Final answer:
The question is about estimating the life expectancy of people born in different years using linear regression and the analysis of trends through the least-squares line method in Mathematics.
Step-by-step explanation:
The subject of this question is Mathematics, specifically related to statistics and linear regression analysis. The problem involves understanding life expectancy trends and using the least-squares line, a statistical tool, to make predictions and analyze the relationship between years and life expectancy.
For part j, we are asked to estimate the life expectancy for an individual born in 1850 using a least-squares line or a best-fit line. We first need the equation of the best-fit line (which could have been calculated using data points in previous parts of the question). However, because we are extrapolating to a year much earlier than the data provided, the estimate is likely to be inaccurate. The least-squares line is most accurate for prediction within the range of the data it was constructed from, called interpolation, not extrapolation to dates before or beyond the given data.
For parts e through c, the student is tasked with calculating the least-squares line equation and using it to find the life expectancy for individuals born in 1950 and 1982. The slope of the least-squares line (part k) represents the average increase in life expectancy per year since 1980, allowing us to understand the general trend in life expectancy growth over time. The correlation coefficient mentioned in part d would help assess the strength of the linear relationship between the year of birth and life expectancy.
The difference between men's and women's life expectancies is also a factor, with women generally having a longer life expectancy as indicated in the given information. This can be observed through frequency tables and related statistical analyses (part 20).