Multiple Linear Regression - Estimated Regression Equation |
Accidents[t] = + 2324.06 -226.385Belt[t] -451.375M1[t] -635.461M2[t] -583.134M3[t] -694.556M4[t] -555.479M5[t] -609.464M6[t] -532.074M7[t] -515.434M8[t] -460.857M9[t] -319.717M10[t] -118.39M11[t] -1.76486t + 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) | 2324.06 | 44.0299 | 52.78 | 1.19695e-110 | 5.98473e-111 |
Belt | -226.385 | 41.0372 | -5.517 | 1.20293e-07 | 6.01464e-08 |
M1 | -451.375 | 53.9429 | -8.368 | 1.67221e-14 | 8.36106e-15 |
M2 | -635.461 | 53.9415 | -11.78 | 4.69922e-24 | 2.34961e-24 |
M3 | -583.134 | 53.9313 | -10.81 | 2.87307e-21 | 1.43653e-21 |
M4 | -694.556 | 53.9222 | -12.88 | 2.98754e-27 | 1.49377e-27 |
M5 | -555.479 | 53.9141 | -10.3 | 8.07739e-20 | 4.03869e-20 |
M6 | -609.464 | 53.9071 | -11.31 | 1.10405e-22 | 5.52025e-23 |
M7 | -532.074 | 53.9012 | -9.871 | 1.32473e-18 | 6.62365e-19 |
M8 | -515.434 | 53.8964 | -9.563 | 9.54296e-18 | 4.77148e-18 |
M9 | -460.857 | 53.8926 | -8.551 | 5.43649e-15 | 2.71825e-15 |
M10 | -319.717 | 53.89 | -5.933 | 1.51883e-08 | 7.59414e-09 |
M11 | -118.39 | 53.8884 | -2.197 | 0.0293158 | 0.0146579 |
t | -1.76486 | 0.240551 | -7.337 | 7.46954e-12 | 3.73477e-12 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.861322 |
R-squared | 0.741876 |
Adjusted R-squared | 0.723025 |
F-TEST (value) | 39.3532 |
F-TEST (DF numerator) | 13 |
F-TEST (DF denominator) | 178 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 152.418 |
Sum Squared Residuals | 4135150 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 1687 | 1870.92 | -183.924 |
2 | 1508 | 1685.07 | -177.073 |
3 | 1507 | 1735.64 | -228.635 |
4 | 1385 | 1622.45 | -237.448 |
5 | 1632 | 1759.76 | -127.76 |
6 | 1511 | 1704.01 | -193.01 |
7 | 1559 | 1779.64 | -220.635 |
8 | 1630 | 1794.51 | -164.51 |
9 | 1579 | 1847.32 | -268.323 |
10 | 1653 | 1986.7 | -333.698 |
11 | 2152 | 2186.26 | -34.2601 |
12 | 2148 | 2302.89 | -154.885 |
13 | 1752 | 1849.75 | -97.7453 |
14 | 1765 | 1663.89 | 101.106 |
15 | 1717 | 1714.46 | 2.54315 |
16 | 1558 | 1601.27 | -43.2693 |
17 | 1575 | 1738.58 | -163.582 |
18 | 1520 | 1682.83 | -162.832 |
19 | 1805 | 1758.46 | 46.5432 |
20 | 1800 | 1773.33 | 26.6682 |
21 | 1719 | 1826.14 | -107.144 |
22 | 2008 | 1965.52 | 42.4807 |
23 | 2242 | 2165.08 | 76.9182 |
24 | 2478 | 2281.71 | 196.293 |
25 | 2030 | 1828.57 | 201.433 |
26 | 1655 | 1642.72 | 12.2839 |
27 | 1693 | 1693.28 | -0.278581 |
28 | 1623 | 1580.09 | 42.9089 |
