Question: The winning time in the Olympic men's 500-meter speed skating race over the years 1924 to 2006 can be described by the following regression equation:
Winning time = 272.63 - 0.1184 (Year)
Note: Beginning with the 1998 Olympics each competitor skated twice and the average of the two times defined the winner. In this analysis the data used for the relevant years is the average of the two times for the winner.
a. Is the correlation between winning time and year positive or negative? Explain how you know, and explain what that means in the context of this situation.
b. In 2010, the actual winning time for the gold medal was 34.91 seconds. Use the regression equation to predict the winning time for 2010, and compare the prediction to what actually happened.
c. Explain what the slope of -0.1184 indicates in terms of how winning times change from one set of Olympic games to the next. Olympic games occur every 4 years.
d. Why should we not use this regression equation to predict the winning time for the men's 500-meter speed skating race in the 2080 Winter Olympics?