Find the regression equation, letting the first variable be the predictor (x) variable. Using the listed lemon/crash data, where lemon imports are in metric tons and the the best predicted crash fatality rate for a year in which there are 475 metric tons of lemon imports. Is the prediction worthwhile? Lemon Imports Crash Fatality Rate 16 15.9 228 262 362 466 512 0 15.7 15.5 14.9 ..... Find the equation of the regression line.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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**Title: Regression Analysis of Lemon Imports and Crash Fatality Rates**

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**Objective:**

Find the regression equation with lemon imports (in metric tons) as the predictor (x) variable to estimate the crash fatality rate (per 100,000 people). Determine the predicted fatality rate for a year with 475 metric tons of lemon imports and assess the prediction's validity.

**Data Provided:**

| Lemon Imports (Metric Tons) | Crash Fatality Rate (per 100,000 People) |
|-----------------------------|------------------------------------------|
| 228                         | 16                                       |
| 262                         | 15.9                                     |
| 362                         | 15.7                                     |
| 466                         | 15.5                                     |
| 512                         | 14.9                                     |

**Task:**

Determine the equation of the regression line:

\[ \hat{y} = b_0 + b_1x \]

- **Calculate coefficients:**
  - \( b_0 \): y-intercept (round to three decimal places)
  - \( b_1 \): slope (round to four decimal places)

**Application:**

- Use the regression equation to find the predicted crash fatality rate for 475 metric tons of lemon imports.
- Evaluate whether this prediction is worthwhile based on the analysis.

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By following these steps, you will understand how lemon imports potentially correlate with crash fatality rates and refine predictive models accordingly.
Transcribed Image Text:**Title: Regression Analysis of Lemon Imports and Crash Fatality Rates** --- **Objective:** Find the regression equation with lemon imports (in metric tons) as the predictor (x) variable to estimate the crash fatality rate (per 100,000 people). Determine the predicted fatality rate for a year with 475 metric tons of lemon imports and assess the prediction's validity. **Data Provided:** | Lemon Imports (Metric Tons) | Crash Fatality Rate (per 100,000 People) | |-----------------------------|------------------------------------------| | 228 | 16 | | 262 | 15.9 | | 362 | 15.7 | | 466 | 15.5 | | 512 | 14.9 | **Task:** Determine the equation of the regression line: \[ \hat{y} = b_0 + b_1x \] - **Calculate coefficients:** - \( b_0 \): y-intercept (round to three decimal places) - \( b_1 \): slope (round to four decimal places) **Application:** - Use the regression equation to find the predicted crash fatality rate for 475 metric tons of lemon imports. - Evaluate whether this prediction is worthwhile based on the analysis. --- By following these steps, you will understand how lemon imports potentially correlate with crash fatality rates and refine predictive models accordingly.
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