Multiple Linear Regression - Estimated Regression Equation |
A1[t] = + 663.989 + 0.639119Accidents[t] -136.639Belt[t] + 398.737M1[t] + 93.668M2[t] -138.647M3[t] -15.7447M4[t] -216.691M5[t] -43.7478M6[t] -147.831M7[t] -81.713M8[t] -100.591M9[t] -136.856M10[t] -125.025M11[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) | 663.989 | 128.955 | 5.149 | 6.9237e-07 | 3.46185e-07 |
Accidents | 0.639119 | 0.057504 | 11.11 | 4.16638e-22 | 2.08319e-22 |
Belt | -136.639 | 37.423 | -3.651 | 0.000343463 | 0.000171732 |
M1 | 398.737 | 54.2532 | 7.35 | 7.05684e-12 | 3.52842e-12 |
M2 | 93.668 | 59.0565 | 1.586 | 0.114507 | 0.0572536 |
M3 | -138.647 | 57.3545 | -2.417 | 0.0166476 | 0.00832381 |
M4 | -15.7447 | 61.2904 | -0.2569 | 0.797565 | 0.398783 |
M5 | -216.691 | 56.577 | -3.83 | 0.000177697 | 8.88483e-05 |
M6 | -43.7478 | 58.4079 | -0.749 | 0.454849 | 0.227424 |
M7 | -147.831 | 55.9542 | -2.642 | 0.00897996 | 0.00448998 |
M8 | -81.713 | 55.4989 | -1.472 | 0.142706 | 0.0713531 |
M9 | -100.591 | 53.961 | -1.864 | 0.0639565 | 0.0319782 |
M10 | -136.856 | 50.558 | -2.707 | 0.00745644 | 0.00372822 |
M11 | -125.025 | 47.6498 | -2.624 | 0.00945383 | 0.00472692 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.896204 |
R-squared | 0.803181 |
Adjusted R-squared | 0.788726 |
F-TEST (value) | 55.5619 |
F-TEST (DF numerator) | 13 |
F-TEST (DF denominator) | 177 |
p-value | 0 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 133.432 |
Sum Squared Residuals | 3151340 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | NA | NA | -34.4486 |
2 | 1687 | 1667.49 | 19.506 |
3 | 1508 | 1534.42 | -26.4243 |
4 | 1507 | 1612.34 | -105.34 |
5 | 1385 | 1338.95 | 46.0499 |
6 | 1632 | 1633.54 | -1.54444 |
7 | 1511 | 1576.04 | -65.04 |
8 | 1559 | 1501.57 | 57.4335 |
9 | 1630 | 1634.6 | -4.59658 |
10 | 1579 | 1840.35 | -261.348 |
11 | 1653 | 1537.82 | 115.184 |
12 | 2152 | 2186.46 | -34.4623 |
13 | 2148 | 2281.7 | -133.702 |
14 | 1752 | 1609.71 | 142.291 |
15 | 1765 | 1691.99 | 73.0082 |
16 | 1717 | 1612.91 | 104.09 |
17 | 1558 | 1574.7 | -16.7022 |
18 | 1575 | 1724.77 | -149.768 |
19 | 1520 | 1447.69 | 72.3098 |
20 | 1805 | 1667.04 | 137.957 |
21 | 1800 | 1891.48 | -91.4837 |
22 | 1719 | 1682.87 | 36.1316 |
23 | 2008 | 2013.73 | -5.72568 |
24 | 2242 | 2124.14 | 117.863 |
25 | 2478 | 2263.4 | 214.601 |
26 | 2030 | 1982.37 | 47.6299 |
27 | 1655 | 1647.53 | 7.46549 |
28 | 1693 | 1670.91 | 22.0924 |
