The Professional Golfers Association (PGA) maintains data on performance and earnings for members of the PGA Tour. For the 2012 season Bubba Watson led all players in total driving distance, with an average of 309.2 yards per drive. Some of the factors thought to influence driving distance are club head speed, ball speed, and launch angle. For the 2012 season Bubba Watson had an average club head speed of 124.69 miles per hour, an average ball speed of 184.98 miles per hour, and an average launch angle of 8.79 degrees. The DATAfile named PGADrivingDist contains data on total driving distance and the factors related to driving distance for 190 members of the PGA Tour (PGA Tour website, November 1, 2012). Descriptions for the variables in the data set follow. Club Head Speed: Speed at which the club impacts the ball (mph). Ball Speed: Peak speed of the golf ball at launch (mph). Launch Angle: Vertical launch angle of the ball immediately after leaving the club (degrees). Total Distance: The average number of yards per drive. a. Develop an estimated regression equation that can be used to predict the average number of yards per drive given the club head speed. b. Develop an estimated regression equation that can be used to predict the average number of yards per drive given the ball speed. c. A recommendation has been made to develop an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive. Do you agree with this? Explain. d. Develop an estimated regression equation that can be used to predict the average number of yards per drive given the ball speed and the launch angle. e. Suppose a new member of the PGA Tour for 2013 has a ball speed of 170 miles per hour and a launch angle of 11 degrees. Use the estimated regression equation in part (d) to predict the average number of yards per drive for this player.

Question

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Answer 1

Textbook Question

Chapter 15.2, Problem 9E

The Professional Golfers Association (PGA) maintains data on performance and earnings for members of the PGA Tour. For the 2012 season Bubba Watson led all players in total driving distance, with an average of 309.2 yards per drive. Some of the factors thought to influence driving distance are club head speed, ball speed, and launch angle. For the 2012 season Bubba Watson had an average club head speed of 124.69 miles per hour, an average ball speed of 184.98 miles per hour, and an average launch angle of 8.79 degrees. The DATAfile named PGADrivingDist contains data on total driving distance and the factors related to driving distance for 190 members of the PGA Tour (PGA Tour website, November 1, 2012). Descriptions for the variables in the data set follow.

Club Head Speed: Speed at which the club impacts the ball (mph).

Ball Speed: Peak speed of the golf ball at launch (mph).

Launch Angle: Vertical launch angle of the ball immediately after leaving the club (degrees).

Total Distance: The average number of yards per drive.

a. Develop an estimated regression equation that can be used to predict the average number of yards per drive given the club head speed.
b. Develop an estimated regression equation that can be used to predict the average number of yards per drive given the ball speed.
c. A recommendation has been made to develop an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive. Do you agree with this? Explain.
d. Develop an estimated regression equation that can be used to predict the average number of yards per drive given the ball speed and the launch angle.
e. Suppose a new member of the PGA Tour for 2013 has a ball speed of 170 miles per hour and a launch angle of 11 degrees. Use the estimated regression equation in part (d) to predict the average number of yards per drive for this player.

a.

Expert Solution

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the club head speed.

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given the club head speed is y^=124.7160+1.3943 (Club Head Speed).

Explanation of Solution

Calculation:

The Professional Golfers Association (PGA) data consist of information regarding to the speed at which the club impacts the ball (club head speed), peak speed of the golf ball at launch (ball speed), vertical launch angle of the ball immediately after leaving the club (launch angle), and the average number of yards per drive (total distance).

Multiple linear regression model:

A multiple linear regression model is given as y^=b0+b1x1+...+bpxp, where y^ is the predicted value of response or dependent variable, and x1,x2,...,xp are the k predictor variables. The quantities b1,b2,...,bp are the estimated slopes corresponding to x1,x2,...,xp, respectively and b0 is the estimated intercept of the line from the sample data.

Denote y as the dependent variable total distance.