29 | 1805 | 1717.4 | 87.5964 |
30 | 1746 | 1661.65 | 84.3464 |
31 | 1795 | 1737.28 | 57.7214 |
32 | 1926 | 1752.15 | 173.846 |
33 | 1619 | 1804.97 | -185.966 |
34 | 1992 | 1944.34 | 47.6589 |
35 | 2233 | 2143.9 | 89.0964 |
36 | 2192 | 2260.53 | -68.5286 |
37 | 2080 | 1807.39 | 272.611 |
38 | 1768 | 1621.54 | 146.462 |
39 | 1835 | 1672.1 | 162.9 |
40 | 1569 | 1558.91 | 10.0872 |
41 | 1976 | 1696.23 | 279.775 |
42 | 1853 | 1640.48 | 212.525 |
43 | 1965 | 1716.1 | 248.9 |
44 | 1689 | 1730.98 | -41.9753 |
45 | 1778 | 1783.79 | -5.78782 |
46 | 1976 | 1923.16 | 52.8372 |
47 | 2397 | 2122.73 | 274.275 |
48 | 2654 | 2239.35 | 414.65 |
49 | 2097 | 1786.21 | 310.79 |
50 | 1963 | 1600.36 | 362.64 |
51 | 1677 | 1650.92 | 26.0779 |
52 | 1941 | 1537.73 | 403.265 |
53 | 2003 | 1675.05 | 327.953 |
54 | 1813 | 1619.3 | 193.703 |
55 | 2012 | 1694.92 | 317.078 |
56 | 1912 | 1709.8 | 202.203 |
57 | 2084 | 1762.61 | 321.39 |
58 | 2080 | 1901.98 | 178.015 |
59 | 2118 | 2101.55 | 16.4529 |
60 | 2150 | 2218.17 | -68.1721 |
61 | 1608 | 1765.03 | -157.032 |
62 | 1503 | 1579.18 | -76.1813 |
63 | 1548 | 1629.74 | -81.7438 |
64 | 1382 | 1516.56 | -134.556 |
65 | 1731 | 1653.87 | 77.1312 |
66 | 1798 | 1598.12 | 199.881 |
67 | 1779 | 1673.74 | 105.256 |
68 | 1887 | 1688.62 | 198.381 |
69 | 2004 | 1741.43 | 262.569 |
70 | 2077 | 1880.81 | 196.194 |
71 | 2092 | 2080.37 | 11.6312 |
72 | 2051 | 2196.99 | -145.994 |
73 | 1577 | 1743.85 | -166.854 |
74 | 1356 | 1558 | -202.003 |
75 | 1652 | 1608.57 | 43.4345 |
76 | 1382 | 1495.38 | -113.378 |
77 | 1519 | 1632.69 | -113.691 |
78 | 1421 | 1576.94 | -155.941 |
79 | 1442 | 1652.57 | -210.566 |
80 | 1543 | 1667.44 | -124.441 |
81 | 1656 | 1720.25 | -64.253 |
82 | 1561 | 1859.63 | -298.628 |
83 | 1905 | 2059.19 | -154.191 |
84 | 2199 | 2175.82 | 23.1845 |
85 | 1473 | 1722.68 | -249.676 |
86 | 1655 | 1536.82 | 118.175 |
87 | 1407 | 1587.39 | -180.387 |
88 | 1395 | 1474.2 | -79.1998 |
89 | 1530 | 1611.51 | -81.5123 |
90 | 1309 | 1555.76 | -246.762 |
91 | 1526 | 1631.39 | -105.387 |
92 | 1327 | 1646.26 | -319.262 |
93 | 1627 | 1699.07 | -72.0748 |
94 | 1748 | 1838.45 | -90.4498 |
95 | 1958 | 2038.01 | -80.0123 |
96 | 2274 | 2154.64 | 119.363 |
97 | 1648 | 1701.5 | -53.4974 |
98 | 1401 | 1515.65 | -114.646 |
99 | 1411 | 1566.21 | -155.209 |
100 | 1403 | 1453.02 | -50.0215 |
101 | 1394 | 1590.33 | -196.334 |
102 | 1520 | 1534.58 | -14.584 |
103 | 1528 | 1610.21 | -82.209 |
104 | 1643 | 1625.08 | 17.916 |
