846154 + 1.54395604395604M1[t] -0.456043956043958M2[t] + 1.40109890109889M3[t] + 0.538461538461531M4[t] -0.153846153846160M5[t] + 0.461538461538454M6[t] + 1.38461538461538M7[t] + 1.99999999999999M8[t] + 1.69230769230768M9[t] + 1.15384615384615M10[t] -0.461538461538467M11[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) | 21.3846153846154 | 1.187911 | 18.0019 | 0 | 0 |
M1 | 1.54395604395604 | 1.649688 | 0.9359 | 0.350856 | 0.175428 |
M2 | -0.456043956043958 | 1.649688 | -0.2764 | 0.782597 | 0.391298 |
M3 | 1.40109890109889 | 1.649688 | 0.8493 | 0.397089 | 0.198545 |
M4 | 0.538461538461531 | 1.67996 | 0.3205 | 0.749029 | 0.374515 |
M5 | -0.153846153846160 | 1.67996 | -0.0916 | 0.927159 | 0.463579 |
M6 | 0.461538461538454 | 1.67996 | 0.2747 | 0.783908 | 0.391954 |
M7 | 1.38461538461538 | 1.67996 | 0.8242 | 0.411164 | 0.205582 |
M8 | 1.99999999999999 | 1.67996 | 1.1905 | 0.235767 | 0.117884 |
M9 | 1.69230769230768 | 1.67996 | 1.0073 | 0.315422 | 0.157711 |
M10 | 1.15384615384615 | 1.67996 | 0.6868 | 0.493272 | 0.246636 |
M11 | -0.461538461538467 | 1.67996 | -0.2747 | 0.783908 | 0.391954 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.200542222804997 |
R-squared | 0.040217183127569 |
Adjusted R-squared | -0.031603299767647 |
F-TEST (value) | 0.559968152626386 |
F-TEST (DF numerator) | 11 |
F-TEST (DF denominator) | 147 |
p-value | 0.858509976817269 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 4.28307523839994 |
Sum Squared Residuals | 2696.67582417582 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 24 | 22.9285714285714 | 1.07142857142861 |
2 | 25 | 20.9285714285714 | 4.07142857142857 |
3 | 30 | 22.7857142857143 | 7.21428571428569 |
4 | 19 | 21.9230769230769 | -2.92307692307692 |
5 | 22 | 21.2307692307692 | 0.769230769230767 |
6 | 22 | 21.8461538461538 | 0.153846153846157 |
7 | 25 | 22.7692307692308 | 2.23076923076923 |
8 | 23 | 23.3846153846154 | -0.384615384615375 |
9 | 17 | 23.0769230769231 | -6.07692307692307 |
10 | 21 | 22.5384615384615 | -1.53846153846154 |
11 | 19 | 20.9230769230769 | -1.92307692307692 |
12 | 19 | 21.3846153846154 | -2.38461538461540 |
13 | 15 | 22.9285714285714 | -7.92857142857143 |
14 | 16 | 20.9285714285714 | -4.92857142857142 |
15 | 23 | 22.7857142857143 | 0.214285714285715 |
16 | 27 | 21.9230769230769 | 5.07692307692308 |
17 | 22 | 21.2307692307692 | 0.769230769230769 |
18 | 14 | 21.8461538461538 | -7.84615384615385 |
19 | 22 | 22.7692307692308 | -0.76923076923077 |
20 | 23 | 23.3846153846154 | -0.384615384615383 |
21 | 23 | 23.0769230769231 | -0.0769230769230741 |
22 | 21 | 22.5384615384615 | -1.53846153846154 |
23 | 19 | 20.9230769230769 | -1.92307692307692 |
24 | 18 | 21.3846153846154 | -3.38461538461539 |
25 | 20 | 22.9285714285714 | -2.92857142857143 |
26 | 23 | 20.9285714285714 | 2.07142857142858 |
27 | 25 | 22.7857142857143 | 2.21428571428572 |
28 | 19 | 21.9230769230769 | -2.92307692307692 |
29 | 24 | 21.2307692307692 | 2.76923076923077 |
30 | 22 | 21.8461538461538 | 0.153846153846155 |