Regression:

Software procedure:

Step-by-step procedure to get regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $B$1:$B$191.
Click the box of Labels.
Under Output Range enter $H$1.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 1

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given the club head speed is y^=124.7160+1.3943 (Club Head Speed).

b.

Expert Solution

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed.

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given the ball speed is y^=117.14+0.9876 (Ball Speed).

Explanation of Solution

Calculation:

The regression equation can be obtained using excel software.

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $C$1:$C$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 2

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed is y^=117.14+0.9876 (Ball Speed).

c.

Expert Solution

To determine

Explain whether developing an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive is useful or not.

Explanation of Solution

Calculation:

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $B$1:$C$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 3

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given both club head speed and ball speed is as follows:

y^=113.85−2.231 (Club Head)+2.515 (Ball Speed).

In the given output, R2=77.14%.

Thus, only 77.14% variability in total distance can be explained by variability in club head and ball speed.

Scatter Diagram:

Software procedure:

Step-by-step procedure to obtain scatter diagram using EXCEL software:

Open the file PGADrivingDist.
Select the cell Range $B$1:$C$191.
Go to insert and select scatter plot.
Click OK

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 4

The scatter diagram exhibits a strong positive linear relationship between ball speed and club head speed. Both the variables in the same model are not recommended as the linear effect of one variable describes the linear effect of the other variable. As a result, the other variable will be of little additional value. Thus, there is a chance of multicollinearity.

Thus, developing an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive is not useful.

d.

Expert Solution

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed and the launch angle.

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given both ball speed and launch angle is as follows:

y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

Explanation of Solution

Calculation:

The regression equation can be obtained using Excel software.

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $C$1:$D$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 5

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given both ball speed and launch angle is as follows:

y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

e.

Expert Solution

To determine

Predict the average number of yards per drive for the new player using the obtained equation in part (d).

Answer to Problem 9E

The predicted average number of yards per drive for the new player is 285.465 yards.

Explanation of Solution

Calculation:

The ball speed of a new PGA player is 170 mph with launch angle of 11 degrees.

From Part (b), it is found that the estimated regression equation that could be used to predict the average number of yards per drive given both club head speed and launch angle is y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

Thus, the predicted average number of yards per drive for the new player is as follows:

y^=81.60+1.0927(170)+1.646(11)=81.60+185.759+18.106=285.465

Thus, the predicted average number of yards per drive for the new player is 285.465 yards.

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Answer 2

Textbook Question

Chapter 15.2, Problem 9E

The Professional Golfers Association (PGA) maintains data on performance and earnings for members of the PGA Tour. For the 2012 season Bubba Watson led all players in total driving distance, with an average of 309.2 yards per drive. Some of the factors thought to influence driving distance are club head speed, ball speed, and launch angle. For the 2012 season Bubba Watson had an average club head speed of 124.69 miles per hour, an average ball speed of 184.98 miles per hour, and an average launch angle of 8.79 degrees. The DATAfile named PGADrivingDist contains data on total driving distance and the factors related to driving distance for 190 members of the PGA Tour (PGA Tour website, November 1, 2012). Descriptions for the variables in the data set follow.

Club Head Speed: Speed at which the club impacts the ball (mph).

Ball Speed: Peak speed of the golf ball at launch (mph).

Launch Angle: Vertical launch angle of the ball immediately after leaving the club (degrees).

Total Distance: The average number of yards per drive.

a. Develop an estimated regression equation that can be used to predict the average number of yards per drive given the club head speed.
b. Develop an estimated regression equation that can be used to predict the average number of yards per drive given the ball speed.
c. A recommendation has been made to develop an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive. Do you agree with this? Explain.
d. Develop an estimated regression equation that can be used to predict the average number of yards per drive given the ball speed and the launch angle.
e. Suppose a new member of the PGA Tour for 2013 has a ball speed of 170 miles per hour and a launch angle of 11 degrees. Use the estimated regression equation in part (d) to predict the average number of yards per drive for this player.

a.

