Multiple Linear Regression - Estimated Regression Equation |
Accidents[t] = + 2165.23 -395.811Belt[t] -442.551M1[t] -617.812M2[t] -567.25M3[t] -680.438M4[t] -543.125M5[t] -598.875M6[t] -523.25M7[t] -508.375M8[t] -455.562M9[t] -316.188M10[t] -116.625M11[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) | 2165.23 | 43.6319 | 49.62 | 1.45481e-106 | 7.27407e-107 |
Belt | -395.811 | 38.6056 | -10.25 | 1.06923e-19 | 5.34613e-20 |
M1 | -442.551 | 61.3737 | -7.211 | 1.50917e-11 | 7.54584e-12 |
M2 | -617.812 | 61.3262 | -10.07 | 3.41462e-19 | 1.70731e-19 |
M3 | -567.25 | 61.3262 | -9.25 | 6.76088e-17 | 3.38044e-17 |
M4 | -680.438 | 61.3262 | -11.1 | 4.19121e-22 | 2.09561e-22 |
M5 | -543.125 | 61.3262 | -8.856 | 8.00478e-16 | 4.00239e-16 |
M6 | -598.875 | 61.3262 | -9.765 | 2.51305e-18 | 1.25653e-18 |
M7 | -523.25 | 61.3262 | -8.532 | 5.95196e-15 | 2.97598e-15 |
M8 | -508.375 | 61.3262 | -8.29 | 2.62012e-14 | 1.31006e-14 |
M9 | -455.562 | 61.3262 | -7.429 | 4.33013e-12 | 2.16506e-12 |
M10 | -316.188 | 61.3262 | -5.156 | 6.64186e-07 | 3.32093e-07 |
M11 | -116.625 | 61.3262 | -1.902 | 0.0588147 | 0.0294073 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.814751 |
R-squared | 0.66382 |
Adjusted R-squared | 0.641282 |
F-TEST (value) | 29.4544 |
F-TEST (DF numerator) | 12 |
F-TEST (DF denominator) | 179 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 173.457 |
Sum Squared Residuals | 5385620 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 1687 | 1722.68 | -35.6757 |
2 | 1508 | 1547.41 | -39.4139 |
3 | 1507 | 1597.98 | -90.9764 |
4 | 1385 | 1484.79 | -99.7889 |
5 | 1632 | 1622.1 | 9.89861 |
6 | 1511 | 1566.35 | -55.3514 |
7 | 1559 | 1641.98 | -82.9764 |
8 | 1630 | 1656.85 | -26.8514 |
9 | 1579 | 1709.66 | -130.664 |
10 | 1653 | 1849.04 | -196.039 |
11 | 2152 | 2048.6 | 103.399 |
12 | 2148 | 2165.23 | -17.2264 |
13 | 1752 | 1722.68 | 29.3243 |
14 | 1765 | 1547.41 | 217.586 |
15 | 1717 | 1597.98 | 119.024 |
16 | 1558 | 1484.79 | 73.2111 |
17 | 1575 | 1622.1 | -47.1014 |
18 | 1520 | 1566.35 | -46.3514 |
19 | 1805 | 1641.98 | 163.024 |
20 | 1800 | 1656.85 | 143.149 |
21 | 1719 | 1709.66 | 9.33611 |
22 | 2008 | 1849.04 | 158.961 |
23 | 2242 | 2048.6 | 193.399 |
24 | 2478 | 2165.23 | 312.774 |
25 | 2030 | 1722.68 | 307.324 |
26 | 1655 | 1547.41 | 107.586 |
27 | 1693 | 1597.98 | 95.0236 |
28 | 1623 | 1484.79 | 138.211 |
29 | 1805 | 1622.1 | 182.899 |
30 | 1746 | 1566.35 | 179.649 |
