Auto Accidents: What’s
responsible?
Group 8
Janelle Chang
Helena Jeanty
Rhiana Quail
DISCLAIMER!!!
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Weather conditions
Drivers’ mental health
Drivers’ physical health
Time of day
Time of year
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
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.
Testing
#1: 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?
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
t-Test (#1)
Rejecting H0
Source |
SS
df
MS
-------------+-----------------------------Model
| 1.1071e-12 1
1.1071e-12
Residual | 4.1075e-13 15
2.7383e-14
-------------+-----------------------------Total
| 1.5179e-12 16
9.4868e-14
Number of obs =
17
F( 1, 15) = 40.43
Prob > F
= 0.0000
R-squared = 0.7294
Adj R-squared = 0.7114
Root MSE
= 1.7e-07
-----------------------------------------------------------------------------reg1normki~d |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
------------+---------------------------------------------------------------reg1normdr~k | 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| > t15
ie. 6.36 > 2.131
Regression:
driverskilled = 1.37e-07+ 125.8276 * drunkdriverskilled
t-Test
Accepting H0
Source |
SS
df
MS
-------------+-----------------------------Model | 6.5849e-14 1 6.5849e-14
Residual | 1.3030e-14 2 6.5150e-15
-------------+-----------------------------Total
| 7.8879e-14 3 2.6293e-14
Number of obs =
4
F( 1, 2) = 10.11
Prob > F = 0.0863
R-squared = 0.8348
Adj R-squared = 0.7522
Root MSE = 8.1e-08
-----------------------------------------------------------------------------reg5normki~d
| Coef.
Std. Err. t
P>|t| [95% Conf. Interval]
-------------+---------------------------------------------------------------reg5normdr~k
| 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| < t2
ie.
-4.303 < 3.18 < 4.303
Regression:
driverskilled = 110.3849 + 1.27e-07 *drunkdriverskilled
Testing
#1: 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?
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
F-Test (#2)
Rejecting H0
Source
|
SS
df
MS
-------------+-----------------------------Model
| 7.0241e-13
2 3.5121e-13
Residual | 3.4191e-13
8 4.2739e-14
-------------+-----------------------------Total
| 1.0443e-12 10 1.0443e-13
Number of obs =
F( 2, 8) = 8.22
Prob > F
= 0.0115
R-squared = 0.6726
Adj R-squared = 0.5908T
Root MSE
= 2.1e-07
11
-----------------------------------------------------------------------------reg1normki~d |
Coef.
Std. Err.
t
P>|t| [95% Conf. Interval]
------------- -----+---------------------------------------------------------------reg1normdr~k | 102.7064 39.55021 2.60 0.032 11.50342 193.9093
personskil~d | -.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 > 4.46
ie. 8.22 > 4.46
peoplekilled = 2.69e-07 + 102.7064 * drunkdrivers
- .0043674 * agekilled
F-Test
Accepting H0
Source
|
SS
df
MS
-------------+-----------------------------Model
| 3.2398e-14 2 1.6199e-14
Residual | 2.2270e-14 5 4.4540e-15
-------------+-----------------------------Total
| 5.4668e-14 7 7.8097e-15
Number of obs = 8
F( 2, 5) = 3.64
Prob > F
= 0.1059
R-squared = 0.5926
Adj R-squared = 0.4297
Root MSE
= 6.7e-08
-----------------------------------------------------------------------------reg3normki~d |
Coef.
Std. Err.
t
P>|t| [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 < 5.79
ie.
2.69 < 5.79
driverskilled = 1.38e-07 + 394.0596 * drunkdrivers -.0011894 * agekilled
Testing
#1: 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?
Confidence Intervals (#3)
Confidence Interval of the mean for the National Data
National Mean of drivers killed:
2.96763E-07
Confidence Interval
(2.96763E-07 - 8.46641E-08 , 2.96763E-07 + 8.46641E-08)
(2.12099E-07, 3.81428E-07)
Region Results with Confidence Intervals
Region
Mean
Lies within
National CI
1
2.92972E-07
Yes
2
1.082E-07
No
3
1.40915E-07
No
4
3.847E-07
No
5
2.8484E-07
Yes
6
6.16645E-07
No
Graph of National Data
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 > F0.95, 3, 2 = 19.2
• F = 7.7631 < 19.2 so accept H0
Conclusions
• Nationally, 4 out of the 6 regions rejected the Ftest null hypothesis => 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.