4.2 The following table gives the winning times (in seconds)

for the men's 400 meters final in each Olympic Games from 1896 to 2012 (data set olympic).

1896 54.2 1928 47.8 1964 45.1 1992 43.50 1900 49.4 1932 46.2 1968 43.8 1996 43.49 1904 49.2 1936 46.5 1972 44.66 1908 50.0 1948 46.2 1976 44.27 1912 48.2 1952 45.9 1980 44.60 1920 49.6 1956 46.7 1984 44.27 1924 47.6 1960 44.9 1988 43.87

(a) Update the data set olympic to include the winning times from the last few Olympics.

(b) Plot the winning time against the year. Describe the main features of the scatterplot.

(c) Fit a regression line to the data. Obviously the winning times have been decreasing, but at what average rate per year?

(d) Plot the residuals against the year. What does this indicate about the suitability of the fitted line?

(e) Predict the winning time for the men's 400 meters final in the 2000, 2004, 2008 and 2012 Olympics. Give a prediction interval for each of your forecasts. What assumptions have you made in these calculations?

(f) Find out the actual winning times for these Olympics (see www. databaseolympics. com).
How good were your forecasts and prediction intervals?