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 = 5x+ (5(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.O 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.O 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.O D. Interpreting the slope is not appropriate.Data tableNow 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.Speed (mph)Distance (feet)O B. 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.110.4427OC. 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.105.5414O D. Interpreting the y-intercept is not appropriate.101.4399100.7396(c) Predict the mean distance of all home runs hit at 107 mph.103.5101.7422411The mean distance of all home runs hit at 107 mph is 5 feet.(Round to one decimal place as needed.)103.640299 3394(d) If a ball was hit with a speed of 107 miles per hour, predict how far it will travel.100.3392102.1392If a ball is hit with a speed of 107 mph, the distance that it is most likely to travel is 5 feet.(Round to one decimal place as needed.)105 4418101.2392(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 farther than the 5 feet that would have been predicted given the speed with which the ball was hit.(Round to one decimal place as needed.)PrintDone(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.耳ae市eDELLTD0A233Morobore 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.Critical values for the correlation coefficient(b) Interpret the slope and y-intercept, if appropriate.Begin by interpreting the slope.Critical Values for Correlation CoefficientA. The slope of this least-squares regression line says that the distance the ball travels increases by the slope with every 1 mile per hoincrease in the speed that the ball was hit.O 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.0.997O 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.40.950O D. Interpreting the slope is not appropriate.50.87860.811Now interpret the y-intercept.0.7540.707O 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 zero0.666O B. 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.100.632OC. 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.0.60211120.576O D. Interpreting the y-intercept is not appropriate.130.553(c) Predict the mean distance of all home runs hit at 107 mph.140.532150.514The mean distance of all home runs hit at 107 mph is 5 feet.160.497(Round to one decimal place as needed.)170.482180.468(d) If a ball was hit with a speed of 107 miles per hour, predict how far it will travel.190.456If a ball is hit with a speed of 107 mph, the distance that it is most likely to travel is 5 feet.(Round to one decimal place as needed.)200.444210.433220.423(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.230.413The ball did not travel farther than the 5 feet that would have been predicted given the speed with which the ball was hit.240.404250.396(Round to one decimal place as needed.)260.388(f) Would you feel comfortable using the least-squares regression model on home runs where the speed of the ball was 122 mph? Explain.270.381280.374O 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.290.367300.361O B. Yes, because the least squares regression model is the most accurate way to predict the distance of all home runs hitOC. 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.O D. 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.PrintDoneTimp 耳DELLTD0A233142Mcrabore

Name: The following data represent the speed at which a ball was hit (in mi
Uploaded: 2022-11-23T13:49:28.000Z
Channel: Bartleby
Description: 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

NOTE: As per the guidelines, we are supposed to solve the first three sub parts of 1st question only. Please repost other question as separate ones. I will surely solve all of them. a).Consider, Speed=variable X Distance=variable Y The following table shows the required calculations for the regression line. X Y X \cdot YX⋅Y X^2X2 Y^2Y2 110.4 427 47140.8 12188.16 182329 105.5 414 43677 11130.25 171396 101.4 399 40458.6 10281.96 159201 100.7 396 39877.2 10140.49 156816 103.5 422 43677 10712.25 178084 101.7 411 41798.7 10342.89 168921 103.6 402 41647.2 10732.96 161604 99.3 394 39124.2 9860.49 155236 100.3 392 39317.6 10060.09 153664 102.1 392 40023.2 10424.41 153664 105.4 418 44057.2 11109.16 174724 101.2 392 39670.4 10241.44 153664 Sum = 1235.1 4859 500469.1 127224.55 1969303 Now, we will calculate the mean for variable X and Y. The calculations are as follows: MeanX=Sum of all valuesTotal number of values =1235.112 =102.925MeanY=Sum of all valuesTotal number of values =485912 =404.917 The general regression equation is y=a+bx, where a-intercept and b-slope.The formula for b and a is as follows:b=SSXYSSXXa=MeanY-MeanX*b The formula and calculations for SSXY and SSXX is shown as follows: Now, substitute these values in a and b. The calculations are shown as follows:b=356.52500000002 101.88249999999 =3.49937 ≈3.499a=404.91666666667−(102.925*3.4994) ≈44.744 Now substitute these values in the general regression line.Hence, the least square regression line is: y^=44.744+3.499*x b). Slope defines the change in dependent variable, i.e, Y with the unit change in the independent variable , i.e, X.Here, the variable X is speed and Variable Y is Distance. Hence, the correct option is: The intercept defines the expected or mean value for dependent variable, i.e, Y when all the independent variable , i.e, X are equal to 0.Here, the variable X is speed and Variable Y is Distance. Hence, the correct option is: c). Now, we need to find mean distance when speed is 107 mph.The least square regression line obtained in part a) is y^=44.744+3.499*x.Substitute x=107 in this equation to find the mean distance. The calculations are as follows: y^=44.744+3.499*107 =419.137 ≈419.1 Hence, the mean distance for all the home runs hit at 107 mph is 419.1 feet.