31 | 1795 | 1641.98 | 153.024 |
32 | 1926 | 1656.85 | 269.149 |
33 | 1619 | 1709.66 | -90.6639 |
34 | 1992 | 1849.04 | 142.961 |
35 | 2233 | 2048.6 | 184.399 |
36 | 2192 | 2165.23 | 26.7736 |
37 | 2080 | 1722.68 | 357.324 |
38 | 1768 | 1547.41 | 220.586 |
39 | 1835 | 1597.98 | 237.024 |
40 | 1569 | 1484.79 | 84.2111 |
41 | 1976 | 1622.1 | 353.899 |
42 | 1853 | 1566.35 | 286.649 |
43 | 1965 | 1641.98 | 323.024 |
44 | 1689 | 1656.85 | 32.1486 |
45 | 1778 | 1709.66 | 68.3361 |
46 | 1976 | 1849.04 | 126.961 |
47 | 2397 | 2048.6 | 348.399 |
48 | 2654 | 2165.23 | 488.774 |
49 | 2097 | 1722.68 | 374.324 |
50 | 1963 | 1547.41 | 415.586 |
51 | 1677 | 1597.98 | 79.0236 |
52 | 1941 | 1484.79 | 456.211 |
53 | 2003 | 1622.1 | 380.899 |
54 | 1813 | 1566.35 | 246.649 |
55 | 2012 | 1641.98 | 370.024 |
56 | 1912 | 1656.85 | 255.149 |
57 | 2084 | 1709.66 | 374.336 |
58 | 2080 | 1849.04 | 230.961 |
59 | 2118 | 2048.6 | 69.3986 |
60 | 2150 | 2165.23 | -15.2264 |
61 | 1608 | 1722.68 | -114.676 |
62 | 1503 | 1547.41 | -44.4139 |
63 | 1548 | 1597.98 | -49.9764 |
64 | 1382 | 1484.79 | -102.789 |
65 | 1731 | 1622.1 | 108.899 |
66 | 1798 | 1566.35 | 231.649 |
67 | 1779 | 1641.98 | 137.024 |
68 | 1887 | 1656.85 | 230.149 |
69 | 2004 | 1709.66 | 294.336 |
70 | 2077 | 1849.04 | 227.961 |
71 | 2092 | 2048.6 | 43.3986 |
72 | 2051 | 2165.23 | -114.226 |
73 | 1577 | 1722.68 | -145.676 |
74 | 1356 | 1547.41 | -191.414 |
75 | 1652 | 1597.98 | 54.0236 |
76 | 1382 | 1484.79 | -102.789 |
77 | 1519 | 1622.1 | -103.101 |
78 | 1421 | 1566.35 | -145.351 |
79 | 1442 | 1641.98 | -199.976 |
80 | 1543 | 1656.85 | -113.851 |
81 | 1656 | 1709.66 | -53.6639 |
82 | 1561 | 1849.04 | -288.039 |
83 | 1905 | 2048.6 | -143.601 |
84 | 2199 | 2165.23 | 33.7736 |
85 | 1473 | 1722.68 | -249.676 |
86 | 1655 | 1547.41 | 107.586 |
87 | 1407 | 1597.98 | -190.976 |
88 | 1395 | 1484.79 | -89.7889 |
89 | 1530 | 1622.1 | -92.1014 |
90 | 1309 | 1566.35 | -257.351 |
91 | 1526 | 1641.98 | -115.976 |
92 | 1327 | 1656.85 | -329.851 |
93 | 1627 | 1709.66 | -82.6639 |
94 | 1748 | 1849.04 | -101.039 |
95 | 1958 | 2048.6 | -90.6014 |
96 | 2274 | 2165.23 | 108.774 |
97 | 1648 | 1722.68 | -74.6757 |
98 | 1401 | 1547.41 | -146.414 |
99 | 1411 | 1597.98 | -186.976 |
100 | 1403 | 1484.79 | -81.7889 |
101 | 1394 | 1622.1 | -228.101 |
102 | 1520 | 1566.35 | -46.3514 |
103 | 1528 | 1641.98 | -113.976 |
104 | 1643 | 1656.85 | -13.8514 |
105 | 1515 | 1709.66 | -194.664 |
