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O Correlation and Simplo Linear Regression
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Interpreting the slope of the least-squares regression line
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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). Based on these data, she computes the least-squares regression line to be \( \hat{y}=-0.017+0.041 x \). This line, along with a scatter plot of her data, is shown below.
\begin{tabular}{|l|l|}
\hline Earnings per share, x (in dollars) & Current stock price, \( y \) (in dollars) \\
\hline 15,95 & 0.92 \\
\hline 43.41 & 1.88 \\
\hline 24.84 & 0.97 \\
\hline 56.95 & 2.85 \\
\hline 59.59 & 2.21 \\
\hline 42.29 & 1.39 \\
\hline 51.70 & 2.77 \\
\hline 29.76 & 1.47 \\
\hline 39.88 & 0.93 \\
\hline 31.21 & 0.84 \\
\hline 48.73 & 1.61 \\
\hline 20.41 & 0.79 \\
\hline 33.11 & 1.85 \\
\hline 15.75 & 0.70 \\
\hline 38.83 & 1.14 \\
\hline 37.19 & 1.44 \\
\hline
\end{tabular}
Based on the analyst's data and regression line, complete the following.
(a) For these data, current stock prices that are less than the mean of the current stock prices tend to be paired with values for earnings per share that are (choose one) 0 the mean of the values for earnings per share.
(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?
\( \square \)
Explanation
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