A financial analyst is examining the relationship between stock prices and earnings per share. She chooses fteen 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 Based on these data, she computes the least-squares regression line to be Iv = 0.214+0.045x. This line, along with a scatter plot of her data, is shown below. Earnings per share, x Current stock price, y (in dollars) (in dollars) x 0 -. .2 hr. 3-- x 9 U ru 0 = 3 g 1 __ XX X X 55 1 x x E x U x 'L- 2!: 3:0 4L 5-L 6:0 Earnings per share 37.25 1.15 (in dollars) 16.41 0.66 19.68 0.66 Send data to calculator v Based on the analyst's data and regression line, complete the following. (a) For these data, values For earnings per share that are greater than the mean of the values for earnings per share tend to be paired with current stock prices that are |(Choose one) Y | the mean of the current stock prices. (b) According to the regression equation, for an increase of one dollar in earnings per share, there is a corresponding increase of how many dollars in current stock price? D Sir Francis Galton, in the late 18005, was the rst to introduce the statistical concepts of regression and correlation. He studied the relationships between pairs 55 of variables such as the size of parents and the size of their offspring. Data similar to that which he studied are given below, with the variable x denoting the height (in centimeters) of a human father and the variabley denoting the height at maturity (in centimeters) of the father's oldest son. The data are given in tabular form and also displayed in the Figure 1 scatter plot. Also given is the product of the father's height and the son's height for each of the fifteen pairs. (These products, written in the column labelled ".T_}-"', may aid in calculations.) Height of Height of son, father, .1: y (in (in centimeters) centimeters) 37,533.54 31,0432 171.9 172.6 29,669.94 184.7 188.1 34,742.07 26,671.32 31,052.53 193.4 191.1 36,958.74 189.3 176.2 33,354.66 27,469.52 35,435.66 201.2 189.9 38,207.88 180.8 188.3 34,044.64 175.5 175.7 27,548.25 30,835.35 181.9 176.5 32,105.35 Cnnrl rlnh in r-'Irlllnl'nr '1 Height of son (in centimeters) Figure 1 160,, 150,, I L. 150 160 170 120 190 200 210 Height of father (in centimeters) 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.) X 5