105 | 1515 | 1677.9 | -162.896 |
106 | 1685 | 1817.27 | -132.271 |
107 | 2000 | 2016.83 | -16.834 |
108 | 2215 | 2133.46 | 81.541 |
109 | 1956 | 1680.32 | 275.681 |
110 | 1462 | 1494.47 | -32.4682 |
111 | 1563 | 1545.03 | 17.9693 |
112 | 1459 | 1431.84 | 27.1568 |
113 | 1446 | 1569.16 | -123.156 |
114 | 1622 | 1513.41 | 108.594 |
115 | 1657 | 1589.03 | 67.9693 |
116 | 1638 | 1603.91 | 34.0943 |
117 | 1643 | 1656.72 | -13.7182 |
118 | 1683 | 1796.09 | -113.093 |
119 | 2050 | 1995.66 | 54.3443 |
120 | 2262 | 2112.28 | 149.719 |
121 | 1813 | 1659.14 | 153.859 |
122 | 1445 | 1473.29 | -28.29 |
123 | 1762 | 1523.85 | 238.148 |
124 | 1461 | 1410.66 | 50.335 |
125 | 1556 | 1547.98 | 8.02253 |
126 | 1431 | 1492.23 | -61.2275 |
127 | 1427 | 1567.85 | -140.852 |
128 | 1554 | 1582.73 | -28.7275 |
129 | 1645 | 1635.54 | 9.46003 |
130 | 1653 | 1774.91 | -121.915 |
131 | 2016 | 1974.48 | 41.5225 |
132 | 2207 | 2091.1 | 115.898 |
133 | 1665 | 1637.96 | 27.0374 |
134 | 1361 | 1452.11 | -91.1117 |
135 | 1506 | 1502.67 | 3.32579 |
136 | 1360 | 1389.49 | -29.4867 |
137 | 1453 | 1526.8 | -73.7992 |
138 | 1522 | 1471.05 | 50.9508 |
139 | 1460 | 1546.67 | -86.6742 |
140 | 1552 | 1561.55 | -9.54921 |
141 | 1548 | 1614.36 | -66.3617 |
142 | 1827 | 1753.74 | 73.2633 |
143 | 1737 | 1953.3 | -216.299 |
144 | 1941 | 2069.92 | -128.924 |
145 | 1474 | 1616.78 | -142.784 |
146 | 1458 | 1430.93 | 27.0666 |
147 | 1542 | 1481.5 | 60.5041 |
148 | 1404 | 1368.31 | 35.6916 |
149 | 1522 | 1505.62 | 16.3791 |
150 | 1385 | 1449.87 | -64.8709 |
151 | 1641 | 1525.5 | 115.504 |
152 | 1510 | 1540.37 | -30.3709 |
153 | 1681 | 1593.18 | 87.8166 |
154 | 1938 | 1732.56 | 205.442 |
155 | 1868 | 1932.12 | -64.1209 |
156 | 1726 | 2048.75 | -322.746 |
157 | 1456 | 1595.61 | -139.606 |
158 | 1445 | 1409.76 | 35.2448 |
159 | 1456 | 1460.32 | -4.31768 |
160 | 1365 | 1347.13 | 17.8698 |
161 | 1487 | 1484.44 | 2.55732 |
162 | 1558 | 1428.69 | 129.307 |
163 | 1488 | 1504.32 | -16.3177 |
164 | 1684 | 1519.19 | 164.807 |
165 | 1594 | 1572.01 | 21.9948 |
166 | 1850 | 1711.38 | 138.62 |
167 | 1998 | 1910.94 | 87.0573 |
168 | 2079 | 2027.57 | 51.4323 |
169 | 1494 | 1574.43 | -80.4278 |
170 | 1057 | 1162.19 | -105.192 |
171 | 1218 | 1212.75 | 5.24562 |
172 | 1168 | 1099.57 | 68.4331 |
173 | 1236 | 1236.88 | -0.87938 |
174 | 1076 | 1181.13 | -105.129 |
175 | 1174 | 1256.75 | -82.7544 |
176 | 1139 | 1271.63 | -132.629 |
177 | 1427 | 1324.44 | 102.558 |
178 | 1487 | 1463.82 | 23.1831 |
