Multiple Linear Regression - Estimated Regression Equation |
Accidents[t] = + 1159.54 -105.214Belt[t] + 0.529803A1[t] -501.87M1[t] -467.045M2[t] -309.641M3[t] -448.737M4[t] -250.577M5[t] -378.195M6[t] -272.154M7[t] -296.465M8[t] -250.653M9[t] -138.378M10[t] -11.7764M11[t] -0.880234t + 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) | 1159.54 | 144.764 | 8.01 | 1.51375e-13 | 7.56876e-14 |
Belt | -105.214 | 37.5856 | -2.799 | 0.00569264 | 0.00284632 |
A1 | 0.529803 | 0.0634167 | 8.354 | 1.90874e-14 | 9.54369e-15 |
M1 | -501.87 | 47.042 | -10.67 | 8.24072e-21 | 4.12036e-21 |
M2 | -467.045 | 49.9689 | -9.347 | 4.07381e-17 | 2.03691e-17 |
M3 | -309.641 | 56.2345 | -5.506 | 1.28085e-07 | 6.40427e-08 |
M4 | -448.737 | 54.3608 | -8.255 | 3.48545e-14 | 1.74273e-14 |
M5 | -250.577 | 58.4881 | -4.284 | 3.01205e-05 | 1.50602e-05 |
M6 | -378.195 | 53.4206 | -7.08 | 3.31701e-11 | 1.6585e-11 |
M7 | -272.154 | 55.2705 | -4.924 | 1.94225e-06 | 9.71127e-07 |
M8 | -296.465 | 52.6589 | -5.63 | 7.00816e-08 | 3.50408e-08 |
M9 | -250.653 | 52.1389 | -4.807 | 3.2657e-06 | 1.63285e-06 |
M10 | -138.378 | 50.5569 | -2.737 | 0.00683529 | 0.00341765 |
M11 | -11.7764 | 47.4054 | -0.2484 | 0.8041 | 0.40205 |
t | -0.880234 | 0.233717 | -3.766 | 0.00022577 | 0.000112885 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.903777 |
R-squared | 0.816813 |
Adjusted R-squared | 0.802241 |
F-TEST (value) | 56.0546 |
F-TEST (DF numerator) | 14 |
F-TEST (DF denominator) | 176 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 129.128 |
Sum Squared Residuals | 2934620 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 1687 | 1763.52 | -76.5156 |
2 | 1508 | 1647.2 | -139.204 |
3 | 1507 | 1627.7 | -120.699 |
4 | 1385 | 1391.34 | -6.34212 |
5 | 1632 | 1761.7 | -129.705 |
6 | 1511 | 1633.76 | -122.76 |
7 | 1559 | 1611 | -51.9994 |
8 | 1630 | 1815.55 | -185.547 |
9 | 1579 | 1774.92 | -195.922 |
10 | 1653 | 1514.85 | 138.151 |
11 | 2152 | 2293.12 | -141.117 |
12 | 2148 | 2180.25 | -32.2475 |
13 | 1752 | 1595.39 | 156.61 |
14 | 1765 | 1819.8 | -54.8006 |
15 | 1717 | 1765.39 | -48.3944 |
16 | 1558 | 1702.44 | -144.435 |
17 | 1575 | 1654.94 | -79.9433 |
18 | 1520 | 1390.97 | 129.034 |
19 | 1805 | 1806.77 | -1.76822 |
20 | 1800 | 1925.05 | -125.051 |
21 | 1719 | 1623.53 | 95.4684 |
22 | 2008 | 1957.37 | 50.6341 |
23 | 2242 | 2090.24 | 151.764 |
24 | 2478 | 2396.52 | 81.4802 |
25 | 2030 | 2120.11 | -90.1125 |
