Ted Thorndike's friend Mary Stuart teaches a statistics course at the local university, and she has asked Ted to stop in and talk to the class about statistics as it relates to sports. Among the topics that Ted thinks might be interesting is a discussion of how Olympic swimming performances for both men and women have improved over the years.

According to Ted, swimmers and other athletes have been getting bigger, faster, and stronger. In addition, training technologies and equipment have im proved by leaps and bounds. Among the data that Ted has collected are the winning times for men and women in the 400-meter freestyle swimming event for Olympics held from 1924 through 2008. The times are shown here and are also listed in data file THORN15. Source: Time Almanac 2009, pp. 841, 842.

1. Using the women's winning time as the dependent variable and year as the independent variable, determine and interpret both the regression equation and the coefficient of correlation. For the year 2016, determine the point estimate and the 95% prediction interval for the winning time in the women's 400-meter freestyle.

2. Repeat question 1, using the men's winning time as the dependent variable.

3. Using the women's winning time as the dependent variable and the men's winning time as the independent variable, determine and interpret both the regression equation and the coefficient of correlation. If the men's winning time were 3.600 minutes in a given Olympics, determine the point estimate and the 95% prediction interval for the winning time in the women's event.

4. For the regression equation obtained in question 3, use a test of your choice in examining the significance of the linear relationship between the variables.