Auto Accidents: What

1
Auto Accidents Whats responsible?

• Group 8
• Janelle Chang
• Helena Jeanty
• Rhiana Quail

2
DISCLAIMER!!!

• Weather conditions
• Drivers mental health
• Drivers physical health
• Time of day
• Time of year

3
Sorting the Data...

• National vs. Regional
• National
• all 50 states (not including DC)
• Regional
• Region 1 North East
• Region 2 South East
• Region 3 South MidWest
• Region 4 North MidWest
• Region 5 South West
• Region 6 North West
• Reasoning
• Allows one to view any type of national behavior
• Allows for comparisons to be made within the
  United States

4
Normalizing Data

• Reason
• Every entry needs to be expressed in a standard
  proportion so that the data can be evaluated
  equally.
• State populations differs
• Number of states per region differ
• Basic assumption more people more cars
  higher number of automobile fatalities.

5
Testing1 Does alcohol affect the number of
drivers killed in car accidents?

• assumption
• Alcohol affects the number of people killed in
  car accidents BUT is not the only contributing
  factor.
• Younger people probably drink more irresponsibly
  so more likely to be involved and be responsible
  for fatal car accidents.

2 Does a combination of age and alcohol affect
the number of people (including drivers) killed
in car accidents?3 Do individual regions
mimic national data?
6
t-Test

• For each region
• H0 ?tot. drivers killed ?drunk drivers killed
• H1 ?tot. drivers killed ? ?drunk drivers killed
• t-Test
• ? 0.05, 95 confidence
• 2-sided test
• df ( obs) - 1

7
t-Test (1)Rejecting H0
Source SS df
MS Number of obs
17 -------------------------------------------
F( 1, 15) 40.43
Model 1.1071e-12 1 1.1071e-12
Prob gt F 0.0000 Residual
4.1075e-13 15 2.7383e-14
R-squared 0.7294 ------------------------
-------------------
Adj R-squared 0.7114 Total
1.5179e-12 16 9.4868e-14
Root MSE 1.7e-07 -----------------------
--------------------------------------------------
----- reg1normkid Coef. Std.
Err. t Pgtt 95 Conf.
Interval ------------- --------------------
-------------------------------------------- reg1n
ormdrk 125.8276 19.78864 6.36 0.000
83.64916 168.0061 _cons
1.37e-07 4.70e-08 2.91 0.011
3.66e-08 2.37e-07 ---------------------------
--------------------------------------------------
-
Reject H0 t gt t15 ie. 6.36 gt 2.131
8
Regression driverskilled 1.37e-07 125.8276
drunkdriverskilled
9
t-TestAccepting H0
Source SS df MS
Number of obs
4 -------------------------------------------
F( 1, 2) 10.11 Model
6.5849e-14 1 6.5849e-14 Prob gt
F 0.0863 Residual 1.3030e-14 2
6.5150e-15 R-squared
0.8348 ------------------------------------------
- Adj R-squared 0.7522 Total
7.8879e-14 3 2.6293e-14 Root
MSE 8.1e-08 -----------------------------
-------------------------------------------------
reg5normkid Coef. Std. Err. t
Pgtt 95 Conf. Interval -------------
-------------------------------------------------
--------------- reg5normdrk 90.53328
28.47673 3.18 0.086 -31.99218
213.0587 _cons 1.85e-07 5.11e-08
3.62 0.069 -3.50e-08 4.05e-07 ------------
--------------------------------------------------
----------------
Accept H0 t lt t2 ie. -4.303 lt 3.18 lt 4.303
10
Regression driverskilled 110.3849 1.27e-07
drunkdriverskilled
11
Testing1 Does alcohol affect the number of
drivers killed in car accidents?

• assumption
• Alcohol affects the number of people killed in
  car accidents BUT is not the only contributing
  factor.
• Younger people probably drink more irresponsibly
  so more likely to be involved and be responsible
  for fatal car accidents.

