Multiple Linear Regression - Estimated Regression Equation |
Accidents[t] = + 1717.75 -396.056Belt[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) | 1717.75 | 20.0003 | 85.89 | 5.68074e-154 | 2.84037e-154 |
Belt | -396.056 | 57.7862 | -6.854 | 9.76295e-11 | 4.88148e-11 |
Multiple Linear Regression - Regression Statistics | |
Multiple R | 0.445227 |
R-squared | 0.198227 |
Adjusted R-squared | 0.194007 |
F-TEST (value) | 46.9748 |
F-TEST (DF numerator) | 1 |
F-TEST (DF denominator) | 190 |
p-value | 9.76296e-11 |
Multiple Linear Regression - Residual Statistics | |
Residual Standard Deviation | 260.004 |
Sum Squared Residuals | 12844400 |
Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
1 | 1687 | 1717.75 | -30.7515 |
2 | 1508 | 1717.75 | -209.751 |
3 | 1507 | 1717.75 | -210.751 |
4 | 1385 | 1717.75 | -332.751 |
5 | 1632 | 1717.75 | -85.7515 |
6 | 1511 | 1717.75 | -206.751 |
7 | 1559 | 1717.75 | -158.751 |
8 | 1630 | 1717.75 | -87.7515 |
9 | 1579 | 1717.75 | -138.751 |
10 | 1653 | 1717.75 | -64.7515 |
11 | 2152 | 1717.75 | 434.249 |
12 | 2148 | 1717.75 | 430.249 |
13 | 1752 | 1717.75 | 34.2485 |
14 | 1765 | 1717.75 | 47.2485 |
15 | 1717 | 1717.75 | -0.751479 |
16 | 1558 | 1717.75 | -159.751 |
17 | 1575 | 1717.75 | -142.751 |
18 | 1520 | 1717.75 | -197.751 |
19 | 1805 | 1717.75 | 87.2485 |
20 | 1800 | 1717.75 | 82.2485 |
21 | 1719 | 1717.75 | 1.24852 |
22 | 2008 | 1717.75 | 290.249 |
23 | 2242 | 1717.75 | 524.249 |
24 | 2478 | 1717.75 | 760.249 |
25 | 2030 | 1717.75 | 312.249 |
26 | 1655 | 1717.75 | -62.7515 |
27 | 1693 | 1717.75 | -24.7515 |
28 | 1623 | 1717.75 | -94.7515 |
29 | 1805 | 1717.75 | 87.2485 |
30 | 1746 | 1717.75 | 28.2485 |
31 | 1795 | 1717.75 | 77.2485 |
32 | 1926 | 1717.75 | 208.249 |
33 | 1619 | 1717.75 | -98.7515 |
34 | 1992 | 1717.75 | 274.249 |
35 | 2233 | 1717.75 | 515.249 |
36 | 2192 | 1717.75 | 474.249 |
37 | 2080 | 1717.75 | 362.249 |
38 | 1768 | 1717.75 | 50.2485 |
39 | 1835 | 1717.75 | 117.249 |
40 | 1569 | 1717.75 | -148.751 |
41 | 1976 | 1717.75 | 258.249 |
42 | 1853 | 1717.75 | 135.249 |
43 | 1965 | 1717.75 | 247.249 |
44 | 1689 | 1717.75 | -28.7515 |
45 | 1778 | 1717.75 | 60.2485 |
46 | 1976 | 1717.75 | 258.249 |
47 | 2397 | 1717.75 | 679.249 |
48 | 2654 | 1717.75 | 936.249 |
49 | 2097 | 1717.75 | 379.249 |
50 | 1963 | 1717.75 | 245.249 |
51 | 1677 | 1717.75 | -40.7515 |
52 | 1941 | 1717.75 | 223.249 |
53 | 2003 | 1717.75 | 285.249 |
54 | 1813 | 1717.75 | 95.2485 |
