The following data represent the speed at which a ball was hit (in miles per hour) and the distance it traveled (in feet) for a random sample of home runs in a Major League baseball game in 2018. Complete parts (a) through (f). Click here to view the data. Click here to view the critical values of the correlation coefficient. (a) Find the least-squares regression line treating speed at which the ball was hit as the explanatory variable and distance the ball traveled as the response variable. y? = [ ]x + ([ ]) (Round to three decimal places as needed.) Data Table Speed (mph) Distance (feet) 105.5 414 98.0 395 110.4 427 100.8 394 103.5 422 101.4 399 103.0 393 101.3 393 103.5 395 107.9 441 104.8 421 103.3 408 Enter your answer in the edit fields and then click Check Answer. Print Done
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\[ \begin{array}{cc} \text{Speed (mph)} & \text{Distance (feet)} \\ 105.5 & 414 \\ 98.0 & 395 \\ 110.4 & 427 \\ 100.8 & 394 \\ 103.5 & 422 \\ 101.4 & 399 \\ 103.0 & 393 \\ 101.3 & 393 \\ 103.5 & 395 \\ 107.9 & 441 \\ 104.8 & 421 \\ 103.3 & 408 \\ \end{array} \] Show more…
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In baseball, is there a linear correlation between batting average and home run percentage? Let $x$ represent the batting average of a professional baseball player, and let $y$ represent the player's home run percentage (number of home runs per 100 times at bat). A random sample of $n=7$ professional baseball players gave the following information (Reference: The Baseball Encyclopedia, Macmillan Publishing Company). $$\begin{array}{c|lllllll} \hline x & 0.243 & 0.259 & 0.286 & 0.263 & 0.268 & 0.339 & 0.299 \\ \hline y & 1.4 & 3.6 & 5.5 & 3.8 & 3.5 & 7.3 & 5.0 \\ \hline \end{array}$$ (a) Make a scatter diagram and draw the line you think best fits the data. (b) Would you say the correlation is low, moderate, or high? positive or negative? (c) Use a calculator to verify that $\Sigma x=1.957, \Sigma x^{2} \approx 0.553, \Sigma y=30.1, \Sigma y^{2}=150.15,$ and $\Sigma x y \approx 8.753$ Compute $r .$ As $x$ increases, does the value of $r$ imply that $y$ should tend to increase or decrease? Explain.
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