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a. Locate the​ 95% prediction interval for driving accuracy​ (y) on the​ printout, and give a practical interpretation of the result. b. Locate the​ 95% confidence interval for mean driving accuracy​ (y) on the​ printout, and give a practical interpretation of the result. c. If you are interested in knowing the average driving accuracy of all golfers who have a driving distance of 300​ yards, determine which of the intervals is relevant. Explain.

a. Locate the​ 95% prediction interval for driving accuracy​ (y) on the​ printout, and give a practical interpretation of the result. b. Locate the​ 95% confidence interval for mean driving accuracy​ (y) on the​ printout, and give a practical interpretation of the result. c. If you are interested in knowing the average driving accuracy of all golfers who have a driving distance of 300​ yards, determine which of the intervals is relevant. Explain.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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a. Locate the​ 95% prediction interval for driving accuracy​ (y) on the​ printout, and give a practical interpretation of the result.

b. Locate the​ 95% confidence interval for mean driving accuracy​ (y) on the​ printout, and give a practical interpretation of the result.

c. If you are interested in knowing the average driving accuracy of all golfers who have a driving distance of 300​ yards, determine which of the intervals is relevant. Explain.

### Driving Performance Analysis Using a Straight-Line Model A group of researchers developed a new method for ranking the total driving performance of golfers on a tour. The method requires knowing a golfer's average driving distance (yards) and driving accuracy (percent of drives that land in the fairway). They construct a straight-line model relating driving accuracy (y) to driving distance (x). A MINITAB printout with prediction and confidence intervals for a driving distance of x = 300 is shown below. #### Data Table ##### MINITAB Output **Predicted Values For New Observations:** | New Obs | Fit | SE Fit | 95% CI | 95% PI | |---------|--------|--------|-------------------|--------------------| | 1 | 61.305 | 0.367 | (60.562, 62.048) | (56.716, 65.894) | **Values of Predictors for New Observations:** | New Obs | DISTANCE | |---------|----------| | 1 | 300 | **Explanation of the Data:** - **Predicted Values For New Observations:** For a driving distance (x) of 300 yards, the predicted driving accuracy (y) is 61.305. - **Fit:** The predicted value of driving accuracy. - **SE Fit:** The standard error of the mean prediction. - **95% CI:** The 95% Confidence Interval for the predicted value, indicating that we can be 95% confident that the true mean value of driving accuracy for a driving distance of 300 yards lies between 60.562 and 62.048. - **95% PI:** The 95% Prediction Interval, which indicates the range in which we can expect to find the individual driving accuracy for a driving distance of 300 yards 95% of the time. The interval is from 56.716 to 65.894. - **Values of Predictors for New Observations:** Shows the value of the driving distance (x) used in the prediction, which is 300 yards in this case.
Transcribed Image Text:### Driving Performance Analysis Using a Straight-Line Model A group of researchers developed a new method for ranking the total driving performance of golfers on a tour. The method requires knowing a golfer's average driving distance (yards) and driving accuracy (percent of drives that land in the fairway). They construct a straight-line model relating driving accuracy (y) to driving distance (x). A MINITAB printout with prediction and confidence intervals for a driving distance of x = 300 is shown below. #### Data Table ##### MINITAB Output **Predicted Values For New Observations:** | New Obs | Fit | SE Fit | 95% CI | 95% PI | |---------|--------|--------|-------------------|--------------------| | 1 | 61.305 | 0.367 | (60.562, 62.048) | (56.716, 65.894) | **Values of Predictors for New Observations:** | New Obs | DISTANCE | |---------|----------| | 1 | 300 | **Explanation of the Data:** - **Predicted Values For New Observations:** For a driving distance (x) of 300 yards, the predicted driving accuracy (y) is 61.305. - **Fit:** The predicted value of driving accuracy. - **SE Fit:** The standard error of the mean prediction. - **95% CI:** The 95% Confidence Interval for the predicted value, indicating that we can be 95% confident that the true mean value of driving accuracy for a driving distance of 300 yards lies between 60.562 and 62.048. - **95% PI:** The 95% Prediction Interval, which indicates the range in which we can expect to find the individual driving accuracy for a driving distance of 300 yards 95% of the time. The interval is from 56.716 to 65.894. - **Values of Predictors for New Observations:** Shows the value of the driving distance (x) used in the prediction, which is 300 yards in this case.
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