55 | 2012 | 1717.75 | 294.249 |
56 | 1912 | 1717.75 | 194.249 |
57 | 2084 | 1717.75 | 366.249 |
58 | 2080 | 1717.75 | 362.249 |
59 | 2118 | 1717.75 | 400.249 |
60 | 2150 | 1717.75 | 432.249 |
61 | 1608 | 1717.75 | -109.751 |
62 | 1503 | 1717.75 | -214.751 |
63 | 1548 | 1717.75 | -169.751 |
64 | 1382 | 1717.75 | -335.751 |
65 | 1731 | 1717.75 | 13.2485 |
66 | 1798 | 1717.75 | 80.2485 |
67 | 1779 | 1717.75 | 61.2485 |
68 | 1887 | 1717.75 | 169.249 |
69 | 2004 | 1717.75 | 286.249 |
70 | 2077 | 1717.75 | 359.249 |
71 | 2092 | 1717.75 | 374.249 |
72 | 2051 | 1717.75 | 333.249 |
73 | 1577 | 1717.75 | -140.751 |
74 | 1356 | 1717.75 | -361.751 |
75 | 1652 | 1717.75 | -65.7515 |
76 | 1382 | 1717.75 | -335.751 |
77 | 1519 | 1717.75 | -198.751 |
78 | 1421 | 1717.75 | -296.751 |
79 | 1442 | 1717.75 | -275.751 |
80 | 1543 | 1717.75 | -174.751 |
81 | 1656 | 1717.75 | -61.7515 |
82 | 1561 | 1717.75 | -156.751 |
83 | 1905 | 1717.75 | 187.249 |
84 | 2199 | 1717.75 | 481.249 |
85 | 1473 | 1717.75 | -244.751 |
86 | 1655 | 1717.75 | -62.7515 |
87 | 1407 | 1717.75 | -310.751 |
88 | 1395 | 1717.75 | -322.751 |
89 | 1530 | 1717.75 | -187.751 |
90 | 1309 | 1717.75 | -408.751 |
91 | 1526 | 1717.75 | -191.751 |
92 | 1327 | 1717.75 | -390.751 |
93 | 1627 | 1717.75 | -90.7515 |
94 | 1748 | 1717.75 | 30.2485 |
95 | 1958 | 1717.75 | 240.249 |
96 | 2274 | 1717.75 | 556.249 |
97 | 1648 | 1717.75 | -69.7515 |
98 | 1401 | 1717.75 | -316.751 |
99 | 1411 | 1717.75 | -306.751 |
100 | 1403 | 1717.75 | -314.751 |
101 | 1394 | 1717.75 | -323.751 |
102 | 1520 | 1717.75 | -197.751 |
103 | 1528 | 1717.75 | -189.751 |
104 | 1643 | 1717.75 | -74.7515 |
105 | 1515 | 1717.75 | -202.751 |
106 | 1685 | 1717.75 | -32.7515 |
107 | 2000 | 1717.75 | 282.249 |
108 | 2215 | 1717.75 | 497.249 |
109 | 1956 | 1717.75 | 238.249 |
110 | 1462 | 1717.75 | -255.751 |
111 | 1563 | 1717.75 | -154.751 |
112 | 1459 | 1717.75 | -258.751 |
113 | 1446 | 1717.75 | -271.751 |
114 | 1622 | 1717.75 | -95.7515 |
115 | 1657 | 1717.75 | -60.7515 |
116 | 1638 | 1717.75 | -79.7515 |
117 | 1643 | 1717.75 | -74.7515 |
118 | 1683 | 1717.75 | -34.7515 |
119 | 2050 | 1717.75 | 332.249 |
120 | 2262 | 1717.75 | 544.249 |
121 | 1813 | 1717.75 | 95.2485 |
122 | 1445 | 1717.75 | -272.751 |
123 | 1762 | 1717.75 | 44.2485 |
124 | 1461 | 1717.75 | -256.751 |
125 | 1556 | 1717.75 | -161.751 |
126 | 1431 | 1717.75 | -286.751 |
127 | 1427 | 1717.75 | -290.751 |
128 | 1554 | 1717.75 | -163.751 |