Expert Solution

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the club head speed.

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given the club head speed is y^=124.7160+1.3943 (Club Head Speed).

Explanation of Solution

Calculation:

The Professional Golfers Association (PGA) data consist of information regarding to the speed at which the club impacts the ball (club head speed), peak speed of the golf ball at launch (ball speed), vertical launch angle of the ball immediately after leaving the club (launch angle), and the average number of yards per drive (total distance).

Multiple linear regression model:

A multiple linear regression model is given as y^=b0+b1x1+...+bpxp, where y^ is the predicted value of response or dependent variable, and x1,x2,...,xp are the k predictor variables. The quantities b1,b2,...,bp are the estimated slopes corresponding to x1,x2,...,xp, respectively and b0 is the estimated intercept of the line from the sample data.

Denote y as the dependent variable total distance.

Regression:

Software procedure:

Step-by-step procedure to get regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $B$1:$B$191.
Click the box of Labels.
Under Output Range enter $H$1.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 1

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given the club head speed is y^=124.7160+1.3943 (Club Head Speed).

b.

Expert Solution

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed.

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given the ball speed is y^=117.14+0.9876 (Ball Speed).

Explanation of Solution

Calculation:

The regression equation can be obtained using excel software.

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $C$1:$C$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 2

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed is y^=117.14+0.9876 (Ball Speed).

c.

Expert Solution

To determine

Explain whether developing an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive is useful or not.

Explanation of Solution

Calculation:

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $B$1:$C$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 3

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given both club head speed and ball speed is as follows:

y^=113.85−2.231 (Club Head)+2.515 (Ball Speed).

In the given output, R2=77.14%.

Thus, only 77.14% variability in total distance can be explained by variability in club head and ball speed.

Scatter Diagram:

Software procedure:

Step-by-step procedure to obtain scatter diagram using EXCEL software:

Open the file PGADrivingDist.
Select the cell Range $B$1:$C$191.
Go to insert and select scatter plot.
Click OK

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 4

The scatter diagram exhibits a strong positive linear relationship between ball speed and club head speed. Both the variables in the same model are not recommended as the linear effect of one variable describes the linear effect of the other variable. As a result, the other variable will be of little additional value. Thus, there is a chance of multicollinearity.

Thus, developing an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive is not useful.

d.

Expert Solution

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed and the launch angle.

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given both ball speed and launch angle is as follows:

y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

Explanation of Solution

Calculation:

The regression equation can be obtained using Excel software.

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $C$1:$D$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 5

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given both ball speed and launch angle is as follows:

y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

e.

Expert Solution

To determine

Predict the average number of yards per drive for the new player using the obtained equation in part (d).

Answer to Problem 9E

The predicted average number of yards per drive for the new player is 285.465 yards.

Explanation of Solution

Calculation:

The ball speed of a new PGA player is 170 mph with launch angle of 11 degrees.

From Part (b), it is found that the estimated regression equation that could be used to predict the average number of yards per drive given both club head speed and launch angle is y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

Thus, the predicted average number of yards per drive for the new player is as follows:

y^=81.60+1.0927(170)+1.646(11)=81.60+185.759+18.106=285.465

Thus, the predicted average number of yards per drive for the new player is 285.465 yards.

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Answer 3

Textbook Question

Chapter 15.2, Problem 9E

The Professional Golfers Association (PGA) maintains data on performance and earnings for members of the PGA Tour. For the 2012 season Bubba Watson led all players in total driving distance, with an average of 309.2 yards per drive. Some of the factors thought to influence driving distance are club head speed, ball speed, and launch angle. For the 2012 season Bubba Watson had an average club head speed of 124.69 miles per hour, an average ball speed of 184.98 miles per hour, and an average launch angle of 8.79 degrees. The DATAfile named PGADrivingDist contains data on total driving distance and the factors related to driving distance for 190 members of the PGA Tour (PGA Tour website, November 1, 2012). Descriptions for the variables in the data set follow.

