Question

In: Statistics and Probability

The data in the table represent the number of licensed drivers in various age groups and...

The data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts​ (a) to​ (c) below.

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<_16   12   227   12   77
16-20   6424   5180   6139   2113
21-24   6936   5016   6816   1537
25-34   18068   8587   17664   2780
35-44   20406   7990   20048   2742
45-54   19898   7138   19984   2285
55-64   14324   4527   14441   1514
65-74   8194   2274   8376   938
>_74   4803   2022   5375   957

​(a) Find the​ least-squares regression line for males treating the number of licensed drivers as the explanatory​ variable, x, and the number of fatal​ crashes, y, as the response variable. Repeat this procedure for females.

​(b) Interpret the slope of the​ least-squares regression line for each​ gender, if appropriate. How might an insurance company use this​ information?

What is the correct interpretation of the slope of the​ least-squares regression line for​ males? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

​(c) Was the number of fatal accidents for 16 to 20 year old males above or below​ average? Was the number of fatal accidents for 21 to 24 year old males above or below​ average? Was the number of fatal accidents for males greater than 74 years old above or below​ average? How might an insurance company use this​ information? Does the same relationship hold for​ females?

Solutions

Expert Solution

(a)

1. Least square regression line for males is y = ???x+ ???

2. Least square regression line for females is y = ???x+ ???

(b) (1) If the number of male licensed drivers increases by 1 (thousand), then the number of fatal crashes increases by 0.342 on average. (round to 4 decimals)

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(b2)
(2) If the number of female licensed drivers increases by 1 (thousand), then the number of fatal crashes increases by 0.104 on average.

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(c) The slope of the regression line for males is greater than as that for females. This means that males tend to be involved in (more fatal as females. An insurance company may use this information to argue for ???.


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(c2) The number of fatal accidents for 16 to 20 year old males was (abovbe average/below average).The number of fatal accidents for 21 to 24 year old males was (above avergae/below average). The number of fatal accidents for males greater than 74 years was (above avergae/below average).


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(c3) Does the same relationship hold true for females?

Yes.

orchestra answered 3 years ago
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