129 | 1645 | 1717.75 | -72.7515 |
130 | 1653 | 1717.75 | -64.7515 |
131 | 2016 | 1717.75 | 298.249 |
132 | 2207 | 1717.75 | 489.249 |
133 | 1665 | 1717.75 | -52.7515 |
134 | 1361 | 1717.75 | -356.751 |
135 | 1506 | 1717.75 | -211.751 |
136 | 1360 | 1717.75 | -357.751 |
137 | 1453 | 1717.75 | -264.751 |
138 | 1522 | 1717.75 | -195.751 |
139 | 1460 | 1717.75 | -257.751 |
140 | 1552 | 1717.75 | -165.751 |
141 | 1548 | 1717.75 | -169.751 |
142 | 1827 | 1717.75 | 109.249 |
143 | 1737 | 1717.75 | 19.2485 |
144 | 1941 | 1717.75 | 223.249 |
145 | 1474 | 1717.75 | -243.751 |
146 | 1458 | 1717.75 | -259.751 |
147 | 1542 | 1717.75 | -175.751 |
148 | 1404 | 1717.75 | -313.751 |
149 | 1522 | 1717.75 | -195.751 |
150 | 1385 | 1717.75 | -332.751 |
151 | 1641 | 1717.75 | -76.7515 |
152 | 1510 | 1717.75 | -207.751 |
153 | 1681 | 1717.75 | -36.7515 |
154 | 1938 | 1717.75 | 220.249 |
155 | 1868 | 1717.75 | 150.249 |
156 | 1726 | 1717.75 | 8.24852 |
157 | 1456 | 1717.75 | -261.751 |
158 | 1445 | 1717.75 | -272.751 |
159 | 1456 | 1717.75 | -261.751 |
160 | 1365 | 1717.75 | -352.751 |
161 | 1487 | 1717.75 | -230.751 |
162 | 1558 | 1717.75 | -159.751 |
163 | 1488 | 1717.75 | -229.751 |
164 | 1684 | 1717.75 | -33.7515 |
165 | 1594 | 1717.75 | -123.751 |
166 | 1850 | 1717.75 | 132.249 |
167 | 1998 | 1717.75 | 280.249 |
168 | 2079 | 1717.75 | 361.249 |
169 | 1494 | 1717.75 | -223.751 |
170 | 1057 | 1321.7 | -264.696 |
171 | 1218 | 1321.7 | -103.696 |
172 | 1168 | 1321.7 | -153.696 |
173 | 1236 | 1321.7 | -85.6957 |
174 | 1076 | 1321.7 | -245.696 |
175 | 1174 | 1321.7 | -147.696 |
176 | 1139 | 1321.7 | -182.696 |
177 | 1427 | 1321.7 | 105.304 |
178 | 1487 | 1321.7 | 165.304 |
179 | 1483 | 1321.7 | 161.304 |
180 | 1513 | 1321.7 | 191.304 |
181 | 1357 | 1321.7 | 35.3043 |
182 | 1165 | 1321.7 | -156.696 |
183 | 1282 | 1321.7 | -39.6957 |
184 | 1110 | 1321.7 | -211.696 |
185 | 1297 | 1321.7 | -24.6957 |
186 | 1185 | 1321.7 | -136.696 |
187 | 1222 | 1321.7 | -99.6957 |
188 | 1284 | 1321.7 | -37.6957 |
189 | 1444 | 1321.7 | 122.304 |
190 | 1575 | 1321.7 | 253.304 |
191 | 1737 | 1321.7 | 415.304 |
192 | 1763 | 1321.7 | 441.304 |
Goldfeld-Quandt test for Heteroskedasticity | |||
p-values | Alternative Hypothesis | ||
breakpoint index | greater | 2-sided | less |
5 | 0.155931 | 0.311862 | 0.844069 |
6 | 0.0664935 | 0.132987 | 0.933506 |
7 | 0.0256738 | 0.0513477 | 0.974326 |
8 | 0.0122174 | 0.0244348 | 0.987783 |