29 | 1623 | 1554.14 | 68.857 |
30 | 1805 | 1722.38 | 82.6235 |
31 | 1746 | 1764.22 | -18.2191 |
32 | 1795 | 1467.13 | 327.869 |
33 | 1926 | 2107.26 | -181.258 |
34 | 1619 | 1593.12 | 25.8837 |
35 | 1992 | 1823.94 | 168.062 |
36 | 2233 | 2433.09 | -200.093 |
37 | 2192 | 1999.62 | 192.381 |
38 | 2080 | 2010.12 | 69.8751 |
39 | 1768 | 1584.02 | 183.978 |
40 | 1835 | 1976.2 | -141.197 |
41 | 1569 | 1397.53 | 171.471 |
42 | 1976 | 1895.03 | 80.9734 |
43 | 1853 | 1549.75 | 303.252 |
44 | 1965 | 1975.75 | -10.7511 |
45 | 1689 | 1701.03 | -12.0319 |
46 | 1778 | 1872.93 | -94.9318 |
47 | 1976 | 1939.21 | 36.7894 |
48 | 2397 | 2145.96 | 251.042 |
49 | 2654 | 2569.25 | 84.7524 |
50 | 2097 | 1731.14 | 365.856 |
51 | 1963 | 2174.77 | -211.774 |
52 | 1677 | 1463.45 | 213.547 |
53 | 1941 | 1716.96 | 224.036 |
54 | 2003 | 1992.07 | 10.9348 |
55 | 1813 | 1605.27 | 207.729 |
56 | 2012 | 1995.32 | 16.6786 |
57 | 1912 | 1684.5 | 227.5 |
58 | 2084 | 1896.62 | 187.382 |
59 | 2080 | 2000.09 | 79.9053 |
60 | 2118 | 2058.43 | 59.5708 |
61 | 2150 | 2260.25 | -110.253 |
62 | 1608 | 1619.7 | -11.6979 |
63 | 1503 | 1486.51 | 16.4931 |
64 | 1548 | 1719.61 | -171.613 |
65 | 1382 | 1420.38 | -38.3772 |
66 | 1731 | 1586.15 | 144.849 |
67 | 1798 | 1807.29 | -9.29349 |
68 | 1779 | 1736.19 | 42.8081 |
69 | 1887 | 1737.58 | 149.417 |
70 | 2004 | 1803 | 200.999 |
71 | 2077 | 1959.82 | 117.178 |
72 | 2092 | 2111.62 | -19.6165 |
73 | 2051 | 2098.3 | -47.3025 |
74 | 1577 | 1802.17 | -225.166 |
75 | 1356 | 1235.51 | 120.493 |
76 | 1652 | 1688.12 | -36.1197 |
77 | 1382 | 1391.43 | -9.42941 |
78 | 1519 | 1535.77 | -16.7675 |
79 | 1421 | 1547.44 | -126.437 |
80 | 1442 | 1520.78 | -78.7786 |
81 | 1543 | 1411.8 | 131.202 |
82 | 1656 | 1851.49 | -195.485 |
83 | 1561 | 1725.41 | -164.412 |
84 | 1905 | 1710.15 | 194.852 |
85 | 2199 | 2541.4 | -342.399 |
86 | 1473 | 1242.58 | 230.418 |
87 | 1655 | 1787.82 | -132.815 |
88 | 1407 | 1437.15 | -30.15 |
89 | 1395 | 1321.85 | 73.1519 |
90 | 1530 | 1712.45 | -182.454 |
91 | 1309 | 1213.39 | 95.613 |
92 | 1526 | 1802.24 | -276.244 |
93 | 1327 | 1344.31 | -17.3129 |
94 | 1627 | 1669.36 | -42.3587 |
95 | 1748 | 1907.35 | -159.345 |
96 | 1958 | 1799.99 | 158.006 |
97 | 2274 | 2279.06 | -5.06285 |
98 | 1648 | 1674.14 | -26.1386 |
99 | 1401 | 1534.93 | -133.928 |
100 | 1411 | 1346.23 | 64.7702 |
101 | 1403 | 1600.7 | -197.702 |
102 | 1394 | 1366.73 | 27.2682 |
