Can the performance of professional golf players in the first round of a professional tournament be used to predict how well they will do by the final round? Data was gathered for a random sample of players from the US Masters Tournament over the last 30 years. The US Masters is one of the four major championships in professional golf and is always played at the same golf course (Augusta National Golf Club).
Each round, the players get a score which is the difference between the number of strokes they took and the par score for the course. (In golf, "par" for the course is the number of strokes an expert golfer is expected to need to complete all the holes on a golf course.) So a score of -5 means they took 5 fewer shots than par while a score of 2 means they took 2 more shots than par. Lower values are better.
The two variables recorded were:
Round1: The players score for the first round of the tournament.
Final: The players final score for the tournament (i.e., the total score for the four rounds).
Assume that linear regression analysis is valid for this data.
(a) The equation of the least squares regression line for this analysis is: [ Select ] ["Average Final = 1.143 + 0.089 × Round1", "Average Round1 = 0.089 + 1.143 × Final", "Round1 = 0.089 + 1.143 × Predicted Final", "Final = 0.089 + 1.143 × Average Round1", "Average Final = 0.089 + 1.143 × Round1"]
(b) Under this regression analysis, we estimate that, on average, players who scored -1 on round 1 would get a final score (to two decimal places) of [ Select ] ["1.23", "-1.14", "-1.05", "-0.71", "-3.42"]
(c) For two players whose first round scores differ by 2, the regression analysis predicts that, on average, their final scores will differ (to two decimal places) by [ Select ] ["2.00", "1.14", "1.32", "2.38", "2.29"]
(d) One player scored 1 in round 1 and then went on to get a final score of 3. Under this regression analysis, the residual is approximately [ Select ] ["-1.9", "2.5", "-1.8", "-2.5", "1.8"]
(e) Which one of the following is NOT a correct interpretation of the P-value of 0.001 in the row for Round1 in the output above?
Statement: [ Select ] ["We have strong evidence that the slope of the true line is not zero.", "There is strong evidence that players with different round 1 scores would be expected to have different final round scores, on average.", "At the 5% level of significance, we may claim there is a linear relationship between Round1 and Final.", "There is strong evidence of a linear relationship between Round1 and Final.", "At the 5% level of significance, we may not claim there is a linear association between Round1 and Final."]
(f) Which one of the following is the best interpretation of the confidence intervals in the table above?
With 95% confidence, we estimate thatt [ Select ] ["the y-intercept of the true regression line is between 0.492 and 1.794.", "players who score 0 on round 1 will have an average final score between -1.52 and 1.69.", "each additional stroke scored in round 1 of the tournament is associated with an average final score being 0.49 higher.", "for each stroke lower scored in round 1 of the tournament, average final score is between 1.69 lower and 1.52 higher.", "each additional stroke scored in round 1 of the tournament is associated with an average final score being between 0.49 and 1.79 lower."]
