Find the equation of the least squares​ line, and graph it on the scatterplot.


The equation of the least squares line (regression line) is:

\[
y = 4.02x + 19.25
\]

where:
- \(m = 4.02\) is the slope of the line.
- \(b = 19.25\) is the y-intercept.

The graph above shows the scatterplot of the data points along with the least squares line.

### Interpretation
- **Slope (\(m = 4.02\))**: For each additional chimpanzee in the hunting party, the percentage of successful hunts is expected to increase by approximately 4.02%.
- **Y-intercept (\(b = 19.25\))**: When the hunting party size is zero (hypothetically), the model predicts a success rate of 19.25%, although this point is outside the range of observed data.

Would you like to explore more about this topic, or do you have any questions?

Here are 5 additional related questions:
1. How do we calculate the coefficient of determination (\(R^2\)) for this linear model?
2. What are residuals in the context of linear regression, and how can we calculate them for this data?
3. How would adding more data points potentially affect the slope and intercept of the least squares line?
4. Can we use this linear model to predict successful hunts for a hunting party size larger than 16?
5. How does this regression line help in understanding the behavior of chimpanzees' hunting success?

**Tip:** When analyzing scatterplots and regression lines, always consider the context of the data and the possible implications of extending the regression line beyond the observed data range.

Learn how to find the equation of the least squares line in linear regression, along with its interpretation. This problem involves calculating the slope and y-intercept of the regression line based on scatterplot data. Suitable for Grades 10-12.

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