103 | 1520 | 1624.35 | -104.349 |
104 | 1528 | 1416.66 | 111.337 |
105 | 1643 | 1732.05 | -89.0484 |
106 | 1515 | 1647.2 | -132.202 |
107 | 1685 | 1764.64 | -79.6375 |
108 | 2000 | 2097.84 | -97.8425 |
109 | 2215 | 1951.05 | 263.951 |
110 | 1956 | 2018.28 | -62.2846 |
111 | 1462 | 1479.72 | -17.719 |
112 | 1563 | 1475.46 | 87.536 |
113 | 1459 | 1669.89 | -210.892 |
114 | 1446 | 1399.18 | 46.8219 |
115 | 1622 | 1594.15 | 27.8471 |
116 | 1657 | 1632.47 | 24.5299 |
117 | 1638 | 1597.77 | 40.2299 |
118 | 1643 | 1809.16 | -166.158 |
119 | 1683 | 1742.68 | -59.676 |
120 | 2050 | 2009.45 | 40.5515 |
121 | 2262 | 2130.18 | 131.816 |
122 | 1813 | 2019.47 | -206.469 |
123 | 1445 | 1265 | 180.003 |
124 | 1762 | 1742.77 | 19.2329 |
125 | 1461 | 1439.82 | 21.1794 |
126 | 1556 | 1553.18 | 2.81923 |
127 | 1431 | 1579.47 | -148.467 |
128 | 1427 | 1487.75 | -60.7483 |
129 | 1554 | 1492.6 | 61.4034 |
130 | 1645 | 1819.43 | -174.428 |
131 | 1653 | 1711.52 | -58.5245 |
132 | 2016 | 1935.86 | 80.141 |
133 | 2207 | 2169.5 | 37.5019 |
134 | 1665 | 1791.85 | -126.855 |
135 | 1361 | 1372.45 | -11.4463 |
136 | 1506 | 1521.94 | -15.9378 |
137 | 1360 | 1499.98 | -139.98 |
138 | 1453 | 1380.27 | 72.7283 |
139 | 1522 | 1636.19 | -114.189 |
140 | 1460 | 1460.75 | -0.753786 |
141 | 1552 | 1698.8 | -146.803 |
142 | 1548 | 1370.11 | 177.887 |
143 | 1827 | 1994.52 | -167.519 |
144 | 1737 | 1800.79 | -63.7873 |
145 | 1941 | 2156.49 | -215.493 |
146 | 1474 | 1526.86 | -52.8631 |
147 | 1458 | 1461.57 | -3.56751 |
148 | 1542 | 1558.04 | -16.037 |
149 | 1404 | 1387.42 | 16.5789 |
150 | 1522 | 1701.95 | -179.952 |
151 | 1385 | 1291.35 | 93.6543 |
152 | 1641 | 1768.76 | -127.757 |
153 | 1510 | 1594.75 | -84.7454 |
154 | 1681 | 1475.84 | 205.162 |
155 | 1938 | 1837.11 | 100.892 |
156 | 1868 | 2135.28 | -267.283 |
157 | 1726 | 1951.18 | -225.184 |
158 | 1456 | 1466.9 | -10.8989 |
159 | 1445 | 1509.64 | -64.6419 |
160 | 1456 | 1488.67 | -32.6679 |
161 | 1365 | 1493.99 | -128.989 |
162 | 1487 | 1396.17 | 90.833 |
163 | 1558 | 1728.55 | -170.552 |
164 | 1488 | 1386.15 | 101.847 |
165 | 1684 | 1799.5 | -115.503 |
166 | 1594 | 1559.92 | 34.0766 |
167 | 1850 | 1844.72 | 5.2827 |
168 | 1998 | 1936.57 | 61.4303 |
169 | 2079 | 1881.57 | 197.433 |
170 | 1494 | 1604.15 | -110.149 |
171 | 1057 | 1097.1 | -40.0962 |
172 | 1218 | 1150.61 | 67.3903 |
173 | 1168 | 1103.29 | 64.7059 |
174 | 1236 | 1289.84 | -53.8444 |