Club Head Speed: Speed at which the club impacts the ball (mph).

Ball Speed: Peak speed of the golf ball at launch (mph).

Launch Angle: Vertical launch angle of the ball immediately after leaving the club (degrees).

Total Distance: The average number of yards per drive.

a. Develop an estimated regression equation that can be used to predict the average number of yards per drive given the club head speed.
b. Develop an estimated regression equation that can be used to predict the average number of yards per drive given the ball speed.
c. A recommendation has been made to develop an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive. Do you agree with this? Explain.
d. Develop an estimated regression equation that can be used to predict the average number of yards per drive given the ball speed and the launch angle.
e. Suppose a new member of the PGA Tour for 2013 has a ball speed of 170 miles per hour and a launch angle of 11 degrees. Use the estimated regression equation in part (d) to predict the average number of yards per drive for this player.

a.

Expert Solution

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the club head speed.

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given the club head speed is y^=124.7160+1.3943 (Club Head Speed).

Explanation of Solution

Calculation:

The Professional Golfers Association (PGA) data consist of information regarding to the speed at which the club impacts the ball (club head speed), peak speed of the golf ball at launch (ball speed), vertical launch angle of the ball immediately after leaving the club (launch angle), and the average number of yards per drive (total distance).

Multiple linear regression model:

A multiple linear regression model is given as y^=b0+b1x1+...+bpxp, where y^ is the predicted value of response or dependent variable, and x1,x2,...,xp are the k predictor variables. The quantities b1,b2,...,bp are the estimated slopes corresponding to x1,x2,...,xp, respectively and b0 is the estimated intercept of the line from the sample data.

Denote y as the dependent variable total distance.

Regression:

Software procedure:

Step-by-step procedure to get regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $B$1:$B$191.
Click the box of Labels.
Under Output Range enter $H$1.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 1

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given the club head speed is y^=124.7160+1.3943 (Club Head Speed).

b.

Expert Solution

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed.

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given the ball speed is y^=117.14+0.9876 (Ball Speed).

Explanation of Solution

Calculation:

The regression equation can be obtained using excel software.

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $C$1:$C$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 2

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed is y^=117.14+0.9876 (Ball Speed).

c.

Expert Solution

To determine

Explain whether developing an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive is useful or not.

Explanation of Solution

Calculation:

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $B$1:$C$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 3

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given both club head speed and ball speed is as follows:

y^=113.85−2.231 (Club Head)+2.515 (Ball Speed).

In the given output, R2=77.14%.

Thus, only 77.14% variability in total distance can be explained by variability in club head and ball speed.

Scatter Diagram:

Software procedure:

Step-by-step procedure to obtain scatter diagram using EXCEL software:

Open the file PGADrivingDist.
Select the cell Range $B$1:$C$191.
Go to insert and select scatter plot.
Click OK

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 4

The scatter diagram exhibits a strong positive linear relationship between ball speed and club head speed. Both the variables in the same model are not recommended as the linear effect of one variable describes the linear effect of the other variable. As a result, the other variable will be of little additional value. Thus, there is a chance of multicollinearity.

Thus, developing an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive is not useful.

d.

Expert Solution

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed and the launch angle.

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given both ball speed and launch angle is as follows:

y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

Explanation of Solution

Calculation:

The regression equation can be obtained using Excel software.

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $C$1:$D$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 5

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given both ball speed and launch angle is as follows:

y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

e.

Expert Solution

To determine

Predict the average number of yards per drive for the new player using the obtained equation in part (d).

Answer to Problem 9E

The predicted average number of yards per drive for the new player is 285.465 yards.

Explanation of Solution

Calculation:

The ball speed of a new PGA player is 170 mph with launch angle of 11 degrees.

