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). Speed (mph) Distance (feet)
103.0 393
105.5 414
101.2 392
103.5 422
101.7 411
103.6 402
105.3 420
107.9 441
103.4 394
103.3 408
105.4 418
101.4 399

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

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+ ( )

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.

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
( ) feet that would have been predicted given the speed with which the ball was hit.