Subjects statistics

Regression Line 2E8D27

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. The problem is to find the regression line for the scatter plot of crime rate vs. poverty rate. 2. The regression line is given by the formula $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. To find $m$ and $b$, we use the least squares method: $$m = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}$$ $$b = \frac{\sum y - m \sum x}{n}$$ 4. Since the exact data points are not provided, we estimate from the description: - Poverty rate ($x$) ranges mostly from 0 to 80. - Crime rate ($y$) ranges mostly from 20 to 70. - No clear linear trend, so slope $m$ is approximately 0. 5. Therefore, the regression line is approximately horizontal near the average crime rate. 6. Estimating average crime rate $b \approx 45$ (midpoint of 20 and 70). 7. Final regression line: $$y = 0 \cdot x + 45 = 45$$ This means crime rate does not significantly change with poverty rate in this data.