132 Sports participation survey. The Sasakawa Sports Foundation conducted a national survey to assess the physical activity patterns of Japanese adults. The next table lists the frequency (average number of days in the past year) and the amount of time (average number of minutes per single activity) Japanese adults spent participating in a sample of 11 sports activities. The data are saved in the JAPANSPORTS file.

a. Write the equation of a straight-line model relating duration ( y ) to frequency ( x ).

b. Find the least squares prediction equation.

c. Is there evidence of a linear relationship between y and x ? Test, using a = .05.

d. Use the least squares line to predict the amount of time Japanese adults participate in a sport that they play 25 times a year. Form a 95% confidence interval around the prediction and interpret the result.

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Activity Frequency x (days/years) Amount of Time y (minutes) Jogging Cycling 135 43 68 99 Aerobics 44 61 Swimming 39 60 Volleyball 30 80 Tennis 21 100 Softball 16 91 Baseball 19 127 Skating 7 115 Skiing 10 249 Golf 5 262 Based on J. Bennett, ed. Statistics in Sport. London: Arnold, 1998 (adapted from Figure 6).