The following data represent the speed at which a ball was hit(in miles perhour) 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).

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(a) Find theleast-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=

nothing

x+(

nothing

)

(Round to three decimal places asneeded.)

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

Begin by interpreting the slope.

A.

The slope of thisleast-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 thisleast-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 thisleast-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.

D.

Interpreting the slope is not appropriate.

Now interpret they-intercept.

A.

They-intercept of thisleast-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.

B.

They-intercept of thisleast-squares regression line shows the distance that the ball would travel when the speed that the ball is hit is zero.

C.

They-intercept of thisleast-squares regression line shows the speed that the ball is hit at when the distance that the ball travels is zero.

D.

Interpreting they-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

nothing

feet.

(Round to one decimal place asneeded.)

(d) If a ball was hit with a speed of 105 miles perhour, 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

nothing

feet.

(Round to one decimal place asneeded.)

(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 havepredicted? Explain.

The ball

traveled

did not travel

farther than the

nothing

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

(Round to one decimal place asneeded.)

(f) Would you feel comfortable using theleast-squares regression model on home runs where the speed of the ball was 122mph? Explain.

A.

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.

B.

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

C.

Yes, because the least squares regression model can accurately predict the distance of home runs with a higher speed than wasobserved, but not lower.

D.

No, because the least squares regression model can accurately predict the distance of home runs with a lower speed than wasobserved, but not higher.