From Part (b), it is found that the estimated regression equation that could be used to predict the average number of yards per drive given both club head speed and launch angle is y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

Thus, the predicted average number of yards per drive for the new player is as follows:

y^=81.60+1.0927(170)+1.646(11)=81.60+185.759+18.106=285.465

Thus, the predicted average number of yards per drive for the new player is 285.465 yards.

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Answer 4

Textbook Question

Chapter 15.2, Problem 9E

The Professional Golfers Association (PGA) maintains data on performance and earnings for members of the PGA Tour. For the 2012 season Bubba Watson led all players in total driving distance, with an average of 309.2 yards per drive. Some of the factors thought to influence driving distance are club head speed, ball speed, and launch angle. For the 2012 season Bubba Watson had an average club head speed of 124.69 miles per hour, an average ball speed of 184.98 miles per hour, and an average launch angle of 8.79 degrees. The DATAfile named PGADrivingDist contains data on total driving distance and the factors related to driving distance for 190 members of the PGA Tour (PGA Tour website, November 1, 2012). Descriptions for the variables in the data set follow.

Club Head Speed: Speed at which the club impacts the ball (mph).

Ball Speed: Peak speed of the golf ball at launch (mph).

Launch Angle: Vertical launch angle of the ball immediately after leaving the club (degrees).

Total Distance: The average number of yards per drive.

a. Develop an estimated regression equation that can be used to predict the average number of yards per drive given the club head speed.
b. Develop an estimated regression equation that can be used to predict the average number of yards per drive given the ball speed.
c. A recommendation has been made to develop an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive. Do you agree with this? Explain.
d. Develop an estimated regression equation that can be used to predict the average number of yards per drive given the ball speed and the launch angle.
e. Suppose a new member of the PGA Tour for 2013 has a ball speed of 170 miles per hour and a launch angle of 11 degrees. Use the estimated regression equation in part (d) to predict the average number of yards per drive for this player.

a.

Expert Solution

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the club head speed.

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given the club head speed is y^=124.7160+1.3943 (Club Head Speed).

Explanation of Solution

Calculation:

The Professional Golfers Association (PGA) data consist of information regarding to the speed at which the club impacts the ball (club head speed), peak speed of the golf ball at launch (ball speed), vertical launch angle of the ball immediately after leaving the club (launch angle), and the average number of yards per drive (total distance).

Multiple linear regression model:

A multiple linear regression model is given as y^=b0+b1x1+...+bpxp, where y^ is the predicted value of response or dependent variable, and x1,x2,...,xp are the k predictor variables. The quantities b1,b2,...,bp are the estimated slopes corresponding to x1,x2,...,xp, respectively and b0 is the estimated intercept of the line from the sample data.

Denote y as the dependent variable total distance.

Regression:

Software procedure:

Step-by-step procedure to get regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $B$1:$B$191.
Click the box of Labels.
Under Output Range enter $H$1.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 1

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given the club head speed is y^=124.7160+1.3943 (Club Head Speed).

b.

Expert Solution

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed.

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given the ball speed is y^=117.14+0.9876 (Ball Speed).

Explanation of Solution

Calculation:

The regression equation can be obtained using excel software.

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $C$1:$C$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 2

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed is y^=117.14+0.9876 (Ball Speed).

c.

Expert Solution

To determine

Explain whether developing an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive is useful or not.

Explanation of Solution

Calculation:

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $B$1:$C$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 3

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given both club head speed and ball speed is as follows:

y^=113.85−2.231 (Club Head)+2.515 (Ball Speed).

In the given output, R2=77.14%.

Thus, only 77.14% variability in total distance can be explained by variability in club head and ball speed.

Scatter Diagram:

Software procedure:

Step-by-step procedure to obtain scatter diagram using EXCEL software:

Open the file PGADrivingDist.
Select the cell Range $B$1:$C$191.
Go to insert and select scatter plot.
Click OK

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 4

The scatter diagram exhibits a strong positive linear relationship between ball speed and club head speed. Both the variables in the same model are not recommended as the linear effect of one variable describes the linear effect of the other variable. As a result, the other variable will be of little additional value. Thus, there is a chance of multicollinearity.

