Each week coaches in a certain football league face a decisionduring the game. On? fourth-down, should the team punt the ball orgo for a? first-down? To aid in the? decision-making process,statisticians at a particular university developed a regressionmodel for predicting the number of points scored? (y) by a teamthat has a? first-down with a given number of yards? (x) from theopposing goal line. One of the models fit to data collected on fiveleague teams from a recent season was the simple linear regression?model, E(y)=?0+?1x. The regression yielded the following?results:y=4.12?0.59x?, r squared equals 0.24.Complete parts a and bbelow.a.

Give a practical interpretation of the coefficient of?determination, r2.

Choose the correct answer below.

A.Sample variations in the numbers of yards to the opposing goalline explain 24% of the sample variation in the numbers of pointsscored using the least squares line. This answer is correct.

B.There is a positive linear relationship between numbers ofyards to the opposing goal line and numbers of points scoredbecause 0.24 is positive.

C.There is little or no relationship between numbers of yards tothe opposing goal line and numbers of points scored because 0.24 isnear to zero.

D.Sample variations in the numbers of yards to the opposing goalline explain 76?%of the sample variation in the numbers of pointsscored using the least squares line.b. Compute the value of thecoefficient of? correlation, r, from the value of r2.

Is the value of r positive or? negative? Why? Select the correctchoice below and fill in the answer box within your choice. ?(Roundto three decimal places as? needed.)

A.The coefficient of? correlation, r=________,is positivebecause the estimator of beta 1?1 is positive.

B.The coefficient of? correlation,r=__________, is positivebecause the estimator of beta 1?1is negative.

C.The coefficient of? correlation,r=___________,is negativebecause the estimator of beta 1?1is negative.

D.The coefficient of? correlation,r=_________,is negativebecause the estimator of beta 1?1 is positive.