179 | 1483 | 1663.38 | -180.379 |
180 | 1513 | 1780 | -267.004 |
181 | 1357 | 1326.86 | 30.1354 |
182 | 1165 | 1141.01 | 23.9864 |
183 | 1282 | 1191.58 | 90.4239 |
184 | 1110 | 1078.39 | 31.6114 |
185 | 1297 | 1215.7 | 81.2989 |
186 | 1185 | 1159.95 | 25.0489 |
187 | 1222 | 1235.58 | -13.5761 |
188 | 1284 | 1250.45 | 33.5489 |
189 | 1444 | 1303.26 | 140.736 |
190 | 1575 | 1442.64 | 132.361 |
191 | 1737 | 1642.2 | 94.7989 |
192 | 1763 | 1758.83 | 4.17388 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
17 | 0.32203 | 0.64406 | 0.67797 |
18 | 0.233521 | 0.467042 | 0.766479 |
19 | 0.180686 | 0.361371 | 0.819314 |
20 | 0.103669 | 0.207338 | 0.896331 |
21 | 0.0559425 | 0.111885 | 0.944057 |
22 | 0.0858422 | 0.171684 | 0.914158 |
23 | 0.0529852 | 0.10597 | 0.947015 |
24 | 0.0568501 | 0.1137 | 0.94315 |
25 | 0.0361193 | 0.0722386 | 0.963881 |
26 | 0.070562 | 0.141124 | 0.929438 |
27 | 0.0627645 | 0.125529 | 0.937235 |
28 | 0.0411067 | 0.0822133 | 0.958893 |
29 | 0.0250035 | 0.050007 | 0.974996 |
30 | 0.0151728 | 0.0303455 | 0.984827 |
31 | 0.0104863 | 0.0209725 | 0.989514 |
32 | 0.00613905 | 0.0122781 | 0.993861 |
33 | 0.0137448 | 0.0274897 | 0.986255 |
34 | 0.00828786 | 0.0165757 | 0.991712 |
35 | 0.00766108 | 0.0153222 | 0.992339 |
36 | 0.0240776 | 0.0481552 | 0.975922 |
37 | 0.0183342 | 0.0366684 | 0.981666 |
38 | 0.0134773 | 0.0269547 | 0.986523 |
39 | 0.00873515 | 0.0174703 | 0.991265 |
40 | 0.00872602 | 0.017452 | 0.991274 |
41 | 0.00844524 | 0.0168905 | 0.991555 |
42 | 0.0062495 | 0.012499 | 0.993751 |
43 | 0.00463134 | 0.00926268 | 0.995369 |
44 | 0.0158598 | 0.0317196 | 0.98414 |
45 | 0.0112735 | 0.022547 | 0.988726 |
46 | 0.00855657 | 0.0171131 | 0.991443 |
47 | 0.00682271 | 0.0136454 | 0.993177 |
48 | 0.0150234 | 0.0300468 | 0.984977 |
49 | 0.0142691 | 0.0285382 | 0.985731 |
50 | 0.0165337 | 0.0330674 | 0.983466 |
51 | 0.0293904 | 0.0587808 | 0.97061 |
52 | 0.0566431 | 0.113286 | 0.943357 |
53 | 0.0646797 | 0.129359 | 0.93532 |
54 | 0.0614233 | 0.122847 | 0.938577 |
55 | 0.0744442 | 0.148888 | 0.925556 |
56 | 0.0761684 | 0.152337 | 0.923832 |
57 | 0.126955 | 0.25391 | 0.873045 |
58 | 0.124808 | 0.249616 | 0.875192 |
59 | 0.308377 | 0.616754 | 0.691623 |
60 | 0.600261 | 0.799478 | 0.399739 |
61 | 0.910335 | 0.179331 | 0.0896654 |
62 | 0.965959 | 0.0680811 | 0.0340405 |
63 | 0.977601 | 0.0447988 | 0.0223994 |
64 | 0.990218 | 0.0195634 | 0.00978168 |
65 | 0.991796 | 0.0164087 | 0.00820437 |
