1. **State the problem:** We need to create a linear model to predict reaction time (REACT, $y$) from age (AGE, $x$) and find the slope of this model.
2. **Formula for linear regression:** The linear model is generally written as $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept.
3. **Slope interpretation:** The slope $m$ represents the change in reaction time for each one-year increase in age.
4. **Finding the slope:** To find $m$, we use the formula $$m = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}$$ where $x_i$ and $y_i$ are individual data points, and $\bar{x}$ and $\bar{y}$ are the means of $x$ and $y$ respectively.
5. **Calculate means:** Calculate $\bar{x}$ (mean age) and $\bar{y}$ (mean reaction time) from the data.
6. **Calculate numerator and denominator:** Compute $\sum (x_i - \bar{x})(y_i - \bar{y})$ and $\sum (x_i - \bar{x})^2$.
7. **Compute slope:** Divide numerator by denominator to get $m$.
8. **Final answer:** The slope $m$ is the value found in step 7, representing how reaction time changes with age.
Since the actual data is not provided here, the exact numerical slope cannot be computed. Please use the data set FALL STATUS to perform these calculations.
**Summary:** The slope $m$ in the linear model $y = mx + b$ predicts how much reaction time changes per year increase in age.
Linear Model Slope 009Ebc
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