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). (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. Data Table Critical Values for the Correlation Coefficient (Round to three decimal places as needed.) (b) Interpret the slope and y-intercept, if appropriate. Begin by interpreting the slope. A. The slope of this least-squares regression line shows the distance that the ball would travel when the speed that the ball is hit is zero. B. The slope of this least-squares regression line shows the increase in the speed that the ball was hit with every 1 foot increase in the distance that the ball was hit. C. The slope of this least-squares regression line says that the distance the ball travels increases by the slope with every 1 mile per hour increase in the speed that the ball was hit. OD. Interpreting the slope is not appropriate. Speed (mph) 101.7 Distance (feet) 411 Critical Values for Correlation Coefficient 99.3 394 11 103.3 408 0.997 105.5 414 4 0,950 107.9 441 = 0.878 99.4 394 6 0.811 103.5 395 7 0.754 8 101.3 0,707 393 9 0,666 103.0 393 Now interpret the y-intercept. 10 0.632 103.5 422 11 0,602 105.4 418 A. The y-intercept of this least-squares regression line shows the distance that the ball would travel when the speed that the ball is hit is zero. 12 0.576 100.8 394 13 0.553 B. The y-intercept of this least-squares regression line shows the increase in the speed that the ball was hit with every 1 foot increase in the distance that the ball was hit. C. The y-intercept of this least-squares regression line shows the speed that the ball is hit at when the distance that the ball travels is zero. 14 0.532 15 0.514 16 0.497 Print Done 17 0.482 OD. Interpreting the y-intercept is not appropriate. (c) Predict the mean distance of all home runs hit at 105 mph. The mean distance of all home runs hit at 105 mph is feet. (Round to one decimal place as needed.) (d) If a ball was hit with a speed of 105 miles per hour, predict how far it will travel. If a ball is hit with a speed of 105 mph, the distance that it is most likely to travel is (Round to one decimal place as needed.) feet. (e) Christian Yelich hit a home run 398 feet. The speed at which the ball was hit was 106.2 mph. Did this ball travel farther than you would have predicted? Explain. The ball farther than the (Round to one decimal place as needed.) feet that would have been predicted given the speed with which the ball was hit. Print Done (e) Christian Yelich hit a home run 398 feet. The speed at which the ball was hit was 106.2 mph. Did this ball travel farther than you would have predicted? Explain. feet that would have been predicted given the speed with which the ball was hit. The ball farther than the (Round to one decimal place as needed.) (f) Would you feel comfortable using the least-squares regression model on home runs where the speed of the ball was 122 mph? Explain. A. No, because the least squares regression model can accurately predict the distance of home runs with a lower speed than was observed, but not higher. B. No, because the least squares regression model cannot predict the distance of a home run when the speed of the ball is outside of the scope of the model. OC. Yes, because the least squares regression model can accurately predict the distance of home runs with a higher speed than was observed, but not lower. OD. Yes, because the least squares regression model is the most accurate way to predict the distance of all home runs hit.