Class Activity #7

Given below are the winning times in seconds for the men’s 1500-meter run in the Olympics from 1900 to 1968:

Year, x	1900	1904	1908	1912	1920	1924	1928	1932	1936	1948	1952	1956	1960	1964	1968
Time, y	246.0	245.4	243.4	236.8	241.8	233.6	233.2	231.2	227.8	229.8	225.2	221.2	215.6	218.1	214.9

1. Use the TI-83 to help you construct the scatterplot.
2. Describe the overall pattern. Is there an outlier?
3. Based on the scatterplot, do you expect the correlation to be positive or negative? near ±1 or not?
4. Compute the correlation r.
5. Predict the winning time for 1992. The actual time is 220.1. Is there a discrepancy. If so, why?

Adapted from http://www.uoregon.edu/~qmshao/fall98/243ch2.pdf

ANSWERS:

1. Here is the scatterplot:
   
2. The pattern seems to be strongly linear. There does not seem to be any outliers.
3. Based on the scatterplot, I expect the correlation to be negative and near –1.
4. r = 0.97.
5. The general linear regression line is: . The linear regression model for this data is: = –0.45 x + 1096. Thus, the predicted winning time for the 1992 Olympics is: = –0.45 (1992) + 1096 = 205 seconds.