26 | 1655 | 1664.96 | -9.95945 |
27 | 1693 | 1653.12 | 39.8837 |
28 | 1623 | 1561.31 | 61.6903 |
29 | 1805 | 1770.24 | 34.7647 |
30 | 1746 | 1736.14 | 9.86161 |
31 | 1795 | 1654.91 | 140.093 |
32 | 1926 | 2207.24 | -281.243 |
33 | 1619 | 1475.99 | 143.012 |
34 | 1992 | 1931.33 | 60.6738 |
35 | 2233 | 2351.9 | -118.905 |
36 | 2192 | 1898.43 | 293.567 |
37 | 2080 | 2073.04 | 6.96014 |
38 | 1768 | 1685.26 | 82.7356 |
39 | 1835 | 1913.79 | -78.7855 |
40 | 1569 | 1297.14 | 271.863 |
41 | 1976 | 1914.27 | 61.7312 |
42 | 1853 | 1719.26 | 133.735 |
43 | 1965 | 2141.41 | -176.411 |
44 | 1689 | 1675.12 | 13.8829 |
45 | 1778 | 1724.66 | 53.3356 |
46 | 1976 | 1732.29 | 243.713 |
47 | 2397 | 2130.23 | 266.77 |
48 | 2654 | 2577.64 | 76.3604 |
49 | 2097 | 1893.48 | 203.516 |
50 | 1963 | 2131.01 | -168.013 |
51 | 1677 | 1289.51 | 387.486 |
52 | 1941 | 1828.66 | 112.339 |
53 | 2003 | 1985.01 | 17.9893 |
54 | 1813 | 1600.51 | 212.49 |
55 | 2012 | 1979.75 | 32.2509 |
56 | 1912 | 1699.7 | 212.3 |
57 | 2084 | 2078.22 | 5.77866 |
58 | 2080 | 2159.82 | -79.8233 |
59 | 2118 | 2196.85 | -78.852 |
60 | 2150 | 2285.06 | -135.056 |
61 | 1608 | 1594.85 | 13.1529 |
62 | 1503 | 1545.74 | -42.7409 |
63 | 1548 | 1640.61 | -92.6064 |
64 | 1382 | 1234.94 | 147.061 |
65 | 1731 | 1573.34 | 157.659 |
66 | 1798 | 1800 | -1.99974 |
67 | 1779 | 1637.74 | 141.258 |
68 | 1887 | 1730.89 | 156.107 |
69 | 2004 | 1948.27 | 55.7257 |
70 | 2077 | 2170.67 | -93.6711 |
71 | 2092 | 2245.51 | -153.514 |
72 | 2051 | 2154.04 | -103.043 |
73 | 1577 | 1683.86 | -106.86 |
74 | 1356 | 1206.3 | 149.703 |
75 | 1652 | 1789.14 | -137.143 |
76 | 1382 | 1436.38 | -54.3759 |
77 | 1519 | 1615.46 | -96.4603 |
78 | 1421 | 1549.7 | -128.701 |
79 | 1442 | 1455.64 | -13.6356 |
80 | 1543 | 1542.08 | 0.922571 |
81 | 1656 | 1921.34 | -265.34 |
82 | 1561 | 1557.73 | 3.27017 |
83 | 1905 | 1800.88 | 104.122 |
84 | 2199 | 2473.89 | -274.891 |
85 | 1473 | 1215.2 | 257.802 |
86 | 1655 | 1898.15 | -243.145 |
87 | 1407 | 1390.78 | 16.2214 |
88 | 1395 | 1434.7 | -39.7005 |
89 | 1530 | 1733.73 | -203.725 |
90 | 1309 | 1283.8 | 25.1996 |
91 | 1526 | 1789.58 | -263.576 |
92 | 1327 | 1230.08 | 96.9229 |
93 | 1627 | 1679.41 | -52.4129 |
94 | 1748 | 1780.24 | -32.2402 |
95 | 1958 | 1796.4 | 161.605 |
96 | 2274 | 2403.06 | -129.063 |
97 | 1648 | 1726.35 | -78.3509 |
98 | 1401 | 1495.01 | -94.0126 |
99 | 1411 | 1378.33 | 32.665 |