31 | 25 | 22.7692307692308 | 2.23076923076923 |
32 | 26 | 23.3846153846154 | 2.61538461538462 |
33 | 29 | 23.0769230769231 | 5.92307692307693 |
34 | 32 | 22.5384615384615 | 9.46153846153846 |
35 | 25 | 20.9230769230769 | 4.07692307692308 |
36 | 29 | 21.3846153846154 | 7.61538461538461 |
37 | 28 | 22.9285714285714 | 5.07142857142857 |
38 | 17 | 20.9285714285714 | -3.92857142857142 |
39 | 28 | 22.7857142857143 | 5.21428571428572 |
40 | 29 | 21.9230769230769 | 7.07692307692308 |
41 | 26 | 21.2307692307692 | 4.76923076923077 |
42 | 25 | 21.8461538461538 | 3.15384615384615 |
43 | 14 | 22.7692307692308 | -8.76923076923077 |
44 | 25 | 23.3846153846154 | 1.61538461538462 |
45 | 26 | 23.0769230769231 | 2.92307692307692 |
46 | 20 | 22.5384615384615 | -2.53846153846154 |
47 | 18 | 20.9230769230769 | -2.92307692307692 |
48 | 32 | 21.3846153846154 | 10.6153846153846 |
49 | 25 | 22.9285714285714 | 2.07142857142857 |
50 | 25 | 20.9285714285714 | 4.07142857142857 |
51 | 23 | 22.7857142857143 | 0.214285714285715 |
52 | 21 | 21.9230769230769 | -0.923076923076921 |
53 | 20 | 21.2307692307692 | -1.23076923076923 |
54 | 15 | 21.8461538461538 | -6.84615384615385 |
55 | 30 | 22.7692307692308 | 7.23076923076923 |
56 | 24 | 23.3846153846154 | 0.615384615384615 |
57 | 26 | 23.0769230769231 | 2.92307692307692 |
58 | 24 | 22.5384615384615 | 1.46153846153846 |
59 | 22 | 20.9230769230769 | 1.07692307692308 |
60 | 14 | 21.3846153846154 | -7.38461538461539 |
61 | 24 | 22.9285714285714 | 1.07142857142857 |
62 | 24 | 20.9285714285714 | 3.07142857142857 |
63 | 24 | 22.7857142857143 | 1.21428571428572 |
64 | 24 | 21.9230769230769 | 2.07692307692308 |
65 | 19 | 21.2307692307692 | -2.23076923076923 |
66 | 31 | 21.8461538461538 | 9.15384615384615 |
67 | 22 | 22.7692307692308 | -0.76923076923077 |
68 | 27 | 23.3846153846154 | 3.61538461538461 |
69 | 19 | 23.0769230769231 | -4.07692307692307 |
70 | 25 | 22.5384615384615 | 2.46153846153846 |
71 | 20 | 20.9230769230769 | -0.923076923076922 |
72 | 21 | 21.3846153846154 | -0.384615384615392 |
73 | 27 | 22.9285714285714 | 4.07142857142857 |
74 | 23 | 20.9285714285714 | 2.07142857142858 |
75 | 25 | 22.7857142857143 | 2.21428571428572 |
76 | 20 | 21.9230769230769 | -1.92307692307692 |
77 | 21 | 21.2307692307692 | -0.230769230769232 |
78 | 22 | 21.8461538461538 | 0.153846153846155 |
79 | 23 | 22.7692307692308 | 0.230769230769230 |
80 | 25 | 23.3846153846154 | 1.61538461538462 |
81 | 25 | 23.0769230769231 | 1.92307692307693 |
82 | 17 | 22.5384615384615 | -5.53846153846154 |
83 | 19 | 20.9230769230769 | -1.92307692307692 |
84 | 25 | 21.3846153846154 | 3.61538461538461 |
85 | 19 | 22.9285714285714 | -3.92857142857143 |
86 | 20 | 20.9285714285714 | -0.928571428571425 |
87 | 26 | 22.7857142857143 | 3.21428571428572 |
88 | 23 | 21.9230769230769 | 1.07692307692308 |
89 | 27 | 21.2307692307692 | 5.76923076923077 |
90 | 17 | 21.8461538461538 | -4.84615384615385 |
91 | 17 | 22.7692307692308 | -5.76923076923077 |
