A financial analyst is examining the relationship between stock prices and earnings per share. She chooses sixteen publicly traded companies at random and records for each the company's current stock price and the company's earnings per share reported for the past 12 months. Her data are given below, with x denoting the earnings per share from the previous year and y denoting the current stock price (both in dollars). A scatter plot of her data is shown in Figure 1. Also given is the product of the earnings per share and the current stock price for each of the sixteen stocks. (These products, written in the column labelled "xy", may aid in calculations.)
Earnings per share, x (in dollars) | Current stock price, y (in dollars) | xy
37.01 | 1.60 | 59.216
28.93 | 0.89 | 25.7477
21.13 | 0.47 | 9.9311
16.48 | 0.59 | 9.7232
41.67 | 1.54 | 64.1718
59.58 | 2.74 | 163.2492
26.52 | 0.98 | 25.9896
57.45 | 2.11 | 121.2195
47.55 | 1.63 | 77.5065
53.38 | 2.66 | 141.9908
37.07 | 1.05 | 38.9235
42.12 | 0.94 | 39.5928
28.66 | 1.32 | 37.8312
13.73 | 0.32 | 4.3936
43.09 | 1.77 | 76.2693
31.65 | 1.75 | 55.3875
Figure 1
What is the sample correlation coefficient for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least three decimal places. (If necessary, consult a list of formulas.)