66 | 0.993424 | 0.0131524 | 0.00657622 |
67 | 0.994887 | 0.0102268 | 0.00511339 |
68 | 0.996512 | 0.00697612 | 0.00348806 |
69 | 0.998415 | 0.00317069 | 0.00158535 |
70 | 0.999071 | 0.00185773 | 0.000928866 |
71 | 0.999417 | 0.00116607 | 0.000583037 |
72 | 0.999769 | 0.000462375 | 0.000231187 |
73 | 0.999925 | 0.000150558 | 7.5279e-05 |
74 | 0.999979 | 4.10032e-05 | 2.05016e-05 |
75 | 0.999975 | 5.09853e-05 | 2.54927e-05 |
76 | 0.999978 | 4.41488e-05 | 2.20744e-05 |
77 | 0.999985 | 2.91821e-05 | 1.45911e-05 |
78 | 0.999991 | 1.88128e-05 | 9.4064e-06 |
79 | 0.999996 | 7.38681e-06 | 3.6934e-06 |
80 | 0.999997 | 6.68404e-06 | 3.34202e-06 |
81 | 0.999995 | 9.43788e-06 | 4.71894e-06 |
82 | 0.999999 | 2.04549e-06 | 1.02275e-06 |
83 | 0.999999 | 1.82999e-06 | 9.14994e-07 |
84 | 0.999999 | 2.46895e-06 | 1.23448e-06 |
85 | 0.999999 | 1.06521e-06 | 5.32606e-07 |
86 | 1 | 8.42633e-07 | 4.21317e-07 |
87 | 1 | 7.14428e-07 | 3.57214e-07 |
88 | 0.999999 | 1.12847e-06 | 5.64237e-07 |
89 | 0.999999 | 1.61043e-06 | 8.05216e-07 |
90 | 1 | 7.52188e-07 | 3.76094e-07 |
91 | 0.999999 | 1.07192e-06 | 5.3596e-07 |
92 | 1 | 1.72646e-07 | 8.63228e-08 |
93 | 1 | 2.91655e-07 | 1.45828e-07 |
94 | 1 | 4.47343e-07 | 2.23672e-07 |
95 | 1 | 7.26818e-07 | 3.63409e-07 |
96 | 1 | 5.86134e-07 | 2.93067e-07 |
97 | 0.999999 | 1.01743e-06 | 5.08714e-07 |
98 | 0.999999 | 1.47984e-06 | 7.3992e-07 |
99 | 0.999999 | 1.23495e-06 | 6.17475e-07 |
100 | 0.999999 | 2.05131e-06 | 1.02566e-06 |
101 | 0.999999 | 1.59251e-06 | 7.96255e-07 |
102 | 0.999999 | 2.80219e-06 | 1.4011e-06 |
103 | 0.999998 | 4.45469e-06 | 2.22734e-06 |
104 | 0.999996 | 7.53474e-06 | 3.76737e-06 |
105 | 0.999997 | 5.74478e-06 | 2.87239e-06 |
106 | 0.999998 | 4.96516e-06 | 2.48258e-06 |
107 | 0.999996 | 8.59237e-06 | 4.29619e-06 |
108 | 0.999995 | 1.01193e-05 | 5.05963e-06 |
109 | 0.999999 | 1.38812e-06 | 6.94058e-07 |
110 | 0.999999 | 2.48235e-06 | 1.24117e-06 |
111 | 0.999998 | 4.17865e-06 | 2.08933e-06 |
112 | 0.999996 | 7.1952e-06 | 3.5976e-06 |
113 | 0.999996 | 8.73655e-06 | 4.36827e-06 |
114 | 0.999995 | 1.00717e-05 | 5.03587e-06 |
115 | 0.999994 | 1.24196e-05 | 6.2098e-06 |
116 | 0.99999 | 1.98114e-05 | 9.90568e-06 |
117 | 0.999984 | 3.27967e-05 | 1.63983e-05 |
118 | 0.999985 | 2.9855e-05 | 1.49275e-05 |
119 | 0.99998 | 3.93655e-05 | 1.96827e-05 |
120 | 0.999994 | 1.23689e-05 | 6.18446e-06 |
121 | 0.999998 | 3.54287e-06 | 1.77143e-06 |
122 | 0.999997 | 6.18767e-06 | 3.09383e-06 |