100 | 1403 | 1572.38 | -169.376 |
101 | 1394 | 1304.11 | 89.8907 |
102 | 1520 | 1594.03 | -74.026 |
103 | 1528 | 1466.07 | 61.9269 |
104 | 1643 | 1814.93 | -171.932 |
105 | 1515 | 1560.51 | -45.5121 |
106 | 1685 | 1631.3 | 53.7002 |
107 | 2000 | 1909.08 | 90.916 |
108 | 2215 | 1994.24 | 220.758 |
109 | 1956 | 2125.97 | -169.967 |
110 | 1462 | 1425.77 | 36.2322 |
111 | 1563 | 1544.3 | 18.6978 |
112 | 1459 | 1595.48 | -136.482 |
113 | 1446 | 1271.1 | 174.904 |
114 | 1622 | 1610.5 | 11.4968 |
115 | 1657 | 1657.85 | -0.854902 |
116 | 1638 | 1668.72 | -30.7203 |
117 | 1643 | 1747.76 | -104.764 |
118 | 1683 | 1567.68 | 115.323 |
119 | 2050 | 1928.01 | 121.989 |
120 | 2262 | 2198.58 | 63.4201 |
121 | 1813 | 1913.64 | -100.643 |
122 | 1445 | 1190.2 | 254.802 |
123 | 1762 | 1836.17 | -74.1703 |
124 | 1461 | 1477.98 | -16.9791 |
125 | 1556 | 1619.81 | -63.8118 |
126 | 1431 | 1537.75 | -106.748 |
127 | 1427 | 1379.44 | 47.5626 |
128 | 1554 | 1527.65 | 26.346 |
129 | 1645 | 1770.26 | -125.261 |
130 | 1653 | 1545.22 | 107.779 |
131 | 2016 | 1920.44 | 95.5648 |
132 | 2207 | 2251.88 | -44.8779 |
133 | 1665 | 1760.67 | -95.6691 |
134 | 1361 | 1307.13 | 53.8679 |
135 | 1506 | 1534.98 | -28.9778 |
136 | 1360 | 1415.91 | -55.9062 |
137 | 1453 | 1360.68 | 92.3207 |
138 | 1522 | 1633.4 | -111.397 |
139 | 1460 | 1421.36 | 38.6419 |
140 | 1552 | 1611.03 | -59.0316 |
141 | 1548 | 1437.31 | 110.693 |
142 | 1827 | 2079.84 | -252.843 |
143 | 1737 | 1749.06 | -12.0573 |
144 | 1941 | 2025.39 | -84.3874 |
145 | 1474 | 1360.91 | 113.086 |
146 | 1458 | 1408.96 | 49.0398 |
147 | 1542 | 1535.49 | 6.51204 |
148 | 1404 | 1403.65 | 0.345284 |
149 | 1522 | 1592.67 | -70.6729 |
150 | 1385 | 1232.25 | 152.749 |
151 | 1641 | 1729.69 | -88.6896 |
152 | 1510 | 1403.22 | 106.783 |
153 | 1681 | 1519.21 | 161.792 |
154 | 1938 | 2108.09 | -170.089 |
155 | 1868 | 2153.9 | -285.899 |
156 | 1726 | 1703.92 | 22.0831 |
157 | 1456 | 1335.81 | 120.185 |
158 | 1445 | 1464.51 | -19.5099 |
159 | 1456 | 1432.36 | 23.6379 |
160 | 1365 | 1368.43 | -3.42959 |
161 | 1487 | 1355.57 | 131.433 |
162 | 1558 | 1639.34 | -81.3445 |
163 | 1488 | 1311.07 | 176.933 |
164 | 1684 | 1745.84 | -61.84 |
165 | 1594 | 1463.55 | 130.447 |
166 | 1850 | 1832.9 | 17.0967 |
167 | 1998 | 1989.21 | 8.78965 |
168 | 2079 | 2195.37 | -116.375 |
169 | 1494 | 1666.17 | -172.17 |
170 | 1057 | 993.169 | 63.831 |
171 | 1218 | 1149.49 | 68.5083 |
172 | 1168 | 1202.28 | -34.2811 |
