Homework SourseA group of legislators wanted to look at factors that affect
A group of legislators wanted to look at factors that affect the number of traffic fatalities. They collected some data for 1992 from the National Transportation Safety Board on the number of fatalities for 50 states and the District of Columbia (DC), the number of licensed drivers, the number of registered vehicles, and the number of vehicle miles traveled. Select the Number of Traffic Fatalities as the dependent variable and the Number of licensed drivers (in thousands), the Number of Registered Vehicles (in thousands) and the Number of Vehicle Miles Traveled (in millions) as independent variables.
What is the value of R2 for this model? Do you think that the model does a good job of explaining the variation in the number of traffic fatalities? Why or why not?
State
Traffic Fatalities
Vehicle Miles Traveled (millions)
Licensed Drivers (thousands)
Registered Vehicles (thousands)
AL
1083
48956
3102
3422
AK
85
4150
443
508
AZ
903
38774
2879
3920
AR
610
24948
1770
1560
CA
4226
271943
20201
21980
CO
585
33705
2620
3144
CT
310
27138
2012
2638
DE
112
7025
512
672
DC
100
3448
366
189
FL
2860
121989
10691
10132
GA
1426
82822
4666
4725
HI
122
7935
791
781
ID
361
11652
779
1173
IL
1554
92316
7029
7692
IN
974
62108
3834
4850
IA
478
25737
1921
3920
KS
442
24678
1794
1965
KY
409
39822
2109
2615
LA
838
37430
2606
7261
ME
201
12469
916
1071
MD
651
44165
3311
2930
MA
440
46990
4209
3956
MI
1419
85183
6819
7599
MN
644
43317
2668
3869
MS
791
28548
1659
2056
MO
1089
57288
3512
4179
MT
202
9116
536
967
NE
271
15466
1102
1490
NV
294
13019
987
983
NH
119
10501
878
1013
NJ
890
60466
5521
5752
NM
447
20480
1162
1472
NY
1782
112970
10444
10428
NC
1431
71928
4779
5462
ND
88
6338
443
687
OH
1371
98200
7722
9647
OK
687
36980
2363
2863
OR
490
29453
2401
2748
PA
1190
92347
8146
8557
RI
63
7095
682
728
SC
847
37245
2458
2764
SD
154
7631
512
845
TN
1214
54524
3583
5150
TX
3186
178348
12012
13287
UT
342
18078
1203
1381
VT
77
6152
435
502
VA
930
67609
4631
5593
WA
638
47428
3741
4654
WV
356
17112
1317
1375
WI
712
50273
3542
4044
WY
144
6689
354
583
| Traffic Fatalities | Vehicle Miles Traveled (millions) | Licensed Drivers (thousands) | Registered Vehicles (thousands) | |
| AL | 1083 | 48956 | 3102 | 3422 |
| AK | 85 | 4150 | 443 | 508 |
| AZ | 903 | 38774 | 2879 | 3920 |
| AR | 610 | 24948 | 1770 | 1560 |
| CA | 4226 | 271943 | 20201 | 21980 |
| CO | 585 | 33705 | 2620 | 3144 |
| CT | 310 | 27138 | 2012 | 2638 |
| DE | 112 | 7025 | 512 | 672 |
| DC | 100 | 3448 | 366 | 189 |
| FL | 2860 | 121989 | 10691 | 10132 |
| GA | 1426 | 82822 | 4666 | 4725 |
| HI | 122 | 7935 | 791 | 781 |
| ID | 361 | 11652 | 779 | 1173 |
| IL | 1554 | 92316 | 7029 | 7692 |
| IN | 974 | 62108 | 3834 | 4850 |
| IA | 478 | 25737 | 1921 | 3920 |
| KS | 442 | 24678 | 1794 | 1965 |
| KY | 409 | 39822 | 2109 | 2615 |
| LA | 838 | 37430 | 2606 | 7261 |
| ME | 201 | 12469 | 916 | 1071 |
| MD | 651 | 44165 | 3311 | 2930 |
