Final answer:
To find the regression equation 'y = mx + b' for men, where 'x' is the number of years since 2000, we use a slope 'm' of approximately 0.09 and calculate the y-intercept 'b' as 35.25 using the provided median values. The regression equation is 'm(x) = 0.09x + 35.25'.
Step-by-step explanation:
The subject of the student's question involves the creation of a regression line equation using given statistical data. To find the line of best fit for the data related to men where 'x' represents the number of years since 2000 and 'y' represents the number of men, we use the linear equation form y = mx + b. Here, 'm' stands for the slope of the line, and 'b' is the y-intercept. From the provided information, the slope 'm' is approximately 0.09. To find the y-intercept 'b', we make use of the formula involving the sum of the median 'x' and 'y' values, which are 1264 and 219.5 respectively. Therefore, calculating 'b' gives us b = 219.5 - 0.09(1264), which simplifies to 35.25.
Thus, the complete regression equation for the given data is m(x) = 0.09x + 35.25, which represents the line of best fit according to the least-squares regression method. This equation can be used to predict the number of men for any given year since 2000 within the range of the data provided.