9 | 0.00437998 | 0.00875996 | 0.99562 |
10 | 0.00224016 | 0.00448032 | 0.99776 |
11 | 0.22358 | 0.44716 | 0.77642 |
12 | 0.503981 | 0.992037 | 0.496019 |
13 | 0.420841 | 0.841682 | 0.579159 |
14 | 0.345366 | 0.690731 | 0.654634 |
15 | 0.270018 | 0.540036 | 0.729982 |
16 | 0.219064 | 0.438129 | 0.780936 |
17 | 0.171075 | 0.34215 | 0.828925 |
18 | 0.140712 | 0.281423 | 0.859288 |
19 | 0.114092 | 0.228184 | 0.885908 |
20 | 0.0900793 | 0.180159 | 0.909921 |
21 | 0.0638848 | 0.12777 | 0.936115 |
22 | 0.088286 | 0.176572 | 0.911714 |
23 | 0.254037 | 0.508073 | 0.745963 |
24 | 0.704135 | 0.591731 | 0.295865 |
25 | 0.709949 | 0.580101 | 0.290051 |
26 | 0.661733 | 0.676534 | 0.338267 |
27 | 0.606522 | 0.786955 | 0.393478 |
28 | 0.559719 | 0.880562 | 0.440281 |
29 | 0.503738 | 0.992525 | 0.496262 |
30 | 0.444961 | 0.889922 | 0.555039 |
31 | 0.390183 | 0.780366 | 0.609817 |
32 | 0.362128 | 0.724256 | 0.637872 |
33 | 0.322725 | 0.64545 | 0.677275 |
34 | 0.31847 | 0.63694 | 0.68153 |
35 | 0.447503 | 0.895006 | 0.552497 |
36 | 0.540191 | 0.919619 | 0.459809 |
37 | 0.562295 | 0.875411 | 0.437705 |
38 | 0.510686 | 0.978628 | 0.489314 |
39 | 0.462278 | 0.924556 | 0.537722 |
40 | 0.443241 | 0.886483 | 0.556759 |
41 | 0.425739 | 0.851477 | 0.574261 |
42 | 0.382074 | 0.764148 | 0.617926 |
43 | 0.362012 | 0.724023 | 0.637988 |
44 | 0.321993 | 0.643985 | 0.678007 |
45 | 0.279428 | 0.558857 | 0.720572 |
46 | 0.265649 | 0.531297 | 0.734351 |
47 | 0.493782 | 0.987564 | 0.506218 |
48 | 0.889938 | 0.220125 | 0.110062 |
49 | 0.901114 | 0.197773 | 0.0988863 |
50 | 0.891931 | 0.216137 | 0.108069 |
51 | 0.874959 | 0.250082 | 0.125041 |
52 | 0.861924 | 0.276151 | 0.138076 |
53 | 0.857742 | 0.284516 | 0.142258 |
54 | 0.833787 | 0.332426 | 0.166213 |
55 | 0.831684 | 0.336633 | 0.168316 |
56 | 0.813452 | 0.373096 | 0.186548 |
57 | 0.82999 | 0.34002 | 0.17001 |
58 | 0.845294 | 0.309412 | 0.154706 |
59 | 0.869887 | 0.260227 | 0.130113 |
60 | 0.899973 | 0.200054 | 0.100027 |
61 | 0.892912 | 0.214177 | 0.107088 |
62 | 0.899814 | 0.200373 | 0.100186 |
63 | 0.898719 | 0.202562 | 0.101281 |
64 | 0.924222 | 0.151557 | 0.0757784 |
65 | 0.910274 | 0.179452 | 0.0897258 |
66 | 0.894793 | 0.210415 | 0.105207 |
67 | 0.87717 | 0.24566 | 0.12283 |
68 | 0.864097 | 0.271805 | 0.135903 |
69 | 0.867874 | 0.264253 | 0.132126 |
70 | 0.887176 | 0.225647 | 0.112824 |
71 | 0.90845 | 0.183101 | 0.0915504 |
72 | 0.92087 | 0.158261 | 0.0791305 |
73 | 0.91601 | 0.167979 | 0.0839897 |
