Auto Accidents: What’s responsible?

Math 70: Group Project

Group 8

Janelle Chang

Helena Jeanty

Rhiana Quail

DISCLAIMER!!!

• 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-TestFor 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 Number of obs = 17-------------+------------------------------ F( 1, 15) = 40.43 Model | 1.1071e-12 1 1.1071e-12 Prob > 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

------------------------------------------------------------------------------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

y vs x with regression linereg1normdrunk

reg1normkilled Fitted values

8.7e-12 6.4e-09

2.8e-08

9.4e-07

t-TestAccepting H0

Source | SS df MS Number of obs = 4-------------+------------------------------ F( 1, 2) = 10.11Model | 6.5849e-14 1 6.5849e-14 Prob > F = 0.0863Residual | 1.3030e-14 2 6.5150e-15 R-squared = 0.8348-------------+------------------------------ Adj R-squared = 0.7522Total | 7.8879e-14 3 2.6293e-14 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

y vs x with regression linereg5normdrunk

reg5normkilled Fitted values

7.4e-11 3.5e-09

1.0e-07

5.0e-07

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-TestFor each region:

• H0: 1 = 2 = 0

• H1: 1 2 (at least one i 0)

• F-Test: = 0.05, 95% confidence1-sided test

F-Test (#2)Rejecting H0

Source | SS df MS Number of obs = 11-------------+------------------------------ F( 2, 8) = 8.22Model | 7.0241e-13 2 3.5121e-13 Prob > F = 0.0115Residual | 3.4191e-13 8 4.2739e-14 R-squared = 0.6726-------------+------------------------------ Adj R-squared = 0.5908TTotal | 1.0443e-12 10 1.0443e-13 Root MSE = 2.1e-07

------------------------------------------------------------------------------reg1normki~d | Coef. Std. Err. t P>|t| [95% Conf. Interval]------------- -----+----------------------------------------------------------------reg1normdr~k | 102.7064 39.55021 2.60 0.032 11.50342 193.9093personskil~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 Number of obs = 8-------------+------------------------------ F( 2, 5) = 3.64Model | 3.2398e-14 2 1.6199e-14 Prob > F = 0.1059Residual | 2.2270e-14 5 4.4540e-15 R-squared = 0.5926-------------+------------------------------ Adj R-squared = 0.4297Total | 5.4668e-14 7 7.8097e-15 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 770.0537agekilled | -.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

(2.96763E-07 - 8.46641E-08 , 2.96763E-07 + 8.46641E-08)

Confidence Interval

(2.12099E-07, 3.81428E-07)

National Mean of drivers killed: 2.96763E-07

Region Results with Confidence Intervals

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

Region MeanLies within National CI

Graph of National Data

National

0

0.0000002

0.0000004

0.0000006

0.0000008

0.000001

0.0000012

0.0000014

0 2 4 6

Region

Drivers Killed

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 F-test 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.