Question: Many attempts have been made to relate happiness with various factors. One such study relates happiness with age and finds that holding everything else constant, people are least happy when they are in their mid-40s (The Economist, December 16, 2010). The accompanying table shows a portion of data on a respondent's age and his/her perception of well-being on a scale from 0 to 100; the complete data are on the text website, labeled Happiness and Age.
a. Calculate and interpret the sample correlation coefficient between age and happiness.
b. Is the population correlation coefficient statistically significant at the 1% level?
c. Construct a scatter plot to point out a flaw with the above correlation analysis.