In a bit of good news for male students, American men have closed the gap with women on life span, according to a USA Today article. Male life expectancy attained a record 75.2 years, and women’s reached 80.4. The National Center for Health Statistics provided the data given in the file titled Life.
a. Produce a scatter plot depicting the relationship between the life expectancy of women and men.
b. Determine the order of the polynomial that is represented on the scatter plot obtained in part a. Produce the estimated regression equation that represents this relationship.
c. Determine if women’s average life expectancy can be used in a second-order polynomial to predict the average life expectancy of men. Use a significance level of 0.05.
d. Use the estimated regression equation computed in part b to predict the average length of life of men when women’s length of life equals 100. What does this tell you about the wisdom (or lack thereof) of extrapolation in regression models?