2. Auto Accidents: Whats responsible? Math 70: Group Project Group 8 Janelle Chang Helena Jeanty Rhiana Quail

3. DISCLAIMER!!! Weather conditions Drivers mental health Drivers physical health Time of day Time of year

4. 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

5. 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.

6. 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?

7. t-Test For each region: H 0 : tot. drivers killed = drunk drivers killed H 1 : tot. drivers killed drunk drivers killed t-Test: » = 0.05, 95% confidence »2-sided test » df = (# obs) - 1

8. t-Test (#1) Rejecting H 0 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 H 0 : | t| > t 15 ie. 6.36 > 2.131

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

10. t-Test Accepting H 0 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 H 0 : | t| < t 2 ie.-4.303 < 3.18 < 4.303

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

12. 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?

13. F-Test For each region: H 0 : 1 = 2 = 0 H 1 : 1 2 (at least one i 0) F-Test: = 0.05, 95% confidence 1-sided test

14. F-Test (#2) Rejecting H 0 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 H 0 : F 0.025, 2, 8 > 4.46 ie. 8.22 > 4.46 peoplekilled = 2.69e-07 + 102.7064 * drunkdrivers -.0043674 * agekilled

15. F-Test Accepting H 0 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 H 0 :F 0.025, 2, 5 < 5.79 ie. 2.69 < 5.79 driverskilled = 1.38e-07 + 394.0596 * drunkdrivers -.0011894 * agekilled

16. 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?

17. 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

18. Region Results with Confidence Intervals RegionMean Lies within National CI

19. Graph of National Data

20. ANOVA Test H 0 : 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 H 0 if F > F 0.95, 3, 2 = 19.2 F = 7.7631 < 19.2 so accept H 0

21. 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.