Question

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.

Age   Number_of_Male_Licensed_Drivers_(000s), Number_of_Fatal_Crashes, Number_of_Female_Licensed_Drivers0000s), Number_of_Fatal_Crashes
<_16   12   227   12   77
16-20   6424   5180   6139   2113
21-24   6936   5016   6816   1550
25-34   18068   8565   17664   2780
35-44   20406   7990   20061   2742
45-54   19898   7126   19984   2285
55-64   14363   4527   14441   1514
65-74   8194   2274   8398   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?

(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?

Answer 1

For males

Step 1 - Put the data in excel as shown and arrange the variables as shown

Step 2 - Select the regression option from the data analysis tab

Step 3- Input the values as shown below.

Step 4 - The output is generated as follows.

The regression equation ( This equation is obtained from coefficient of the regression output. Highlighted in yellow)

a. Regression equation

Number_of_Fatal_Crashes = 1000.759 + 0.3422 Number_of_Male_Licensed_Drivers_(000s)

An increases 0f 1000 males drivers increase the number of fatal crashes by 0.3422

For females
Step 1 - Put the data in excel as shown and arrange the variables as shown

Step 2 - Select the regression option from the data analysis tab

Step 3- Input the values as shown below.

Step 4 - The output is generated as follows.

The regression equation ( This equation is obtained from the coefficient of the regression output. Highlighted in yellow)

a. Regression equation

Number_of_Fatal_Crashes = 512.3959 + 0.1040 Number_of_Female_Licensed_Drivers_(000s)

An increases 0f 1000 females drivers increase the number of fatal crashes by 0.1040

Hence the insurance company must take note that the increases in males drivers causes more fatal crashes than female drivers.

(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?