# Question

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.

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.

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