Question

The following data is a regression model where the U.S. Department of Transportation has tried to relate the rate of fatal traffic accidents (per 1000 licenses) to the percentage of motorists under the age of 21. Data has been collected for 42 major cities in the United States. SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.83938748 0.70457134 0.69718562 0.58935028 42 ANOVA df MS Regression Residual Total 33.13441764 33.1344 95.3964 13.89335048 0.34733 47.02776812 40 Coefficients Standard Error t Stat P-value Intercept Percent Under 21 1.5974138 0.28705317 0.029389769 9.76711 3.79E-9 0.371671454 -4.2979 0.00010 a.) What percentage of the variability in fatality rates can be attributed to variations in the percentage of motorists under the age of 21? b.) If a city had 10% of its motorists under the age of 21, how many fatalities should it expect for every 1000 licenses it issues? c.) Test the notion that the percentage of motorists under 21 does not impact the fatality rate, against the notion that it does impact the rate, using an α = .01

Answer 1

Ans:

a)Coefficient of determination,R^2=0.7046 or 70.46%

Which indicates that 70.46% of the variation in fatality rates can be attributed to variations in percentage of motorists under the age 21.

b)

Fatality rate=-1.597+0.28705*percent under 21

when percent under 21=10%

Fatality rate=-1.597+0.28705*10=1.2735

c)

Test statistic:

t=0.28705/0.02939

t=9.767

p-value=0.0000

As,p-value<0.01,we reject the null hypothesis.

There is sufficient evidence to conclude that percentage of motorists under 21 impact the fatality rate.