Thus, developing an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive is not useful.

d.

Expert Solution

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed and the launch angle.

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given both ball speed and launch angle is as follows:

y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

Explanation of Solution

Calculation:

The regression equation can be obtained using Excel software.

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $C$1:$D$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 5

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given both ball speed and launch angle is as follows:

y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

e.

Expert Solution

To determine

Predict the average number of yards per drive for the new player using the obtained equation in part (d).

Answer to Problem 9E

The predicted average number of yards per drive for the new player is 285.465 yards.

Explanation of Solution

Calculation:

The ball speed of a new PGA player is 170 mph with launch angle of 11 degrees.

From Part (b), it is found that the estimated regression equation that could be used to predict the average number of yards per drive given both club head speed and launch angle is y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

Thus, the predicted average number of yards per drive for the new player is as follows:

y^=81.60+1.0927(170)+1.646(11)=81.60+185.759+18.106=285.465

Thus, the predicted average number of yards per drive for the new player is 285.465 yards.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a.

Expert Solution

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the club head speed.

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given the club head speed is y^=124.7160+1.3943 (Club Head Speed).

Explanation of Solution

Calculation:

The Professional Golfers Association (PGA) data consist of information regarding to the speed at which the club impacts the ball (club head speed), peak speed of the golf ball at launch (ball speed), vertical launch angle of the ball immediately after leaving the club (launch angle), and the average number of yards per drive (total distance).

Multiple linear regression model:

A multiple linear regression model is given as y^=b0+b1x1+...+bpxp, where y^ is the predicted value of response or dependent variable, and x1,x2,...,xp are the k predictor variables. The quantities b1,b2,...,bp are the estimated slopes corresponding to x1,x2,...,xp, respectively and b0 is the estimated intercept of the line from the sample data.

Denote y as the dependent variable total distance.

Regression:

Software procedure:

Step-by-step procedure to get regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $B$1:$B$191.
Click the box of Labels.
Under Output Range enter $H$1.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 1

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given the club head speed is y^=124.7160+1.3943 (Club Head Speed).

b.

Expert Solution

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed.

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given the ball speed is y^=117.14+0.9876 (Ball Speed).

Explanation of Solution

Calculation:

The regression equation can be obtained using excel software.

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $C$1:$C$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 2

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed is y^=117.14+0.9876 (Ball Speed).

c.

Expert Solution

To determine

Explain whether developing an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive is useful or not.

Explanation of Solution

Calculation:

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $B$1:$C$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 3

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given both club head speed and ball speed is as follows:

y^=113.85−2.231 (Club Head)+2.515 (Ball Speed).

In the given output, R2=77.14%.

Thus, only 77.14% variability in total distance can be explained by variability in club head and ball speed.

Scatter Diagram:

Software procedure:

Step-by-step procedure to obtain scatter diagram using EXCEL software:

Open the file PGADrivingDist.
Select the cell Range $B$1:$C$191.
Go to insert and select scatter plot.
Click OK

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 4

The scatter diagram exhibits a strong positive linear relationship between ball speed and club head speed. Both the variables in the same model are not recommended as the linear effect of one variable describes the linear effect of the other variable. As a result, the other variable will be of little additional value. Thus, there is a chance of multicollinearity.

Thus, developing an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive is not useful.

d.

Expert Solution

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed and the launch angle.

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given both ball speed and launch angle is as follows:

y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

Explanation of Solution

Calculation:

The regression equation can be obtained using Excel software.

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $C$1:$D$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 5

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given both ball speed and launch angle is as follows:

y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

e.

Expert Solution

To determine

Predict the average number of yards per drive for the new player using the obtained equation in part (d).

Answer to Problem 9E

The predicted average number of yards per drive for the new player is 285.465 yards.