92 | 19 | 23.3846153846154 | -4.38461538461538 |
93 | 17 | 23.0769230769231 | -6.07692307692307 |
94 | 22 | 22.5384615384615 | -0.538461538461538 |
95 | 21 | 20.9230769230769 | 0.076923076923077 |
96 | 32 | 21.3846153846154 | 10.6153846153846 |
97 | 21 | 22.9285714285714 | -1.92857142857143 |
98 | 21 | 20.9285714285714 | 0.0714285714285749 |
99 | 18 | 22.7857142857143 | -4.78571428571428 |
100 | 18 | 21.9230769230769 | -3.92307692307692 |
101 | 23 | 21.2307692307692 | 1.76923076923077 |
102 | 19 | 21.8461538461538 | -2.84615384615385 |
103 | 20 | 22.7692307692308 | -2.76923076923077 |
104 | 21 | 23.3846153846154 | -2.38461538461538 |
105 | 20 | 23.0769230769231 | -3.07692307692308 |
106 | 17 | 22.5384615384615 | -5.53846153846154 |
107 | 18 | 20.9230769230769 | -2.92307692307692 |
108 | 19 | 21.3846153846154 | -2.38461538461539 |
109 | 22 | 22.9285714285714 | -0.928571428571431 |
110 | 15 | 20.9285714285714 | -5.92857142857143 |
111 | 14 | 22.7857142857143 | -8.7857142857143 |
112 | 18 | 21.9230769230769 | -3.92307692307692 |
113 | 24 | 21.2307692307692 | 2.76923076923077 |
114 | 35 | 21.8461538461538 | 13.1538461538462 |
115 | 29 | 22.7692307692308 | 6.23076923076923 |
116 | 21 | 23.3846153846154 | -2.38461538461538 |
117 | 25 | 23.0769230769231 | 1.92307692307693 |
118 | 20 | 22.5384615384615 | -2.53846153846154 |
119 | 22 | 20.9230769230769 | 1.07692307692308 |
120 | 13 | 21.3846153846154 | -8.38461538461539 |
121 | 26 | 22.9285714285714 | 3.07142857142857 |
122 | 17 | 20.9285714285714 | -3.92857142857142 |
123 | 25 | 22.7857142857143 | 2.21428571428572 |
124 | 20 | 21.9230769230769 | -1.92307692307692 |
125 | 19 | 21.2307692307692 | -2.23076923076923 |
126 | 21 | 21.8461538461538 | -0.846153846153846 |
127 | 22 | 22.7692307692308 | -0.76923076923077 |
128 | 24 | 23.3846153846154 | 0.615384615384615 |
129 | 21 | 23.0769230769231 | -2.07692307692308 |
130 | 26 | 22.5384615384615 | 3.46153846153846 |
131 | 24 | 20.9230769230769 | 3.07692307692308 |
132 | 16 | 21.3846153846154 | -5.38461538461539 |
133 | 23 | 22.9285714285714 | 0.0714285714285696 |
134 | 18 | 20.9285714285714 | -2.92857142857142 |
135 | 16 | 22.7857142857143 | -6.78571428571429 |
136 | 26 | 21.9230769230769 | 4.07692307692308 |
137 | 19 | 21.2307692307692 | -2.23076923076923 |
138 | 21 | 21.8461538461538 | -0.846153846153846 |
139 | 21 | 22.7692307692308 | -1.76923076923077 |
140 | 22 | 23.3846153846154 | -1.38461538461538 |
141 | 23 | 23.0769230769231 | -0.0769230769230741 |
142 | 29 | 22.5384615384615 | 6.46153846153846 |
143 | 21 | 20.9230769230769 | 0.076923076923077 |
144 | 21 | 21.3846153846154 | -0.384615384615392 |
145 | 23 | 22.9285714285714 | 0.0714285714285696 |
146 | 27 | 20.9285714285714 | 6.07142857142857 |
147 | 25 | 22.7857142857143 | 2.21428571428572 |
148 | 21 | 21.9230769230769 | -0.923076923076921 |
149 | 10 | 21.2307692307692 | -11.2307692307692 |
150 | 20 | 21.8461538461538 | -1.84615384615385 |
151 | 26 | 22.7692307692308 | 3.23076923076923 |
