Question

Golf Scores In a professional golf tournament the players participate in four rounds of golf and the player with the lowest score after all four rounds is the champion. How well does a player's performance in the first round of the tournament predict the final score? Table 9.6 shows the first round score and final score for a random sample of 20 golfers who made the cut in a recent Masters tournament. The data are also stored in MastersGolf. Computer output for a regression model to predict the final score from the first-round score is shown. Use values from this output to calculate and interpret the following. Show your work. (a) Find a \(95 \%\) interval to predict the average final score of all golfers whoshoot a 0 on the first round at the Masters. (b) Find a \(95 \%\) interval to predict the final score of a golfer who shoots a -5 in the first round at the Masters. (c) Find a \(95 \%\) interval to predict the average final score of all golfers who shoot a +3 in the first round at the Masters. The regression equation is Final \(=0.162+1.48\) First \(\begin{array}{lrrrr}\text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \\ \text { Constant } & 0.1617 & 0.8173 & 0.20 & 0.845 \\ \text { First } & 1.4758 & 0.2618 & 5.64 & 0.000 \\ S=3.59805 & R-S q=63.8 \% & \text { R-Sq }(a d j) & =61.8 \%\end{array}\) Analysis of Variance Source Regression Residual Error Total \(\begin{array}{rrrrr}\text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\ 1 & 411.52 & 411.52 & 31.79 & 0.000 \\ 18 & 233.03 & 12.95 & & \\ 19 & 644.55 & & & \end{array}\)

Short answer

The predicted final scores for golfers who scored 0, -5, and +3 on the first round at the Masters tournament, using the given regression model, are 0.162, -7.22, and 4.602 respectively. The 95% prediction intervals would be found using the specified SE, coefficient and T values from the regression table.

Step-by-step solution

Understand the Regression Model

Inspect the output of the regression model. Final score for golfing games is being predicted based on the first round of scores and this is represented by the equation Final = 0.162 + 1.48*First.

Predict for a First Round Score of 0

As per the given regression equation, we have: Final = 0.162 + 1.48*(0). This simplifies to the value 0.162. This is the predicted final score for a golfer who scores 0 in the first round. To calculate the 95% interval for the average final score, use the provided SE, coefficient and T values.

Predict for a First Round Score of -5

Again, using the regression equation: Final = 0.162 + 1.48*(-5). This gives us -7.22. This is the predicted final score for a golfer who scores -5 in the first round. The 95% interval for the final score can again be calculated using the SE, coefficient and T values.

Predict for a First Round Score of +3

Substitute into the regression equation: Final = 0.162 + 1.48*(3). This brings the value to 4.602. This is the predicted final score for a golfer who scores +3 in the first round. The 95% interval for the average final score is calculated as before, using the SE, coefficient and T values.