74 | 0.940403 | 0.119195 | 0.0595975 |
75 | 0.931292 | 0.137416 | 0.0687078 |
76 | 0.946956 | 0.106088 | 0.0530439 |
77 | 0.945882 | 0.108237 | 0.0541184 |
78 | 0.953436 | 0.0931274 | 0.0465637 |
79 | 0.957767 | 0.0844662 | 0.0422331 |
80 | 0.954412 | 0.0911765 | 0.0455882 |
81 | 0.945791 | 0.108418 | 0.0542088 |
82 | 0.940175 | 0.11965 | 0.059825 |
83 | 0.936131 | 0.127738 | 0.0638689 |
84 | 0.966339 | 0.0673229 | 0.0336614 |
85 | 0.966916 | 0.0661679 | 0.0330839 |
86 | 0.960164 | 0.0796718 | 0.0398359 |
87 | 0.965277 | 0.0694459 | 0.0347229 |
88 | 0.970379 | 0.0592411 | 0.0296205 |
89 | 0.967464 | 0.0650719 | 0.0325359 |
90 | 0.977737 | 0.0445254 | 0.0222627 |
91 | 0.975323 | 0.0493547 | 0.0246774 |
92 | 0.982128 | 0.0357448 | 0.0178724 |
93 | 0.977904 | 0.0441921 | 0.0220961 |
94 | 0.97258 | 0.0548399 | 0.02742 |
95 | 0.973652 | 0.0526956 | 0.0263478 |
96 | 0.992148 | 0.0157043 | 0.00785213 |
97 | 0.989944 | 0.0201116 | 0.0100558 |
98 | 0.99108 | 0.0178391 | 0.00891953 |
99 | 0.991852 | 0.0162959 | 0.00814795 |
100 | 0.992689 | 0.0146217 | 0.00731084 |
101 | 0.993588 | 0.0128241 | 0.00641203 |
102 | 0.992587 | 0.0148251 | 0.00741253 |
103 | 0.991334 | 0.0173314 | 0.00866569 |
104 | 0.988787 | 0.0224268 | 0.0112134 |
105 | 0.987197 | 0.0256051 | 0.0128026 |
106 | 0.983489 | 0.0330225 | 0.0165113 |
107 | 0.98621 | 0.0275799 | 0.0137899 |
108 | 0.995481 | 0.00903755 | 0.00451877 |
109 | 0.996074 | 0.00785132 | 0.00392566 |
110 | 0.995808 | 0.00838357 | 0.00419179 |
111 | 0.994713 | 0.0105749 | 0.00528744 |
112 | 0.994384 | 0.0112326 | 0.00561628 |
113 | 0.994203 | 0.0115945 | 0.00579723 |
114 | 0.992372 | 0.0152562 | 0.00762811 |
115 | 0.989937 | 0.0201256 | 0.0100628 |
116 | 0.98689 | 0.0262201 | 0.0131101 |
117 | 0.983039 | 0.0339225 | 0.0169612 |
118 | 0.978201 | 0.0435979 | 0.021799 |
119 | 0.985499 | 0.0290019 | 0.014501 |
120 | 0.997274 | 0.00545252 | 0.00272626 |
121 | 0.996841 | 0.006319 | 0.0031595 |
122 | 0.996604 | 0.00679134 | 0.00339567 |
123 | 0.995732 | 0.00853619 | 0.0042681 |
124 | 0.995232 | 0.00953613 | 0.00476806 |
125 | 0.993836 | 0.0123286 | 0.00616428 |
126 | 0.993579 | 0.0128418 | 0.00642089 |
127 | 0.993394 | 0.013213 | 0.0066065 |
128 | 0.991525 | 0.0169506 | 0.00847531 |
129 | 0.988655 | 0.022689 | 0.0113445 |
130 | 0.984959 | 0.0300813 | 0.0150406 |
131 | 0.990222 | 0.0195567 | 0.00977837 |
132 | 0.99828 | 0.00344002 | 0.00172001 |
133 | 0.997592 | 0.00481675 | 0.00240838 |
