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 corelation coefficient.... ..(b) Interpret the slope and y-intercept, if appropriate.Critical values for the correlation coefficientBegin by interpreting the slope.O 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.Critical Values for Correlation CoefficientO 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.0.99740.950Now interpret the y-intercept.50.8780.811O 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.0.754O 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.0.70780.666O C. 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.100.632O D. Interpreting the y-intercept is not appropriate.110.602120.576(c) Predict the mean distance of all home runs hit at 107 mph.130.553The mean distance of all home runs hit at 107 mph is(Round to one decimal place as needed.)feet.140.532150.514160.497(d) If a ball was hit with a speed of 107 milles per hour, predict how far it will travel.170.482If a ball is hit with a speed of 107 mph, the distance that it is most likely to travel is(Round to one decimal place as needed.)180.468feet.190.456200.444(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.210.433220.423The ballfarther than thefeet that would have been predicted given the speed with which the ball was hit230.413(Round to one decimal place as needed.)240.404(f) Would you feel comfortable using the least-squares regression model on home runs where the speed of the ball was 122 mph? Explain.250.396260.388O 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.270.381O B. Yes, because the least squares regression model is the most accurate way to predict the distance of all home runs hit280.374290.367O C. 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.300.361O 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.PrintDoneO TimeDETCOA2334403u 10-8-2014MAINTCOA2330401 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 corelation 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(Round to three decimal places as needed.)(b) Interpret the slope and y-intercept, if appropriate.Begin by interpreting the slope.Data tableO 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.Speed (mph)Distance (feet) OO 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.110.4427O D. Interpreting the slope is not appropriate.105.5414101.4399Now interpret the y-intercept.100.7396103.5422O 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.101.7411O 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.103.6402O C. 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.99.3394O D. Interpreting the y-intercept is not appropriate.100.3392102.1392(c) Predict the mean distance of all home runs hit at 107 mph.5.4418101.2392The mean distance of all home runs hit at 107 mph is(Round to one decimal place as needed.)feet.(d) If a ball was hit with a speed of 107 miles per hour, predict how far it will travel.PrintDoneIf a ball is hit with a speed of 107 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 ballfarther than thefeet 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.O 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.DOTCOA2334403U 10-8-2014MAINTCOA2330401

“Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.” The line of best fit is the line of regression which gives the best estimate to the value of one variable for any particular value of the other variable. It is obtained by the principle of least squares. In the bivariate distribution xi,yi, (i=1,2,...,n), let Y be the dependent variable and X be the independent variable, the line of regression of Y on X be given as: y^=a+bx^ Here, a is intercept term and b is slope estimated by using principle of least square, i.e., a=∑i=1nyin, b=∑i=1nxiyi∑i=1nxi2(a.) Let X denotes the speed and Y denotes the distance. In order to obtain the regression line, we will do the following calculation. Here, n=12. Calculation Table: xi xi2 yi xiyi 110.4 12188.2 427 47140.8 105.5 11130.3 414 43677 101.4 10282.0 399 40458.6 100.7 10140.5 396 39877.2 103.5 10712.3 422 43677 101.7 10342.9 411 41798.7 103.6 10733.0 402 41647.2 99.3 9860.5 394 39124.2 100.3 10060.1 392 39317.6 102.1 10424.4 392 40023.2 105.4 11109.2 418 44057.2 101.2 10241.4 392 39670.4 Total 127224.6 4859 500469.1Using above calculation table, we have a=∑i=1nyin=485912=404.9167 b=∑i=1nxiyi∑i=1nxi2=500469.1127224.6=3.9337 Therefore, the blank should be filled with 3.934 and 404.917 respectively.(b.) From above calculation we get, the slope is 3.9337. In option (B.), the dependent variable is speed and the independent variable is distance which is incorrect. Since slope of regression coefficient implies the increment in the value of dependent variable to unit change in the independent variable which means that there will be 3.9337 feet increment in distance with unit change in speed so, option (A.) is correct and option (C.) is incorrect. We know that by intercept we mean, the value of dependent variable when the value of independent variable is 0 so, option (B.) is correct. In option (A.), the dependent variable is speed and the independent variable is distance which is incorrect. Option (C.) shows slope of regression line X on Y which is also incorrect here.(c.) Put the value of a and b in regression line, we get y^=3.9337x^+404.9167 Put x^=107 in it, we get y^=3.9337×107+404.9167=420.9059+404.9167=825.8226 Therefore, the blank should be filled with 825.8.