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 ModelA 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.

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

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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.

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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