106 | 1685 | 1849.04 | -164.039 |
107 | 2000 | 2048.6 | -48.6014 |
108 | 2215 | 2165.23 | 49.7736 |
109 | 1956 | 1722.68 | 233.324 |
110 | 1462 | 1547.41 | -85.4139 |
111 | 1563 | 1597.98 | -34.9764 |
112 | 1459 | 1484.79 | -25.7889 |
113 | 1446 | 1622.1 | -176.101 |
114 | 1622 | 1566.35 | 55.6486 |
115 | 1657 | 1641.98 | 15.0236 |
116 | 1638 | 1656.85 | -18.8514 |
117 | 1643 | 1709.66 | -66.6639 |
118 | 1683 | 1849.04 | -166.039 |
119 | 2050 | 2048.6 | 1.39861 |
120 | 2262 | 2165.23 | 96.7736 |
121 | 1813 | 1722.68 | 90.3243 |
122 | 1445 | 1547.41 | -102.414 |
123 | 1762 | 1597.98 | 164.024 |
124 | 1461 | 1484.79 | -23.7889 |
125 | 1556 | 1622.1 | -66.1014 |
126 | 1431 | 1566.35 | -135.351 |
127 | 1427 | 1641.98 | -214.976 |
128 | 1554 | 1656.85 | -102.851 |
129 | 1645 | 1709.66 | -64.6639 |
130 | 1653 | 1849.04 | -196.039 |
131 | 2016 | 2048.6 | -32.6014 |
132 | 2207 | 2165.23 | 41.7736 |
133 | 1665 | 1722.68 | -57.6757 |
134 | 1361 | 1547.41 | -186.414 |
135 | 1506 | 1597.98 | -91.9764 |
136 | 1360 | 1484.79 | -124.789 |
137 | 1453 | 1622.1 | -169.101 |
138 | 1522 | 1566.35 | -44.3514 |
139 | 1460 | 1641.98 | -181.976 |
140 | 1552 | 1656.85 | -104.851 |
141 | 1548 | 1709.66 | -161.664 |
142 | 1827 | 1849.04 | -22.0389 |
143 | 1737 | 2048.6 | -311.601 |
144 | 1941 | 2165.23 | -224.226 |
145 | 1474 | 1722.68 | -248.676 |
146 | 1458 | 1547.41 | -89.4139 |
147 | 1542 | 1597.98 | -55.9764 |
148 | 1404 | 1484.79 | -80.7889 |
149 | 1522 | 1622.1 | -100.101 |
150 | 1385 | 1566.35 | -181.351 |
151 | 1641 | 1641.98 | -0.976393 |
152 | 1510 | 1656.85 | -146.851 |
153 | 1681 | 1709.66 | -28.6639 |
154 | 1938 | 1849.04 | 88.9611 |
155 | 1868 | 2048.6 | -180.601 |
156 | 1726 | 2165.23 | -439.226 |
157 | 1456 | 1722.68 | -266.676 |
158 | 1445 | 1547.41 | -102.414 |
159 | 1456 | 1597.98 | -141.976 |
160 | 1365 | 1484.79 | -119.789 |
161 | 1487 | 1622.1 | -135.101 |
162 | 1558 | 1566.35 | -8.35139 |
163 | 1488 | 1641.98 | -153.976 |
164 | 1684 | 1656.85 | 27.1486 |
165 | 1594 | 1709.66 | -115.664 |
166 | 1850 | 1849.04 | 0.961107 |
167 | 1998 | 2048.6 | -50.6014 |
168 | 2079 | 2165.23 | -86.2264 |
169 | 1494 | 1722.68 | -228.676 |
170 | 1057 | 1151.6 | -94.6027 |
171 | 1218 | 1202.17 | 15.8348 |
172 | 1168 | 1088.98 | 79.0223 |
173 | 1236 | 1226.29 | 9.70975 |
174 | 1076 | 1170.54 | -94.5402 |
175 | 1174 | 1246.17 | -72.1652 |
176 | 1139 | 1261.04 | -122.04 |
177 | 1427 | 1313.85 | 113.147 |
