MATLAB: An Introduction with Applications
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Transcribed Image Text:### Cigarette Content Data
The following table presents data on the content of various cigarettes. The measurements include the level of Tar, Nicotine, and Carbon Monoxide (CO) present in different samples. These metrics can help understand the composition and potential health impacts of different cigarette brands.
| Tar | Nicotine | CO |
|-----|----------|----|
| 6 | 0.4 | 4 |
| 17 | 1.0 | 18 |
| 17 | 1.2 | 16 |
| 13 | 0.8 | 18 |
| 13 | 0.7 | 18 |
| 14 | 0.9 | 14 |
| 16 | 1.1 | 17 |
| 16 | 1.1 | 15 |
| 16 | 1.1 | 16 |
| 9 | 0.8 | 13 |
| 14 | 0.9 | 17 |
| 13 | 0.7 | 17 |
| 14 | 0.8 | 18 |
| 16 | 1.0 | 16 |
| 2 | 0.2 | 3 |
| 15 | 1.0 | 17 |
| 15 | 0.9 | 16 |
| 13 | 0.7 | 18 |
| 14 | 1.1 | 14 |
| 14 | 0.9 | 16 |
| 17 | 1.2 | 15 |
| 16 | 1.2 | 15 |
| 6 | 0.7 | 7 |
| 18 | 1.3 | 16 |
| 14 | 1.0 | 15 |
### Explanation of the Data
- **Tar (mg):** A measure of the tar content in milligrams found in the cigarette.
- **Nicotine (mg):** A measure of the nicotine content in milligrams present in
![## Introduction to Regression Analysis for Nicotine Content Prediction
The accompanying table provides data for tar, nicotine, and carbon monoxide (CO) contents in a certain brand of cigarette. The objective is to find the best regression equation for predicting the amount of nicotine in a cigarette.
### Instructions to Determine the Best Regression Equation
To determine the most suitable regression equation for predicting nicotine content, consider the predictor variables of tar and carbon monoxide (CO).
**Task:** Select the correct equation and fill in the required values. Round to three decimal places if necessary.
#### Possible Regression Equations:
1. **Option A:** Nicotine = [BLANK] + ([BLANK]) * Tar
2. **Option B:** Nicotine = [BLANK] + ([BLANK]) * CO
3. **Option C:** Nicotine = [BLANK] + ([BLANK]) * Tar + ([BLANK]) * CO
### Selection Criteria
#### Why is this equation the best?
Evaluate based on the following statements:
1. **Option A:** It is the best equation of the three because it has the highest adjusted \( R^2 \), the lowest P-value, and only a single predictor variable.
2. **Option B:** It is the best equation of the three because it has the lowest adjusted \( R^2 \), the highest P-value, and only a single predictor variable.
3. **Option C:** It is the best equation of the three because it has the highest adjusted \( R^2 \), the lowest P-value, and removing either predictor noticeably decreases the quality of the model.
4. **Option D:** It is the best equation of the three because it has the lowest adjusted \( R^2 \), the highest P-value, and removing either predictor noticeably decreases the quality of the model.
### Model Validation
#### Is the best regression equation a good predictor of nicotine content?
Analyze this question by choosing one of the following statements:
1. **Option A:** Yes, the small P-value indicates that the model is a good fitting model, and predictions using the regression equation are likely to be accurate.
2. **Option B:** No, the small P-value indicates that the model is not a good fitting model, and predictions using the regression equation are unlikely to be accurate.
3. **Option C:** Yes, the large P-value indicates that the model is a good fitting model, and predictions using the regression equation are likely to be accurate.
4](https://content.bartleby.com/qna-images/question/94a522d8-ef89-4b5b-a14c-d37c6cf2440e/114d97d1-a7a8-4388-a475-6a1a1ec86a9e/anc3wg_processed.png)
Transcribed Image Text:## Introduction to Regression Analysis for Nicotine Content Prediction
The accompanying table provides data for tar, nicotine, and carbon monoxide (CO) contents in a certain brand of cigarette. The objective is to find the best regression equation for predicting the amount of nicotine in a cigarette.
### Instructions to Determine the Best Regression Equation
To determine the most suitable regression equation for predicting nicotine content, consider the predictor variables of tar and carbon monoxide (CO).
**Task:** Select the correct equation and fill in the required values. Round to three decimal places if necessary.
#### Possible Regression Equations:
1. **Option A:** Nicotine = [BLANK] + ([BLANK]) * Tar
2. **Option B:** Nicotine = [BLANK] + ([BLANK]) * CO
3. **Option C:** Nicotine = [BLANK] + ([BLANK]) * Tar + ([BLANK]) * CO
### Selection Criteria
#### Why is this equation the best?
Evaluate based on the following statements:
1. **Option A:** It is the best equation of the three because it has the highest adjusted \( R^2 \), the lowest P-value, and only a single predictor variable.
2. **Option B:** It is the best equation of the three because it has the lowest adjusted \( R^2 \), the highest P-value, and only a single predictor variable.
3. **Option C:** It is the best equation of the three because it has the highest adjusted \( R^2 \), the lowest P-value, and removing either predictor noticeably decreases the quality of the model.
4. **Option D:** It is the best equation of the three because it has the lowest adjusted \( R^2 \), the highest P-value, and removing either predictor noticeably decreases the quality of the model.
### Model Validation
#### Is the best regression equation a good predictor of nicotine content?
Analyze this question by choosing one of the following statements:
1. **Option A:** Yes, the small P-value indicates that the model is a good fitting model, and predictions using the regression equation are likely to be accurate.
2. **Option B:** No, the small P-value indicates that the model is not a good fitting model, and predictions using the regression equation are unlikely to be accurate.
3. **Option C:** Yes, the large P-value indicates that the model is a good fitting model, and predictions using the regression equation are likely to be accurate.
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