SOLUTION: 1. A study is conducted to determine the relationship between a driver’s age and the number of accidents he/she has over a 1-year period. The data are shown below. Test the sig

Algebra ->  Probability-and-statistics -> SOLUTION: 1. A study is conducted to determine the relationship between a driver’s age and the number of accidents he/she has over a 1-year period. The data are shown below. Test the sig      Log On


   

Question 1187775: 1. A study is conducted to determine the relationship between a driver’s age and the number of
accidents he/she has over a 1-year period. The data are shown below. Test the significance of the
correlation coefficient at
a= 0.01.
Driver’s age (x) = 16 24 18 17 23 27 32
No.of accidents (y) =3 2 5 2 0 1 1
a. Draw the scatter plot.
b. Compute the value of the correlation coefficient.
c. Test the significance of the correlation coefficient at a = 0.01.
d. Determine the regression line equation.
e. Predict the number of accidents of a driver who is 28.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the following regression tool ill help you answer at least some of these questions.

https://www.graphpad.com/quickcalcs/linear1/

hee are the results.





answers to some of your requirements and questions are showon below:

a. Draw the scatter plot.

the scatter plot with the linear regression line are shown above.
they indicate a negative correlation, i.e. as the age of the driver goes up, the number of accidents over a one year period goes down.

b. Compute the value of the correlation coefficient.

this software shows the R^2, which is a goodness of fit indicater.
the correlation coefficient is equal to the square root of the goodness of fit indicator.
it also takes the sign of the correlation into account.
R^2 = .3722.
R = plus or minus sqrt(.3722) = minus .61008, in this case.

c. Test the significance of the correlation coefficient at a = 0.01.

the p-value of the correlation is .1458.
this is well above the critical p-value of plus or minus .01.
this indicates the results of the correlation are not significant.

d. Determine the regression line equation.

the regression line equation is y = -.1701 * x + 5.816.
the slope of the line is equal to -.1701.
the y-intercept of the line is equal to 5.816.

e. Predict the number of accidents of a driver who is 28.

to predict the number of accidents in a 1 year time, replace x in the regression equation with 28 and solve for y.

you get:

y = -.1701 * 28 + 5.98 = 1.0532.

the prediction is that a driver who is 28 years old will have approximately 1.0532 accidents, on average, in one year's time.