59. The authors of the paper Objective Effects of a Six Months Endurance and Strength Training Program in Outpatients with Congestive Heart Failure (Med.

Sci. Sports Exercise, 1999: 1102—1107) presented a correlation analysis to investigate the relationship between maximal lactate level x and muscular endurance y. The accompanying data was read from a plot in the paper.

yi  47.92, y2i

 130.6074, xiyi  5530.92 n  18, xi  1950, x2i

 251,970, x 400 750 770 800 850 1025 1200 y 3.80 4.00 4.90 5.20 4.00 3.50 6.30 x 1250 1300 1400 1475 1480 1505 2200 y 6.88 7.55 4.95 7.80 4.45 6.60 8.90 A scatter plot shows a linear pattern.

a. Test to see whether there is a positive correlation between maximal lactate level and muscular endurance in the population from which this data was selected.

b. If a regression analysis were to be carried out to predict endurance from lactate level, what proportion of observed variation in endurance could be attributed to the approximate linear relationship?

Answer the analogous question if regression is used to predict lactate level from endurance and answer both questions without doing any regression calculations.