152 | 24 | 23.3846153846154 | 0.615384615384615 |
153 | 29 | 23.0769230769231 | 5.92307692307693 |
154 | 19 | 22.5384615384615 | -3.53846153846154 |
155 | 24 | 20.9230769230769 | 3.07692307692308 |
156 | 19 | 21.3846153846154 | -2.38461538461539 |
157 | 24 | 22.9285714285714 | 1.07142857142857 |
158 | 22 | 20.9285714285714 | 1.07142857142858 |
159 | 17 | 22.7857142857143 | -5.78571428571428 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
15 | 0.864751796938915 | 0.27049640612217 | 0.135248203061085 |
16 | 0.876431217950371 | 0.247137564099257 | 0.123568782049629 |
17 | 0.79506818688698 | 0.409863626226042 | 0.204931813113021 |
18 | 0.829136782556346 | 0.341726434887308 | 0.170863217443654 |
19 | 0.764523509147891 | 0.470952981704218 | 0.235476490852109 |
20 | 0.675163692568172 | 0.649672614863657 | 0.324836307431828 |
21 | 0.656673592590036 | 0.686652814819927 | 0.343326407409964 |
22 | 0.564902847924592 | 0.870194304150815 | 0.435097152075408 |
23 | 0.473316258646911 | 0.946632517293821 | 0.526683741353089 |
24 | 0.391394633611533 | 0.782789267223067 | 0.608605366388467 |
25 | 0.314853585609012 | 0.629707171218023 | 0.685146414390988 |
26 | 0.259617639576978 | 0.519235279153957 | 0.740382360423022 |
27 | 0.20381603189129 | 0.40763206378258 | 0.79618396810871 |
28 | 0.18384653790972 | 0.36769307581944 | 0.81615346209028 |
29 | 0.144556319229767 | 0.289112638459534 | 0.855443680770233 |
30 | 0.128327837249788 | 0.256655674499576 | 0.871672162750212 |
31 | 0.0964945352096202 | 0.192989070419240 | 0.90350546479038 |
32 | 0.078611709888819 | 0.157223419777638 | 0.921388290111181 |
33 | 0.157323120455648 | 0.314646240911295 | 0.842676879544352 |
34 | 0.360411812413372 | 0.720823624826744 | 0.639588187586628 |
35 | 0.375996959283984 | 0.751993918567968 | 0.624003040716016 |
36 | 0.552187412365217 | 0.895625175269566 | 0.447812587634783 |
37 | 0.63385406055876 | 0.732291878882481 | 0.366145939441241 |
38 | 0.617622811123999 | 0.764754377752002 | 0.382377188876001 |
39 | 0.590852600399279 | 0.818294799201442 | 0.409147399600721 |
40 | 0.660715028671013 | 0.678569942657973 | 0.339284971328987 |
41 | 0.643117677020397 | 0.713764645959205 | 0.356882322979603 |
42 | 0.644533530820981 | 0.710932938358038 | 0.355466469179019 |
43 | 0.783084811697851 | 0.433830376604297 | 0.216915188302149 |
44 | 0.742370971430964 | 0.515258057138073 | 0.257629028569036 |
45 | 0.713149342333033 | 0.573701315333934 | 0.286850657666967 |
46 | 0.696692459302374 | 0.606615081395252 | 0.303307540697626 |
47 | 0.665974625849455 | 0.66805074830109 | 0.334025374150545 |
48 | 0.825203411183597 | 0.349593177632805 | 0.174796588816403 |
49 | 0.801238503056153 | 0.397522993887695 | 0.198761496943847 |
50 | 0.797323016458846 | 0.405353967082309 | 0.202676983541155 |
51 | 0.77365767583678 | 0.452684648326441 | 0.226342324163221 |
52 | 0.739216949871929 | 0.521566100256143 | 0.260783050128071 |
53 | 0.710063118905153 | 0.579873762189694 | 0.289936881094847 |
