To find the regression line equation for the given data, we'll use the least-squares method to determine the slope ($m$) and the y-intercept ($b$) of the line in the form: $y = mx + b$

Here is the data provided:

• $x$ values: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
• $y$ values: 27.1, 27.9, 30.1, 34.6, 35.8, 40, 43.6, 46.7, 49.7, 49.1, 53.8, 56.5, 59, 60.7

I'll compute the slope ($m$) and intercept ($b$) using the formulas: $m = \frac{n \sum(xy) - \sum x \sum y}{n \sum(x^2) - (\sum x)^2}$ $b = \frac{\sum y - m \sum x}{n}$

Let me calculate these values.The regression line equation for the given data is: $y = 2.75x + 20.56$

This means the slope of the line is $2.75$, and the y-intercept is $20.56$.

Would you like a detailed explanation of how these values were derived or have any further questions?

Here are five related questions that might expand your understanding:

1. What does the slope of the regression line represent in this context?
2. How can we interpret the y-intercept of this regression line?
3. What is the coefficient of determination (R-squared) for this regression line?
4. How do outliers affect the regression line calculation?
5. What are some limitations of using linear regression for predictions?

Tip: The closer the slope and intercept are to real-world values, the more accurate your prediction is likely to be!