f. The equation of the linear regression line is: a (Please show your answers to two decimal places) g. Use the model to predict the runs scored at a game that has an attendance of 34,000 people. Runs scored = (Please round your answer to the nearest whole number.) h. Interpret the slope of the regression line in the context of the question: O For every additional thousand people who attend a game, there tends to be an average increase of 0.20 runs scored. As x goes up, y goes up. The slope has no practical meaning since the total number runs scored in a game must be positive. i. Interpret the y-intercept in the context of the question: O The best prediction for a game with 0 attendance is that there will be -0 runs scored. If the attendance of a baseball game is 0, then -0 runs will be scored. The y-intercept has no practical meaning for this study. The average runs scored is predicted to be -0.

f. The equation of the linear regression line is: a (Please show your answers to two decimal places) g. Use the model to predict the runs scored at a game that has an attendance of 34,000 people. Runs scored = (Please round your answer to the nearest whole number.) h. Interpret the slope of the regression line in the context of the question: O For every additional thousand people who attend a game, there tends to be an average increase of 0.20 runs scored. As x goes up, y goes up. The slope has no practical meaning since the total number runs scored in a game must be positive. i. Interpret the y-intercept in the context of the question: O The best prediction for a game with 0 attendance is that there will be -0 runs scored. If the attendance of a baseball game is 0, then -0 runs will be scored. The y-intercept has no practical meaning for this study. The average runs scored is predicted to be -0.

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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The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.

Question

I need help with parts f,g and h

# Understanding Linear Regression in Baseball Game Analysis

### Exploring Baseball Game Runs through Linear Regression

Linear regression can be an insightful tool for predicting the number of runs scored in baseball games based on the attendance at each game. Consider the following points:

**Check Your Understanding**

1. **41% of all games will have the average number of runs scored.**
2. **Given any fixed attendance, 41% of all of those games will have the predicted number of runs scored.**
3. **There is a 41% chance that the regression line will be a good predictor for the runs scored based on the attendance of the game.**
4. **There is a large variation in the runs scored in baseball games, but if you only look at games with a fixed attendance, this variation on average is reduced by 41%.**

### Finding the Regression Line

**Equation of the Linear Regression Line**

\[ \hat{y} = \_\_\_ + \_\_\_x \]
*(Please show your answers to two decimal places)*

**Using the Model for Prediction**

Use this model to predict the runs scored at a game that has an attendance of 34,000 people.

\[ \text{Runs scored} = \_\_\_ \]
*(Please round your answer to the nearest whole number.)*

### Interpreting the Slope and Y-Intercept

**Interpreting the Slope in Context**

* For every additional thousand people who attend a game, there tends to be an average increase of 0.20 runs scored.
* As $x$ goes up, $y$ goes up.
* The slope has no practical meaning since the total number runs scored in a game must be positive.

**Interpreting the Y-Intercept in Context**

* The best prediction for a game with 0 attendance is that there will be 0 runs scored.
* If the attendance of a baseball game is 0, then 0 runs will be scored.
* The y-intercept has no practical meaning for this study.
* The average runs scored is predicted to be 0.

### Relationship Between Attendance at Major League Ball Games and Runs Scored

#### Data:
The following table shows attendance figures (in thousands) and the runs scored for 12 randomly selected games:

| Attendance | 47 | 39 | 50 | 48 | 51 | 35 | 34 | 38 | 47 | 47 | 51 | 33 |
|------------|----|----|----|----|----|----|----|----|----|----|----|----|
| Runs | 6 | 6 | 11 | 10 | 11 | 9 | 9 | 6 | 6 | 9 | 12 | 6 |

#### Problem:
What is the relationship between the attendance at a major league ball game and the total number of runs scored?

#### Tasks:
a. **Correlation Coefficient:**
- Find the correlation coefficient ($ r $).
- Round to two decimal places.

b. **Hypotheses for Correlation:**
- Null Hypothesis ($ H_0 $): $ \rho = 0 $
- Alternative Hypothesis ($ H_1 $): $ \rho \ne 0 $
- The p-value is: _____ (Round to four decimal places)

c. **Conclusion of Hypothesis Test:**
- Use a level of significance of $ \alpha = 0.05 $ to state the conclusion of the hypothesis test in the context of the study:
- There is statistically significant evidence to conclude that a game with higher attendance will have more runs scored than a game with lower attendance.
- There is statistically significant evidence to conclude that a game with higher attendance will have fewer runs scored than a game with lower attendance.
- There is statistically significant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the regression line is useful.
- There is statistically insignificant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the use of the regression line is not appropriate.

d. **Coefficient of Determination:**
- $ r^2 = _____ $ (Round to two decimal places)

e. **Interpret $ r^2 $:**
- 41% of all games will have the average number of runs scored.
- Given any fixed attendance

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