4.10 Coral Reefs. Exercise 4.2 discusses a study in which scientists examined data on mean sea surface temperatures (in degrees Celsius) and mean coral growth (in centimeters per year) over a several-year period at locations in the Gulf of Mexico and the Caribbean. Here are the data for the Gulf of Mexico: Sea surface temperature Growth 26.1 26.7 26.6 26.6 26.5 26.3 0.85 0.85 0.79 0.86 0.89 0.92

(a) Make a scatterplot. Which is the explanatory variable? The plot shows a negative linear pattern.

(b) Find the correlation r step by step. You may wish to round off to two decimal places in each step. First, find the mean and standard deviation of each variable. Then, find the six standardized values for each variable. Finally, use the formula for r. Explain how your value for r matches your graph in part (a).

(c) Enter these data into your calculator or software, and use the correlation function to find r. Check that you get the same result as in part (b), up to roundoff error. CORAL