The following table gives the completion times for the winners in the women’s 200-meter dash finals in the Summer Olympic Games from 1972 to 2008. The times are in seconds rounded to the nearest 1/100 second.
Olympic Year Time (seconds)
1972.............. 22.40
1976.............. 22.37
1980.............. 22.03
1984.............. 21.81
1988.............. 21.34
1992.............. 21.81
1996.............. 22.12
2000.............. 21.85
2004.............. 22.05
2008.............. 21.74
a. Assign a value of 0 to 1972, 1 to 1976, 2 to 1980, and so on. Call this new variable Year. Make a new table with the variables Year and Time.
b. With year as an independent variable and time as the dependent variable, compute SSxx, SSyy, and SSxy.
c. Construct a scatter diagram for these data. Does the scatter diagram exhibit a linear negative relationship between year and time?
d. Find the least squares regression line
e. Give a brief interpretation of the values of a and b calculated in part d.
f. Compute the correlation coefficient r.
g. Predict the time for the year 2016. Comment on this prediction.