175 | 1076 | 1075.59 | 0.406659 |
176 | 1174 | 1373.78 | -199.781 |
177 | 1139 | 1052.86 | 86.1365 |
178 | 1427 | 1290.14 | 136.862 |
179 | 1487 | 1498.34 | -11.3368 |
180 | 1483 | 1763.37 | -280.371 |
181 | 1513 | 1521.59 | -8.59148 |
182 | 1357 | 1400.05 | -43.0529 |
183 | 1165 | 1104.03 | 60.9727 |
184 | 1282 | 1311.6 | -29.596 |
185 | 1110 | 1053.96 | 56.042 |
186 | 1297 | 1272.52 | 24.4779 |
187 | 1185 | 1229.27 | -44.2656 |
188 | 1222 | 1287.65 | -65.6461 |
189 | 1284 | 1237.11 | 46.894 |
190 | 1444 | 1381.47 | 62.5259 |
191 | 1575 | 1492.12 | 82.8836 |
192 | 1737 | NA | NA |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
17 | 0.468955 | 0.93791 | 0.531045 |
18 | 0.386685 | 0.77337 | 0.613315 |
19 | 0.345255 | 0.69051 | 0.654745 |
20 | 0.254208 | 0.508417 | 0.745792 |
21 | 0.179153 | 0.358306 | 0.820847 |
22 | 0.352536 | 0.705072 | 0.647464 |
23 | 0.287445 | 0.574891 | 0.712555 |
24 | 0.271397 | 0.542794 | 0.728603 |
25 | 0.480499 | 0.960998 | 0.519501 |
26 | 0.396442 | 0.792884 | 0.603558 |
27 | 0.315762 | 0.631523 | 0.684238 |
28 | 0.245307 | 0.490614 | 0.754693 |
29 | 0.19096 | 0.381919 | 0.80904 |
30 | 0.186751 | 0.373503 | 0.813249 |
31 | 0.140456 | 0.280912 | 0.859544 |
32 | 0.223249 | 0.446499 | 0.776751 |
33 | 0.218066 | 0.436132 | 0.781934 |
34 | 0.203283 | 0.406567 | 0.796717 |
35 | 0.187689 | 0.375379 | 0.812311 |
36 | 0.252792 | 0.505584 | 0.747208 |
37 | 0.287083 | 0.574167 | 0.712917 |
38 | 0.236772 | 0.473544 | 0.763228 |
39 | 0.257463 | 0.514926 | 0.742537 |
40 | 0.250587 | 0.501173 | 0.749413 |
41 | 0.260542 | 0.521085 | 0.739458 |
42 | 0.236633 | 0.473267 | 0.763367 |
43 | 0.420728 | 0.841455 | 0.579272 |
44 | 0.430189 | 0.860378 | 0.569811 |
45 | 0.38925 | 0.7785 | 0.61075 |
46 | 0.342977 | 0.685954 | 0.657023 |
47 | 0.296392 | 0.592784 | 0.703608 |
48 | 0.449143 | 0.898285 | 0.550857 |
49 | 0.409151 | 0.818302 | 0.590849 |
50 | 0.642942 | 0.714117 | 0.357058 |
51 | 0.712203 | 0.575594 | 0.287797 |
52 | 0.803082 | 0.393835 | 0.196918 |
53 | 0.844771 | 0.310459 | 0.155229 |
54 | 0.81606 | 0.36788 | 0.18394 |
55 | 0.853005 | 0.293989 | 0.146995 |
56 | 0.844282 | 0.311436 | 0.155718 |
57 | 0.926182 | 0.147636 | 0.073818 |
58 | 0.954792 | 0.0904152 | 0.0452076 |
59 | 0.947174 | 0.105653 | 0.0528265 |
60 | 0.93468 | 0.13064 | 0.0653198 |
61 | 0.936481 | 0.127039 | 0.0635195 |
62 | 0.931802 | 0.136396 | 0.068198 |
