1. 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.

Speed (mph) Distance (feet) 100.7 396 101.3 393 104.8 421 105.4 418 100.3 392 105.5 414 99.3 394 103.0 393 102.1 392 103.5 422 103.4 394 103.6 402

Click here to view the critical values of the correlation coefficient.

n Critical Values for Correlation Coefficient 3 0.997 4 0.950 5 0.878 6 0.811 7 0.754 8 0.707 9 0.666 10 0.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 28 0.374 29 0.367 30 0.361

(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.)

(b) Interpret the slope and y-intercept, if appropriate.

Begin by interpreting the slope.

A. 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.

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 shows the distance that the ball would travel when the speed that the ball is hit is zero.

D. Interpreting the slope is not appropriate.

Now interpret the y-intercept.

A. 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.

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 distance that the ball would travel when the speed that the ball is hit is zero.

D. Interpreting the y-intercept is not appropriate.

(c) Predict the mean distance of all home runs hit at 103 mph.

The mean distance of all home runs hit at 103 mph is enter your response here feet.

(Round to one decimal place as needed.)

(d) If a ball was hit with a speed of 103 miles per hour, predict how far it will travel.

If a ball is hit with a speed of 103 mph, the distance that it is most likely to travel is enter your response here

feet.

(Round to one decimal place as needed.)

(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 (did not travel/traveled) farther than the ( ) feet that would have been predicted given the speed with which the ball was hit.

(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. 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.

B. 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.

C. Yes, because the least squares regression model is the most accurate way to predict the distance of all home runs hit.

D. 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.