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. Title: Ranking Driving Performance of Golfers: Minitab Analysis---**Introduction**A group of researchers has developed a new method for assessing the total driving performance of golfers on a tour. This method requires data pertaining to a golfer's average driving distance (measured in yards) and driving accuracy (the percentage of drives that successfully land in the fairway). By constructing a straight-line model, the researchers relate driving accuracy (y) to driving distance (x). Below is a Minitab output providing the predicted values and confidence intervals for a driving distance of x = 300.![Minitab Data Table](#)**Minitab Output Explanation**1. **Predicted Values For New Observations** - **New Obs:** The observation entry number. - **Fit:** The predicted value of driving accuracy, which in this case is 61.308. - **SE Fit:** The standard error of the fit, which is 0.367. - **95% CI:** The 95% confidence interval for the predicted value, which ranges from 60.565 to 62.051. - **95% PI:** The 95% prediction interval for new observations, which ranges from 56.719 to 65.897. These values provide an estimate and associated intervals within which the actual driving accuracy for the specified driving distance can be expected to fall.2. **Values of Predictors for New Observations** This section displays the driving distance input for the new observation: - **New Obs:** The observation entry number. - **DISTANCE:** The input driving distance for this observation, which is 300.The table clearly summarizes the predicted driving accuracy and the associated confidence intervals for a driving distance of 300 yards.**Statistical Interpretation**- The **predicted driving accuracy** for a driving distance of 300 yards is approximately **61.308%**.- The **95% confidence interval** indicates that we can be 95% confident that the true mean driving accuracy for a driving distance of 300 yards lies between **60.565% and 62.051%**.- The **95% prediction interval** provides a range in which we can expect 95% of individual driving accuracies to fall, which is between **56.719% and 65.897%**.**Conclusion**This Minitab analysis assists researchers and golfing professionals in estimating driving accuracy

a. The MINITAB output is given.

Answered: a. Locate the 95% prediction interval…

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.

Title: Ranking Driving Performance of Golfers: Minitab Analysis

---

**Introduction**
A group of researchers has developed a new method for assessing the total driving performance of golfers on a tour. This method requires data pertaining to a golfer's average driving distance (measured in yards) and driving accuracy (the percentage of drives that successfully land in the fairway). By constructing a straight-line model, the researchers relate driving accuracy (y) to driving distance (x). Below is a Minitab output providing the predicted values and confidence intervals for a driving distance of x = 300.

![Minitab Data Table](#)

**Minitab Output Explanation**

1. **Predicted Values For New Observations**

- **New Obs:** The observation entry number.
- **Fit:** The predicted value of driving accuracy, which in this case is 61.308.
- **SE Fit:** The standard error of the fit, which is 0.367.
- **95% CI:** The 95% confidence interval for the predicted value, which ranges from 60.565 to 62.051.
- **95% PI:** The 95% prediction interval for new observations, which ranges from 56.719 to 65.897.

These values provide an estimate and associated intervals within which the actual driving accuracy for the specified driving distance can be expected to fall.

2. **Values of Predictors for New Observations**

This section displays the driving distance input for the new observation:

- **New Obs:** The observation entry number.
- **DISTANCE:** The input driving distance for this observation, which is 300.

The table clearly summarizes the predicted driving accuracy and the associated confidence intervals for a driving distance of 300 yards.

**Statistical Interpretation**

- The **predicted driving accuracy** for a driving distance of 300 yards is approximately **61.308%**.
- The **95% confidence interval** indicates that we can be 95% confident that the true mean driving accuracy for a driving distance of 300 yards lies between **60.565% and 62.051%**.
- The **95% prediction interval** provides a range in which we can expect 95% of individual driving accuracies to fall, which is between **56.719% and 65.897%**.

**Conclusion**

This Minitab analysis assists researchers and golfing professionals in estimating driving accuracy

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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