Q1.(10 pts)Review the output of driving distance.What is sample mean?When we estimate the true mean of driving distance with 95% confidence interval using this sample, what is the margin of error?

Interpret your margin of error in the relation between mean of this sample (data from one randomly chosen tournament) and the true mean of population (all possible top player's performance).

Q2.(5 pts)With the answer of Q1, calculate95% confidence interval, [low endpoint, upper endpoint]for true mean of driving distance of top professional male golfers.Interpret the interval.

Let's describe theassociationbetween two characteristics.We call this bivariate analysis.

(Excel output: 10 pts)Run ExcelScatter Plotof"Club Head Speed" vs. "Driving Distance".

(Excel output: 5 pts)Run ExcelCorrelationbetween"Club Head Speed" vs. "Driving Distance".

Use the Scatter plot and correlation coefficient answering Q3.

Q3.(10 pts)Do you output verify the common sense (faster ball flies farther)?Explain the shape (direction and how tightly clustered) of the scatter plot of "Club Head Speed" vs. "Driving Distance".Does correlation coefficient support what scatter plot shows? Explain correlation coefficient's sign and magnitude and relate them with shape of scatter plot.

Let's check more details of the relation.To predict Driving Distance based on Club Head Speed, following linear model is examined usingregressionanalysis. (Assumptions about error term in simple linear regression are checked to be satisfied.)

y=b₀+b₁x

Q4.(4 pts)We are going to use two variables, "driving distance" and "club head speed" in regression, to predict "driving distance" based on "club head speed".Then, out of these two variables, which is Y and which is X?

(Excel output: 15 pts)Using driving distance" and "club head speed", runregressionin Excel data analysis. In regression option assignment, assign variables for X and Y as you answered in Q4.

Use regression output for answering Q5 through Q10.

Q5.(6 pts) Find the estimated y-intercept and estimated slope.Round your answer to three decimal places.

y-intercept:

slope:

Using all information above, write down the full equation of the regression model:

Q6.(5 pts)According to the estimated linear model, when the club head speed increases by one mile per hour, what happens to the estimated driving distance (in yards)?Use the estimated value from regression output.

Q7.(5 pts)Let's say you are going to predict/estimate certain player's driving distance using this linear model.If the player's club speed is 110.00 mph, what is the predicted driving distance?Round your answer to three decimal places.

Q8.(7 pts)Let's say there is a man who just started practicing and his club head speed is 83 mph.Would it be reasonable to predict his driving distance using the regression model you figured out above? Why or why not?

Q9.(8 pts)Report the coefficient of determination in three decimal places from regression output.What does this value mean?"Interpret" the value of coefficient of determination.

Q10.(for extra credit 5 pts)You used club head speed as the "sole predictor" of driving distance in this "simple" linear regression.What is (are) the possible limit(s) of this simple linear regression in predicting Driving Distance?

- ZOOM + Players (Do not use this column Club Head Speed Driving Distance in data analysis. Player's names (mph) (yds) are just for your information.] Aaron Wise 115.05 302.20 Abraham A 111.12 290.00 Adam Hadwin 113.70 94.60 Adam Long 111.48 89.60 Adam Scott 119.74 07.70 Billy Horschel 114.56 293.10 Brendan Steele 118.0 299.80 Brendon Todd 105.27 275.80 Brian Harman 110.51 292.40 Brian Stuard 105.82 281.20 Bryson DeChambeau 132.83 320.80 Cameron Percy 110.84 283.80 Cameron Smith 114.21 296.86 les Howell Ill 119.22 97.90 Charley Hoffman 118.10 07.30 Chris Kirk 110.84 290.40 Collin Morikawa 115.02 293.90 Corey Conners 116.11 294.50 Daniel Berger 117.3 297.90 Denny Mccarthy 111.59 295.10 Doug Ghim 112.18 95.20 Dustin Johnson 119.56 313.30 Dylan Frittelli 120.05 310.60 Harold Varner II 115.42 301.80 Harry Higgs 118.21 297.40 J.T. Poston 115.89 301.00 James Hahn 114.86 99.80 Jason Day 117.26 300.60 Jason Kokrak 119.43 304.10 Jhonattan Vegas 122.17 304.70 Joaquin Niemann 119.72 12.70 on Rahm 119.28 06.10 Jordan Spieth 115.17 97.50 Justin Thomas (Winner) 117.90 300.40 Keegan Bradle 115.68 300.00 Kramer Hickok 114.47 293.10 Kyoung-Hoon Lee 114.22 298.50 Lanto Griffin 121.11 303.80 Lee Westwood 114.58 95.20 Louis Oosthuizen 111.65 97.20 Lucas Glover 113.28 94.40 Martin Laird 115.24 296.00 Matt Fitspatrick 116.03 287.10 Matt Jones 118.28 305.30 Michael Thomson 108.75 89.30 Nate Lashley 110.71 92.80 Nick Taylor 111.63 94.10 Patrick Reed 115.60 87.40 Patrick Rodgers 120.05 306.10 Patton Kizzire 115.15 301.60 Paul Casey 117.03 02.10 Phil Michelson 119.20 01.40 Rory Sabbatin 110.42 88.40 Russell Knox 112.08 291.10 Ryan Armour 106.86 279.50 Ryan Moore 108.36 288.00 Ryan Palmer 117.84 02.90 Scott Brown 116.41 97.50 Scott Harrington 120.78 06.70 Scott Piercy 111.60 291.90 Sergio Garcia 121.07 308.60 Shane Lowry 115.69 299.40 Si Woo Kim 114.57 97.80 Sungjae Im 113.95 97.40 Talor Gooch 118.75 DO.20 Tom Hoge 112.13 289.20 Tyler McCumber 122.44 308.40 Victor Perez 119.17 295.00 Will Zalatoris 120.47 307.90 Zach Johnson 110.82 290.60