1. **State the problem:** We have data for Lemon Imports and Crash Fatality Rate over five points. We want to understand the relationship between these two variables, possibly by finding a linear model.
2. **Formula used:** To find a linear relationship, we use the equation of a line:
$$y = mx + b$$
where $y$ is the Crash Fatality Rate, $x$ is Lemon Imports, $m$ is the slope, and $b$ is the y-intercept.
3. **Calculate slope $m$:** The slope is given by
$$m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$$
We can use the first and last points:
$$m = \frac{15.5 - 15.6}{530 - 221} = \frac{-0.1}{309} \approx -0.000323$$
4. **Calculate intercept $b$:** Using point $(221, 15.6)$:
$$15.6 = -0.000323 \times 221 + b$$
$$b = 15.6 + 0.000323 \times 221 = 15.6 + 0.0714 = 15.6714$$
5. **Linear model:**
$$y = -0.000323x + 15.6714$$
6. **Interpretation:** The slope is very small and negative, indicating a slight decrease in Crash Fatality Rate as Lemon Imports increase.
7. **Summary:** The data suggests a nearly flat linear relationship with a slight negative trend.
Lemon Imports F02267
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