173 | 1236 | 1337.81 | -101.809 |
174 | 1076 | 1100.2 | -24.2022 |
175 | 1174 | 1259.93 | -85.9315 |
176 | 1139 | 963.32 | 175.68 |
177 | 1427 | 1455.3 | -28.2982 |
178 | 1487 | 1676.81 | -189.808 |
179 | 1483 | 1651.58 | -168.584 |
180 | 1513 | 1350.73 | 162.271 |
181 | 1357 | 1338.02 | 18.9759 |
182 | 1165 | 1083.82 | 81.175 |
183 | 1282 | 1294.84 | -12.8363 |
184 | 1110 | 1041.99 | 68.0103 |
185 | 1297 | 1311.56 | -14.5643 |
186 | 1185 | 1208.39 | -23.3879 |
187 | 1222 | 1177.8 | 44.2007 |
188 | 1284 | 1157.58 | 126.421 |
189 | 1444 | 1382.74 | 61.258 |
190 | 1575 | 1546.87 | 28.1326 |
191 | 1737 | 1779.59 | -42.5917 |
192 | 1763 | NA | NA |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
18 | 0.542719 | 0.914562 | 0.457281 |
19 | 0.373288 | 0.746575 | 0.626712 |
20 | 0.242414 | 0.484827 | 0.757586 |
21 | 0.296179 | 0.592357 | 0.703821 |
22 | 0.218679 | 0.437357 | 0.781321 |
23 | 0.215346 | 0.430693 | 0.784654 |
24 | 0.171258 | 0.342517 | 0.828742 |
25 | 0.283565 | 0.567131 | 0.716435 |
26 | 0.259884 | 0.519768 | 0.740116 |
27 | 0.192463 | 0.384925 | 0.807537 |
28 | 0.13686 | 0.27372 | 0.86314 |
29 | 0.0960343 | 0.192069 | 0.903966 |
30 | 0.0744401 | 0.14888 | 0.92556 |
31 | 0.0511569 | 0.102314 | 0.948843 |
32 | 0.10209 | 0.204179 | 0.89791 |
33 | 0.0726649 | 0.14533 | 0.927335 |
34 | 0.0687461 | 0.137492 | 0.931254 |
35 | 0.137898 | 0.275797 | 0.862102 |
36 | 0.132068 | 0.264135 | 0.867932 |
37 | 0.106663 | 0.213326 | 0.893337 |
38 | 0.0790544 | 0.158109 | 0.920946 |
39 | 0.0799122 | 0.159824 | 0.920088 |
40 | 0.0912589 | 0.182518 | 0.908741 |
41 | 0.0722279 | 0.144456 | 0.927772 |
42 | 0.0570865 | 0.114173 | 0.942913 |
43 | 0.14617 | 0.29234 | 0.85383 |
44 | 0.115282 | 0.230565 | 0.884718 |
45 | 0.0958854 | 0.191771 | 0.904115 |
46 | 0.0882728 | 0.176546 | 0.911727 |
47 | 0.138939 | 0.277877 | 0.861061 |
48 | 0.1178 | 0.235599 | 0.8822 |
49 | 0.114283 | 0.228567 | 0.885717 |
50 | 0.179834 | 0.359667 | 0.820166 |
51 | 0.295363 | 0.590726 | 0.704637 |
52 | 0.27546 | 0.55092 | 0.72454 |
53 | 0.244074 | 0.488148 | 0.755926 |
54 | 0.254867 | 0.509734 | 0.745133 |
55 | 0.230894 | 0.461789 | 0.769106 |
56 | 0.300691 | 0.601383 | 0.699309 |
57 | 0.268908 | 0.537815 | 0.731092 |
58 | 0.512985 | 0.974031 | 0.487015 |
59 | 0.762445 | 0.47511 | 0.237555 |
60 | 0.925447 | 0.149106 | 0.074553 |
61 | 0.927284 | 0.145433 | 0.0727163 |
62 | 0.915738 | 0.168524 | 0.0842618 |