2 Does a combination of age and alcohol affect
the number of people (including drivers) killed
in car accidents?3 Do individual regions
mimic national data?
12
F-Test

• For each region
• H0 ?1 ?2 0
• H1 ?1 ? ?2 (at least one ? i ? 0)
• F-Test
• ? 0.05, 95 confidence
• 1-sided test

13
F-Test (2)Rejecting H0
Source SS df MS
Number of obs 11 -----------------
-------------------------- F( 2,
8) 8.22 Model 7.0241e-13 2
3.5121e-13 Prob gt F
0.0115 Residual 3.4191e-13 8
4.2739e-14 R-squared
0.6726 ------------------------------------------
- Adj R-squared 0.5908T Total
1.0443e-12 10 1.0443e-13 Root MSE
2.1e-07 ----------------------------------
-------------------------------------------- reg1n
ormkid Coef. Std. Err. t
Pgtt 95 Conf. Interval ------------
- -----------------------------------------------
---------------------- reg1normdrk 102.7064
39.55021 2.60 0.032 11.50342
193.9093 personskild -.0043674 .0144079
-0.30 0.770 -.037592 .0288572 _cons
2.69e-07 2.30e-07 1.17
0.275 -2.61e-07 7.99e-07 -----------------
--------------------------------------------------
-----------
Reject H0 F0.025, 2, 8 gt 4.46 ie.
8.22 gt 4.46
peoplekilled 2.69e-07 102.7064
drunkdrivers - .0043674 agekilled
14
F-Test Accepting H0
Source SS df MS
Number of obs 8 --------------------
----------------------- F( 2, 5)
3.64 Model 3.2398e-14 2 1.6199e-14
Prob gt F 0.1059 Residual
2.2270e-14 5 4.4540e-15
R-squared 0.5926 -------------------------
------------------ Adj R-squared
0.4297 Total 5.4668e-14 7 7.8097e-15
Root MSE 6.7e-08 ----------------
--------------------------------------------------
------------ reg3normkid Coef.
Std. Err. t Pgtt 95 Conf.
Interval ---------------------------------------
-------------------------------------- reg3normdr
k 394.0596 146.2681 2.69 0.043
18.06551 770.0537 agekilled
-.0011894 .0022405 -0.53 0.618
-.0069489 .0045701 _cons
1.38e-07 4.85e-08 2.85 0.036
1.36e-08 2.63e-07 -----------------------------
-------------------------------------------------
Accept H0 F0.025, 2, 5 lt 5.79 ie. 2.69 lt
5.79
driverskilled 1.38e-07 394.0596
drunkdrivers -.0011894 agekilled
15
Testing1 Does alcohol affect the number of
drivers killed in car accidents?

• assumption
• Alcohol affects the number of people killed in
  car accidents BUT is not the only contributing
  factor.
• Younger people probably drink more irresponsibly
  so more likely to be involved and be responsible
  for fatal car accidents.

2 Does a combination of age and alcohol affect
the number of people (including drivers) killed
in car accidents?3 Do individual regions
mimic national data?
16
Confidence Intervals (3)
Confidence Interval of the mean for the National
Data
National Mean of drivers killed 2.96763E-07
Confidence Interval
(2.12099E-07, 3.81428E-07)
(2.96763E-07 - 8.46641E-08 , 2.96763E-07
8.46641E-08)
17
Region Results with Confidence Intervals
Lies within National CI
Region
Mean
18
Graph of National Data
19
ANOVA Test

• H0 ?national ?reg 1 ?reg 2 ... ?reg 6
• The number of divers killed in car accidents is
  independent of the region in which they occur.
• Reject H0 if F gt F0.95, 3, 2 19.2
• F 7.7631 lt 19.2 so accept H0

20
Conclusions

• Nationally, 4 out of the 6 regions rejected the
  F-test null hypothesis gt there is a correlation
  between age, BAC, and the number of drivers
  killed.
• Regionally, 4 out 6 supported the national data
  trend. The regressions carried out confirm that
  the number of people killed depends on the number
  of drunk drivers.
• Regions do not reflect the national trend for the
  average number of drivers killed.
• The number of drivers killed does not depend on
  the region in which they occur.