| MA | 440 | 46990 | 4209 | 3956 |
| MI | 1419 | 85183 | 6819 | 7599 |
| MN | 644 | 43317 | 2668 | 3869 |
| MS | 791 | 28548 | 1659 | 2056 |
| MO | 1089 | 57288 | 3512 | 4179 |
| MT | 202 | 9116 | 536 | 967 |
| NE | 271 | 15466 | 1102 | 1490 |
| NV | 294 | 13019 | 987 | 983 |
| NH | 119 | 10501 | 878 | 1013 |
| NJ | 890 | 60466 | 5521 | 5752 |
| NM | 447 | 20480 | 1162 | 1472 |
| NY | 1782 | 112970 | 10444 | 10428 |
| NC | 1431 | 71928 | 4779 | 5462 |
| ND | 88 | 6338 | 443 | 687 |
| OH | 1371 | 98200 | 7722 | 9647 |
| OK | 687 | 36980 | 2363 | 2863 |
| OR | 490 | 29453 | 2401 | 2748 |
| PA | 1190 | 92347 | 8146 | 8557 |
| RI | 63 | 7095 | 682 | 728 |
| SC | 847 | 37245 | 2458 | 2764 |
| SD | 154 | 7631 | 512 | 845 |
| TN | 1214 | 54524 | 3583 | 5150 |
| TX | 3186 | 178348 | 12012 | 13287 |
| UT | 342 | 18078 | 1203 | 1381 |
| VT | 77 | 6152 | 435 | 502 |
| VA | 930 | 67609 | 4631 | 5593 |
| WA | 638 | 47428 | 3741 | 4654 |
| WV | 356 | 17112 | 1317 | 1375 |
| WI | 712 | 50273 | 3542 | 4044 |
| WY | 144 | 6689 | 354 | 583 |
Solution
Coefficient of determination = ratio of y-y bar/actual y-ybar square
| Y | x1 | x2 | x3 | |
| AK | 85 | 4150 | 443 | 508 |
| AZ | 903 | 38774 | 2879 | 3920 |
| AR | 610 | 24948 | 1770 | 1560 |
| CA | 4226 | 271943 | 20201 | 21980 |
| CO | 585 | 33705 | 2620 | 3144 |
| CT | 310 | 27138 | 2012 | 2638 |
| DE | 112 | 7025 | 512 | 672 |
| DC | 100 | 3448 | 366 | 189 |
| FL | 2860 | 121989 | 10691 | 10132 |
| GA | 1426 | 82822 | 4666 | 4725 |
| HI | 122 | 7935 | 791 | 781 |
| ID | 361 | 11652 | 779 | 1173 |
| IL | 1554 | 92316 | 7029 | 7692 |
| IN | 974 | 62108 | 3834 | 4850 |
| IA | 478 | 25737 | 1921 | 3920 |
| KS | 442 | 24678 | 1794 | 1965 |
| KY | 409 | 39822 | 2109 | 2615 |
| LA | 838 | 37430 | 2606 | 7261 |
| ME | 201 | 12469 | 916 | 1071 |
| MD | 651 | 44165 | 3311 | 2930 |
| MA | 440 | 46990 | 4209 | 3956 |
| MI | 1419 | 85183 | 6819 | 7599 |
| MN | 644 | 43317 | 2668 | 3869 |
| MS | 791 | 28548 | 1659 | 2056 |
| MO | 1089 | 57288 | 3512 | 4179 |
| MT | 202 | 9116 | 536 | 967 |
| NE | 271 | 15466 | 1102 | 1490 |
| NV | 294 | 13019 | 987 | 983 |
| NH | 119 | 10501 | 878 | 1013 |
| NJ | 890 | 60466 | 5521 | 5752 |
| NM | 447 | 20480 | 1162 | 1472 |
| NY | 1782 | 112970 | 10444 | 10428 |
| NC | 1431 | 71928 | 4779 | 5462 |
| ND | 88 | 6338 | 443 | 687 |
| OH | 1371 | 98200 | 7722 | 9647 |
| OK | 687 | 36980 | 2363 | 2863 |
| OR | 490 | 29453 | 2401 | 2748 |
| PA | 1190 | 92347 | 8146 | 8557 |
| RI | 63 | 7095 | 682 | 728 |
| SC | 847 | 37245 | 2458 | 2764 |
| SD | 154 | 7631 | 512 | 845 |
| TN | 1214 | 54524 | 3583 | 5150 |
| TX | 3186 | 178348 | 12012 | 13287 |
| UT | 342 | 18078 | 1203 | 1381 |
| VT | 77 | 6152 | 435 | 502 |
| VA | 930 | 67609 | 4631 | 5593 |
| WA | 638 | 47428 | 3741 | 4654 |
| WV | 356 | 17112 | 1317 | 1375 |
| WI | 712 | 50273 | 3542 | 4044 |
| WY | 144 | 6689 | 354 | 583 |
| Mean | 555.608 | 32910.48 | 2539.858 | 2783.296 |
| Slope | 0.016 | 0.013 | 0.012 | |
| 526.5676 | 33.01815 | 33.39955 |