63 | 0.91482 | 0.170361 | 0.0851804 |
64 | 0.921599 | 0.156802 | 0.0784012 |
65 | 0.917968 | 0.164065 | 0.0820323 |
66 | 0.932458 | 0.135084 | 0.0675422 |
67 | 0.93098 | 0.138039 | 0.0690196 |
68 | 0.937643 | 0.124714 | 0.0623569 |
69 | 0.96142 | 0.0771598 | 0.0385799 |
70 | 0.980888 | 0.0382237 | 0.0191119 |
71 | 0.979442 | 0.041116 | 0.020558 |
72 | 0.974058 | 0.051884 | 0.025942 |
73 | 0.969281 | 0.0614378 | 0.0307189 |
74 | 0.984504 | 0.0309927 | 0.0154964 |
75 | 0.983728 | 0.0325447 | 0.0162724 |
76 | 0.978828 | 0.0423445 | 0.0211722 |
77 | 0.97399 | 0.0520192 | 0.0260096 |
78 | 0.967084 | 0.0658312 | 0.0329156 |
79 | 0.969741 | 0.0605179 | 0.030259 |
80 | 0.967993 | 0.0640145 | 0.0320072 |
81 | 0.963911 | 0.0721773 | 0.0360886 |
82 | 0.975018 | 0.0499645 | 0.0249823 |
83 | 0.978846 | 0.0423076 | 0.0211538 |
84 | 0.982002 | 0.0359968 | 0.0179984 |
85 | 0.994947 | 0.0101058 | 0.00505291 |
86 | 0.997394 | 0.00521112 | 0.00260556 |
87 | 0.997484 | 0.0050312 | 0.0025156 |
88 | 0.996499 | 0.00700157 | 0.00350079 |
89 | 0.995457 | 0.00908672 | 0.00454336 |
90 | 0.996711 | 0.00657811 | 0.00328905 |
91 | 0.99575 | 0.00850026 | 0.00425013 |
92 | 0.998804 | 0.00239216 | 0.00119608 |
93 | 0.998299 | 0.00340237 | 0.00170119 |
94 | 0.997646 | 0.00470847 | 0.00235424 |
95 | 0.997595 | 0.00480959 | 0.0024048 |
96 | 0.998514 | 0.00297226 | 0.00148613 |
97 | 0.997908 | 0.00418353 | 0.00209177 |
98 | 0.99723 | 0.0055403 | 0.00277015 |
99 | 0.997379 | 0.00524138 | 0.00262069 |
100 | 0.996531 | 0.00693888 | 0.00346944 |
101 | 0.997472 | 0.00505625 | 0.00252812 |
102 | 0.996518 | 0.00696308 | 0.00348154 |
103 | 0.995837 | 0.00832568 | 0.00416284 |
104 | 0.995391 | 0.00921894 | 0.00460947 |
105 | 0.994798 | 0.0104035 | 0.00520176 |
106 | 0.994765 | 0.01047 | 0.00523501 |
107 | 0.993166 | 0.0136685 | 0.00683424 |
108 | 0.993037 | 0.0139255 | 0.00696277 |
109 | 0.9983 | 0.0033995 | 0.00169975 |
110 | 0.997824 | 0.00435243 | 0.00217621 |
111 | 0.996885 | 0.00623008 | 0.00311504 |
112 | 0.996097 | 0.0078064 | 0.0039032 |
113 | 0.996789 | 0.00642242 | 0.00321121 |
114 | 0.996372 | 0.00725517 | 0.00362758 |
115 | 0.99608 | 0.00784021 | 0.0039201 |
116 | 0.995073 | 0.00985305 | 0.00492652 |
117 | 0.993172 | 0.0136554 | 0.0068277 |
118 | 0.994396 | 0.0112085 | 0.00560426 |
119 | 0.992833 | 0.0143338 | 0.00716689 |
120 | 0.996299 | 0.0074019 | 0.00370095 |
121 | 0.997585 | 0.00482969 | 0.00241484 |
