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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!!!. 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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  1. Auto Accidents: What’s responsible? Math 70: Group Project 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. 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?

  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 > 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

  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 > 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

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

  11. 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?

  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 > 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

  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 > 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

  15. 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?

  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 > F0.95, 3, 2 = 19.2 • F = 7.7631 < 19.2 so accept H0

  20. 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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