178 | 1487 | 1453.23 | 33.7723 |
179 | 1483 | 1652.79 | -169.79 |
180 | 1513 | 1769.42 | -256.415 |
181 | 1357 | 1326.86 | 30.1354 |
182 | 1165 | 1151.6 | 13.3973 |
183 | 1282 | 1202.17 | 79.8348 |
184 | 1110 | 1088.98 | 21.0223 |
185 | 1297 | 1226.29 | 70.7098 |
186 | 1185 | 1170.54 | 14.4598 |
187 | 1222 | 1246.17 | -24.1652 |
188 | 1284 | 1261.04 | 22.9598 |
189 | 1444 | 1313.85 | 130.147 |
190 | 1575 | 1453.23 | 121.772 |
191 | 1737 | 1652.79 | 84.2098 |
192 | 1763 | 1769.42 | -6.41525 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
16 | 0.477412 | 0.954825 | 0.522588 |
17 | 0.317783 | 0.635566 | 0.682217 |
18 | 0.191885 | 0.38377 | 0.808115 |
19 | 0.219496 | 0.438993 | 0.780504 |
20 | 0.182871 | 0.365743 | 0.817129 |
21 | 0.138851 | 0.277701 | 0.861149 |
22 | 0.247067 | 0.494134 | 0.752933 |
23 | 0.186573 | 0.373146 | 0.813427 |
24 | 0.268174 | 0.536349 | 0.731826 |
25 | 0.375317 | 0.750635 | 0.624683 |
26 | 0.298471 | 0.596942 | 0.701529 |
27 | 0.239925 | 0.479851 | 0.760075 |
28 | 0.213045 | 0.42609 | 0.786955 |
29 | 0.213769 | 0.427538 | 0.786231 |
30 | 0.229775 | 0.45955 | 0.770225 |
31 | 0.194772 | 0.389543 | 0.805228 |
32 | 0.207765 | 0.41553 | 0.792235 |
33 | 0.162157 | 0.324313 | 0.837843 |
34 | 0.148116 | 0.296233 | 0.851884 |
35 | 0.117831 | 0.235663 | 0.882169 |
36 | 0.0973821 | 0.194764 | 0.902618 |
37 | 0.141401 | 0.282802 | 0.858599 |
38 | 0.129782 | 0.259565 | 0.870218 |
39 | 0.139773 | 0.279546 | 0.860227 |
40 | 0.110585 | 0.221171 | 0.889415 |
41 | 0.184125 | 0.368249 | 0.815875 |
42 | 0.234899 | 0.469799 | 0.765101 |
43 | 0.29165 | 0.5833 | 0.70835 |
44 | 0.255254 | 0.510509 | 0.744746 |
45 | 0.231934 | 0.463868 | 0.768066 |
46 | 0.20391 | 0.407819 | 0.79609 |
47 | 0.243148 | 0.486295 | 0.756852 |
48 | 0.473888 | 0.947776 | 0.526112 |
49 | 0.569199 | 0.861603 | 0.430801 |
50 | 0.726419 | 0.547162 | 0.273581 |
51 | 0.688397 | 0.623206 | 0.311603 |
52 | 0.888242 | 0.223515 | 0.111758 |
53 | 0.944877 | 0.110245 | 0.0551225 |
54 | 0.954655 | 0.0906909 | 0.0453454 |
55 | 0.981115 | 0.0377696 | 0.0188848 |
56 | 0.986514 | 0.0269721 | 0.013486 |
57 | 0.997848 | 0.004304 | 0.002152 |
58 | 0.998563 | 0.00287421 | 0.00143711 |
59 | 0.9985 | 0.00299942 | 0.00149971 |
60 | 0.998543 | 0.00291356 | 0.00145678 |
61 | 0.999072 | 0.00185654 | 0.000928269 |
62 | 0.999115 | 0.00176979 | 0.000884896 |
63 | 0.998872 | 0.00225619 | 0.00112809 |
64 | 0.99891 | 0.00217931 | 0.00108965 |