122 | 0.997507 | 0.0049869 | 0.00249345 |
123 | 0.998979 | 0.00204201 | 0.00102101 |
124 | 0.998578 | 0.00284358 | 0.00142179 |
125 | 0.997971 | 0.00405795 | 0.00202898 |
126 | 0.997011 | 0.00597728 | 0.00298864 |
127 | 0.996696 | 0.00660836 | 0.00330418 |
128 | 0.995371 | 0.00925743 | 0.00462872 |
129 | 0.993421 | 0.0131582 | 0.00657911 |
130 | 0.996186 | 0.00762794 | 0.00381397 |
131 | 0.995394 | 0.00921246 | 0.00460623 |
132 | 0.999169 | 0.00166265 | 0.000831327 |
133 | 0.998901 | 0.00219806 | 0.00109903 |
134 | 0.99858 | 0.00284085 | 0.00142043 |
135 | 0.997804 | 0.00439117 | 0.00219559 |
136 | 0.996763 | 0.00647323 | 0.00323661 |
137 | 0.996022 | 0.00795563 | 0.00397781 |
138 | 0.994976 | 0.010049 | 0.00502448 |
139 | 0.993496 | 0.0130089 | 0.00650446 |
140 | 0.99046 | 0.0190798 | 0.00953991 |
141 | 0.990818 | 0.0183644 | 0.0091822 |
142 | 0.988877 | 0.0222454 | 0.0111227 |
143 | 0.992211 | 0.0155789 | 0.00778943 |
144 | 0.989976 | 0.0200473 | 0.0100236 |
145 | 0.992407 | 0.0151869 | 0.00759346 |
146 | 0.989032 | 0.0219362 | 0.0109681 |
147 | 0.983961 | 0.0320784 | 0.0160392 |
148 | 0.976571 | 0.0468571 | 0.0234285 |
149 | 0.966432 | 0.0671357 | 0.0335679 |
150 | 0.962548 | 0.0749045 | 0.0374522 |
151 | 0.965797 | 0.0684055 | 0.0342027 |
152 | 0.955647 | 0.0887063 | 0.0443531 |
153 | 0.938855 | 0.12229 | 0.0611452 |
154 | 0.938746 | 0.122507 | 0.0612536 |
155 | 0.917702 | 0.164595 | 0.0822976 |
156 | 0.946647 | 0.106706 | 0.0533528 |
157 | 0.983894 | 0.0322129 | 0.0161065 |
158 | 0.97465 | 0.0506998 | 0.0253499 |
159 | 0.970529 | 0.0589415 | 0.0294708 |
160 | 0.965105 | 0.0697895 | 0.0348947 |
161 | 0.965195 | 0.069611 | 0.0348055 |
162 | 0.951047 | 0.0979054 | 0.0489527 |
163 | 0.938346 | 0.123308 | 0.0616541 |
164 | 0.937828 | 0.124344 | 0.062172 |
165 | 0.969026 | 0.0619486 | 0.0309743 |
166 | 0.968378 | 0.0632431 | 0.0316216 |
167 | 0.985688 | 0.0286242 | 0.0143121 |
168 | 0.971358 | 0.0572835 | 0.0286417 |
169 | 0.986743 | 0.026513 | 0.0132565 |
170 | 0.97734 | 0.0453209 | 0.0226605 |
171 | 0.967141 | 0.0657185 | 0.0328593 |
172 | 0.950914 | 0.0981713 | 0.0490857 |
173 | 0.888457 | 0.223087 | 0.111543 |
174 | 0.808386 | 0.383227 | 0.191614 |
175 | 0.631765 | 0.736469 | 0.368235 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 44 | 0.27673 | NOK |
5% type I error level | 76 | 0.477987 | NOK |
10% type I error level | 99 | 0.622642 | NOK |