Explanation of Solution

Calculation:

The ball speed of a new PGA player is 170 mph with launch angle of 11 degrees.

From Part (b), it is found that the estimated regression equation that could be used to predict the average number of yards per drive given both club head speed and launch angle is y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

Thus, the predicted average number of yards per drive for the new player is as follows:

y^=81.60+1.0927(170)+1.646(11)=81.60+185.759+18.106=285.465

Thus, the predicted average number of yards per drive for the new player is 285.465 yards.

Answer 8

a.

Expert Solution

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the club head speed.

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given the club head speed is y^=124.7160+1.3943 (Club Head Speed).

Explanation of Solution

Calculation:

The Professional Golfers Association (PGA) data consist of information regarding to the speed at which the club impacts the ball (club head speed), peak speed of the golf ball at launch (ball speed), vertical launch angle of the ball immediately after leaving the club (launch angle), and the average number of yards per drive (total distance).

Multiple linear regression model:

A multiple linear regression model is given as y^=b0+b1x1+...+bpxp, where y^ is the predicted value of response or dependent variable, and x1,x2,...,xp are the k predictor variables. The quantities b1,b2,...,bp are the estimated slopes corresponding to x1,x2,...,xp, respectively and b0 is the estimated intercept of the line from the sample data.

Denote y as the dependent variable total distance.

Regression:

Software procedure:

Step-by-step procedure to get regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $B$1:$B$191.
Click the box of Labels.
Under Output Range enter $H$1.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 1

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given the club head speed is y^=124.7160+1.3943 (Club Head Speed).

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the club head speed.

Answer 13

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given the club head speed is y^=124.7160+1.3943 (Club Head Speed).

Answer 14

Explanation of Solution

Calculation:

The Professional Golfers Association (PGA) data consist of information regarding to the speed at which the club impacts the ball (club head speed), peak speed of the golf ball at launch (ball speed), vertical launch angle of the ball immediately after leaving the club (launch angle), and the average number of yards per drive (total distance).

Multiple linear regression model:

A multiple linear regression model is given as y^=b0+b1x1+...+bpxp, where y^ is the predicted value of response or dependent variable, and x1,x2,...,xp are the k predictor variables. The quantities b1,b2,...,bp are the estimated slopes corresponding to x1,x2,...,xp, respectively and b0 is the estimated intercept of the line from the sample data.

Denote y as the dependent variable total distance.

Regression:

Software procedure:

Step-by-step procedure to get regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $B$1:$B$191.
Click the box of Labels.
Under Output Range enter $H$1.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 1

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given the club head speed is y^=124.7160+1.3943 (Club Head Speed).

Answer 15

b.

Expert Solution

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed.

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given the ball speed is y^=117.14+0.9876 (Ball Speed).

Explanation of Solution

Calculation:

The regression equation can be obtained using excel software.

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $C$1:$C$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 2

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed is y^=117.14+0.9876 (Ball Speed).

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed.

Answer 20

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given the ball speed is y^=117.14+0.9876 (Ball Speed).

Answer 21

Explanation of Solution

Calculation:

The regression equation can be obtained using excel software.

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $C$1:$C$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 2

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed is y^=117.14+0.9876 (Ball Speed).

Answer 22

c.

Expert Solution

To determine

Explain whether developing an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive is useful or not.

Explanation of Solution

Calculation:

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $B$1:$C$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 3

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given both club head speed and ball speed is as follows:

y^=113.85−2.231 (Club Head)+2.515 (Ball Speed).

In the given output, R2=77.14%.

Thus, only 77.14% variability in total distance can be explained by variability in club head and ball speed.

Scatter Diagram:

Software procedure:

Step-by-step procedure to obtain scatter diagram using EXCEL software:

Open the file PGADrivingDist.
Select the cell Range $B$1:$C$191.
Go to insert and select scatter plot.
Click OK

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 4

The scatter diagram exhibits a strong positive linear relationship between ball speed and club head speed. Both the variables in the same model are not recommended as the linear effect of one variable describes the linear effect of the other variable. As a result, the other variable will be of little additional value. Thus, there is a chance of multicollinearity.