65 | 0.998931 | 0.00213875 | 0.00106938 |
66 | 0.999398 | 0.00120499 | 0.000602494 |
67 | 0.999505 | 0.000990481 | 0.00049524 |
68 | 0.999761 | 0.000478573 | 0.000239286 |
69 | 0.999948 | 0.000103089 | 5.15444e-05 |
70 | 0.99998 | 4.00488e-05 | 2.00244e-05 |
71 | 0.99998 | 3.9388e-05 | 1.9694e-05 |
72 | 0.999984 | 3.20918e-05 | 1.60459e-05 |
73 | 0.999989 | 2.24415e-05 | 1.12208e-05 |
74 | 0.999994 | 1.18084e-05 | 5.90421e-06 |
75 | 0.999992 | 1.57216e-05 | 7.86078e-06 |
76 | 0.999991 | 1.84852e-05 | 9.24259e-06 |
77 | 0.999992 | 1.65881e-05 | 8.29404e-06 |
78 | 0.999993 | 1.36074e-05 | 6.8037e-06 |
79 | 0.999997 | 6.58202e-06 | 3.29101e-06 |
80 | 0.999997 | 6.4345e-06 | 3.21725e-06 |
81 | 0.999995 | 9.24198e-06 | 4.62099e-06 |
82 | 0.999999 | 2.17048e-06 | 1.08524e-06 |
83 | 0.999999 | 1.88926e-06 | 9.44632e-07 |
84 | 0.999999 | 2.34076e-06 | 1.17038e-06 |
85 | 1 | 9.72555e-07 | 4.86277e-07 |
86 | 1 | 6.92191e-07 | 3.46095e-07 |
87 | 1 | 5.55464e-07 | 2.77732e-07 |
88 | 1 | 8.27693e-07 | 4.13846e-07 |
89 | 0.999999 | 1.0317e-06 | 5.15849e-07 |
90 | 1 | 4.34139e-07 | 2.17069e-07 |
91 | 1 | 5.31761e-07 | 2.65881e-07 |
92 | 1 | 8.13219e-08 | 4.06609e-08 |
93 | 1 | 1.3024e-07 | 6.51202e-08 |
94 | 1 | 1.97943e-07 | 9.89717e-08 |
95 | 1 | 2.77558e-07 | 1.38779e-07 |
96 | 1 | 1.7184e-07 | 8.592e-08 |
97 | 1 | 2.79756e-07 | 1.39878e-07 |
98 | 1 | 3.49958e-07 | 1.74979e-07 |
99 | 1 | 3.06098e-07 | 1.53049e-07 |
100 | 1 | 5.05691e-07 | 2.52845e-07 |
101 | 1 | 3.74833e-07 | 1.87417e-07 |
102 | 1 | 6.29696e-07 | 3.14848e-07 |
103 | 1 | 9.02247e-07 | 4.51123e-07 |
104 | 0.999999 | 1.41555e-06 | 7.07774e-07 |
105 | 0.999999 | 1.27095e-06 | 6.35473e-07 |
106 | 0.999999 | 1.4055e-06 | 7.0275e-07 |
107 | 0.999999 | 2.08254e-06 | 1.04127e-06 |
108 | 0.999999 | 1.69571e-06 | 8.47854e-07 |
109 | 1 | 1.60297e-07 | 8.01486e-08 |
110 | 1 | 2.57826e-07 | 1.28913e-07 |
111 | 1 | 4.78788e-07 | 2.39394e-07 |
112 | 1 | 8.32068e-07 | 4.16034e-07 |
113 | 0.999999 | 1.01035e-06 | 5.05177e-07 |
114 | 0.999999 | 1.03946e-06 | 5.19732e-07 |
115 | 0.999999 | 1.0952e-06 | 5.47599e-07 |
116 | 0.999999 | 1.67425e-06 | 8.37126e-07 |
117 | 0.999999 | 2.93825e-06 | 1.46913e-06 |
118 | 0.999998 | 3.01449e-06 | 1.50725e-06 |
119 | 0.999998 | 3.35416e-06 | 1.67708e-06 |
120 | 1 | 7.64266e-07 | 3.82133e-07 |
121 | 1 | 2.13253e-07 | 1.06627e-07 |
122 | 1 | 3.62777e-07 | 1.81389e-07 |
123 | 1 | 1.01287e-07 | 5.06434e-08 |