63 | 0.926156 | 0.147687 | 0.0738436 |
64 | 0.923307 | 0.153385 | 0.0766927 |
65 | 0.93055 | 0.1389 | 0.0694501 |
66 | 0.93368 | 0.13264 | 0.0663201 |
67 | 0.941714 | 0.116573 | 0.0582863 |
68 | 0.958777 | 0.0824453 | 0.0412226 |
69 | 0.964383 | 0.071234 | 0.035617 |
70 | 0.975275 | 0.0494503 | 0.0247252 |
71 | 0.979836 | 0.0403274 | 0.0201637 |
72 | 0.98109 | 0.0378193 | 0.0189096 |
73 | 0.981183 | 0.037635 | 0.0188175 |
74 | 0.98343 | 0.0331408 | 0.0165704 |
75 | 0.984637 | 0.0307268 | 0.0153634 |
76 | 0.98313 | 0.0337394 | 0.0168697 |
77 | 0.980292 | 0.0394151 | 0.0197075 |
78 | 0.980737 | 0.0385255 | 0.0192628 |
79 | 0.974762 | 0.050475 | 0.0252375 |
80 | 0.967794 | 0.0644116 | 0.0322058 |
81 | 0.985184 | 0.0296312 | 0.0148156 |
82 | 0.980457 | 0.0390857 | 0.0195429 |
83 | 0.980257 | 0.039486 | 0.019743 |
84 | 0.990914 | 0.0181715 | 0.00908574 |
85 | 0.996317 | 0.00736566 | 0.00368283 |
86 | 0.997901 | 0.00419875 | 0.00209937 |
87 | 0.997054 | 0.00589277 | 0.00294638 |
88 | 0.996148 | 0.00770478 | 0.00385239 |
89 | 0.997404 | 0.00519159 | 0.00259579 |
90 | 0.996395 | 0.00721014 | 0.00360507 |
91 | 0.998759 | 0.00248144 | 0.00124072 |
92 | 0.998601 | 0.0027972 | 0.0013986 |
93 | 0.998125 | 0.00375094 | 0.00187547 |
94 | 0.997406 | 0.00518889 | 0.00259445 |
95 | 0.998251 | 0.00349713 | 0.00174856 |
96 | 0.997966 | 0.00406885 | 0.00203442 |
97 | 0.9974 | 0.0051991 | 0.00259955 |
98 | 0.99752 | 0.00495988 | 0.00247994 |
99 | 0.996578 | 0.00684431 | 0.00342215 |
100 | 0.997274 | 0.00545269 | 0.00272634 |
101 | 0.996748 | 0.00650433 | 0.00325216 |
102 | 0.995797 | 0.0084065 | 0.00420325 |
103 | 0.994638 | 0.0107231 | 0.00536155 |
104 | 0.99622 | 0.00756012 | 0.00378006 |
105 | 0.995863 | 0.00827324 | 0.00413662 |
106 | 0.994437 | 0.0111269 | 0.00556343 |
107 | 0.994158 | 0.0116844 | 0.00584219 |
108 | 0.998162 | 0.00367567 | 0.00183784 |
109 | 0.998115 | 0.00376904 | 0.00188452 |
110 | 0.997507 | 0.0049852 | 0.0024926 |
111 | 0.996463 | 0.007073 | 0.0035365 |
112 | 0.996448 | 0.00710353 | 0.00355176 |
113 | 0.997223 | 0.00555397 | 0.00277698 |
114 | 0.996541 | 0.00691829 | 0.00345914 |
115 | 0.995156 | 0.00968784 | 0.00484392 |
116 | 0.993465 | 0.0130703 | 0.00653514 |
117 | 0.994019 | 0.0119619 | 0.00598097 |
118 | 0.994262 | 0.011476 | 0.005738 |
119 | 0.997133 | 0.00573349 | 0.00286674 |
120 | 0.998193 | 0.00361315 | 0.00180658 |
121 | 0.997535 | 0.0049308 | 0.0024654 |