134 | 0.997893 | 0.00421437 | 0.00210719 |
135 | 0.997294 | 0.0054122 | 0.0027061 |
136 | 0.997678 | 0.00464462 | 0.00232231 |
137 | 0.997355 | 0.00529082 | 0.00264541 |
138 | 0.996547 | 0.00690689 | 0.00345345 |
139 | 0.996045 | 0.00790942 | 0.00395471 |
140 | 0.994687 | 0.0106261 | 0.00531303 |
141 | 0.992957 | 0.0140851 | 0.00704257 |
142 | 0.992033 | 0.015934 | 0.00796699 |
143 | 0.989584 | 0.0208325 | 0.0104162 |
144 | 0.992082 | 0.0158367 | 0.00791834 |
145 | 0.990449 | 0.019101 | 0.00955052 |
146 | 0.98895 | 0.0221006 | 0.0110503 |
147 | 0.985456 | 0.0290879 | 0.0145439 |
148 | 0.985571 | 0.0288577 | 0.0144289 |
149 | 0.98178 | 0.0364397 | 0.0182198 |
150 | 0.983523 | 0.0329546 | 0.0164773 |
151 | 0.977249 | 0.0455022 | 0.0227511 |
152 | 0.97264 | 0.0547198 | 0.0273599 |
153 | 0.962926 | 0.0741489 | 0.0370745 |
154 | 0.967303 | 0.065395 | 0.0326975 |
155 | 0.966686 | 0.0666289 | 0.0333145 |
156 | 0.957192 | 0.0856166 | 0.0428083 |
157 | 0.951104 | 0.0977923 | 0.0488962 |
158 | 0.946573 | 0.106853 | 0.0534267 |
159 | 0.94199 | 0.11602 | 0.0580102 |
160 | 0.953946 | 0.0921072 | 0.0460536 |
161 | 0.951782 | 0.096436 | 0.048218 |
162 | 0.943782 | 0.112437 | 0.0562183 |
163 | 0.948853 | 0.102294 | 0.0511472 |
164 | 0.93387 | 0.132261 | 0.0661304 |
165 | 0.932018 | 0.135964 | 0.067982 |
166 | 0.908408 | 0.183183 | 0.0915916 |
167 | 0.896696 | 0.206609 | 0.103304 |
168 | 0.946325 | 0.10735 | 0.0536751 |
169 | 0.925762 | 0.148476 | 0.074238 |
170 | 0.932074 | 0.135852 | 0.0679259 |
171 | 0.912199 | 0.175603 | 0.0878014 |
172 | 0.89714 | 0.20572 | 0.10286 |
173 | 0.867972 | 0.264055 | 0.132028 |
174 | 0.884055 | 0.231889 | 0.115945 |
175 | 0.871741 | 0.256518 | 0.128259 |
176 | 0.87598 | 0.248039 | 0.12402 |
177 | 0.829472 | 0.341055 | 0.170528 |
178 | 0.781249 | 0.437502 | 0.218751 |
179 | 0.723085 | 0.553829 | 0.276915 |
180 | 0.668098 | 0.663804 | 0.331902 |
181 | 0.573634 | 0.852731 | 0.426366 |
182 | 0.540064 | 0.919872 | 0.459936 |
183 | 0.449856 | 0.899712 | 0.550144 |
184 | 0.491029 | 0.982059 | 0.508971 |
185 | 0.403463 | 0.806925 | 0.596537 |
186 | 0.428896 | 0.857791 | 0.571104 |
187 | 0.488141 | 0.976282 | 0.511859 |
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
Description | # significant tests | % significant tests | OK/NOK |
1% type I error level | 18 | 0.0983607 | NOK |
5% type I error level | 63 | 0.344262 | NOK |
10% type I error level | 83 | 0.453552 | NOK |