124 | 1 | 1.75868e-07 | 8.79338e-08 |
125 | 1 | 3.15452e-07 | 1.57726e-07 |
126 | 1 | 5.33745e-07 | 2.66872e-07 |
127 | 1 | 6.21597e-07 | 3.10799e-07 |
128 | 0.999999 | 1.12245e-06 | 5.61224e-07 |
129 | 0.999999 | 2.12864e-06 | 1.06432e-06 |
130 | 0.999999 | 1.14455e-06 | 5.72274e-07 |
131 | 0.999999 | 1.21801e-06 | 6.09003e-07 |
132 | 1 | 1.28511e-07 | 6.42555e-08 |
133 | 1 | 1.0862e-07 | 5.43101e-08 |
134 | 1 | 1.68881e-07 | 8.44404e-08 |
135 | 1 | 3.45391e-07 | 1.72695e-07 |
136 | 1 | 6.37774e-07 | 3.18887e-07 |
137 | 1 | 9.67357e-07 | 4.83679e-07 |
138 | 0.999999 | 1.56366e-06 | 7.8183e-07 |
139 | 0.999999 | 2.42979e-06 | 1.2149e-06 |
140 | 0.999998 | 4.70826e-06 | 2.35413e-06 |
141 | 0.999998 | 4.97522e-06 | 2.48761e-06 |
142 | 0.999995 | 9.87784e-06 | 4.93892e-06 |
143 | 0.999998 | 4.52434e-06 | 2.26217e-06 |
144 | 0.999996 | 7.06157e-06 | 3.53079e-06 |
145 | 0.999995 | 1.02752e-05 | 5.1376e-06 |
146 | 0.99999 | 1.94565e-05 | 9.72823e-06 |
147 | 0.999981 | 3.81091e-05 | 1.90546e-05 |
148 | 0.999963 | 7.49737e-05 | 3.74869e-05 |
149 | 0.999928 | 0.000143134 | 7.15671e-05 |
150 | 0.999894 | 0.000211995 | 0.000105997 |
151 | 0.999894 | 0.000211958 | 0.000105979 |
152 | 0.999817 | 0.000365517 | 0.000182758 |
153 | 0.99965 | 0.000700059 | 0.00035003 |
154 | 0.999531 | 0.000937633 | 0.000468817 |
155 | 0.999252 | 0.0014958 | 0.000747898 |
156 | 0.999848 | 0.000303027 | 0.000151513 |
157 | 0.999822 | 0.000356452 | 0.000178226 |
158 | 0.999647 | 0.000706672 | 0.000353336 |
159 | 0.999472 | 0.00105551 | 0.000527753 |
160 | 0.999162 | 0.00167612 | 0.000838058 |
161 | 0.998794 | 0.00241114 | 0.00120557 |
162 | 0.998132 | 0.00373516 | 0.00186758 |
163 | 0.996541 | 0.00691736 | 0.00345868 |
164 | 0.996431 | 0.00713872 | 0.00356936 |
165 | 0.996303 | 0.00739417 | 0.00369709 |
166 | 0.992625 | 0.0147504 | 0.00737518 |
167 | 0.986949 | 0.026102 | 0.013051 |
168 | 0.990915 | 0.0181706 | 0.00908528 |
169 | 0.982271 | 0.0354579 | 0.017729 |
170 | 0.971877 | 0.0562457 | 0.0281228 |
171 | 0.949755 | 0.10049 | 0.0502448 |
172 | 0.912201 | 0.175598 | 0.087799 |
173 | 0.852462 | 0.295076 | 0.147538 |
174 | 0.782357 | 0.435285 | 0.217643 |
175 | 0.656943 | 0.686114 | 0.343057 |
176 | 0.550073 | 0.899854 | 0.449927 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 109 | 0.677019 | NOK |
5% type I error level | 115 | 0.714286 | NOK |
10% type I error level | 117 | 0.726708 | NOK |