Concept explainers
Videos
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.
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
Explanation of Solution
Calculation:
The Professional Golfers Association (PGA) data consisting 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
Regression:
Software procedure:
Step by step procedure to get regression equation using MINITAB software is given as,
- Choose Stat > Regression > Regression > Fit Regression Model.
- Under Responses, enter the column of Total Distance.
- Under Continuous predictors, enter the columns of Club Head Speed.
- Click OK.
The output using MINITAB software is given as,
Thus, the estimated regression equation that could be used to predict the average number of yards per drive given the club head speed is
b.
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
Explanation of Solution
Calculation:
Regression:
Software procedure:
Step by step procedure to get regression equation using MINITAB software is given as,
- Choose Stat > Regression > Regression > Fit Regression Model.
- Under Responses, enter the column of Total Distance.
- Under Continuous predictors, enter the columns of Ball Speed.
- Click OK.
The output using MINITAB software is given as,
Thus, the estimated regression equation that could be used to predict the average number of yards per drive given the ball speed is
c.
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.
Explanation of Solution
Calculation:
Regression:
Software procedure:
Step by step procedure to get regression equation using MINITAB software is given as,
- Choose Stat > Regression > Regression > Fit Regression Model.
- Under Responses, enter the column of Total Distance.
- Under Continuous predictors, enter the columns of Club Head Speed and Ball Speed.
- Click OK.
The output using MINITAB software is given as,
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,
In the given output,
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 MINITAB software is given as,
- Choose Graph > Scatter plot.
- Choose Simple, and then click OK.
- Under Y variables, enter a column of Ball Speed.
- Under X variables, enter a column of Club Head Speed.
- Click Ok.
The MINITAB output is given as,
The scatter diagram exhibits a strong positive linear relationship between ball speed and club head speed. Both variables in the same model is 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.
Explain whether developing an estimated regression equation that uses both club head speed and launch angle to predict the average number of yards per drive.
Answer to Problem 9E
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,
Explanation of Solution
Calculation:
Regression:
Software procedure:
Step by step procedure to get regression equation using MINITAB software is given as,
- Choose Stat > Regression > Regression > Fit Regression Model.
- Under Responses, enter the column of Total Distance.
- Under Continuous predictors, enter the columns of Club Head Speed and Launch Angle.
- Click OK.
The output using MINITAB software is given as,
Thus, 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,
e.
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 previous part (b) it is found that 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
Thus, the predicted average number of yards per drive for the new player is,
Thus, the predicted average number of yards per drive for the new player is 285.465 yards.
Want to see more full solutions like this?
Chapter 15 Solutions
Bundle: Statistics for Business & Economics, Loose-Leaf Version, 13th + MindTap Business Statistics with XLSTAT, 1 term (6 months) Printed Access Card
- Bicycling, the world's leading cycling magazine, reviews hundreds of bicycles throughout the year. Their "Road-Race" category contains reviews of bikes used by riders primarily interested in racing. One of the most important factors in selecting a bike for racing is the weight of the bike. The following data show the weight (pounds) and price ($) for 10 racing bikes reviewed by the magazine.t Brand Weight Price ($) FELT F5 17.8 2,100 PINARELLO Paris 16.1 6,250 ORBEA Orca GDR 14.9 8,370 EDDY MERCKX EMX-7 15.9 6,200 BH RC1 Ultegra 17.2 4,000 BH Ultralight 386 13.1 8,600 CERVELO S5 Team 16.2 6,000 GIANT TCR Advanced 2 17.1 2,580 WILIER TRIESTINA Gran Turismo 17.6 3,400 SPECIALIZED S-works Amira SL4 14.1 8,000 (a) Use the data to develop an estimated regression equation that could be used to estimate the price for a bike given the weight. (Round your numerical values to the nearest integer). %3D (b) Compute r. (Round your answer to three decimal places.) ,2 = Did the estimated regression…arrow_forwardA high school guidance counselor analyzed data from a sample of 200 community colleges throughout the United States. One of his goals was to estimate the annual tuition costs of community colleges in the United States. Describe the population and variable of interest to the guidance counselor. Why?arrow_forwardA data set has five values. The smallest value is 13. The median is 18. The mode is 27. What is the range?arrow_forward
- A local construction company is trying to reduce costs. It found that the price of steel bars varies considerably from manufacturer to manufacturer. The table below shows the cost of one steel bar from different manufacturers. Calculate the IQR. Cost for One Steel Bar Emerson $4.31 Mannix $6.20 United $5.67 American $2.79 National $3.20 Pracox $3.57 Steelco $5.32 Cost per Steel Bar 7 6 4 3 2 1 O $2.47 O $2.53 O $4.32 O $5.36arrow_forwardThe Toyota Camry is one of the best-selling cars in North America. The cost of a previously owned Camry depends on many factors, including the model year, mileage, and To investigate the relationship between the car’s mileage and the sales price for Camrys, the following data show the mileage and sale price for 19 sales (PriceHub Web site, February 24, 2012). Miles (1000s) Price ($1,000s) 22 16.2 29 16.0 36 13.8 47 11.5 63 12.5 77 12.9 73 11.2 87 13.0 92 11.8 101 10.5 110 8.3 28 12.5 59 11.1 68 15.0 68 12.2 91 13.0 42 15.6 65 12.7 110 8.3 Develop an estimated regression equation…arrow_forwardUse excel to do all calculations. Please show all work.arrow_forward
- The top 14 speeds, in miles per hour, for professional drag racing over the past two decades are listed below. Find the median speed. 181.1 202.2 190.1 201.4 201.2 193.2 201.2 194.5 A. 196.1 B. 196.7 C. 201.2 D. 195.8 191.3 201.4 199.2 192.2 196.0 196.2arrow_forwardBicycling, the world’s leading cycling magazine, reviews hundreds of bicycles throughout theyear. Their “Road-Race” category contains reviews of bikes used by riders primarily interested in racing. One of the most important factors in selecting a bike for racing is the weightof the bike. The following data show the weight (pounds) and price ($) for 10 racing bikesreviewed by the magazine (Bicycling website, March 8, 2012). Brand Weight Price ($)FELT F5 17.8 2100PINARELLO Paris 16.1 6250ORBEA Orca GDR 14.9 8370EDDY MERCKX EMX-7 15.9 6200BH RC1 Ultegra 17.2 4000BH Ultralight 386 13.1 8600CERVELO S5 Team 16.2…arrow_forwardThe scores of the top ten finishers in a recent Buick Open are listed below. Find the median score. 65 66 67 66 67 70 67 70 71 68arrow_forward
- The median annual income for someone who has an Associates Degree is $31,936. The median annual income for someone with a high school degree is $26,123. Based on the median income, how much more would someone with an associate's degree earn than someone with a high school degree over 40 years?arrow_forwardFind the median?arrow_forward16 20 40 60 80 100 Miles (1000s) 120 Scatter diagram 1 b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? Negative relationship c. Develop the estimated regression equation that could be used to predict the price ($1000s) (to 4 decimals). 16.469 .0588 I d. Test for a significant relationship at the 0.05 level of significance (to 3 decimals). p-value= less than α = 0.05. e. Did the estimated regression equation provide a good fit? Yes f. Provide terpretation for the slope of the estimated regression equation (to 4 decimals but dollar value to the nearest cent). Enter negative values as negative numbers. The slope of the estimated regression is -.0588. Therefore, every additional 1,000 miles on the car's odometr will result in a $ predicted price. decrease in the g. Suppose that you are considering purchasing a previously owned 2007 Camry that has been driven 60,000 miles. Using the estimated regression equation developed in…arrow_forward
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL