Auto accidents what s responsible
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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:

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Auto Accidents: What’s responsible?

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Auto accidents what s responsible

Auto Accidents: What’s responsible?

Math 70: Group Project

Group 8

Janelle Chang

Helena Jeanty

Rhiana Quail


Disclaimer

DISCLAIMER!!!

  • Weather conditions

  • Drivers’ mental health

  • Drivers’ physical health

  • Time of day

  • Time of year


Sorting the data

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

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

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

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 h 0

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

Regression:driverskilled = 1.37e-07+ 125.8276 * drunkdriverskilled


T test accepting h 0

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 > 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

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

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

Regression: driverskilled = 110.3849 + 1.27e-07 *drunkdriverskilled


Testing 1 does alcohol affect the number of drivers killed in car accidents1

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

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 h 0

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 > 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

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

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 h 0

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 > 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

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

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 accidents2

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 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)


Region results with confidence intervals

Region Results with Confidence Intervals

Lies within National CI

Region

Mean


Graph of national data

Graph of National Data


Anova test

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

    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.


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