Number of Number of Number of Age Group Number of Male Licensed Drivers Crashes Female Licensed Crashes Involving a M Drive Involving a F 16 816 244 764 178 17 1198 233 1115 175 18 1342 243 1212 164 19 1454 229 1333 145 20-24 7866 951 7394 618 25-29 9356 899 8946 595 30-34 10121 875 9871 571 35-39 10521 901 10439 566 40-44 9776 692 9752 455 45-49 8754 667 8710 390 50-54 6840 390 6763 247 55-59 5341 290 5258 165 60-64 4565 218 4486 133 65-69 4234 191 4231 121 70-74 3604 167 3749 104 75-79 2563 118 2716 77 80-84 1400 61 1516 45 > 85 767 34 767 20 Male versus Female drivers The data given represents the number of licensed drivers in various age groups and the number of accidents within the age group by gender. a. Draw scatterplots for male and female separately, treating number of licensed drivers as the explanatory variable, x, and the number of crashes, y, as the response variable. Describe the pattern, (form, strength, and direction) that you observe in the scatterplots. b. Find the value of Pearson's linear correlation coefficient for each gender and test if they are significant using critical value from the table. Write your conclusions. c. Find the coefficient of determination for both the data. Write you interpretation of them. d. Find the least square regression line for males, treating number of licensed drivers as the explanatory variable, x, and the number of crashes, y, as the response variable. e. Repeat the above procedure of part (c) for females. f. Interpret the slope of the regression line for each gender, if appropriate. How might an insurance company use this information? g. Predict the number of accidents for males if there were 8700 thousand licensed drivers. Predict the number of accidents for females if there were 8700 thousand licensed drivers. Compare the results for males and females and explain. h. Draw residual plots for males and females and describe the plots. Does the plot suggest that the linear fit is good for the data?