Car Accidents & Cell Phones

By: Hongtao XuSasha HochstadtLogan McLeodHeather SamovilleChristian HellandMeng Yu

Objective Why?• Recent Legislation

• Is it Valid? Justifiable?

What?• To determine a possible correlation between traffic fatalities and

cell-phone users

How?• Collect data of traffic fatalities and cell-phone subscription

• Setup valid model and find relationship between them

Initial Hypothesis

– Traffic accidents are increasing over time

– After the introduction of cell phones traffic accidents will increase at a higher rate

Gathered Data

• Estimated # of Cell Phone Subscribers 1985-2002

• Traffic Fatalities 1966-2000

• # of Registered Vehicles 1966-2000

• # of Licensed drivers 1966-2000

• Resident Population 1966-2000

• Fatality Rate per 100k Registered Vehicles 1966-2000

Cell Phone Subscribers 1985-2002

-

20,000,000

40,000,000

60,000,000

80,000,000

100,000,000

120,000,000

140,000,000

160,000,000

1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

Year

# o

f Su

bs

cri

be

rs

Annual Motor Vehicle Fatality Rate per 100K Registered Vehicles

10

15

20

25

30

35

40

45

50

55

6019

66

1967

1968

1969

1970

1971

1972

1973

1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

Year

Fa

tali

tie

s p

er

10

0,0

00

re

gis

tere

d v

eh

icle

s

Modified Hypothesis

• Findings:– Fatalities from car accidents are actually decreasing

over time– Cell phone subscribers are increasing exponentially

over time As fatalities continue to decrease over time, the

introduction cell phones will cause them to decrease at a slower rate

• In order to show this we must compare the periods before and after cell phone use

BeforeCellPhoneUse

AfterCellPhoneUse

Fatalities as a Function in % Change of Cell Phone Subscribers

Year

LN

(Fat

aliti

es)

Error

y = 6E+32e-0.0364x

R2 = 0.9308

18

23

28

33

38

43

48

53

58

1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985

Year

Fata

litie

s pe

r 100

,000

Reg

iste

red

Vehi

cles

y = 3E+22e-0.0245x

R2 = 0.9142

1985 1987 1989 1991 1993 1995 1997 1999 2001

Before Cell Phone After Cell Phone

Annual Motor Vehicle Fatalities per Registered Vehicles

Variable Coefficient

Std. Error

t-Statistic Prob.

C 75.55324 4.620644 16.35124 0YEAR1 -0.036407 0.002339 -15.56541 0

R-squared 0.930844 3.631358Adjusted R-squared

0.927002 0.223244

S.E. of regression 0.060316 -2.68379

Sum squared resid

0.065485 -2.58422

Log likelihood 28.83791 242.2818

Durbin-Watson stat

0.92692 0

Dependent Variable: LOG(FATALITY1)Method: Least SquaresDate: 11/26/02 Time: 18:09Sample: 1 20Included observations: 20

Mean dependent S.D. dependent

Akaike info

Schwarz criterion

F-statistic

Prob(F-statistic)

Variable Coefficient

Std. Error t-Statistic Prob.

C 53.46605 4.441925 12.03668 0YEAR2 -0.02527 0.002229 -11.33718 0

R-squared 0.908148 3.10726Adjusted R-squared

0.901082 0.118578

S.E. of regression 0.037294 -3.61639

Sum squared resid

0.018081 -3.52198

Log likelihood 29.12292 128.5316

Durbin-Watson stat

0.421127 0

Akaike info

Schwarz criterion

F-statistic

Prob(F-statistic)

Dependent Variable: LOG(FATALITY2)Method: Least SquaresDate: 11/26/02 Time: 18:13Sample(adjusted): 1 15Included observations: 15 after adjusting endpoints

Mean dependent S.D. dependent var

LN(FATALITY) = 75.5532 - 0.0364069*YEAR LN(FATALITY) = 53.4660 - 0.0252678*YEAR

Before Cell Phone After Cell Phone

Regression Results in time series

Quantifying the Cell Phone Effect

• Extrapolate pre-cell phone regression into cell phone regression

• Calculate expected # of fatalities and % difference from actual

• Find relationship between % error and # of cell phone subscribers

% Error in Expected Number of Fatalities

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

1965 1970 1975 1980 1985 1990 1995 2000

Year

% E

rro

r

Region of Dramatic Deviation from Expected Values.

Impact of Cell-Phone Subscribers on % Error in Estimated Fatalities

0

0.05

0.1

0.15

0.2

0.25

0.3

0 20,000,000 40,000,000 60,000,000 80,000,000 100,000,000

# of Cell-Phone Subscribers

% E

rro

r

Results

-0.02

-0.01

0.00

0.01

0.02

0.030.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2 3 4 5 6 7 8 9 10

Residual Actual Fitted

FATALITY = -1.309 + 0.08443*LOG(CELLPHONE)

Dependent Variable: FATALITY Method: Least Squares Date: 11/26/02 Time: 16:54 Sample: 1 10 Included observations: 10

Variable Coefficient Std. Error t-Statistic Prob.

C -1.309085 0.073278 -17.86472 0.0000 LOG(CELLPHONE) 0.084429 0.004264 19.79814 0.0000

R-squared 0.979998 Mean dependent var 0.139765 Adjusted R-squared 0.977498 S.D. dependent var 0.079272 S.E. of regression 0.011891 Akaike info criterion -5.849160 Sum squared resid 0.001131 Schwarz criterion -5.788643 Log likelihood 31.24580 F-statistic 391.9665 Durbin-Watson stat 2.053131 Prob(F-statistic) 0.000000

Results

Conclusions

• A strong correlation between cell phone subscriptions & fatality rate exists.

• Our model exhibits a logarithmic relationship.

• We estimate that since 1991, cell phones have caused more than 40,000 deaths.

Questions?