54 | 0.75288985023446 | 0.49422029953108 | 0.24711014976554 |
55 | 0.82330666181787 | 0.353386676364261 | 0.176693338182131 |
56 | 0.78856478060516 | 0.422870438789681 | 0.211435219394841 |
57 | 0.763952998316855 | 0.47209400336629 | 0.236047001683145 |
58 | 0.726261312125159 | 0.547477375749682 | 0.273738687874841 |
59 | 0.686364412936928 | 0.627271174126144 | 0.313635587063072 |
60 | 0.795058755298117 | 0.409882489403766 | 0.204941244701883 |
61 | 0.760402879879232 | 0.479194240241536 | 0.239597120120768 |
62 | 0.738293462864896 | 0.523413074270208 | 0.261706537135104 |
63 | 0.708167134307789 | 0.583665731384422 | 0.291832865692211 |
64 | 0.673358136658039 | 0.653283726683921 | 0.326641863341961 |
65 | 0.646408286417026 | 0.707183427165948 | 0.353591713582974 |
66 | 0.800804603675093 | 0.398390792649814 | 0.199195396324907 |
67 | 0.76589427475951 | 0.468211450480979 | 0.234105725240489 |
68 | 0.752141025039457 | 0.495717949921086 | 0.247858974960543 |
69 | 0.750049383258682 | 0.499901233482637 | 0.249950616741318 |
70 | 0.722463032397216 | 0.555073935205569 | 0.277536967602784 |
71 | 0.68163359643706 | 0.63673280712588 | 0.31836640356294 |
72 | 0.638701703178038 | 0.722596593643923 | 0.361298296821962 |
73 | 0.632767423035874 | 0.734465153928252 | 0.367232576964126 |
74 | 0.597012326738653 | 0.805975346522695 | 0.402987673261347 |
75 | 0.574351944562522 | 0.851296110874956 | 0.425648055437478 |
76 | 0.538512527074804 | 0.922974945850391 | 0.461487472925196 |
77 | 0.491717776803143 | 0.983435553606287 | 0.508282223196857 |
78 | 0.443341627394073 | 0.886683254788147 | 0.556658372605927 |
79 | 0.395759178033614 | 0.791518356067227 | 0.604240821966386 |
80 | 0.359590816328295 | 0.71918163265659 | 0.640409183671705 |
81 | 0.3238020132973 | 0.6476040265946 | 0.6761979867027 |
82 | 0.354341856412602 | 0.708683712825205 | 0.645658143587398 |
83 | 0.319106416007349 | 0.638212832014699 | 0.680893583992651 |
84 | 0.308345311323664 | 0.616690622647327 | 0.691654688676336 |
85 | 0.300767648357083 | 0.601535296714167 | 0.699232351642917 |
86 | 0.262616735426485 | 0.525233470852969 | 0.737383264573515 |
87 | 0.266944981924703 | 0.533889963849406 | 0.733055018075297 |
88 | 0.233193966323901 | 0.466387932647802 | 0.766806033676099 |
89 | 0.276038627407287 | 0.552077254814573 | 0.723961372592713 |
90 | 0.293053485342617 | 0.586106970685234 | 0.706946514657383 |
91 | 0.331333987553568 | 0.662667975107135 | 0.668666012446433 |
92 | 0.330410037056704 | 0.660820074113408 | 0.669589962943296 |
93 | 0.37724561213505 | 0.7544912242701 | 0.62275438786495 |
94 | 0.331548952030314 | 0.663097904060628 | 0.668451047969686 |
95 | 0.288623519788016 | 0.577247039576033 | 0.711376480211984 |
96 | 0.606890963048471 | 0.786218073903058 | 0.393109036951529 |
97 | 0.570558547558209 | 0.858882904883583 | 0.429441452441791 |
98 | 0.522719150259515 | 0.95456169948097 | 0.477280849740485 |
99 | 0.526028907545675 | 0.94794218490865 | 0.473971092454325 |