123 | 0.999999 | 1.18958e-06 | 5.94792e-07 |
124 | 0.999999 | 1.76073e-06 | 8.80366e-07 |
125 | 0.999999 | 2.8773e-06 | 1.43865e-06 |
126 | 0.999997 | 5.27958e-06 | 2.63979e-06 |
127 | 0.999996 | 7.94192e-06 | 3.97096e-06 |
128 | 0.999993 | 1.41023e-05 | 7.05116e-06 |
129 | 0.999987 | 2.50997e-05 | 1.25499e-05 |
130 | 0.99999 | 1.93397e-05 | 9.66985e-06 |
131 | 0.999991 | 1.70676e-05 | 8.53378e-06 |
132 | 1 | 6.58826e-07 | 3.29413e-07 |
133 | 1 | 1.84612e-07 | 9.2306e-08 |
134 | 1 | 3.77425e-07 | 1.88712e-07 |
135 | 1 | 7.20351e-07 | 3.60176e-07 |
136 | 0.999999 | 1.48119e-06 | 7.40597e-07 |
137 | 0.999999 | 2.96027e-06 | 1.48013e-06 |
138 | 0.999999 | 2.5435e-06 | 1.27175e-06 |
139 | 0.999997 | 5.04296e-06 | 2.52148e-06 |
140 | 0.999996 | 7.83248e-06 | 3.91624e-06 |
141 | 0.999993 | 1.39609e-05 | 6.98044e-06 |
142 | 0.999988 | 2.38691e-05 | 1.19345e-05 |
143 | 0.999987 | 2.60271e-05 | 1.30135e-05 |
144 | 0.999984 | 3.11448e-05 | 1.55724e-05 |
145 | 0.999972 | 5.65915e-05 | 2.82958e-05 |
146 | 0.999957 | 8.64351e-05 | 4.32175e-05 |
147 | 0.999933 | 0.000134643 | 6.73213e-05 |
148 | 0.999881 | 0.000238216 | 0.000119108 |
149 | 0.999788 | 0.000424319 | 0.00021216 |
150 | 0.999618 | 0.000764971 | 0.000382486 |
151 | 0.999849 | 0.000301305 | 0.000150652 |
152 | 0.999712 | 0.000575089 | 0.000287544 |
153 | 0.999567 | 0.000866972 | 0.000433486 |
154 | 0.999832 | 0.000335167 | 0.000167584 |
155 | 0.999689 | 0.000621923 | 0.000310961 |
156 | 0.999814 | 0.000371985 | 0.000185992 |
157 | 0.999664 | 0.000672498 | 0.000336249 |
158 | 0.999343 | 0.00131309 | 0.000656544 |
159 | 0.999054 | 0.00189113 | 0.000945564 |
160 | 0.998551 | 0.00289829 | 0.00144915 |
161 | 0.998007 | 0.00398547 | 0.00199273 |
162 | 0.997327 | 0.00534618 | 0.00267309 |
163 | 0.994901 | 0.010198 | 0.00509899 |
164 | 0.996193 | 0.00761404 | 0.00380702 |
165 | 0.996595 | 0.0068105 | 0.00340525 |
166 | 0.993103 | 0.0137935 | 0.00689677 |
167 | 0.988737 | 0.0225264 | 0.0112632 |
168 | 0.997981 | 0.00403737 | 0.00201869 |
169 | 0.994934 | 0.0101319 | 0.00506595 |
170 | 0.987867 | 0.0242662 | 0.0121331 |
171 | 0.97365 | 0.0526999 | 0.02635 |
172 | 0.979706 | 0.0405872 | 0.0202936 |
173 | 0.957668 | 0.0846644 | 0.0423322 |
174 | 0.902218 | 0.195564 | 0.0977819 |
175 | 0.832348 | 0.335305 | 0.167652 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 99 | 0.622642 | NOK |
5% type I error level | 130 | 0.81761 | NOK |
10% type I error level | 137 | 0.861635 | NOK |