The accompanying data on x = UV transparency index and y = maximum prevalence of infection was read from a graph in the article "Solar Radiation Decreases Parasitism in Daphnia" (Ecology Letters, 2012: 47-54):

Summary quantities include Sxx = 25.5224, Syy = 5593.0588, and Sxy = 264.4882.
a. Calculate and interpret the value of the sample correlation coefficient.
b. If you decided to fit the simple linear regression model to this data, what proportion of observed variation in maximum prevalence could be explained by the model relationship?
c. If you decided to regress UV transparency index on maximum prevalence (i.e., interchange the roles of x and y), what proportion of observed variation could be attributed to the model relationship?
d. Carry out a test of H0: ( = .5 versus Ha: ( > 5 using a significance level of .05. [The cited article reported the P-value for testing H0: ((= 0 versus H0: ( ‰  0.]

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