100 | 0.510633686222591 | 0.978732627554817 | 0.489366313777409 |
101 | 0.497213898991802 | 0.994427797983605 | 0.502786101008198 |
102 | 0.491691449370183 | 0.983382898740366 | 0.508308550629817 |
103 | 0.47608134417759 | 0.95216268835518 | 0.52391865582241 |
104 | 0.436676298111581 | 0.873352596223161 | 0.56332370188842 |
105 | 0.423321737319179 | 0.846643474638358 | 0.576678262680821 |
106 | 0.467268568395091 | 0.934537136790181 | 0.53273143160491 |
107 | 0.456857518342823 | 0.913715036685645 | 0.543142481657177 |
108 | 0.427010952276396 | 0.854021904552793 | 0.572989047723604 |
109 | 0.381495633962788 | 0.762991267925576 | 0.618504366037212 |
110 | 0.4225617119994 | 0.8451234239988 | 0.5774382880006 |
111 | 0.534319128048304 | 0.931361743903392 | 0.465680871951696 |
112 | 0.523793756923973 | 0.952412486152055 | 0.476206243076027 |
113 | 0.583081234031432 | 0.833837531937137 | 0.416918765968568 |
114 | 0.928100484601733 | 0.143799030796535 | 0.0718995153982675 |
115 | 0.945128037619163 | 0.109743924761674 | 0.0548719623808371 |
116 | 0.932015456432582 | 0.135969087134835 | 0.0679845435674175 |
117 | 0.91138555192106 | 0.177228896157881 | 0.0886144480789407 |
118 | 0.90931157058905 | 0.181376858821900 | 0.0906884294109499 |
119 | 0.883108321007247 | 0.233783357985507 | 0.116891678992753 |
120 | 0.915169902631809 | 0.169660194736382 | 0.0848300973681909 |
121 | 0.89851638087058 | 0.202967238258840 | 0.101483619129420 |
122 | 0.906400670409298 | 0.187198659181405 | 0.0935993295907026 |
123 | 0.916340617232858 | 0.167318765534285 | 0.0836593827671425 |
124 | 0.902050247376216 | 0.195899505247569 | 0.0979497526237843 |
125 | 0.898065544576503 | 0.203868910846995 | 0.101934455423497 |
126 | 0.863573329402 | 0.272853341196 | 0.136426670598 |
127 | 0.824367328486195 | 0.351265343027609 | 0.175632671513805 |
128 | 0.775277126760681 | 0.449445746478638 | 0.224722873239319 |
129 | 0.771169727108326 | 0.457660545783347 | 0.228830272891674 |
130 | 0.724846079890096 | 0.550307840219808 | 0.275153920109904 |
131 | 0.667218848225922 | 0.665562303548155 | 0.332781151774078 |
132 | 0.64887029611554 | 0.70225940776892 | 0.35112970388446 |
133 | 0.57122230409691 | 0.85755539180618 | 0.42877769590309 |
134 | 0.609975907344255 | 0.78004818531149 | 0.390024092655745 |
135 | 0.619857593514923 | 0.760284812970154 | 0.380142406485077 |
136 | 0.595573340527665 | 0.80885331894467 | 0.404426659472335 |
137 | 0.707254164627692 | 0.585491670744616 | 0.292745835372308 |
138 | 0.617296062616984 | 0.765407874766032 | 0.382703937383016 |
139 | 0.585272276821922 | 0.829455446356156 | 0.414727723178078 |
140 | 0.486055092611856 | 0.972110185223712 | 0.513944907388144 |
141 | 0.477021115569851 | 0.954042231139702 | 0.522978884430149 |
142 | 0.730684502424978 | 0.538630995150045 | 0.269315497575022 |
143 | 0.632504715224611 | 0.734990569550779 | 0.367495284775389 |
144 | 0.480971305322613 | 0.961942610645226 | 0.519028694677387 |
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 |