122 | 0.99943 | 0.00114075 | 0.000570374 |
123 | 0.999226 | 0.00154896 | 0.000774479 |
124 | 0.998913 | 0.00217357 | 0.00108679 |
125 | 0.998388 | 0.00322413 | 0.00161207 |
126 | 0.997889 | 0.00422266 | 0.00211133 |
127 | 0.997028 | 0.00594372 | 0.00297186 |
128 | 0.99573 | 0.0085392 | 0.0042696 |
129 | 0.996747 | 0.00650677 | 0.00325339 |
130 | 0.997651 | 0.00469878 | 0.00234939 |
131 | 0.999763 | 0.000473433 | 0.000236716 |
132 | 0.999928 | 0.000143975 | 7.19877e-05 |
133 | 0.999881 | 0.000237462 | 0.000118731 |
134 | 0.999818 | 0.00036348 | 0.00018174 |
135 | 0.999698 | 0.000604407 | 0.000302204 |
136 | 0.999506 | 0.000988509 | 0.000494255 |
137 | 0.999598 | 0.000804261 | 0.000402131 |
138 | 0.999381 | 0.00123758 | 0.000618792 |
139 | 0.999185 | 0.00162966 | 0.000814831 |
140 | 0.998758 | 0.00248398 | 0.00124199 |
141 | 0.998276 | 0.00344827 | 0.00172414 |
142 | 0.998573 | 0.00285404 | 0.00142702 |
143 | 0.998242 | 0.00351591 | 0.00175796 |
144 | 0.997248 | 0.00550321 | 0.0027516 |
145 | 0.996491 | 0.00701719 | 0.0035086 |
146 | 0.995356 | 0.00928722 | 0.00464361 |
147 | 0.993155 | 0.0136897 | 0.00684483 |
148 | 0.989887 | 0.0202262 | 0.0101131 |
149 | 0.985035 | 0.0299307 | 0.0149653 |
150 | 0.99324 | 0.0135204 | 0.0067602 |
151 | 0.9897 | 0.0206004 | 0.0103002 |
152 | 0.986874 | 0.0262528 | 0.0131264 |
153 | 0.994323 | 0.0113533 | 0.00567663 |
154 | 0.992502 | 0.0149964 | 0.00749821 |
155 | 0.995417 | 0.00916554 | 0.00458277 |
156 | 0.993308 | 0.0133841 | 0.00669206 |
157 | 0.989066 | 0.0218688 | 0.0109344 |
158 | 0.985922 | 0.0281567 | 0.0140783 |
159 | 0.983413 | 0.0331736 | 0.0165868 |
160 | 0.983514 | 0.032971 | 0.0164855 |
161 | 0.976366 | 0.0472681 | 0.023634 |
162 | 0.96152 | 0.0769599 | 0.0384799 |
163 | 0.968466 | 0.0630684 | 0.0315342 |
164 | 0.968887 | 0.0622265 | 0.0311132 |
165 | 0.948975 | 0.10205 | 0.0510249 |
166 | 0.925349 | 0.149303 | 0.0746514 |
167 | 0.985729 | 0.0285424 | 0.0142712 |
168 | 0.970407 | 0.0591852 | 0.0295926 |
169 | 0.951913 | 0.0961733 | 0.0480866 |
170 | 0.914524 | 0.170952 | 0.0854762 |
171 | 0.933567 | 0.132866 | 0.0664331 |
172 | 0.858511 | 0.282978 | 0.141489 |
173 | 0.725039 | 0.549922 | 0.274961 |
174 | 0.585352 | 0.829296 | 0.414648 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 57 | 0.363057 | NOK |
5% type I error level | 91 | 0.579618 | NOK |
10% type I error level | 100 | 0.636943 | NOK |