1. **Stating the problem:** We have two sets of data: Midterm scores ($x$) and travel times ($y$). We want to analyze the relationship between these two variables, typically by finding the correlation and the equation of the best-fit line (linear regression). 2. **Formula used:** The linear regression line is given by $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Important rules:** - The slope $m$ is calculated by $$m = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}$$ - The intercept $b$ is calculated by $$b = \frac{\sum y - m \sum x}{n}$$ - $n$ is the number of data points. 4. **Calculate sums:** - $n = 42$ - $\sum x = 1593$ - $\sum y = 1035$ - $\sum x^2 = 61835$ - $\sum y^2 = 41415$ - $\sum xy = 39315$ 5. **Calculate slope $m$:** $$m = \frac{42 \times 39315 - 1593 \times 1035}{42 \times 61835 - 1593^2} = \frac{1657230 - 1648755}{2599470 - 2538249} = \frac{8475}{61221} \approx 0.1385$$ 6. **Calculate intercept $b$:** $$b = \frac{1035 - 0.1385 \times 1593}{42} = \frac{1035 - 220.7}{42} = \frac{814.3}{42} \approx 19.39$$ 7. **Equation of best-fit line:** $$y = 0.1385x + 19.39$$ 8. **Interpretation:** For each additional point in midterm score, the travel time increases by approximately 0.1385 minutes on average. 9. **Summary:** We found the linear relationship between midterm scores and travel times using linear regression. Final answer: $$y = 0.1385x + 19.39$$