Thus, developing an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive is not useful.

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

Explain whether developing an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive is useful or not.

Answer 27

Explanation of Solution

Calculation:

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $B$1:$C$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 3

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given both club head speed and ball speed is as follows:

y^=113.85−2.231 (Club Head)+2.515 (Ball Speed).

In the given output, R2=77.14%.

Thus, only 77.14% variability in total distance can be explained by variability in club head and ball speed.

Scatter Diagram:

Software procedure:

Step-by-step procedure to obtain scatter diagram using EXCEL software:

Open the file PGADrivingDist.
Select the cell Range $B$1:$C$191.
Go to insert and select scatter plot.
Click OK

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 4

The scatter diagram exhibits a strong positive linear relationship between ball speed and club head speed. Both the variables in the same model are not recommended as the linear effect of one variable describes the linear effect of the other variable. As a result, the other variable will be of little additional value. Thus, there is a chance of multicollinearity.

Thus, developing an estimated regression equation that uses both club head speed and ball speed to predict the average number of yards per drive is not useful.

Answer 28

d.

Expert Solution

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed and the launch angle.

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given both ball speed and launch angle is as follows:

y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

Explanation of Solution

Calculation:

The regression equation can be obtained using Excel software.

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $C$1:$D$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 5

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given both ball speed and launch angle is as follows:

y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

Answer 29

d.

Expert Solution

Answer 30

d.

Expert Solution

Answer 31

Expert Solution

Answer 32

To determine

Find the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed and the launch angle.

Answer 33

Answer to Problem 9E

The estimated regression equation that could be used to predict the average number of yards per drive given both ball speed and launch angle is as follows:

y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

Answer 34

Explanation of Solution

Calculation:

The regression equation can be obtained using Excel software.

Regression:

Software procedure:

Step-by-step procedure to get the regression equation using EXCEL software:

Open the file PGADrivingDist.
Select Data > Data Analysis > Regression.
Click OK.
Under Input Y Range enter $E$1:$E$191.
Under Input X Range enter $C$1:$D$191.
Click the box of Labels.
Under Output Range enter $H$24.
Click OK.

Output obtained using EXCEL software is given as follows:

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List), Chapter 15.2, Problem 9E , additional homework tip 5

Thus, the estimated regression equation that could be used to predict the average number of yards per drive given both ball speed and launch angle is as follows:

y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

Answer 35

e.

Expert Solution

To determine

Predict the average number of yards per drive for the new player using the obtained equation in part (d).

Answer to Problem 9E

The predicted average number of yards per drive for the new player is 285.465 yards.

Explanation of Solution

Calculation:

The ball speed of a new PGA player is 170 mph with launch angle of 11 degrees.

From Part (b), it is found that the estimated regression equation that could be used to predict the average number of yards per drive given both club head speed and launch angle is y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).

Thus, the predicted average number of yards per drive for the new player is as follows:

y^=81.60+1.0927(170)+1.646(11)=81.60+185.759+18.106=285.465

Thus, the predicted average number of yards per drive for the new player is 285.465 yards.

Answer 36

e.

Expert Solution

Answer 37

e.

Expert Solution

Answer 38

Expert Solution

Answer 39

To determine

Predict the average number of yards per drive for the new player using the obtained equation in part (d).

Answer 40

Answer to Problem 9E

The predicted average number of yards per drive for the new player is 285.465 yards.

Answer 41

Explanation of Solution

Calculation:

The ball speed of a new PGA player is 170 mph with launch angle of 11 degrees.

From Part (b), it is found that the estimated regression equation that could be used to predict the average number of yards per drive given both club head speed and launch angle is y^=81.60+1.0927 (Ball Speed)+1.646 (Launch Angle).